. ‘ L. ‘ x. . E a a. .a «x -.__.<_. ._ , ,, » 7 - . . -v, ,. .7 -. rw a "y .t.:£$ This is to certify that the thesis entitled DIGITAL ANALYSIS OF THE DYNAMIC RESPONSE WITHIN TRUNK SHAKER HARVESTER SYSTEMS presented by Henry AIbert Affeldt, Jr. has been accepted towards fulfillment of the requirements for _H._$.__ degree in ' _ . W Mew 0 Major professor John B. Gerrlsh Date—iflfllL/i 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES .—z_—_ RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. DIGITAL ANALYSIS OF THE DYNAMIC RESPONSE WITHIN TRUNK SHAKER HARVESTER SYSTEMS BY Henry Albert Affeldt Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1984 DIGITAL ANALYSIS OF THE DYNAMIC RESPONSE WITHIN TRUNK SHAKER HARVESTER SYSTEMS BY Henry Albert Affeldt Jr. Date: Approved: Major Professor Approved: Department Chairman Approved: Committee Member Approved: Committee Member ABSTRACT DIGITAL ANALYSIS OF THE DYNAMIC RESPONSE WITHIN TRUNK SHAKER HARVESTER SYSTEMS BY Henry Albert Affeldt Jr. The decline in productivity of commercial cherry orchards in Michigan has called attention to mechanical fruit harvesting as a potential cause of bark damage to trees; the dynamic characteristics of commercially- available tree shakers had to be measured in order to establish operating procedures which would be safe for the trees. A C-clamp eccentric mass trunk shaker harvester for cherries was instrumented with transducers to characterize rigid body acceleration, hydraulic circuit pressure and mass and clamp arm position. A 2 MHz 6502 microprocessor—based data—acquisition system was assembled capable of digitizing l4 analog signals at a rate of 21 KHz and processing the resultant data. Accelerations were integrated to displacement and compared with other physical events. The critical time of putative tree damage appeared to occur during the start—up transient of the shaker. A clamp 'pad relaxation‘ effect was observed. To the Spirit of my father and mother, of which I am so much a part. ii r 9 th WI ACKNOWLEDGMENTS The author would like to express his deepest gratitude to the following persons and organizations for their contribution to this study: To Dr. John B. Gerrish, my major professor, for his professional guidance, cooperation and support provided throughout the duration of the graduate program. To my guidance committee, Dr. Galen K. Brown (Research Leader, Fruit and Vegetable Harvesting, U.S. Department of Agriculture) and Dr. Clark J. Radcliffe (Assistant Professor Mechanical Engineering) for their time, constructive counsel, and professional interest. To USDA Mechanical Engineering Technician Richard Wolthius, USDA Electronic Technician Joe Clemens, and undergraduates Phil Richey and Paul Speicher who each contributed many hours of valuable assistance and experience to the project. To cherry growers David and Philip Friday and the Friday Tractor Company (Hartford, MI) for contributions of equipment and advice which made this project feasible, to technical representative Leonard Wilming (Orchard Machinery Corporation) for the information rendered based on his experience, and to the Vanner Corporation for the loan of a test model sine wave inverter. To the Agricultural Research Service, U.S. Department of Agriculture for financial assistance (Research Engineer Recruitment and Development Program) and continued interest in the agricultural foundations of these United States. To my mother June, my sister Tara, and the branching tree of family and friends whose unfailing love, confidence, and understanding have been a continuing source of strength and encouragement. TABLE OF CONTENTS ACKNOWLEDGEMENTS. . . . . . . . . . LIST OF TABLES . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . CHAPTER 1. INTRODUCTION. . . . . . . . . . General Information. . . . . 1.1 The Bark Damage Problem . . . 1.2 Extent of Cherry Production . . 1.3 Need for Shaker Analysis . . 1.4 Objectives of the Study . . . 2.‘ LITERATURE REVIEW . . . . . . . History of the Problem. . . . . 2.1 General Causes of Bark Damage . . 2.2 Harvester Factors in Bark Damage . 2.3 Bark Structure . . . . . . 2.4 Bark Strength. . . . . . . . 2.5 Shaker Pads . . . . . . . 2.6 Tree Response. . . . . . . . 2.7 Suggestions for Reducing Bark Damage 2.8 Triboelectric Phenomena . . . . 2.9 The Need for Tree Preservation . . 3. THEORETICAL CONSIDERATIONS . . . . . 3.1 Sampling Rate and Resolution. . . 3.2 Frequency Response . . . . . . 3.3 Numerical Integration . . . . . 4. EXPERIMENTAL TECHNIQUES . . . . . . Material and Method. . . . . . 4.1 Triboelectric Phenomena . . . 4.2 The Trunk Shaker. . . . . . . CHAPTER 4. EXPERIMENTAL TECHNIQUES - Continued Sensing Elements and Calibration . The Acquisition Processor Hardware. The Acquisition Processor Software. Data Capture . . . . . . . Transcription to Disk . . . . . Displacement Tests . . . . . . Method of Data Analysis . . . . PDPhPPP O D O I O I O \DCXJNOXU‘IPW 5. RESULTS AND DISCUSSION . . . . . . Data Outcome . . 5.1 The Triboelectric Test on Shaker Clamp Pads . . . . 5.2 Pad Deformation by Displacement Measurements . . . . . . 5.3 Firmness of Clamp . . . . . 5.4 Pressure Factors in Slip . . . 5.5 Real- -Time Mass Position V. . . . 5.6 Centrifugal System Reactance. . . 5.7 Acceleration to Displacement. . . 5.8 Discrete Time Domain . . . 5.9 Future Systems . . . . . . . 6 O SUWARY O O O I O O I C O O O 7. CONCLUSIONS . . . . . . . . . . 8. RECOMMENDATIONS FOR FUTURE RESEARCH . . APPENDIX A: 6502 ASSEMBLY LANGUAGE DATA COLLECTION OPERATING PROGRAM APPENDIX B: 6502 ASSEMBLY AND SOS LANGUAGE DRIVER FOR THE ANALOG-TO-DIGITAL CONVERTER BIBLIOGRAPHY . . . . . . . . . - vi PAGE 123 124 134 143 151 160 184 187 189 194' 196 200 212 222 TABLE 5.2 5.5 LIST OF TABLES PAGE Michigan Cherry Tree Production by Variety (1982). O O O O O O O C O O O O O I I O l O O 7 Output voltage (volts) from the charge generated by compression of a rubber shaker Clamp pad (triboelectric phenomena). Position reference Figure 5.1 . . . . . . . . . 118 Physical measurements at tree-shaker interface. (C.f. Figure 5.4). All measurements in cm. . . . . . . . . . . . . . . 125 Linear movement of the shaker clamping arm during harvest. (All values in mm). Positive values indicate a loosening action, negative values indicate a tightening action . . . . . . . . . . . . . . . 127 Clamping cylinder pressures resulting from trunk shaking cherry trees (Target pressure is 49.3 kg/cm (200 psi)) . . . . . . . . . . . 139 Forces generated by clamping cylinder pressures on a tree trunk in the —X direction. All forces in Newtons (pounds-force). Target force = 18190 N (4089 lb) . . . . . . . . . . . . . . . . . . . 142 LIST OF FIGURES FIGURE Michigan Cherry Trees by Age - 1982 Survey. (Michigan Dept. of Agriculture, 1983b) . . Possible stress directions when using trunk shaker harvesters . . . . . . . . . . . . . Two piece trunk shaker harvester for Cherries Tart cherry tree trunk six months after trunk shaker harvesting. No apparent evidence of bark damage . . . . . . . . . . . . . . . . Tart cherry tree trunk 18 months after trunk shaker harvesting. 'Obvious tree decline from uncorrected ba:k damage . . . . . . . . . . . Some possible epicyclic trunk shaker patterns. (Orchard Machinery Corp., Yuba City, CA) . . Comparison of integration accuracy of several waveforms: (a) 5-point digitized triangular wave (b) 32-point digitized sine wave and (c) a perfect (infinite point) sine wave. . C—clamp style eccentric mass trunk shaker used in commercial fruit harvesting. . . . . . . . Rubber shaker Clamp pad mounted on a 422 kg/cm2 hydraulic press for the triboelectric test. Clip leads extend from the electrodes inserted in the pad to a Charge amplifier and oscilloscope for charge quantization. . . . . C-clamp eccentric-mass inertial trunk shaker mounted on the lift of a 56 PTO Hp Hydro 84 International tractor. . . . . . . . . . Top view Of trunk shaker revealing strategic locations of sensors for detection of. acceleration, displacement, and pos1tIOn. . viii PAGE 17 18 22 24 51 62 73 75 77 82 FIGURE ' PAGE 4.5 Dimensioned trunk shaker showing accelerometer and LVDT locations. (All measurements in mm) . 83 4.6 Orthogonal location of X and XY accelerometer blocks mounted on a cherry tree trunk . . . . . 84 4.7 Accelerometer mounted on a fixed- -displacement variable- frequency reciprocating plunger unit for calibration . . . . . . . . . . . . . . . 86 4.8 Hardware (double) integrator circuit using operational amplifiers. (Amplifier power is + 12 VDC) 0 o o o c I o n o o o c o o o o o o o 87 4.9 Hardware block diagram Of the microprocessor— based data acquisition system for trunk shaker vibration analyses. . . . . . . . . . . . . . . 91 4.10 The data acquisition equipment was assembled in an air conditioned van to protect it from dust and temperature . . . . . . . . . . . . . 92 4.11 Simplified block diagram of the Allocation Field Of the Analog-to—Digital Converter Device Driver. I D O I O O O I I I O O I I O O O O O O 97 4.12 Flow diagram Of the Execution Field of the Analog- to- Digital Device Driver . . . . . . . . 98 4.13 Device Driver address incrementation routine that allows maximum utilization of internal memory without the production of system- fatal memory pointers . . . . . . . . . . . . . . 101 4.14 Simplified block diagram of the Header Field of the Analog-to—Digital Converter Interpreter . . . . . . . . . . . . . . . . . . 103 4.15 Flow diagram Of the Execution Field Of the Analog-to-Digital Converter Interpreter . . . . 104 4.16 Data storage locations for the 6502—based data acquisition system in the Sophisticated Operating System Environment. . . . . . . . . . 107 4.17 Cherry tree trunk centered in shaker clamping jaw. Flaps between the tree and the cylindrical pads are coated with grease to reduce shear stress on the bark . . . . . . . . 110 ix FIGURE 4.18 5.1 Physical location of tilt detecting sensors relative to the tree and the shaker . . . . ; Geometry of probe connections on rubber pads. (r=7o m) 0 I O O D O I O O O O O O I O O I O Amplified response of rubber Clamp pads to applied load. . . . . . . . . . . . . . . . . Output charge increment for a load applied to rubber clamp pads . . . . . . . . . . . . . Tree and shaker geometry depicting variables measured for trunk shaker vibration tests . . . Linear Voltage Differential Transformer Trace displaying clamp arm movement. Test: Eta, 9.3 Hz, No Tree . . . . . . . . . . . . . . Linear Voltage Differential Transformer Trace displaying clamp arm movement. Test: Zeta, 14.0 Hz, No Tree. .F. . . . . . . . . . . . . . Linear Voltage Differential Transformer Trace displaying clamp arm movement. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree . . . . . . . . . . Linear Voltage Differential Transformer Trace displaying Clamp arm movement. Test: Beta, 14.0 Hz, 16 cm (6.5 in) Tree. . . . . . . . . . Linear Voltage Differential Transformer Trace displaying Clamp arm movement. A tightening occurs in the clamp arm immediately after shaking begins. Test: Omicron, 9.3 Hz, 11 cm (4.5 in) Tree . . . . . . . . . . . . . . . . . Clamping cylinder pressure trace revealing peak pressures during shake harvesting of cherry trees. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree . . . . . . . . . . . . . . . Clamping cylinder pressure trace revealing peak pressures during shake harvesting of Cherry trees. Test: Delta, 14.0 Hz, 16 cm (6.5 in) Tree . . . . . . . . . . . . . . . . 0 PAGE 112 119 120 121 126 128 129 130 131 133 135 136 Clamping cylinder pressure trace revealing peak pressures during shake harvesting of cherry trees. (4.5 in) Tree . Test: Omicron, 9.3 Hz, 11 cm I o o a o o o o o o o o o I o 0 Clamping cylinder pressure trace revealing peak pressures during shake harvesting of cherry trees. (4.5 in) Tree . Test: Theta, 14.0 Hz, 11 cm 9 o o o O O I o o a a o a O o 0 Real time proximity trace of rotating mass A with no tree in the Clamp. Pulse height and spacing both indicate rotational velocity. Test: Eta, 9.3 Hz, No Tree I I I I I I I I I I Real time proximity trace of rotating mass B with no tree in the clamp. Pulse height and spacing both indicate rotational velocity. Test: Eta, 9.3 Hz, NO Tree I I I I I I I I I I Real time proximity-trace of rotating mass A with no tree in the Clamp. Pulse height and spacing both indicate rotational velocity. Test: Zeta, 14 .0 Hz, No Tree . . . . . . . . . Real time proximity trace of rotating mass B with no tree in the Clamp. Pulse height and spacing both indicate rotational velocity. Test: Zeta, l4 .0 Hz, NO Tree . . . . . . . . . Real time proximity trace of rotating mass A with a 11 cm (4.5 in) tree in the clamp. Test: Omicron, 9.3 Hz, 11 cm (4.5 in) Tree . . Real time proximity trace of rotating mass B with a 11 cm (4.5 in) tree in the Clamp. Test: Omicron, 9.3 Hz, 11 cm (4.5 in) Tree . . Pressure plot of drive motor B on the trunk shaker harvester with no tree in the clamp. Operational speed set at 9.3 Hz. Test: Eta. . Pressure plot of drive motor B on the trunk shaker harvester with no tree in the clamp. Operational speed set at 14.0 Hz. Test: Zeta. Pressure plot of drive motor B on the trunk shaker harvester with a 11 cm (4.5 in) tree in the Clamp. Test: Omicron. Operational speed set at 9.3 Hz. a o o o o o o o o o c o o o o xi PAGE 137 138 144 145 146' 147 148 149 '153 154 155 Pressure plot of drive motor B on the trunk shaker harvester with a 16 cm (6.5 in) tree in the Clamp. Operational speed set at 9.3 Hz. Test: Alpha. . . . . . . . . . . . . . . . . . Pressure plot of drive motor B on the trunk shaker harvester with a 16 cm (6.5 in) tree in the clamp. Operational speed set at 14.0 Hz. Test: Delta . . . . . . . . . . . . . . . Pressure plot of drive motor B on the trunk shaker harvester with a 11 cm (4.5 in) tree in the Clamp. Operational speed set at 14.0 Hz. Test: TThetao o o o l o o o n o o o I I o o o o Uncalibrated acceleration trace from the -X direction sensor on the tree. Channel 2. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree . Uncalibrated acceleration trace from the +x direction sensor at_the center of gravity on the shaker. Channel 4. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree . . . . . . . . . . . . . . Uncalibrated acceleration trace from the +X direction sensor at the bark—pad interface on the shaker. Channel 6. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree . . . . . . . . . . Uncalibrated acceleration trace from the +x direction sensor at the bark-pad interface on the shaker. Channel 6. Test: Beta, 14.0 Hz, 16 cm (6.5 in) Tree. . . . . . . . . . Uncalibrated acceleration trace from the +X direction sensor at the center of gravity on the shaker. Channel 4. Test: Beta, 14.0 Hz, 16 cm (6.5 in) Tree . . . . . . . . . . . . . . Uncalibrated acceleration trace from the -X direction sensor on the tree. Channel 2. Test: Beta, 14.0 Hz, 16 cm (6.5 in) Tree . . . Uncalibrated acceleration trace from the +X direction sensor at the bark-pad interface on the shaker. Channel 6. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree . . . . . . . . . . PAGE 156 157 158 161 162 163 164 165 166 169 Acceleration trace from Figure 5.32 with a single line regressed on all data points and subtracted (Channel 6). . . . . . . . . . Velocity trace from the integration of the acceleration curve of Figure 5.33. Integration was conducted using piecewise quadratic methods (Channel 6) . . . . . . . . . . . . . Velocity curve from Figure 5.34 with the front end drift integral removed and a single line regressed on the remaining points. Subtraction of the regressed line translates the base value (Channel 6) . . . . . . . . . . . . . Displacement curve from the integration of the velocity curve shown in Figure 5.35. Note the single cycle underlying the desired waveform. (Channel 6). . . . . . . . . . . . Uncalibrated displacement curve from Figure 5.36 where lines regressed on 50 data points per interval were removed to translate the base value. This removes the low frequency wave viewed in the previous figure (Channel 6). Final calibrated displacement curve for Channel 6 in this test. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree . . . . . . . . Displacement trace from integrated accelerometer channel 2. Sensor is in the -X direction on the tree. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree . . . . . . . . . . . . . Displacement trace from integrated accelerometer Channel 4. Sensor is in the +X direction at the center of gravity on the shaker. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree. . . . . . . . . . . . . . . . . . . . Displacement trace from integrated accelerometer channel 6. Sensor is in the +X ‘direction at the bark-pad interface on the shaker. Test: Alpha, 9.3 Hz, 16 cm (6.5 in) Tree. . . . . . . . . . . . . . . . . . . . . xiii PAGE 170 171 172 173 174 175 176 177 178 Displacement trace from integrated accelerometer channel 2. Sensor is in the -X direction on the tree. Test: Beta, 14.0 Hz, 16 cm (6.5 in) Tree . . . . . . . . . . . . . Displacement trace from integrated accelerometer channel 4. Sensor is in the +X direction at the center of gravity on the shaker. Test: Beta, 14.0 Hz, 16 cm (6.5 in) Tree. 0 o o O I O o o o I a C o o I o O o o 0 Displacement trace from integrated accelerometer channel 6. Sensor is in the +X direction at the bark-pad interface on the shaker. Test: Beta, 14.0 Hz, 16 cm (6.5 in) Tree. . . . . . . . . . . . . . . . . . . . PAGE 179 180 181 I'F CHAPTER 1 INTRODUCTION Mechanically induced damage to the world's varied it and nut trees has been a continuing international cern, particularly with the adoption in the early 0's of mechanical shake—and—catch harvesters. The roduction of the mechanical harvester brought about reases in labor efficiency and production capability. k damage associated with the use of these harvesters in commercial cherry orchards of Michigan has caused reasing alarm. Growers' observations of tree and Iard decline, particularly among the younger plantings, 2 also suggested dynamic shaker loading as a possible :e of internal tree damage. An estimated 20 to 30 :ent of the cherry trees in some orchards annually show ence of some sort of injury (Brown, 1982). A means of uating the dynamic action of a trunk shaker as a ntial cause of bark damage was needed. This study describes the development of the rare, software, and methodology to characterize the rior of an eccentric mass trunk shaker and a tree in to evaluate the detrimental effects of trunk shakers tree bark. The information obtained can be employed in ther investigations to determine the stress and strain the bark. Estimates of stress and strain can be ived from peak displacements of the tree and shaker tem. Knowledge of applied bark loading coupled with vious studies of bark and cambium strength could help dict the presence and extent of tissue rupture within living tree. The instrumentation and analytical cedures developed in this investigation are expected to 1y to other fruit and nut shake-harvest systems. 1.1 The Bark Damage Problem The first mechanical cherry harvesters introduced 1958 (Levin et a1.) caused tree damage through the ipping of bark resulting from excessive forces exerted the shaker. Insects and disease, especially canker, Ld enter through the damaged tissue and spread to Lthy tissue, often resulting in the death of the tree. California, the disease causing fungus, ItOCYStiS fimbriata, is carried by insects into damaged area where a favorable environment allows d spreading_ into healthy bark and wood (Devay et a1. , 1962, 1965). Fungal vectors can be carried from to tree on shaker pads when continuous harvesting is Jcted in a diseased orchard. Temperature and soil :ure strongly affect the spread of infectious canker. Fu en S9 In Fungal growth and activity are favored by a warm and moist environment typical of the June and July Cherry harvest season in Michigan. The distribution of the clamping and shaking forces on the limb or trunk not only determines external damage but has an appreciable effect on internal damage. Internal stresses in the bark are minimized when the minimum necessary force is transmitted over the largest possible contact area. This is a function of the pad design, clamping pressure, and shaking force. Excessive clamping forces were found to cause crushing of the bark apd internal tissues of the tree (Frahm, 1983). Vital nutrients cannot pass through the ruptured cells to the fruit, leaves, fruit bearing limbs, and roots. Upper limits on clamping pressure have been established which will avoid injury in the static nonvibratory state. The first limb shakers oscillated in a back—and—forth linear motion. Most modern trunk shakers, however, transmit forces in epicyclic patterns such as Cycloids, hypocycloids, cardioids, N—leaved roses, and spirals. The operator can adjust the pattern either by resetting the eccentric masses or stepping through a learned series of hand motions on the hydraulic motor drive controls. Cycloidal patterns require that the shaker pads conform to the tree to provide sufficient CC tE contact area for minimized compressive, longitudinal and tangential stresses. The physiological condition of the cambium plays an important role in bark strength. In the Spring, the cells in the cambium take in moisture, enlarge radially, and begin to divide causing the cell walls of the two newly formed cells to be thinner than the original parent cell wall (Bukovac, 1984). The cell interiors, as well as the intercellular spaces, become filled with liquid. The cambium readily breaks down at this stage when shear stress is applied and the bark slips over the wood. By Fall, when moisture, cambial activity, and cell growth have begun to decrease, the cell walls have thickened from the growth of the cellulose layers forming the wall. As the cells lose moisture to the environment and shrink, the protoplasm turns to a gel and aligns itself against the cell wall for winter insulation (Priestley, 1930). At this point, the cambial cell walls are less elastic and the intercellular spaces have also lost their liquid contents. This deactivated state (preparing for dormancy) greatly reduces the occurrence of slip (Fridley et al., 1970). This physiological condition also varies during the crop season with Changes in environmental and soil conditions. The highly variable physiological activity of the tree can elude the machine operator's efforts to prevent bark damage. .._...- 1.2 Extent of Cherry Production In 1982, Michigan ranked first in the United States in the production value of tart cherries. Sweet Cherry production ranked third, with Washington and Oregon ranking first and second, respectively. This corresponded to 117,936 tonnes (260,000,000 lbs) or 83.6% of the. nations tart cherries and 30,391 tonnes (67,000,000 lbs) or 21.2% of the nations sweet cherries. The State's production value totalled 26.8 million dollars for tarts and 10.9 million dollars for sweets. The 1982 Michigan tart Cherry crop was the second largest since records were started in 1925. 1 Ninety-seven percent of all tar. cherries and 92% of all sweet cherries harvested in Michigan are processed; the small remainder supplies the fresh fruit market. Tart cherries go into juice, wine, jam, and pie, while sweet Cherries go into juice, jelly, ice cream, and frozen goods. In 1982, Michigan reported 4,500,000 red tart cherry trees and 887,000 sweet Cherry trees of all ages (Michigan Dept. of Agriculture, 1983b). This was a 17% increase in the number of tart Cherry trees and a 9% decrease in the number of sweet cherry trees since the 1978 fruit tree survey (Michigan Dept. of Agricuture, 1979). Although tart tree numbers increased 17%, acreage increased only 14%. This was due to Closer tree spacing. Tree spacing becomes a significant factor in harvester speed, size, operating efficiency and tree damage potential. Practically all of the tart cherry trees (99%) are of the Montmorency variety, (See Table 1.1). The sweet Cherry trees are slightly dominated (31%) by the Napoleon variety. With 82% of the cherry trees in the state as tarts, the uniformity of variety throughout the state aids in design and analysis of mechanical harvest systems. Over 98% of the Michigan cherry production occurs in the northwest, west central, and southwest districts of the lower peninsula bordering Lake Michigan. Tree ages range from 1 to 22 years or more, (See Figure 1.1). Trunk diameters of commercially harvested trees typically range from 50 mm (2 in) to 406 mm (16 in). As the older plantings die out and become unproductive, they are replaced with young plantings. Until this occurs, however, the common practice is to replace each damaged and unproductive tree with a new tree. This creates a highly non-uniform orchard and is a significant factor contributing to tree damage when operators fail to reset shakers for different tree sizes. 1.3 Need for Shaker Analysis Limb and trunk shakers have been used for many .mmme .LoQODOo .OLSBHsoflumd mo ucwEuumdoo :mmfigoflz 8mm.mm mmH.N ooo.ewm.m aaeoe N.mH oom.mHH tenuo e.e oom.em “omega: H.m ooe.ee cemcnoaeeem w.oa oom.em mflucmnm LOLOQEm H.~H oom.eoa Danaeum m.eH oom.mmH moaoo o.Hm oom.mem comaoaez mmm.e mes o.nca ooo.emw emmzm meo oom1ma nonuo e.mm oom.ame.e sucetoeucoz eom.mH mmm.H o.ooa ooo.oom.e emae mamaeomm mmmzomo ezmomma mmmme semam<> me >3 cowuosvonm cone mononu :mmfinufiz .H.H dance i‘I‘EAR 2-3 YEARS 4-6 YEARS ?-11 VEARS 12—21 trans 22+ YEARS IVEAH 2-3 YEARS 4-6 runs. 7-H wanes . 12—21 VEARS . 1 22+VEAR3 ' I l l L I I l I —r I 250 500 750 1000 1250 THOUSANDS OF TREES Figure Ll Michigan Cherry Trees by Age - 1982 Survey- (Michigan Dept. of Agriculture, 1983M years for the mechanized removal of fruits and nuts (Brown, 1983). Over 95% of the cherries annually harvested in Michigan are removed with mechanical shake-and—catch systems (Brown et al., 1982). The majority Of these systems use trunk shakers because they provide greater speed, lower harvest cost, and minimized human effort in comparison to limb shakers. Studies of cherry bark strength indicate that cherry bark is easier to damage than apple or peach fruit tree bark in both longttudinal and tangential directions (Diener et al., 1968). In apple and peach trees, the bark tissue is not rigidly attached to the inner tissues. This provides a tangential bark strength four times that of Cherry tree bark, where the bark tissues are rigidly attached. The force developed by the shaker must overcome the inertia Of the tree and provide limb acceleration large enough to detach the fruit from the stem. This force should be transmitted to the tree without exceeding the bark strength properties. Design and operating parameters for mechanical harvesters have been determined which presumably do not damage the tree. Static forces have been applied to tree trunks through shaker pad—Clamp systems with no evidence of bark damage. After shaking, however, tree decline (defined as a reduction in yield, vigor, or total tree numbers per c II. .( i ‘ 10 orchard i.e. tree death), continues to be of great concern to growers. The static forces applied to tree bark do not adequately explain the bark damage problem. Factors that continue to be of concern as potential causes include operator error, clamping force, shaking force, carrier slip, improper shaker and clamp adjustments, improper machine maintenance, inadequate orchard maintenance, and poor choice of harvest date, harvest practice or production practice (Cargill et al., 1982). Several of these factors only occur during the actual process of tree vibration. From these causes and others, repeated machine harvesting has shortened— the life of cherry orchards in Michigan (Brown, 1982, Friday, 1983). With 658,042 new tart cherry trees planted since 1978 (15% of the total number of tart cherry trees reported in 1982), the impact of harvesting equipment damage on young trees has become a particular concern. Young trees are more easily damaged than mature trees. To pursue the causes of the bark damage problem, I decided to conduct an analysis of the real-time dynamic behavior of the tree and shaker system. The stresses Which are applied to the tree trunk during mechanical shaking vary in both magnitude and direction. Previous studies of the dynamic behavior of the shaker and tree have not made estimates of these stresses possible. Measurements of the maximum displacements of the tree and ll shaker body would provide information which could be used to estimate the maximum imposed stress and strain on the bark. SinCe the pad is composed Of elastic material, relative displacements between shaker and tree act as a strong indicator of stress. 1.4 Objectives of the study The goal of this study was to determine the relative dynamic displacements between a cherry tree trunk and the attached trunk shaker. Resulting relative displacements would be analyzed for critical maxima. The displacement data could__aid in the estimation of force, stress, and strain applied to the bark during shaking, and provide new knowledge useful for the reduction of bark damage. The following specific objectives were selected to meet the need of the investigation: 1. Design a microprocessor-based data-acquisition system capable of characterizing the real—time dynamic behavior of a tree trunk with various vibratory driving forces. The accuracy of digitizing signals with such a system would be evaluated and a process selected so that the relative displacement data were representative. 2- Develop the methodology for analyzing the accelerometer data and obtaining displacement results T—i therefrom. 3. Determine the peak X, Y, Z and 9 relative displacements between the tree and shaker at the Clamp area for several driving force situations. CHAPTER 2 LITERATURE. REVIEW Compared with other fruits, Cherries are relatively small and have a short harvest season. Levin (1960) states that yield per worker is quite low when harvesting Cherries, meaning long hours of slow picking. Ten times as many man—hours are required to pick a tonne of cherries as are required to pick the same amount of apples, peaches, or pears:— Manual harvesting of the cherry crop requires many migrant workers, so many that the cost of labor during harvest can amount to half the farm value of the crop (Brown, 1980). Public Law (PL) 78, commonly called the "bracero program", allowed supplementary foreign workers to enter the U.S. to meet high seasonal needs. With the termination of PL 78, growers had to Choose between mechanical harvesting, switching crops or Changing vocation. Recognizing the high long-term investment of orchard crops, growers looked to mechanization and discovered they could economically mechanize and supply the consumer market at lower cost than with hand labor. Shortage and cost of hand labor, labor unrest, 14 final product cost to consumers, rough handling, economic risk and other economic barriers had been primary problems in managing a steady flow of produce from the field to the consumer in competitive markets, according to Drake (1983). A non-destructive, non-damaging means of mechanically harvesting fruits, specifically cherries, was sought. Work was begun in 1956 by Levin et al. to develop a method of mechanically harvesting cherries. The first step was to study the effectiveness of separating red tart cherries from trees with hand and pole shaking methods. Detachment was accomplished by causing the fruit to oscillate until a failure of the stem at the spur or at the fruit occurred. Very little tree damage resulted with the hand and pole method. Finding this procedure unacceptable due to worker fatigue, however, hand-carried ’mechanical shakers were built in 1957 which hooked to individual tree limbs. These units were heavy, transferred excessive shock to the user, caused slight tree damage, and worked successfully only on the smaller limbs. In 1958, a tractor-mounted, hydraulically— activated boom shaker, used previously on the West Coast for harvesting nut crops, was tried on sour cherries by Levin et al.. It operated at 12-17 Hz (700-1000 cpm) and used a 3.8 cm (1.5 in) stroke. It provided 95% fruit 15 removal in seconds with little operator fatigue. The clamp was a bear—hug style covered with rubber padding to cushion tree contact. Bark damage to limbs due to Clamp slip, excessive pressure, or» deviation from a 90 degree attachment angle ranged from no damage to very serious damage. Removal of sweet cherries with this same shaker caused considerable tree damage due to the violent action required to remove immature fruits for the brining market. Adrian et a1. (1963, 1965) described their attempts to transfer forces from shakers to fruit and nut trees with minimal tree damage. Metallic fasteners were placed permanently or semi-permanently into main scaffold limbs or trunks for shaker attachment. This permitted direct transfer of force to the structural wood rather than through the vulnerable bark and growing tissues. After repeated occurrences of fastener bending, breakage, withdrawal and limb splitting, Adrian et a1. concluded that direct clamping of a shaker to a tree through a cushioning pad was the most efficient method of trunk or limb attachment. When mechanical harvesting was adopted in Michigan in the 1960‘s,» drastic modification of tree structure was necessary for efficient harvesting. Large scaffold limbs trained low to the ground for hand harvesting were eliminated leaving only three or four main scaffolds. Willowy branches were pruned to improve fruit removal by eliminating the damping effect of a long branch. Newer, younger orchards were trained for mechanical harvesters, too. Harvester design also Changed through the 1960's. Small limb shakers with little power yielded to large trunk shakers with greater forces and redesigned Clamps and pads. Larger stresses, varying in magnitude and direction (i.e. radial—compressive, tangential, longitudinal) were imposed on the tree, Figure 2.1. Mechanical harvesting of cherries is presently accomplished by securely attaching the shaking mechanism to a single limb or trunk through a thick rubber pad to transmit the energy into the tree system for fruit detachment, Figure 2.2. Mechanically harvested fruits are most often used for processing. Tennes and Brown (1981) have noted that conventional low density orchards of 75 to 200 trees/ha are presently being harvested at acceptable rates with these stop-and—go shaker harvester systems. Higher density plantings (200—400 trees/ha) may have lower yield per tree, and therefore require higher speeds for equivalent volume per unit time. Continuously-moving harvesting systems are being developed for these high density orchards (Peterson and Monroe, 1977, Peterson, 1984). Trunk shakers with self-propelled catching frames Scan harvest 60—120 Cherry trees per hour. Thanks to mechanization over the last 20 years, 65 man-hours per l7 // RADIAL \\(COMPRESS!VH ' TANGENTIAL LONGITUDINAL Figure 2.1 Possible stress directions when using trunk shaker harvesters. 18 .mOHMHOEO Mom Houmo>nmc Hoxmsm xCSHe ocean 039 N.N oHSMMm wzmmhbuHmm ....... ....... hec mar SWE prc IIIEI 19 hectare of hand picking have been reduced to 4 and 8 man-hours per hectare to mechanically harvest tart and sweet cherries, respectively. Labor shortage and costs in New South Wales prompted Hutton and Brown (1981) to attempt to mechanically harvest Cherries, peaches, plums, pears, apples and apricots in the orchards of the Murrumbidgee Irrigation areas with the new trunk shakers. Harvesting proved satisfactory in most crops. .Cherries were harvested for the fresh and canning markets but fresh market harvesting proved feasible only on dark colored, firm fleshed varieties. a Mechanical harvesters are common in most commercial orchards- for reasons of speed and economy. Brown et al. (1982) reports that 95% Of the sweet and sour cherry trees in Michigan in 1982 were harvested mechanically. According to the Michigan Department of Agriculture (1982), this amounts to 5,118,000 trees of bearing age. Reports by growers have indicated that orchards of all ages are showing signs of tree deterioration (Brown, 1982, Friday, 1983). The negative impact of tree decline in the fruit industry, particularly cherries, has prompted current efforts to determine and eliminate the causal factors. Cherry trees have a long productive life exceeding 50 years; bark damage can shorten the life of a tree by 10 20 years or more. Tree damage, as analyzed by Cargill et a1. (1982), occurs in three forms: 1) damage to the bark at the point of shaker attachment, 2) breakage of large stiff limbs and, 3) breakage of small branches or detachment of leaves and other new, young growth. The authors list 19 possible factors that can result in bark damage on trees. These causes, exacerbated by repeated machine use, may shorten the productive lives of cherry trees and orchards. Brown et a1. (1982) noted that untrained operators are often unaware of the damage caused by their machines. The separation of the bark from the wood at the cambial zone is often externally invisible to these operators, yet later can provide an ideal environment for disease organisms and inseCts. Unattended tree damage, combined with adverse winter weather, insect and disease attack, poor nutrient supply from the soil, improper use of growth regulators or poor irrigation practices, can cause an orchard to decline quite rapidly. 2.1 General Causes of Bark Damage Bark damage is easily recognized when conditions exist that cause stripping, cracking or wetting of the bark at the trunk or limb of the tree. Often, however, conditions only cause a slight cracking or internal se; Fig III'II um am BI" to or of sh th re vi Cc ir 21 separating of the bark from the wood at the cambium, Figure 2.3. This lesser injury is not apparent to the untrained machine operator and thus, goes unnoticed and uncorrected. The influence of disease, weather, insects and obstructions of nutrient flow with time in the damaged area add up to a major problem of total tree decline (Figure 2.4). Diener et a1. (1968) studied damage problems and found that the amount of bark damage inflicted on a limb or trunk is determined by the bark prOperties, the radius of the limb or trunk, and the resistive forces of the shaken object. 4 Fridley and Adrian (1960) attempted to determine the power and optimum frequency of vibration in fruit removal with minimal tree damage. One possibility was to vibrate the tree at the natural frequency of the fruit. Combinations of frequency and displacement that cause instability at the point of fruit suspension, however, were difficult to transmit through the branched tree system due to colliding limbs and damping by leaves. Collision of fruit and limbs when the shaker frequency reached the natural frequency of a limb could cause damage to tree and fruit. The other possibility was to vibrate the tree at one Of the natural frequencies of the tree. The selection of the proper natural frequency was dependent on the 22 Figure 2.3 Tart Cherry tree trunk six months after trunk shaker harvesting.-—No apparent evidence of bark damage. 23 24 Figure 2.4 Tart cherry tree trunk 18 months after trunk shaker harvesting. Obvious tree decline from uncorrected bark damage. 25 v. 0...: ..... ‘5‘ I ;f. I; )' ‘1 l .3 . n — i . .. . .~ .. a". . . ’1. b . . . l . ~ . » r. r . _ a l- I. I a. l A. f. I u .0 V u 1 I. c . .. . . x x . 1 . .. ta 4 . r... . . r . . 2 . J i . . ea 1 u. .u . . . e-l . r. . \. . .J . . .2 .3 . u a . t. . . L p. o .. . e .. . 1 m. e. . _ P. I. o.,\ .u . D A... . . I. u r. a U. . J . ul‘. I . 1.... at) . . e .‘I m e. I I . Av I ‘7 26 stroke needed to remove the fruit at that frequency, the power required and the resulting tree and fruit damage. Power was needed to remove a volume of fruit with long strokes and low frequency; increase of either stroke or frequency, however, caused an increase in tree damage, though stroke was the 'major determinant. Placing the clamp at an anti—node for a given natural frequency allowed the stroke to reach a maximum for that frequency. Higher frequency with shorter strokes resulted in minimum damage. A force must be exerted perpendicular to the trunk or limb to minimize damage and power required, for as the included angle -between the shaker and the object deviated from 90 degrees, a component of force parallel to the trunk or limb induced shear and was identified as a direct cause of bark damage. Bukovac (1983) suggested that tree decline is a result of shaking with "unnecessary force" when fruit removal is low which causes an operator to shake harder and longer. Other than the common damage at clamp points, Bukovac believes that improper shaker usage may result in "breaking of roots, interfering with the conduction systems, and doing other harm which is not so apparent". Bukovac's solution is the use of plant regulators to loosen fruit and get high crop yields without stressing the trees and causing premature death to orchards. Beljakov et a1. (1979) studied the effects of ’9. \ ,I 3,_ . ' I 27 shaker harvest on the root systems of sweet and sour cherries, peaches and plums. The exciting fOrce was developed by an eccentric mass trunk shaker, clamped 20 cm (7.9 in) above the earth and operated at 15—18 hz with 2.4—3.0 cm (1.0-1.2 in) strokes. A radioactive tracer, P-32, was injected into the soil and along with C-14, was applied to leaves to study photosynthetic activity. Results indicated that there was no adverse effect on tree growth, and only an insignificant number of roots were severed (less than 0.05% of the roots by weight of diameter 0.1 cm (0.04 in) or smaller). Heavy wind and— rainfall in August and September of 1979 blew over or loosened many 7.6-12.7 cm (3-5 in) diameter peach trees in Northern Virginia. The following Spring, trees grew poorly, failed to produce normal leaves and died. Investigation by Lyons and Yoder (1981) revealed dead crown roots which had been broken by wind and killed by excess soil moisture or pathenogenic _infestation. Further investigation found poorly anchored trees, in general, had deeper crown roots and were more susceptable to breakage by external attack from wind or shaking. Brown et a1. (1982) and Cargill et a1. (1982) made direct field observations and classified ten general causes behind the bark damage problem as follows: 1. Operator error and inadequate operator 28 training (Operators, due to a lack of time or training constraints, may not follow recommended procedures to minimize bark damage). 2. -Improper shaker adjustment. 3. Improper clamp adjustment and maintenance. 4. Improper shaker clamp attachment. 5. Poor judgement in selection of a machine for young trees and/or failure to adjust existing machines for tree size. 6. High cambial activity at harvest due to excessive irrigation, rainfall, or physiological activity. 7. Immature fruit requiring an excessive force for removal (this tempts the operator to overshake for satisfactory fruit removal). 8. Improper machine design. 9. Settling or moving of the shaker due to soft soil conditions or excessive side hill slope. 10. Improperly pruned trees requiring excessively long shaking cycles. The critical concept is the transmission of the proper force to a tree to remove fruit, but to do so without harming the living tissues of the tree. This is a ‘1 "7" di ca le 0C b) an ex a1: di at wa le Ta pr IIIG le TC IC 36 29 difficult task for, as Brown et a1. (1982) noted, bark and cambium damage on cherry trees will occur at lower stress levels than on other fruit trees. 2.2 Harvester Factors in Bark Damage Halderson (1966) suggests that damage to trees occurs in three forms: a) physical injury by the shaker, b) trunk injury by positioning catching frames or shaker and, c) root damage from tree vibration. In field experiments, all movement of the roots ceased approximately 15.2 cm (6 in) below the soil surface and did not appear to be ta major problem. Bark damage by attachments was minimized with good clamp design. Level ground, providing perpendicular attachment to the tree, was. considered such an important factor as to necessitate leveling devices on catching frames and harvesters. Tangential clamp slip and twist were observed to cause problems, though not always immediately apparent. Many details of tree and fruit response to mechanical harvesting have yet to be resolved. Gentry (1980) developed a citrus harvester in 1978 to harvest lemons. Rotating masses totalling 114 kg (250 lbs) were rotated up to 5 Hz (300 cpm) in order to shake trees up to 40 cm (16 in) in diameter. The shaker mechanism weighed 565 kg (1245 lbs) and was attached at a height of 36 cm to 1 m (14—40 in) above the tree base. After 30 repeatedly running into the skinned trunk problem on lemon trees, Gentry switched to grapefruit, finding less damage after shaking due to a tougher bark. Without explanation, however, in three consecutive years, Gentry's grapefruit harvest steadily increased and tree appearance improved when using the mechanical shaker. Tennes and Brown (1981) developed a sway bar shaker for the continuous harvest of horticultural tree crops. A pair of horizontal bars was pivoted at the front end of the harvester and was powered at the back end by two synchronized rotating eccentric masses. A roller assembly was mounted along each bar to eliminate sliding motion between the bark and the contact surface of the bars. The entire harvester was found to move 3-6 cm (1—2 in) during each cycle of the sway bar. Bark damage to the central leader of apple trees was still observed to be a problem; the putative cause of bark failure was the shearing impact discussed by Fridley et a1. (1970). A solution to prevent bark damage was needed before a shaker of this design would become practical. In 1982, Helden removed fruit from Valencia and Hamlin orange trees with two shakers, one providing a linear motion and the other being a multidirectional shaker. Average shaken tree diameter was 16.2 cm (6.4 in). Static clamping pressures were 6.5 kg/Cm2 (93 PSi) for the linear shaker and 12.4 kg/Cm2 (176 psi) 31 for the multidirectional shaker. Minimal bark damage was observed in all tests, even for the Valencia orange trees which are in a growth state at the time of harvest. Millier et a1. (1983) developed and tested a- recoil impact shaker for fruit removal from apple trees. Force was applied in a single linear direction at the trunk of the tree. Four displacement cycles were applied in 30 s with a 141 kg/cm2 (2000 psi) pressure at a 30 L/m (8 gpm) flow rate. Tests showed that the linear shaker performed better on Y—shaped trees than did a multidirectional shaker, easily removing fruit on limbs parallel to the applied force, but requiring violent action to remove fruit on limbs perpendicular to the applied force. No obvious trunk damage occurred. I The general design of some shakers naturally induces damage to the shaken tree. Counter-rotating masses are usually Offset from the shaker Clamp so as to locate the center of rotation of the shaking force several centimeters away from the center of gravity of the tree. This Offset induces a torque as the shaker moves through a select pattern because the center of force is at a point other than the center of gravity of the tree. As the shaking occurs, different twisting effects are induced and energy is applied to the shaker mounts and carrier. Part of the input energy goes into friction as the tree and Pads attempt to resist the torque. A lubricated flap 32 between the pad and tree reduces the shear and torque transmitted to the bark. Shear may also be reduced by increasing the pad contact area. The pressure on the bark is reduced as a fixed applied force is transmitted through a larger and larger bark contact area. Many other studies conducted on mechanical fruit harvesters have reported that bark damage can be serious in some cases. Conditions under which shaking is performed such as weather, environment, soil, terrain, labor, cultivation practice, tree type or variety, or machine are seldom the same; hence, pinpointing the most likely common causes of tree damage and decline has been difficult. In 1982, Brown et a1. expanded their general observations of bark damage in order to isolate specific operator and machine -inaccurracies that may account for the observed tree damage. The list of critical points included: 1. Failure to center the clamp on the trunk. 2. Clamping too firmly to the tree causing excessive radial stress, hence, crushing and splitting of the bark. 3. Clamping too loosely during shaking where the pads tend to scuff and tear the bark (tangential shear). 4. Clamp pads not slipping internally due to the wrong pad design or improper lubrication 33 of slip surfaces causing high shear forces (e.g. pads becoming heated, sticking together, inducing shear force and deteriorating). 5. Excessive eccentric mass setting causing excessive tree displacement and bark strain. 6. Excessive power applied to small trees. 7. Shaker "gallop" during startup and stop (causing torque (shear) in the bark). 8. Settling of the shaker carrier into the earth during shaking (causing excessive longitudinal-shear). 9. Shaking forces not perpendicular to the trunk (causing longitudinal shear). 10. Clamping too low to the ground where trunk is most rigid (causing excessive forces to be applied to the trunk). 11. Clamp pads too small or firm causing high stress in the bark due to a small contact area. 12. Longitudinal shear caused by Clamping to a leaning trunk. 13. Longitudinal shear caused if shaker is tilted when Clamping to trunk. The above list of causal factors fell into three main categories: '34- 1) Operator error during shake and clamp, 2) Improper pad design, and 3) Improper machine design or setting. Little damage can be blamed on a well—trained, well—informed and experienced operator. Shaker pads have been studied in a static state and will be discussed in the succeeding sections. Machine design and selection of operating settings require knowledge of static and dynamic biological tree tolerances, as well as the dynamic reaction of shaker pads to force transmission. Little work has been done to define the dynamic reaction of the pads and bark because of the lack of practical measurement and analysis technologies. 2.3 Bark Structure Diener et a1. (1968) describe the Structure of Cherry bark as having a thin, nonliving outer periderm, a large, spongy, nonfunctioning phloem in the center and a thin, functioning phloem next to the cambium. The directional strength properties of cherry bark can be accounted for from the alignment of the constituent cells. Phloem cells have their long axis in a longitudinal (vertical on the trunk) direction, whereas periderm cells have their long axis in the tangential (horizontal on the trunk) direction. The periderm consists of thin-walled dead cells encrusted with waxes which lubricate the dead 35 tissue and allow slippage between cells (Esau, 1965). When the bark is damaged so that it separates from the wood (xylem) of the tree, the flow of fluids containing the essential life sustaining elements is interrupted in that area. Usually, hairline cracks are formed in the bark tissue, through which air enters and oxidizes the cambial tissues so that they appear brown (Adrian et a1. 1965). Devay et a1. (1962) notes that these damaged areas are open invitations for insects and disease, especially tree canker, a gummosis disease caused by the fungus Ceratocystis fimbriata, evidenced in the fruit orchards of California. The fungus, g; fimbriata infects bruised bark tissue, gradually spreading to healthy surrounding tissue, slowly causing tree death. A depression in the infected tissues, accompanied by the production of an orange frothy gum, characterizes the canker attack (Devay, 1960). In 1960, Devay et al. reported increasing incidence of canker in California almond orchards as a result of fungus attack in damaged bark areas caused by mallets and mechanical shakers. The cause of the spread of the fungus is not primarily a search for nutrients but rather to escape its own lethal environment of dead bark cells and tissues. Hence, the live fungi are only found at the canker margin. The fungus expansion occurs all year, but is most rapid in the warm and moist months. In 19' mo de1 thl suc Fur f n wor tre has obv ind of myc thu OCC Par. (19' a11m I'hil feel 36 1965, Devay et a1. discovered that extremes in bark moisture do not greatly affect fungus growth (canker development) but that soil moisture plays a primary role in the spread Of the fungus by insects from tree to tree; the spread is most pronounced when soil moisture is high such as within the first few weeks after irrigation. Fungus development is particularly pronounced on stone fruit trees that are irrigated 1-2 weeks before injury. A wound dressing (Cerano) was successfully developed to treat canker wounds in almond and plum trees. Damage by a powerful trunk shaker affects the base structure of the entire tree. Damage to the trunk is ‘obviously much more critical than damage caused to individual scaffold limbs by limb shakers. Continued use of shakers in diseased orchards can spread spores and Lmycelial fragments to bruised tissues of healthy trees, thus propagating tree cankers. Death of injured trees can occur within a few years. 2.4 Bark Strength Bark strength was studied to develop design parameters for mechanical harvest systems. Fridley et a1. (1970) studied the bark strength of prune, peach, apricot, almond, and olive trees. They reported that the stress which bark can withstand is directly related to seasonal factors such as moisture content and cambial activity. Wht b6] de: bai ma di' co no l9 :1 th an SI II 12 _T_—_—______—____—__—__—______—___“IIIIT' 37 When moisture content or cambial activity is high, the bark slips easily and bark strength is low. "Slip", as defined by Cargill et a1. (1982), is the separation of bark from the wood at the cambium zone. Slip occurs mainly in the Spring when cells are enlarging radially and dividing. Cell contents Change from a solid to a liquid consistency. The walls of cells at this time of year are not as thick due to continuous cell division (Bukovac, 1984). Therefore, cells tend to break easily and the bark slips. In the Fall, cambial activity ceases, cell walls thicken as moisture content drops in the bark and cambium, ‘and slip does not occur because of the toughened fibers. Shear strength of cherry bark decreases as cells are ruptured by excessive radial forces. Directional strength properties of the periderm Vlayer were opposite to that of the bark of cherry according to Diener et a1. (1968). Periderm strength was highest in the tangential direction, parallel to the long axis of the constituent cells. The periderm exhibited five or six times the tangential elongation before rupture as did the phloem. The important fact here is that tangential shear stress or strain from shaker torsion or Clamp pressure can cause the phloem underneath the periderm to rupture without rupturing the periderm itself, therefore the phloem damage can be concealed. di Re ta in pe e1 qu re di 1 ti fa 2 if I 38 Phloem strength was greatest in the direction parallel to the long axis of its cells, the longitudinal direction, and weakest in the tangential direction. Results indicated that Cherry bark would typically have a tangential strength of approximately 420 N (95 lb) per inch of width rather than 110 N (25 lb) if the cherry periderm was not attached to the bark. Rupture due to elongation of Cherry phloem and periderm was found to be quite dependent on direction; this is opposite the response of peach and apple bark. Failure of bark cells in the longitudinal direction was found to occur from incremental fiber and tissue rupture, accompanied by sliding and continued failure. Bark behaved as a viscoelastic material until yield occurred. Failure at the cell borders with tangential loading took place at very low forces; in tangential loading, a force was applied perpendicular to the long axis of the cells. On a curved surface, bark tended to realign its tissues in the direction of the Iapplied force. The amount of stress absorbed increased slightly with time until rupture. Sweet cherry bark is about twice as easy to damage as tart cherry bark on equal diameter trees. Young cherry bark (up to 8 cm trunk diameter) damages more easily than bark of older trees. Brown et al. (1982) demonstrated that compressive failure in the cambium of SWI 301 C01 C01 'I 39 sweet cherries occurred at surface pressures on the bark above 10.5 kg/cm2 (150 psi). Sour cherry compressive failure was evident above 24.6 kg/cm2 (350 psi). Compressive tests showed that cherry bark ruptures completely at 84.4 kg/cm2 (1200 psi). Pressures of 10.5 kg/cm2 (150 psi) and 24.6 kg/Cm2 (350 psi) for sweet and sour cherry, respectively, were accepted as clamping pressure limits. The pressure limits can vary from these values subject to moisture content and cambial activity. Shear strength for. sweet Cherry bark was also lower than for sour cherry. Average cherry cambial shear strength was suggested by Brown et a1. (1982) to be only 4-7 kg/cm2 (60-100 psi). Sweet Cherry bark shear strength decreased as moisture content increased but this trend was not convincing for tart cherry bark. The shear strength increased as clamping pressure increased, apparently due to friction. According to Adrian et al. (1965b), tangential shear failure in fruit and nut trees occurred only with complete bark failure and at significantly lower stress levels than those which caused cambium browning following compression. Dynamic stress in tests by Adrian et al. (1965b) was only 75% of static stress and still caused cambium browning. This would indicate that acceptable static clamping pressures may be much too high to prevent tree damage in a dynamic T—‘75—‘_—___—__—_—______7__"“IIII'[ 4o (shaking) state. Radial design stress was limited to 17.6 kg/cm2 (250 psi). Tangential stress was limited to 7.0 kg/Cm2 (100 psi) to prevent tissue injury in prunes, peaches, almonds, olives, and apricots. Fridley et a1. (1970) used cambium browning as an indicator of radial stress failure. Browning increased with increasing pressure. The inner bark appeared porous and degenerated when browning occurred. Radial stress of 70.3 kg/cm2 (1000 psi) visibly cracked bark to the cambium in 20-year—old prune trees, with subsequent occurrences of C. fimbriata canker. Cracking and canker in six-year-old trees occurred at 75% of these stress values. As radial stress increased, strength decreased at high moisture content but increased at low moisture content. Bark was found to withstand three or four times the radial stress (compression) as longitudinal or tangential stress (shear). Fridley et a1. (1970) found that the inner bark (phloem) of prune trees resisted the glongitudinal loading while the outer bark (periderm) resisted tangential loading. Outer bark failed at 10% of the ultimate longitudinal tension making a clean break. Inner bark failed similarly under small tangential loads. Fridley et a1. (1970) demonstrated that a primary Ifactor in bark injury is the application of forces having either a tangential or longitudinal component with the 'I 41 limb. Field tests of total tangential shear stress showed that injury and infection occurred only when bark failed completely. Shear failure at the cambium and tensile failure at the bark combined to cause injury with the tensile failure occurring both perpendicular and longitudinal to the bark fibers. Results showed that tangential shear strength was 50-70% of total tangential strength. Low shear strength occurred at high moisture while high shear strength occurred at low moisture. As moisture increased, the presence of radial stress became less effective in preventing longitudinal shear failure. This demonstrates the importance of avoiding irrigation near harvest if bark damage prevention is desired. Since slip depends on moisture content, irrigation and rainfall during periods of rapid growth will reduce bark strength. The' harvesting of Michigan cherries in June and July makes this crop more susceptible than most other fruit trees. Bark strength varies from location to location, depending on climate, soil type and practices of ‘production. The susceptibility of young trees makes these factors a particular concern when looking at methods of reducing damage. Excessive Clamping pressure and shear forces can combine to increase the likelihood of bark damage when moisture content is high. CI in ~——i - I 42 2.5 Shaker Pads Forces are transmitted from the shaker body to the tree through a pad which acts as cushion, damper, and spring. Minimum stress occurs in the bark when the required vibrational energy is transmitted over the largest possible area. Longitudinal and tangential forces from the epicyclic shaking patterns must be efficiently communicated to the tree by means of a pad that conforms well to the tree structure. The pad must be firm enough to transmit shaking energy without pad slip, but not such that compression and splitting result. Scouring of the bark or excessive shear stress may result if pad contact area or clamping pressure are insufficient. During shaking, these inefficiencies may be observed as slipping action (tangential Or longitudinal) or beating action (radial). If contact area is sufficent, but clamping pressure is too great, the bark may be crushed or split. As clamping pressure is increased, shaker pads become stiffer (smaller pad deflection per force increment) and a harder shake is imposed on the tree. Excessive torque may arise during shaking if Clamping pressure is very high, because the pad is unable to internally flex or slip. Until recently, pad design has been a trial-and-error process. The use of a poorly designed pad would likely cause bark damage regardless of attempts to control other damage factors during shake harvesting. 43 Methods of pad construction have included a round hollow tube, bags filled with sand or ground nutshells, solid rubber pads with small holes drilled parallel to the tree trunk axis, preformed clamp jaws and rubber pads, and other conforming materials. In 1982, Brown et a1. made preliminary tests of C—clamp shaker pads for contact area and peak contact pressure at the manufacturer's recommended hydraulic circuit clamping pressures. This hydraulic pressure range was assumed to cover the unknown peak pressures between the pad and the tree during shaking. They found peak pressures between the pad and bark of 23.9 kg/cm2 (340 psi), 35.2 kg/Cm2 (500 psi), and 42.2 kg/cm2 (600 psi) on an 11 cm (4.5 in) diameter trunk (actually an instrumented steel pipe). This suggests that certain Irecommended clamping pressures may be excessive and cause compressive failure of high moisture cambium for both sweet and sour Cherries, as well as, splitting of the inner bark in sweet Cherries. Failure of the cambium from compressive stress (radial) was initiated at lower Clamping pressure on sweet cherry 10.2 kg/Cm2 (145 psi) than on tart Cherry 23.5 kg/cm2 (335 psi). Brown also states that "Peak contact pressures higher than observed in these stationary tests certainly occur during shaking, but we have not progressed to the point of estimating dynamic pressures". 44 Frahm et a1. (1983) evaluated four commercial trunk shaker pads for peak bark pressure, bark contact area and pad stiffness. Pad pressure patterns are not uniform and differ for each manufacturer. If a peak bark pressure of -21.1 kg/cm2 (300 psi) was not exceeded, when bark contact area and pad stiffness were adequate, the pads were judged to be safe. This pressure presumably would not cause compressive failure in sour cherry tree bark, which exhibited an average ultimate compressive strength of 24.6 kg/cm2 (350 psi) and it would cause only minimal damage in sweet Cherries, with a corresponding strength of 10.5 kg/Cm2 (150 psi). Results showed that recommended manufacturer's clamping pressures on all pads developed peak pressures exceeding the estimated 21.1 kg/cm2 (300 psi) limit, indicating that all tested pads could potentially cause bark damage. Reduced clamping pressures which would limit the peak pressure under the pads to 21.1 kg/cm2 (300 psi) were identified. This procedure was possible on some pads but resulted in insufficient contact area on others. The Friday Tractor CO. (1982) has developed a "tri—Clamp" composed of three pads contacting areas of a tree trunk 120 degrees apart to completely surround the tree. An eccentric rotating mass was centered in line on each side of the tree to provide a center of gravity of the masses at the center of gravity of the tree. This 45 design provided a complete wrap of the pads around the tree for no-slip and presumably directed all forces through the center of gravity of the tree to prevent torque damage. A firmer grip on the tree was the result. 2.6 Tree Response Kronenberg (1964) studied the effects of fruit detachment forces in attempting to mechanically harvest cherries. He found the detachment force decreased as the fruit ripened. The difference between the force ten days before harvest and that on the traditional picking day varied with the equation: Y = —48X + 428 Where X = 9 - Number of Days before Harvest Y = Grams Force Unripe cherries came off with stems, whereas ripe Cherries did not. With careful shaking, healthy leaves would not come off with mature fruit. This suggests that cherries might be harvested selectively and should first be harvested 4—7 days prior to the traditional picking day. Halderson (1966) studied the relationship between percentage of cherry fruit removal and elapsed shaking time. He found that long shaking time was required for over 85% removal when fruit was immature, but little 46 shaking time was required when fruit was mature. The rate of fruit removal was determined mainly by the shaking frequency. Eighty—five percent removal was obtained in 2 s of shake with 95% removal after 8 s at a frequency of 16 Hz (950 cpm). A frequency of 13 Hz (800 cpm) was 'determined _to be a minimum for adequate removal. A maximum stroke of 1.9 cm (.75 in) was adequate at frequencies of 17 Hz (1000 cpm). Using this setting, the fruit fell straight to the ground (no whipping action). Tests by Adrian and Fridley (1958) indicated that fruit removal was affected by applied acceleration and the number of hangers (limber fruit-bearing branches) in a given tree, as well as, the frequency and stroke of shake. More fruit were removed on rigid trees than on trees with an abundance of hangers; breakage of limbs increased with increasing stroke. Minimum damage occurred between 12-15 (Hz (700—900 cpm). Studies by Fridley and Adrian (1960) showed ‘minimum force and power were needed to vibrate a tree when jclamping was at an anti—node and shaking speed was at a natural frequency. The first resonant frequency of a vibrating cherry tree is very low (e.g. 50 cpm) (Halderson, 1966). Less power was needed with larger strokes and lower frequencies although tree and fruit damage increased. Clamping closer to a tree trunk and increasing the trunk or limb size each increased the power BI 47 and force requirements. According to Cargill et a1. (1982) the force and power when shaking fruit trees vary with frequency, stroke, shaker design, clamp position on the tree, diameter of the tree trunk, tree species, tree yield and fruit stem detachment strength. Power for increasing trunk displacement is proportional to the square of the ratio of the increased displacement to the original displacement. Power required to increase frequency varies as the cube of the frequency. The proper frequency and stroke required for adequate fruit removal depend on the type of fruit and maturity level. In 1976, Alder et a1. investigated the effect of the applied frequency and the point—of—force application on resultant amplitudes at the points of fruit suspension and at the zone of force application on orange trees. Vibrations that developed at these points were described ,by harmonic displacements. The tree system, when excited ‘by a shaker, went from a transient-state to a steady-state ‘and back to a transient-state during a shaking test. The vibration amplitudes in a shaken branch at points of fruit suspension were found to increase as the force application Point was moved further from the main branching point. If a constant force was applied, then the momentum transferred to nearby branches through the joint link remained constant as the application point was moved. 48 Vibration amplitudes at points of fruit suspension remained the same with and without attached fruit. Except at very low frequencies or very low amplitudes, changing applied frequency and amplitude had little effect on cherry fruit removal unless the combination resulted in a change in acceleration (Bruhn, 1969). Frequencies of 16—20 Hz (1000-1200 cpm) with a stroke of 3.8 cm (1.5 in) provided adequate removal of tart cherries. Accelerations at outer portions of a tree exceeded those applied to the trunk or base limb in all cases. Bruhn's conclusion was confirmed by Tennes et al. (1981) in later tests of a sway bar shaker for over-the-row harvesting of apples. The magnitudes of acceleration on apple trees increased proportionally with the frequency and the distance from the point—of—force application. I Yung and Fridley (1975) developed three special elements that mathematically described the components of a general hanging fruit tree system. Elements were standard geometric shapes assumed to be elastic, homogeneous, and isotropic. The tree system was assumed to be made up of: a) a tree structure consisting of trunk, secondary branches and hanger branches; b) fruits and stems, and; c) leaves and twigs. The three elements were incorporated into a finite element analysis of several tree models to accurately predict tree response to free and forced 49 vibration. Yamamoto (1979) investigated the response of total limb—branch systems of cherry and oak trees. He studied the natural frequency of each branch of the system from limb excitation and analyzed the resultant oscillatory wave through a range of frequencies. He found that the fruit became injured when the main branch system in a limb was excited at the first resonant mode. The fruit and twigs at the fruit zone responded in an unstable fashion as the amplitudes of branch tops magnified considerably. Resonance of two branches adjacent to one another occurred in cases where a phase angle of 3.14 radians was present between the motions. If the natural frequency of one branch differed from the other, the two branches could collide and break, damaging the tree. Finally, when the first resonant mode of a main limb ‘occurred, almost all branches on it were moving in linear paths with large amplitudes, parallel to the exciting direction. When the frequency was such that the small branches on they limb were resonant from exciting frequencies of 4—8 Hz, the trajectory of each branch became an ellipse or circle which had components perpendicular to the exciting force. He concluded that the elliptical pattern effectively detached fruit but it may have induced undesirable reaction forces at the force application point. Vibrations can be transferred to a tree via a number of shaker patterns. On some machines, patterns can be preset, while on other machines there is an undefined pattern which continuously changes with each movement of the controls by the operator. The common patterns listed by one manufacturer are shown in Figure 2.5. With inadequate clamping force, force transmission in many of these patterns may induce reactive forces in undesirable directions causing radial stress, shear stress, or vertical slip of the machine or carrier. Often, shaker force and pattern are not independently adjustable. Shaker patterns that present only a few strokes per complete cycle of a pattern (i.e. a 3-1eaved rose presents three strokes per pattern cycle) deliver a lower frequency shake to the tree at a given power setting than a pattern that produces many effective strokes per pattern cycle. Increasing the frequency of the few stroke pattern requires a higher rpm of shaker masses and more power. Higher shaker mass rpm requires a higher hydraulic system pressure, and on some machines may result in excessive clamping pressure where the clamp and shaker motor circuits are interconnected. 2.7 Suggestions for Reducing Bark Damage Adrian et a1. (1962) found that a linear shaker which would apply force to the tree in line with the I TRIANGLE ' DUAL TRIANGLE (Cycloidal) (Cycloidal) THINNING STAR MODIFIED STAR (Hypocycloidal) C6—Leaved Rose) (lZ—Leaved Rose) SPIKES STANDARD SPIRAL (Cardioidal) (Cycloidal) (Spiral) Figure 2.5 Some possible epicyclic trunk shaker patterns. (Orchard Machinery Corp., Yuba City, CA) 52 generated force resulted in minimum bark damage. Adjusting the shaker properly, pruning trees to accommodate the shaker mechanism and employing attentive operators were significant factors in damage prevention. Advising operators to avoid canker infected areas on trees and employing preventive sanitation measures to retard the spread of disease mitigated orchard losses. Adrian and Fridley (1963) developed four possible pad designs which would minimize damage. A pad containing magnetic particles and oil caused no injury but was unacceptable due to its weight and deformation characteristics. Two parallel flat belts were tried as a conforming clamp surface for limbs and showed no evidence of limb injury. Bolts mounted permanently into tree trunks proved to be strong and remained secure in younger trees, but failed in older trees. A flexible inelastic pad filled with an incompressible viscous fluid was designed but not evaluated. Devay et al. (1965) prevented and controlled 2; fimbriata canker by: avoiding bark injuries that provide insect attractive environments; shaving away bruised bark tissue and painting the wood with an appropriate dressing (Cerano); cutting away diseased internal tissues and applying a subsequent dressing, or lastly; removing entire infected limbs or scaffolds. All the diseased tissue removed was immediately collected and 53 burned. Adrian et al. (1962) used a C—type clamp on shakers because it resulted in minimal damage at the point of attachment. In summary, adequate removal of cherries by mechanical shakers requires a stroke of approximately 3.8 cm (1.5 in) and a frequency of vibration of 15—20 Hz (900—1200 cpm) (Gaston et al. 1966, Bruhn 1969, AERD 1964). Shaking periods of 3-5 5 gave the best results in fruit removal without excessive tree damage, trash accumulation, or bruising of fruit (AERD, 1964). 2.8 Triboelectric Phenomena I investigated the feasibility of making direct force measurements between the shaker pad and the tree bark using a phenomenon called triboelectricity. A dielectric material (such as the rubber composing the shaker pads) exhibits certain electrical characteristics which may be calibrated and interpreted as meaningful physical events. The compression of a dielectric material on a hard substance causes strain in the intermolecular structure. When a piece of rubber, a dielectric, is stretched or compressed, the surfaces under stress become Charged, similar to the piezoelectric effect. This charge is sufficiently large as to be useful (Memmler, 1934). Richards (Memmler, 1934) conducted tests on rubber pads as dielectrics and found that pressure applied by a hard surface to these rubber pads resulted in very small negative charges. The charge on rubber in contact with steel was found to be —l7.2 esu/cm2 and in contact with lead was -l7.0 esu/cmz. This effect has been attributed to a combination of the piezoelectric effect, the Volta effect and the rubber's surface expanding under pressure causing friction. Since the charge has been found to be proportional to strain for a given contact area and material, it would also be proportional to stress. q~e =I=4_l_ E L The stress for a given area then determines a force. v: n+1: It would then be possible to obtain force measurements from the charge output of rubber pads. Where A has been found invariant (Brain and Richards (Davis et al., 1937)). Shaw (Davis et al., 1937) showed that triboelectrification was influenced by surface conditions, the composition of material and other factors. He found h.‘ at least ten factors that determine the sign and magnitude of charge when two materials are brought into contact. Coehn (Memmler, 1934) noted that a material of higher dielectric constant assumed a positive charge when brought into contact with a material of lower dielectric constant. Since rubber is toward the negative and of the triboelectric series, it normally takes a negative charge. Soft rubber has a dielectric constant of 2.1 to 4.2 while hard rubber is around 3.02 (the ratio of the capacitance with a dielectric to the capacitance in a vacuum is called the dielectric constant of a material where the vacuum capacitance is given the base value 1.0). Deodhar, however, noted various anomalous responses of both hard and soft rubber, which may be explained in part by Shaw's factors determining charge. Later investigations by Brain and Richards (Davis et al., 1937) found that electrification was in the rubber itself and was not a friction or voltaic effect. Compressing the rubber against seven different hard surfaces produced no variation in results which could be attributed to the nature of the contact surface. Brain found that for small loads, the charge was proportional to the load, but for large loads, the charge increased more slowly. Hysteresis and fatigue were also observed. This behavior was attributed to a piezoelectric effect similar to the effect in some crystals. 111i SI 56 Brain and Richards showed that small loads produced a charge independent of the cross section of the specimen. Hard rubber developed charges of 0.02 esu/kg-load up to 0.151 esu/kg-load. When the load was removed, the charge was opposite in sign and equal in magnitude to that obtained when the load was applied. Soft rubber developed greater charges when compressed, in the range of 15.5 to 21.7 esu/cmz. Loads ranged up to 2 kg/cm2 (28 psi). At low pressures, the electrification increased with increasing pressure but raising the pressure from 2-5 kg/cm2 (28-71 psi) produced no increment in the electrification. 2.9 The Need For Tree Preservation Fruit and nut growers have a high, long term investment in their crops (Brown, 1980). The cost of switching to another crop requires major changes financially. Problems of obtaining and economically managing labor have led growers to mechanize production and harvesting. Mechanization of labor-intensive fresh market crops is presently occurring in the U.S., Japan, Australia, New Zealand, Israel, South Africa, the Socialist Block Countries, Canada, and many countries in South America. Efficiency and reliability in production have been necessitated by the world population growth, as well as the competition in food production and marketing. 'I 57 The need to preserve existing crops while increasing productive land and methodology has an immediate impact in prevention of near-future crop,failures and shortages. CHAPTER 3 THEORET I CAL CONS I DERAT I ON S 3.1 Sampling Rate and Resolution Bruhn (1969) states that vibratory harvesters remove cherries from their stems by applying modified sinusoidal- acceleration to the tree or major limbs. Acceleration is transmitted through the tree structure to the stems. If the arriving acceleration levels for an inertial force exceed the stem—to-cherry attachment strength of 1.5 to 2.9 N when ripe, then the cherry detaches. If the cherry is not immediately removed, assuming the induced force is less than the attachment strength, then the attachment strength will gradually be reduced by succeeding cycles of vibration which result in bending fatigue failure. Characterizing shake-harvesting of fruit involves an analysis of dynamic events which are continuous (analog) during the shaking period. An analog signal can be characterized by an integral number of points in a specified time, provided that each interval of time is sufficiently small to detect the changes occurring during the course of the event. Since most sensors, such as 58 accelerometers, have analog output while most data acquisition and processing is now done with digital computers, an analysis of the required conversion speed between the two forms is necessary. A triangular wave can be thought of as an extremely rough approximation of a sine wave. Digitally characterizing a triangular“ wave (originally of unknown form) would require a minimum of five points per cycle taken at equal time intervals. The inclusion of additional points between any two given endpoints increases the accuracy of modelling the time-dependent analog signal. Sampling a signal for digital data analysis is usually performed at equally spaced time intervals. The problem of determining the appropriate sampling interval a; involves a knowledge of the highest desired frequency of interest. The sampling of points at an extremely short time interval can yield correlated and highly redundant data. Sampling at a time interval too large will lead to confusion between low and high frequency components of the original data. This latter problem, called aliasing, can be avoided by sampling data at twice the highest frequency of interest (Bundat and Piersol, 1971). This sampling frequency is termed the 'Nyquist frequency' and has a cutoff of: 60 The Nyquist frequency was developed on the theoretical consideration that at least two samples per cycle were required to define a frequency component in original data where the original sampling interval was,At. Thus, the Nyquist frequency sampling interval becomes ZAt. With the Nyquist frequency as a minimum, aliasing can be avoided by choosing At sufficiently small so that it is physically unreasonable to find data above an associated cutoff frequency. Vibration of cherry trees at 20 Hz (1200 cpm) then dictates a Nyquist sampling frequency of 40 Hz (2400 cpm). However, it may be desirable to sample at a frequency higher than this when looking for peak amplitudes from bumps at the shaker—tree interface. Work by Fridley and Adrian (1960), Yamamoto (1979) and others revealed sinusoidal or nearly sinusoidal response when trees and limbs are forced to vibrate by eccentric mass inertial shakers. Halderson (1966) notes that when a tree is vibrated, it displays nodes and anti-nodes similar to those appearing on a vibrating cantilever beam. In order to digitize an analog accelerometer signal for computer storage, an accurate sampling rate had to be determined. Taking the midpoint of each segment forming one cycle of the triangular wave, and then the 61 midpoints of the segments formed by those points, a total of 16 points results when added to the endpoints (the final endpoint is ignored in this cycle and counted as the initial point for the next cycle). A safety factor of two was assumed giving a total of 32 points to characterize a cycle of a sinusoidal input wave, Figure 3.1. Operating at the lower frequency for removal of cherry fruits, a sampling rate of 900 cycles * 1 min * _32 points = 480 points min 60 5 cycle 5 was required. At the upper end of the frequency range, the sampling rate is: 1200 cycles * 1 min * 32 points = 640 points 5 min 60 5 cycle These sampling rates fulfill the Nyquist frequency requirement for a 15 Hz (900 cpm) or a 20 Hz (1200 cpm) input wave, respectively. Using a standard 16 channel analog-to-digital converter (ADC) with the same sampling rate for each channel, the sum of all channels would require a sampling rate of: 640 points * 16 channels = 10,240 points 5 per channel 5 62 ' a) 5—POINT DIGITIZED Y(a) TRIAN'GULAR WAVE §§% = 0.7857 d < b) 32—POINT DIGITIZED SINE WAVE fit?) . 0.9999 YCb) r‘f ) < C) PERFECT (INFINITE POINT) SINE WAVE §% = 1.0000 Y(c) <fl Figure 3.1 Comparison of integration accuracy of several waveforms; . (a) 5—point digitized triangular wave (b) 32-p01nt digitized sine wave and (c) a perfect (infinite point) sine wave. 63 This is the minimum required sampling rate to operate the ADC for response curves of cherry harvest vibrations at frequencies up to 20 Hz (1200 cpm). This speed must accomodate the sample and hold, conversion, and settling time of the ABC's internal amplifiers. The digital processor must process the program instructions, access the ADC ports and access memory for storage in less than 1/10,240 seconds. The input increment required to give a small definite numerical change in output is the 'resolution' of a device (Doeblin, 1983). Resolution is extremely important in analog-to—digital conversions where an analog signal must be characterized over a limited digital interval. The interval is bounded by the number of bits for which it was designed. A typical 12 bit ADC has 212 = 4096 increments for a processing interval of 0-4095; thus one increment of input is 1/4096 of the selected processing range. Converters usually have processing ranges of 0 to +5 volts, 0 to +1 volt, O to +0.5 volts and 0 to +0.1 volts, as well as bipolar ranges of -5 to +5 volts, —1 to +1 volts, -0.5 to +0.5 volts, and -0.1 to +0.1 volts. Ranges above and below these are available, but are not standard. The resolution of a 0 to +1 volt processing interval is 1/4096 of +1-0=+l or 244 PV. When digital bits represent analog signals, there is an inherent 64 quantization error of plus or minus half of the least significant bit (1 1/2 LSB) orztl/2n+1 * voltage range (Vmax'Vmin)- The above example has a quantization error of i 122 FV' In analog-to—digital data conversion, it is wise to select the processing range closest to but greater than the expected input signal limits. Suppose a 0 to +4 volt sine wave is collected on a 0 to +5 volt range in a 12 bit ADC: then the resolution is 1.22 mv. The resolution on a 0 to +10 volt range would be 2.44 mv. Twice as many points would characterize the signal on the smaller range as on the larger. 3.2 Frequency Response The use of physical sensing elements in measuring real world events requires knowing the sensor's capabilities to detect those events. The expected output is a function of the input signal and the transformation performed by the instrument itself. The transfer function for second order instruments such as accelerometers is of the form (Doeblin, 1983): e. (D) = [kq/(Cwnt )] *“i’D x; (07w; 4 25’D/wn + 1)(‘rD + 1) where K$ is the static sensitivity, wn is the undamped natural frequency, 77 is the time constant, and S’ is the 65 damping ratio. For a sinusoidal input, the transfer function takes the form: _gJL(iw) = K x; HWWQL+2fiwmn+l Where K = K /Cw Z *37D JTD + l i is the complex operator Then: ei9‘ eg/K (iw) = 1 . X: [l - (w/wn)z]1 + 4fle/wn'L $25 = tanT’ 22 :1 w/wh - wn/w It is evident that increasing wn increases the frequency range for which the amplitude ratio curve is constant (flat). Most piezoelectric accelerometers have a very high natural frequency (wn) caused by mechanical resonance at 30—40 kHz. Such a high value of wn allows shock and high frequency vibration measurements at lower frequencies. The low frequency response is limited by the piezoelectric characteristic TTD/(TD + 1). A largeTV will give accurate low frequency response; a large OT requires the use of high impedance voltage amplifiers or "charge amplifiers". The time constant is 37= RC where C normally depends upon the amplifier output capacitance and R depends on the data-logging instrument input impedance. A time constant also exists between the transducer and its fi—v T 66 amplifier. However, the theoretical infinite input impedance of an amplifier makes ?7 quite large and therefore, it can be neglected in most instrumentation operations. Time constants are offered in a variety of ranges by manufacturers. Built-in impedance converters of piezoelectric accelerometers act like emitter-followers, producing a linear output at a low impedance of nominally 100 ohms. Accelerometers are capable of delivering linear output signals to full scale when used to measure vibration. The damping in piezoelectric accelerometers occurs normally as a result of material hysteresis absorbing some energy. The damping ratio is therefore very low (about 0.01) and can be taken as 0 for practical purposes. With a zero damping ratio, ¢ = tan'1 (0) = 0. No phase lag is evident between the input and the output of such a sensor. Adrian et al. (1960, 1963b), Adrian (1964), AERD (1964), and Bruhn (1969) suggest applying sinusoidal energy to a trunk or limb at 10-20 Hz (600—1200 cpm). The response of limbs to excitation was studied by Adrian et al. (1963b) and Hussain et al. (1975). The natural frequencies of experimental apple limbs were in the range of 2-4 Hz for the first mode, 10-13 Hz for the second mode and 20—30 Hz for the third mode of vibration. The response of the tree as a total system was around 1.0 Hz. 67 Therefore, the frequencies of interest are far below the natural frequency of the instrument and should indicate the exact magnitude of the actual acceleration with negligible phase lag. The fact that the frequency of forced vibration is in the same range as the natural frequency of the tree and limb may suggest that upon startup, during shake, and/or during shutdown, the shaker may induce resonance in the tree system. Tree resonance could result in large vibration amplitudes at the point of shaker attachment, and in turn cause magnified reactive forces against the shaker. Ultimately, these forces along with tilting or twisting of the shaker, may develop excessive radial, tangential, and/or longitudinal stresses in the bark system. As these magnified stresses may exceed the ultimate strength '1evels of the bark, visible and invisible bark damage may occur. 3.3 Numerical Integration Numerical integration or, numerical quadrature involves the estimation of the quantity: b I(f) = (f(xmx O... A problem occurs when the integration cannot be performed exactly due to a messy function or when the function f(x) is known only at a finite number of points. If x0, x....xn are n+1 distinct points on the real axis and f(x) is a E( l! 68 real-valued function defined on an interval (a,b) containing these points, then there is at least one polynomial p,((x) of degree 1 n which interpolates f(x) at the points x0...xh and satisfies: p(xi) = f(x;) for i = 0...n The polynomial form employed to develop this interpolating equation is called the LaGrange formula (Conte et al., 1980) and is written as: p(x) = aoro(x) + a'r‘(x) + ... + anrn(x) l1 with the weights rK(x) = II x—xz k=0,1...n . xx" x; (=0 'LfiK and rK(xi) = 1 i=k i=0,1...n o ifk The function rK (x) is the product of n linear factors which makes it a polynomial of degree n. The value of the integral I(f) can then be approximated by I(pk ) where pl<(x) is the LaGrange polynomial of degree < n that agrees with f(x) at the points xo ...xh. The approximation of I(f) can be written as I(pK) = Aof(x°) + A,f(x.) +...+ Ahf(xh) 69 where f(xo )... f(xn) are the known function values. The weights are calculated as A¢<= I(rK) with rK(x) being the ith LaGrange polynomial where: n rK(xi) = - x—xz k = 0,1. .n l i xK—x; i=0 L¢K Thus, for any point xi: 0. p(x{) = :aKeri) = a1 i= 0,1...n K=o Therefore, the coefficients ao ...an in the LaGrange polynomial are the values of the polynomial pK(x) at the points x0...xq. It follows that: h p(x) = :E f(xK)rK(x) K=o for any arbitrary function f(x). If f(x) is smooth on an interval (c,d) and f(x) = pK(x) + f(xo...xK, x) YK(X) K where ‘fK(x) = _rrIx—xj) J=° then the error in the estimate of I(f) is: b E(f) = I(f) - I(pK) = ijxo...xK, x] K(x)dx a The general nature of the curve to be integrated suggests the type of polynomial fit for least error (best 70 fit). A triangular wave is characterized by a finite series of trapezoids divided at points of inflection. The trapezoid rule of numerical integration (k=1 case of LaGrange) sums the areas over the total interval (a,b) of the individual trapezoids each with area: t f(x _) + f(X ) l (X " X ) - b-a f(x _) + f(X )l ——LL.____K_ - — k 2 K K, 2 I: i K Since f(x) = f(xo) + f[x°,x‘](x—xo) + f[xo,xl,x]‘fi(x), the trapezoidal rule becomes: 6 ’)f(x)dx = b—a [f(xo) + 2f(xL) + 2f(x2) + ... + f(xn)] 2n 0... With a characteristic sine curve and many substantial divisions with a cycle, a piecewise quadratic function f(x) = pz(x) + f[xo,x',x2,x] 7;(x) provides a closer fit (k=2 case of LaGrange). Each fit requires a minimum of three points for quadratic regression: P = f(xo)+E(X1)'f(Xo)i(X-X;J+E(xo)-2f(X.)+§I(13ch)((x-xo)(x—xi) h The individual areas under the quadratic piece fitting are summed for the integral of p(x) where: 71 XL a§p(x)dx==lflf(xo)+4f(x,)+f(x1)] 3 xl - b—a [f(xo)+4f(x|)+2f(xz)+4f(x3)+...+f(xh)] 3n This rule, known as Simpson's Rule, holds for any continuous function on (a,b). The maximum error terms for the trapezoid (b—a)3M/12n2 and Simpson's (b-a)SM/180nt+ (M is the maximum of the numbers lf”(x)l for trapezoid and f”" (x) for Simpson's) suggest that the latter is preferred for a sufficiently smooth f(x) and the former otherwise, without the complexity of high degree polynomial ‘ntegration. Therefore, the selection of an integration procedure depends on the nature of the recorded signal. CHAPTER 4 EXPERIMENTAL TECHNIQUES A high-speed microprocessor—controlled data- acquisition system was assembled to characterize the real time dynamic behavior of a mechanical tree shaker and a cherry tree. The shaker was obtained from the Friday Tractor Co., Hartford, MI, a company with similar research interests. The C—clamp shaker was typical of those employed in commercial cherry orchards, Figure 4.1. At any point in time, sensors and signal conditioning devices provided the microprocessor system with digital inputs that represented the X, Y, and Z accelerations of the tree and shaker, the position of the rotating masses, the relative linear position of the clamping arm and the pressure in the clamping cylinder. The high rate of data sampling across 16 channels provided accurate digital characterization of analog transducer inputs. Waveforms were reconstructed from digitized data; accelerations were integrated twice to give absolute displacements and relative displacements between the trunk shaker and the tree. 72 TAMI N l ‘W m, I!” . war mm Figure 4.1 C-clamp style eccentric mass trunk shaker used in commercial fruit harvesting. 74' 4.1 Triboelectric Phenomena In order to determine the feasibility of measuring a force between the shaker and the tree directly from the output charge of a rubber pad, tests were conducted to verify the phenomenon and, if present, to calibrate the charge with shaker pad compression. A rubber cylindrically shaped shaker pad was mounted on a 422 kg/cm2 (6000 psi) hydraulic press with its cylindrical axis horizontal. On each circular end of the pad, four wire electrodes were inserted at a radius of 70 mm (2.8 in) 90 degrees apart. The pad face was forced against a 20 cm X 25 cm (8 in X 10 in) steel plate at various pressures. (See Figure 4.2). Probes from a Kistler Model 503 charge amplifier were connected to the electrodes. Output from the charge amplifier was observed on a Tektronix oscilloscope. The variation in charge was recorded for increments of pressure, both increasing and decreasing. Remaining charge after pressure release and the effects of charged objects passing nearby were observed. Results of this test (Table 5.1) showed that direct force measurements from pad compression would not be possible because of hysteresis phenomena and the sensitivity of the output charge of the pad to environmental electrical effects. A possible alternate solution to detect force transmission between the shaker . .cowuwwwpcmSU omemzo How omoomofififiomo pee Hofimflfimsm omsmao m ou and 0:» ea popHomCH moposuooHo may Eoym pcopxo mpwofi QHHU .umou oflsuooaoonfihu exp mom mmosm oflflsmppxz NEo\wx mmv a co poucsos and meHo Hoxmcm Hobbzm N ..v oHDMHm 5 7 » " ‘ I '. . - ., . .Jg‘ — . :é u- -. -, u ' . K n 9 .4 _v‘ 1' ‘- .' ' 5'- , _- - .u u . , x ' .. . ml -' 'I 3 (34*. f r 3"} _ ,1 .‘l, . . ‘ . i A ‘ ‘ - “ . n. ." ' 4 i , ‘ ‘, ‘ n . 1' ‘ I \ .‘ . .. . fit“ 3 - 1 an. +3. . , . I. 1 . .- . ¢ . . 4 , h . - , - ' H. .1" 1 A. , . . ' r L r ' .A ' .‘ >.' . I, .... . -. .71. . ,. 1 “ » .. . .5. ”.II " ‘ ' ' . '. . I ‘- . u . .1 ‘ ' ‘. . . I . . . . ' 1“ . . . ‘ I u ,t, -_. 4 , r v A ., , ' - \.- .-I (a? . _ ._ ’. L . I . - _ r. ' .. , w y . ,4 J .L . ' I . a, . .. , . 5 , i: k . . _ .‘ - . . . , I v A: (' . .‘x ,« ‘5’ 1‘ . . ' ,3 .. x X _ ' , J ,, _ . 4. .: .. ...; 1'. ..i ‘.' . c I -‘\|V . . .. v . - _ . 6.. ‘ 7 . . .. ' ' . \ . .. j . 't .- r.‘ .. _ - ' - ., J. . . , . w - v ,, . . - a - 1‘ «e .' \, _ . , fl , . .1 -.€ ' n . . . 1": . “ t i: .. . .. . -.. ,. . , . r. . 1.." . .L. 1’ ' a s. v I II C' In. a \ l a i. , , . . . II 76 and the tree was to measure the tree and shaker real-time displacements and from these data, simulate the critical maximum displacements in a laboratory (test. Using pressure trahdUcers on a model tree, the forces generated from simulated maximum displacements could be estimated. 4.2 The Trunk Shaker A C-clamp eccentric-mass inertial trunk shaker having a total mass of 544 kg (1200 lbs), including two 40 kg (88 1b) semicircular unbalanced rotating masses, was mounted on a 56 PTO Hp Hydro 84 International Tractor (See Figure 4.3). The radius of each semicircular mass was 17.1 cm (6.75 in). Each mass was attached to a shaft, chain—driven by individual 2.8 L/s (44 gpm) 105 kg/cm2 (1500 psi) counter—rotating Vickers hydraulic vane motors. The location of the center of gravity of the trunk shaker was obtained by balancing the machine on the tip of a S‘cm x 5 cm (2 in X 2 in) piece of angle iron on two orthogonal) axes. Thev eccentric masses were not removed due. to the difficulties involved in disassembly. Instead, the center of gravity was corrected for the presence of the. masses by taking measurements on the appropriate axis with both masses inward, then outward and then calculating an average. This provided an accurate measurement of the location of the center of gravity of the shaker without the masses. {Sissilit Aw .HOpowpp HmGOAHMCHoucH em opus: 9: Ohm -o m.e magma» cm a mo pmfla esp co woucsoa poxmzm xcsep Hafiuhocfi mmeEuoHHpcoooo mEmHo 77 1.1.3.1 ...rr\ ‘ .L . .3 , l 1 ... . v I v _ ... . .m. .... . . . . . .. . . ... 78 The shaker was mounted on the 2250 Mount-O—Matic loader frame of the Hydro 84 International Tractor. A frame was constructed on the loader to Suspend the shaker at three points as recommended by the manufacturer. Rubber bushings were used on both ends of the suspension bars to minimize the .amount of vibration transmitted to the tractor and to damp oscillations fed back from the tractor. The tilt mechanism of the loader frame was used to level the shaker during attachment to the tree. A separate hydraulic system was mounted on the rear of the tractor to power the shaker drive motors. A 35 tooth sprocket was mounted on the PTO shaft and chained to a 13 tooth sprocket on a Hydreco hydraulic gear pump. This provided a 2.7:1 increase in pump drive rpm. A 150 L (40 gal) reservoir, equipped with a master shut off valve and return line oil filter, was mounted above the PTO shaft. Engine (and PTO rpm.were monitored on the tractor tachometer. During shake, the engine was set first at 1500 rpm and later at 2200 rpm, corresponding to pump outputs of 1.9 L/s (30 gpm) and 2.5 L/s (40‘ gpm), respectively, at 105 kg/cm2 (1500 psi). The hoses used to distribute the flow were at least 1.9 cm (0.75 in) ID. A 50-50 flow divider allocated equal fluid volume to an individual continuously variable flow valve controlling each shaker drive motor. The separate variable flow control valves regulated oil flow to each shaker drive —___———-— ... 1.. C I O ... .. .. ...» . .. . . , .L A... . . (. 5.4 . J x . . T. k 79 motor such that speed for each motor could be independently selected. Each shaker drive motor then transmitted power from a 45 tooth sprocket to an 18 tooth sprocket mounted on the shaft of the eccentric mass. At any given engine speed, the full rotational frequency of each mass (assuming both were being driven) followed the equation: Frequency = [Engine RPM - 100] * 0.4 60 Where Frequency is in Hertz Frequencies of 9.3 Hz (560 cpm) and 14.0 Hz (840 cpm) corresponded to engine test settings of 1500 and 2200 rpm, respectively. . I A double acting 8 cm ID X 61 cm stroke (3 in X 24 in) hydraulic cylinder, mounted on the back of the shaker, activated the opening and closing of the C-clamp. The clamping pressure for shaking 11.4 cm (4 in) to 15.2 cm (6 in) diameter trunks was set at 49 kg/cm2 (700 psi), as recommended by Frahm et al. (1983). The cylinder clamping pressure was monitored on the hydraulic system with a 105 kg/cm2 (1500 psi) pressure gauge. Check valves in the clamping circuit presumably prevented clamp movement during shake. The clamping cylinder was connected directly to .. . . . . rt 1 L. .r .. . . . . i .. (I . . . an. . i 3.. .— ) x: 3 ...; .. l . L. . t I \ 1 .. ... I. .1. v. s. s. . . . L T r .t . . . .1. fl.— .. .. _ ... b. . . v; .. . 7. .. . . . . .. . . . x . . . . . . . ., . . . .H . ... .. r . 5 . ... _ . a; . r . .... . r . “u 7. ' .... . . . . . y . Y! . . . y... T . .4 . .. . .l. . . e _. a .4 . . .... . .. p . .. _z , . a. . ,. . ._ . . . .... . _. . , . . 2. . .... l . . . l . .. . a nu .. . . . : .3. . n: .. . . A Q 1} . .. DC .. . . .... \ (a 5 . . a ._ ... . .1 . . . :. . .. s . . ... . f. \ . . . I ... p .. . .. . . . .. . . _ p . . .. t . . . . ... . ._ k e .v. . a .1 .. .. .... .. . . (I . v . a . . . .7. . . 1. . . . . o . . m .. ... . . - r . v i .. . L . _. . .l 1. ( _. . . . . . . . . . . a. . an ..n .5 . . ' .-.. l. . . . . . 2 m r .. :1 - ... . .. 1.. a . v. r ‘ \ _. i .... we. .... « . . . I~ _ — .. y. u . . v» . n . l .. . . a . . . . . . . r, i. 4 .. . _. .. ... a . x i v . . \ : . x I . 4 —. ' ... _ ...y \. . u \v . .. C . c . .... . . . i. . \ 4 I'J . . . .. . a .. l .. . ”a. _. z 1;. v.5. . . . . .... . ... .... .... ..W . z . y .. . ... .. .. . 1... . ... ... . .n . . 3 . . i —. . . t D; ‘r\ 80 the tractor's hydraulic system which operated at 0.7 L/s (11.0 gpm) 127 kg/cmz (1800 psi) at 2200 engine rpm and operated at 0.4 L/s (6.2 gpm) 127 kg/cm2 (1800 psi) at 1500 engine rpm. Clamp pressure was set at 49 kg/cm2 (700 psi). Clamping to the tree was then accomplished independently of the operation of the shaker motor hydraulic system. This configuration prevented any interaction between the clamping pressure on the tree trunk and the pressure required to drive the shaker motor at the desired shaking frequency. Two cylindrical rubber pads (19 cm OD, 8 cm ID and 55 cm long) were fastened in support slings within the clamping jaw. The facing of each sling was coated with a lubricant (grease) and covered with an attached rubber flap. This followed the manufacturer's recommended practice for reducing shear force on the tree bark by allowing the slip to occur between the pad sling and the flap. 4.3 Sensing Elements and Calibration Sensors were placed at strategic points on the trunk shaker to characterize the planar motion of the inertial shaker in real time. Planar motion can be described by a minimum of three accelerometers, two at one location and a third at a known fixed distance from the two. Three accelerometers were placed in such 'IF . I'. g. . w - «. 81 configuration, both on the shaker and on the tree. Accelerometers were located at the shaker's center of gravity to detect X and Y motion, and a set of three accelerometers were located at the base of the pad on the shaker frame to detect X, Y, and Z motion (See Figure 4.4). A second 2 axis accelerometer was centered on the clamp arm at the pad base to complement the first 2 axis accelerometer and define the vertical shaker position as vectors at opposite sides of the tree (See Figure 4.5). Vertical motion (Z) of the tree was assumed zero. Two 0.8 cm (5/16 in) diameter holes were drilled radially in each tree trunk at 90 degrees separation and 46 cm (18 in) above' the ground plane. In one hole, a single X axis accelerometer was placed. In the second, a 16 cm3 (1 in3) aluminum block was mounted and X and Y axis accelerometers were then mounted on the block, Figure 4.6. This combination of three accelerometers permitted calculations of X and Y linear displacement of the trunk, as well as angular displacement of the trunk. Sunstrand (Sunstrand Data Control Inc., Redmond, WA) and General Radio (General Radio Co., Concorde, MA) accelerometers were used in all tests. Resonant frequencies of the accelerometers were 40 Khz, well above the operating range of the shaker system. The time constant of each accelerometer was 20 5 allowing frequency response of 0.02 to 5000 Hz with 5% low error at the low .0. N... dofiflmom pew .ucoEoomHmmflo .coflmsoaooom mo :ofloouop pom mHOmcmm mo mcoflaooH oflwmumspm mcfimgme Sufism 5:53. mo 33> more vé madman as . . is : , 1' i 'K . .. ‘ . ., ‘ h ,1 i Q i "14”.: xi ‘ I ...-o- 83 ameoaoEwHHfiE ca mucoEoHSmon HH; tam Hopoaosofiooow mcflsonm Hoxmcm x:sep po:o«mcoefia m.¢ OHDMHm .T 1 ..TI .... 1i Ill 0 \ul VIII/111117114 G)" 22‘ O N) N 'lll'lIlll’lla m< nopcfiflxu mando— 415+— Ho>q X+ 84 .xcssp omen xssoao m :o popcsoe mxopo HopoEopoHooom >x paw x mo :oapmooH Hmcomonupo o. a mesmHm +_ a t 1 nl. Kid 1 . . ... . . a. y. . r .0 I 1 Ga... . . r. .. . ,. :1... . . .( i. . . . .... I. \ an. . . I n .x . .. U1 ... I7 I . s . ~ .~ .... \ . ~ ‘ .1 . .. k . w . C \ v a . q. R. . .. ( . . , . . ,v. . u .A ... . . . ,A. . ...r. 31.4 . .a. r VI \\ 74y .. . .......\ I .... ‘ I n .. _ . . . ...l ., . VI. . . ... 6.... As . I .... r ,1 . . _ 1 .— Elk ..‘4‘ ._ 1 n1 ,.... .. \ )- . , .. . _ 4. i .. ... .... .. ...; ..\ m . .r. . . .1 . . a. a. . er. .. . 85 frequencies and 5% (high error at the high frequencies. This covered the shaker operating range with an amplitude response of almost exactly ,one. Acceleration range was :250 g (1 g = 9.8 m/sz) with t 1% linearity in amplitude. . Each accelerometer was calibrated in a separate test for output voltage per unit displacement. A fixed linear displacement plunger unit was mounted on a lathe. The lathe provided rotation (to the input shaft of the unit, Figure 4.7. A teflon disk (swash plate) was attached to the input shaft of the unit and was inclined at 30 degrees. Two Spring-loaded plungers rested on the swash .plate 180 degrees apart. Upon rotation of the swash plate, Cthe plungers were forced in-and out, each_providing a Isinusoidal displacement with time. Peakéto—peak displacement was 1.09 cm (430/1000 in). Ioperating frequency‘ was 676 cpm (11.3 Hz). Trunk and 'shaker displacement in fieldr tests were expected to be about 10 mm at this frequency. Each accelerometer was mounted on the plunger shaft, and its output was amplified with a Piezetron Coupler or a Kistler Model 503 charge amplifier, then integrated twice by hardware integrators (See Figure 4.8). The integrator input and output signals were monitored on an oscilloscope and recorded on a strip chart recorder. Several signals were also recorded on a four .:0flpmhbfifimo How was: Howcsflm , Mm m :o poucsoe Houoaoaoaooo< n.v QHSMHm mafipmoosmwooh socoscosmnofibmflsm> ucosoowfimmflpspox 86 I . '.~ 1 -‘ . . 4' _ ' . e' ‘ i 5 4 4 .‘ .f . r“ ‘ u 4- f._ ‘ ‘ ' ‘. ‘ ‘ ' \ ... 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' ~ ' I'- I I. . ‘ -—~ ~ ~ On- q; | , I. ' I ' . ' fl ' ‘v " c- w . ' ‘0 If , g -1 . ' .I A Q. " ' : ‘ I . - 4 a _ . 7. ¢ ‘0 .c t , v 1' ‘I‘ ,I v .4-- ' p a ‘T '- ' ‘ I I: ‘ H. . ' ‘ . v. v . _ . " r .- ~ I "1, y a: j— \ . .. ' ' . ‘ - «a w , J . _. § ~ 1’ ‘ ~ ..‘0 -q . . '1 4 's u I ’1..~_ 1" -.. f” k . 0. on 'I.I:’ q‘e ‘0‘ ”I ‘ . . u- v -\ ‘ ' J \ . r. i ‘5» w ' a- ‘ .. n r‘lcg x J .4 - .... 1 ..‘h - . . 2 d ,1 moo> NH.H Hdzom eoflwHHmE ... zEEE. m I. » izudm An: o.H AH: o.H. AW cfl> :5 :6 flags Nana“ "is. Ho. me use :0 > [Iowan > 8.: 2 5522.. N . 5: . GE... 0 . _ USHENH a «\h 1 I‘ ll‘ . I a . 2 . . .1 x A .... A: . n I n . .u ‘ ~ . . .. . n. . w ..I.. .. a s on . I .... .. . pH. . . c r i n c a V. y ( “a. a. A nu -. .w ‘9 . d .l . a . .. .u r. w. .. ., . y In ..u 4 . . . p . r .. I e... . w .y a . .\ . . .... a v . . . . 2.- N . I. .. . ~ ~ . c v .p . I I n l n n . . r . r . . . (. \.. p . . .V' t: 1. T {5 t. .J i . in h . . ... .... s f . .. u . . n u .. . . . ~.. ... ,L ... n w L. 2... a . r. . u. A m. . . ... w ....u . . ...1. r1 . . ... r. . . t.“ . . ..u . . . . . . . a . u . ..... . : 1 . . . . . . . . ... . . a. .. .( .... . . . . u . , . . . . i. . . I . .n .1 ... . x u I . ...... . c. _. . 3 w 1 t . r. w . . f. . a. . . .. . ... .r 1. . . .. a... . . , » ~ . .. 2 .. . \ . .1 : . ... . a ‘J . «a h.“ . r . . 3 AL . . . . a . . .. . .... , . . . . . a. . . .. x 1 9 . . L . . . . ..x .\ . . . . . .... 2 .. . . . - T. . . . . l . 1 . .. . . n . s . r. .. 3 . x. ... - o a. . .fi fi 1 1 V‘ I 1! IFIC . . w . ..v‘. a fl r v a . . 7 H... . l. .... . . . . .J .. . .. a .... . . .3 x . J .. u. . . . . ...” r..J , a i .i . . . . a. .. . . .. «I l .u . . . .I. vw . u. . .y- . u n .... v. n . u . .1 4; .. . ... . .. v . . . ... a u a: . > . . . U. . u . . ... r . . .. . i. . A ... . a 1. . .0 a . . ... .... . . .. .L . . . .u he .. a a . . . .. a . . . 4 y . . P . . . S a .. .. .4 . a . \ I a v u ~11 .0‘ II . i. . _ . . . .I . . v ‘ x I a ( . .I. .- -.~ . . L . I p. - . . . . .1 ... h . . ... ... M . a . . ... A . ._ p . , . . . . .. 1.. .. ....H U. u .. . . 1 . 1 . . . . . . . J . 1 w... a... . my .. J .L L . 1 .- . .1. 1.. L . . . . 1.! . . .u ( . . . ... . 2 .. .. . u r. y .. a w. . . y . r1 ... . . u . .¢ . i .1. . .. r. A- .. . . _ . I .l— . . . . ,, . s 1. .. . . .. . m . . A . x . . A . ol ... . .9 . . . . _ . .t . \ m p .. . s A . . 4 n n. t ... J y . r . v I . . 4L . x. . ., ... .u . .. . . a. .. 4 . m .1 , . .. .1 . ...r p .. _ a i. .. . . .. ...». _ x. . . ... .2 . L . . t. _ .. . : . - . _ , . l J . .... . \ p 88 channel analog tape recorder for future reference. Voltage ranges were tentatively selected from these tests for setting scales in the ADC data acquisition routine. A proximity sensor on the shaft of each eccentric mass provided both frequency and angular position information for each mass. The proximity sensors operated on electromagnetic induction principles whereby the change in reluctance in a magnetic field induced a current in an internal coil. A small rectangular steel bar protruding from the side of each shaft provided the change in reluctance needed to cause a flux change in the magnetic field of the proximity sensor each time the shaft was in a particular position. Pulse voltage was proportional to angular shaft velocity. These‘ proximity pickups were adjusted (by adjusting the gap between sensor and shaft) to provide a maximum -5 to +5 volt pulse at shaker operating frequencies. The shaker drive motors were unidirectional in operation. For purposes of uniformity, the proximity sensor leads were connected to respond with a positive lead pulse from each shaft. To detect relaxation or tightening of the clamp, a linear voltage differential transformer (LVDT) was connected across the back side of the clamp opening. A Daytronic Model 300C amplifier with a Type 61 Module provided a 3 volt excitation for the LVDT. The output ...c . fl... . . . .a f ... ... .. . , ‘ . I . ...) . . . . r... . 5 I . _ .... t .L . ...: . . . . z . . . .. 1 a . . . n a . . . . 1. in . . ... . J. . _. .... . . r . ~— ... . i w . 2 89 voltage from the LVDT was linearly proportional to rod displacement on the It 0.025 cm (I 0.010 in) scale. The output voltage range was t 40 millivolts DC. The LVDT provided information on clamp opening or closing movement during the shake which may not have been accompanied by a noticeable change in the hydraulic pressure of the clamp cylinder. The Daytronic amplifier and LVDT were calibrated by zeroing the amplifier output, incrementally displacing the transformer rod, and recording the output voltage as it varied from zero. A 0—211 kg/cm2 (0—3000 psia) Servonic potentiometric pressure transducer (Servonic Instruments Inc., Costa Mesa, CA) was mounted in the pressure line to the clamping cylinder to monitor clamp pressure. Resonant frequency of this device is very high; it is well suited for vibration measurements. Input excitation of i 10 volts DC provided a linear output of 0 to 3 volts. A 422 kg/cm2 (6000 psi) hydraulic press was used to apply pressure to the pressure transducer for calibration. Electrical output was recorded for a unit change in pressure . 4.4 The Acquisition Processor Hardware A data acquisition system was assembled that was capable of operating at very high speeds, collecting up to r "a “r" ‘ '5. 1“ 1.1.. p. ",3: — u) b ’\ JJ .-5 ..J -- — x.‘ . .r. ... i \n 90 16 channels of data sequentially, and storing this information on a "floppy disk" (See Figure 4.9). An analog-to-digital converter (ADC) (Interactive Structures, Inc.) and a 6502 ‘microprocessor system (Apple Computer, Inc.) were selected and interfaced. All direct and amplified transducer signal carrier lines were connected to a common terminal box where they merged into three main cables. These cables, each of four pair twisted shielded wire, linked the sensing element outputs to the ADC and the microprocessor housed inside an air conditioned van that provided protection from dust and temperature effects (See Figure 4.10). Writing to the disk was a sensitive process and could have failed if tiny particles of foreign matter got between the disk and the writing head of the disk drive. The box also contained three Piezetron couplers which provided a current source and amplified the accelerometer signals on the tree. IA variable DC power supply energized the clamp-cylinder pressure transducer with i: 10 VDC. Six Kistler Model 503 Charge Amplifiers, fastened to a portable cart, amplified six of the accelerometer signals from the shaker. The lG—channel, 12-bit ADC unit provided software—scaling of signals on 8 ranges with 0.024% resolution. Each channel was read in 20 P5 with a sample-and-hold amplifier circuit. ADC ranges were ‘ a a; w. .. ... .u .._,. "‘F-(v ._. . ;’ . -.. -r z.” *- - o‘- y . .5: 7 . -.. y ...“..ubc \u ht. V . ..y . 5‘ ‘ , v ‘ t x I: - 3 ' . , I 9. h. "'3. I . n' “o .. v .- .....f“ . A. . ' . L- ‘. . . , A ' ' Ty . I ' ~ __ . -. i \- 5. a, I‘ ' .. ¢ . u» '- ‘ ..m I -. . my «I . A . ‘ .... a .mommecm cowuaabfl> Hogan 0:55 8m 53?? 53335.. 3% womanéommooogmofifle 9:. mo 52%? goo; Susana: 3. 93m: mmm9m20¢mamuu< 1/ / / ./ E: 9:. EEE >Amm3m mmzom mmHqum2< mmUDQmZq «OHHZOZ Mmzom mqu 282325: mmbmmmmm , I AEJ :2: EL «Sam: 3: 92 <5 izuHm mmomzmm >szonmm HszH q pocosgcoo Haw Em. :H pofibfiommw mm: pacemfisco soapflmflswom dump 9:. 3;. 95m: 92 i9: sf: is bit... .1 I: .. . ,. . . . L a .5 . .“ ~. 4... .1 « r . L . . 5. it ,1 . I. . 7.. . . ..I. ...- W. a. .. . . z I e .. a... t ..E .. c «. ... y .r A. Ital . . . u... .43.. 3 ... 1 a.) .. $5., .. w 9 , selected by programming the microprocessor to access the proper I/O port. Range, channel, order and sampling speed were software-controlled. The 6502 microprocessor system was the hardware operating system of the Apple III Computer. A 2 Mhz crystal 'controlled the system speed. Expanded memory provided 256 Kilobytes (1 byte = 8 bits) of Random-Access-Memory (RAM) with 2 Kilobytes of masked Read—Only—Memory (ROM). An interface between the keyboard and the video screen provided easy programming of the microprocessor. A system disk drive allowed storage of 140 K of data on a 13 cm (5.25 in) soft diSk. Buffered I/O ports permitted. the addition of a second 140 K disk drive, as well as connection to the ADC. The microprOceSsor Controlled the operation of the ADC, retrieved and stored values in RAM, and dumped all information to the two 50ft disks at the end of a test. User-friendly meSSages were directed to the video screen to provide information on the status of a test. With the video screen on, the microprocessor speed was reduced to 1.4 Mhz. Therefore, during actual data collection the screen was shut off (by the software) thereby increasing clock frequency to 1.8 MHz. 4.5 The Acquisition Processor Software The main function of the software was to control the conversion of analog data signals in the ADC and place the information into memory for later disk storage. The program was written as a series of subroutines to keep sections of operation independent of each other. This provided eaSe in troubleshooting when failure occurred or when paramEters needed to be altered. Programs were written in 6502 assembly code. A Pascal operating system was available to assemble the program code. A central software program called the Sophisticated Operating System (SOS) (Apple Computer, Inc.) controlled the means by which all programs could use the machine hardware. This operating system was located on the main system disk and was needed to start up and run the system. All I/O devices and system hardware communicated only thr0ugh 'SOS. SOS looked at all peripherals (console, disk drives, speaker, printers, etc.) as devices. This was Similar to looking at each peripheral as a file. A device is a part of the system hardware or a piece of external equipment_that can allow information to be passed (between the system and the outside world. SOS acknowledges two types of devices: a character device, which normally gets information into and out of the system; and a block device, which normally stores and retrieves information. SOS contains special programs called device .. ., L ... .. x . . . . . d. n I .— . _. I . . . ... I» .x. ... a / . I. .\ A . . A . .... ,. . . ... I. .6. . . . . .. , . L. I. . ....4 t . r41. . . . «4 (rs.- ._ ... _ . . I ... . ;. . a u ., .l . ... . u c . .. . p 4.. . . ..t .l 4 . . ). ., .4 e. .. . A . . ... . . . .I . . . a) . .. . . T . i ...r. .. ..| . .5 .. .. . .. . .... \ ... I . . . . .. ... .a . .1. ...; .... . . .x .1 . ... . _ J .. .2. ‘. é. . .4. ..5. i, . .. . .. Jr. _ ...} ... . ..... . ...cfl . . . ... f v. v _ i . A o l .. A 4 L . _ drivers. These take information from SOS and translate it into a machine action, or take a machine action and convert it into information for SOS. Any message sent to a device must first be sent to SOS by a program. SOS will then send it to the driver and the driver will send it to the device. Therefore, any device added to the system, not inherent in the operating system, must be accompanied by a special device driver program. Device drivers for the disk drives, the console, the speaker and several printers are part of the system start—up diskette. The ADC is a general purpose piece of hardware (intended for use with many microcomputers. No device driver program existed for the ADC; a device driver had to be written for the ADC so that SOS could recognize the ADC as a device and communicate with it. The ADC was a character device, receiving streams of characters, and processing them one at a time. An explanation of the complete operation of SOS would be voluminous and is beside the point of this subsection. A brief explanation of the function of the device driver program will be presented followed by a discussion of the actual acquisition program. The annotated ADC device driver program is given in Appendix B. When SOS starts the system, it checks all device drivers to verify the existence of their accompanying devices. At this time, absent devices or device driver programs are noted to let SOS know what resources are available. The needed devices are initialized and any required internal resources are allocated. Any time a user program wishes access to a device, it must "open" the device through the device driver program by a 'Call' to SOS. The device driver required for the ADC was written to allow a 'Read Data' request to be implemented from an operating program. FFFE (65,534) bytes of information were requested in one call. The driver accepted the request, probed the ADC device with a preprogrammed Channel-gain sequence and returned the data to a buffer memory. The channel—gain sequences were preprogrammed in the driver; this permitted greater operating speed and a reduction in programming time. To change the sequence, however, required a significant amount of reprogramming. It is suggested that the next version of this driver should accept keyboard entered requests of the channel and gain that can be passed from the user keyboard through SOS to the driver. Figures 4.11 and 4.12 show the block diagrams for the ADC device driver program preparation and execution fields. The ADC appears to $08 as a block of memory locations. The address of the block is determined by the expansion slot number in the machine, indicating in which slot the ADC is located. The starting address of this memory block was (hexadecimal) ADC = C080 + SLOT * 10. A EQUATE SOS CALL CODES ALLOCATE LOCAL STORAGE l—J‘ D I MEN SI ON INTERNAL RESOURCE PARAMETERS INITIALIZE CHANNEL AND GAIN BUFFERS \ _‘ _J POST CALLER'S DRIVER ENTRY POINT Figure 4.11 Simplified Block Diagram of the Allocation Field of the Analog-to-Digital Converter Device Driver. 98 DR IVER EIIT R’I" PO INT RETURN TO C ALLER IN IT I AL IZE DRIVER REPORT DISP LTCH ®; / DUTIES ERROR RETURN TO C ALLER ALLOC hTE INTERN M. RESOURCES ‘ OPEN RETURN TO C ALLER END IIO AND INTERRUPTS FREE SLOT CLOSE INITIALIZE ALL 3”" £33291 couuTs auto ”1%“ @9 Mg“ a _ ADDRESSING I MHz STORE 55"“) SPEEDUP RETURN RETURN CLOCK T0 T0 coum 2 MHz CALLER Figure 4.12 Flow Diagram of the Execution Field of the Analog-to— Digital Device Driver. J: : . ._ s . ... Lu ; _ m .. .... v we K . . . A . 99 single "Write" command directed to one of the locations in a memory block caused the ADC to read a selected channel on a chosen voltage range (selectable gain). The result of the conversion was then returned in two bytes from the same memory location. Since the result was a 12 bit value of 0—4095, two bytes were used but the upper half (4 bits) of the most significant byte was not used and was stripped off before data storage. All ranges were electronically calibrated such that zero corresponded to the low end and 4095 to the high end. When an amplified conversion required the 0.5 or 1.0 volt range, a timing delay of 45 microseconds had to be inserted into the software to allow hardware settling of the sensitive amplifier gain settings. This delay was subsequently inserted in the device driver program to cover this situation, as well as to keep the time interval between all data points constant. When the requested datum was entered in the buffer memory by the read request in the user program, control was returned to the user program. At the end of the user program's need for the device, a SOS call to 'Close' the device had to be implemented. This call finished any I/O, disabled all interrupt capability, confiscated any device-dedicated resources and returned control again to the user program. At this point, the device no longer existed in the "eyes" of the user 100 program. The ADC device driver was written in the prescribed format for SOS. At first, operation of the driver program produced fatal misbehavior of the system. Careful examination of, the microcomputer programming manual revealed an addressing routine which incorrectly allowed the user to dedicate a buffer memory in an area which was actually reserved for SOS. The addressing 'routine would fail when more than 32 kilobytes of data were sent to the buffer memory. The routine was then rewritten to utilize the maximum amount of memory available, Figure 4.13. In summary, the ADC device driver makes possible communication between the ADC device and the user program through a master program called SOS. Thusfar, the main program in the machine has been referred to as the user program. Here follows a discussion of this user program. The start-up routine of the 6502 system consisted of loading and operating three programs from a disk. SOS always resides in memory even while the machine is in use and is referred to as the 'Kernel'. The Kernel Should only be altered by the manufacturer. All special device communication programs were stored in a special SOS format in a file called the 'Driver‘ file. Finally, a machine code user program was written in a file called the 'Interpreter'. The Interpreter was loaded thirdly and ' » A . 4 _. o 6502 ASSEMBLY LANGUAGE MACRO FOR ADC DEVICE DRIVER INCREMENTS 3 BYTE ADDRESS AND CHECKS FOR PROHIBITED RESULTS ************************************************************** .MACRO INCADR ;Begin Address Increment Macro INC %1 ;Increment Low Byte of Address BNE $310 ;If not zero, then skip Hi byte INC %l+1 ;If low byte is 0, Inc. Hi byte LDA %1+l ;Load the Hi byte for checking CMP #OAO ;Are we in SOS Hi address? BEQ $120 ;If so, fix it so we are not $110 CMP #00 ;Are we in SOS Low address? BNE $310 ;If not, skip this correction SEC ;We are, so fix it . ROR %l+l ;Reset Hi byte of Address INC %l+l401 ;Increment to next memory bank JMP $310 ;Leave $120 LDY %l+l40l ;Where in SOS are we? CPY #8F ;Are we in the zero bank? BNE $130 ;If not, repair differently LDA #80 ;If so, do a general fixup STA %l+l ;Set Hi byte to 80 STA %l+l401 ;Set extension bank to 80 JMP 5310 ;Done, now leave $130 CMP #00 ;Are we in SOS zero page? BNE $310 ;If not, we are OK SEC ;If so, fix it ROR %1+l ;Reset Hi byte of address INC %l+l401 ;Increment next memory bank $310 .ENDM ;End of Macro ************************************************************** Device driver address incrementation routine that allows maximum utilization of internal memory without the production of system-fatal memory pointers. Figure 4.13 102 contained programmed code (which I wrote in a special SOS format) that directed the machine to carry out specific actions. I wrote the Interpreter program in such a way that the machine could ‘execute the program from a "cold start" in the field, i.e. all initial user rituals were bypassed. The Interpreter, communicating through SOS and the device drivers, first allocated 196 kilobytes of RAM for data storage, opened the screen and keyboard (console) for reading and writing, and set up the ADC driver to acquire transducer signals. Block diagrams of the Interpreter program header and execution fields are shown in Figures 4.14 and 4.15. All communication to devices through drivers by user programs such as the Interpreter required information in a SOS executable format. This formatted information is noted in the Interpreter program documentation in Appendix A. 4.6 Data Capture The Interpreter made. a 'Call‘ to read the ADC driver three times, each time requesting FFFE (65,534) bytes. This totalled 196,602 bytes of data. The starting and ending time of each read call was obtained from the system clock as the linear time base for the real-time analysis. The video screen was turned off by the Interpreter program before data collection to increase the 103 START DIMENSION HEADER FOR KERNEL INITIALIZE CALL CODES AND BUFFER POI NTERS .a-f- 1 9031' USER'S “‘ BEGIN poun' l' Figure 4.14 Simplified Block Diagram of the Header Field of the Analog-to-Digital Converter Interpreter. OPEN CONSOLE FOR RE AD I‘I'RITE (L OPEN ADC FOR RE ADIVRITE J, ; SEND USER PROMPT TO SCREEN .E RE AD CONSOLE BUFFER 104 E? @ CREATE FILES “mm“ MEMORY FOR 0" ”"5" STOR AGE OPEN FILES CORRECT FOR VRITmO ADDRESSING wRITE ALL SHOT DOVH DATA TO DISK SCREEN FOR SPEED VRI‘I‘E TIME OBTAIN TIME TO DISK FROM CLOCK J. .L CLOSE FILES READ 65 KB‘IVI'ES OF ADC DATA 2.5 CLOSE ALL FILES AND DEV ICES TERHIN ATE OPERATION TURN SCREEN ON Figure 4.15 Flow Diagram of the Execution Field of the Analog-to- Digital Converter Interpreter. "d , . "T 105 system speed to 1.8 Mhz. The video was turned on at the end of the data collection in order to send messages to the user. System clock speed then reduced to 1.4 Mhz. Data in memory could then be stored on two 13 cm (5.25 in) "floppy disks". Specific data sent to SOS allowed a disk driver program to create, open, write to, and finally, close 'data' files and one 'time' file. The system was then prepared to make another test. As a safety feature, data in memory were not destroyed unless another test was begun or the machine was turned off. Therefore, if a disk problem arose or if the user forgot to insert disks into the drives, new disks could be inserted and the data restored. 4.7 Transcription to Disk Six 'write-to—disk' operations transferred the data of the three 'read ADC' operations to disk. Although a write operation could accept up to FFFF (65,535) bytes, SOS memory management did not allow continuous data in memory to be written to a file without inserting undesired information from a reserved buffer. The memory of the SOS system consisted of fifteen 32 kilobyte areas called banks. Two special memory areas, at low address (0000 to OOEF) and at high address (A000 to FFFF), were reserved for SOS. Between this area (2000 to 9FFF), one of the fifteen banks could be called for data access. Extended 106 indirect addressing, which specified a bank and a two byte memory address via a pointer, was utilized to store and retrieve information. The Interpreter program stored the data as high byte first, low byte second, starting at a low memory address. 'Fourteen codes were continuously cycled in the driver program indicating to the ADC which channel and gain to select. Data storage locations are speCified in Figure 4.16. Overall collection rate was 196,602 data bytes in 9.148 5. Out of the 9.148 s, an average tree shake lasted 3-6 5; thus there was enough time to cover the shaker startup and shutdown activity. The 'write-to-disk' process required 1.9 minutes. Two bytes of data were required to produce one value in a code range of 0-4095. The first 7 of the 14 channels of data were each characterized by 7,023 data points in 9.148 s. The second set of seven channels received 7,020 data points. The missing three points of the channels in the second set occurred because the three ‘read requests' were not multiples of 28, which was the required number of bytes for 14 channels. 4.8 Displacement Tests A Vanner Model 80-500 (12 VDC to 120 VAC, 60 Hz, 500 Watt) sinusoidal voltage inverter, lent by the Vanner 107 User Identified Data Storage Locations ADDRESSABLE MEMORY 2000-9FFF 8000-FFFF 8000-FFFF 8000-FFFF 8000-FFFF 8000-FFFF 8000-FFFF SYSTEM MEMORY CONTENTS ZOOO-AOOO 2000-A000 2000-A000 ZOOO-AOOO 2000-A000 2000-A000 2000-A000 DATA DATA DATA DATA DATA DATA DATA Reserved Operating System Memory Locations BANK NO. BANK ID. 0 8F 1 80 2 81 3 82 4 83 5 84 6 85 LOW S BANK OF HI S BANK 10 LOW S BANK OF LOW S BANK OF LOW S BANK OF LOW S BANK OF LOW S BANK OF LOW S BANK OF HI 5 BANK 10 HI S BANK 10 HI S BANK 10 OOOO-IFFF AOOO-FFFF lAOO-lAFF 1600-16FF lBOO-lBFF 1800-18FF l400-14FF OlOO-OlFF FFEF A000-B7FF B800-FFFF (Apple Computer, Inc.) OOOO-IFFF AOOO-FFFF ilAOO-lAFF 1600—16FF lBOO-lBFF 1800-18FF l400-l4FF OlOO-OlFF FFEF A000-B7FF B800-FFFF KERNEL OPERATIONS KERNEL OPERATIONS INTERP INTERP INTERP ZERO PAGE EXTEND PAGE STACK DRIVER/SOS ZERO PAGE DRIVER/SOS EXTEND PAGE DRIVER/SOS STACK BANK SELECT REGISTER INTERP/DRIVERS SOS KERNEL Figure 4.16 Data storage locations for the 6502-based data acquistion system in the Sophisticated Operating System Environment. A. i . t t; L.“ , ., m 1 t p. r _A “ ... v ‘ £ . v . L . _ 1 ... _f i . . . . ..w \ . .. . 108 Corporation (Columbus, Ohio), provided electric power at 120 VAC. Our acquisition system full load voltage was 120.2 VAC with smooth sinusoidal output. No-load voltage was 123.8 VAC with a voltage spike at points of maxima and minima in the output waveform. Frequency was constant at 60 Hz with and without load. The inverter was connected to the battery posts of the van for input power. During use, the engine idle on the van was increased to maintain the necessary charging capacity. The van body was taken as ground potential when connecting electrical devices. Problems later arose with charge build-up in the van body from the frictional charge—separating action of the engine fan belts on the pulleys. A galvanized-steel ground—rod was driven 76 cm (30 in) into the soil near the vehicle and connected to the vehicle body with #12 stranded copper wire. This eliminated the charge build—up problem. Displacement tests were conducted on tart cherry trees in the Michigan State University Horticultural Orchards. All trees were in the same general location and were presumed to have the same soil base. Six trees were chosen to be shaken. A period of three days was required for data collection. Trees were tested twice each, once at 1500 shaker rpm and once at 2200 shaker rpm. These speeds provided frequencies of 9.3 and 14.0 Hz, 109 respectively, for each of the two eccentric masses. The actual frequency of vibration imparted to the tree was a combination of individual frequencies. Three trees of 11 cm} (4.5 in) and three of 16 cm (6.5 in) trunk diameter at clamp height were selected for testing. The clamp was positioned according to common practice, which, on older trees, was normally 25—30 cm (10-12 in) above ground level. The shaker body was positioned orthogonal to the tree axis. The trunk was centered in the pad, Figure 4.17. For greater accuracy in shaker clamp positioning, the tractor driver was guided to the trunk by a flagman; in production operations, this precaution is not taken due to the time and expense of a second worker. The following were recorded: clamp height above the soil surface, clamp opening, and accelerometer location with respect to the tree center and the soil surface, date, engine rpm, and tree identification data. All amplifiers were zeroed before each test. The LVDT slide rod was centered for zero readout and was then fastened to the clamp. The tree was clamped at a recommended pressure of 49 kg/cm2 (700 psi). The desired engine speed was obtained and the control system was initialized for data collection. After 1—2 s, the shaker operator was signaled to begin the shake. A shake lasted 3-5 s. The shaker operator was then signaled to end the shake; there were 2—3 s of shut-down data at the 110 .xHMQ ocw co mmohum ymozm @odgwrfiswemdoew LOH3 woumoo one moan Hmoflhpcflfixo ozp paw oohp may coozuob madam .3mn mcflmeHo noxmzm :H wowopcoo xcseu omgu xeeonu wa.v ohzwfim 1 $19,151-} . . QM... .. . ... . u. . . a . . . r.“ u . ‘ .... vi 1 . a .| .14 . I I . u ' ... S "1.. ... .. p. . .. 3 .. .a ..p s a g r . . n . In“. .... a. - A. .I . o. . . . . . - ... . .5..- ‘ ...... . x; .r .IHI c n,- . . . u ’1 I ..lrf. . 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N 1 ..P .. .fl . .r .. , . .. h I l I l I u I . . .. we 3,. . .. .. 7 .. . ...), ,. 111 end of the data acquisition period. The data were stored on two 140 kilobyte "floppy disks". While the 196' kilobytes of transducer data and time information were being transferred to the magnetic media (1.9 minutes), the LVDT was unfastened and the clamp was released from the tree. The process was repeated for each test such that all instrument settings and clamping pressures were the same at the start of every run. For each tree diameter, the last tree to be shaken' was analyzed for pivot motion about the tree base. The XY block of accelerometers was removed from the tree and a hole was drilled in the tree in the X direction below the pad, vertically in line with the previous single X Sensor. Average height from soil surface was 8 cm (3 in), Figure 4.18. Shaking tests were repeated with the sensor at this point. Therefore, X movement was detected at 8 cm (3 in) and 46 cm (18 in) above soil surface. The relative difference would be an indicator of pivot motion about the tree base. A test at each engine speed was conducted for free shake (no tree in the clamp) and free idle (tree in clamp with no shaking, engine running at shaking speed). This information may be useful for detecting otherwise unnoticed vibrations inherent in the mechanism. The pressure of the clamping cylinder was checked for constancy and maximum deviation during a test. The 112 .WW: 0 O O LOWER seemsmnersn 4:1 9%., o" . f n— ax '\ ... -. .x-n. -":-'. ' s-s’ifi- -'.' . . . I (I I . 53552-353: '--~-'-‘-‘""-'i$'.-:. . lfilfil‘lfil ll'ufiufi lfin" I. n‘ I’ I If ~-'v..'.-..:-;...i..i..~ ... '.~ ;i,i.-.i:..3'i-... viii-3553'}? iiiiiiiiiiii ‘.-.= :- x.~.--.«us.as;-_.'-_-.\:_-_.os-\-sAnn-M5-5? “Hp-V5“""""""":""".-..a‘.'.- Figure 4-18 Physical Location of Tilt Detecting Sensors Relative to the Tree and the Shaker. . ».; 113 LVDT correlated clamp displacement with time. The electromagnetic sensors detected the times at which masses were in a known position. The microprocessor's real—time clock provided the time to which all physical events occurring during the shaker tests were referred. 4.9 Method of Data Analysis Data on each floppy disk were analyzed with a Pascal—programmed integration and calibration algorithm. The original order of data in a file was high byte, low byte starting at low memory address. Every two bytes represented the code of one voltage reading. Since 14 consecutive channels were scanned, every 28th and 29th bytes starting with bytes 0 and 1 were Channel 0 data. A program was written to read the original encoded information by byte and display the codes on the video screen in order to verify the data. The Pascal language required an integer to be in the form low byte, high byte. Therefore, in order to read coded information with UCSD (University of California, San Diego) Pascal into the integration and calibration program, it was necessary to flip the byte order fOr each integer. During this process, the data were separated into files according to channel number, then re-stored in six files with file seven containing time. Calibration was accomplished with constants - I. . l . 4 a , - u d... s .- -A u r s . . . .... I. . . . ... x) .... v ... . .... . . 7v» . C. . . _ . . . . s . .o 4 y I . .~ .. . 114 obtained in laboratory tests with the instruments employed. The integration—calibration program read in the coded information, converted codes to voltages (knowing the scale from which the ADC read a channel), filtered amplifier offsets from the voltages, integrated acceleration data twice to get displacement, and finally, plotted the results as they varied with time. The maxima and minima of the values were secured and displayed. The plots could be stored on disk for later retrieval and printing. The double integration was a digital linear quadratic fitting process. Piecewise quadratic integration allowed a smooth fit to a sinusoidal curvature without the oscillations of higher—powered fittings. More complex methods would not have necessarily provided a better fit for a simple waveform. Observations of collected data verified sinusoidal or nearly sinusoidal acceleration waveforms for the shaker and tree tests conducted. Difficulties arising from variable frequencies and irregular amplitudes prevented calculation of displacements in all directions on the shaker. Displacement vectors were obtained in the X direction only for the sensors at the bark-pad interface. Digital integration of the acceleration traces produced superimposed displacement waveforms in several 115 frequencies. Some low frequency components prevented accurate interpretation of the higher frequency displacements of major interest. Therefore, attempts were made to remove any low frequency components and/or amplifier drift or external unidentified interference. Using piecewise linear regression to translate the data base did not provide an easy, intelligible means of interpreting results. Steady state shaker traces were less obscured by this method than the transient start-up and shut—down regions of an accelerometer waveform. System memory and processing time constraints prevented programming of high order polynomials to remove undesired underlying signals. Several traces with amplifier drift displayed exponential waveforms underneath the true data. The time constant of this exponential was usually much longer than the period of data acquisition and was not estimable. The resulting displacement traces were meaningful but not completely accurate. Therefore, not all accelerometer traces were integrated. For purposes of presenting the difficulties encountered, several of the displacement traces are presented in Chapter 5. CHAPTER 5 RESULTS AND DISCUSSION Rubber clamp pads were investigated for the triboelectric phenomenon as a tool for force measurement. Machine and tree response to shaker vibration were characterized in digital waveform with the instruments and data acquisition system described in Chapter 4. Shaker frequencies of 9.3 and 14.0 Hz were applied to both 11.0 cm (4.5 in) and 16.5 cm (6.5 in) diameter trees. Acceleration data were twice integrated to displacement for determination of critical maxima in the X direction. Clamping cylinder pressure was evaluated for constancy; clamping motion of the clamping arm was also monitored. A discussion of the error associated with the digital data acquisition process, including suggested improvements, concludes this chapter. 5.1 The Triboelectric Test on Shaker Clamp Pads The compression of a rubber clamp pad (a dielectric) on a 20 cm x 25 cm (8 in x 10 in) steel plate in a (hydraulic press produced small negative charges similar to those described by Richards (Memmler, 1934). 116 117 These results are shown in Table 5.1 with probe position shown in Figure 5.1. Measurements are in volts as detected by the measurement system. Conversion to a unit standard employs the following relation: ggiygn_yolts * 3.2828 = _JflflLjr. Given Pressure (psi) kg/cm = 1 electrostatic unit = l Stat-couloumb = 3 x 10E-9 Coulombs Where esu As pressure was applied to the pad, small negative voltages were monitored from the charge produced in the dielectric. A typical plot is shown in Figure 5.2. The small negative charges which developed in the pad were linearly) proportional to the applied load for loads up to 2.8 kg/cm2 (40 psi), but for larger loads, the increase in charge diminished. At large loads, there is probably discharging from the rubber to the surroundings overriding the charge increase for any further increase in load. The charge increase per load increment is shown in Figure 5.3. For small loads up to 2.8 kg/cm2 (40 psi), when the load was removed, the charge was opposite in sign and equal in magnitude to that resulting from the applied load. 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Eo\wx\:mo bow cu QNmN.m an “wa\wuao> hadwuazz .~.n ouswwm oucmuouwu :oHunom .AmcoEocosd ofiuuowaoonfinuv pod aEmHu poxmzm nonbsumm mo :OfimmwudEoo >9 noumuocmm omumco ecu Eouw AwuHo>v ammuHo> unnuso .s.m mamas (ll I)||I l 119 FRONT (0, 90, 180, 270 DEG) REAR (45, 135, 225, 315 DEG) Figure 5.1 Geometry of probe connections on rubber pads. (r=70 mm). I ‘ 1—1 120 .bmoH pofiammm ou mpmm mEmHo Hannah mo omcommoe coHMHHQE< gun om: 01¢ Huzoxozc umzmwumm Home ems mIc m m w m u s o _ _ _ _ _ . _ .--: -11.-.. ....... - l ....... al----- I ‘ |lll Illllll‘lllllll‘lllllll‘ 'IIIIIII‘CI lllll.lllllll‘ll III I I}! II: {I 14.1.---5 a czuxozwzm ...: «Howl—mom H z... N.m magmas moon“. «---. wmommdlla WI w. NI 0“ ODHmDH >OJHM .mpmm mEdHo Hogans ow wofiammm wmofi a How acoEoHoCH omsmco bamboo m.m whamem umozmelic game code olc . mIc umozmarlh o 353$ 358$... 33 8 m w v n N a P bl L _ 121 #I mb.on I mN.oI -..-II-£..I-.II£ ......&....l.« I II. 11 (III! I c: DZHP o:¢¢¢m ~Nt0\ox\:wm zu uczcro huzau czmzozuzm o~xhuu4uom_¢h i|||i|| 122 pressure where the final charge was greater than the charge during application of the load. This charge was also dependent on the geometry (direction of strain) in the pad as can be observed from the different charges arising at different measurement locations on the pad for the same load. The charges observed for small loads (0-3 kg/cmz) agree with those presented by Brain and Richards (Davis et al., 1937) for a material that might be classified as a pliable, semi-hard rubber. These charges ranged from -0.2 to —0.4 esu/kg/cm2 load. An impulse created with a steel hammer produced charge impulses proportional to the applied force. After repeated impulse application, however, charge was produced on both the hammer and the rubber pad which appeared to be opposite in signs. Movement of the statically charged hammer near the charged pad produced a momentary change in the charge exhibited by the pad. This effect caused me to notice, that the charge responded to the passing of any charged object near the pad. Interference of the two electric fields apparently altered the electron-hole density distribution regulated by the pad's static field. The above observations covered static and impulse loadings. Observation of dynamic loading starting at very low frequencies (30 cpm) revealed a charge saturation effect occurring after only a few cycles. The depletion of charge upon removal of the load appeared to have a 123 definite time constant which I could not reproduce at a frequency above this. Observation of this application of this low cyclic loading suggested material fatigue. Material fatigue would prevent the reproducible recording of a time varying force from a charge measurement. The exhibition of hysteresis and saturation, the susceptibility to weak stray electric fields, and the low maximum loading which produced an output change in the pad charge made the triboelectric phenomena impractical for force measurement on the cherry shaker. Perhaps for small, near—static loading in an electrically isolated environment, the triboelectric effect could be useful. 5.2 Pad Deformation by Displacement Measurements A new idea for a two step (indirect) force measurement was conceived. The measurement of shaker and tree displacement would allow reproduction of maximum displacement conditions of the shaker and tree in a laboratory environment where pressure transducers, mounted inside a model tree (steel pipe), could characterize the concentration of force beneath the pad's surface. In this manner, the simulation of the tree and shaker could provide critical information leading to the classification of maximum potentially—damaging stress conditions imparted by the shaker. Accurate real-time displacement measurements could be obtained by the double integration of acceleration measurements. This process was carried out as in Chapter 4. The results of the shaker and tree sensors follow. 5.3 Firmness of Clamp This investigation of the forces a shaker imparts to a cherry tree was initiated partly on the hypothesis that tree decline results? from internal (unseen) trunk damage caused by shaker harvesters. A sub—hypothesis is that trunk damage may result from the unintended beating of the tree by a loosened clamping—arm. Inadequate or variable clamping pressure would cause the clamp arm to periodically) grip and release as the forces change direction. Clamp arm movement was detected using a linear voltage differential transformer (LVDT) which had a conversion factor of 4.0 mV/mm. Several tests were conducted on trees of different diameters. Data for these tests are given in Table 5.2 (C.f. Figure 5.4). The results of clamping force tests are shown in Table 5.3. All data are presented in Figures 5.5-5.8. The initial values are the values of the LVDT before shaking began. This is given in the table to be consistent with the graphs and to allow meaningful difference calculations. A positive—bound peak in the plot indicates a motion of the 125 .e.m .mHu mam .H as Lowaazu cw commsomwc ammo spew wumrmaom a sore can =n= 2n empacmwmwv came * mN N\me mN - - NHHNH NH .nm mm\NH\a NN as NN H m NH NH as mmHNH\N om He . MN H m NH NH m mm\NH\m . wN as mN H m NH NH e MNHNHHN mN m\He . mN - I NN\NH mH ism meNH\m mN He mN NH HH .mH aH am - , mmHNHm mm mm eN . QH _ HH eH NH N mmHAHm MN we wN oH mH ON NH HH mm\w\m .HWMMHJHMHH ...mfimfime .. . .. 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The clamp arm appears to be tightened during a period of transient action of the harvester and then momentarily releases during a transient response to the harvester or tree as a system. This initial motion could be caused by stickiness in the clamp where the initial vibration allows the clamp to seek its final position. Clamp arm movement inward could also be related to air in the cylinder and hoses, as well as hose expansion. The diameter of the tree may even change slightly as the rough protruding bark is compressed by clamping forces. While these very small clamp arm displacements may be insignificant in terms of tree damage, they do give a very important indication that tree damage potential may .093. AH: m1: :8 HH .N: m.m $8.325 ”pooh .mcfimob mHHUHmHHm seams AaoumflpoEEH 5.5 new: 23 H: 3300 wcficouamfiu < 5:285: Eye mfiwao wixmfimmflo oomfl. Hofisomgmhh Hmfiucosommfio omwufio> 53:3 m.m 0.5%: as e- H” We... . . _H ...HHHHHEHHHHHHHH. L 9%."... E .. . 2 Huh? . (.133. 33 H as H: REESE/jam; Ema. E530 134 be more crucial during the transient operations of start-up and shut-down than during the quasi—steady state operation. This, in turn, may be due to a response by the shaker or the tree passing through frequencies of resonance . 5.4 Pressure Factors in Slip A major concern in damage to stone fruit trees, particularly cherries, has been the slippage of the shaker pads across the surface of the tree. This slippage can occur longitudinally, tangentially, or in combination. Changes from the recommended clamping pressure (49.3 kg/cmz, 700 psi) were considered critical since a significant increase in pressure could cause the bark to split or crush while a significant decrease in pressure could allow the pad to slip over the bark. A pressure sensor placed in the clamp's high pressure line monitored the clamp pressure throughout each test (Figures 5.10-5.13). The results are presented in Table 5.4. The clamping pressure exhibited a worst case of 14% overclamp and 11% underclamp from the recommended pressure. The average pressures are observed to be within 15% or less for all tests. 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One other maximum pressure case occurs as observed in Figure 5.24. This reveals a short period during the shake when a very low pressure minimum occurs. This minimum can be attributed to a synchronization of the masses, the shaker, and tree. The extent of the minimum gives an indication of the significance of this phase relation. However, this minimum could have resulted from the second mass engaging and drawing more hydraulic fluid to start rotating. In Figure 5.23, the pressure falls to a very low level just after a short period of resistance-compliance and resistance—only. This minimum suggests resonance 'with the clamped tree. In all cases, after one occurrence of a very low minimum, the pressure tends to reach a stable operating level. Further tree resonance effects are not apparent when the tree is being shaken at a frequency above its fundamental resonant frequency. Pressures need to be monitored at other points in the hydraulic circuit before any conclusions can be made. When the shaker is shut down, hydraulic pressure is immediately removed from the drive motor. Therefore, no information is received about shaker action and reaction at shut-down. The value of quasi—steady state operating 160 pressure is in the range of 49-63 kg/cm2 (700-900 psi) while startup and recovery maxima reach 92 kg/cmz (1300 psi) in some cases with minima of ll-21 kg/cm2 (150-300 psi). This great variability in pressure relates to varied power requirements for shaker operation. 5.7 Acceleration to Displacement The objective of this study is to characterize forces imposed upon a cherry tree trunk by the dynamic action of an eccentric mass trunk shaker. Observation of the pressures generated in the clamping cylinder provide some insight into the magnitude of these forces. The simulation of real world dynamic displacements in the laboratory environment may, however, present a more realistic account as to the stress and strain undergone by the bark of a tree. Accelerometers on the tree and shaker were to resolve X, Y, and Z displacements. Accelerometer data were quickly and accurately accumulated by the ADC operating system for digital processing. Digital integration of the accumulated accelerometer signals, however, produced non-uniform velocity and displacement waveforms. Several of the acceleration waves are shown in Figures 5.26-5.31 for comparison. 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