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Text follows. y ^ ____________________________________ University Microfilms International A SIMULATION STUDY OF THE DISPLACEMENT BEHAVIOR OF A TRUNK SHAKER SYSTEM DURING CHERRY HARVEST BY Ghassan Al-Soboh A DISSERTATION Submitted to Michigan State University in partial fullfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1986 ABSTRACT A SIMULATION STUDY OF THE DISPLACEMENT BEHAVIOR OF A TRUNK SHAKER SYSTEM DURING CHERRY HARVEST BY GHASSAN AL-SOBOH Mechanical harvesting is now the only harvesting the sweet or sour cherries for are in Michigan. grown Nearly all method processing mechanical for that harvesting systems use a trunk shaker. Currently, growers are reporting an increased problem with bark damage due to trunk shaking. Many believe bark damage contributes to cherry tree (early loss of tree vigor and With the operational to the Mechanisms computer of yield). goal of identifying some shaker design changes that would help reduce physical tree bark, behavior decline a simulation study of the a trunk shaker was conducted. Program modeling, (IMP) was selected as or damage vibrational The the Integrated tool for and the Friday C-clamp trunk shaker was modeled since it is widely used for cherry harvesting. During the study, the the required physical properties shaker and young cherry trees were measured, of analyzed and used in the IMP program. runs, the Through free-shake simulation IMP program successfuly predicted dynamic shaker displacement behavior similar to that observed in field tests. The simulated free-shake found to startup, shaker conditions shift and behavior during (no tree clamped in the shaker) and gallop then displacement (large to drift when displacements) operated at was during harvesting frequency. These conditions are believed to create excessive stress on the tree bark. Shaker mass, physical eccentric rotating properties mass, changes and (housing rotating mass eccentricity) and changes in rotating mass accelerations p,nd starting phase angles were studied to find ways to reduce the undesirable shaker displacements. The undesirable displacements were eliminated when the eccentricity set at zero then increased to cause the desired shaking action, or when the the rotating masses was initially a particular rotating mass position was used in starting degrees. should bark of Such phase angle between the two masses changes in the shaker design and was 225 operation reduce undesirable displacements and thereby damage. which reduce Tests with a modified shaker will be required to verify these simulation results. ACKNOWLEDGMENTS I thank my god who gave me the health and the power to accomplish this work successfully. I thank my family, my loving wife Nuha, my son Yasser, and my daughter Moor, for their encouragement, support and patience during my study. The author would like to express his deepest gratitude to the following persons and organizations for the Fruit and contribution to this study: To Dr. Vegetable Galen K. Harvesting, Brown (Research Leader, L’.S Department of Agriculture), my major professor, for his professional guidance, cooperation, support, and editorial help provided throughout the duration of my Ph.D program. To Dr. and Gary L. Cloud (Professor Metallurgy, Mechanics Materials Professor Science), Dr. Gary R. Agricultural Engineering), (Assistant Professor U.S. Van Ee and Dr. Department of (Assistant Clyde Burton Agriculture) for their time, cnstructive counsel, and professional interest. To Henry Affeldt (Ph.D Gradute Student), Tom Eash (Ph.D Gradute USDA), Student), for their and Dale Marshall (Agricultural Engineer contribution of valuable assistance experience to the projectduring the experimental and stage. To AID program, and U.S. Department of Agriculture for their educational and financial assistance during ray study in the United States. To Student Dr. Kenneth Ebert (Specialist, International Dean) for his time and effort with the USDA and the university to keep the program going successfully. To my family in Syria, and my friends who have been a continuing source of strength and encourgement. TABLE O F CONTENTS PAGE ii i ACKNOWLEDGEMENTS....................................... LIST OF TABLES......................................... viii LIST OF FIGURES........................................ ix CHAPTER J : 1. INTRODUCTION......................................... 1.1 1.2 1.3 1.4 1.5 Cherry Production ............................... Mechanical Harvesting......................... The Bark Damage Problem.......................... The Need For A Shaker Model............... Objective Of The Study .................... 1 5 10 14 16 18 CHAPTER 2: 2. LITERATURE REVIEW................................... 2.1 2.2 2.3 2.4 Bark Damage And Causes.......................... Bark Structure And Strength.................... Shaker Pads, Forces, And Pressures............. Dynamic Response Of Trees.......... 20 20 27 32 36 CHAPTER 3: 3. COMPUTER MODELING.................................... 3.1 IMP Program....................................... 3.2 Model Development ............................... 3.2.1 Model Assumptions.......................... 3.2.2 Model Development Of C-Clamp Trunk Shaker............................... 3.2.3 Model Development Of C-Clamp Trunk Shaker-Tree System......................... v 46 46 48 48 52 58 CHAPTER 4: 4. EXPERIMENTAL MEASUREMENTS........................... 4.1 Tree Measurements............................... 4.1.1 Cherry Tree Height, Center Of Gravity, And Mass Measurements........... 4.1.2 Stiffness And Damping Measurements........ 4.2 Trunk Shaker Description........................ 4.3 Trunk Shaker Physical Properties ............... 4.4 Rotating Mass Velocity Measurements............. 61 61 62 85 101 CHAPTER 5: 5. SHAKER DISPLACEMENT RESULTS 5.1 Free-Shake Vibration............................ 5.2 Shaker-Tree Vibration System........... ........ 5.3 Model Verification............. ... ............. 10 9 117 125 CHAPTER 6: 6. SENSITIVITY ANALYSIS STUDY OF DISPLACEMENT 6.1 Variation Of The Magnitude Of The Shaker Housing Mass ........... .................. 130 6.2 Variation Of The Magnitude of the Rotating Masses........................................... 137 6.3 Variation of The Rotating MassAcceleration 143 6.4 Variation Of The Rotating Masses Eccentricity... 148 6.5 Variation Of The Rotating Mass PhaseAngle..... 158 CHAPTER 7: 7. SUMMARY AND CONCLUSIONS 7.1 Summary......................................... . 7.2 Conclusions...................................... 7.2.1 Scope And Limitations..................... 7.2.2 Future Research Needs..................... REFERENCES............................................... 201 205 208 209 211 APPENDIX A Free-Shake C-Clamp Trunk Shaker Model......... A.l APPENDIX B Shaker-Tree C-Clamp Trunk Shaker Model......... B.l APPENDIX C Optical Free-Shake Displacement Results....... C.l APPENDIX D Optical Shaker-Tree Displacement Results...... vii D.l LIST OF TABLES TABLE 1.1 1.2 4.1 4.2 4.3 4.4 4.5 6.1 PAGE Michigan Sour Cherry Production And Utilization...................................... 6 Michigan Sweet Cherry Production And Utilization.................... 8 Linear Stiffness And Damping Properties Of The Sour Cherry Tree............................ 76 Rotary Stiffness And Damping Properties Of The Sour Cherry Tree............................ 83 Shaker Moment Of Inertia Determined By Swinging.............. 92 Stiffness And Damping Constants For Shaker Mounts.............. 100 Summary Of The Physical Properties Of Friday C-Clamp Trunk Shaker And A 63 mm Sweet Cherry Tree Used In IMP Model............ 107 Summary Of The Simulated Displacement Results At Different Rotating Mass Starting Phase Angles..................................... 180 *•• V||| *. LIST OF FIGURES FIGURE 1.1 1.2 2.1 3.1 3.2 3.3 4.1 4.2 4.3 4.4 PAGE Sour Cherry Production In Michigan Between 1981 To 1985....................................... 7 Sweet Cherry Production In Michigan Between 1981 to 1985....................................... 8 Bark Damage On A Cherry Tree Trunk As A Result Of Mechanical harvesting................... 21 Top View Of Friday C-Clamp Trunk Shaker As Defined For The IMP Model......................... 53 Side View Of C-Clamp Trunk Shaker As Defined For The IMP Model.................................. 54 Top View Of Friday C-Clamp Trunk Shaker-Tree System As Defined For The IMP Model............... 60 Sweet Cherry Tree Height Vs. Tree Trunk Diameter........................................... 63 Sour Cherry Tree Height Vs. Tree Trunk Diameter................................. 64 Sweet Cherry Tree Center Of Gravity Vs. Tree Trunk Diameter..................................... 66 Sour Cherry Tree Center Of Gravity Vs, Tree Trunk Diameter............................. 67 4.5 Sweet Cherry Tree Mass Vs. Tree Trunk Diameter..., 4.6 Sour Cherry Tree Mass Vs. Tree Trunk Diameter 69 4.7 Tree Pull Test Setup For Linear Stiffness........ 72 4.8 Linear Displacements Measurements Of A 63 mm Diameter Cherry Tree Trunk ....................... 74 Linear Force Measurements Of A 63 mm Diameter Cherry Tree Trunk Versus Time..................... 75 Tree Twister Setup For Rotary Stiffness.......... 78 4.9 4.10 ix 68 4.11 Angular Displacements Versus Time Of A 63 mra Diameter Cherry. Tree Trunk ....................... 80 4.12 Experimental Torque Measurements Of A 63 mm Diameter Cherry Tree Trunk ................... 81 4.13 Friday C-Clamp Trunk Shaker 86 4.14 Shaker Physical Dimensions.................. 89 4.15 LVDT Locations And Damping Measurements Of The Trunk Shaker............................... 99 ........ 4.16 Inside Rotating Mass Frequency Of A Free Shaker... 103 4.17 Outside Rotating Mass Frequency Of A Free Shaker.. 104 4.18 Inside Rotating Mass Frequency Of A Shaker Attached To A 63 mm Diameter Cherry Tree Trunk ... 105 4.19 Outside Rotating Mass Frequency Of A Shaker Attached To A 63 mm Diameter Cherry Tree Trunk ... 106 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6.1 Free Shaking Displacement Vs. Time At A Mass Rotating Frequency Of 5 H z ........................ 113 Free Shaking Displacement Vs. Time At A Mass Rotating Frequency Of 10 H z ....................... 114 Free Shaking Displacement Vs. Time At A Mass Rotating Frequency Of 15 H z ....................... 115 Rotating Masses Are Running According To Simulated Transient Velocity Function............. 116 Tree Displacement At A Mass Rotating Frequency Of 5 Hz With Wo Tree Stiffness Or Damping........ 119 Tree Displacement At A Mass Rotating Frequency Of 10 Hz With No Tree Stiffness Or Damping....... 120 Tree Displacement At A Mass Rotating Frequency Of 15 Hz With No Tree Stiffness Or Damping....... 121 Tree Displacement At A Shaker Rotating Mass Frequency Of 15 H z ................................ 123 Rotating Masses Are Running According To Simulated Velocity Function For A Shaker Housing Mass Of 317 k g ............................ 133 x 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 Free Shaking Displacement Vs. Time At A Mass Rotating Frequency Of 15 Hz, And Shaker Housing Mass Of 317 k g ....................... 134 Rotating Masses Are Running According To Simulated Transient Velocity Function For A Shaker Housing Mass Of226.5 k g .................... 135 Free Shaking Displacement Vs. Time At Mass Rotating Frequency Of 15 Hz And Shaker Housing Mass Of 226. 5 k g ................................... 136 Rotating Masses Are Running According To Simulated Velocity Function For A Mass Of 31.7 k g ......................................... 139 Free Shaking Displacement Vs. Time At Frequency Of 15 Hz And Shaker Rotating Mass Of 31.7 k g ......................................... 140 Rotating Masses Are Running According To Simulated Transient Velocity Function For A A Mass Of 18.12 k g ...... .............. 141 Free Shaking Displacement Vs. Time At Frequency Of 15 Hz And Shaker Rotating Mass Of 18.12 k g ........................................ 142 Rotating Masses Are Running According To Simulated Transient Velocity Function For Two Different Acceleration Levels, 280 And 270 rad/s. ................ 145 6.10 Rotating Masses Are Running According To Simulated Transient Velocity Function For Two Different Acceleration Levels, 280 And 260 rad/s. ................................ 146 6.11 Rotating Masses Are Running According To Simulated Transient Velocity Function For Two Different Acceleration Levels, 328 And 246 rad/s.s............................... 6.12 Sliding Rotating Mass Model....................... 6.13 Rotating Masses Are Running According To Simulated Transient Velocity Function With Moving Eccentricity AtRate Of 217 mm/s............ 6.14 Rotating Masses Are Running According To xi 147 149 152 Simulated Transient Velocity Function With Moving Eccentricity At Rate Of 190 nun/s...... 153 6.15 Rotating Masses Are Running According To Simulated Transient Velocity Function With Moving Eccentricity At Rate Of 165 mm/s.......... 154 6.16 Rotating Masses Are Running At Steady Frequency Of 5 Hz With Moving Eccentricity At Rate Of 217 mm/s........................................ 155 6.17 Rotating Masses Are Running At Steady Frequency Of 10 Hz With Moving Eccentricity At Rate Of 217 mm/s........................................ 156 6.18 Rotating Masses Are Running At Steady Frequency Of 15 Hz With Moving Eccentricity At Rate Of 217 mm/s........................................ 157 6.19 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 0 Degrees. ........ 160 6.20 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 0 Degrees .................................... 161 6.21 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 0 Degrees.......................................... 162 6.22 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 45 Degrees......................................... 163 6.23 Shaker Displacement In The y Direction. Masses . Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 45 Degrees..................... 164 6.24 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 328 And 246 rad/s,s. At A Starting Phase Angle Of 45 Degrees......................................... 165 6.25 Shaker Displacement In The x Direction. Masses xii Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 90 Degrees......................................... 166 6.26 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 90 Degrees......................................... 167 6.27 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 90 Degrees................................. 168 6.28 Shaker Displacement. In The x Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 135 Degrees........................................ 170 6.29 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 135 Degrees.............................. 171 6.30 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 135 Degrees...................................... 172 6.31 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 180 Degrees........................................ 173 6.32 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 180 Degrees........................................ 174 6.33 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 328 And 246 rad/s,s. At A Starting Phase Angle Of 180 Degrees........................................ 175 6.34 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 225 Degrees............................. 176 6.35 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 225 Degrees.................................... 177 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 225 Degrees....... ............................ 178 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 270 Degrees.................................... 181 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 270 Degrees.................................... 182 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 270 Degrees.................................... 183 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 315 Degrees.................................... 184 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 315 Degrees.................................... 185 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 328 And 246 rad/s.s. At A Starting Phase Angle Of 315 Degrees ................................... 186 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 358 And 276 rad/s.s. At A Starting Phase Angle Of 225 Degrees.................................... 189 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 358 And 276 rad/s.s. At A Starting Phase Angle Of 225 Degrees.................................... 190 Shaker Displacement In The x-y Plane. Masses xiv Are Running At Accelerations Of 358 And 276 rad/s.s. At A Starting Phase Angle Of 225 Degrees.................................... 191 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 358 And 276 rad/s.s. At A Starting Phase Angle Of 0 Degrees.................... ................. 192 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 358 And 276 rad/s.s. At A Starting Phase Angle Of 0 Degrees............ .......... .............. 193 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 358 And 276 rad/s.s. At A Starting Phase Angle Of 0 Degrees...................................... 194 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 298 And 216 rad/s.s. At A Starting Phase Angle Of 225 Degrees......... .......................... 195 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 298 And 216 rad/s.s. At A Starting Phase Angle Of 225 Degrees................................... 196 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 298 And 216 rad/s.s. At A Starting Phase Angle Of 225 Degrees.................................... 197 Shaker Displacement In The x Direction. Masses Are Running At Accelerations Of 298 And 216 rad/s.s. At A Starting Phase Angle Of 0 Degrees ............................. . 198 Shaker Displacement In The y Direction. Masses Are Running At Accelerations Of 298 And 216 rad/s.s. At A Starting Phase Angle Of 0 Degrees............................ ...... . 199 Shaker Displacement In The x-y Plane. Masses Are Running At Accelerations Of 298 And 216 rad/s,s. At A Starting Phase Angle Of 0 Degrees...................................... 200 xv CHAPTER 1 1. INTRODUCTION Mechanical harvesting of cherries has played an important role in cherry production areas in Michigan, where over 95% of harvested the sour and sweet mechanically systems. Nearly because all using cherry trees are shake-and-catch of these systems use being harvesting trunk shakers, they provide faster harvest and lower harvest cost than limb shakers. Over the from years, mechanical tree shakers have improved a simplepush boom or pull cable attached to mechanism on a tractor to inertia programmed options for shaking stroke, frequency. Today, machines a crank providing force, direction and powerful trunk shakers are available, and the shaker clamp systems have been enlarged and improved. In recent years, growers have reported tree decline (loss of vigor and yield, the that early replacement of orchard) is an increasing problem where the harvesting of cherries is being practiced. damage has been found, is high dynamic mechanical Internal and a possible cause of this forces during cherry shaker tree damage operation. At present there is a need to analyze the trunk shatter design used for cherry harvesting, 1 with the goal of 2 identifying damage design changes that would help reduce to the tree bark system of young trees. physical The cherry tree trunk diameters considered in this study ranged from 63 mm (2.5 in.) to 165 mm (6.5 in.). The startup of tree shaking have been observed to be most likely times for bark damage been to observed phase occur. that and the stopping phase Large unstable displacements can result in large shear have and compression forces and stresses being transmitted to the bark. largo displacements can be eliminated, If these the large forces and stresses should also be eliminated. Thus, bark damage should be reduced. shaker The startup and steady state operation were studied. studied, since although that phases of the The stopping phase was not may be a source of serious damage the shaker is not in a controlled (powered) state at that time. To study the displacement behavior and identify design changes that displacement, Mechanisms would a Program help computer (IMP) eliminate program was large undesirable entitled selected as Integrated a tool for mechanical system simulation . The IMP program is capable of simulating two-or three-dimensional rigid link mechanical systems having single or multiple degrees of freedom. different modes can be simulated by this program: Three kinematic (geometric), static (equilibrium), or dynamic (time response). 3 With these considerations in mind, was developed dynamic time. and a free-shake mode] used in the IMP program to study the behavior of a C-clamp trunk shaker as a function of Through this approach, introduced and evaluated possible design changes for their ability to were reduce conditions likely to cause bark damage. A shaker-tree model was also developed and used in the IMP program to simulate the displacement behavior trunk attached to the Friday C-clamp trunk shaker. properties of mass, of a The tree damping and stiffness were measured for use in this model. In the first modeling stage, the mass and inertia properties of a 63 mm (2.5 in.) diameter sour cherry tree trunk were introduced in the IMP model, stiffness or damping were displacement results experimental field tests. to those simulated tree in In a second modeling stage, the tree stiffness and damping properties were added in the IMP not close The tree measured model. were omitted. but the Unfortunately, the simulated tree displacements were realistic problems in and the the simulation stiffness matrix aborted due to of IMP program. the some Consequently, the simulation results presented in this study deal with shaker. the the free-shake displacement behavior of the These results are believed to be very indicative of actual displacement behavior of the shaker when clamped to young trees having trunk of 63 to 114 mm (2.5 to 4.5 in.) 4 diameter. properties In can the future, the stiffness and damping be added to the shaker-tree model when program has been corrected, IMP 5 1.1 Cherry Production Cherry production has continued to play an important role in Michigan agricultural production. Production of sour cherries, in Montmorency variety, 1985 while {Napoleon, Windsor, In Golds, and the varieties Schmidt, the for sweet Emperor Francis, 1985 nation’s leading sour production (215,000,000 lbs), bearing main cherries Hedelfingen, others) declined marginally from 1984 levels. Michigan, state, the in Michigan was up slightly estimate cherry was producing 97,523 tonnes Trees planted in the late 1970's are now and will help sustain future production at present levels. Perfect weather conditions prevailed throughout much of the growing season in 1985, and Only intermittent hailstorms windstorms affected production and quality. Utilized production was about 95,255 tonnes (210,000,000 lbs) in 1985 and had Michigan a farm gate value of $52,395,000. sour A cherry production in the last 5 summary of years is presented in Table 1.1 and Figure 1.1. Sweet (62,000,000 $15,128,000. in 1.2. the cherry lbs) in production 1985 and had a A summery of last 5 years was about farm 28,800 gate tonnes value of Michigan sweet cherry production is presented in Table 1.2 and Figure 6 Table 1.1 Michigan Sour Cherry Production And Utilization. UTILIZED PRODUCTION CROP YEAR * TOTAL PRODUCTION* PROCESSED (Tonnes) (Tonnes) FRESH (Tonnes) 1985.... 99,660 2, 265 97,395 1984 .... 95,130 2, 265 88,335 1983 .... 39,410 905 38,500 1982 .... 117,780 2,265 86,070 1981 ... . 39,865 905 38,958 Total production defined as production avilable for harvest. Source: Michigan Agricultural Statistical 1985. SOUR CHERRY PRODUCTION IN MICHIGAN YEAR FIGURE 1.1 SOUR CHERRY PRODUCTION IN MICHIGAN BETWEEN 1981 TO 1 9 8 5 8 Table 1.2 Michigan Sweet Cherry Production And Utilization, UTILIZED PRODUCTION CROP YEAR TOTAL PRODUCTION* (Tonnes} FRESH (Tonnes) PROCESSED (Tonnes > 1985.... 28,086 2,720 25 ,368 193*1* .« . 29,900 2,720 25,368 1983.... 16,310 1,810 14,500 1982 .... 28,086 1,810 21,290 1981 .... 20,840 1 ,360 19,480 * Total production defined as production available for harvest. Source: Michigan Agricultural Production Statistics, 1985. SWEET CHERRY PRODUCTION IN MICHIGAN T 81 82 83 84 85 YEAR FIGURE 1 .2 SWEET CHERRY PRODUCTION IN MICHIGAN BETWEEN 1981 TO 1 9 8 5 . 10 1.2 Mechanical Harvesting Over the years, manual harvesting of cherries has proved to be uneconomical and inefficient. Manual harvesting of the cherry crop required many migrant workers. of labor during harvest reached to half the farm the crop (Brown, IBraoero 1980). Program), that Kith The cost value the termination of allowed supplementary of PL 78 foreign workers to enter the U.S. to meet high seasonal labor needs, growers had switching to crops recognized harvesting choose or between mechanical changing vocation. The that a high long-term investment equipment consumer market would permit harvesting, them growers in to with cherries at an economical Shortage and cost of hand labor, soon mechanical supply the cost. labor unrest, rough handling, economic risk and other economic barriers had been the from primary problems in managing a steady flow the field to the consumer in of produce competitive markets, according to Drake (1983). The trees first attempt to mechanize the shaking of was begun shaking methods cherries from causing by Levin et a l . had been studied the trees. (1956). to cherry Hand and pole separate red tart Detachment was accomplished the fruit to oscillate until a failure of the by stem 11 at the spur or at the fruit occured. To overcome the worker fatique due to hand shaking, hand-carried mechanical shakers were built in 1957 which hooked to individual tree These units were heavy, user, caused tree damage, limbs. transfered excessive shock to and worked successfully only the on the smaller limbs. Levin et al. (1958) hydraulically-activated, boom next used a shaker for tractor-mounted, harvesting tart cherries. This machine provided 95% fruit removal in seconds with little operator fatigue. The clamp was a bear-hug style covered damage with rubber padding to cushion tree to limbs was reported due to clamp clamping pressure, slip, cherries excessive Considerable bark damage resulted when the same shaker was used for sweet Barit or deviation from a 90 degree attachment angle between the shaker and limb. also contact. harvesting ( due to violent action required to remove immature fruits ) for the brining market. The first inertia-shakers were designed by Adrian Fridley (1965). The shaking force were: masses arid; tree. Their two mechanisms used to generate and the (1) a pair of counter-rotating eccentric (2) a slider-crank with the slider fixed to the clamp was a C-clamp style covered with rubber pading to cushion tree contact. Metallic fasteners were also placed permanently or semi-permanently into main limbs or trunks for shaker attachement. scaffold These were compared to the rubber-covered clamps. The fastener permitted direct transfer of force to the structural wood rather than through the vulnerable bark and growing tissues. As a result of several experiments, they concluded that the direct clamping of a shaker to a tree through a cushioning pad was the faster and preferred method of trunk or limb attachment. Mechanical in Michigan mechanical harvesting of cherries was rapidly adopted in the mid-1960's. The initial adoption harvesters required drastic modification of of the existing trees. The number of scaffolds were reduced to 3 or 4, low hanging branches were removed or cut back to make way for the catching frame and the willowy branches were stubbed to improve fruit removal. Equally development Initially, dramatic of have harvesting equipment relatively over the years, changes occured since in the the 1960’s. small limb shakers were used. Then, larger and more powerful trunk shakers were introduced. Peterson and Monroe (1977) reported the development of a compact trunk shaker mounted on a catching would automatically sequence, while the frame from one tree to frame moved continuously. Compared to the that next, standard stop-and-go harvesting, harvest rate (trees/h) was increased about 50% on a time trial basis. The continous harvest rate, ranged from 210 to 284 trees/h for trees spaced 2.74 m (9 13 ft) in the row and 155 to 198 trees/h for trees spaced 6.1 m (20 ft) in the row. The trunk shaker did not perform well on large trees with large limbs. void of Also, the tree trunk must be limbs to a height of 1 m (3.3 ft) to permit easy shaker attachment and good shaking action. Limb years 1983). in for and mechanized removal of fruits systems speed, arid for nuts many (Brown, In 1982, over 95% of the sweet and sour cherry trees Michigan catch trunk shakers have now been used were harvested mechanically systems (Brown et al., use lower trunk 1982). shakers because harvest cost, comparison to limb shakers. using shake-and- The majority of these they provide greater and minimized human effort in 14 1.3 The Bark Damage Problem The area of attachment of the shaker with the bark has frequently been found to be damaged. tree Tests of the strength characteristics of bark showed that the bark injury was usually caused be excessive tangential or stresses Adrian, at the cambium under the shaker clamp with tree age, inc rease from spring t.o fall Excessive the cherry bark the decrease with turgidity, and and (Fridley et a l . 1970). clamping force was found to cause and cambium tissues of both trees (Frahm, through ( F r i d l e y 1966). The stresses at which the cambium is damaged increase of longitudirial 1983). ruptured cells to tart Vital nutrients the fruit, crushing and sweet cannot leaves, pass fruit bearing limbs, and roots. In California, fimbriata. of a disease-causing fungus, Ceratocyst.is can be carried by insects into the damaged prune or peach tree bark, where a favorable environment allows rapid spreading into healthy bark and wood (Devay al. from is 1960, 1962, area et 1965), Fungal vectors can also be carried tree to tree on shaker pads when continuous harvesting conducted potentially prematuraly, in a diseased orchard. The disease is serious and can cause the limbs or tree to die 15 Injury using a clamp distribute stress to tree bark can be virtualy designed with adequate eliminated contact by area to the clamping force and the shaking force so that remains at safe levels. positioned Also, the shaker must perpendicular to the limb or trunk to longitudinal stresses. well-designed clamp, Experience the eliminate has shown that clamping force can be be with set a high enough to ensure adequate contact area between the clamp and the tree during shaking, but still low enough not to exceed the stress allowable radial cambium. have stresses the bark by installing two layers belting over the clamp the the manufacturers to minimized at transmission pads and lubricating the between the belts to create a slip surface. of of Most shear smooth interface 16 1•4 Need For Shaker Model In recent years, growers have reported tree decline (loss of vigor and yield, that cherry early replacement of the orchard) is an increasing problem. Tree decline has been noted in orchards of all ages throughout Michigan (Brown et al . 1982). Research has been conducted on various aspects of the bark damage problem, to define bark strength limits ( Diener et al., 1968; Fridley evaluate various et a l ., 1970; Brown et al., 1984) to designs and operation methods for clamps (Adrian and Fridley, shaker 1968), and to define the static pressure applied to the bark when clamping the shaker to the tree (Brown et a l ., 1982; Frahm et a l . 1983). Previous contact research on cherry bark strength showed that pressures on the bark above 1035 kPa ( 150 psi) on sweet cherries and 2413 kPa (350 psi) on sour cherries were likely to initiate compressive failure in the cambium, even without the addition of shaking force (Brown Studies to tree et a l ., 1982). have also shown that static clamping forces applied bark do not adequately explain the problem because some damage occur may not be bark evident damage until several weeks after shaking. Recently, the dynamic displacements of the cherry tree 17 trunk with and the clamp area of a Friday C-clamp trunk two independent rotating masses, were shaker, studied to estimate the relative deflections between the shaker and the tree trunk (Affeldt, deflection of substantially the 1984; Affeldt trunk within the pad was greater during shaker steady-state operation (Affeldt Brown clamping when and et et a l ., 1984). Relative a l ,, (1984) found startup than to be during et a l ., 1984). reported that the initial shaker startup phases were the primary bark damage was most likely to occur, and the times shaker startup on a 16.5 cm (6,5 in) diameter trunk appeared to add about 517 to 860 kPa (75 to 125 psi) of dynamic compressive stress to the recommended static clamping stress of 1136 kPa (1G5 psi). With these considerations in mind, analyze the dynamic behavior identifying tree-trunk-shaker under dynamic system real operation, it is necessary to and to study the with the goal design changes that will, help of reduce physical damage to the tree bark system. To accomplish this goal, a mathematical model can be used to describe the shaker behavior as a function of Through this introduced, approach, then possible design changes evaluted for their conditions likely to cause bark damage. ability time. could to be reduce 18 1.5 Objective Of The Study The overall objective of this study is to analyze the vibrational behavior of the Friday C-clamp trunk shaker now widely used for cherry harvesting, and to evaluate design or operational changes displacements started. that These that may reduce the undesirable frequently occur when the large shaker is large displacements are believed to lead to large shear and compression stresses being applied to trunk bark arid to be the cause of some of the bark damage. In order to meet the overall objective, the the specific objectives are as follows: 1. Define the dimensional and main physical properties of the Friday C-clamp-trunk shaker. 2. Define the properties dimensional of and main physical cherry trees having different- trunk diameter sizes. 3. Use a computer Mechanisms study the shaker program Program (IMP) as dynamic displacement Bystem as a entitled a Integrated modeling tool to behavior of the functionof time during the startup phase. 4. Evalute possible shaker design changes that may reduce the large displacements that occur when the 19 shaker is started. displacement Accomplish this through a sensitivity analysis of the following factors: a. variation of the magnitude of the shaker housing mass. b. variation of the magnitude of the rotating masses. c. variation of the rotating mass acceleration. d. variation of the rotating mass eccentricity. e. variation of the starting phase angle the rotating masses. between CHAPTER 2 2. LITERATURE REVIEW 2.1 Bark Damage And Causes Bark damage is easily recognized by stripping, cracking or wetting of the bark in the area where the shaker was attached to the trunk or limb of the tree. A slight cracking or internal separation of the bark from the cambium is not apparent to the untrained machine operator, the operator does not correct the improper and thus procedure or machine adjustment. After the passage of time, the influence of disease, weather, insects and obstructions of nutrient flow in the damaged areas add up to a major problem of total tree decline, Figure 2.1. Halderson {19GG) suggested that damage to trees occurs in three forms : damage by 1) physical damage by the shaker, 2) trunk positioning catching frames or shakers root damage from tree vibration. all movement In his field and, 3) experiments, of the roots ceased approximately 15.2 cm (6 in.) below the soil surface and did not appear to be a major problem. good Bark damage at attachment areas was minimized with clamp design. attachment Level ground, to the tree, providing was considered such perpendicular an important factor as to necessitate leveling devices on catching frames 20 FIGURE 2.1 B ^ K DAMAGE ON A CHERRY TREE TRUNK AS A RESULT OF MECHANICAL HARVESTING. 22 and harvesters. observed Tangential clamp to cause damage problems, slip and twist were although they were not always immediately apparent. Diener et al. (1968) studied bark damage problems and found that the amount of damage inflicted on a limb or trunk was determined limb or by the bark properties, trunk, and the radius of the resistive forces of the the shaken object. Fridley power and Adrian (1960) attempted to determine and optimum frequency of vibration in fruit the removal with minimal tree damage. One possibility was to vibrate the tree at the Combinations natural frequency of the fruit of frequency and displacement instability at the point of fruit suspension, difficult stem system. that cause however, were to transmit through the branched tree system due to colliding limbs and damping by leaves. Collisions between fruit and limbs, when the shaker frequency natural frequency of a limb, reached were observed to cause the damage to tree and fruit. The of the other possibility was to vibrate the tree at natural selection frequencies of the tree or limb. of the proper natural frequency was dependent one The on the stroke needed to remove the fruit at that frequency, the power a required minimum and the resulting tree and power level was needed to remove fruit a damage, volume of 23 fruit with long strokes and low either strohe or frequency, tree damage, Placing however, increase of caused an increase in although long strokes caused the most damage. the frequency frequency; clamp allowed at an anti-node for a given the stroke to reach a maximum natural for that frequency. Higher frequency with shorter strokes resulted in minimum damage. A force must be exerted perpendicular to the trunk or limbto minimize damage and power the included trunk for as angle between the shakerand the trunk or limb deviated from the required, 90 degrees, or a component,of force parallel limb induced shear and was identified as to a direct cause of bark damage. Beljakov et. al . harvest on peaches and plums. eccentric the the (1979) studied the effects of root system of sweet injected into the soil, photosynthetic shaking cherries, The and 3.0 radioactive tracer P-32 the cm was C-14 was applied to leaves, to activity. Results indicated had no adverse effect on tree growth, trunk and only insignificant number of roots were severed (less than of an clamped 20 cm (7.9 in.) above and operated at 15 to 18 Hz with 2.4 to (1.0 to 1.2 in.) strokes. study sour The exciting force was developed by mass trunk shaker, earth and shaker an 0.05% roots (by weight) of diameter 0.1 cm (0.04 in.) or smaller). Brown et a l . (1982) and Cargill et. a l . (1982) made 24 direct field observations and classified 10 general causes behind the barlt damage problem as follows: 1. Operator error and inadequate (operators, due constraints, to may a operator training lack of time or training 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 trees selction of a and/or failure to machine for young adjust existing machines for tree size. 6. High cambial activity at harvest due to excessive irrigation, rainfall, or physiological activity. 7. Immature removal fruit requiring (this an excessive force tempts the operator to for 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 force to critical a concept is the transmission tree to remove fruit, but to do of so proper without 25 harming the living tissues of the tree. task for, damage This is a difficult as Brown et a l . (1982) noted, on bark and cherry trees will occur at lower cambium stress levels than on other fruit trees. In 1982,Brown observations operator of et al. expanded bark damage in order to their general isolate specific and machine inaccuracies that may account for the observed tree damage. The list of critical points included: 1. Failure to center the clamp on the trunk. 2. Clampingtoo excessive firmly radial to the stress, tree causing hence, crushing and during shaking where the splitting of the bark. 3. Clamping pads too loosely tend to scuff and tear the bark (tangential shear). 4. Clamp wrong pads not slipping internally due to pad design or improper lubrication surfaces becoming causing heated, high shear forces sticking together, the of slip (e.g. pads including shear force and deterioration). 5. Excessive eccentric setting causing excessive tree displacement and bark strain. 6. Excessive power applied to small trees. 7. Shaker "gallop" during startup and stop, 26 causing torque (shear) in the bark. 8, Settling of the during shaking shaker carrier into the (causing excessive earth longitudinal shear). 9. Shaking forces not perpendicular to the trunk (causing longitudinal shear). 10. Clamping most too low to the ground where the trunk is rigid (causing execssive forces to be applied to the trunk)» 11. Clamp pads too small or firm causing high stress in the bark due to small contact area. 12. Longitudinal shear caused shear caused by clamping to a leaning trunk. 13. Longitudinal if shaker is tilted when clamping to a vertical trunk. The above list of causal factors fell main categories: 1. Operator error during shake and clamp. 2. Improper pad design 3. Improper machine design or setting. into three 27 2.2 Bark structure and strength Diener et a l . (1968) described the structure of cherry bark as having a thin nonliving periderm( a large spongy nonfunctioning phloem in the center, phloem next properties of alignment greatest to the cambium. cherry bark can directional be strength accounted for the tensile strength in the direction parallel to the cells (horizontal Phloem cells have their long axis (vertical on the trunk) direction, whereas have their long axis on the trunk) direction. thin-walled lubricate The tissues from have in a longitudinal oT The of the constituent cells. long axis of their cells. periderm and a thin functioning dead cells encrusted in the tangential The periderm consists with waxes which the dead tissue and allow slippage between cells (Esau, 19G5), When the bark is damaged so that it separates from the wood (xylem) of the tree, essential area.. life Usually, tissue, through tissues so Devay the flow of fluids containing the sustaining elements is interrupted in that hairline bark cracks are formed in the which air enters and oxidizes the that they appear brown (Adrian et al. cambial 1965). et a l . (1962) notes that these damaged areas are open invitations for insects and disease, especially tree canker, 28 a gummosis fimbriata. The disease caused evidenced fungus by the fungus Ceratocysti s in the fruit orchards of gradually spreads to healthy California. surrounding bark tissue, slowly causing tree death. In design the early development of tree shaker of shaker clamps, systems operation of shakers for the minimum bark damage, and the strength of fruit tree bark in relation to the stresses applied during mechanical harvesting were studied by several investigators between 1962 and 1970. compressive systems and shear strength of intact bark and for prune trees were found to change during the strength growing season (Fridley was lowest early in the et The cambium significantly a l ., season, 1970). when Bark combial activity was high. Clamping pressure above 2100 to 2400 kPa, in the absence of shear stress, browning marked in the bark, was shown to cause and above 4100 to 5200 kPa faint caused browning in the cambium and was likely to split the bark on 6-yeai— old prune trees at harvest time. Adrian by applying injury both et al. known 5 loads to the bark and evaluating visually and by inoculation of the with a pathogen. to (1963) conducted bark strength studies test the area The maximum radial stress at failure was 4 times greater than the maximum tangential stress at failure. Considering both fungus infection and visible discoloration 29 of the barlt, an allowed radial stress (including a factor of safety for tree variability) of approximately 1700 kPa was selected. Brown influence (1965) of conducted moisture a study to and normal pressure determine on the strength between the bark and limb of fruit trees. moisture was found to affect the force required bark from a fruit tree limb. with low shear strength and low moisture with strength. The bark shear associated high shear Also, the shear strength could either increase or decrease some shear to High moisture was the with an increase in normal pressure according critical differences moisture were also conditions. Variety found to exist in and shear to specie strength value. Diener et a l . (1968) conducted a study of the strength properties Cherry of the bark of apple, bark was environmentally tensile, peach and cherry trees. removed from the tree and placed in controlled chamber to test its compressive, and viscoelastic strength properties. that the shear strength of the bark was largest They found directional, being in the longitudinal direction and decreasing to the lowest values in the tangential direction. peach an ruptured extruding in compression. at the about 8300 kPa tangential Both cherry compressive direction at stress about and by 45% 30 Fridley et a l . (1970) summarized their strength studies on the characteristics and magnitudes of tree bark. concluded that injuries by injury to bark and infection of Ceratocystis canker were associated magnitude and direction of stress applied to the bark could applied or withstand about 3 to 4 times as radially as when stress was applied tangentially to the limb. about 50 to 70 % tangential bark or injury They these* with the baric. The much stress longitudinally The shear stress contributed of the total tangential strength, and the longitudinal stress was a primary factor compared with radial stress. Maximum in radial strength was found in the range of 3450 to 6900 kPa. Bark moisture content the force had a substantial affect on required to shear bark from a fruit tree limb. High moisture was associated with low shear strength, and low moisture with high shear strength. Brown et a l . resulting that from clamping (browning) cherry. sweet on (1982) conducted a study on bark trunk shaking of cherry trees. pressure sweet above 1000 They kPa caused cherry compared to 2400 kPa found failure on sour At 1300 kPa radial pressure, compressive failure on cherry was low and constant observed. increased as bark moisture increased. 9-mm At 4000 over moisture bark damage kPa, the range of compression Sweet thick was not split at 2750 kPa but cherry had bark failure trunk slight 31 splitting at 4000 kPa. Sour cherry trunk bark 9-mm thick did not that split even at pressure up to 5500 kPa. clamping They must be firm enough to efficiently restated transmit the shaking energy without the pad slipping on the bark, but not so firm that compression and splitting damage result. 32 2.3 Shaker Pads, Forces, and Pressures Forces tree are transmitted from the shaker body through a pad which acts as spring. cushion, the damper, and Minimum stress occurs in the bark when the required vibrational area. a to energy is transmitted over the largest possible Longitudinal and tangential forces from the epicyclic shaking patterns must be efficiently transmitted to the tree by means of a pad that conforms well to the tree trunk. Scouring if of the bark or excessive shear stress may pad contact area or clamping pressure are During shaking, slipping these action action (radial). pads become increment) Excessive pressure or observed longituinal) or a (smaller harder pad deflection shake is imposed on very high, because the pad is shaker per force the tree. torque also may arise during shaking if is as beating As clamping pressure is increased, stiffer and insufficient.. inefficiencies may be (tangential result clamping unable to internally flex or slip. Until recently, pad design has been a trial-and-error process. would likely The use of a poorly designed pad cause bark damage regardless of attempts to control other factors during shake harvesting. Designs rubber tube, for shaker pads have included a round bags filled with sand or ground hollow nutshells, 33 rubber pads with small holes drilled parallel to the trunk axis, preformed steel clamp jaws covered by tree rubber pads, and other conforming materials. Brown et a l . shaker the (1982) made preliminary tests of C-clamp pads for contact area and peak contact pressure manufacturer's recommended hydraulic pressures. This cover the unknown peak pressures between the pad tree during pressures psi), hydraulic circuit shaking. pressure range was The results at clamping assumed indicated and that between the pad and the bark were 2345 to the peak kPa (340 34 50 kPa (500 psi) and 4140 kPa (600 psi) on a 114 mm (4.5 in.) diameter trunk (an instrumented steel pipe). This showed were that certain recommended clamping excessive and caused compressive failure of cambium for both sweet and sour cherries. cambium from compressive stress (radial) was pressures high moisture Failure of initiated the at lower clamping pressure on sweet cherry 2300 kPa (335 psi). Brown stated that "peak contact observed in these stationary tests shaking, but we have not pressures higher certainly occur progressed to the than during point of estimating dynamic pressures". Frahm commercial contact the pad et al. (1983) continued studies trunk shaker pads for peak bark area and pad stiffness. on pressure, four bark The results indicated that pressure patterns are not uniform and differ for 34 each manufacturer. psi) was not stiffness If a peak bark pressure of 2070 kPa (300 exceeded, were adequate, when bark contact area and the pads were judged to be pad safe. This pressure presumably would not cause compressive failure (browning) average and with in sour cherry tree bark, which exhibited ultimate compressive strength of 2400 kPa (350 psi) it would cause only minimal a corresponding Reduced clamping manufacturer’s pad damage in sweet strength of 1030 pressure was kPa recommended thereby cherries, (150 psi). for each so as to avoid peak pressures bark exceeding the estimated 2070 kPa (300 psi) on the limit, and avoid compressive damage. The Friday Tractor Co. composed of 3 (1982) developed a "Tri-clamp" pads contacting areas of a tree trunk degrees apart (surrounding the trunk in a triangle), of the tree so their center of gravity is and about the bark, and wrap minimizes slip between the pad minimizes rotation of the the trunk to prevent torque damage. the tree was the result. each located within the tree trunk. This design provides a complete of the pads around the tree, 120 A pair of eccentric rotating masses are positioned in line on side an shaker body A firmer grip on 35 2.4 Dynamic Response of TreeB Years ago, be detached farmers learned that the tree fruit by hitting theprimary scaffold limbs could with a mallet attached to about a 1-m long handle. The mallet was a hard rubber pad. Hitting the limbs amplitude, high frequency vibration that stiff trees. However, generated a low transmitted well in the successful application of the vibratory concept did not start until the 1960's. Since then mechanical means of detaching tree fruits have improved and enhanced both machine performance and fruit quality. Adrian and Fridley (1958) found that fruit removal when using a boom-type shaker on the limb of prune trees was affected primarily by four variables: 1. The frequency of the shake. 2. The length of the stroke. 3. The force required to remove the fruit divided by the weight of the fruit, f/w, A. The number of limber fruit-bearing hangers in any given fruit tree. They also found that limb breakage increased with increasing stroke, However, minimum limb breakage occured frequency range of 11 to 15 Hz. within a 36 Fridley frequency et of al. (I960) reported that the operation was at a natural frequency optimum of the system, and the natural frequency selected depended upon the following: 1. The stroke required to remove fruit at the frequency. 2. The power required. 3. The resulting tree and fruit damage. Higher result in frequencies less and shorter strokes tree and fruit damage, but seemed required to more power. Adrian (196 3) studied the amplitude and developed along frequency and the position that limbs as a function of exciting of force application. He found increasing the frequency resulted in a general increase due the acceleration to in acceleration after passing an associated reduction in through stroke. linear resonance, Also, greater power and force were evidenced when the vibrator was located closest to the fixed end of the limb. Kronenberg detachment sour (1964) forces cherries. studied in attempting the to effects of mechanically fruit harvest He found the detachment force decreased the fruit ripened. The difference between the force 10 before harvest and that on the traditional picking as days day 37 varied with the equation: Y = -48 X + 428 Where : X = 9 - Number of days before harvest Y = Crams force for fruit detachment Unripe cherries came off with stems, whereas ripe cherries came off without stems. Kith careful shaking, healthy l e a v e s would not conic off with mature fruit. Levin et a l . suitable that time to mechanically harvest cherries. average their (1968) conducted a study to identify the pull force required to remove They found cherries stems decreased from over 9.8 N (2.20 lbs) from to about 8.8 N (1.98 lbs) during the 20-day harvest period, while the force required decrease to detach stems from branches substantially during this period. that the recovery of fruit increased, attached stems decreased, did not They also found and the proportion of as the date of mechanical harvest was delayed. Cook and Rand (1969) described a mathematical analysis of the dynamic simultaneous was harvested of the fruit and stem horizontal and vertical forcing of support structure. be behavior the during fruit The analysis indicated that cherries may with stems attached if the shaking in the range of 4.16 to 5.41 Hz, and harvested frequency without 38 stems if the shaking frequency was in the range of 16.6C t j 28.33 He . instability twice They also found that the greatest dynamic of the fruit occured at a shaking frequency the natural frequency when the upper end of the of stem undergoes small, planer, elliptic displacements. Adrian and inert.ia-t,vpc Fridley limb (1965 ) shakers developed according to a model the c.f following assumptions: 1. The system has a single degree of freedom. 2. The exciting force varies sinusoidally. 3. The restoring force is proportional to displacement. 4. Damping is viscous (damping force is proportional to velocity), 5. Steady state vibration occurs. 6. Energy is conserved by the shaker. The vibration analysis was found to be sufficiently accurate for estimating shakers. Field the design criteria for tests inertia-type indicated that it was tree possible to reliably predict the following: 1. The shaker mass ratio and eccentricity required to develop a certain stroke. 2. The force requirements and to torque developed vibrate and a limb at the a power certain 39 stroke and frequency. Halderson (1966) studied the relationship between percentage of cherry fruit removal and elapsed shaking time. He found that a long shaking time was required for over removal time when fruit was immature, but only a short was required when fruit was mature. removal was determined mainly by the 85% shaking The rate of fruit shaking frequency. Removal was 85% in 2 s of shake, with 95% removal after 8 s, at a frequency of 1G Hz. A frequency of 13 Hz was determined to be a minimum for adequate removal. A maximum stroke of 19 mm this (0.75 in.) was adequate at. a frequency of 17 setting, the fruit fell straight to the Hz. Using ground (no whipping action). Phillips et a l . to simulate physical forces. the vibrations of a limb as properties, They (1970) developed a mathematical model found configuration and affected by type applied of that the analysis of a tree limb its must have the capability of dealing with the following: 1. Mass distribution, which is not uniform along the length of the limb. 2. Enternal and external damping. 3. Effect of rotary inertia and shear deformation. 4. Variations in the rigidity of the base support. 5. Existence of secondary branches. 40 6. Curvature of the neutral axis. 7. Effect of the longitudinal forces and di splacemcrits. They found that at lower natural frequencies, the deflection amplitudes from were large when the shaker was attached the base of the limb. At higher frequencies, range of the third and fourth normal modes, amplitudes to the further the in deflection were larger when the shaker was attached base. Computed phase angle the and closer frequency relationships for the limb showed that all points along the limb the were approximately 90 degrees out of phase with applied force when the frequency ratio (limb frequency limb natural frequency, that a f/fn) was near 1.0. They also found damping factor of 0.1 for olive limbs gave approximation to over the steady-state response for a good simulated compared to experimental results. Hoag et measurement tree al. (1971) continued their experimental of internal and external damping properties limbs. In this experiment they used the of logarithmic decrement method to investigate the damping factor and, with the aid of photography, the rate of limb vibration decay was measured. They found that the logarithmic almond wood varied from 0.0667 to 0.1015 in tested when the saturating point. decrement three moisture contents were above the of samples fiber- External damping of tree limbs due to the 41 limb moving through the air was non-linear in nature and seemed to be proportional to the square of the velocity. The report also indicated that the air drag on limbs could 1.5. When external vibrating tree be a constant drag coefficient equal to only branches without leaves about were present, be neglected damping forces were small enough to unless the velocities were very large. Berlage during et a ] . the 1971 and 1972 harvest seasons to practical cherry value removal smal1-displacement vibrations for They found vibrations fruit Lowering the frequency resulted removal. the sweet that the applied removal. The of the in increasing In trunli-shaker harvesting, low frequency range distributed however, a the shake pattern through-out the variable tree structure better a to Sweeping higher frequencies did not promote additional removal. sweep determine frequency at which fruit released from cherry limbs 40 Hz. fruit high frequency did not provide any significant highest was of with minimal damage. high-frequency limbs (1974) conducted experimental studies fixed frequency. vibrating Nodes and anti-nodes formed than on the 1imb moved along the limb as frequencies changed, thus, preventing "dead0 spots with zero displacement. Young et simulate the purpose, a al. (1975) used finite element vibration of complete tree whole-tree system was systems. methods For considered to this as a 42 combination of three portions: 1. A tree limbs, structure which consists of tree trunk, secondary branches and hanger branches. 2. The fruit and stem. 3. The leaves and twigs. They found using mathematical models developed the finite element method were in agreement with available system by that the three answers in 1975. the The natural frequencies of the obtained by approximating the curved hanger branches a series of straight elements resulted agreement between in the Ritz method and the very finite close element method. In 1976, applied frequency resultant at Alper et a l . and investigated the effect of the the point-of-force application amplitudes at the points of fruit suspension the zone of force application on orange shaker, went The tree system, were moved by when excited by a from a transient-state to a steady-state back to transient-state during shaking tests. amplitudes and trees. Vibrations that developed at these points were described harmonic displacements. on and The vibration in a shaken branch at points of fruit suspension found to increase as the force application further from the main branching point. force was applied, point was If a constant then the momentum transferred to nearby 43 branches through application the joint link remained constant point moved. as the Vibration amplitudes at points of fruit suspension remained the same with and without attached frui t . Except at very low frequencies or very low amplitudes, changing applied frequency and amplitude had little on cherry fruit removal by limb sour combination 1969). resuited Frequencies in a change in of shaking unless acceleration the (Bruhn, 16 to 20 Hz with a stroke of 38 (1.5 in.) provided adequate fruit removal. the effect mm Accelerations at outer portions of a tree exceeded those applied to the trunk or base limb in all cases. Khaljlian adding et al. (1978) determined the effects a spring-1oading feature to a slider-crank of inertia- type limb shaker on limb displacement, and maximum force and power required to shake the limbs, found that required addition maximum approximate 1y stiffness and of force equal crank this and of an olive tree. feature peak power to the product of amplitude at the by both an added frequencies second natural frequency of the system. also reduced They the amount spring above the However, the spring caused an increase in maximum force required to start the shaker. Upadhyaya et a l . (1979) used the finite element method to investigate the dynamic response of a tree limb subjected 44 to an impact force. beam theory for leaves, was Their model was based upon a linearized and accounted for transverse shear as well twigs, secondary branches and fruit. The fruit modeled as a spherical pendulum. scheme was system. A direct used to obtain the transient They as found that the integration response model of the predicted experimentally observed results quite closely. the Furthermore, it was found during the course of this study that use of the Timoshenko lead to beam theory with the finite element ill-conditioned associated with the matrices problem is if the small. method shear may energy Therefore, the complementary energy approach was used to provide a solution to the problem. Kirk et al. (1979) studied the damage sources in mechanically harvested sweet cherries. The results indicated that the fruit size, pull force, factors the and stage if maturity as indicated by stem maximum trunk displacement were the only which showed a highly significant correlation with fruit damage for both the 1975 and results on the harvest indicated trunk movement during 1976 seasons. mechanical that the shaken tree was moving in The cherry some form of an orbiting pattern, but the maximum acceleration or displacement was never constant. The motion of the tree often forms a daisy pattern as indicated from simultaneous X and Y recordings. Examples of patterns observed were 45 straight line motion, daisy pattern, circular patterns, and all these. combinations displacements forces of can result and stresses Large unstable in large shear tree and trunh compression being transmitted to the bark and can lead to bark damage. Ortiz-Canavote multidirectional et al. (1980) developed trunk shaker for harvesting olives. a They found that shakers with two eccentric masses, each driven by a separate hydraulic motor in a series circuit produced more controlled vibration than those having the two motors in divided-flow parallel circuit. olive better trees They also reported that results were obtained when the a in two counter-rotating masses were of equal magnitude. According to Cargill et al. required stroke, when (1982) the force and power shaking fruit trees varies with frequency, 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 to increase frequency varies as the cube of the frequency. frequency and stroke required for adequate The fruit depend on the type of fruit and maturity level. proper removal CHAPTER 3 3. COMPUTER MODELING 3.1 IMP Progran The Integrated Mechanisms Program (IMP) is a computeraided design and analysis system which can be used for simulation of mechanical systems . The IMP program is capable of simulating two-or threedimensional multiple rigid link mechanical systems having single degrees of freedom . revolute (pinned), The simulation can prismatic (sliding), screw, or include spur gear, cylindric, universal, spheric (ball and socket), and planar joints any open or closed-loop combination. in Linear or non-linear springs and viscous dampers may also be included, either on within the joint or acting between specified the moving links. Mass and gravity effects points can be simulated. The system can be driven either by applied forces or input motions which can be specified functions of time or system geometry . The three IMP different (equilibrium), modes system IMP modes is capable of simulation in : kinematic (geometric), or dynamic (time response). can calculate 46 the any of static In any of these requested positions, 47 velocities, forces, accelerations, natural static frequencies, and dynamic damping constraint ratios and small oscillation transfer function (principal vibration modes) of the system simulated. With these considerations in mind, the IMP program was selected to be used as a tool to study the dynamic of the Company C-clamp trunk shaker developed by for harvesting cherries and to Friday help in studies for shaker operation or design improvements. behavior Tractor further 48 3.2 Model Development 3.2.1 Model Assumptions The C-clamp trunk shaker in this study was mounted on the 2250 Mount-O-Matic International tractor. of loader frame of a Hydro-84 A frame was constructed on the front the loader from which the shaker was suspended at three points. Rubber bushings (Friday standard parts) were used on the ends of the suspension bars to minimize the amount of vibration transmitted to the tractor. In the IMP model, the C-clamp trunk shaker was assumed to be points suspended on three suspension bars from three fixed in space. large The tractor was thus modeled as a fixed mass (ground) to maintain simplicity and to focus only on the dynamic behavior of the shaker. To allow the shaker to undergo unrestricted planar motion, Bpherical joints were introduced bushings at used both at ends of the ends of the the suspension suspension bars. The bars were assumed to have no affect on the shaker planar motion. In the free-shake model the shaker was assumed to run freely with no tree attached to it. pads In this caBe the rubber between the clamp and tree trunk would have no on the shaker displacements, so the affect shaker main frame could 49 be modeled as one link. However, in the shaker-tree model, the shaker was attached to a tree, be as the rubber pads would clamped to the tree trunk and expected to deflect during shaking . Field and video film observations shaking operation deflect about 6mm to 37 mm (.25 to 1.5 in.) indicated clamping force However, for simplicity , was ignored shaken and that the tree size) under during rubber the pads will (depending dynamic on conditions. the deflection of the clamp pads in the model, assuming that the trees were small enough that the pad deflection being was small compared to the shaker movement. In field tests, Affeldt (1984) showed that the rotating when mass velocity passes through a velocity increases rapidly during the After about 1 s, the rotating steady state velocity mass shatter critical period startup time. velocity exceeds the and oscillates until it Betties at the steady state. Early test results unrealistic to compare displacement vs. time curve and the model displacement vs. time curve curve using the IMP model show between by feeding the actual into the computer model. the rotating it actual mass is shaker velocity The difficulties with this approach are: 1. The simulated rotating mass velocity curve 50 cannot an natch the actual velocity curve, approximation is possible. in velocity would cause a difference in rotating mass would affect small significant positions, the only Any difference turn ao final which in displacement simulation. 2. The initial positions of the rotating are always different each time the shaker The random match starting the impossible actual to position and velocity match the starts. inability curves actual masses makes and to it simulated displacements. With these selected was to by feeding considerations in mind, simulate the transient the IMP model the the approach shaker displacements rotating mass velocity as a linear function with a slope equal to the mass acceleration, and to simulate the shaker steady-state frequency levels of 5, with 10, displacements and 15 Hz to compare the actual the simulated displacements at these adopting this simulation method, could at the computer frequencies. time required be reduced, and the transient as well By for as the steady-state displacement at different frequencies could be estimated. During displacement, the the dynamic simulation of the trunk shaker initial positions of the shaker rotating 51 masses defined 3.1. When counter for IMP model were set as shown the shaker to each other, displacement that was as shown, started in Figure they turned to simulate the highest might occur during shaking operations. 52 3.2,2 Model Development Of C-Clamp Trunk Shaker The system firstphase of model development of a using analysis the IMP of the program system. must This be mechanical the analysis topological includes the recognition of the number of links, the number and types of joints, links the arranged, order and in which other the characteristcs and joints such as are t speed, acceleration, applied forces, etc. existing in the system. The Friday connecting 6 trunk shaker was modeled using links to describe the machine they are illustrated in Figures is presented in Appendix A. 8 joints components as 3.1 and 3.2. The model code These machine components can be described as follows: Link 1 , LI : This link which represents the consists of the bearings, hydraulic motors, cylinder frame housing, 2 rubber for mounted on the back of the total mass of shaker this beams, pads, the and C-clamp shaker. The link was estimated to be 465.36 kg (31.89 slug). Joint 1 , J1 : A the revolute joint which connects inner rotating mass and the between shaker J 3 .J 4 SUSPENSION POINT MASS POSITION 01 CO MOTORS J7.J8 SUSPENSION POINT BEAM SUSPENSION FIGURE 3.1 J5.36 n POINT CYLINDER HOUSING J 6 .J 4 MASSES MOTORS BEARING L5,L4 J 5 , J3 HOUSING BEAM CYLINDER FIGU?£*3*S,SiSE«Y©tf 0F FRIDAY C-CLAMP TRUNK SHAKER AS DEFINED FOR THE IMP MODE3L. 55 housing. the This inner generate was set to allow rotating mass to rotate force shaker. joint joint The was enough to vibrate initial position set to and of the this be 90 degrees (outer position). Link 2 , L2 : The inner 2 , J2 : mass which connected to the shaker housing revolute joint Jl. set Joint rotating A to the The total mass was slug). revolute joint which connects between This joint shaker. initial was set to shaker to allow mass to rotate force enough to The the was set outer rotating generate joint kg outer rotating mass and housing. the 39.9 by (2.734 the be is be 90 vibrate position and the of this degrees, (outer position). Link 3 , L3 : The outer connected revolute rotating to masswhich is the shaker -housing by joint J2. The total mass the was set at 39.9 kg (2.734 slug). Link 4 , L4 : The rightside suspension bar which carries the shaker. This bar was set to havea 4.5 kg (0.308 total mass of 56 slug). Joint 3 , J3 : A spherical shaker shaker. 4 , J4 : A the right side carries the reason for selecting this bar, The to the L4 which of joint was to allow motion Joint connects housing suspension type joint which free for the shaker during spherical right joint which side planar operation. connects suspension bar to the the tractor frame (ground). Link 5 , L5 : The left side connects between (ground) and total mass the suspension the bar which tractor shaker frame housing. of the bar was set The at 4.5 connects the kg (0.308 slug). Joint 5 , J5 : A spherical left side joint which suspension bar to the shaker housing. Joint 6 , J6 : A spherical left side joint which suspension connects bar to the the tractor frame (ground). Link 6 , L6 : The rear suspension bar connects between the (ground) and shaker the total mass of the bar was tractor beam. which frame The set at 4.5 kg 57 (0.308 Joint 7 , J7 : A slug). spherical rear joint suspension bar which connects to the the shaker bean. Joint 8 , J8 : A rear spherical joint which connects the suspension bar to the tractor frame {ground). The second phase of model development was to specify link mass moments of inertia. These are calulated in Chapter 4 and summarized in Table 4.5. 58 3.2.3 Model Development Of C-Clamp Trunk Shaker-Tree System The Friday adding a Cherry tree trunk shaker-tree system was tree to the previous free-shake with a 63 mm (2.5 in.) trunk modeled model. diameter A by sweet and a total mass of 9.345 kg (0.6404 slug) was selected to be used in the IMP model. The tree mass moment of inertia relative to the tree center was calculated by assuming the tree had a cylindrical shape and applying the following equations: Ix = Iy = m.r2/4 + m.L^/12 Iz = m.r2/2 Where: Ix, Iy, Iz: The mass moment of inertia of the tree in x, y, and z direction, m :The tree mass (9.345 kg (0.64 slug)), r :The trunk radius (31 mm (1.25 in.)). L :The tree height (3.25 m (128 in.)). The calculated results of mass moments of inertia (Ix, Iy, and Iz) of the selected tree were found to be 8.233, 2 2 8.233, 0.0047 kg.m (73, 73, 0.0417 lbm.in ), respectively. The Friday trunk shaker clamped to a tree was modeled 59 using of 9 jointsconnecting 7 links. Six of these the jointswere already described for links and 8 thefree-shake model. The other joint and link are: Link 7 , L7 : This link represents is connected which pads by is a directions The per total free equal to joint. The link and by a spring and a damper. stiffness set at 0.31 N/mm s), 51 and 12.69 spring mm (2 N/ram (71 s (1.8 per length in.) trunk springs and damper the link L7 and y damping respectively. expected tree shaker x and lb/in. the the were lb/in.) trunk both spring factor tree to revolute connected in the The was (the set maximum displacement). The connect between the ground, as shown in Figure 3.3. Joint 9 , J9 : A revolute between tree to the link L7. joint shaker which connects housing LI and the This joint was selected allow for the translation of motion link. from the shaker to the linear tree FIGURE 3.3 TO P WEW O F FRIDAY C—Cl i u p t r i iu v SHAKER-TREE SYSTEM A S DEFINED FDR THE IMP MOC CHAPTER 4 4. EXPERIMENTAL MEASUREMENTS 4.1 Tree MeasurmentB Experiments have important have shown that tree physical affects on detachment efficiency, trunk-shaker properties behavior, and the amount of trunk bark fruit damage caused during the harvesting operation. This suggests that a meaningful to take modeling analysis of into account the tree trunk shaker behavior physical properties has that contribute significantly in a displacement simulation study. To achieve this goal, selected physical properties for both sweet and tart cherry trees were the 1985 cherry harvesting season. investigated during The purpose of the study was to determine the following cherry tree properties: 1- Height, center of gravity, and mass above ground. 2- Linear and torsional stiffness of the trunk. 3- Linear and torsional damping coefficient at the shaker attachment height. 61 effective 62 4.1.1 Cherry Tree Height, Center Of Gravity And Mass Measurnents During the 1985 cherry harvesting season, 65 sweet and 45 sour cherry trees that were about 10 years old were cut to determine tree height, gravity. and mass different tree trunk center of diameter sizes. Each tree for trunk diameter was measured 228 mm (9 in.) above the ground level, The sweet cherry tree trunk diameters ranged from 58 to 97 mm (2.3 to 3.8 in.) with an average value of 79 mm (3.1 in.) and standard deviation of 9.5 mm (0.38 in.). The sour cherry tree trunk diameters ranged from 61 to 89 mm (2.4 to in.) with an average value of 76 mm (3.04 in.) 3.5 and standard deviation of 7 mm (0.284 in.). The sweet cherry tree heights ranged from 2.90 to 4.67 m (114 to 184 in.) with an average value of 3.80 mm in.) and standard deviation of 0.62 m (24.56 in.). (149.7 The sour cherry tree heights ranged from 2.94 to 4.49 m (116 to 176.8 in.) with standard tree sweet an average value of 3.50 m deviation of 0,33 m (13 in.). height cherry. distributed (137.9 Thus, the in.) average was 0.30 m (12 in.) less for sour cherry Although when Figures 4.1 and 4.2, the plotted tree against heights tree were trunk and than linearly diameter, the correlation factors between height and diameter were very small (r = 0.2 for sweet cherry, and SWEET CHERRY TREE HEIGHT VS. 500-1 TREE TRUNK DIAMETER 450- (c m ) 350- HEIGHT 300- TREE 400- 250- •• 200 - 150- 100 TRUNK DIAMETER (c m ) FIGURE 4.1 SWEET CHERRY TREE HEIGHT VS. TREE TRUNK DIAMETER. SOUR CHERRY TREE HEIGHT VS. TREE TRUNK DIAMETER 4 5 0 -, 250- TREE HEIGHT (c m ) 350- 150- 50 5 .0 5 .5 6.0 6 .5 7 .0 7.5 8.0 TRUNK DIAMETER (c m ) FIGURE 4 .2 SOUR CHERRY TREE HEIGHT VS. TREE TRUNK DIAMETER. 8 .5 9.0 65 0.28 for sour cherry). The center of gravity above ground of each cherry tree was determined after the tree was cut, edge beam, balanced on a knife and measured. The center of gravity of the sweet cherry trees ranged from 1.07 to 1.78 m (42 to 70 in.) with an average value of 1.53 m (60.3 in.) and standard deviation of 0.13 m (5 in.). trees ranged from The center of gravity of the sour cherry 1.25 to 1.85 m (50 to 74 in.) with an average value of 1.85 m (59.4 in.) and standard deviation of 0.12 m (4.8 in.). Although the relationship between the tree mass center of gravity and the trunk diameter for both sweet and sour cherry trees was also linear, Figures 4.3 and 4.4, as illustrated the correlation factors were in again found to be small (r = 0.20 for both sweet and sour cherry). The weighing cherry mass of each cherry tree the tree after it had been cut. trees with an average was determined by The mass of sweet ranged from 8 to 37.1 kg (17.6 to 81.8 lb) of 19.9 kg (43,9 lb) and standard deviation of 6.2 kg (13.67 lb). Sour cherry tree mass ranged from 10.2 to 30,9 kg (22.5 to 68.1 lb) with an average of 20.5 kg (45.2 lb) and standard deviation of 5.37 kg (11.84 lb). When the relationship between tree mass and trunk diameter was fitted with a power curve, a high correlation was found (r = 0.83) for sweet cherry and 0.84 for sour 4.5 and 4.6. cherry), Figures SWEET CHERRY TREE CENTER OF GRAVITY VS. 200-1 TREE TRUNK DIAMETER 150- 125- CENTER 100 75- TREE OF GRAVITY (c m ) 175- 50- 25- TRUNK DIAMETER (c m ) FIGURE 4 .3 SWEET CHERRY TREE CENTER OF GRAVITY VS. TREE TRUNK DIAMETER. SOUR CHERRY TREE CENTER OF GRAVITY VS. TRUNK DIAMETER 200-1 175- IS O — 125- 100 - TREE CENTER OF GRAVITY (c E 75- 50 5.0 5.5 6.0 6.5 7.0 7.5 8.0 TRUNK DIAMETER (c m ) FIGURE 4 .4 SOUR CHERRY TREE CENTER OF GRAVITY VS. TREE TRUNK DIAMETER. 8.5 9 .0 SWEET CHERRY TREE MASS VS. TRUNK DIAMETER —.83 4 0 -, b = 2 .4 7 3 20 a> 03 - TREE MASS (kg) 30- 10- TRUNK DIAMETER (c m ) FIGURE 4 .5 SWEET CHERRY TREE MASS VS. TREE TRUNK DIAMETER. SOUR CHERRY TREE MASS VS. TREE TRUNK DIAMETER r=.84 cn 20 co - TREE MASS (kg) 30- 10 - 5 .0 5 .5 6.0 6 .5 7.0 7 .5 8.0 TRUNK DIAMETER (c m ) FIGURE 4 .6 SOUR CHERRY TREE MASS VS. TREE TRUNK DIAMETER 8 .5 9 .0 70 4.1.2 Stiffness And Damping Measurements The during many dynamic displacements of a cherry tree trunk the shaking operation have been the main concern studies strength, and This dynamic behavior of the tree trunk during harvesting can be simulated using the IMP trunk related to bark damage, displacement modeling. bark of program, if the the stiffness and the damping of cherry tree trunks are determined. During the 1985 cherry harvesting season, conducted to measure both linear and torsional sour (Montmorency factors variety) for tree corresponding diameters (small, selected a study was to medium, trunk three stiffness different and damping tree trunk and large). These diameters were to be 63 mm (2.5 in.) for small, medium, and cherry 114 mm (4.5 in.) 165 mm (6.5 in.) for large tree trunks. Three trunks of each size were analyzed. Force applied to for the linear stiffness and damping tests the cherry tree trunks using two sizes was of hydraulic cylinders. A 63 mm (2.5 in.) inside diameter (ID) hydraulic cylinder, with a 25.4 mm (1 in.) diameter rod used small trunks. to hydraulic pull the A 89 mm in.) ID cylinder with a 38 mm (1.5 in.) diameter rod was used to pull the medium and large trunks. (3.5 was 71 The pressure hydraulic pressure (1000 Each developing cylinders was transducers psi), the pulling monitored by force two in strain (San-Sym LX0540A for up to gage 6894 transducer was calibrated by recording electrical output for incremental changes in pressure was press. developed The kPa model LX0560A for up to 20680 kPa (3000 psi)). pressure that the press pressure gage. bjr a 41360 kPa (6000 psi) cylinder was equipped with its input hydraulic a precision Figure 4.7 shows the tree pull test setup as it was used in the field. The hydraulic cylinder used in trunk damping experiments was fastened to tractor drawbar. ended with chain about tree The stiffness and a beam extending from cylinder rod was connected to a lock mechanism. anarm This arm was connected to 2 m (80 in.) long circling around the a cherry trunk to transmit the pulling force from the hydraulic cylinder rod and the arm mechanism to the tree trunk. During operation the cylinder rod moved backward pulling mechanism with it and causing the chain to pull the the arm tree trunk to a new position. The arm mechnism lock then released causing the tree trunk A linear voltage calibrated trunk the to oscillate to rest. differential transformer (LVDT) was and connected to the cherry trunk to detect the horizontal displacement resulting from application of pulling force. The LVDT was mounted in a holder and a FIGURE 4 . 7 TREE PULL TE S T SETUP FOR UNEAR STIFFNESS. 73 positioned ground. The screw. test horizontal mounted above the LVDT rod was attached to the tree trunk by Undesired were at about 255 mm (10 in.) a lateral and vertical movements during the eliminated with the use of a spring absorber in-line between the tree attachement point and the LVDT rod. The LVDT signals were from the pressure transducers recorded on a Racal 4DS and four-channel the analog instrumentation tape recorder (Racal Recorders Inc., Covina, CA) A at data a tape 6000 Precision, speed spectral Danvers, MA) of 190.5 waveform was mm/s ( analyzer 7.5 in./s (Analogic used to digitize the ). Data analog signals to 6000 points over a period of 20 s. Each digitized signal were was recorded on a floppy disk. then used Calibration to convert the signal values force values or displacement values. factors into either A HP 7475A plotter was used to plot the results as graphs of force and displacement versus time, as shown in Figure 4.8 and 4.9. The stiffness factors (K) were determined from the force and curves. An and ..the displacement appropriate time along the curves was selected corresponding force and displacement ratio were calculated. In Figures 4,8 and 4.9 the selected time was 5,5 s and the corresponding force and displacement were and 10.86 30.2 mm, N/mm. respectively, 328 giving a stiffnesB factor The damping ratios were approximated by N of using LINEAR DISPLACEM ENTS M EASUR EM EN TS V E R S U S TIME 40 — 1 - 30— DISPLACEMENT (m m 20 - 10 - 0- - 10- -20- 1— i— i— |— i— i— i— |— i— i— i— |— i— r— i— |— i— i— i— ]— ■— i— i— |— i— i— i— |— r 2 4 6 8 10 12 14 TIME -1 0 -4 0 0.2 0 .3 TIME (s ) FIGURE 6.3 ROTATING MASSES ARE RUNNING ACCORDING TO SIMULATED TRANSIENT VELOCITY FUNCTION FOR A SHAKER HOUSING MASS OF 2 2 6 .5 kg. 0 .4 DISPLACEMENT (m m ) SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME SHAKER CO O) 1 11I 0 .4 TIME (s) FIGURE 6 .4 FREE SHAKING DISPLACEMENT VS. TIME AT MASS ROTATING FREQUENCY OF 15 HZ, AND SHAKER HOUSING MASS OF 2 2 6 .5 kg. 13 7 6.2 Variation Of The Magnitude Of The Rotating Masses Two smaller rotating mass values were evaluate their affect on shaker displacements. period of 0.353 s was again used, were a and the tested to A simulation rotating masses assumed to run counter to each other after starting at phase angle of zero degrees (mass initial starting posi t.ion ). The two rotating masses where first kg (2.17 slug) each 0.137, 0.137, directions, and reduced to 31.75 with mass moment of inertia equal 2 0.2756 kg.m in the x, y, and respectively. to z The transient frequency function again ranged from 0 to 15.66 Hz with an acceleration of 278 2 rad/s . The simulated shaker displacement in the x direction was about 20 mm (0.78 in.), 3 mm (0.12 in.) less than displacement using the original masses, this simulation left and drifted Figure 6.5. the During the shaker shifted 9 mm (0.35 in.) to the 8 mm (0.31 in.) to the right from the rest position. At (94.24 a steady state rotating mass frequency of 15 Hz rad/s) the simulated shaker displacement was 20 mm (0.78 in.) with a shaker shift of 11 mm (0.43 in.) and drift of 22 mm (0.86 in.), Figure 6.6. 13 8 Decreasing (1.24 the rotating masses further to 18.12 kg slug) each with mass moment of inertia equal to 0.07, 2 and 0.14 kg.m in the x, y, and z directions, 0.07, respectively, and the transient frequency function, resulted in a simulated shaker displacement in the x about 14 direction mm (0.55 in.) with a shaker shift of 8 mm of (0.31 in.) and drift of 7 mm (0.27 in.), Figure 6.7. At rad/s), in.) of a steady rotating mass frequency of 15 the Hz (94.24 simulated shaker displacement was 14 mm (0.55 with a total shaker shift of 8 mm (0.31 in.) and drift 17 mm (0.67 in.), Figure 6.8. From these displacement results the conclusions are: 1- The average decrease to ratio the of the shaker displacement rotating mass decrease was 4.4 average shaker shift or drift decrease to the mm/10 kg (0.78 in./lO lbs). 2- The shaker rotating (0.027 in./lO mass decrease was lbs). 1.5 mm/10 kg SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME 20 SHAKER -10H - 139 DISPLACEMENT (m m ) 10 -= 20- : -3 0 -: -5 0 0.0 0.1 0.2 0 .3 TIME (s ) FIGURE 6 .5 ROTATING MASSES ARE RUNNING ACCORDING TO SIMULATED TRANSIENT VELOCITY FUNCTION FOR A MASS OF 3 1 .7 kg. 0 .4 SHAKER DISPLACEMENT (m m ) SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME -1 0 -20 -3 0 -4 0 -5 0 - 0.0 0.1 0.2 0 .3 TIME ( s ) FIGURE 6 .6 FREE SHAKING DISPLACEMENT VS. TIME AT FREQUENCY OF 15 HZ. AND SHAKER ROTATING MASS OF 3 1 .7 kg. 0 .4 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME SHAKER DISPLACEMENT (m m ) 10-: -20 -3 0 -4 0 -5 0 -^ - 0.0 0.1 0.2 0 .3 TIME (s ) FIGURE 6 .7 ROTATING MASSES ARE RUNNING ACCORDING TO SIMULATED TRANSIENT VELOCITY FUNCTION FOR A MASS OF 1 8 .1 2 kg. 0 .4 -20 SHAKER DISPLACEMENT (m m ) SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME -3 0 -4 0 0.0 0.1 0.2 0 .3 TIME (s ) FIGURE 6 .8 FREE SHAKING DISPLACEMENT VS. TIME AT FREQUENCY OF 15 HZ, AND SHAKER ROTATING MASS OF 18.12 kg. 0 .4 143 6.3 Variation Of The Rotating Mass Acceleration During these tests, three different rotating acceleration combinations were chosen to study their on the stage. rest shaker displacement behavior during The the mass affect transient rotating masses were assumed to start from position at an initial phase angle (mass initial starting position). of zero the degrees The selected combinations of rotating mass accelerations were: 2 1- 280 and 270 rad/s . 2 2- 280 and 260 rad/s . 2 3- 328 and 246 rad/s . The of these tests indicated that rotating 2 mass accelerations of 280 and 270 rad/s for the inside and outside results rotating masses, respectively, decreased the simulated shaker maximum displacement slightly from 25 mm (1 in.) to 22 mm (0.86 in.). The total shaker shifted 15 mm (0.59 in.) to the left in the first cycle then drifted 24 mm (0.94 in.) to the right by the fifth cycle, Figure 6.9. 2 At 280 and 260 rad/s acceleration levels for the inside and outside rotating masses, respectively, the shaker maximum displacements decreased from 25 mm (1 in.) to 15 mm (0.59 as in.). The shaker shift and drift were the same 14 4 previously observed, Figure 6.10. The 328 greatest and difference in acceleration levels 2 rad/s resulted in a marked difference 246 displacement behavior. The largest shaker displacement of in was 25 mm (1 in.), and occured when both rotating masses were in phase. the The smallest displacement was phase angle between masses was shaker shift and drift were the Figure 6.11. 4 mm (0.15 in.), when nearly 180 degrees. The same as previously observed, From these results the following conclusions can be made: 1- Changing the acceleration levels of the inside outside rotating masses changes the and phase angle between the masses during startup and results in displacement followed by gallop (large small displacement in cycles) during startup. displacement two following The most noticeable gallop occured for the acceleration combination of 328 and 2 246 rad/s . 2- Changing the range the rotating mass accelerations, 2 of 328 to 246 rad/s , does not the shaker shift or drift. within affect SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME SHAKER DISPLACEMENT (m m ) 20-n -1 0 -20 -3 0 -4 0 -5 0 0.0 0.1 0.2 0 .3 0 .4 TIME ( b) FIGURE 6.9 ROTATING MASSES ARE RUNNING ACCORDING TO SIMULATED TRANSIENT VELOCITY FUNCTION FOR TWO DIFFERENT ACCELERATION LEVELS, 2 8 0 AND 2 7 0 rad/s.B. 0 .5 SHAKER DISPLACEMENT (m m ) SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME -1 0 -20 -3 0 -4 0 -5 0 - 0.0 0.1 0.2 0 .3 0 .4 TIME (s ) FIGURE 6 .1 0 ROTATING MASSES ARE RUNNING ACCORDING TO SIMULATED TRANSIENT VELOCITY FUNCTION FOR TWO DIFFERENT ACCELERATION LEVELS. 2 8 0 AND 2 6 0 ra d /s .s . 0 .5 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME 20-a SHAKER DISPLACEMENT (m m ) 10-: -10-E —20*: - 3 0 -E - 4 0 -E -5 0 0.0 0.1 0.2 0 .3 0 .4 TIME (s) FIGURE 6.11 ROTATING MASSES ARE RUNNING ACCORDING TO SIMULATED TRANSIENT VELOCITY FUNCTION FOR TWO DIFFERENT ACCELERATION LEVELS, 3 2 8 AND 2 4 6 ra d /s .s . 0 .5 148 6.4 Variation Of Eccentricity Of The Rotating Masses To vary the shaker rotating free-shake joint IMP eccentricity, model was modified by introducing a between the axis of rotation and the center for each rotating mass, of mass each Figure 6.12. slider of mass The center of gravity rotating mass was assumed to be initially 0,0025 mm (0.001 in.) away the from the mass axis of located rotation. The motion of each rotating mass slider joint was controlled by a slider opening the position command inside slider joints at the a specified IMP model. rate the center of gravity of each rotating mass would move causing mass rates shaker larger were tested (217, Three different slider 190, and 165 mm/s ) mass outward, forces to be produced as a result eccentricity product. By of the opening during the displacement simulation using the transient rotating mass frequency function . The starting phase angle between the rotating masses was zero. The model results indicated that by using two rotating masses opening at a gravity can reach 76 mm simulated increased shaker uniformly rate of 217 mm/s center of (3 in.) eccentricity in 0.353 s) the displacement started (their from zero to a maximum displacement of 25 mm and (1 149 FIGURE 6 .1 2 SLIDING ROTATING MASS MODEL 150 in.) as the frequency of 15.66 Hz was reached following transient function. The shaker drift during the the simlation was 7 ram (0.27 in.) and no shaker shift was observed, Figure 6.13. By decreasing simulated shaker from zero, the mass opening rate to 190 mm/s displacements again but at a slower rate. increased The maximum the uniformly displacement would have equalled the same 25 mm (1 in.) after 0.4 s. shaker The drift was stable at the same previous value of 7 mm (0.27 in.) and again no shaker shift, Figure 6.14. At the simulated from lowest mass opening rate of shaker displacements still zero, but at the slowest 165 mm/s, increased rate. uniformlly Final maximum displacement would again have been 25 mm (1 in.) after s because shaker of the final eccentricity and the 0.46 frequency. drift was again 5 mm (0.19 in.) and no shaker The shift was observed over the simulated period, Figure 6.15. The affects of using three different constant rotating mass frequencies (5, of 217 mm/s displacement always were would rotating 10, and 15 Hz) and a mass opening rate studied to determine "if increase uniformly if the but shaking was initiated by the shaker masses moving were the masses outward. The model results indicated that at mass frequencies of 5, 10, or 15 Hz, steady rotating the simulated shaker 1 51 displacement increased uniformly from zero to a maximum. The shaker drift was 5 mm (0.19 in.) at a frequency of 5 Hz and 9 and mm (0.35 in.) at 10 and 15 Hz, Figures 6.16, 6.17, 6.18. These test results lead t.o the following conclusions: 1- No shaker gallop or shift occured during startup period of the transient frequency when the function the rotating mass eccentricity was increased from zero at different rates. 2- Shaker drift frequency was minimized function eccentricity from by zero during the transient increasing to 76 mm the mass (3 in.) at shaker displacement was reached in about the different rates. 3- Full same time (0.353 s) by increasing the mass eccentricity at 217 mm/s while running at 15 Hz or by following the transient function to reach 15 Hz, although about twice as many shaking cycles were developed at the 15 Hz constant frequency. 4- These simulation results indicate that the gallop, shaking shift, drift operations and displacements might be shaker during controlled by increasing the rotating mass eccentricity from zero to the desirable position during either a transient frequency startup. startup or a steady state frequency SHAKER DISPLACEMENT (m m ) SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME CH- -1 0 -20 -3 0 -= -4 0 -5 0 0.0 0.2 0 .3 TIME (s ) FIGURE 6 .1 3 ROTATING MASSES ARE RUNNING ACCORDING TO SIMULATED TRANSIENT VELOCITY FUNCTION WITH MOVING ECCENTRICITY AT RATE OF 2 1 7 m m /s . 0 .4 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME 153 -20- SHAKER DISPLACEMENT (m m ) 10-= - 4 0 -= r-r-r-i 0.1 0 .3 0.2 TIME (s ) FIGURE 6 .1 4 ROTATING MASSES ARE RUNNING ACCORDING TO SIMULATED TRMSIENT VELOCITY FUNCTION WITH MOVING ECCENTRICITY AT RATE OF 190 m m /s . 0 .5 SHAKER DISPLACEMENT (m m ) SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME -1 0 -20 -3 0 -4 0 -5 0 - 0.0 0.1 0.2 0 .3 0 .4 TIME (s ) FIGURE 6.15 ROTATING MASSES ARE RUNNING ACCORDING TO SIMULATED TRANSIENT VELOCITY FUNCTION WITH MOVING ECCENTRICITY AT RATE OF 165 m m /s . 0 .5 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME SHAKER DISPLACEMENT (m m ) 20 -1 0 -3 0 -4 0 -5 0 - 0.0 0.1 0.2 0 .3 TIME (s) FIGURE 6 .1 6 ROTATING MASSES ARE RUNNING AT STEADY FREQUENCY OF 5 HZ WITH MOVING ECCENTRICITY AT RATE OF 2 1 7 m m /s . 0 .4 SHAKER DISPLACEMENT (m m ) SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME -10-j — 20~ —3D-= -4 0 -5 0 -- 0.0 0.1 0.2 0 .3 TIME (s ) FIGURE 6 .1 7 ROTATING MASSES ARE RUNNING AT STEADY FREQUENCY OF 10 HZ WITH MOVING ECCENTRICITY AT RATE OF 2 1 7 m m /s . 0 .4 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME 20- h SHAKER DISPLACEMENT (m m ) 10*: -10-: -20 -3 0 -= -4 0 -= -5 0 0.0 0.1 0.2 0.3 TIME (s) FIGURE 6 .1 8 ROTATING MASSES ARE RUNNING AT STEADY FREQUENCY OF 15 HZ WITH MOVING ECCENTRICITY AT RATE OF 2 1 7 m m /s . 0.-4 1 58 6.5 Variation Of The Starting Phase Angle Between The Hasses This starting shaker study was conducted to examine the affect of the phase angle between the rotating displacements. rotating masses between 2 rad/s on the During these shaker simulations the followed the transient frequency zero and 15.66 Hz at accelerations of 328 for respectively. the The inside and outside The shaker and rotating s, displacements were 246 mass, reach respectively. tested angles ranging from 0 to 360 degrees, inside function inside and the outside mass would the maximum frequency in 0.3 and 0.4 phase masses for starting by keeping the rotating mass at its original starting position reseting degrees resulting the outside rotating mass at counterclockwise from its original shaker displacements in the x, directions were then plotted, increments y, of position. and 45 The and x-y plane and are presented in Figures 6.19 to 6.42. The simulation displacement results indicated that using degrees starting between phase the angles ranging from rotating masses, zero the to by 360 shaker displacements in the x and y directions fluctuated between a maximum value of 25 mm (1 in.), when both masses were in 1 59 phase, and a minimum value of 4 mm (0.15 in.), when the masses were out of phase by 180 degrees. However, the shaker shift and drift were unstable at different phase angles. At a starting phase angle of zero degrees, the shaker planar motion was unstable during the simulation. The shaker shifted about 14 mm (0.55 in.) and drifted 14 mm (0.55 in.) in the x direction, and shifted 2 mm (0.07 in.) and drifted only 5 mm (0.19 in.) in the y direction. in the x direction was grater than displaced 42 mm The shaker in y direction. (1.65 in.) in the x direction and (1.18 in.) in t.he y direction, gallop respectively, It. 30 mm resulting in large shaker drift, Figures 6.19, 6.20, and 6.21. At a starting mass phase angle of shaker was also unstable . in.) and 6 mm respectively. to (0,23 45 degrees, the The shaker shift was 11 mm (0.43 in.) in the x and y directions, The shaker drift in the y direction increased 10 mm (0,39 in.) while it was only 12 mm (0.47 the x direction. in.) in The shaker gallop was observed in both the x and y directions, Figures 6,22, 6.23, and 6.24. At shifted a 90 degree starting mass phase angle, 5 mm (0.19 in.) and 9 mm (0,35 in.) in the x and directions, decreased (0.59 the shaker respectively. to The drift was x direction 5 mm (0.19 in.) while it increased to in.) in the y direction. direction in the observed to 15 The shaker gallop in the be smaller than y in the mm x y SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME 401 SHAKER 10160 DISPLACEMENT (m m ) 30- -20- -3 0 - -4 0 r-r-i-i 0.0 0.1 0.2 0 .3 0 .4 TIME (s ) FIGURE 6.19 SHAKER DISPLACEMENT IN THE X DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 3 2 8 AND 2 4 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 0 DEGREES. 0 .5 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE Y DIRECTION VS. TIME 40-1 (m m ) itH SHAKER 20H DISPLACEMENT 30 H CD -20 -30 -40 0.0 0.1 0.3 0.2 0 .4 TIME (s) FIGURE 6 .2 0 SHAKER DISPLACEMENT IN THE Y DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 3 2 8 AND 2 4 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 0 DEGREES. rr r~| 0.5 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X -Y PLANE VS. TIME (m m ) 20- SHAKER 100- 162 DISPLACEMENT 30- IN Y DIRECTION 40 ^ -10-20-3 0 - -4 0 -4 0 -3 0 -2 0 i— r-1'M| i i i i |i i i i | i i i i— ["T r i i ) i i i i ] -1 0 0 10 20 30 40 SHAKER DISPLACEMENT IN X DIRECTION (m m ) FIGURE 6,21 SHAKER DISPLACEMENT IN THE X -Y PLANE. MASSES ARE RUNNING AT ACCELERATIONS OF 3 28 AND 246 ra d /B .s . AT A STARTING PHASE ANGLE OF 0 DEGREES. SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME 4Q-i (m m ) 10H SHAKER 20H DISPLACEMENT 30 H 05 CO -1 0 -20 -3 0 H -4 0 + i 0.0 0.1 0.2 0 .3 0 .4 nGURE 6 .2 2 SHAKER DISPLACEMENT IN THE X DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 3 2 8 AND 2 4 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 4 5 DEGREES. 0 .5 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE Y DIRECTION VS. TIME SHAKER DISPLACEMENT (m m ) 4 0 -, 20- 10- -10 -3 0 - r-i-n -4 0 0.0 0.1 0.2 0 .3 0 .4 FIGURE 6.23 SHAKER DISPLACEMENT IN THE V DIRECTION MASSES ARE RUNNING AT ACCELERATIONS OF 32BI AND 2 46 ra d /s .s . AT A STARTING PHASE ANGLE OF 4 5 DEGREES. 0 .5 SHAKER DISPLACEMENT IN Y DIRECTION (m m ) SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X -Y PLANE VS. TIME 3020- 100-10- -20- -4 0 -4 0 -3 0 -20 -10 20 30 SHAKER DISPLACEMENT IN X DIRECTION (m m ) FIGURE 6 .2 4 SHAKER DISPLACEMENT IN THE X -Y PLANE. MASSES ARE RUNNING AT ACCELERATIONS OF 3 2 8 AND 246 ra d /s .s . AT A STARTING PHASE ANGLE OF 45 DEGREES. SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME SHAKER DISPLACEMENT (m m ) 302010- to -1 0 -20 -30H -40 0,0 0.1 0.2 0.3 T IM E ( s ) rad/s.s. ft* n r-t-T-i 0.5 0.4 d ir e c t io n . SIMUUTED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X -Y P U N E VS. TIME (m m ) 20- DISPLACEMENT 30- IN Y DIRECTION 4 0 -. 10-^ 00 -10-j - SHAKER 00 0- 20- -3 0 - -4 0 -4 0 iiIii -3 0 i [ i i T ' i [ i t i i-1 t~r~ i ) p r ' i i <~ f 'i > i i | i i -2 0 -1 0 0 10 20 30 SHAKER DISPUCEMENT IN X DIRECTION (m m ) FIGURE 6 .3 9 SHAKER DISPUCEMENT IN THE X -Y P U N E . MASSES ARE RUNNING AT ACCELERATIONS OF 328 AND 2 46 ra d /s .s . AT A STARTING PHASE ANGLE OF 2 7 0 DEGREES. 1 1I 40 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME (m m ) 10 - SHAKER 20 DISPLACEMENT 30- - 03 -1 0 -20 -3 0 - T T l-f -4 0 0.0 0.1 0.2 0 .3 0 .4 TIME (s ) FIGURE 6 .4 0 SHAKER DISPLACEMENT IN THE X DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 3 2 8 AND 2 4 6 rad/s.B ? A t A STARTING PHASE ANGLE OF 3 1 5 DEGREES. 0 .5 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE Y DIRECTION VS. TIME 40 n 20 H SHAKER DISPLACEMENT (m m ) 30 oo Cl -10H -20H —3 0 —^ -4 0 0.0 0.2 0 .3 0 .4 TIME (s ) FIGURE 6.41 SHAKER DISPUCEMENT IN THE Y DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 32B AND 2 46 ra d /s .s . AT A STARTING PHASE ANGLE OF 3 1 5 DEGREES. 0 .5 SIMULATED SHAKER DISPUCEMENT AT THE PAD CENTER IN THE X -Y PLANE VS. TIME 40 30 20 10 0 10 20 30 40 f i' r i' | i i i i - [ r ' i i t | i i i i j i i i i j i i i i j i i t i | i i it -] ) -3 0 -2 0 -1 0 0 10 20 30 40 SHAKER DISPUCEMENT IN X DIRECTION (m m ) FIGURE 6 .4 2 SHAKER DISPUCEMENT IN THE X -Y PLANE. MASSES ARE RUNNING AT ACCELERATIONS OF 3 2 8 AND 2 46 ra d /s .s . AT A STARTING PHASE ANGLE OF 3 1 5 DEGREES. 18 7 180 and 225 degrees. 3- The shaker shift, drift and gallop problem can be essentially eliminated by using a starting phase of 225 degrees. The above shaker displacement results for different starting phase angles between the rotating masses raised the question whether rotating mass acceleration, between them. angles 6.21) the shaker drift was related To answer this question, selected small the or to the starting phase angle two starting that resulted in large drift (zero and to drift (225 degrees, degrees, Figure phase Figure 6.36) were for tests at both higher and lower accelerations. 2 The higher accelerations were 358 and 276 rad/s , and the 2 lower were 298 and 216 rad/s , for the inside and outside masses, respectively. The phase model results indicated that by using a angle accelerations of starting 225 degrees between the masses and two 2 of 35B and 276 rad/s , the simulated shaker displacement was observed to be stable. (0.1.9 in.) and 3 mm (0.11 in.), Drift was only 5 mm with no shift, in the x and y directions, respectively, Figures 6.43, 6.44, and 6.45, using Changing the starting phase angle to zero degrees and 2 the same acceleration values (358 and 276 rad/s ) resulted in unstable shaker displacements. The shaker shift 1 88 was 14 mm (0.55 in.) and 2 mm (0.07 in.) in the x and y direction, respectively. The shaker drifted 17 mm (0.66 in.) and 7 mm (0.27 in.) in the x and y directions, respectively, Figures 6.46, 6.47, and 6.48. These results reflect the same obtained at degrees, Figures 6,21 same shaker displacement the same starting phase angles but at 2 acceleration levels (328 and 246 rad/s ). The and 6.36) displacement results (zero and two results 225 different were also obtained using lower acceleration levels of 298 and 216 2 rad/s , compared with the original acceleration levels (328 2 and 246 rad/s ) at starting phase angles of zero and 225 degrees, Figures 6.49 to 6.54. The results regarding shaker displacement behavior using high and low acceleration levels at two starting phase angles was not of zero and 225 degrees indicated that shaker drift affected by using different unequalrotating mass accelerations. Shaker drift seems only related starting phase angle between the rotating masses. to the SIMUUTED SHAKER DISPUCEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME 4 0 -] (m m ) 20 DISPUCEMENT 30- 10 - - 03 CO SHAKER - 10 - -20- -3 0 - m-j -4 0 0.0 0.1 0.2 0 .3 0 .4 TIME ( s ) FIGURE 6 .4 3 SHAKER DISPUCEMENT IN THE X DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 3 5 8 AND 2 76 r a d /s . 3. AT A STARTING PHASE ANGLE OF 2 2 5 DEGREES. 0 .5 SIMULATED SHAKER DISPUCEMENT AT THE PAD CENTER IN THE Y DIRECTION VS. TIME 4 0 -] (m m ) 10- SHAKER 20- DISPUCEMENT 30- -10- -20-3 0 - -4 0 0.0 0.1 0.2 0 .3 0 .4 TIME (s ) FIGURE 6 .4 4 SHAKER DISPUCEMENT IN THE Y DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 3 5 8 AND 2 7 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 2 2 5 DEGREES. 0 .5 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X -Y PLANE VS. TIME (m m ) 20- SHAKER DISPLACEMENT 30- IN Y DIRECTION 40 ^ 10- 0co -10- -20-3 0 - -4 0 T I I— I |— I I— I I— |— I— I— I— I— |— I— I— I— I— ]— I— I— I— I— | 1 1 I— I— |— -4 0 -3 0 -2 0 -1 0 0 10 20 — I— i— i— r n 30 SHAKER DISPLACEMENT IN X DIRECTION (m m ) FIGURE 6 .4 5 SHAKER DISPLACEMENT IN THE X -Y PLANE. MASSES ARE RUNNING AT ACCELERATIONS OF 35B AND 2 7 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 2 2 5 DEGREES. 40 SHAKER Z 6 I DISPLACEMENT (m m ) 40- SIMULATEO SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME r-r-r-, 0 .5 TIME (s) FIGURE 6 .4 6 SHAKER DISPLACEMENT IN THF" y niBFPTinw MASSES ARE RUNNING AT ACCELERATIONS OF 3 58 AND 2 7 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 0 DEGREES. SIMUUTED SHAKER DISPUCEMENT AT THE PAD CENTER IN THE Y DIRECTION VS. TIME 40-t (m m ) SHAKER 10- 193 20- DISPUCEMENT 30 -10- -20- -3 0 -4 0 0.0 0.1 m-i 0.2 0 .3 0 .4 TIME ( s ) FIGURE 6 .4 7 SHAKER DISPUCEMENT IN THE Y DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 3 5 8 AND 2 76 ra d /s .s . AT A STARTING PHASE ANGLE OF 0 DEGREES. 0 .5 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X -Y PLANE VS. TIME (m m ) 20- SHAKER DISPLACEMENT 30- IN Y DIRECTION 4 0 -. 0- (O a -1 0 -20- -3 0 - -4 0 -4 0 -3 0 -20 -1 0 20 30 SHAKER DISPLACEMENT IN X DIRECTION (m m ) FIGURE 6 .4 8 SHAKER DISPLACEMENT IN THE X -Y PLANE. MASSES ARE RUNNING AT ACCELERATIONS OF 3 5 8 AND 276 ra d /s .s . AT A STARTING PHASE ANGLE OF 0 DEGREES. 40 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME 40-i (m m ) 20- DISPLACEMENT 30- 10CD Ol SHAKER -10- - 20- -3 0 -4 0 - 0.0 0.1 0.2 0 .3 0 .4 TIME (s ) FIGURE 6 .4 9 SHAKER DISPUCEMENT IN THE X DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 2 9 8 AND 216 ra d /s .s . AT A STARTING PHASE ANGLE OF 2 2 5 DEGREES. 0 .5 SIMULATED SHAKER DISPUCEMENT AT THE PAD CENTER IN THE Y DIRECTION VS. TIME (m m ) 10 - SHAKER 20- DISPLACEMENT 30- - 10 - - 20 - -3 0 -4 0 0.0 0.1 0.2 0 .3 0 .4 TIME (s ) FIGURE 6 .5 0 SHAKER DISPUCEMENT IN THE Y DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 298 AND 2 16 ra d /s .s . AT A STARTING PHASE ANGLE OF 225 DEGREES. 0 .5 CENTER IN THE X -Y PLANE VS. TIME (m m ) 20 SHAKER DISPLACEMENT 30 IN Y DIRECTION 4 0 -. 0(O -j -1 0 •20 30 -4 0 -3 0 -20 -10 0 io 20 40 SHAKER DISPLACEMENT IN X DIRECTION (m m ) FIGURE 6.51 SHAKER DISPLACEMENT IN THF y - y p i a w e MASSES ARE RUNNING AT ACCELERATIONS OF 2 9 8 AND 2 1 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 2 2 5 DEGREES. * SIMUUTED SHAKER DISPUCEMENT AT THE PAD CENTER IN THE X DIRECTION VS. TIME 30- - SHAKER DISPUCEMENT (m m ) 20 - 10 - - 20 - -3 0 - -4 0 0.0 0.1 0.2 0 .3 0 .4 TIME (a) FIGURE 6 .5 2 SHAKER DISPUCEMENT IN THE X DIRECTION MASSES ARE RUNNING AT ACCELERATIONS OF 2 9 8 AND 2 1 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 0 DEGREES. 0 .5 SIMULATED SHAKER DISPUCEMENT AT THE PAD CENTER IN THE Y DIRECTION VS. TIME (m m ) 30- SHAKER DISPUCEMENT 10 - - 10 - - 20 - -3 0 - -4 0 0.0 0.1 0.2 0 .3 0 .4 TIME (s) FIGURE 6 .5 3 SHAKER DISPUCEMENT IN THE Y DIRECTION. MASSES ARE RUNNING AT ACCELERATIONS OF 2 9 8 AND 2 1 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 0 DEGREES. 0 ,5 SIMULATED SHAKER DISPLACEMENT AT THE PAD CENTER IN THE X -Y PLANE VS. TIME 3020 - 10 - 200 SHAKER DISPLACEMENT IN Y DIRECTION (m m ) 4CH 0- - 10 - - 20- -3 0 -4 0 i— i— i— i— [— i— i— i— i— |— i— i— i— i— [— i— i— i— i— i— i— i— i— i— |— i— i— i— i— [— i— i— i— r-[-1 * * * I -4 0 -3 0 -2 0 -1 0 0 10 20 30 40 SHAKER DISPLACEMENT IN X DIRECTION (m m ) FIGURE 6 .5 4 SHAKER DISPLACEMENT IN THE X -Y PLANE. MASSES ARE RUNNING AT ACCELERATIONS OF 2 9 8 AND 2 1 6 ra d /s .s . AT A STARTING PHASE ANGLE OF 0 DEGREES. CHAPTER 7 7. SUMMARY AND CONCLUSIONS 7.1 SUMMARY In tree recent years, growers have reported that decline (loss of vigor and yield, cherry resulting in early of the orchard) is an increasing problem where mechanical harvesting of cherries is being practiced. Trunk bark often replacement damage (crushed cambium, split and torn bark) occurs during trunk shaking, and can result in tree decline. A possible cause of this damage is the transmission of high dynamic forces between the shaker and the bark during shaker operation. A Program C-clamp computer program entitled Integrated Mechanisms (IMP) was selected as a tool for modeling a trunk harvesting. The shaker goals that is widely used of the study were to shaker displacements with and without tree for Friday cherry simulate the attachment, and to study the affects on shaker displacement behavior caused by changing some shaker physical properties or operating procedures. During physical the 1985 properties cherry harvesting for both sweet and sour season, some cherry trees were measured and analyzed. The properties determined were : 201 20 2 tree center of gravity above ground, tree mass above ground, trunk stiffness coefficients (linear and torsional), and tree damping coefficients as related to trunk diameter. The shaker physical were properties of a Friday C-clamp trunk measured and analyzed to determine the shaker housing mass, mass moment of inertia, eccentrici1y , linear and torisonal stiffness and damping of the suspension bars, rotating mass, and the physical dimensions mass of the shaker. These used as tree and shaker physical properties parameters in the free-shake and simulation the models. free-shake frequency were then shaker-tree The displacement results obtained vibration model stage were compared. during the IMP from transient The simulation indicated a maximum displacement in the x direction of 23 mm (0.90 in.), only 2 mm (0.07 in.) less than the value obtained photographic study conducted by others. The total from a shaker shift simulated by the shaker model was 11 mm (0.43 in.) and the shaker drift was 15 mm (0.59 in.), 5 mm (0.19 in.) less than the value obtained from the photographic study. steady state simulation at a frequency of 15 During Hz the displacement was 25 mm (1 in.), almost the same displacement obtained simulated from the shaker shift by the model was 9 mm (0.35 in.) while the drift was 34 mm (1.33 in.), photographic study. The only 5 mm (0.19 in.) larger than that 203 found in the photographic study. Thus, the IMP model appears to agree closly with the results obtained during actual free-shaking operation. The shaker-tree model, with no tree damping was used to simulate tree trunk results indicated stiffness displacement. maximum x displacements of 20 to The 25 (0,78 to 1 in.) at three steady state frequencies of 5, and 15 Hz. When the introduced in before reached the it testing the tree the model, stiffness the program specified and simulation IMP program in several ways it that the stiffness matrix algorithm was not tests were stopped time. was mm 30, damping simulation or After concluded accurate, thus requiring a nonzero stiffness matrix (the shaker-tree model) could not be conducted. Tests their of several shaker physical property changes and affect on the shaker displacement behavior indicated that : the average ratio of the shaker displacement increase to the shaker housing mass decrease was 11 mm/100 kg in./100 lbs); decrease to the average ratio of the shaker displacement the rotating mass decrease was 4.4 mm/ (0.08 in./lO lbs); (0.19 10 kg the average ratio of the shaker shift or drift increase to the shaker housing decrease was 4.4 mm/100 kg (0.07 in./lOO lbs); the average shaker shift or drift decrease to the shaker rotating mass decrease was 1.5 mm/10 kg (0.027 in./lO lbs). 204 The shaker displacement was simulated using different transient accelerations for the rotating masses. The results indicated that there was no relationship between the magnitude of equal accelerations for the rotating masses and the shaker drift. However, using unequal accelerations for the inside and outside rotating masses did change the angle between the masses, the drift of the shaker, phase and the displacement behavior of the shaker. A uniform, or regular, increase in shaker displacement is believed operation. (change to The be desirable when affect eccentricity startup) was increase uniformly, of using starting shaking rotating masses from zero to a maximum during shaker simulated. and The movable the displacement shaker shift was and found drift to were minimi zed. Finally, to determine gallop could be minimized, phase angles maximum shift, angle of degrees. related Starting not have gallop. zero This only if shaker shift, drift and different rotating mass starting were tested using the free-shake model. The drift and gallop occured at a starting phase degrees shift, and the drift minimum occured and gallop was to the rotating mass starting acceleration at found phase to shift, be angles. or final steady state frequency a significant affect on shaker 225 drift did or 205 7.2 Conclusions According program to to the results obtained from using the model the Friday C-clamp trunk IMP shaker displacement behavior, the following conclusions were drawn: 1- The IMP program was a useful tool in modeling displacements of the C-clamp trunk shaker the because of the following: a. The IMP model displacements, b. The predicted shift, the and free-shake drift. IMP model was capable of testing different shaker physical property changes and their effect on the shaker displacement behavior. 2- The average ratio of the shaker displacement increase to the shaker housing mass decrease was 11 mm/100 kg (0.19 in./ 100 lbs). 3- There was no relationship between the magnitude of acceleration of the rotating masses and the shaker shift or drift. 4- The average ratio of the decrease to mm/10 kg (0.78 in./lO lbs). 5- The average increase to shaker displacement the rotating mass decrease was ratio of the shaker shift the shaker housing decrease or was 4.4 drift 4,4 206 mm/100 kg (0.07 in./lOO lbs). 6- The average decrease ratio of the shaker or Bhift drift to the shAker rotating mass decrease was 1.5 mm/10 kg (0.027 in./lO lbs). 7- The shaker gallop, shift the transient controlled that by and drift behavior during startup of the using a movable shaker mass could eccentricity is zero when the shaker starts and a within 0,353 results were initially to 0.45 s after be maximum startup. also obtained when the Similar shaker was running at the steady state frequency of 15 Hz. 8- The shaker gallop, could be minimized by using a particular position angle shift and drift during startup starting for the inside mass and a starting of 225 degrees counterclockwise phase between it and the starting position of the outside mass. 9- The largest shaker gallop, at shift and drift occured a starting phase angle of zero degrees between the masses. 10- The the shaker shift and drift was starting phase related angle between the only to rotating masses. 11- The tree IMP program was not able to displacements. modelthe The program was not shakerable to 2 07 numerically handle shaker-tree model. the tree stiffness in the 208 7.2-1 Scope And Limitations Some limitations were encountered during this study, which can be summarized as follows: 1- The of IMP program can only handle a degrees-of-freedom analysis which in a vibration involved a 9 is larger limited than system. degree-of-freedom the IMr number My system, designers had previously tested. 2- The stiffness algorithm apparently is nonfunctional in the dynamic mode of the IMP program. 3- Because of shalier-trep the stiffness algorithm displacement. simulated as planned. behavior problem, could not the be 2 09 7.2-2 Future Research Needs The author believes that further simulation and field research is needed in the following areas; ]- Since the tractor which carries the shaker modeled as a fixed mass (ground) in the IMP model, a more accurate model could taking into into However, the increased before the IMP shaker be developed tractor vibration shaker-tree system. consideration the contribution was program capability must the tractor contribution can be be modeled. 2- During the modeling stage, properties were ignored, damping trunk some shaker physical such as the stiffness and of the pad used between the shaker and the in the tree-shaker stiffness and damping, stiffness and damping. model, and suspension clamping bar cylinder These properties should be evaluated in future studies. 3- Studies forces the tree are needed which measure the dynamic generated between the shaker clamp pads and tree trunk, and the corresponding shaker displacements. information might Careful analysis of lead to a better shaker and that design 2 10 and result in reduce trunk bark damage. 4- More information on the actual displacements observed when shaking cherry tree trunks of various diameters would be very helpful for verification of simulation results. 5- The displacement of cherry tree trunks might modeled more accurately using a different procedure, such Appropriate applied forcing finite three trunk modeling element functions, analysis. from to the finite element model describe 6- A as be 3 above, might better behavior. dimensional model for the shaker-tree system is needed to take into shaker and tree properties in a.l 1 three dimensions and z), consideration (x, y, tree displacements in all three dimensions. the and to invesigate the shaker and 7- The apparent benefits of reduced shaker gallop drift should shaker to : a maximum These the trunk permit starting the rotating masses at phase angle of 225 degrees on each permit for be tested by redesigning and increasing during trunk, the eccentricity from zero to each trunk. two changes appear to offer the best chance eliminating the startup phase on and; the shaker gallop and drift that are believed to contribute to bark damage. REFRENCES References 1. Adrian, P. A. and R. B. Fridley. Mechanical Fruit Tree Shaking. California Agriculture 12(10): 3, 1958. 2. Adrian, P. A. Forced Vibration OfA Tree Limb, ASAE No. 63-642 D, 1963. Paper 3. Adrian, P. A. and R. B. Fridley. Dynamics And Design Criteria Of Inertia-type Tree Shaker. Transactions of the ASAE 8(1):12-14, 1965. 4. Adrian, P. A., R. B. Fridley, D. H. Chaney, and K. Uriu. Shaker-Clamp Injury to Fruit and Nut Trees. Calif. Agric. 19(8):8-10, 1965. 5. Affeldt, H. A. Digital Analysis Of The Dynamic Response Within Trunk Shaker Harvester Systems. M.S. Thesis, Agr. Eng. Dept., Mich. State Univ., E. Lansing, MI 48824. 226 p, 1984. 6. Alper, Y., A. Foux and U. M. Peiper. Experimental Investigation of Orange Tree Dynamics Under Mechanical Shaking. J. Agr. Eng. Res. 21 (2) :121-131, 1976. 7. Beljakove, V., P. Manolov and A. Nikolov. Effect of Mechanical Harvesting Using Tree Shakers On The Root System And Physiological Processes of Fruit Trees. Selskostopanska Tehnika 16(6):3-14, 1979. 8. Berlage, A. G., and Willmonth, F. M. Fruit Removal Potential Of High Frquency Vibrations. Transactions of the ASAE 17(2):233-234, 1974. 9. Brown, G. K. Some Factors Affecting The Longitudinal Shear of Bark From Fruit Tree Limbs. M. S. Thesis'. Agr. Eng. Dept., Univ. of California, Davis, 1965. 10. Brown, G. K. Harvest Mechanization Status Horticultural Crops. ASAE Paper No. 80 - 1045, 1980. For 11. Brown, G. K . , J. K. Frahm, R. L. Ledebuhr, and B. F, Cargill. Bark Damage When Trunk Shaking Cherry Trees. ASAE paper No. 82-1557, 1982. 12. Brown, G. K., J. R. Frahm, L. J. Segerlind, and B. F. 2 11 2 12 Cargill. Shaker Damage To Cherry Bark--Causes & Cures. Proc. Int’l Symp. Fruit, Nut, and Veg. Harv. Mech., Spec, pub. 5-84, ASAE, 2950 Niles R d ., St. Joseph, Ml 49085. p. 364-371, 1984. 13. Brown G, K., L. J. Segerlind, and P. L. Richey. Bark Stress Caused By Trunk Shaker Displacements. ASAE paper, No. 84-1066, 1984. 14. Cargill, B. F . , G. K. Brown and M. J. Bukovac. Factors Affecting Bark Damage To Cherry Trees By Harvesting Machines. Mich. State Univ., CES, AEIS Bull. No. 471. June, 6 pp. 1982. 15. Cook, J. R., and R. H. Rand. Vibratory Fruit Harvesting: A Linear Theory Of Fruit-Stern Dynamics. J, Agr. Eng. Res. 14(3): 323-330, 19C8. 16. Devay, J. E . , W. H. English, F. L. Lukezic and H, J. O' Reilly. Mallet Wound Canker of Almond Trees. Calif. Agric. 14(8):8-9, I960 17. Diener, R. G., F. H. Buelow, and G. E. Mase. Viscoelastic Analysis Of The Behavior And Properties Of Cherry Bark And Wood Under Static And Dynamic Loading. Transactions of the ASAE 11(3): 323-330, 1968. 18. Diener, R. G., J. H. Levin, and Strength Properties Of Cherry, The Influence Of Limb Mass And Transactions Of the ASAE 11(6): B. R. Tennes. Directional Apple, and Peach Bark And Diameter On Bark Damage. 788 and 791, 1968. 19. Drake, S. R. Introduction to The Symposium- The Influence Of Mechanical Harvesting On The Quality Of Horticultural Crops. Hort. Sci. 18(4): Spec. Insert p.406, 1983. 20. Esau, K. Plant Antatomy. John Wiley and Sons, Inc., New York, 1965. 21. Frahm, J. R . , G. K. Brown, and L. J. Mechanical Properties Of Trunk Shaker Pads. No. 83-1078, 1983. 22. Fridley, R. B . , and P. A. Vibratory Fruit Harvesting. January, 1960. Segerlind. ASAE Paper Adrian. Some Aspects Of Agr. Eng. 41(1):28-31, 23. Fridley, R. B . , G. K. Brown, and P. A. Adrian. Strength Characteristics of Fruit Tree Bark, Hilgardia 40(8):205222, August, 1970. 213 24. Halderson, J. L. 1966. Fundamental Factors in Mechanical Cherry Harvesting. Transactions of the ASAE, 9(5):481— 684, 1966. 25. Hoag, D. L., J. R. Hutchinson, and R. B. Fridley, Effect of Proportional, Nonproportional and Nonlinear Damping On Dynamic Response Of Tree Limbs. Transactions of the ASAE 13{6) : 879-884, 1970. 26. Hoag, D. L . , R. B. Fridley, and J. R. Hutchinson. Experimental Measurement Of Internal and External Damping Properties Of Tree Limbs. Transactions of the ASAE 14(1): 20-24, 1971. 27. Hussain, A. A. M . , G. E Rehkugler, and W. W. Gunkel. Tree Limb Response To Periodic Discontinuous Sinusoidal Displacement. Transactions of the ASAE 18(4): 614-615, 1975. 28. Khalilian, A., and W, J. Chancellor. Analysis and Testing Of A Spring-Load Tree Shaker. ASAE Paper No. 78-1019, June, 1978. 29. Kirk, D. E . , and D. E. Booster. Identifying Damage Sources In Mechanically Harvested Sweet Cherries. Transactions of the ASAE 22(1): 21-26, 1979. 30. Kirk, D, E., L. C. Jenson, and D. E. Booster. To Measure Tree Trunk Movement During Mechanical Cherry Harvest. Agr. Eng. 61(11): 15-17, November 1980. 31. Kronenberg, H. G. Possibilities For Mechanical Harvesting. J. Agr. Eng. Res. 9 (2):194-196, 1964. Fruit 32. Levin, J. H., H. P. Gaston, S. L. Hedden and R. T. Whittenberger. Mechanizing The Harvest Of Red Tart Cherries. Quart Bull. 42(4):42-60. Mich. State Univ. Agr. Expt. Sta. E. Lansing, MI 48824. May, 1960. 33. Marshall, D. E Determining motion of mechanical harvesting system with photographic techniques. ASAE Paper No. 86-1556, 1986. 34. Mitchell, A. E., and J. H. Levin. Tart Cherries Growing, Harvesting, and Processing for Good Quality. Ext. Bull. E-654, Farm Science Series, 1969. 35. Moini, S., and J. A. Miles. Simulation Of Tree Response To Vibration. ASAE Paper No. 80-3526, 1980. 2 14 36, Michigan Department Of Agriculture, Michigan Agricultural Statistics. 80 pp. P. O. Box 20008, Lansing, Mi 4890], 1985. 37. Ortiz-Canavate, J., J, R. Gil, and F. J. Juste. Design and Testing Of Tree Shaker. ASAE Paper No. 80-1045, 1980. 38. Peterson, D. L. and G. E. Monroe. Continuously Moving Shake-Catch Harvester, Transactions of the ASAE 20{2): 202-205, 209, 1977. 39, Phillips, A. L . , J. R, Hutchinson, and R. B. Fridley. Formulation of Forced Vibrations of Tree Limbs With Secondary Branches. Transactions of the ASAE 13(1): ISS­ U E , 1970. 40, Upadhyaya, S. K., J. R. Cooke, and R. H. Rand. Limb Impact Harvesting, Part 1. Finite Element Analysis. ASAE Paper No. 79-1054, 1979. 41. Young, C., and R. B. Fridley. Simulation Of Vibration Of Whole Tree Systems Using Finite Elements. Transactions of the ASAE 8(3):475-481, 1975. APPENDIX A Free Vibration C-Clamp Trunk Shaker Model o a *d o o a - a *d 0 2 0 0 0 0 0 2 >0>>>>>0 g > go 55° > ►3 *3 *6 >-3 •-* > > > > 2 ► 2 > > > > > 2 >>2 •3 *3 'OH—'•a *d *d *d•*" 53-—• 2 2 2 2 2 ' - ' ootr1O O O O t 1 0 0 0 0 0 0 0 0 >— 2 2 2 ? 2 *— ! 22^ ►3 ►J « ►3 >3 *0n »3 *3 >3 *3 n >lii 2 2 2 • o * a * a * o 2 c i 2 2 2m *d *d m CTi' O it * CO M M ' m M o HU>CO «*J« * ' TJ ' •Q' ^ *0 to M " > > > > 10 ' > > > 00 CD CD CD CD CD CD" > > M > CD tS CD" 01 01 01 01 oi oi 2 a u H Eo cn cn w 2 ' — ' — CO tn n« O'-'w(D w *J)— n n b " II D II ii ii " II n ii i—• n o o o id if* M M if* 4 * m 2 M O M UIIDIOOH Id o O VOCO O if* O O ' O" " " o UUMHH " to M M " CO CD co co o o cn WUIlP ltl U O O * 0 oo a s- f.l•« « ' -sj - o o O ' O O M •a O M A.1 ►o Co 2 M O o o o o o 2 2 a a c n o a c n o o w a o c n o o w r a > > 2 > > 2 > > 2 > > 2 > > 2 so 2 2 e s 2 2 0 0 1 3 0 0 6 0 0 0 S 0 0 w 0 0 65 ' l-H l— l H H ^ H H - - S H H —' M M 0 ss 55 0 2 2 0 2 S S diS Cl pt 2 •“* 2 2 O " —* -H**" 0 "*H sj * i i t - , 2 0 0 0 2 0 2 0 B 0 2 0 2 0 3 3 0 2 D < T il-'C T v ta tO 50 Cl M Cl 2 4* a O 3)* ^ b ^ ^ 3* 1 31" — ' — 31 " 31 n 2 ci Ci ci n 2 ci 2 r)C0vDD0O3OoC4fe0"JC0tncnMb0ciEd — -o 'j 'j M" ' ' 4* M 4* 4* " • 01O 9H O O OI 1 — 1 MM 4* Cl jj 1 ^ • Cl Cl • M ' ' cn 4* X I— CO to 00 M" 0 0 ' '• M it* to ' ' • M po ' • ' oa a> cji it* '• '• M O'! M 03 if* -O ' '• 4* 4* B oa ' ' MM MM • • Cl M O" " 0 M if* M i— i 0 «• * Cl Cl 4* O CO -J it* M"> M Cl H ' '• 03 CO M 4* 4* M O M M 4* 2 0 M " M • M «• * • C l " 00 03" Cl O OJ* nJ Q3 ^ « O CJI Cl 01 '• " ' 4* CO to 03 ' it* it* 1 — 1 O ' CD" "J it* M O "• 4* > 00" O O '• ► d it* 0 01 m • "• Cl M Cl m ' ro 'C i O 4* • it* "• Cl M Cl O O • "a M 4* • • M Cl M M " O it* • Cl • " C J1 M" O O • M■ O O 2 -*J !>" '♦ *«•»• CO M ^ • if*cn r~!m M' M" m M • " • M" ^ M • ^ MM It* M" * M • it* « % "• " ^ 4 M M M • 4*• M" O O W O 2 O 2 Cl > > 2 > H > H 2 *3*3W *3< »3< 0 > > cd > o > o c a 0 0 z O O S m c d c o H l-H — 0 *3 CD *3 II 2 2 0 < ca < cd a 2 2 M O - ' O - ' W " 0 o 0 0 > 0 o o c m g m x 4* M 4* *3" •’3 " H •» •* — CD O CD 0 G C| II — U> — M if* 4* C_| C-j — C| — ' —'—4* W || to II — Ci -— Cl It It II CO II ro a im 4* 4* M 4* •» *0 M * 4* 4* Cl Cl M M * • •a ^ Cl Cl Cl Cl • a O O "• "• Cl Cl " " 01 OI 0 0 4* 4* "• "a " " M 4* M 4* O M 'O M • " " M M " ■ O Cl "• " * " Cl M 4* O " "• 4* OI M 4* • " to Cl CJI ' to Cl Cl Cl (J1M " O M' O O Cl * • * % Cd 2 > W M 2 ► 3 a 0 a c n M 2 Ci *3 X CD Vi 2 > Pi CD » Ci O l-H 2 *3 m • • • • M M • O "« M "J * Cl O "• 4* * M * • • O • • • • O • # Cl " M " M O *■ — . O "• M >4 • ■ "• 4* M • Cl « «* CJI " 0 CJI " 0 • Cl • • « • m * • • cn *> 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 to 4 ► H 4 a 4 4 > 4 4 4 O 1 4 n 4 4 c > 4 2 4 53 4 4 -2 4 2 *3 4- 4- 4 444444- * * * * 44' 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 4 2 4 > 401 4 4 4 4 > *< 2 4 r* G 4 1 2 4 Oi 2 4 -0 4 m 2 2 4 0 4 2 > 4 Pi 4 C D 4 2 4 4 2 4 O 4 a 4 CD 4 r 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 POINT*LI)=P12,P13,P14,P15,P12 DATA POINT*P13,ABS)=20,45,0 DATA POINT*P14,ABS)=64,45,0 DATA POINT*P15,ABS>=69,38,0 POINT(LI)=P19,P18,P16,P17 DATA POINT*P16,ABS)=47,45,0 DATA POINT(P17,ABS)=41,83,0 DATA POINT(P18,ABS)=45,45,0 DATA POINT(P19,ABS)=40,76,0 POINT*L1)=P23,P22,P20,P21 DATA POINT(P20,ABS)=28,45,0 DATA POINT(P21,ABS)=34,76,0 DATA POINT(P22,ABS)=26,45,0 DATA POINT(P23,ABS)=33,83,0 POINT*LI)=P17,P25,P24,P23,P17 DATA POINT*P24,ABS)=33,76,0 DATA POINT(P25,ABS)=41,76,0 POINT(L1)=P26,P27,P28,P29 DATA POINT(P26,ABS)=35,83,0 DATA POINT(P27,ABS)=28,89,0 DATA POINT(P28,ABS)=26,87,0 DATA POINT(P29,ABS)=33,81,0 POINT*LI)=P30,P31,P32,P33,P34,P35,P36,P37,P30 DATA POINT(P30,ABS)=50,36,0 DATA POINT*P31,ABS)=75,36,0 DATA POINT(P32,ABS)=75,38,0 DATA POINT(P33,ABS)=78,38,0 DATA POINT(P34,ABS)=78,13,0 DATA POINT*P35,ABS)=75,10,0 DATA POINT*P36,ABS)=75,35,0 DATA POINT*P37,ABS)=50,35,0 POINT*LI)=P38,P39,P40,P41,P42,P35,P38,P41 DATA POINT*P38,ABS)=74,10,0 DATA POINT*P39,ABS)=66,10,0 DATA POINT*P40,ABS)=66,33,0 DATA POINT(P41,ABS)=74,33,0 DATA POINT(P42,ABS)=75,33,0 REMARK INTRODUCING THE INSIDE ROTATING MASS SHAPE........ POINT(L2)=P50,P51,P52,P53,P54,P55,P56,P57,P58,P59,P57,P50 DATA POINT(P50,ABS)=41.5,19,0 DATA POINT(P51,ABS)=38,20,0 DATA POINT(P52,ABS)=36, 22,0 DATA POINT(P53,ABS)=35,25,5,0 DATA POINT(P54,ABS)=36,29,0 DATA POINT(P55,ABS)=38,31,0 t DATA POINT*P56,ABS)=41.5,32, 0 DATA POINT*P57,ABS)=41.5,25.5,0 DATA POINT(P5B,ABS)=43,25.5,0 DATA POINT*P59,ABS)=40,25.5, 0 POINT*LI)=P500 DATA POINT(P500,ABS)=59,22,0 REMARK INTRODUCING THE OUTSIDE ROTATING MASS SHAPE....... POINT(L3)=P60,P61,P62,P63,P64,P65,P66,P67,P68,P69,P67,P60 DATA POINT(P60,ABS)=27.5,19,0 DATA POINT(P61,ABS)=24,20,0 DATA POINT(P62,ABS)=22,22,0 DATA POINT(P63,ABS)=21,25,5,0 DATA POINT(P64,ABS)=22,29,0 DATA POINT(P65,ABS)=24,31,0 DATA POINT(P66,ABS)=27.5,32,0 DATA POINT(P67,ABS)=27.5,25.5,0 DATA POINT(P68,ABS)=29,25.5,0 DATA POINT(P69,ABS)=26,25.5,0 POINT(LI)=P70,P74,P78,P8 2,P70 DATA POINT(P70,ABS)=65,41.5,0 DATA POINT{P74,ABS)=64,40.5,0 DATA POINT(P78,ABS)=63,41.5,0 DATA POINT{P82,ABS)=64,42.5,0 POINT(Ll)=P71,P75,P79,P83,P71 DATA POINT(P71,ABS)=65,41.5,1 DATA POINT(P75,ABS)=64,40.5,1 DATA POINT(P79,ABS)=63,41.5,1 DATA POINT(P83,ABS)=64,42.5,1 POINT(L I )=P70,P71 POINT(LI)=P74,P75 P0INT(L1)=P78,P79 P0INT(L1)=PB2,PB3 REMARK INTRODUCING THE RIGHT SIDE SUSPENSION BAR SHAPE.... POINT(L 4 )=P72,P76,P80,P84,P72 DATA POINT(P72,ABS)=65,41.5,.25 DATA POINT(P76,ABS)=64,40.5,.25 DATA POINT(P80,ABS)=63,41,5,.25 DATA POINT(P84,ABS)=64,42.5,.25 POINT=65,41.5,13 DATA POINT{P88,ABS)=64,40.5,13 DATA POINT(P90,ABS)=63,41.5,13 DATA POINT(P92,ABS)=64,42.5,13 POINT(FRAME)=P87,P89,P91,P93,P87 DATA POINT(P87,ABS)=65,41.5,14 DATA POINT(P89,ABS)=64,40.5,14 DATA POINT(P91,ABS)=63,41.5,14 DATA POINT(P93,ABS)=64,42.5,14 POINT(FRAME)=P86,P87 POINT(FRAME)=P88,P89 POINT (FRAME) =P90,P91 POINT(FRAME)=P92,P93 POINT(FRAME)=P94,P95,P96,P97,P94 DATA POINT(P94,ABS)=70,47,14 DATA POINT(P95,ABS)=70,37,14 DATA POINT(P96,ABS)=60,37,14 DATA POINT(P97,ABS)=60,47,14 POINT(L1)=P100,P101,P102,P103,P100 DATA POINT(P100,ABS)=23.5,41.5,0 DATA POINT(P101,ABS)=22,5,40.5,0 DATA POINT(P102,ABS)=21.5,41.5,0 DATA POINT(P103,ABS)=22.5,42.5,0 POINT(Ll)»P104,P105,P106,P107,P104 DATA POINT(P104,ABS)=23.5,41.5,1 DATA POINT(P105,ABS)=22.5,40.5,1 DATA POINT(P106,ABS)=21.5,41.5,1 DATA POINT(P107,ABS)=22.5,42.5,1 POINT(Ll)=P100,P104 POINT(L1)=P101,P105 POINT(L1)=P102,P106 POINT(L1)=P103,P107 REMARK INTRODUCING THE LEFT SIDE SUSPENSION BAR SHAPE POINT(L5)=P108,Pi09,P110,Pill,P108 DATA POINT(P106,ABS) = 23.5,41.5,.25 DATA POINT(P109,ABS)=22.5,40.5,.25 DATA POINT(P110,ABS)=21.5,41.5,.25 DATA POINT(Pill,ABS)=22.5,42.5,.25 P0INT(L5)=P112,P113,P114,P115,P112 DATA POINT(P112,ABS)=23.5,41,5,13.75 DATA POINT(P113,ABS)=22.5,40.5,13.75 DATA POINT(P114,ABS)=21.5,41.5,13.75 DATA POINT(P115,ABS)=22.5,42 ,5,13.75 POINT(L5)=P108,P112 POINT(L5)=P109,P113 POINT(L5)=P110,P114 P0INT(L5)=P111,P115 POINT(FRAME)=P116,P117,P118,P119,P116 DATA POINT(P116,ABS)=23.5,41.5,13 DATA POINT(P117,ABS)=22.5,40.5,13 DATA POINT(P118,ABS)=21.5,41.5,13 DATA POINT(P119,ABS)=22.5,42.5,13 POINT(FRAME)=P120,P121,P122,P123,P120 DATA POINT(P120,ABS)=23.5,41.5,14 DATA POINT(P121,ABS)=22.5,40.5,14 DATA POINT(P122,ABS)=21.5,41.5,14 DATA POINT(P123,ABS)=22.5,42.5,14 POINT(FRAME)=P116,P120 POINT(FRAME)=P117,PI21 A.4 POINT(FRAME)=P118,P122 POINT(FRAME)=P119,P123 POINT(FRAME)=P124,P125,Pl26,P127,P124 DATA P0INT(P124,ABS)=25,48,14 DATA P0INT(P125,ABS)=25,37,14 DATA POINT(Pi26,ABS)=15,37,14 DATA POINT(P127,ABS)=15,48,14 POINT(L1)=P130,P131,P132,P133,P130 DATA POINT(P130,ABS)=29,87,0 DATA POINT(P131,ABS)=28,86,0 DATA POINT(P132,ABS)=27,87,0 DATA POINT(P133,ABS)=28,88,0 P0INT(L1)=P134,P135,P136,P137,P134 DATA POINT(P134,ABS)=29,87,1 DATA POINT(P135,ABS)=28,86,1 DATA POINT(P136,ABS)=27,87,1 DATA POINT(P137,ABS)=28,88,1 POINT(L1)=P130,P134 POINT(Ll)=P131,P135 P0INT(L1)=P132,P136 POINT(Ll)=P133,P137 REMARK INTRODUCING THE REAR SUSPENSION BAR SHAPE POINT(L6)=P138,P139,P140,P141,P138 DATA POINT(P138,ABS)=29,87,.25 DATA POINT(P139,ABS)=28,86,.25 DATA POINT(P140,ABS)=27,87,.25 DATA POINT(P141,ABS)=28,88,.25 POINT(L6)=P142,P143,P144,P145,P142 DATA P0INT(P142,ABS)=29,87,13.75 DATA POINT(P143,ABS)=28,86,13.75 DATA POINT(P144,ABS)=27,87,13.75 DATA POINT(P145,ABS)=28,88,13.75 POINT(L6 )=P13B,P142 POINT(L6)=P139,P143 POINT(L6)=P140,P144 POINT(L6)=P141,P145 POINT(FRAME)=P146,P147,P148,P149,P146 DATA POINT(PI46,ABS)=29,87,13 DATA POINT(P147,ABS)=28,86,13 DATA P0INT(P148,ABS)=27,87,13 DATA POINT(P149,ABS)=28,88,13 POINT(FRAME)=P150,P151 ,P152,P153,P150 DATA POINT(P150,ABS)=29,87,14 DATA POINT(PI51,ABS)=28,86,14 DATA POINT(PI52,ABS)=27,87,14 DATA POINT(PI53,ABS)=28,88,14 POINT(FRAME)=P146,PI50 POINT(FRAME)=P147,PI51 POINT(FRAME)=P148,P152 POINT(FRAME)=P149,P153 POINT (FRAME)=P154,P155,P156,P157,P154 DATA POINT(PI54,ABS)=32,92,14 DATA POINT{P155,ABS)=32,80,14 DATA POINT(P156,ABS)=23,80,14 DATA POINT(P157,ABS)=23192 f14 REMARK INTRODUCING THE SHAKER MASSES.................... UNIT MASS=.002591 DATA GRAVITY=0,0,-386.1 DATA MASS(LI,J2)=1.813;-5,-1,0 DATA MASS(L2,J2)=.2279;0,-3,0 DATA MASS{L3,J3)=.2279;0,-3,0 DATA MASS(L4,J4)*.0259,0,0,7 DATA MASS(L5,J6) = .0259,0,0,7 DATA MASS(L6,J8)=.0259,0,0,7 REMARK INTRODUCING THE SHAKER MOMENT OF INERTIA......... DATA INERTIA(L4,J4)=.8625,.8625,0,0,0,0 DATA INERTIA(L5,J6)=.8625,.8625,0,0,0,0 DATA INERTIA(L6,J8)=.8625,.8625,0,0,0,0 DATA INERTIA(L2,J2)=1.39,1.39,2.79,0,0,0 DATA INERTIA(L1,J 8 )=6423.8,1115.36,10761,0,0,0 DATA INERTIA(L3,J3)=1.39,1.39,2.79,0,0,0 REMARK INTRODUCING DYNAMIC MODE SOLUTION................. FIND DYNAMIC REMARK INTRODUCING THE TIME INTERVAL AND INTEGRATION TIME___ DATA TIME=.5,.002,.002 REMARK INTRODUCING THE ROTATING MASS FREQUENCY............. VALUE (SP1)=164*TIME*TIME VALUE (SP2)=-123*TIME*TIME DATA MOTION(J2)=SPl DATA MOTION(J3)=SP2 REMARK INTRODUCING SOME CONTROL STATEMENTS................... ZERO SPRING=.00001 ZERO FORCE=.07,.7 ZERO POSITION*.0001 ZERO DATA=.00001 ZERO INERTIA*. 0001 ZERO SYSTEM*.00001 LIST POSITION(P500) PRINT ON = SP1 RETURN APPENDIX B C-Clamp Trunk Shaker-Tree Model ************************************************************** * FRIDAY C-CLAMP TRUNK SHAKER-TREE MODEL * * BY * * GHASSAN AL-SOBOH * ************************************************************** REMARK INTRODUCING THE SHAKER JOINTS......................... GROUND=FRAME REVOLUTE(L1,L3)=J2 DATA REVOLUTE(J2)=41.5,25.5,0;41.5,25.5,10;41.5,10,0;41.5,5,0 REVOLUTE=22.5,41.5,0;22.5,10,0;22.5,41.5,10 SPHERE(L6,FRAME)=J7 DATA LINK{L6,J7>=22.5,41.5,14;22. 5,10,14,*22.5,41.5,0 DATA LINK(FRAME, J7) =22. 5,41.5,14,*22.5,41.5,0,*22.5,10,14 SPHERE(LI,L7)=J8 DATA LINK(LI,J8>=28,87,0;28,87,10;32,84,0 DATA LINK(L7,J8)=28,87,0;32,84,0;28,87,10 SPHERE(L7,FRAME)=J9 DATA LINK(L7,J9)=28,87,14;32,84,14;28,87,0 DATA LINK(FRAME,J9)=2B,87,14;28,87r0;32,84,14 REMARK INTRODUCING THE TREE JOINT........................ REVOLUTE(LI,L 9 )=Jll DATA REVOLUTE(Jll>=62.5,22,0;62.5,22,10;70,22,0;62.5,30,0 REMARK INTRODUCING THE SHAKER HOUSING SHAPE............. POINT(L I )=P1,P 2 ,P3,P 4 ,P 5 ,PI DATA POINT(Pl,ABS>=20,10,0 DATA POINT(P2,ABS>=49,10,0 DATA POINT(P3,ABS)=49,33,0 DATA POINT(P4,ABS>=20,33,0 DATA POINT(P5,ABS>=20,18,0 POINT(LI)=P5,P6 DATA POINT(P6,ABS)=49,18,0 POINT(L l )=P7,P8,P9,P10,P7,P2,P3,P10 DATA POINT{P 7 ,ABS>=50,10,0 DATA POINT(P9,ABS>=59,10,0 DATA POINT(P9,ABS)=59,33,0 DATA POINT(P10,ABS>=50,33,0 POINT(L1)=P10,P11,P12,P4,P10 DATA POINT(Pl l ,ABS>=50,38,0 DATA POINT(PI2,ABS)=20,38,0 B.1 0 i2Z'6S={SSY'£0*d).LNIOd ViVd 0*9*SZ*S*Z9a {SSY*20td)NIOd YJ.YQ O tJ O O D O a O o o o > > O D O O d d o o a a a o a a a a > > > ° > > > > > > > ►3 *3 3 H « ► 3 m *3 ►3 *3 *3 *3 *3 *3 > > > > > > > % > ► 3 a • f l '- 'D a a a a a a a ' - ' o f M M WW W M l-H >>o > O ►3 M *3 *3 *3 M *3 5 5 ►3 h3 5 > Z > > >>% B > > > Z > > > > > > a a aa 0 a •a a a a * a a a a o H a o o o o o o o o 0H H o tr1 o O 0 0 0 ^ 0 O O O O o h h h ^ h W l-H H z z — z — z z z z Z'-'Z z ► 3 II 5 5 3 «3 II *3 •3 II >-1 ■-3 --s a .■ — »a A»0 A *3 A A A ||A ►3 *3 a a a a a a a co a a a a to *0 a a a a a a *0 *0 T) Ifl a a co a C Oo to to to to cn It* < k U U U l U co to u to co co CO O CO O CO CO CO CO CO C J1it*CO toI—>O ' CD 0 3 -j cn' O U H 9 Q > ] o> cn it* CON> |-J O' -J cn ( m •. a - • * ^ « ^ * • a * ^ —— a CO > > CO > > > > ro > > > > a B E E B E S a i-> a a a a 5 B B S 2 B E E cd m oi a E Oi m t n m idm CO CO CO 01 GOOI to - co cn cn cn co cn cn W ' m m 01 CO' >> > o > it n n n a n u n n u it u ii co ii ii ti ii n ii n n co n ii n n to -J c r v 0 3 'O if* tn '0 '0 'J 'J -0 '-J c n M in 'J - -J 'J 'J 'J 'J c n r o c jjfo to c J C D • t » c n c n i f * o o c n t n c i 3 C D c n c n O ' o a a C D C D t n c n o - oo cn cd cn- *q iq - - a WWHHtlWWHHUUIUClUUUHHUUWUUaXnOOOltO o o a Oddd D O O d 3 3 > > Z > > !> > z> > > > > > > o a d d d n > o >> > o ►3 i —i i-3*-3»-3•—< > 5 5 ° h ►3 *3 *3 *3 ►H *3 *3 *3 *3 o o r oH oH oH oH Hd HO HO HO O d O O O d h h h h h h a A A A if an ii ^ *3 ait <-3 »-3 ii 5 5 5 5 7 5 5 5 A A a a a H* a a a a to a a a to to to to to to U H H H H V O H H H cn it*- COto t— «o a i—* a a a i—’ > > a a COCO' II Cn Cn CO CO II to n ii n n cn co a to n it n CO' ii h o o a o o o o a ** to * a 00 a * a oo CD a it* a CO — — — — — — — — — O O O O O O O O a CO o o o o 1^ It* a a a a a Co cn CO CO CO CO * a CO a cn a -4 'J aCO CO o a o ii w COit* O ' ' a ——— a O O O O ' — — — — — — — — — — — ' n ii it*cn cncnro if* i t * OO i t * co to to to O if* if* if* M OOco cn >f* cd- o cn '-J ' a' ' CO CO CO' — a — '- '— a o o c o o o i f * c n c n o o o c » a c n c n c J c n a i o o o o D o o c n c n o o H , 'Ju3oocD O O O O O O O O W ' COOD'l o\' cn it*coa' ' ' - a - ' ' a ro > > > > M > > > M ro cn s s s s a a a a 03 cna a co — — a —— — — 'O -J to CD it* -J it* to 'J it* CD cn cn oo oj cn cn cji M O IU 1 U — i—1' % > > > * a — a a a —' a a —• a a a a — a a a if*V-*CO it*if*M ui'iaoitnui o o o o o o o a M to DATA POINT(P404,ABS)=62.5,18.5,0 DATA POINT(P405,ABS)=66,18.5,0 REMARK INTRODUCING THE INSIDE ROTATING MASS SHAPE....... POINT(L3)=P50,P51,P52,P53,P54,P55,P56,P57,P58,P59,P57,P50 DATA POINT(P50,ABS)=41.5,19,0 DATA POINT(P51,ABS)=38,20,0 DATA POINT(P52,ABS)=36,22,0 DATA POINT(P53,ABS)=35,25.5,0 DATA POINT{P54,ABS)=36,29,0 DATA POINT(P55,ABS)=38,31,0 DATA POINT(P56,ABS)=41.5,32,0 DATA POINT(P57,ABS)=41.5,25.5,0 DATA POINTtrrtriiim n |n ■ii11iniitt 900 1200 1050 i 150 300 450 600 750 1350 TIM E I ms) FIGURE C.2 EXPERIMENTAL FREE SHAKER DISPLACEMENT VS. TIME AT THE PAD CENTER DURING SHAKER STEADY STATE FREQUENCY (MARSHALL. 1 9 8 6 ). 30 30 1 i i i u i n i i n ii [n i im i i i i i i i J m i i i i i i Mi i i | i M i n ii n i u iJ m ; i i i i i i i i n | i i m i i i i m u ] i i i i i . i M i M i iln m i n i m i r |n m n i i i i i ii 3450 3600 3750 3900 4050 TIM E 4200 I ms) 4350 45 00 4650 4800 APPENDIX D Optical Shaker-Tree Displacement Results FIGURE D.1 EXPERIMENTAL DISPLACEMENT VS. TIME OF A 63 m m DIAMETER CHERRY TREE TRUNK DURING SHAKER STARTUP (MARSHALL, 1 9 8 6 ). TREE DISPLACEMENT |mm| 30 20 10 - 4 ----- -10 \ n t ii_ _ i -20 -30 150 300 450 750 600 TIME I ms) 900 1050 1200 1350 DISPLACEMENT ( mmj FIGURE D.2 EXPERIMENTAL DISPLACEMENT VS, TIME OF A 63 m m DIAMETER CHERRY TREE TRUNK DURING SHAKER STEADY STATE FREQUENCY (MARSHALL, 1 9 8 6 ) TREE v r■ 1500 ! ! ! 1 ■i! l l ; ! 1111 n 'l 'IT . I f l 111 I I 11) f l 11 n ] 11 ■I . I . . 16 5 0 1800 1950 i : i I I I ) . . I • I ■I ■■iT T ~ il i 11 ■) 2100 T I M E I ms ) 2250 . . t . , . 1 ■, , . ^ ^ ■ - r r r - A 2400 2550 2700 2850