- u an. IV a .3. . Artful-av. a.f.thf .5“... ‘ w...” m... - nee-w .. . 1 . J .a 9.1 b.“ I , - ‘C—O . In . . h. . . . (a. my nun-9.. V . . ‘1 ... . ’ Han-UV. ~.l¢..¢.a.».. . . .th. . , :1 1 kn. H1 Graham. . . kafiéwumvs ’éhvfimaflrtwfiflmw 1.? w‘\VH.Fhu..I out: 2.5% I . . ‘ .3 '4 0‘ . ‘ . A. .. u. 1 $52.... .1“: a... ) . 0 .. I 3. ., DR... 0:. OIA..-'. r? .75... ‘ 7 fin. I P... F5747 .s‘ h D 3r I) V f 3, «1 I a- _ _.. at? up“. . I .5 ‘4‘ " D. 2 - "I «I. x -"l.v‘1-‘ ~ ...-.4 . .qu3.fl?a:.: I!!- I: d...o~ . ...I.:u.l. . s .1. J :1 00.5.... .11.. . fin...” .u‘Ii-a .. v. 1-. :. waif ..'. 2.? .r... J. I; an? 39%;“. d. . .x , I .. I . I: ._ r L: a. v9... 2.. #3.. :m ,1 t MI #3. 1.14 .v tn,” “.1 .I I" ....,..,‘ "-1 W." -...4||...I..III!D....4.1).I.,I11IIJ . A.» .. I I n. A. g. LIBRARY 1 A Michigan State “at. University VEHICULAR MECHANICS OF A TRACTOR OPERATING 0N YIELDING SOILS by Arnold G. Berlage AN ABSTRACT Submitted to the Colleges of Agriculture and Engineering - of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN AGRICULTURAL ENGINEERING Department of Agricultural Engineering ’ 1962 Approved by %, 'fgtpx/é TfH Elvin 1 tract {rear axle t front wheel .‘hese data if aquations pr nudity. $011 Va tho obovc to mother set the porter: conditions { Indie were obta 9' Pertineni ; in late; g moored “What 4 Rear axle l' 583137391 c LIBRARY ‘ Michigan State University ABSTRACT A tractor was instrumented to record dynamic data (rear axle torque, weight transfer, rolling resistance of front wheel and slip) at various constant drawbar pulls. These data were applied to a set of dynamic vehicular equations proposed by Buchele (1961) in order to test their validity. Soil values were measured with a Bevameter at the time the above tests were run. These values were applied to another set of vehicular equations (Buchele 1961) to predict the performance of the vehicle operating under various soil conditions. Indications of weight transfer and rolling resistance were obtained by attaching strain gages directly to the pertinent members of the vehicle thus making the transducers an integral part of the vehicle. Actual drawber pull was measured by using a strain gage dynamometer between the drawbar and load cable when lifting a constant dead weight. Rear axle torque was obtained by means of a specially designed compression ring torque transducer. Construction and operation of the torquemeter are described. Excitations from the strain gage bridges were amplified and recorded. The recorded data were processed and the ex- perimental results were plotted for comparison. 111 Experimental data were substituted into the theoretical equations and the weight transfer calculated. The calcula- ted weight transfer closely agreed with the experimentally determined weight transfer data. Weight transfer was shown to vary directly as drawbar pull while front wheel rolling resistance varied inversely as the pull. Soil values were obtained with a Bevameter following the procedure suggested by Stong (1960). The prediction of vehicle performance by substituting these soil values into the vehicular mechanics equation cannot be Justified by this study. S ubnit of fl“ VEHICULAR MECHANICS OF A TRACTOR OPERATING ON YIELDING SOILS by Arnold G. Berlage A THESIS Submitted to the Colleges of Agriculture and Engineerin; of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN AGRICULTURAL ENGINEERING Department of Agricultural Engineering 1962 ACKNOWLEDGEMENTS The author wishes to express his sincere appreciation to his major professor, Dr. Wesley F. Buchele, for the guidance, encouragement and assistance throughout the course of the project. Sincere thanks are also extended to the following indi- viduals and organizations for their aid and assistance: Land Locomotion Laboratory of the Detroit Ordnance District, the project sponsors, for the financial support. Massey Ferguson Inc., Detroit, Michigan, supplied the Massey Ferguson 50 test tractor. - The Timken Bearing Company who donated the tapered roller bearings used in the construction of the compression ring torque transducer. Mr. Roy Ohler of the Michigan State Highway Department research division for the loan of portable highway scales. Dr. 0. A. Tatro, Applied Mechanics Department, Michigan State University, for information concerning strain gage theory and for the use of test equipment. Dr. P. H. Busiow for his interest and assistance regarding various transducer and instrumentation problems. Mr. J. B. Cawood and staff of mechanical technicians for their assistance and suggestions concerning the construction of the test equipment. III. :1. to"! wii‘v V: Dre. C. J. Mackson and G. H. Martin for serving on the author ' s guidance commi ttee. The author's wife, Marian, and children, Steven and James, for their cooperation and understanding. . 1M.m'&.'lfim. -, TABLE OF CONTENTS Page Inrnowcnon........_.............. 1 Lirnmmnsnsnsw . APPARATUS up INSTRUMENTATION . . . . . . . . . . . . Rear ”1. Torque O O O O O O O O O O O O O 0 O O 03 CD (D #' Tomuemeterdesiweeeeeeeeeeeee Operational analysis of the torquemeter . . 13 Bridge circuit . . . . . . . . . . . . . . . 1} Calibration . . . . . . . . . . . . . . . . 16 Drawbar’Pull . . . . . . . . . . ... . . . . . . l7 WeightTranefer................. 25 Front Wheel Rolling Resistance . . . . . . . . . 25 Amplification and Recording . . . . . . . . . . . 28 ~Soil values . . . . . . . . . . . . . . . . . . . 30 clip . . . . . . . . . . . . . . . . . . . . . . 34 Theoretical Travel’. . . . . . . . . . . . . 34 Actual Travel . . . . . . . . . . . . . . . 34 EXPERIMENTALPROCBDURB................ 37 stnrsmnniscussmn................ 40 Analysis of Dynamic Vehicular Mechanics Equations 40 Results involving experimental force values 40 Integration of soil values with experimental result.’ 0 O O O O O O O O O O O O O O O O O 48 viii AryLICATI ON OF RESULTS 0 O O O O O O O O O SMARY 0 O O O O O O O O O O O O O O O 0 CONCLUSIONS 0 O O O O O O O O O O O O O O RECOMMENDATIONS FOR FUTURE INVESTIGATIONS REFERENCESeee‘eeeeeeeeeeeee- Page 56 58 61 figure 10 ll 12 13 14 LIST OF FIGURES Figure Page 1 Compression ring torque transducer . . . . . . 10 Negative No. 26907-1 . 2 Torquemeter inner plate assembly . . . . . . . 10 Negative No. 62l841-A 3 Torquemeter outer plate assembly . . . . . . . 12 Negative No. 621841-1 'A Torquemeter with protective shields in place . 12 Negative No. 6218 1-6 5 Torquemeter clam ing ring and support . . . . 14 Negative No. 621 l-S 6 Static calibration of torquemeter . . . . . . 14 ; Negative No. 621253-6 ' 7 Strain gage bridge circuit . . . . . . . . . . 15 8 Dynamic calibration of torquemeter . . . . . . 18 Negative No. 621645-2 9 Torquemeter with sensing element removed . . . 18 Negative No. 6218kl-3 lo Static and dynamic calibration curves for compression ring torque transducer . . . . . . 19 ll Strain gaged ring drawbar dynamometer . . . . 21 Negative No. 621 41-2 12 Calibration arrangement for drawbar dynuomoureeeee 0000000000021 Negative No. 621569-2 1.3 Calibration curve for drawbar dynamometer . . 22 14 Loading arrangement for a constant drawbar pull... eeeeeeeeeee23 Negative No: 62l831z7. p: a..." ' ........ and we 15 17 Roi 198 05 19) P 21 22 2) 24 35 26 jFigure 15 16 17 18 19a 19b 21 22 23 24 25 26 137 £253 Calibration of weight transfer transducer .... Negative No. 621273-2 Calibration curve for rear axle weight transfer transducer . . . . . . . . . . . . . Rolling resistance transducer . . . . . . . . Negative No. 26907 Calibration of rolling resistance transducer . Negative No. 621231-3 Calibration curve for front wheel rolling reaiamce transducer e e e e e e e e e e e e Pres body diagram of tractor . . . . . . . . . Major Professor and author observing instruments................. Negative No. 621575-3 Bevameter setup for recording the shear force Negative No. 621522-2 Microswitch indicating theoretical travel . . Negative No. 621575-2 Microswitch indicating actual travel . . . . . Negative No. 621522-1 Oscillograph chart paper showing direct writing ink recording of (from left to right) theoretical travel, weight transfer, torque, rolling resistance and actual travel . . . . . Negative No. 621843 Pregb°dyd138morframe e_e e e as e e e e Weight transfer curves comparing the experimental value with the theoretical values obtained from equations 2, 5 and roflsedequation2.............. Variation of rolling resistance with drawbar pu1;eeeeeeeeeeeeeeeeeeeee Variation of slip and torque with drawbar pull Variation of slip with coefficient of traction Page 23 26 27 27 29 31 33 33 35 35 2.2 45 46 49 51 one “ Table II III IV LIST OF TABLES Heights used for drawbar pull . . . . . . Drawbar pull with weights on load cable . Weight transfer values for a given drawbar pulleeeeeeeeeeeeeeeeeee Weight transfer error obtained from theoretical equations . . . . . . . . . . Experimental soil values . . . . . . . . . Page 24 24 44 47 52 , INTRODUCTION , The state of the design of mobile equipment is such that if further progress is to be made, the empirical approach must be replaced by a theoretical approach to g F? secure optimum design. The high cost of constructing a single full scale experimental model to test empirical i n . designs makes such a practice unfeasible. Decreased produc- . g tion lead time necessitates a rapid design analysis. During the past decade the problems of land locomotion and the methods required for their solution have gained wide interest. The ability of the soil to. support a given vehicle and the ability of that vehicle to transport or tow a given load is determined by the soil strength. Vehicle stability is also related to the soil strength. Behker (1955) presented a means (the soil value system) for classifying a given soil in relation to its ”strength”. Since the development of this system, an empirical approach to the mobility problem has been possible. A theoretical aPproseh is now desired. . A relationship between the soil values and vehicle (19313;; papameters would enable a designer to analyze in ‘ theoretical manner many possible solutions to a given “8181: problem. Vehicle performance and/or stability °°u1d be predicted for each given situation. Such a ~ .axit theoretical approach through vehicular mechanics would reduce the expense, time and material which are encountered in the "experimental model” type of approach. The result would be an Optimum design produced with a minimum of expense. Buchele (1961) developed such a set of vehicular mechanics equations which related soil strength to vehicle performance. The resulting equations provide a means of utilising soil value information for the prediction of vehicular performance under various soil conditions. The purpose of this investigation is to test the proposed theoretical dynamic vehicular equations and the application of the soil value system to wheeled vehicles Operating on yielding soils. The results as determined from the equations were compared with experimental data obtained with the use of strain gage transducers. The required experimental values were: 1. Rear axle torque 2. Drawbar pull 3. Weight transfer 4. front wheel rolling resistance The soil values were determined from experimental 4‘“ obtained with a Bevameter and consisted of the 1billowing: Kc, the modulus of col. sion KW the modulus of deformation n , the terrain coefficient 6 , the angle of internal friction C , the soil cohesion Additional test data determined were: 1. 2. 3. 4n Soil bulk density Soil moisture Theoretical forward travel of vehicle Actual forward travel of vehicle I); I.) Ii LI TERATURE REVI EH The application of strain gage techniques for the design of various transducers has become an important phase of many research analyses. A convenient test system consists of a strain gage transducer, amplifier, and direct writing oscillograph. Lockery (1959) lists the available torque-measuring devi see in two classes as follows: 1. Angular-twist types: (a) Optical ' 1 (b) Electrical: (1) Variable capacitance (ii) Variable coupling (iii) Variable reluctance (iv) Frequency sensitive (v) Phase sensitive 2- Surface stress or strain types: (a) Variable permeability (b) Photostress type (c) 8394 strain gage 0: th. above devices, the 33-4 strain gage is most appli- c‘bl. for detemination of dynamic torque measurements on T nge axle. _ The conventional method of determining the driving ¥ vino-I... torque of a powered shaft consists of applying strain gages along 45° helices on the shaft surface. A brush- giip ring system is required to collect the strain indi- cations of the rotating shaft. Perry and Lissner (1955) suggest three general methods for combatting the problems 1nherent in slip ring systems. . Hayes (1961) obtained an indication of rear axle torque by applying strain gages along the 45° helices of * ( a reduced section of the power shaft ahead of the final dd. 70. A brush-slip ring assembly was used to transmit the excitation and signal voltages. The strain gage and slip ring method of determining rear axle torque was used by Davis (1961).. Four gages were attached to each rear axle shaft, and the slip ring assembly was used to connect the gages to a terminal box. Trabbic (1959) obtained rear axle torque by applying straln gages on the axle but did not use a slip ring collector. The test runs were relatively short; the strain 838. load cable wrapped around the axle and unwrapped 2' the tractor was backed to the starting point. The wheel '“ Jacked up and turned until the additional rotation due t° .111) was unwound. 30 th Hayes and Davis obtained vertical weight transfer by atinterling strain gages to the rear axle housings in the tree °t laximum loading moment. The gages were placed at the same location on the centerline of both r13ht :1 ti 50m Rages and left axle housings. lewbury (1961) obtained an indication of front wheel rolling resistance by redesigning the Junction between front wheel spindle and axle. The strain gage transducer was essentially a flexible paralleogram Joining the spindle and “1‘s Walters and Jensen (1954) measured front wheel rolling resistance on both a row crop and general purpose tractor. The technique used to check rolling resistance on the row crop tractor consisted of placing strain gages on a cantilever member which was located so as to resist the fore and aft movement of the steering spindle. The steer- 138 linkage of the general purpose tractor was rebuilt ‘0 Pro vide center point steering. Morehouse proving rings were installed in the tie rod to either side of the center steering point. The strain gaged proving rings provided an indi cation of the rolling resistance force. J Onsen (1954) reports that drawbar pull was satis- ractor1xy obtained by using a steel ring with four strain 3‘3” ‘Dplied so that two were in tension while two were in compression. The torquemeter described by Jensen “3318th o: a strain gaged shaft with a brush and slip ring °Ollsctor. , Th. drawbar dynamometer described by Clyde (1955) °°nu9t°d of two linked beams pivoted on clevises. Strain 833” "er. applied at points of maximum bending. The circuit used was a modification of that used by Jensen. Trabbic (1959) obtained the actual distance traveled per test run by attaching a microswitch to the pulley support of the dead weight loading frame so that the switch was activated twice per revolution of the pulley over which the load cable passed. The theoretical distance traveled was indicated by a microswitch operating against The drawbar load placed the lug bars of the rear tire. on the tractor consisted of various amounts of cast iron weigh 158 lifted over a pulley arrangement. APPARATUS AND INSTRUMENTATION The test vehicle (a Massey Ferguson 50 tractor) was instrumented by attaching strain gages and strain gage transducers to the vehicle to obtain the dynamic values of the rear‘axle torque, drawbar pull, rear axle weight change or weight transfer, and front wheel rolling resis tance. Rear Axle Torque The literature survey indicated that the most suitable method currently available for the indication of rear axle torque consisted of four SR-4 strain gages attached (0!! 45° helices) to a reduced section of the axle shaft. The excitation and signal voltages were transmitted through a bru sh—slip ring assembly. Because of the problems in- herent. in slip ring systems and in theturning down and "1111113 of a rear axle shaft, a more reliable method of obtaining the axle torque was desired. W m” A compression ring torque transducer (Figure l) '“ d.81gned. The design requirements for the instrument "I“ ‘8 follows: (1 ) Easily attached to either left or right rear axle (2) No moving or sliding electrical connections (3) Able to withstand field service (4) Easily removed strain sensitive component so that the test vehicle would be capable of serving multiple requirements The basic principle of the Buchele hydrostatic torquemeter (1951) was used in the final design of the transducer which consists of one rotating and one stationary assembly. Since the wheel mounting flange of the test vehicle is an integral part of the axle shaft, the re- tating assembly had to include a component which would attach to the mounting flange (Figure 2). This member consists of an 11 1/2 in.,diameter steel plate, 1 in. thick, press fit and welded on a 2 1/2 in. diameter shaft 14 1/2 in. long. The plate has a bolting circle consisting of sight bolt holes with recessed lug nut seats which matches the bolt circle of either axle flange. Thus the plate and stub axle assembly is attached to the flange by the existing lug bolts in the flange. Also in the plate are eight conical, hardened seats equally spaced around anv8 7/8 in. circle concentric with the shaft center. The stub axle shaft is threaded to receive a 2 1/2 in. national fine thread nut. A second component of the rotating assembly consists of a matching steel plate welded concentrically to a hub which provides the centering guide for the wheel and ( ) 1 L Figure 1. Compression ring torque transducer 11 the seat for one of the Timken roller bearings (Figure 3). The eight lug bolts required to attach the wheel to the transducer are pressed into the lug bolt holes. Bronze bushings are pressed into each end of the hub and the entire hub assembly is positioned on the 2 1/2 in. diameter*shaft so that the eight conical seats in each plate are exactly opposite each other. Eight 1 1/8 in. diameter hardened steel ball bearings are placed in the matching seats and separate the two plates by approximately 1/4 in. A rubber dust sealing band is placed around the plates to protect the balls and seats from excessive abrasive wear which might occur if dirt were allowed to enter between the plates. A second Timken roller bearing was pressed on a collar which rides on. the outer end of the shaft. - The stationary assembly (the compression ring) was made from a length of 8 1/2 in. diameter tubing 8 in. long. The wall thickness of the three inch center section was reduced to 3/16 in. to provide increased sensitivity for strain gage application. The outer races of the two Timken bearings were pressed into the machined ends of the tubing. Dust shields made of circular galvanized sheet steel pieces were placed at each end of the'compression ring to prevent foreign material from entering the bearings. A protective sheet steel cover was placed around the reduced section of the tubing to Figure 3. Figure 4. Torquemeter 1.15:3. _ a Torquemeter outer plate assembly with protective shields in place 13 protect the strain gages (Figure 4). A clamping ring was placed around the nut end of the compression ring. Two rods were fastened to the clamp and anchored to a support to resist the tendency to rotate caused by hearing friction. The support extended from the redesigned foot rest and provided a convenient attaching point for the strain gage cables (Figure 5). Operational analysis‘gg the torguemeter When the final drive of the test vehicle is engaged, the axle flange and inner plate assembly of the torquemeter rotate as a unit. The outer plate and hub assembly, with vehicle wheel attached, receive tangential and axial force components from the inner plats through the caming action of the eight steel balls. This action tends to force the outer plate around and outward thus exerting torque on the wheel and compression on the stationary compression ring. The compression ring riding on the Timken high angle roller bearings, resists the axial force components. Any outward movement of the outer plate and hub assembly and inner bearing is restricted by the 2 1/2 in. nut and outer bearing on the shaft of the inner plate assembly. Bridge circuit The stationary compression ring is strain gaged so as to indicate the compressive (axial) loads but cancel bending and torsional loads. Four type A-5, SR—4, strain Figure 6. Static calibration of torquemeter 15 gages were applied to the outer surface of the reduced section. Two of the gages were placed with their axes parallel to the csnterline of the tubing. These primary sensing ele- ments were temperature compensated by placing the other two gages in a Poisson arrangement, that is with their axes per- pendicular to the csnterline. The pair of gages in each arrangement were placed diametrically opposite each other, and because of their arrangement in the Wheatstone bridge, forces other than compression and tension (which is not possible with this design) were canceled. A schematic drawing of the bridge circuit is shown in Figure 7. - INPUT PROM OSCILLATOR 3 g ~——————e> OUTPUT (TO AMPLIFIER) ‘3. 1 ”FM, ' -e Figure 7. Strain gage bridge circuit 16 A layer of Petrosene-A wax was applied over each gage for water proofing. The strain gage cable was securely fastened to the stationary ring so the strain gages would not be injured if tension were accidentally applied to the 03b13e Calibration The torquemeter was first calibrated statically by placing known weights on a fabricated rectangular bar at a distance of ten feet from the wheel center. The bar was fastened rigidly to the wheel which was not in contact with the floor. The axis flange and inner plate assembly were locked in place by the brake. As weights were added to the calibration bar, the known torque caused the outer plate assembly and wheel to apply a compressive force to the strain gaged stationary compression ring. Figure 6 shows the static calibration arrangement. A dynamic calibration was made and compared with the static torque calibration. One end of a series of three tire chains was fastened to the rim.of the wheel attached to the torquemeter. A rigid member with a center pull point was welded between the side links at the opposite and of the chain. The torque sensing wheel was raised off the ground and the vehicle was anchored to the rear. The chains were arranged in a straight line directly ahead of the 17 tire and fastened to a load cable. When torque was applied to the wheel, the chains began to wrap around the tire thereby applying a known load at a known radius. The calibration arrangement is shown in Figure 8. The resulting calibration curves are shown in Figure 10. Linearity is excellent for torque values above 900 1b-ft. The transducer is capable of operation in more than one torque range simply by machining additional compression rings with various wall thicknesses. The rings can be interchanged merely by removing the 2 1/2 in. nut and the outer bearing. When the compression ring and both bearings are replaced with a spacer ring, the vehicle may be used for other operations (Figure 9). Drawbar*Pull A constant drawbar pull was desired to facilitate experimental data analysis. The minimum.1ength of test run was to be twenty feet. _ . The two requirements were satisfied by erecting a thirty five foot power pole with a special crossarm mounted at the top. The top of the pole was notched to receive two channel iron crossarms, one on each side. A five inch pulley was placed between and at each end of . the crossarms. The assembly was braced and bolted to the pole. The pulleys were placed an equal distance to either side of the pole center so that no unbalanced moment would Figure 8. Dynamic calibration of torquemeter Figure 9. Torquemeter with sensing element removed 19 aooscmnenp season wean unannounaoo hon moehno soapsupaamo oasmehn use causam .oa shaman A... .m._ .. “some dmzz «Em. comm ooom ooem com—1. comp . com o . o . . \.\V . o _\ .\ \ao\o . \\ a \ x \ i8 \ \ .8 ov~+>m.mo7x 222535 25231-7: o Ave“ Nam; mémux 20:53:20 3.25 SENI'I - NOIiOEl'IJBG N3d 20 act about this center. A 3/8 in. cable passed over the crossarm pulleys and under an identical pulley which was anchored to the base of the pole. The bottom of the lower pulley was positioned at the height of the tractor pull points. Since the lower links of the three-point hitch were float- ing, the load cable was level during test runs. One end of the cable was connected to the drawbar and the other end was hooked to the desired number of weights. The weights consisted of four, large, discarded steam- radiators. A strain gaged ring drawbar dynamometer was connected between the drawbar and the cable prior to the - actual test runs (Figure 11). The dynamometer had previous- ly been calibrated for lines of oscillograph pen deflection versus a known load as shown in Figure 12, and the result- ing calibration curve is shown in Figure 13. Each load was pulled through the test run and its drawbar pull, as indicated by the dynamometer, was re- corded. All successive runs were made without the dynamometer. Figure 14 shows the loading arrangement. Table I gives the individual static weight for each of the four weights. The dynamic (static weight plus pulley friction) drawbar pull values of the individual weights as well as the pull of the combinations used in the test runs are given in Table II. L..___. n. h 21 Figure 11. Strain gaged ring drawbar dynamometer .a "fir. Figure 12. Calibration arrangement for drawbar dynamometer 22 “00.0308ng Hdnlgv “OH Obhfio QOHQQHDAHGO end .mmn - 443a mamzama opom coma Doha com >~.Fm u x madman SBNIT - N0|1031J30 N3d m w my!!!“ Figure 14. Loading arrangement for a constant drawbar pull Figure 15. Calibration of weight transfer transducer 24 TABLE I WEIGHTS USED FOR DRAWBAR PULL Identification Pounds Number ' Static Weight 4 397 5 469 6 475.5 7 54# TABLE II DRAWBAR PULL WITH VEIGHTS ON LOAD CABLE Identification _ Pounds Number' ‘ Drawbar Pull 4 481 5 576 7 666 4,6 *' 1082 4.7 1161 5,6 “ _ 1193 4.5.6 1688 4,6,7 1761 5.6.7 ‘ 1851 4.5.6.? 2289 25 Weight Transfer Weight transfer was determined by recording the change in rear axle weight. This increase over the static weight 1 was obtained by applying four SRpk strain gages to the rear axle housings. The gages were placed on the center- 1ine of the axle housings and as close to the differential 5, u . r 1‘ T1 housing as possible for maximum cantilever action. Two gages were applied directly opposite each other on both E) housings, and all four gages were connected into a bridge and arranged for'maximum sensitivity. The calibration arrangement is shown in Figure 15. A single support was placed under the center of the differential housing so that the rear wheels were not in contact with the floor. Weight platforms were constructed to fit the tire contour and, with rear wheels locked, known weights were placed on the platforms. Figure 16 shows the rear axle calibration curve. Front Wheel Bolling Resistance An indication of rolling resistance was obtained from the front wheel spindle. A short length near the center of the spindle was reduced in diameter so as to increase the strain sensitivity in torsion (Figure 17). Four type Ac? Spr strain gages were applied in a torsion arrangement (diametrically opposite along 45° helices). Since the point of contact between the tire and the ground 26 noosumnsup nonhuman unwaoa cane some you opaso.aoapounaaao .wa oasmum .mmn - madmzm.m~ . x SEINI'I - NOIlOI-TIJEJO N3d 27 Figure 17. Rolling resistance transducer Figure 18. Calibration of rolling resistance transducer 28 is outside of the spindle center line, the rolling_resis- tance places the spindle in torsion. The resulting torsion- al strain was calibrated as shown in Figure 18. The tire was placed on a smooth board which was supported by a series of rollers. With the test vehicle level and with the front wheels subjected to their normal . ,1a static load, the board was drawn between the rollers and ' tire. After rolling approximately 18 in., a cleat, shaped L» to fit the tire curvature, contacted the tire. The cleat was to simulate rolling resistance in a yielding soil and afford a means of applying an increasing torsional strain to the spindle. Figure 19a shows the resulting calibration curve. Amplification and Recording Shielded cables (four conductor) were used to connect the bridge circuit of each transducer to a Brush amplifier. The individual cables were taped together and directed from the vehicle to the amplifiers along the torquemeter support (Figure 5). Coil springs were attached to the end of the support to assure maximum cable flexibility and reduce the possibility of cable damage should the cables become entangled with the rear wheel. The amplifier outputs were connected to a portable Brush direct writing oscillograph for recording of the dynamic loads applied to each transducer. The instruments are shown in Figure 20. 29 scoscumenp ooaepuamoa mmaaaou Hoes: paoAH you abuse soapmnnaaao .mma shaman .mmm .. mozfiflmmm wz_._._om P 4 1. OS om? cm? 8 pm 9... o (5 N - NOILOB'HEG N36 E) co SHNI'I >225. x :5 V here 30 Soil Values The equations proposed by Buchele (1962) are listed as follows (see Figure 19b): Dynamic weight transfer when soil conditions are limiting (wheels may spin): R 1x21 + RgAYza - P2Y2 - R22’22 - R12’12 (1) x15 Dynamic weight transfer when engine torque is limiting VD: (engine may stall): w - TR32 - P222 - 2T 2 (2) D - X15 where: "D : Dynamic weight transfer . - R21 = Vertical soil reaction on rear tires 121 = Horizontal distance to 321 R24 = Horizontal soil reaction to tire lug Y24 = Vertical distance to 324 P2 = Drawbar pull 22 = Vertical distance to P2 322 = Rolling resistance at rear wheels 122 = Vertical distance to 822 R12 = Rolling resistance at front wheels 112 = Vertical distance to 312 115 = Tractor wheel base 3 II Rear axle torque access» no seawsau boon eeum .an 8:» .2 _.x 32 When the soil values are substituted into equations 1 and 2 respectively, the following equations are formed: ("23+"D)x21 * [1321.20 + ("2a+"n)tan flYza - P2Y2 "D = 1‘15 at; 9:. " ' Y2? T (121729)n (map) n (n+1)(K +b K ) n 2 L1 c LL x _ (3) l5 n+1 fig "la-"D‘s- ' T232 - 132:2 - (n+l)(K +b K )l/n T up = ° M (A) X15 where: we = Static weight on rear wheels - H18 = Static weight on front wheels b2 = Width of rear wheel contact patch bl = Width of front wheel contact patch L2 = Length of rear wheel contact patch L1 2 Length of front wheel contact patch (C,K¢,K°,¢ and n.= Soil values defined in the introduction values of 0, Kg; Kc, ¢ and n were obtained through the use of a Bevameter (Figure 21); an apparatus which records the force required to penetrate the soil with var- ious diameter probes as well as the torque required to shear the soil when various amounts of normal pressure are applied. Soil moisture and bulk density were obtained Figure 20. Major Professor and author observing instruments Figure 21. Bevameter setup for recording the shear force 34 from soil samples taken with a Uhland sampler. Slip In order that vehicle slip could be determined, the actual and theoretical distance traveled was obtained through the use of microswitches. Theoretical travel One switch was placed directly above the power-take-off shaft and activated by a bolt which extended through the shaft (Figure 22). The switch made contact twice during each shaft revolution. It was electrically connected in the oscillograph left event marker circuit. The operating lever for the power-take-off shaft was placed in the ”ground drive” position. In this posi- tion the shaft speed was determined by the angular velocity of the vehicle drive wheels rather than by the engine speed. The ratio between shaft and drive wheel rotations was found to be 8.72 to 1. The forward travel per wheel revolution was found to be 157 inches. Actual travel A second switch was fastened to the lower pulley bracket as shown in Figure 23. The switch was closed twice per revolution by cams welded to the pulley. The switch was electrically connected in the oscillograph right event marker circuit. indicating theoretical travel Figure 23. Microswitch indicating actual travel 36 The length of cable displaced per pulley revolution was calculated and then verified experimentally to be 17 inches. The actual travel was then obtained by deter- mining the number of event marks on the right side of the chart paper for all or any part of the test run. 5'. . -_‘ _ l....U.M..HI.-4.d 3N! FM. Ana .2, EXPERIMENTAL PROCEDURE The instrumented test vehicle was operated on a plot approximately 15 ft. by 40 ft. The soil was a typical agricultural soil classified as a Miami fine sandy loam. A test series consisted of four runs, each with a different drawbar pull. Prior to each series of runs the soil was prepared by a rototilling operation fol- lowed by a firming operation accomplished with a roller. After preparing the soil, Bevameter recordings were made and soil samples were taken. - The wheel spacing of the front wheels was 49 in; that of the rear wheels was 72 in. With this arrange- ment, both front and rear wheels traveled in undisturbed soil. Each test run was made with a known constant draw- bar pull. The variables recorded during each run were rear axle torque, weight transfer, front wheel rolling resistance, theoretical forward travel and actual forward travel. After the amplifiers were warm, the bridge of each transducer was balanced and electrically calibrated to insure identical amplifier sensitivity for all succeed- ing runs. The first few trial runs indicated the 38 necessity of limiting the engine speed to a maximum of 900 revolutions per minute. Mechanical vibrations were transmitted to the rear axle housing at engine speeds above this maximum limit, and the resulting oscillograph pen oscillation precluded the accurate recording of the weight transfer. The front wheel rolling resistance transducer was balanced and the amplifier sensitivity checked prior to each run. This procedure was followed after the wheel had been Jacked up and was free of any soil con- tact. The vehicle operator was in position when the wheel was returned to the soil. The torquemeter and rear axle bridge balance and amplifier sensitivity were then checked with operator in place. The function of the operator was to start the engine, engage the transmission in its lowest forward gear, adjust the engine throttle and engage the clutch causing the vehicle to travel forward at a constant velocity. Following each test the vehicle was reposi- tioned for the subsequent run. At that time the steer- ing wheel was placed in the position necessary to guide the vehicle through undisturbed soil without manipu- lating the steering mechanism during the run. Such manipulation would have been indicated as a change in rolling resistance. Immediately after the weights were freely suspended on the cable and the vehicle was 39 traveling at a constant velocity, the drawbar pull was found to be constant and all variables thus recorded were a function of the constant pull. RESULTS AND DISCUSSION EXperimental data were substituted into the vehicular equations, and an error analysis of the results was conducted. Analysis of Dynamic Vehicular Mechanics Equations Experimental values obtained from the transducers described in the previous section were substituted into equations 2 and 4. Equation 2 consists of force values exclusively while equation 4 involves soil values in combination with force values. Results involving exgerimental force values The dynamic torque value was extremely uniform for each test run. Weight transfer and the percent slip (calculated from the theoretical and actual forward travel) varied only slightly during a run. Rolling resistance values obtained from the oscil- lograph chart were determined by counting the lines of deflection from the "zero” line about which the bridge was balanced. An initial pen deflection, which was not repeatable, occurred when the static front and weight acted on the wheel when lowered after the bridge was balanced. This initial deflection, when it occurred, appeared as if a rolling resistance force were acting 41 on the wheel with the vehicle in reverse motion. The zero line, rather than the line of initial deflection, was used as the base from which the number of lines deflection were counted because it was found, by a series of no-load forward runs on concrete, that regardless of the initial deflection the rolling resis- tance on concrete was always the same number of lines from the zero line. The initial pen deflection varied due to the different amount of torsional strain induced in the spindle when the static weight was placed on the wheel after balancing. It was theorized that this var- iation occurred because of the relative difference in the position of the spindle each time the wheel was lowered. When the above procedure was followed in the analysis of data, the resulting indications of rolling resistance were repeatable for a given drawbar pull. Figure 24 shows a section of oscillograph chart paper with the recording of theoretical travel, weight transfer, torque, rolling resistance, and actual travel for a constant drawbar pull of 2289 lbs. An average value for lines of pen deflection over a given chart ‘ length was determined for the weight transfer, torque and rolling resistance values. Theoretical and actual travel were computed for the same chart length. The experimental values of the above terms were obtained from the recorded pen deflections by means of " _J Figure 2b. Oscillograph chart paper showing direct writing ink recording of (from left to right) theoretical travel, weight transfer, torque, rolling resistance and actual travel .’~ 43 the calibration curves obtained for each transducer. The dynamic calibration curve of Figure 10 was used to obtain the experimental torque values. The classical vehicular equations as presented by Berger (1952) express the change in soil reactions R1 (vertical component of soil reaction against traction wheels) and R2 (vertical component of soil reaction against front wheels) as: FYI Weight transfer = —x- (5) 1 . . where: P = Drawbar pull Y1 = Vertical distance between pull point and the point of reaction between soil and tire x1 2 Horizontal distance between centers of front and rear axle (wheel base) Table III compares weight transfer for four draw- bar pull values. The experimental values obtained by the weight transfer transducer are greater than the values obtained from equations 2 and 5 in all cases. . Weight transfer values obtained from equation 5 were determined using the experimental values of draw- bar pull. The tenms Y1 and x1 were measured on the test vehicle. Results obtained from equation 2 involve the eXperimental values of torque, drawbar pull and rolling 44 resistance. The measured values of Y2, Y12! and x15 I were used. TABLE III WEIGHT TRANSFER VALUES FOR A GIVEN DRAWBAR.PULL Weight Transfer Drawbar Experimental Equation 2 Revised Equation 5 Pull Equation 2 Pounds 666 319 255 275 164 1082 403 343 361 266 1688 590 536 549 915 2289 832 807 816 563 In the derivation of equation 2 it was assumed that the front wheel rolling resistance force, R12, acted horizontally at the point of reaction between the soil and wheel (Figure 19b). If instead it is assumed that 312 acts at the center of the front wheel (Figure 25) and '112 is the vertical distance between rear wheel and front wheel centers, the computed weight transfer is then in closer agreement with the experimental weight transfer values obtained from the rear axle transducer. Figure 26 shows a comparison of weight transfer vs. drawbar pull curves for values obtained from the rear axle transducer, from equations 2, 5 and from revised E J Equation Ed 45 H a H - 46 N noaaesdo coedbon use m .m soapssao sown cosaeono mamas» Hooaaonoomv one mad: osaa> Hopuosaneawo on» maaamaaoo mo>aso newness» panda: .wm shaman .wmn - 44:2 mamzama 8% 8: 8%: 8w: 2% as .o 'SG'I - HBJSNVHI 1H9|3M 4? equation 2 (with R12 acting at the front wheel center). The linear regression method presented by Dixon (1957) was used to determine the best straight line available from the experimental data. These data are on file in the Agricultural Engineering Department, Hichigan State University, East Lansing, Michigan. ‘ It is evident that the results obtained from equa- tion 2 and from revised equation 2 are in much closer agreement with the weight transfer obtained experimen- tally than the values obtained from equation 5. An error analysis was conducted for the various weight transfer values given in Table IV. The error equation is as follows: - _ calculated wei ht transfer ‘ % error ' 10° (1 experimentEI weIgEt transfer) (6) TABLE IV WEIGHT TRANSFER.ERROR OBTAINED PROM THEORETICAL EQUATIONS Experimental Percent Error Weight Transfer mation Wuation 5" 319 20.1 13.8 . 48.6 403 . 14.9 10.4 34.0 590 9.2 5.9 29.7 832 3.0 1.9 32.3 The error becomes less as weight transfer increases, but revised equation 2 provides the most accurate results. The curve for weight transfer'as obtained from the re- 48 vised equation 2 approaches the experimental weight transfer curve much closer at low drawbar pull values than at higher values. This occurs because the term, R§2Y12. 15 is much smaller in the revised equation; therefore the resulting difference between results obtained from the revised equation and results obtained from.the original equation is greater when the rolling resistance values are large. The assumption here is that rolling resistance values vary inversely with drawbar pull. The above assumption appears valid since it would be expected that the front wheel rolling resistance should decrease as drawbar pull increases due to the transfer of weight from the front to the rear drive wheels. This was verified experimentally and Figure 27 shows the resulting curve of rolling resistance vs. drawbar pull. Figure 28 shows the results obtained when slip and torque values are plotted versus drawbar pull. The variation does not appear to be linear. Both terms increase more rapidly at the higher values of drawbar pull. The variation of slip with the coefficient of traction is shown in Figure 29. Coefficient of traction is defined as the ratio of drawbar pull to dynamic rear axle weight. Integration.gg ggil values with egperimental results The Bevameter recordings taken prior to each series of test runs were processed and their data used to determine 49 Hana soprano spa: oomopaamoa mnaaaoa no soapmdus> .mmn.- 442a almanac 8+2 8a 3mm 2mm _ 8: at T____.l -_. -_ .hm ohmmdm O C 5 co car A 13—. °ss1 - BONViS|838.9NI1108 \)l|lll|lal"iv ‘ Hana seasons and: emuaop use aaan.uo soapeaum> .mm oasmam opFN .mmn - sham.m