THE APPLICANON OF TILLAGE ENERGY BY VEBRATEON Thesis for ”ma Degree of NM D. MECHEGAN STATE UNIVERSZTY James G. Hendrick, III 1962 THESlS 43.1, Date ”~OIMuu-n .u. ;' LIBRAR 1' Michigan ban: University This is to certify that the thesis entitled The Application of Tillage Energy By Vibration presented by James G. Hendrick, III has been accepted towards fulfillment of the requirements for Ph.D Agricultural Engineering degree in ajor professor November 21, 1962 7 i d. d k THE.APPLICATION OP TILLAGE ENERGY BY VIBRATION By James G. Hendrick, III AN ABSTRACT OF A THESIS Submitted to Michigan State university in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1962 Approved @ /: M fl' 4/f/2- ABSTRACT THE APPLICATION OF TILLNGE ENERGY BY VIBRATION by James G. Hendrick, III Soil tillage requires more power than any other single agricultural Operation. Any method which would reduce the power required to perform basic tillage Operations could result in large savings to the American economy every year. One method by which the efficiency of tillage can be increased is by transmitting energy from the tractor engine directly to the plow body by mechanical means. This would be more efficient than the present method of transmitting the energy through the soil-tire linkage, which has a re- latively low efficiency. In order to use the energy transmitted directly to the plow, the plow must be capable of imparting the energy to the soil. Tests were conducted to study the effect of ap- plying energy by a vibrating plow body. A model tillage tool, an inclined plane, was deve10ped which could be vibrated in such a manner as to apply forces to the soil in a more efficient direction. Equipment and instrumentation were deve10ped which permitted measurement of the individual forces acting upon the model tool. Labo- ratory tests were conducted using the model tool in a mo- bile soil bin to compare the draft force and energy re- quirement of a vibrating tillage tool with those of a rigid tillage tool. iJames G. Hendrick, III The draft force of the vibrating tool was found to be less than that of an identical rigid tool. The reduction in draft was a function of the soil parameters, vibrational frequency, and amplitude of vibration. The energy require- ment of the vibrating tool was found to be less than that of a rigid tool at low frequencies, but became greater as the frequency was increased due to the formation of more soil shear planes and soil acceleration and deformation, eSpecially at large amplitudes of vibration. THE APPLICATION OF TILLNGE ENERGY BY VIBRATION 3)! . 9,9? James G.‘\\Hendrick, III A THESIS Submitted to Michigan State university in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1962 Approved 14?“:2fifgi:¢’¢éif;5ég:: (,5 ACKNOWLEDGMENTS The author wishes to express his gratitude to the fol- lowing peOple who assisted in this investigation and made the preparation of this thesis possible: .Dr. W. F. Buchele, the author's major professor, who provided guidance, encouragement, and enlightening discus- sions during this study. Mr. C. M. Hansen, who served on the guidance committee and rendered many useful suggestions and gave encouragement on many occasions. Major R. A. Liston of the U. 8. Army Ordnance Tank- Automotive Command, who supported the project by lending instrumentation equipment. {Dr. L. E. Malvern and Dr. J. H. Stapleton, members of the guidance committee who contributed several helpful sug- gestions for the preparation of this manuscript. Dr. A.‘W. Farrell, Head of the Agricultural Engineer- ing Department, who gave support in providing the assis- tantship for this work. Mr. A. C. Bailey and members of the staff who assisted in the construction of the necessary equipment. Most especially to the author's wife, Kathy, who helped in the preparation of this manuscript, and whose loyalty, devotion, and understanding made this study pos- Siblee In TABLE OF CONTENTS INTRODLETION.......... REVIEWOP LITERARRE. . . . . . EQUIPMENT AND PRCCEDIRES . . . . Dynamometer . . . . . . . . . The Tillage Tool . . . . . . . Coefficient of Friction . . . Method of Vibration . . . . . Measurement of Vibrating Force Soil Saw . . . . . . . . . . . Soil Bin . . . . . . . . . . . Soil Conditioning Equipment . Analog Computer x-YPIOttereeeeeeoee THEORETICALwCONSIDERATIONS . . . Calculation of the Draft Force on a Rigid Tool Discussion of Draft Reduction by a Vibrating 1.111.399.1001 e e e e e e e e e 0 RESULTS Simulation of Cutting Resistance . Reduction of Draft Force . . . . . Energy Requirement of the Vibrating Blade SUMMARY CONJLUSIONS AND OBSERVATIONS . . . . . . . . Conclusions iii Page 11 11 20 27 29 31 37 35 39 #2 1+5 1+9 1+9 51 55 55 71 79 81 81 ObseI 5156551 REFEREb APPENDI APPEND'. TABLE OF CONTENTS (continued) Page Observations....................81 SKEGESTIONS Fm FIRTHER INVESTIGATIWS . e . . e e e . 83 REPEREMZES......................81l- APPENDIXA. Sample Problem . . . . . . . . . . . . . 87 APPENDIXB. Tables....o....o.o.oo..89 iv LIST OF TABLES TABLE 1. 2. 3. 9. 10. ll. 12. 13. Dynamometer and Pressure Cell Calibration Information . . . . . . . . . . . . . . . . . Tool Pressure Cell Calibration . . . . . . . . Normal Load vs. Tangential Force for Mild Steel and Teflon at Various Moisture Contents Force Exerted on the Blade by the Solenoid . . Average Draft values for a Rigid Tool Run at 30° and h0° Wbrking Angles . . . . . . . . . Energy Transmitted to the Blade by the Solenoid in Soil at 17.5 % Moisture . . . . . Relative Draft Data for a working Angle (S) of h0° and 1% % Soil Moisture . . . . . . . . Relative Draft Data for a Working Angle (S) of h0° and 17.5 % Soil Moisture . . . . . . . Relative Draft Data for a working Angle (S) of 30° and 1% % Soil Moisture . . . . . . . . Relative Draft Data for a working Angle (S) of 30° and 17.5 % Soil Moisture . . . . . . . Tabulation of Values used for Comparing Measured Draft Force and Computed Draft Force for a Rigid Blade (6.. ’+O°) . . . . . . Physical Description of Brookston Sandy Loam Soil . . . . . . . . . . . . . . . . . . Bevameter Penetrometer Sinkage Data . . . . . . V PAGE 89 90 91 93 9’4- 95 97 99 101 102 103 101+ PIGU LIST OF FIGURES FIGURE 1. 2. 3. 9. 10. 11. Reproduction of a Curve by Dubrovskii Showing the Relation Between Speed and Draft for Rigid and Oscillating Tillage Tbols . . . . . . . . . . . . . . . . . . Force Diagrams of a Rigid and of a Vibrating Tillage Tool . . . . . . . . . Strain Gage Dynamometer, Three-quarter View (62251-1)* . . . . . . . . . . . . . Strain Gage Dynamometer, Bottom View (62251-3) . . . . . . . . . . . . . . . . Dynamometer Dimensions and Strain Gage Location . . . . . . . . . . . . . . . . Dynamometer Strain Gage Bridge Arrangement Dynamometer Calibration Curve Where are 72°, x = 0.5' and y a 1.0' . . . . . . . . . . Dynamometer Calibration Curves for d -.- 90°, 0.5‘, and y =- 1.0' and for 6.: 0°, 0.5‘, and y a 1.0' . . . . . . . . . X X Dynamometer Calibration.Curve for d.= h9°, x:0.5',and_y=1.0' ......... The Instrumented Tillage Tool . . . . . . . Tillage Tbol in Mounted Position (6213661) Lab * Numbers in parentheses refer to MSU Photo negative numbers. vi PAGE 12 12 13 1h 17 18 19 21 2.2 LIST or FIGLRES (continued) FIGURE 12. 13. 11;. 15. 16. 17. 18. 19. 20. 21. 22. 23. Wiring Diagram of the Diaphragm Pressure Cell Strain Gage Bridge . . . . . . . . . . . Method for Using a Mercury Column to Calibrate the Diaphragm Pressure Cells . . . . . . . . Calibration1Curve for the Diaphragm Pressure Cells . . . . . . . . . . . . . . . . . . . . Method Used for Measuring Apparent Coefficient of Friction (fi') . . . . . . . . . . . . . . Apparent Coefficient of Friction of Brookston Sandy Loam on Polished Steel and on Teflon as a Function of Moisture Content . . . . . . The Soil Saw (62329-1) . . . . . . . . . . . . Soil Conditioning Equipment (62230-2) . . . . . Schematic of the Mobile Soil Bin and Related Equipment . . . . . . . . . . . . . . Bevameter Used to Measure Soil Parameters (6212&7) O O O O O O O O O O O O O O O O O 0 General View of Recording Equipment (62532-1) .. Soil Parameters "c" and "Internal Angle of Friction" for Soil at 1% $4Moisture and Bulk Densities of 1.12 and 1.23 . . . . . . . Soil Parameters "c" and "Internal Angle of Friction” for Soil at 17.5'% Moisture and Bulk Densities of 1.12 and 1.23 . . . . . . . vii PAGE 2% 25 26 28 30 , 3h 3% 36 #1 1+1 ‘+3 1+3 LIST OF FIGIRES (continued) FIGURES 21+. 25. 26. 27. 28. 29. 30- 31. 32. 33. 31+. 35. Wiring Schematic for Recording the Integrated Draft Signal 0 e e e o e e e e e Mosley X-Y Plotter (A), Strain Gage Balance and Calibration Unit (B), and Performance Test rug ((2) (6226k-3) . . . . . . . . Strain Gage Balance and Calibration Unit wiringDiagram .............. Performance Test Rig Wiring Diagram . . . . . Horizontal Force of Cutting for No Wires As a Function of velocity . . . . . . . . . Draft Ratios of a Vibrating and Rigid Tool for S=h0°and f-10°..... ..... Draft Ratios of a Vibrating and Rigid Tool for 6=1+0°and (=15°...... .... Draft Ratios of a Vibrating and Rigid Tool for 6=h0°and (=20°.. . . .. .. .. Relation of Draft Ratios for 5: er° and d’: 10°, 15°, and 20° at 1# fl Soil Moisture Relation of Draft Ratios for 6 = 1+0" and 6’: 10°, 15°, and 20° at 17.5 % Soil Moisture . . . . . . . . . . . . . . . . . Draft Ratios of a Vibrating and Rigid Tool for 5=30°and {35° .......... Draft Ratios of a Vibrating and Rigid Tool for 6330°_.and {31000000000000 V111 RAGE 1+6 2+8 1+8 56 59 60 61 62 63 6M LIST or FIGURES (continued) FIGURE PAGE 36. Draft Ratios of a Vibrating and Rigid Tool for S=30°and (=15°............ 65 37. Draft Ratios of a Vibrating and Rigid Tool for 6-.3o°and {=2o°............ 66 38. Relation of Draft Ratios for 6 a 30° and (fa-.- 5°, 10°, 15°, and 20° at 1h % Soil Moisture ................... 67 39. Relation of Draft Ratios for 6-.- 30° and I: 5°, 10°, 15°, and 20° at 17.5 % Soil Moisture . . . . . . . . . . . . . . . . . . . 68 1+0. Percent Energy Applied by Draft and Solenoid Action of a Vibrating Tool Compared to a Rigid Tool Where 6: 1+0° and 3’: 10° at 17.5%Soi1Moisture ............. 71+ 1+1. Percent Energy Applied by Draft and Solenoid Action of a Vibrating Tool Compared to 3 Rigid Tool Where 6... 1+0° and r: 15" at 17.5%Soi1Moisture ............. 75 1+2. Percent Energy Applied by Draft and Solenoid Action of a Vibrating Tool Compared to a Rigid Tool Where 6: 1+0° and {a 20° at 17.5%SoilMoisture ............. 76 ix LIST OF FIGLRES (continued) FIGLRE . PAGE b(3. Percent Energy Applied by Draft and Solenoid Action of a Vibrating Tool Compared to a Rigid Tool Where 5. 30° and d’: 10° at 17.5%5011Moisture ............. 77 111+. Percent Energy Applied by Draft and Solenoid Action of a Vibrating Tool Compared to a Rigid Tool Where 5.. 30° and d2.- 20" at 17.5%SoilMoisture . . . . . . . . . .. . . 78 INTRODUCTION Research workers in the field of tillage and soil me- chanics have continually striven to reduce the draft and energy requirements of tillage tools. A recent concept under study is the vibration of tillage tools in which a portion of the tillage tool is moved in various planes by mechanical means. One of the main disadvantages of basic tillage tools such as moldboard plows and subsoilers is the draft re- quired to force them through the soil in a manner much like a rigid wedge. The drawbar pull of a tractor is limited by the soil-tire dynamics and the soil strength properties as well as by the power of the tractor engine. The draft of the tractor frequently can be increased by adding weight to the wheels: this, however, has the following objectionable results: (a) increased soil compaction, (b) increased me- chanical impedance to plant roots, (c) reduced water infil- tration rate, and (d) reduced air permeability and water holding capacity. Most tractors develOp maximum draft at 15 to 20 percent tire slip. The rolling resistance of the tractor consumes another 15 to 20 percent of the power. Thus the efficiency of a tractor in the field is the product of the above effi- ciencies (50 to 70 percent). Because mechanical power tranp smission is much more efficient. the tillage efficiency of the tractor-tool system could be increased by mechanically 2 by-passing the soil-tire relationship even if the efficien- cy of the tillage tool was not increased. By imparting movement directly to the tillage tool the efficiency can be increased by: (a) applying forces in a more favorable manner, (b) separating the various forces acting on a tillage tool into their separate horizontal and vertical components by means of mechanical movement rather than by overcoming all of the forces by their horizontal component, i.e. draft, (c) breaking up the soil into smal- ler particles or clods. Vibrating tillage tools Offer these two basic advan- tages: (a) the farm tractor could reduce the drawbar pull of an implement by mechanical motion via the power-takeeoff shaft or other means, thus transmitting the engine power more effectively to the tool, and (b) the vibrating tillage tool breaks the soil into smaller particles or clods. This advantage offers the possibility of eliminating the need for secondary tillage Operations. A vibrating tillage implement could be pulled with light, high-powered tractors, which would result in reduc- ing the soil compaction problem and reduce tractor cost. The three basic objectives of this study were as fol- lows: (l) to develOp equipment and methods for measuring the forces acting on a simple tillage tool, (2) to develOp a method for determining tillage forces and energy of rigid 3 and vibrating tools, and (3) to compare the energy require- ments of rigid and vibrating tillage tools. REVIEW OF LITERATURE The first investigation concerning the application of mechanical movement to a tillage tool was conducted by Gunn and Tramontini (1955). They performed a series of eXperi- ments in which a simple, small blade (shaped like a sub- soiler chisel) was attached to a vertical standard. The standard was pivoted at its upper end and connected to a pittman drive near the blade so that the blade and standard could be oscillated fore and aft at a controlled rate and frequency. The tests were run in relatively dense, dry soils: the amplitudes of the strokes most frequently used ‘were 0.322 in. and 0.6h5'in. The tests indicated that the average net draft could be greatly reduced by oscillating the orperimental chisel. They reported that "the decrease was slight for oscillation velocities that were less than the tractor speed." A rapid reduction in draft occurred when the forward speed of the tractor was reduced in comparison with the oscillating ve- locity. The orperimenters used several dimensionless para- meters, one of which was: where: Vt a forward speed of the tractor, K I 3 fte/‘GCO wr w a the angular velocity of the pittman. radians per sec. r a eccentricity of the crank, ft. The greatest reduction in draft occurred when K had a value less than 1. That is, under conditions such that the maxi- 5 mum rearward velocity of the tool exceeded the forward speed of the tractor, which resulted in the tool's moving rearward with respect to the ground during a portion of its stroke. ' Gunn and Tramontini found no large or significant re- duction in total power due to the power required to oscil- late the tool, but at a value of K.= 0.25, a 60 percent re- duction of draft was Obtained. As the value of K increased, the amount of draft reduction decreased. Another result was that the oscillating tool appeared to give better soil frag- mentation than a nonpvibrating tool. In an investigation by Dubrovskii (1956) a series of tests using a simple wedge-shaped model tool in sand were conducted using three modes of vibration: (a) the tool moved forward and back at an upward angle of about #5° to the horizontal, (b) the tool moved fore and aft, and (c) the tool moved in a “V“ shaped path in which it was moved downward in the first portion of the stroke, and then up- ward. The greatest saving in draft occurred when using the first mode. The results of Dubrovskii's experiment can be shown best by Figure 1, in which curve no. 1 is the noncoscillat- ing relationship between draft and Speed. Curves 2, 3, and h are draft curves at various frequencies of oscillation (mode Of oscillation not specified). In all cases the vi- brating tool resulted in a reduction of drawbar pull up to .maoop woodman mcwpoaadomo ocm paman Mom ammuo one omen» cesspon cowumfion one mewsonm «axm>ounaa >n o>noo m we couvonoondom .H shaman omwam Om<3mom fl&.l l: 1V, >an 3080:! idVBO 7 a certain forward speed and then showed an increase in drawbar pull beyond that speed. The dashed curves in Figure l join points where the lengths Of oscillation are equal. Dubrovskii noted that as these lines approached the non-vibratory curve, they merged with it, indicating that in actuality the Operation of a rigid tool is a vibratory process. The experimental re- sults showed that where the forced oscillation had a wave length with respect to forward travel less than the wave length of the shearing action of the rigid tool, the draft resistance was reduced. Eggenmueller (1958) performed a series of tests with vibrating tillage tools in which the basic objectives were to reduce draft by the following tillage tool movements: (a) throwing soil upward so that at the instant the tool moved forward into untilled soil the tool surface was free of friction, (b) no lifting Of the soil occurring during the forward tool motion, (c) reducing the cutting angle Of the blade by driving it more directly into the soil, and (d) dividing the forces required for the individual pro-1 cesses of cutting, lifting, shearing, and accelerating the soil into distinct horizontal and vertical forces by means of the oscillating drive rather than by having the horizon- tal component overcome all forces as is the case with rigid tools. Figure 2 shows Eggenmueller's description of the 8 force components as presented by Soehne (1956) for the ri- gid tool and for the vibrating tool. Eggenmueller considered various combinations of fre- quency, amplitude, direction of movement, and forward Speed in a fine sandy loam under constant soil conditions. He found the direction of oscillation to be of particular imp portance, and that a direction of 30° to the horizontal was more favorable than a fore and aft movement in the reduction of draft. A movement as illustrated by Figure 2 B and C ap- peared to be the most favorable. Another important factor was the relationship between length of stroke and height of lift. A maximum ratio of 2 for lengthzheight of stroke was recommended. A maximum reduction in draft of 75 percent was reported under optimal conditions. Eggenmueller apparently did not consider the relation- ship between the natural frequency of shear plane formation and the frequency of forced vibrations; however, it was noted that the vibrational frequency required for the same reduction in draft increased with the forward speed of the vehicle. From charts in the text, the minimum reported frequency of 16 cycles per sec. appeared to be a little greater than the natural shear plane frequency of the soil at the maximum reported forward Speed of 0.8 meters per sec. He found that relatively small amplitudes of movement resulted in a considerable reduction in draft. From the power standpoint, it was preferable to Operate at low fre- .Hoou mundane acapmunw> a mo new mama“ m mo memnmmuo oonom .N ousmwm 82:“...3 82:58 3.2.3.08 .0 02.23.08 .m .53 06;. .4 .7invmo > m: m 9 lO quencies due to the movement of the soil mass, tool accel- eration, etc. A reduction of #0 percent to 50 percent could be attained with the same total power input. Another factor mentioned was that soil crumbling and mixing appeared to be greater with the vibrating tool. Hendrick (1960) found that a cohesive soil required less total energy to cause tensile failure at high loading rates. The ultimate stress was constant; the reduction in strain energy was obtained because the soil strained less under rapid loading rates. EQUIPMENT AND’PROCEDURES W- In order to measure the soil forces acting on the til- lage tool, a dynamometer (Figures 3 and H) was constructed which could measure independently the vertical force, the horizontal force, and the moment about the dynamometer cen- terline caused by the resultant of the vertical and horizon- tal forces. The dynamometer was found to be independent of lateral forces and moments. By measuring these forces and moment, and by knowing the equation of the surface of the tillage tool (an inclined plane), the point of application of the resultant force on the tool surface could be calcu- lated. 58-h strain gages were used as sensing elements to mea- sure the strain in the dynamometer arms. Figure 5 is a drawing of the dynamometer showing strain gage placement. Figure 6 shows the arrangement of the three strain gage bridges used to yield the horizontal force, vertical force, and the bending moment independently. Gages l, 2, 3, and h sensed the strain in the dynamometer arms due to forces in the horizontal plane in the direction of travel (draft). Gages 5, 6, 7, and 8 sensed the strain in the dynamometer arms due to vertical forces. Gages 9, 10, ll, and 12 sensed the strain in the dynamometer arms due to the moment caused by applied forces about a lateral axis through the dynamometer centerline. 12 Figure 3. Strain gage dynamometer, three-quarter View. Figure #. Strain gage dynamometer, bottom view. :5: 9- Sui-(Ty -<1) SPHERICAL ROD END BEARING (0.3125" SHAFT) x2-'-"x ."uo SQUARE 2STEEL TUBING —\ (TOOL MOUNTING) 2- I"x I" x .07" SQUARE SR - 4 STRAIN GAGES l2“ STEEL TUBING 4 If- . C33 3- I2 8 T BOTTOM C 5 ....I_. O 7‘ k) ---‘ 1;? I" k) - :1“ p —:.-.:.;I-H dr-q) - - - -nde q--p-----4p [fit END VIEW DYNAMOMETER MOUNTING FRAME Figure 5. Dynamometer dimensions and strain gage location. 11+ © © @0 $@ @0 fig» (9% 0© ©§ 0+ DRAFT BRIDGE © VERTICAL FORCE BRIDGE @é’ «be» ©% 0@ TORQUE BRIDGE Figure 6. Dynamometer strain gage bridge arrangement. . 15 The body of the dynamometer was made Of 2-1/2 in. x 2-1/2 in. x 0.10 in. square steel tubing (weight per ft. = 3.2 lbs.). The strain arms (Figure 5) of the dynamometer were made of l in. x l in. x 0.070 in. square steel tubing. The square steel tubing increased the rigidity and sensi- tivity of the dynamometer while the weight was reduced; this increased the resonant frequency of the body. The re- sonant frequency of the dynamometer with a tillage tool at- tached was determined by applying a force and removing it suddenly. The resulting oscillograph trace showed a re- sonant frequency of 55 cps. TO check the frequency res- ponse of the oscillograph, a cathode ray oscilloscOpe was attached to the draft-measuring channel Of the oscillograph and polaroid pictures were made of the oscilloscOpe trace as the tool was vibrated. The recordings of the oscillo- scOpe and of the oscillograph were compared and found to be identical provided the maximum pen deflection Of the oscil- lograph was limited to lS'mm. The outer ends of the strain arms were fitted into spherical rod end bearings. The strain arms thus acted as cantilever beams fixed at the dynamometer body and free at the end in the bearings. The tillage tool standard was clamped to the dynamome- ter body in such a manner that the axis Of rotation of the tool was directly below the lateral axis Of symmetry of the dynamometer. 16 A series of calibration tests were made and the re- sults are shown in Figures 7, 8, and 9. The dynamometer was calibrated by applying a known force (F) at a known an- gle (a) to the horizontal (Figure 7), and at a known loca- tion with respect to the dynamometer centerlines (x and y). The horizontal and vertical measurements were found to be independent Of one another, and the results of measured torque and calculated torque were found to be in agreement within 2 percent. Table 1 contains calibration data for each Of‘the recorded forces. The line of the resultant force could be determined from the recorded forces when the equation of the plane of the tillage tool'was known. The point Of application of the resultant force on the tillage tool could be calculated. Appendix A shows a sample calculation. To determine the rigidity of the dynamometer, a force of 160 pounds was applied in a horizontal direction (Fx) at y = 1.0 ft.: the deflection along the line of travel was 0.06 in. With Fy 2 160 lbs. and y a 0.0 ft., the vertical deflection was 0.06 in. The maximum sensitivity of the dynamometer was calcu- lated to be 2.5 mm deflection on the oscillograph per pound applied in either the longitudinal or the vertical direc- tion. The maximum sensitivity as determined by calibration was 3.5'mm deflection per pound. 17 on. ..o.H n > mam ..m.o u x . ms nu when: o>HsO coapmnnaamo novoEOEmc>Q $0230.”: 93.. 024.34 9.. on. cm. 0: ow. om om ox. ow on o.e on om o. - 4 II III. UDOKOF HZdF 1 A... some Pub: 0 I I I I .58 #4... o» use mmoI I I m. 8:352. m. 8 use Home» .5 onsmwm omI .00] l nu w .oeI n :. .oul um .I. .o .d nu m ION nu .6 .o¢ .00 as OQOOH u > 6:“ Oomio "I x .00 “Ha now new .0; u > ocm . .m .o .I. x .ooa no How mo>H3o cowpmnnwamo HomeoEmc>Q AmoZDOm. Guiana 040... On. OW. on. om. o: 00. cm om Oh OW o_m o_.v o_m ON 0. J: or .a p m“ OJ ”90¢ J... W fr 000 I . n, Go 6 r0/\\ «0’ a 00 + a w rnW.Ou# . T o.,..o\\ I . .0). m... .0 + ’ oo. voooo A a W h— L ea 0 or - x0 o too/oz “EI IAI Ve/ l a; 4 IT I A (\x IT .w 933m 10 .ON 8 a be 0 n .00 M 9 :8 m m w .00.“. 0 -o~_N \_h 8 -028 v.00. 19 .0 933m ..o.H u > mam . .m .o .I. x .09; no How m>Hso :owvmnnwamo HopoEoEmc>o 3.: 9‘04 054%; 09 OS 02 ON. 0: oo_ om om on Ow on 0v on ON 0. o r. T + + + i I_ I r i + i r i + omI II OVI or 0;. I ON: use H.520.” omb‘ ozooqo to W m 9% \\ \ .2 m. mnemoe\ \ fie ones )6 \ \ maze: our 1 \ M wDO¢Ok 990¢OV ._| \$\oe m9 woo u. m. I oo 8 \ Vt ( \ *W 0 ..0m x... Myr— I_ x _ I 8. x ION_ ( "' 20 W. The simple tillage tool designed for this investigation is illustrated in Figure 10. The dimensions of the mild steel tool were 3/16 in. thick, S'in. wide, and 2-1/2 in. long. The forward edge was machined to a l/6h in. radius and blended into a 20° bevel. The tool was mounted in bearings located at the rear edge. It rotated in the bear- ings about an axis through the tap surface Of the tool (Fi- gure 11). When the tool was rotated, the forward edge of the tOOl swung upward describing an arc. This method of tool movement was employed for three reasons: (1) the maximum displacement of the soil was in the region of the shear plane, (2) maximum acceleration of the soil mass occurred only at the cutting edge of the tool, and (3) rigid mounting of the standard minimized the tool mass to be actuated. In order to measure the forces acting normal to the tool surface, a series Of five diaphragm pressure cells were provided as illustrated (see Figure 10). The dia- phragms were made of 0.005 in. thick stainless steel shim stock. In order to make the diaphragms flush with the tool surface, the 9/16 in. holes were counterbored to 5/8 in. diameter and 0.006 in. deep and the round shim stock dia- phragms were silver-soldered into place. The tool was covered with a h mil layer of pressure sensitive Teflon. The Teflon layer reduced the sliding re- 21 l I I I I I (c) 0.005" STAINLESS I STEEL DIAPHRAGIIII I __).> g. 5" III I13" '5 I TOP VIEW SECTION A-A Figure 10. The instrumented tillage tool. 22 .cOHpamoo oopcaoe ca Hoov mmmHHHH .HH musmwm 23 sistance Of the soil on the tool face and smoothed the slight imperfections which develOped during soldering the pressure diaphragms onto the tOOl. It also prevented soil from sticking to the surface and "bridging over" the pres- sure cells. In order to prevent the leading edge of the Teflon layer from being disturbed or peeled Off by the sail, a 0.006 in. layer of steel was machined from the tool face a distance Of l/h in. behind the leading edge (Figure 10). This permitted the leading edge Of the Teflon layer to be protected by steel and thus remain in place. Sanders-Roe foil diaphragm strain gages (Radshaw l/2-2ED) were attached to the underside of each diaphragm to measure the diaphragm strain. Figure 12 shows the wir- ing diagram for the pressure cell bridges. Calibration of the pressure cells showed them to be linear within M percent up to 15 psi (this was well above the unit pressures recor- ded during the tests). A method of calibrating the pres- sure cells was devised in which a column Of mercury was used to provide a known unit pressure. Figure 13 shows a schematic of the system employed. By setting the height of the mercury column, the normal pressure on each cell was determined. The calibration curve for the five pressure cells is shown in Figure 1h; each point is the average of four tests. Table 2 contains the individual readings for each cell. The maximum sensitivity was found to be 10 mm deflection per psi. COMPRESSION 2t. TENSION ELEMENT 2 6 n. ELEMENT 2 6n. 3 —_|.- Ioon "’ IOOM Wiring diagram of the diaphragm pressure cell strain gage bridge. Figure 12. 25 A MERCURY-FILLED CLEAR PLASTIC TUBE WHICH CAN BE RAISED To ADJUST h h 5 / i z FORCE TO KEEP CHAMBER SEALED CHAMBER FILLED WITH MERCURY L ”//xxmxxxyxmxm~%%/////% GASKET /////////////AIVl//l "///////////////’" RADSHAW GAGE \\\\\\\\\\\\\\ \b \\ GAGE WIRES TO OSCILLOGRAPH Figure 13. Method for using a mercury column to calibrate the diaphragm pressure cells. 26 l3 IG‘I ' I. I4- I § ._ I2- U) a 1 I g DJ E :3 m d (D ‘62 8‘ a. . § 8 s F- <1 9. /i O 4 z /D /3 — CELL NO. I 2 .‘ "IDEIJ. hiCli! / v- CELL N 0.3 l- CELL N 0.4 ' D-CELL No. 5 o 5 4 s B IO I2 I4 APPLIED PRESSURE-psi Figure 1%. Calibration curve for the diaphragm pressure cells. 27 Another method.wms used to check the calibration of the pressure cells at frequent intervals. A 3/8 in. thick layer Of foam rubber was cut to fit over a cell. A Soil- test model CLp700 penetrometer was pressed on the center of each rubber-covered cell until a penetrometer reading of h.5”was registered. This force then correSponded to a nor- mal load on the tool of 10 psi. The pressure cells were found to be in calibration each time they were tested. A second tool was made of thinner material, sharpened to a more acute angle and not fitted with pressure cells. This tool was used for‘working at more acute angles to the horizontal than the instrumented tool. WWII- The apparent coefficient of friction (AR) of the soil on the Teflon layer of the tillage tool had to be deter- mined in order to calculate the energy expended in over- coming the sliding resistance of the soil on the tool face. A series of tests was run to find the apparent coefficient of friction, and to compare the friction of Teflon with that of steel. Figure 15 shows a schematic Of the method used. The soil sample was loaded with the normal force (N), and then pulled first along the steel surface and then across the Teflon surface. The bottom of the sample was shaved off after each test to provide a fresh soil surface for the next test. 28 ARV coavownm mo pcoaowmmooo econoaam ocwnommoe Rom pom: conga: “memo“. 02.1 040... J<_FZUGZ<.—vv \\\ x t \\ \\\\K\\\K\ \\\h\\\\\\\\\\\\\\\\ \DIK ._.AI JmMPm harm—Jon. 204nm... 4.0m mmoqor 4.0m GomoL .2285 Z .. .3 33$ 29 Three replications each were run at three normal weights (N = 2.2 lb., 522 lb., 7.2 lb.) and at seven mois- ture contents (0.65'fi, 6.0 f, 9.1 i, 11.“ fl. 15". 19.7 $1 and 26.5 5) on a drwaeight basis. The graphs illustrating the results for both polished mild steel and Teflon are Shown in Figure 16, and the data are presented in Table 3. These results agree closely with those of Nichols (1931) for a soil having 16 percent colloid; the soil used in this experiment contained 17 percent colloid, Stong (1960). Ni- chols prOposed four basic phases Of soil and metal friction. These phases were the compression phase, the friction phase, the adhesion phase, and the lubrication phase. This inves- tigation was concerned with the last three phases. According to Nichols, the friction phase is from 0 % to 7.5 % moisture, the adhesion commences at 7.5'% and in- creases to a maximum at 1% % moisture for a soil with 17 % colloid content. The results Of this investigation had a close correlation with those of Nichols. Nichols found the average apparent coefficient.of friction in the friction phase to be 0.h0 for soil on steel. For the adhesion phase the maximum coefficient of friction was 0.56. Excess mois- ture causes a film Of water to reduce the coefficient of friction in the lubrication phase. M f V b . The plunger of an electrical solenoid was attached to one edge of the tillage tool by a flexible cable (Figure 11). 30 ‘I 30 25+“ POLISHED STEEL 7.5 (I) O a 20 .. >5 . .E .9 g TEFUON I g “I c / O ,. .5 . ,I .. / E / g / 5 Ix >032: .mm 833 M7 Locomotion Laboratory, U. S. Army. The Strain Gage Balance and Calibration Unit allows the plotter to be used directly with a strain gage bridge without an external amplifier, and is essentially equivalent to the strain gage input box of the Brush universal amplifier, except that no method for capicitance balance was included. The input to the Strain Gage Balance and Calibration Unit was designed in order that a number of methods of connection could be used. The input connections are Seway binding posts and female Amphe- nol fittings. The wiring diagrams of the Amphenol fittings and the binding posts are the same as the Brush universal amplifier: the connectors used for the plotter can be used on other strain gage equipment. Figure 26 is the wiring diagram for the Strain Gage Balance and Calibration Unit. Figure 2MIC is the Performance Test Rig for the XPY plotter, as outlined in the Mosley instruction manual. Fi- gure 27 is the wiring diagram of the Performance Test Rig. This device can be used to test the performance of both axes of the plotter simultaneously and any irregularities in the resultant trace will indicate a malfunction in the Operation of either axis. A page in the instruction manual pOints out Specific malfunctions, how they will look, and how to rectify them. HI Y BATTERY «(— ! , AXIS STRAIN GAGE BRIDGE T0 <— )‘ «of IAXIS X BATTERY Figure 26. Strain Gage Balance and Calibration unit wiring diagram. ' Figure 27. Performance Test Rig wiring diagram. milun‘e .Na‘ln.’i"oh pm. a. . .‘ILIIUU..I.41 n. . . THEORETICALICONSIDERATIONS Qals2l2ii2n_2i_ihs42rafi_E2rss_en_a_Bisid_Ieel- Soehne (1956) presented the following equation for the horizontal resistance (draft) Of an inclined plane moving through the soil: Fx -.-No (Sins ”1'0 COSS) + kb where: Fx - Draft force (1b.) N a Force acting normal to the plane (1b.) 0 8 3 Angle Of inclination Of the plane to the horizontal (degrees) k 2 width Of the soil slice (in.) b = Uhit resistance of the soil to being cut by the plane edge (lb. per in.) . weds: '_ J: "W 5-1 I 3 h ‘p}° Apparent coefficient Of friction of t e soil on the plane surface Prior to this time there has been no satisfactory me- thod of confirming the theoretical analysis by laboratory tests since the individual values could not be measured se- parately. Soehne states that, "Agreement between the cal- culated and measured values is not particularly good". With the equipment employed in this investigation, however, all the individual components were separated and measured. Fx was measured directly, and S was held fixed. A close esti- mate of Nb could be made from the pressure cells installed on the face of the tool, and kb was measured by simulating the cutting action Of the plane edge by substituting a wire for the tool. [1'0 was determined from a series of tests. 50 To confirm the theoretical equation, a series of cal- culations was made from data gathered on a tool at an angle of inclination 83 ‘00", soil moisture 17.5 5, bulk density 1.23 gm/cc, and a forward velocity of 2.0 fps. From the coefficient of friction tests, the value of p30 was found to be O.k8 for the first l/M in. of the tool (steel), and 0.31 for the remainder of the surface (Teflon). A value of kb 8 15.5'1b. was determined from the tests using a wire to represent the cutting edge. An average value for N61 for the Teflon-covered portion of the tool was calculated from the measured normal forces by the following procedure: 1. The average pressure across the tool was calcula- ted from the pressures indicated by cell nos. 2, h, and 5. 2. The average pressure acting across the tool was divided by the pressure indicated by cell no. 2 to obtain the pressure distribution across the plane (pressure distribution coefficient, q). 3. The recorded pressures of cell nos. 1, 2, and 3 ‘were averaged to obtain the average normal pres- sure distribution along the longitudinal center- line of the plane. h. The averages of cells 1, 2, and 3 were then.mu1- tiplied by the pressure distribution coefficient, q, which resulted in an overall average value for 51 the unit pressure. The unit pressure was then multiplied by the Teflon-coated area to obtain the value for N61. The value for the average normal pressure acting on the steel edge of the tool (Nbs) was determined from the product of the pressure recorded by cell no. 1 and the co- efficient, q. The calculated value was smaller than the ac- tual normal pressure. It is, however, the best information available and must be used until a method can be develOped to measure normal pressure on a very narrow strip of mate- rial. The theoretical draft equation for a tool consisting of two different surface materials is as follows: _ Px -.-. NoT(51"S+P'T CosS) + Nos(Sin{+ F's CosS) 4- kb The calculated values for Fx and the measured value for Fx are shown in Table 11. The letter "M" following the test number indicates that the maximnn recorded forces were used in the calculation and the letter ”A" indicates that the average recorded forces were used. The average value for the ratio of calculated draft to the measured draft was found to be 0.91. A better agreement could probably be ob- tained by using an actual measured value for the normal force acting on a steel edge. .‘s age L‘. -,9‘ so. .3 "' 0,0 .-_ ‘ By considering each of the forces acting on a rigid tillage tool separately, one can determine which forces hi0? I “VH1 52 would be increased or decreased by the use of vibrating energy. The force due to the apparent coefficient of friction and normal force (p3Nb in Figure 2) would be increased dur- ing the portion of the cycle in which soil was being accel- erated upward. Immediately following the upward movement, soil would be lifted upward and exert little or no normal force for a short period of time, and then fall back onto the tool surface in a loosened condition. Forcing the tool into the soil at a more acute angle (in the plane of the tool) would reduce the "bulldozing" effect and reduce the value of N . The cutting force (8) would be reduced only in the case ‘where the leading edge of the tool was not actively cutting into new soil during a portion of the time, as in the case of Eggenmueller's and Gunn's eXperiments. ‘ Resistance to shear plane formation (of + Plnl) could be decreased by reducing either the soil cohesion (c) or the normal force acting upon the shear plane (N1). The area of the shear plane (F) and the internal coefficient of friction Gui) appear to be fixed for any one tool and soil type. No practical method of reducing cohesion is known. However, under rapid loading rates there is evidence to in- dicate that the total strain energy required to overcome the cohesive force is reduced (Hendrick, 1960). Thus, a- mode of vibration in which the shear plane is formed very 53 rapidly would result in less strain energy required to form each shear plane. The author observed during Harris's (1961) research (in which a plate was forced downward upon soil in a con- tainer while recording the resulting internal soil stresses) that regardless of the amount of normal force applied, and regardless of the initial deformation of the soil surface, a very slight reduction in applied force resulted in a cor- responding reduction in soil internal stress. After an in- itial soil deformation of as much as 2 in., if the applied force was reduced to zero, the internal soil stress reduced to zero also, even when the rebound of the loading plate ‘was negligible. Thus, if the mode of vibration of a til- lage tool were such that the tool tip moved at an angle of more than 90° to the angle of shear plane formation, any thermal force (Ni) acting on the soil shear plane‘would be reduced, causing a resulting reduction in the shearing re- sistance. No method is available to measure this force under Operating conditions. Forces due to soil acceleration (A) during the vibra- ting cycle would be greatly increased during the lifting portion of the tool movement, depending upon the accelera- tion imparted to the tool. A small accelerating force ‘would also act as the tool moved forward into new soil. The force due to the soil weight (6) would act any time the soil was on the tool surface. This force could be 5:, reduced by making the tool short to reduce the soil suppor- ted by the tool at any instant. RESULTS W- In order to determine the portion of the total force due to the cutting action of the leading edge of the tool, a wire was substituted for the tillage tool and run through the soil at the depth of the tool edge. TWO diameters of wire were used: 0.008 in. and 0.0‘+l in. The 0.0'+l in. di- ameter wire closely matched the thickness of the cutting edge of the instrumented tool, and the 0.008 in. diameter wire matched the cutting edge of the second tool. Figure 28 illustrates the horizontal force due to the cutting action of the two wires in relation to the cutting velocity at 17.5 1 moisture and the tw0 bulk densities used in the tillage tool tests. An interesting result was the small increase in cutting resistance as the velocitywas in- creased. A similar result was obtained in tests at the Nat- ional Tillage Machinery Laboratory (1961). The average force increased 9 X with a velocity increase of from 1 ft. per sec. to 1+ ft. per sec. When the wire was run a second time in the same cut, the force was 0.1+? that of the origi- nal force. At the lower bulk density the ratio of average cutting force of a wire to total draft of the rigid tool was 0. 51s; at the higher density the ratio was found to be 3. 56. . Thus, any mode of Operation in which the cutting edge 31" the tool. moves into the soil only a portion of the time 56 .>v«ooae> mo couvocsm m on men“: 03» How ocuppso mo eonom Hmucomwno: ozoomm mun. Sun. 53% e n m . one o + u n n u 0 m5; .245 .._¢o..|.l. e mm; .245 .80. .e o\0 .‘G\ Q nUII ~__om (\{\\ .m \\\.\\\ 4! '. 'm...'om' .' ' II@V®|II® G1 mu..\ou\ rm. .0. .wm enamwm ‘lavao sounoa 57 would result in a considerable reduction in the cutting force. In the modes of vibration employed by both Eggen- mueller and Gunn the tool did not cut forward into new soil during a portion of the operating cycle. W- The draft ratio (ratio of the average draft of a vi- {" brating tool to the average draft of a rigid tool: Dv/Da) E was less than one for all but 5’of the 15% tests conducted. I Figures 29, 30, and 31 are graphs of draft ratio versus cycles per foot in eXperiments run at a working angle (8) Lee of’h0° at 10°, 15°, and 20° displacement angles (angles the blade was rotated by the solenoid) and in soils at 1% % moisture and 17.5 % moisture. Each point is the average of h replications. The notation h0°/10° represents a working angle (5) of k0° and a displacement angle (1) of 10°. Fi- gures 32 and 33 illustrate the draft ratio as the angle of action was increased. Figures 3%, 35, 36, and 3? illustrate the decrease in the draft ratio in eXperiments run at a working angle of 30° and displacement angles of 5°, 10°, 15°, and 20° for soil moisture contents of 1% fl and 17.5 %. Figures 38 and 39 illustrate the decrease in draft ratio as the diSplacement angle was increased. The data for all tests are tabulated in Tables 7, 8, 9, and 10. 58 .ooH m5 new 00: rm mom Hoe» mama“ ocm-mcavmnnw> m we moavmn ummna .mm onsmwm ._.oo.._ mum mmuoro N. m v «N o~.m__. ...+r _oo a q - - .56: 8.: 0| . 8. .562 we: AVIII mkmwk emu-8.? H. .v .. 2. u o ..| l. M \ \I I. 00. '0 4 AU . - om. LOO.- 59 .03 l. as 001 "w “8 H08. 33“ use @533? a .8 338 :25 .on 33E Poo..— mum mm...o>o VN ON w._ 4 N. m e . . _ _ . . a a _ . m . O .552 .3: 4| II Av .562 .21 O m‘kmmk .04. .oa 1 8. 4 4 a V . 9. in O 4 O O \ .IIII ' 4 .. O / low. m \I/4 / .. fl 4 / . /4/ G 4 m / -o. o 4 / . am 0 o. / - oo._ 6O 1 PW a .oom me new co: u» now Hoop vane“ use mampmnnm> a mo mompmu omega .Hm «gamma .68 mum $36 e .. Le e . L. L L. . it . Ho .56: we: 4' ..| .552 .3. O . 8. memme .ousoe nu Amt r “a V n... .0 a A I a V 1 00.. 61 l~|+ul| . . .enzpmaos Hue» e :H on com ace .mH .ooH me can .0: u» now woman“ semen mo converse .mm shaman Pooh. mum mun—ore e «N on 8.. u. m . +4 , no ‘ - J .56: .2: com \oo¢ l O 5. Olive so. $O¢ ‘1 o0. \eOQI‘ 'O/Ml 62 . . . , .onaumfios Haom e m S em com .2; .3 03 i. use so: u... n8 838 $8.0 mo 533%.. .mm 98m: 5.00.... mun. muqoro IIJFvu L Low . e._ 4 ~._ . m¢4w.m10 18. F902 80.: L H V . 2... u , .0 oON\eO¢I‘ .. A0 oD—\eo.¢l‘ 100. W .o_\.oe\ :00. 100.. 63 «F33 «Fear. . f‘l I‘ll .om n». «Em com "w mom Hoov 3a.: new 9.3.8.305 m mo modem." pmmna ....m mnsmwm Pooh. mun. mmmo>o cm ON 8. N. o . e oo 4 a 8 d u u q q 4 4 — u u M j L 0m. .56... $3.41!] . a .56: 810 III. N .. o» m mkmmh .m\.om . 0 A / Low. 0 V O o o .. om. Q: Q / G J \<\ o o / ZLoo; OH "x“. new com um mom Hoop 33.9 new acupmnna> m mo moapmu :35 .mm 9.25.: .50... mum mm..o>o cw ON 8. . N. m . e o . . q . . a . . a a — 1 a F0 O .562 so: a [1| .562 «.2 all. .. 8. $8» .058 l O . N VO/ACI OliVH I 0 Q L 00.. 65 .oh. "xx ocm com "me new Hoop 3.3.” new mcwpmnfig m mo weapon ”Emma .50... mm... mumoro .om onsmflm .v IIJLVN . 0_N . 0.. . Ne. - 40 .4. . H0 . l 8. ....m.0.z oxow. 3mm... .98» . . a N G G 1 0h mm 0 e m 0 Q G 100. 'mu 0 . G @ .. cm. .60.. .oom wk. new com u» H00 H00» 3a.?» new mcwpmunf, m we mowwmn ”:th .mm 0933.... A .50.. mm... 3.85 - cm cm 8. N. m .V o d q q 4 J u d a q d m d 1 ho . 4 G . .. 8. .562 «.3. elm: II / a / a .55.). .2: all . v / 1 OF H... % allege .oIIII~\.on 0 a la 0 e e .. a G M e 8. m :1 JG 0 G om. 8.. 6.7 . .onnumwos Haom m +3 p. .9... .8. a? ..o. .2. n... .23 .om aw now .038 82.. cc .3323. .mm 8:3". .60.... mun. mun.0>o em ON 8. N. m . . e o . q _ 1 d W J a a a _ J 4 +0 . . 1 O@. H20... .8! w I. . u 95» on 0 83m 0 II. . A 0:0» W 1 0m. axon, .. om. - 00.. 68 . .ouspmwoe Haom & méa am now new cm.” .03 . om u... can com uw now 839mm "Coup .«o c0323. .mm shaman. #00... mm... mmdoro . o e I]: II... . . L. . . I1 .M. 5.0.2.89... . .8. eON\e0n . 8 V . 2. . u .0 . O \ A .058 -8. m V -om. .9.8\ .09. 1... r.n4.rlflfll%.ulhm.. dalJIaghn-Ud .. 69 An F test was made to test the hypothesis that the mean draft ratios were equal for experiments conducted at the same working angle and displacement angle but in 1‘4» x and 17.5 5 soil moistures for corresponding values of cycles per foot. The hypothesis was rejected at the .05 level of significance for all tests except the W°/10° and 30°/5°ex- periments. From this it can be concluded that for at least one value of cycles per foot in each rejected test the re- duction ratio was significantly less for the 17.5 f mois- ture tests than for the 1% % moisture tests. Closer ob- servation of the data indicates that the draft ratio was generally lower at 17.5 i moisture than at 1% % moisture. An F test was made to test the hypothesis that the mean draft ratio was equal for experiments conducted at different displacement angles but at the same working angle and soil moisture. The hypothesis was rejected at the .05 level of significance for all but the 30°/15° vs. 30°/20° and 1+0°/l5° vs. '+0°/20° experiments. Itcan therefore be concluded that for at least one value of cycles per foot in each rejected test the reduction in draft was signifi- cantly greater for the larger displacement angle. Closer observation of the data indicates that in general a larger diSplacement angle reduced the draft ratio. As may be expected, there was a tendency for the draft ratio of the tool run at a working angle of 30° to be less at each correSponding displacement angle than for tools 70 run at a working angle of lt0°. This would appear to be due to either or both of two factors: (a) at the 30° working angle the tool tip moved upward at an angle at or greater ~than 90° to the soil shear plane, which reduced the normal force (N1) on the soil shear plane, and (b) a larger por- tion of the force transmitted by the solenoid acted in the horizontal direction when a working angle of 1+0° was used. .Due to the design of the model tool, and from the results of the tests conducted to determine the forces the solenoid exerted upon the tool, the second factor can be neglected since the point of attachment between the flexible cable and the tool resulted in a smaller moment being exerted up- on the tool at a h0° working angle at a specified solenoid force, and since the force exerted upon the tool by the solenoideas virtually the same for both 30° and h0° work- ing angles. The greater reduction in draft force at an angle of 30°*was, therefore, probably due to a reduction of N1, since the tool tip did move at an angle greater than 90° to the shear plane. The soil shear planes created by the tillage tool were observed to have an angle of 28° to 30° with the soil surface. Unfortunately, there is no reliable method available for measuring the normal force acting on the shear plane. .By activating the tool tip upward, the applied force was more nearly parallel to the direction of the soil shear 71 plane and soil diSplacement: this resulted in a more effi- cient application of the tillage forces. Energy Requirement 9f the Vibrating glagg. A comprehensive analysis of the soil forces during 0p- eration of the vibrating tillage tool is not possible at the present time. Many of the variables which must be con- sidered cannot be measured, or even estimated with any de- gree of accuracy. The normal force acting upon the soil shear plane (N1) cannot be measured, even though the reduction of that force is one of the possible advantages of a vibrating blade. Another soil force, the cohesion acting on the soil shear plane, cannot be measured under extreme loading rates. The reduction of total strain energy by reducing the dis- placement required to cause failure of the cohesive bonds by rapid loading was another possible advantage of the vi- brating tillage tool. An observation was made, however, that when the blade was moved slowly (by hand) through an angle of 10°, a shear plane was not develOped; when the blade was moved rapidly through the same arc by activating the solenoid a shear plane develOped. In a preliminary investigation to determine the accel- eration of a soil slice by the vibrating blade, the verti- cal diSplacement of a rigid body placed on the blade at the point of percussion and accelerated by the action of the blade was calculated. If the blade was at a working angle 72 (8) Of1h0° and activated by the solenoid through an angle Of 10°, the rigid body would have been diaplaced a total distance of 1.1 in. in the vertical direction. Since the observed vertical displacement of the soil slice was less than half an inch, the remaining diSplacement and energy must have been absorbed in shattering and compacting the soil on or near the tool face. The only remaining method of determining the energy requirement was to measure the energy applied to the soil by the combination of draft force and solenoid action. The input energy due to the draft force was simply the product of average draft force times unit distance. The input en- ergy due to the solenoid was calculated from the solenoid movement, the force applied to the blade, and the frequency of Operation. Table 6 lists the solenoid energy input to activate: (l) the blade alone. (2) the blade and loose .soil, and (3) the blade in forming a new shear plane for one cycle. In order to determine the energy the vibrating blade applied to the soil compared with the energy requirement of a rigid blade, the draft of a rigid blade per unit of tra- vel was considered as 100 %. The relative draft Of the vi- brating tool was then one energy input, and the energy of the solenoid was the other input (the solenoid energy re- quired to accelerate the blade alone was subtracted from the total solenoid energy since it was not actually applied 73 notfim soil). Figures 40 through NM illustrate the compar- ative energy input to a vibrating tool under various condi- tions of working angle and diSplacement angle as a function of the number of cycles per foot of travel. In general, the energy requirement Of the vibrating tool was Observed tO be less than that Of the rigid tool for a narrow range Of low frequencies; it then exceeded the energy requirement of a rigid tool. It should be noted. however, that at the higher vibrational frequencies (10 to 15 cycles per foot Of travel) more shear planes were formed per unit distance traveled by the vibrating tool than by the rigid tool, resulting in better particle size reduction. The shear plane formation Of the rigid tool was very nearly constant at 5 shear planes per foot. At frequencies above 15 cpf, the blade did not return to its maximum working an- gle before it was activated again, which resulted in its Operating through a smaller diSplacement angle during each cycle; therefore, it did not form distinct shear planes. That condition was observed during the analysis of the recorded forces: when frequencies above 15 epf were used, the rigid-tool pattern Of shear plane formation was record- ed with small forces superimposed upon them each time the soleno id was actuated. 7'4- .OnsumHoE 30m x mKH pm 00H "(a 0:0 00.... "w 08...; H00... 3me m 0.... oomeEOo Hoop 05.8.3.3 0 mo 00.300 30:38 new ”Como .5 .0339... image peoonom .0... 0.33m #00... mm...— mw40>0 em 00 0. u. 0 . e .0 3 N memme .0_\.0¢ . 00 m. 9 . A . 0.. m n :1. u... . 8 a o 3 . N I. L 00 . 00. 6.30.306 30m R mé; pm om” n... 0:0 00.. um when; H00» 3me m on 00900500 Hoop ucwvmmna> 0 mo cowpum owocoHOm 0cm pmmuo >n nowaamm >mnoce pcmonom .H: magnum P00... mun. mm40>0 n. - .. . ._ - ._ - . who”... \ 3 8 9 . A :7; I Loan 0. .I. a.“ .Avw H. 0 3 l “N 1 II. 00 00. 76 .3339: 30m & m4; um com us 28 no: uw 3ch ~03 39.9 m op umumqsoo Heap mcapmnnw> m mo cowpom uHocmHOm cam pmmnv >n nmaaaam >mumcm ucwonmm FOO... mum mw40>o mkmwk oON \o0¢ .N: mnzmwm 8 ASBBNB CD 1? C) (0 15130334 ‘LndNI CD 00 co. 77 .mnapmwoe Haom R_m.ma um ooH "a van oom n» mama: Hoop udmwu m on vamQEOo Hoe» mcwumund> m mo cowuow uwocwaom van pmmuv >n nowaaam >mnmcm pcmonmm PO 0 u. mmm mw40>o ‘Vm .QN _W_ N. .0 .V Av a . u p w p «P . u . LL10 :1 D—Ozmn—Om FmNF .0- \00m f 6 N A983N3 6 c0 .LNBOHBd ‘Lndm .9 83$ Pmamo %om \ \InmtdkO P / . .3338. :3 R m.§ pm oomuk “Em com nw mag; #03 33H m 3 @3353 Hoop acapmunw> m mo cowuom cwocwaom tam ammuv >3 vmwaaam >mnmcm pcmoumm .J: mnsmwm #00“; «mm mMJo>o mm . ow . w. . ~._ . m. . w. 00 . 3 m ION a 9 IA FmMF OON \oon w % lio¢ u .4. r 0 Item d 3 “d nu .T 3 N l. $00 \I'/ r \va \)4 :oo. SWJIUXRY Laboratory tests were conducted in a mobile soil bin to determine the draft and energy requirements of a simple vibrating tillage tool. The draft and the energy require- ments of a rigid and of a vibrating tool were compared. Equipment was built and instrumentation was develOped to determine the various components of the soil forces act- ing Upon a tillage tool, and to locate the point of appli- cation of the resultant soil force on a flat tool. A strain gage dynamometer was used to measure the re- sultant soil forces on the tool, and pressure cells were mounted in the surface of the tool to measure the normal force exerted by the soil. Tests were conducted to determine the amount of force required to merely cut the soil in an effort to determine that portion of the draft force required to separate the soil slice. The vibrating tool was a simple inclined plane, mount- ed in such a way that the leading edge could be forced up- ‘ward about a horizontal axis through its trailing edge. The tool was powered by an electric solenoid. The rigid tool was simply the above tool locked in position. The draft of the vibrating tillage tool (compared with the rigid tool) decreased rapidly as the vibrational fre- quency approached the natural shear plane frequency of a rigid tool; beyond that frequency the draft reduction was 80 slight. The energy requirement of a vibrating tillage tool was computed on the basis of the draft force and the energy provided by the vibrating mechanism. The energy requirement of the vibrating tool was in general less than that of a ri— gid tool at low frequencies, and exceeded the rigid tool energy as the frequency was increased. The draft reduction was generally greater for larger amplitudes of vibration and for soil with a higher shear strength. Better soil crumbling was observed with the vibrating tool than with the rigid tool, which may lead to seedbed preparation in a single field Operation. COI‘C LUSIONS AND OBSERVATIONS l. The draft of a simple tillage tool can be reduced by pivot mounting the tool in order that the leading edge can be swung upward to cause soil failure. 2. The draft decreased as the frequency of vibration was increased up to the natural frequency of shear plane formation for a rigid tool. Beyond that frequency. the draft reduction was slight. Other factors affec- ting the amount of draft reduction were soil physical properties and magnitude of tool movement. U) o Vibrating the tool did not materially reduce the total tillage energy requirement of the soil. h. Approximately 50 Z of the total draft force of a rigid tool of the type used in these tests can be attributed to the cutting force on the leading edge of the tool. 5. The instrumentation and methods developed in this study can be used for further studies of vibrating tillage tools. b va . 1. Since the resistance to cutting soil increases only slightly with an increase in speed, a mode of vibra- tion which prevents the tool from cutting during a portion of the tillage cycle should further reduce draft. 3. 82 Better soil crumbling was observed when the vibrating tool was used. Therefore, a vibrating blade can be used to control clod size and thus reduce the need for secondary tillage Operations. An analysis of the efficiency of a vibrating tillage tool based on the mean clod size will probably show that the vibrating tool is a more efficient tillage tool than this study or previous investigations have actually indicated. l. 2. 3. 1r. 5. 7. SIEGESTIONS Fm FERN-E1 INVESTIGATIONS Studies should be conducted to determine the effect of vibrations on the values of cohesion and internal angle of friction of soils. A study should be made in which the efficiency of 0p- eration of a vibrating tillage tool is based on soil clod size reduction. Methods should be devised to measure the forces acting in a soil mass during the operation of rigid and vi- brating tillage tools. A technique should be develOped to measure more com- pletely the normal and tangential forces acting on the surface of a tillage tool. Vibrating tillage tools employing many different modes of vibration should be studied. Tests using the present tillage tool should be conduc- ted in various soil types to further study the effect of the soil parameters upon draft reduction and energy requirements. Study the possibility of applying mechanical movement to a plow body from a separate power source. REFERENCES Austin. E. I. (19h8). Earth-mover blade with vibrating attachment. U. 5. Patent Office No. 2.hh3,h92. Brewer, C. A. (1927). Soil-vibrating apparatus. U. 8. Patent Office No. 1,61%,273. Casagrande, A. and Shannon. I. L. (l9k8). Stress-deforma- tion and strength characteristics of soils under dyna- mic loads. Proc. of the Second Internatl. Conf. on 5011 “93“. and Found. Engre. V01. 5. p. 29. . (19MB). Research on stress-deformation and strength characteristics of soils and soft-rocks under transient loading. Harvard Grad. School of Engr. 8‘11. ”+8. Demenlenaer. Go (1936). P1”. Us 5. Patcnt Office Pb. 2.0670639. [Dubrovskii. A. A. (1956). Influence of vibrating the tools of cultivating implements upon draft resis- tance. Shornik Trud. semled Mekhan. Lenin Akad. selko 2. Rank GCaterpillar Translation No. 221). Eggenmuller. A. (1958). versuche nit Gruppen gegeneinan- der schwingender Hackwerkzeuge (Experiments with al- ternately oscillating hoe tines). Grundl. Land- tech.. heft 10, p. 70 (Caterpillar Translation No. 221 . . (1958). Feldversuche mit einem schwingenden fiflugkorper (Field expgriments with an oscillating plow body). Grundl. ndtech., Heft 10. p. 79 (Caterpillar Translation No. 221). . (1953). Untersuchungen an schwingenden Hanfel- koropern (Investigations on oscillating ridging bodies). Grundl. Landtech.. Heft 10, p. 1R3 (Caterpillar Translation No. 221). . (1958). Schwingende bodenbearbeitung swerk- :uege: kinematik und versuche mit einzelnen modell- 'werkzeugen (Oscillating implements: ‘Kinematics and experiments with models of individual tools). Grundl. Landtech.. Heft 10, p.-55 GSaterpillar Translation No. 221). (Sarst, D. (191%). Means for clearing the surface of dirt working tools. U. S. Patent Office No. 2,087,639. 85 Gill, M. R. and McCreery. s. F. (1959). The effect of the size of cut of two types of tillage tools on clod sire and efficiency of Operation. Paper presented at 1;” lighter A.S.A.E. Meeting. Chicago. 111.. Dec. Gunn, Jack T. and Tramontini. V. N. (1955). Oscillation of gigs” implements. Agr. Engr., Vol. 36. Mo. 11. PO e . Harris. I. L. (1960). Dynamic Stress Transducers and the Use of Continuum Mechanics in the Study of Various Stress Strain Relationships. Unpub. Ph. D. Thesis. Michigan State University. East Lansing. Hendrick. James G. (1961). Strength and energy relations of a dynamically loaded clay soil. Transactions of th. AeSeAeEe. V010 ‘I'. lb. 1. DO 310 Hendrick. James G. (1962). The tillage energ of a vibra- ting tillage tool. Paper presented at t Annual 15%? :0 Meeting of A.S.A.E.. lashington, D. (3.. June Hubert. L. A. (1909). Gang plow. U. 3. Patent Office No. 939.132. Kaburaki. H. and Kisu. M. (1959). Studies on cutting characteristics of plo hs. Jour. of the Kanto-Tosan Agr. Exp. Sta.. No. 12 NIAE Translation No. 79). Koudner. R. L. (1960). A Mon-Dimensional Approach to the Vibratory Cutting. Compaction. and Penetration of Soils. The Johns Hepkins Univ" Baltimore. Md. 183 pp- Lambe. T. I. (1951). Soil Testing for Engineers. Chapt. XIII. John Uiley and Sons. N. Y.. Po 93. National Tillage Machinery Laboratory (1961). Soil-tool Relationships. A portion of the N.T.M.L. 1961 Annual Report. Nichols M. L. (1931). The dynamic prOperties of soils. 11. Soil and mu friction. Agric. Engr.. Vol. 12. No. 8. p. 321. Payne. P. C. J. (1956). The relationship between the mech- anical prOperties of soil and the performance of sim- ple cultivation implements. Jews. of Agr. 'Engr. Re- search. Vol. 1. No. l. p. 23. 86 Rhoten, C. M. (1950). Heating and vibrating means for plow moldboards. U. 8. Patent Office No. 2.304.173. Seed. H. B. and Lundgren, R. (1990). Investigation of the effect of transient loading on the strength and de- formation characteristics of saturated sands. ASTM MCO. V010 9". p0 1288e Shkurenko. N. S. (1960). Experimental data on the effect of oscillation on the cutting resistance of soil. J. of Agric. Engr. Res" Vol. 5. No. 2. p. 226. Soehne. I. (1956). Eini e Grundlagen fur eine Landtechni- sche Bodenmechanik Some basic considerations of soil mechanics as applied to agricultural engineering). (irundils.3 der Landtech.. Heft 7. p. 11 (HIAE Translation Mo. . Stong. Jack V. (1960). Basic Factors Affecting the Strength and Sinkage of Tillable Soils. Unpub. M. S. Thesis. Michigan State University. East Lansing. Taylor. D. I. and Ihitman. R. V. (1990). The Behavior of Soils Under Dynamic loadings. Rpt. No. 3. Mass. Inst. of Tech.. Soil Mech. Lab.. Boston. Terzaghi. Karl (1953). Theoretical Soil Mechanics. John liley and Sons. New York. +91 APPENDDC A SAMPLE ROBLEM Given: Find: Solution: A T “L I DYNAMOMETER CENTER ‘— STAN DAR D e =- ’+ 1b., M s 120 ill-11)., ct = 30°, Fx 2 10 1b., F Y. = 10' Y Resultant force (R and point of application on the blade (x and y . 1) RtJsz-l- r5 .-. no.9 lb. 2) Equation of the plane of the blade: y=y’*‘TCfl¢eeeeeeeeeeeee(a) 3) Equation of the resultant force direction: y=y"-xTcn9 O O O I O O I O O O O. O O (b ) h) Solving (a) and (b) for x and y: y'+ xTcn¢ = y"-xTcn8 y: y'+ xTcnK F Tonp: _Fl : 0.40 1: TON“ = 0.58 I|_ _M__=|_2_o__ .. F“ | - I2.0 l2.0-|0.0 _ " ' .se+.4o " 2‘06 Y = I0.0 + (2.06)(0.58)= ".2" APPENDIX B 89 TABLE 1 Dynamometer and Pressure Cell Calibration Information (Brush Model 520 Amplifiers) Recorded I’ Calibration I Operation Force Attenuator mm Attenuator mm pet I Sbtting (Deflection Setting lunit Load W: 1 Draft (Ex) 2 32.5 2 2 1b/m vertical (FY) 2 33.5 2 2 lb/hm Moment (M) 5 19.0 5 2 ft-lb/hm 3%: #'l 5 21.3 2 0.5 psi/hm # 2 5 21.9 2 0.5 psi/mm # 3 5 17.0 2 0.5 psi/mm # ‘+ 5 15.2 2 0.5 psi/m #‘5 5 29.8 2 0.5'psi/mm 90 TABLE 2 Tool Pressure Cell Calibration Applied Pressure Chart Readin mm Defl c n , psi in. Hg Cell Cell Cell Cell Cell 1M# 2 # 3 # h # 5 1 2.1/32 108 2.0 2.0 2.0 2.0 1.8 2.0 2.0 1.8 2.0 2.0 2.0 1.8 1.9 2.0 2.0 2.0 1.9 1.8 1.8 2 l+-1/16 3.8 tho ‘+.0 3.8 3.8 .0 1+.0 tho 3.8 3.9 I+00 “.0 3.8 3.7 3.8 3.6 1+.0 2.8 3.8 .0 3 6-1/3 5-8 5-7 -0 5-5 5-5 5-5 5-3 6-0 5-5 5-5 5-6 5-9 5-8 5-5 5-5 5-7. 6-0 5-9 5-5 5-9 '+ 8- 5/32 7- 5 7.6 7.8 7- 5 7-3 7e 3.9 Boo 705 70g 70 DO 705 700 70 706 8.0 706 705 7.5 5 10-3/16 9. 5 9.8 9.8 9.6 9.6 9-5 9-3 10-0 9.5 9.6 9. 5 9- 9 9. 5 9.3 10.0 7 5 5-1/!+ 13’; 13'; 1'95'6 13"; 13'? 11+. 5 1‘0. 9 15.0 1%. 5 111.0 11+. 5 1‘59 1 5.0 11:. 5 1 5.0 l’+. 5 1):. 9 11+. 7 1%. 5 11+.0 10 20-3/8 20.0 20.0 20.2 20.0 20.0 20.0 20.0 20. 5 19. 8 19. 5 20.0 19. 7 20. 0 20.0 21 . 0 2 :2"? 5%?- ?? 3% $22? 12. 2 1 . . . . . 5 5. 3/3 25.5 211.5 25.7 25.g 25.0 25.5 21:.9 25.5 25. 26.5 25.0 21+.6 25.0 25.5 25.0 1 5 30-1/2 31.0 30.0 31. O 30. 5 30. 5 31. 5 30.0 31.5 31.6 30.5 31.0 30.0 30.5 31.5 32.0 30.0 30.0 30.0 31. 5 91 TABLE 3 Normal Load vs. Tangential Force for Mild Steel and Teflon at Various Moisture Contents Moisture Norma1* I Tangential Force (1b,) (5) Load Steel Teflon (1b.) 1.05 0.65 2.20 1.00 0.60 0.85 0.55 2.60 1.k5 0.65 5.20 2.60 1.h5 2.65 1.50 3.70 1.90 7.20 3.60 1.90 3-50 1-90 0.95 0.60 2.20 0.85 0.65 0.90 0.60 2.10 1.k0 6.0 5.20 2.10 1. 0 2.10 l. 0 3.10 2.00 7.20 2.90 1.30 2.80 2. l 0.65 0.55 2.20 0.70 0.65 0.70 0-70 1.50 1.h5 9.1 5.20 1.50 l.#0 1.55 1.h5 3.00 2.10 7.20 2.60 1.80 20% 20m 0.70 0.60 2.20 0.65 0.k5 0.85 0.57 1.90 1.20 1.1."? 5020 1°80 1'20 1.90 1.10 2.30 1.‘+5 7.20 20 5 1.50 2.30 l.h0 1030 0080 2.20 1.20 0.70 1.10 0.70 2.55% i0lg95 1 .l .20 2. . 5 5 2.50 .60 3*;3 as: 020 3. . 7 3.50 2.15 92 TABLE 3 (continued) Moisture Normal* Ta ential Force (1b,) (1) Load §teeI Teflon (1b.) 1.05 0.80 2.20 1.10 1.00 1.10 0.80 2.20 1.60 19.7 5.20 2.10 1.60 2.15 1.65 2.70 1.85 7.20 3.00 2.20 2.60 2.20 0.60 0.70 *i 2.20 0.50 0.55 0.70 0.70 1.00 1.10 26.5 5.2 1.20 1.20 1.00 1.30 *‘ Cross-sectional area of the soil sample s 0.7% in2. *! At 26.5' moisture, water was squeezed from the sample at 5.2 Normal Load. 93 TABLE 1+ Force Exerted on the Blade by the Solenoid Material working Displacement Solenoid Maximum Actuated Angle Aggle Movement Force (8 ) ( ) (19.) (1b.) Blade Alone 30 10 .19 19 30 15 .2 25 a8 20 .3 39 10 .19 18 #0 15 .2 22 no 20 .3 31 Blade in 30 10 .19 22 Loose 505.1 30 15 .2 38 0 2o , .3 55 0 10 .19 23 MO 15 .2 3g #0 20 .3 Blade in 30 10 0.19 2“ 0.2526351; 33 :3 -§ 2: 0 CC 0 g 30 10 .19 25 #0 15 .2 M6 ( m/ ) Itg $8 .139 g 1.2 cc 3 . 3 g 30 15 .2 56 fig 20 .3 7 10 .19 2 no 15 .2 55 MO 20 .3 70 91+ TABLE 5 Average Draft Values for a Rigid Tool Run at 30° and W‘ working Angles lorking Bulk Parcent Forward Average Standard Angle Densit Moisture Speed Draft Deviation (8 ) (gm/cc (fps) (1b.) (1b.) 30 1.12 1h 1 6.2 1.3 0 1.12 11+ 2 8.1 2.0 30 1.23 1h 1 9.8 1.5 38 1.23 1‘: 2 11.6 2.7 1.12 11+ 1 8.8 1.6 1+0 1.12 1‘: 2 10.1 1.3 1+0 1.23 1‘: 1 10.0 1.1 ‘00 1.23 1’+ 2 11.8 1.9 30 1.12 17.5 1 13.2 2.6 30 1.12 17.5 2 9.5 1.6 30 1.12 17.5 1+ 12.9 2.0 30 1.23 17.5 1 1g.9 2.):- 13.3 1.23 17.5 2 1 .‘t 2.5 1.12 17.5 1 12.2 12.3 1:0 1.12 17.5 2 16.5 . 1:0 1.23 17.5 1 lg.1 2.6 E 1&0 1.23 17.5 2 l .0 2.1: s = TABLE 6 Energy Transmitted to the Blade by the Solenoid in Soil at 17.5 f Moisture hog-king Displacement Ene r C cle (ft-1b) Angle Angle Bare ose ac , (6") ( ) Tool Soil 1.12 9 cc 1. 3 9 cc 0 10 0.19 0.21 0.23 0.2 3 1 5 0.112 0. 51 0. 62 0. 7g 20 0.87 1.12 1.21. 1.118 1:0 10 0.16 0.253 0.25 0.28 15 0.1411- 0. 0.65 0.78 20 0.92 1.20 1.35 1.62 95 62. 2a m~.2 2 “2 mo. “2 m~.2 2 m2 m . s m~.2 2 m2 2 . 2 m~.2 2 m2 .25. 2“ «2.2 2 m2 «w. m ~2.2 2 «2 m . o «2.2 2 M2 as. 2 «2.2 2 m2 mm. 2~ «2.2 2 02 cm. a «2.2 2 62 o . 2 «2.2 2. 02. a . 2m m~.2 ~ o2 2m. «2 m~.2 m 62 mm. 62 m~.2 m 62 mm. o m«.2 m 62 «a. o m~.2 m 02 2a. 2 m~.2 m 02 as. 2w «2.2 m 62 on. m «2.2 m 02 22.2 2 «2.2 ~ 02 2b. 2~ «2.2 2 o2 so. 22 «2.2 2 62 mm. o «2.2 2 62 . 2 «2.2 2 62 2m. 2N «2.2 2 62 mm. m ~2.2 2 02 «o. 2 ~2.2 2 02 ace2coaacoauv one oo a an omuom a as aw? xomeaovenm 330W we mm one?" «and; 23023322, 228 5.2 2.2.8.293 easy-«o: 226w “.22 new so: we “my o~u¢< madman: m Hem sumo.umeaa e>nuu2rm u mqmomeauwum a2mflew macaw ewwrw 1%.. 223223222, 22am :3 «cos-8222.3 euavndoz 2aow R.m-b~ ucm 00: mo “my e~o¢< mfldxuol m new mvmo.ammha.e>damaem w mqm 2302282; 228 :22 «cos-8232a 2em=c2pcouV m m2m0.mo2&voum saunv— weoww mac". «am-Nana; 2802232222 228 :22 23.8.2328 .usu.2o: 22.» u 0.22 on. .om mo 2w2 o2nc< 2:22223 e 202 «ago 2222a..>2ua2om m .392. lOO NM. 2N 2N.2 2 8 N . o MN.2 2 ON 2&- 2 MN.2 2 ON N . 2N N2.2 N 0N bu. N2 N2.2 N 0N m . w N2.2 N ON 5 . 2 N2.2 N 0N mm. 2N N2.2 2 ON 2m. m N2.2 2 ON 2». 2 N2.2. 2 ON a . 2N 2N2 2 8 o . N2 MN.2 2 ON 2m. N mN.2 2 3 2 . o MN.2 2 ON a . 2 MN.2 2 ON 2n. 2N mN.2 N m2 wm. m MN.2 N m2 . 2 MN.2 N M2 22.. 2N N2 .2 N m 2 an” m N2.2 N m2 mm 2 N2.2 N m2 auo2co2ec052o emu on u an ewnom among uwm >uwonuwum vdmwow. Moomw ommrw. - 280228222, 228 :3 2358.233 2603:2vcoov m w2momeauwnm mv2fiuew weomw emmrw N 3520922; 222.5 Sm «rescalin— 22323. 228 u “.2 65 .on No 23 .2922 822.23 a .28 38 3.8 2.22.2.2. 02 N29: TABLE 11 Tabulation of Values Used for Com Measured Draft Force paring and Computed Draft Force for a Rigid Blade (5 =- ‘10“) N2 Test 1.01 00 .36 .33 .92 81+ .72 1.07 .93 U:o:.-:ch?O\O\ O O O O O O 0 m2ommm mum :m:MMN NJN OQONMbOmOG NONHHONONO MBNBMNOMOQ 000 NHHOHHHHHO MOOOMNNOON eeee (GI-:mNHHF-IHMN mmmoommmmm no 00000 NHNHNHNHNH homomommoo 0.00.0000. mmmJMNoNbN 2<2