INFLUENCE OF TRACK SHOE SHAPE AND SPACING ON PERFORMANCE IN SOFT SOIL Thesis for the Degree of M. S. MICHIGAN STATE umvsasm Toshimichi lkeda 19.6.6 masts LIBRARY Michigan State Univcr: it] R8513? .: ABSTRACT INFLUENCE OF TRACK SHOE SHAPE AND SPACING ON PERFORMANCE IN SOFT SOIL by Toshimichi Ikeda Considerable effort has been made for the improve- ment of mobility performance of tracked vehicles. One possible direction of improvement is the spaced link track which was proposed by Bekker. Tests, however, showed that a spaced link track produces more sinkage than conventional tracks on soft soil and it behaves like the latter when-the slip is excessive. This study was intended to investigate the perfor- mance of the Raised Edge Shoe which might be one means of improving the spaced link track. Another objective of this study was to examine the performance of the triangle shoe which is used at present for soft soil conditions. The test was performed by using seven different model track shoes on a fairly cohesive soil with high moisture content. Horizontal force and sinkage were measured as functions of displacement for different vertical loads. Besides seven single model shoes, twin model shoes for Toshimichi Ikeda three types were tested to investigate the effect of spacing. The results indicate that more traction and less sinkage can be expected by using the Raised Edge Shoe. It was observed that spacing was more effective with the Raised Edge Shoe than with other models at higher loads. The test revealed that the triangular shoe cannot be recommended for spaced link track because of its ex- cessive sinkage. The sinkage phenomenon observed in this test was not explained by theories presently available. Approved Major Professor Approved (0’1 M w“ Department Chairman INFLUENCE OF TRACK SHOE SHAPE AND SPACING ON PERFORMANCE IN SOFT SOIL By Toshimichi Ikeda A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering ACKNOWLEDGMENTS The author expresses his sincere gratitude to Dr. Sverker Persson as major professor for his continual suggestions and guidance. Acknowledgment is extended to Dr. L. E. Malvern for serving on the Guidance Committee and his helpful suggestions. The author is indebted to Mr. Ronald A. Liston of the U. S. Army Tank-Automotive Center for his suggestions and for supplying material. The financial assistance of Hitachi Ltd., Japan, during the author's study in this country is greatly appreciated. The author is indebted to Mr. Sugihara, General Manager, Mr. Murata, Mr.~UJiharavand Mr. Kimura at Adachi Works of Hitachi for their encouragement. The author appreciates Dr. 0. Kitani's helpful suggestions on instrumentation and Dr. Z. S. Topolski's assistance in building the apparatus. The assistance of Messrs. J. Cawood, G. Shiffer, H. Brockbank and M. Curtis are sincerely appreciated. ii TABLE OF CONTENTS Page ACKNOWLEDGMENTS O O O I O O O O O 0 O O O 0 ii LIST OF FIGURES . . . . . . . . . . . . . . iv LIST OF TABLES . . . . . . . . . . . . . . Vi SYMBOLS USED . . . . . . . . . o . . . . . vii I. INTRODUCTION . . . . . . . . c . . . I II. REVIEW OF LITERATURE . . . . . . . . . 3 Traction Problem . . . . . . . . . . 3 Slip Sinkage Problem . . . . . . 7 III. THEORETICAL CONSIDERATIONS . . . . a . . 10 Feature of "Raised Edge Shoe" . . . . . lO Traction O O O O O O O O O O 9 o l“ Sinkage . . . . . . . . . . . . . 17 IV. EQUIPMENT AND PROCEDURE . . . . . . . . 25 Soil Bin and Measuring Device . . . . . 25 Model Track Shoes. . . . . . o . . . 33 Instrumentation . . . . . . . . . . 36 Soil Preparation and Test Procedure . . . 37 V. RESULTS AND DISCUSSION . . o . . . . . . 39 Results of Measurement . . . . . . . . 39 Comparison of Single Models . . . . . . 55 Effect of Spacing . . . . . . . . . 63 VI. SUMMARY AND CONCLUSIONS . . . . . . . . 70 Conclusions. . . . . . . . . . . . 71 VII. SUGGESTIONS FOR FURTHER INVESTIGATION . . . . 72 REFERENCES. 0 O O O O O O 0 O 0 O O D O O '7)4 iii Figure \OCDN 1o. 11. 12. 13. 14. 15. 16. i7. 18. .19. .20.. LIST OF FIGURES Force diagram of a track shoe Soil failure of a spaced link track Raised Edge Shoe Shear pattern of a spaced link track. Geometrical relation of Raised Edge Shoe Function of Raised Edge Shoe Relative traction increase . . General view of the apparatus Soil conditioning tools Shear test Penetration teSt with 3-inch round plate Shear test data. Measuring and drive device Measuring device Twin model track shoes Single model track shoes. ‘DimensiOns of model track shoes ‘Recorded data, Single Model A. iRecorded data, Single Model B. Recorded data, Single Model C. iv Page 12 12 13 13 18 26 26 28 29 3O 31 32 32 3A 35 A0 Al A2 Figure Page 21. Soil deformation of single models . . . A3 22. Development of soil deformation. . . . AA 23. Recorded data, Twin Model A—OS . . . . U6 2“. Recorded data, Twin Model A-2S . . . . A7 25. Recorded data, TWin Model C-2S . . . . A8 26. Soil Deformation of twin models. . . . “5 27. Example of determining Hmax and K . . . 50 28. Slip of vehicle . . . . . . . . . 53 29. Hmax of single models . . . . . . . 59 30. E of single models . . . . . . . . 61 31- Slip sinkage of single models . . . . 62 32. Behavior of triangle shoe. . . . . . 53 33. Effect of spacing with Model A on Hmax 65 34. Effect of spacing with Model B on“Hmax 66 35. Effect of Spacing with Model C*on Hmax 67 H 68 36. Effect of Spacing with Model C on Table mum LIST OF TABLES Physical description of soil Vertical loads, kg. Parameters H K. . . . . . . . max’ Average traction H in kg for J = 1“ cm . max Sinkage in cm at J = 14 cm . Vi Page 27 27 51 56 57 O 0 ml AH max {3‘ max xxcaudl. SYMBOLS USED Area of shear failure surface. Contact area Width of track shoe or plate Cohesion of soil Horizontal force for track shoes Average horizontal force or traction Traction force produced at the end of track shoe Maximum horizontal force Grouser height Effective grouser height of Raised Edge Shoe Soil deformation or displacement of track shoe Soil deformation of the i—th track shoe in a track Maximum soil deformation Constant value: modulus of shear deformation Pure soil number determined by ¢ Pure soil number determined by d Pure soil number determined by ¢ Contact length of a track Contact length Soil parameter, or number of track shoes Pure soil number depending on o Pure soil number depending on d vii pcrit 1 p crit max Pure soil number depending on ¢ Pure soil number determined geometrically related to e and 9 Pure soil number determined geometrically related to d and 6 Pure soil number determined geometrically related to ¢ and 9 Contact pressure Contact pressure of static bearing capacity Contact pressure of bearing capacity Relative increase of traction Relative increase of bearing capacity of soil Length of track shoe Effective length of Raised Edge Shoe Slip of vehicle Gross traction or Soil parameter Vertical weight Bearing capacity of soil Distance between front idler and the i—th track shoe Total sinkage Slip sinkage Static sinkage Angle of internal friction for soil Soil bulk density Arctan (H/V) Shear force Maximum shear force viii I. INTRODUCTION Vehicle mobility on soft soil is one of the major problems in "Off-the-Road" locomotion. In construction work, "bogging down" of crawler tractors is a great pro— blem and the satisfactory Operation on soft ground is re— quired. Since low ground pressure is thought to improve vehicle flotation, tractors with wider and longer tracks have been developed. The lowest ground pressure of the crawler tractors presently manufactured for soft soil condi- tion is about 0.25 kg/cm2 while that of ordinary crawlers is from 0.5 to 0.6 kg/cm2. The present trend is to develop tractors with ground pressure less than 0.25 kg/cm2. There are, however, practical limitations to track width and track length. Excessive track width or length causes difficulties in designing track mechanisms and creates steering problems. "Bogging down" is not a problem of only flotation because sinkage of a vehicle is caused not only by the static weight but also by the slip of the track. The latter should receive the greatest emphasis when studying the mobility of a tractor on soft soil. A track which will give less sinkage for the same tractive force is one solution. A track which will pro— duce more tractive force for the same sinkage is an alternative one since tractive force is produced by slip and sinkage generally increases with slip. The spaced link track proposed by Bekker (1958) was based on the latter approach. Bekker's objective was to improve traction rather than to reduce sinkage. The prototype proved that the spaced link track considerably increased traction force in certain soil conditions but not in others. The disadvantage of the spaced link track was that it behaved like the conventional track for high slippage and the sinkage is generally larger than for the conventional type. The objective of this study was to investigate the possibility of improving the spaced link track by adopting a "Raised Edge Shoe.” The study was performed by comparing seven different types of model track shoes. The performance of the "Tri-. angle Shoe,” which is widely used in Japan as track shoe for soft soil, was also examined. II. REVIEW OF LITERATURE Traction Problem The basic equation for the traction of vehicles was first introduced by Micklethwait (Bekker, 1960): T = A0 + w tan ¢ (1) This equation is applicable only to a simplified case and the actual phenomenon is more complicated. Bekken (1960, p. 119), assumed a failure pattern as shown in Fig. 1 and derived equations (7). This theory was verified experimentally and extensive investigation on the influence of shoe configuration on traction performance was conducted. Bekker arrived at the following conclusions from his broad study: 1. An increase of track width beyond the present size is limited and does not pay as the corres- ponding increase of motion resistance in weak soil is greater than the respective gain in flotation. 2. An increase of track length beyond a certain ratio of the length to track tread is impossible because the vehicle will not steer. V v91 .r._____s-_.._.__b‘._.., \ _ \ ,2 I ; $&//31 "1‘... H I g g / b [ l E $/ \ .c' / . 1 \ V ISO-HHS) P. Pp . P Pp+Pp=Pp ' Bekker "‘ZPp Fig.l Force diagram of a track shoe V . s - -- 93—3 9 ~/ ///// Fig.2 Soil failure ofa spaced link track 3. Any change in spud design and cleat form of conventional tracks produces a rather insignifi- cant improvement in traction. He suggested that to increase soft ground perfor- mance one must follow a path which exc1udes the above limiting factors. Bekker proposed adopting a spaced link track as the only method of improvement. The spaced link track was develOped from the idea that making use of the full length of the soil failure area (Fig. 2) in each shoe gives more shear force. A prototype with spaced link track was con- structed and tested in various soil conditions. The result showed that the spaced link track was superior in several critical loose soils supported by a firm subgrade and in strong soils, while it was inferior in the range of soils between these two types. The spaced link track will possi- bly improve vehicle performance, but is not the solution for all soil conditions. The tension distribution along the track, related to slip, was calculated by Bekker (1956, pp. 263—270). A. P. Sofiyan and E. J. Maksimenko (1960) measured the vertical force and horizontal force exerted in a track element while it travels along the contacting ground face. They observed that the distribution of the tan— gential reactions of the soil on the track cleats depends on the value of the drawbar load. For low drawbar loads the main tangential force was produced by the front cleat when it penetrated the soil and the maximum value oc— curred near the first track roller. At higher drawbar loads, the distribution was similar to a parabola and the maximum occured at the center of the track. A similar experiment was conducted by G. E. VandenBerg and I. F. Reed (1962). Their results were almost the same as the previous one. D. O. Kuether and I. F. Reed (1964) investigated the effect of track shoe design on traction at the request of the Tractive and Transport Efficiency Committee of ASAE. They tested five different types of shoes in four different soils. The shoes were selected from those which were com— monly used on industrial and agricultural crawler tractors. They observed that every shoe gave almost the same pull. In this test, however, extreme soil conditions such as a hard pan or high moisture content were not encountered. F. A. Reidy and I. F. Reed (1965) investigated the traction performance of a track on a soil submerged under water for the purpose of exploring the use of a tractor at the bottom of the ocean. The objectives were to in- vestigate if submerged soil yields enough traction and to determine track and vehicle parameters. It was shown that traction capability on submerged sand soil was lower than that obtained on dry sand. The tests also indicated that a narrow track, with the center of gravity ahead of J. 'v 'ack center, operating at as slow a speed as possible, "i was preferable. Slip Sinkage Problem The first equation for slip sinkage was introduced by Bekker (1960, p. 136), in the form of equation (11). Bekker's equation was rewritten in a different form by A. Soltynski (1965): Tmix = J— (2) p ‘ p crit Zj p' crit = p crit + Y Nq ZJ (3) _ l p crit — 0N + y zS Nq + 5 b NY where c = Cohesion of soil y = Bulk density of soil 28 = Static sinkage zJ = Slip sinkage b = Width of plate j = Soil deformation Nc = Pure soil number depending on d Nq = Pure soil number depending on ¢ NY = Pure soil number depending on a Tmax = Maximum shear force p = Pressure Soltynski observed that the deformation 2 appears only J as a result of a unit load p > p' according to the crit equation (2). He, however, proved by experiments that in some soils, such as dry and loose sandy loam, the deformation ZJ also occurs when p < p'crit' and proposed another equation: 2 p 1/2 —p crit + (p crit + A Y Nq p811) J: 2YNq (L1) where U) ll Slip Contact length and showed that the relationship between vertical deformation zJ and horizontal deformation 3 might be expressed by a parabolic equation: N p 2 Y 9 crit = ZJEPJ+ZJEPJJ (5) These equations were Justified by experiments. Slip sinkage phenomenon was analyzed by A. R. Reece (1964) from a different standpoint. He assumed a long plate sliding on the ground simulating the track. His theory be- gins by assuming a triangular element under the sliding plate,which was demonstrated by experiment. He reasoned that slip sinkage occurs because the effective shear strength of the soil, for supporting vertical loads, is' diminished as some of the shear strength is used in sup- porting the horizontal load. J. H. Taylor and G. E. VandenBerg (1965) also in— vestigated this problem from the standpoint of a slip—pull relation. They considered that, since the Coulomb equation ignores displacement, the actual soil traction system in which stress varies with displacement could not be described satisfactorily by this equation. They tried to establish a stress strain relationship of the form: “r = f(p,J) where T = Shear force p = Normal pressure 3 = Soil deformation They derived the equation: I = c + T pl_r1 jn (6) where: c e Cohesion of soil T = Soil parameter n = Soil parameter and demonstrated that this fits experimental results. III. THEORETICAL CONSIDERATIONS Feature of "Raised Edge Shoe" The spaced link track proposed by Bekker appears to be the only possible method of improving conventional tracks, although some disadvantages occur in certain soil conditions. According to Bekker's report, spaced link track vehicles achieved higher drawbar pull in hard soil and in several critical loose soils supported by a firm subgrade, but were inferior to conventional tracked vehicles in other soils. The Spaced link track showed more sinkage in some range of weak soil conditions. The only presently proposed method for further im- provement is adopting articulated vehicles. Prototype tests indicated that articulated vehicles were fairly successful and this is a possible solution in the future. The articulated vehicle, however, is not the form which can be applied directly to the current crawler type tractor. As the one possible way to improve spaced link track within the current form of the tractor, the "Raised Edge Shoe" was proposed in this study and its performance on soft soil was investigated. The "Raised Edge Shoe" is a track shoe to the end of which an extra plate is attached at A5 degree angle, as illustrated in 10 ll 7‘1 Fig. 3. This is the result of preliminary studies of \ basic shoe configurations. It is considered to have the following characteristics. 1. Traction will increase as the sinkage cccurs. 1f the track shoe sinks some amount, than the effective height is considered to have in- creased, consequently more traction is ex— pected. 2. Floating ability will increase as the sinkage occurs. If the track shoe sinks some amount, then the contact area increases, which provides more flotation. Consequently, less Sinkage is expected (Fig. A and 5). The contact length of the shoe increases as it sinks and the spacing between shoes is reduced. This is not a problem, however, because of the following reasons: The length of spacing required for a spaced link track to be effective depends upon soil conditicns. In the case of high frictional soil, 13 (Fig. 2) is large, but small in cohesive soil. The spaced link track is therefore designed so that the spacing is effective for the hardest soils encountered. by the vehicle. In hard soil, the "Raised Edge Shce" wilf not sink so much as to affect the Spacing effect, (i.e., the failure can be fully developed between Shoes). The shoe will sink on soft soil reducing the distance of l2 ' Fig.3_ Raised Edge Shoe Conventional shoe , \' \\\ \ /‘ ‘ /¢, Raised Edge Shoe ///, Fig.4 Shear pattern of a spaced link track / l3 E o 7 7IIIIIII Fig.5 Geometrical relation of Raised E d g e S h o e I | s :‘\\\\\\\\\\\1-;Tv $\\\\\\\\\\ k ’44 fl Frictional hard soil .‘ \ ‘ I §/}/ A I/ ’ Cohesive sofi soil Fig.6 Function of ‘Raised Edge Shoe 14 Spacing, but 18 is small in this case and the reduced space is still enough for 18 (Fig. 6). Summarizing the above discussion, the "Raised Edge Shoe" is expected to have the following characteristics: 1. For relatively hard soil, it will perform similarly to the ordinary spaced link track. 2. For soft soil it will provide more traction. 3. For soft soil it will show less sinkage. Traction Following Bekker (1960, pp. 199-230) the track shoe is replaced by a foundation along line a-b (Fig. 1). The angle 6 is determined by the ratio H/V. Based on Terzaghi's foundation theory, Bekker derived the expressions: H .2 b n so + n sz + n s sin e ( c Y q Y Y ) < u . 2 b n so + n 82 + n s cose ( c Y q Y Y ) where b = Width of a track shoe 3 = Length of a track shoe y = Bulk density of soil c = Cohesion of soil 2 = Sinkage nY are given by the following equations: l5 (cose + g-sine) n = K G pq 0082¢ h h (cose + E sine) (E sine — cose) cose n = K Y pq 0082¢ (cose + 2 sine)2 sin(¢ + 6) + K 3 pY Acos ¢ (cose + 2 sins) n = K 0 pc 2 cos ¢ where h = Grouser height ¢ K Angle of internal friction for soil pq’ pr, Kpc = Pure soil number determined by ¢ In the case of Raised Edge Shoe, the length and the grouser height are considered to be variables and corresponding equations are as follows: H' b(n'cs C J 2 . + 's, an J ) Sine (8) V! 2 b n'cs + n's cose ( c Y Y J ) J where s. J hj - Effective grouser height Effective length of shoe The change of angle 9 was neglected for simplicity. l6 qu h (cose + s' sine)(s% sine - cos6)cose D. n' e K 2 Y pq cos ¢ h (cose + g1 sine)2 sin(¢ + 6) ‘ 3 Acos ¢ Relative increase in traction is given by: _H' —H x RH — ——H—— 100 (%) (9) For simplicity the following approximation is made. 11mm»; S- S+Z S 3 Then n' = n , n' = n Y Y C C Equation (9) will become: 2 (n c + 2Yn s - Yn s) z + Yn 2 R = C Y 9 Y (10) 2 n cs + n s + n sz C YY Yq 17 The following numerical values obtained in this test are used to evaluate the value of R . H s = 7 cm h _ g - 0.55 c = 0.025 kg/cm2 ¢ = 28° y = 1.82 x 10"3 kg/cm3 n c’ nq, nY are obtained from Bekker's calculation. The result of numerical calculation is shown in Fig. 7, which indicates that the increase of traction approximately proportional to sinkage is expected in the wide range of 6. Since the value of e seldom exceeds 70° in actual case, the increase of at least “0% is attained at z = 3.20m which corresponds to the case when the top of the raised edge is level with the surface. In the above calculation, the resistance force which occurs at the both ends of track shoe was not taken into consideration. A similar argument, however, can be de- veloped, following Bekker's equation, and it can be shown that increased traction is also expected from the resis— tance force at the both ends of the track shoe. Sinkage It was reported by Bekker (1960, p. 136) that the following equation for slip sinkage fits the experimental results with fair accuracy: 18 mmmmmocfi cofipompp m>HpmHom s .mfim :3 N .3326 .22: n N — _ I. om a V. «J 1. cm I . nu “N 2. m nu n. a. V. On 3 a. 8% ’lo 2. ii = H O (11) where ZJ = Slip sinkage J = Soil deformation V = Vertical force H = Horizontal force WO is the bearing capacity of soil expressed by Terzaghi's equation: wO = bs{ch + y(zs + zj)Nq + %ysNy} (12) where b = Width of shoe 3 = Length of shoe y = Bulk density of soil 0 = Cohesion of soil 28 = Static sinkage NC = Constant soil value depending on ¢ Nq = Constant soil value depending on ¢ NY = Constant soil value depending on ¢ For the Raised Edge Shoe this is written in the form: . l v = r .7 v v . v I v v wo b\s + 4 + Z ){CNC + y(ZS + ZJ)Nq + 2y(s + zS + z )} (l3) 1 s j J Relative increase in the bearing capacity when the static sinkage and the slip sinkage attained the same value for 20 each case is calculated by neglecting second order terms to give the following results: wo' — wo R (%) = ———-————-(x 100) wo WO (1“) = (ZS + al){ch + y(zs + Z§):q + ysNY} (x 100) s{ch + 1((2.s + 2,3)Nq + -2-SNY} Since the term ySNY is much smaller than the term cNC in this test, the following approximation can be made without large error. .. 'S Rwo(%) ~ ——S———i (15) This indicates that increased bearing capacity proportional to the sinkage is expected with a Raised Edge Shoe. About “8% increase is achieved at ZS + 23 = 3.2 cm. Equation (ll) was transformed by Bekker into the following form using equation (12). 1 = J{v - sb(ch + yNdZS + EwSNy)} Zj H + N bsj (16) q H is given by Bekker's equation: H H = bs cn + Z n + sn + n a + 2AH z l E c Y S q Y Y Y q JJ/_§____§_ ( J) ( 7) H + V where nc, nq, n = Pure soil number determined geometrically related to ¢ and e 21 AH = Traction force at the side of shoe calculated by Bekker When the value of J and V are given, H and zJ are deter- mined by these two equations (16), (1?). Assume that H and zJ were determined for certain values of J and V, satisfying the equation: 2. o —s.l = —— (11) J Next consider the equation for the Raised Edge Shoe. V - WO' “71'1"“— (18) J The values of zj, W0' and H' can be determined in the same manner as the above discussion, but these values must be different from those of 23, wo and H previously determined. In the foregoing discussion it was shown that NO and H in— crease as z‘j increases. Therefore in order to satisfy equation (18) a smaller value than 23 must be selected for 23, which means less sinkage is expected with the Raised Edge Shoe. The trial numerical calculation based on the results of this experiment shows that the value of WC is too large to give reasonable value for 23' 22 Example: V = 16.0 kg NC = 32 H = 25.0 kg Nq = 18 S = 6.7 cm NY = 17 b = 16.0 cm y = 1.82 x 10"3 kg/cm3 Zs = 1,8 cm 0 = 0.025 kg/cm2 J=7cm . l ZJ = J{V - bSEEN: quggjj + EYSNYJ} = 7fl5-0 - 15 x 6.7[2.5 x 10'2 x 32 + 1.82 x 10‘3 x 1.8 x 18 25 + 18 x 16 x 6.7 x 1.82 x 10"3 x 7 . . + 0.5 x 1.82 x 10‘3 x 6.7 x 17]} —l2.9 cm . (19) The corresponding value of Z obtained in the experiment 3 is +0.3 cm. The value (19) seems to be absurd. The possible reasons are as follows: a. The experiment from which the equation (11) was derived appears to have been conducted in a 8 manner such that the ratio of H to V was held_ constant. The phenomenon of slip sinkage, however, is quite different from such a condi— tion. b. The soil used in this study was very soft and sometimes showed behavior similar to a fluid. 23 It is doubtful that Terzaghi's theory for bearing capacity is applicable to such a soft soil. It is questionable to discuss the performance of the Raised Edge Shoe by using equation (11), however, this has been done since this equation is one of few theories pre- sently available. Soltynski (1965) proposed another equation for slip sinkage in the following form: Z 3.1%,?— (20) 0 Following this equation and using the previous results, it is seen that less sinkage is expected with Raised Edge Shoe. Soltynski's equation does not give negative sinkage. In this experiment, however, it was observed, in many cases, that the track shoe rises as the soil deformation develops. Soltynski's equation does not contain any horizontal force while Bekker's does. It appears that the horizontal force should be included in some form. Although this study was not aimed at investigating the slip sinkage mechanism, the results seem to indicate that the following equation gives curves more similar to the actual phenomena than Bekker's. 2D 2 7%.: ZE%_§§ (21) o where a and B are parameters for each shoe configuration. IV. EQUIPMENT AND PROCEDURE Soil Bin and Measuring Device The general view of the apparatus used for this study is shown in Fig. 8. The soil bin was a 3 feet wide, 2 1/3 feet high and 8 feet long steel box. The box was filled to 70% depth with soil. The physical description of the soil is shown in Table l. The moisture content was 27.0 i 0.3% throughout the experiment. Soil strength parameters measured by shear ring test and penetration test are presented in Fig. 10 and Fig. 11 respectively. Fig. 12 shows original data for shear test. The sensing and drive device was connected to rails on both sides of the soil bin. The schematic diagram is given in Fig. 13 and general view in Fig. 14. A hydraulic cylinder was used to drive the unit and the speed was con— trolled by a flow control valve. The model track shoe was attached to the bottom of the vertical bar which was sup- ported by ball bearings. The vertical bar was allowed to move only in the vertical direction. On the top of the vertical bar there was a plate on which weights were placed to provide vertical load to the model track shoe. 25 Q V g. 1“ ’ awi .. ‘. P "r. iI |_‘II I I'llgIl'OMQMOMS 5: u s Fig. 8 General View of the apparatus Fig. 9 Soil conditioning tools TABLE 1.-—Physical description of soil. 27 Mechanical analysis: awA2Ou 9.3% M201~v2AOp 10.5% 240 .. 500 36.7% 50 r~' 5H 25.5% 51: ~ 18.0% Plastic Limit 19.5% Liquid Limit 24.0% Bulk Density at Test 1.82 x 10_3 kg/cm3 Water Content at Test 27.0 i 0.3% TABLE 2.--Vertical loads, kg. Nominal Mean Pressure kg/cm 0.0518 0.097“ 0.1u3 0.188 Single Model Type A, B, C 5.8 10.9 16. 21.1 Single Model Type D, E, F, G -— 10.9 16.0 21.1 Twin Model Type A, B, C -- 21.8* 32.0* 42.2* *Total load on two shoes. 28 pmmp tmmgm OH .mfim «on9x a .mmawwwmm L _ _ _ a 30.0 _.o . o S H \\\\\\\\\\‘ a. V a as No 1 a 3 as .523 nwoduo .s o ‘ %~.+ s 06 ztun/bx kg/cm2 p PRESSURE. '0 29 TIUV U r 41111 1 1 1111111 1 1 Llljjl LO IO SINKAGE, 2 cm Fig. 11 Penetration test with 3—in. round plate 30 some Lamp nmmcm ma .mflm Eu .sz22woafifmm_o on ON 0. o — _ q 11l111IIllllllllllllllllllllllr ~Eo\ox vv_.o 11 Q .539. , m 3.0 .539. mmeoua popoEmflo poccfi .cfiIm pmpoEmflo Lopso .CHIQH mcflp pmmcm ;. l N 7 C) CD 5 '33803 UVBHS K) C) zwo/bfl 31 oofi>oo o>flpo ocm wcflLSmmoz ma .mE oosm goo: .muoz 3o.om octomn :om u:_:m\\\\1 >o__:d\ .035 323:5 Ea 0.3a 22»; O can BBEoEoc; ooaoo c 33m .0023) couczxo 0:305»: Zacom / .oo 3.30 355:3 .2 £32; / can au_=w hwuméc .355 2:38“. 0:; c2... o_ucoz Vertical bar A: B: Plate C: Model track shoe D: Potentiometer E: Strain gauge dynamometer F: Handle Fig. 1“ Measuring device Fig. 15 Twin model track shoe A - Model A, B - Model C, C - Model B 33 The frame supporting the vertical bar was fixed to the strain gauge dynamometer. The same dynamometer that J. G. Hendrick (1962) constructed for his study was used here. Although three force components could be measured with it, only the horizontal force was measured in this test. The sinkage was measured in such a manner that the relative movement of the vertical bar to the supporting frame was picked up by a potentiometer. In the same way the displacement of the tool was measured with a potentiometer placed between the measur- ing unit and the supporting frame. Model Track Shoes The model track shoes investigated in this study are shown in Fig. 16 and their dimensions in Fig. 17. Model A is a simplified shoe often used in the study of this kind as a basic configuration of conventional track shoes. ' Model B is a special track shoe called "Triangle Shoe" which is prevalently used with tractors for soft ground operation in Japan. This was prepared to investi— gate whether it actually provides better performance on soft soil than a conventional one as is generally thought. The horizontal projection area and the height were made the same as those of Model A. Y I - ’ ‘- Fig. 16 Single model track shoe 35 111 E ~1—-—— 7 o ———-+ . n 7 o -——-1 =F «3 N 1""111‘111171- L '0 1 4-3 aJ F 7 0 -—-.*+ O? i 1'?» “3' ‘ ‘ C b ' G 8 70 -—~' _._______70 u . L.) ““““ ““““ f0 “ “u“ ““““ 4’ u 1 1s v- 5 '° N _ J1 ~--3 21 Fig.l7 Dimensions of Model Truck Show Unit mm Width = ISO mm 36 Model C is a "Raised Edge Shoe" prOposed in this study. The dimensions except the extra plate at the end are exactly the same as those of Model A. Model D is for examining the same effect of the extra plate on the triangle shoe Model B. Model B and F are for checking the effect of the extra plate on sinkage and how much traction is available with plane plate. Model G is a normal shoe except for a high grouser. The high grouser is not practicable in actual design due to the difficulty of steering and large drag force. The effect of grouser height has been studied by many re- searchers. Here it was used to roughly check its effect. With Models A, B, and C the effect of spacing was investigated. Fig. 15 shows the device used for this. The spacing is adjustable in three positions: zero spac— ing, one pitch spacing and double pitch spacing. Instrumentation The strain gauge bridge for measuring horizontal force and the two potentiometers for measuring sinkage iand displacement were connected to A.C. amplifiers and the output of each was fed into a chart recorder. The dynamometer was calibrated by applying a hori— zontal load consisting of dead weights to the stem-of the shoe as shown in Fig. 13. The friction of the pulley was small enough to be neglected. 37 Sinkage and displacement were calibrated by direct measurement with a scale. Calibration was done before and after each series of tests because the fluctuation in the powerline was significant. The apparatus and the instrumentation for measuring soil properties were the same that X. J. R. Avula (1964) used for his study. Soil Preparation and Test Procedure The soil was prepared with a hand tiller and a com- pacting roller (Fig. 9). First the soil was mixed by a tiller to a constant depth which was approximately ten times the height of the model shoe. Then the roller was passed along the bin once forward and backward. This rolling operation was repeated after making surface even. Finally, to obtain a flat surface, a 3-inch diameter steel pipe was rolled across the soil by hand. Since the soil was soft and plastic, it was not difficult to get a uniform condition. To observe the soil movement a punched steel plate was used. A fine check pattern was obtained by pressing the plate against the soil. After the soil preparation was made, the tool frame was lowered by turning the screw until the top of the shoe slightly touched the surface. The chart recorder was turned on and the sinkage line and the displacement line were adjusted to zero positions. 38 Then vertical bar was released from the frame by removing the pin allowing the tool to settle on the soil surface and sinking due to its own weight and the weight of the vertical bar. Usually the grouser penetrated to their full height. The horizontal force line on the recorder was ad— justed to zero position at this stage because this situ- ation represented the state in which no forae was applied to the dynamometer. Then the weights were placed on the plate at the tOp of the vertical bar. After five seconds the control valve was operated causing the measuring unit to move. The Speed was 2 cm/sec. throughout the test. Horizontal force, sinkage and displacement were re- corded continuously on the chart until the unit had moved the entire stroke of the cylinder (20 cm). The procedure described above was repeated twice for each model with each weight which is listed in Table 2. The procedure was also the same in investigating the effect of Spacing. The weights for twin models were twice of corresponding weights for single models. V. RESULTS AND DISCUSSION Results of Measurement Horizontal force, sinkage and displacement were measured for each case as follows: a. Single shoe models A through G with verticai loads listed in Table 2. b. Twin shoe models A, B, and C for three different Spacing with vertical loads listed in Table 2. Example of results for Single Shoe models A, B, and C are presented in Fig. l8, 19, 20. The photographs in Fig. 21 Show examples of the final state of soil defor— mation for each shoe model with vertical load V = 16.0 kg. The development of soil deformation is Shown in Fig. 22. Figs. 23, 24, 25 are example results of twin shoe models. Fig. 26 is represented to Show the soil deformation in the case of twin model shoes. The curves in the data Sheets were drawn as the average of the two measurements. The value of H for a single Shoe was subtracted from that of the corresponding valve for the twin model to give the net traction produced by the second shoe- This was done under the assumption that the load for the twin model was equally distributed to the first Shoe and the second shoe. The procedure was performed using the average curve of measured values for each case. 39 7O 1 ’ 7 7 o l I [ l I .x 6C>”"“‘ ’ .15 \/=:2|.l kg ' 350—— -..“ v=10.9kg ““— EM ‘ E "mu-00V V :: 5.8 kg _, 40————' IN" E Lav—"T A 2: ""J -—-""—- o 30 . J . / '—_—'—‘- I ,6" .__.-—---—-°‘——"—"""""" 0 p . V. ' I 20‘ .3; r ‘” ~~fl~~ 0‘10““. “to“. ~_ — 10 '- r 14 [NSPLACEMENT, cm, 0 ‘ ‘- ' i 2 4 6 8 |C> l2 I? IS H3 20 ' " “‘5..ng N’i 2 a," _ _ j 3 ,z' .2“ 4 life, A» ‘. " ./' . S; 5:. ‘6‘ "—4 d /" . - a _.a_q1——I--ii"— u1 6' :;§:T'-"O ’*1{4_"— <9 a&—+ . 1 x:'7 z: E; 8 9 IO Fig. 18 Recorded data, single model A 41 70 l I I 1 I I I a» "‘ _ H V=2l.l kg , B 60“— "“ W V:|6.0 kq 4—— . ‘ ¢ -_"-_' ”Er V'::|039 k9 ‘\\\///’ 11.150 """ 09' V = 5.8 kg 0 ”—_ 1 a: 1 C) LL 4C) -' 1 E /Mr 253C) - r ,4; .—— o . ....—«--1r"""" N /‘—.—a. ____..—-i-- .gp.?__—d__ E .Afdi" 0 .‘ ..-——i"" C>ZC) - _’,_11 v . I . . ° ’ ----J-o.o. . 4‘?) ‘~-~~“~ ~ IO ,' { W Y’fi1u___ ov‘a. ___:_-3T 0 DISPLACEMENT, cm 29 2 4' 6 53 IC) l2 i“? LifiL—uwfilw-T:% I -.... 1.-) E r... «o—- i #9“. 7 2 2”1 . fl 0'» ‘ gar" ar‘fl 3 "'rr«)-r ,4 E, . L a o , - 4 . & -\”-—-—_ Ef 1 LI; 5 \ B " -—11-———_..“ _____.__:¢ (9 1A “\. < 5 ix 3: 1 Z ¢\4\ " 7 L ow 1 a) p b\‘ 8 \\;, ‘\ ‘\ ~ \ A 9 \\\g\\ ‘;~!‘\ A \> ID \ \ Fig. 19 Recorded data, single model B 42 I l i 1 Ad _._._..acf ----- oer V=2|.| 1 k9 \I=:l6.0 kg V:I0.9 kg . v: 5.8 kg “‘1" £5I—dpu—II- ”1 ”J --d.~. ' .W; “k 70 060 x. “.50 o a: o 11.40 .1 < '"30 2 C) N, E220 O 1’ IO 0 l 2 3 54 o . .5. “J . 05' < x 27 23.3 9 10. W U flf‘ "(D-Qu- ~.q~€ 1--..-..._ ~ ....__:‘:ng . .——1p— T— V DISPLACEMENT , cm 1 20 8.— IO 12’ I 4 I . - ' v p $‘_JB--2% is" .——J "bfl-4 A .1 ' Fig. 20 .—-n-.-—.. . n I . - -_~..—dL.-. ——1 - Recorded data, single model C Fig.2l Soil deformation of single models Load = l6.0 kg Diaplocement = 20 cm —(l) deformation soil of Fig.22 Development 45 A-ZS V=32.0 kg V= 32.0 kg C-ZS. . I I . . 0 .““ n ‘ " D | . ' II‘ 0“ :1... .0 I ‘8! .1...o t8tlI‘ . u. 29.. :.| .DOIUI‘IOUI V= lO.9 kg IOOIOIIII auto 600000500. ...“..u 0 if... I...’ C. 42.2 kg V 14°25. kg 42.2 c-zs.v ...... p g. of twin models -(2) Fig.22 46 A-OS, V= 42.2 kg .b (3 HORIZONTAL FORCE, N 01 C) (3 'IO DISPLACEMENT, cm 8 IO 12 14 I6 18. 20 SINKAGE, cm (3 (D (D ~4 0) (I 4: CI to A. Fig. 23 Recorded data, twin model A-OS HORIZONTAL FORCE , kg Cl“ SINKAGE. mwmuaum 7O 0) (D (h (3 .5 C) (fl (3 “3 C3 6 47 A-ZS, V= 42.2kg .A .A A. A! r—‘l— lit—23‘1" l l l DISPLACEMENT, cm 8 IO l2 l4 l6 IO 20 l’f—S‘l— Recorded data, twin model A—2S 48 TO —_ 3 C‘ZS, V = 42.2 kg 60 _ O 8 '50 at C) a: 840 .J g . z 30 0 F4 3 2° S-lr-Zs I: V» "-_’I 5 DISPLACEMENT, 8 IO 12 n4 H5 IO 20 CHI O ' i i "“1“ E 2 ‘ s+—zs ° 3 l—J V P . m. 4. 3 x 5 516 U) 7 8 Fig. 25 Recorded data, twin model C-2S 49 In order to make numerical comparisons each set of data was approximated by the following equation: _ -J/K H — Hmax(l — e ) (22) Hmax and K were determined in the following way. Taking the logarithm of both sides of equation (22) and transforming, H max _ K J - affigg 10% fi;;;:fi (23) This is a straight line on semi-logarithmic paper. By trial and error a value of Hmax was selected so that the value; gave a straight line when plotted against j. The value of K was determined from the slope of the line. The pro- cedure for the case of Model A, with V = 16.0 kg is pre- sented in Fig. 27 as an example. Only observations of H up to the point where H had a maximum value or up to j = 14 cm were included in this analysis. The values for all cases determined in this manner are listed in Table 3. ' Another method for comparison was tried as follows: 50 X6 E: mCHCHEmeoU do oHQmem mm .wflm m Ucm IIXOEI onI 00. d4,4ld d _ n.Nn _ . x . n «IN.» 230 x \19A‘ WNNXUEI @N u KOEI afiNnixochI QNHXUEI O. ‘1N3W30V1d810 IUD 51 TABLE 3.——Parameters Hmax’ K. Hmax kg cm V kg 5.8 10.9 16.0 21.1 35.8 10.9 16.0 21.1 A 17.5 21.5 26.0 30.0 0.6 1.5 2.3 2.4 H B 15.0 22 23.5 35.0 2.0 3.2 2.0 5.7 § 0 18.0 21.5 27.5 38.5 1.0 2.2 1.8 3.0 E D 25.0 28.0 38.0 2.6 3.0 3.5 g) E 18.0 13.5 21.0 5.8 3.9 6.3 m F 23.0 28.0 30.5 4.5 4.9 2.8 G 37.0 39.0 50.0 2.0 5.3 6.2 v kg 21.8 32.0 42.2 21.8 32.0 42.2 * A—O 15.0 11.5 8.5 7.2 3.6 1.5 A-S 17.0 18.5 18.0 1 .0 2.7 H A-2S 16.5 21.5 22.0 2 3.3 2.6 E B-0 10.0 10.0 12.0 4.5 1.1 0.6 g B-S 15.0 17.0 14.0 5.8 1.4 0.6 5 IB—2S 18.0 23.0 20.0 2.8 3.0 1.9 c—s 17.5 24.0 23.0 1.8 3.1 3.3 c-2s 23.0 25.0 28.5 1.8 1.7 1.1 “The values refer to the second shoe Model: H = H max (1 _ e-J/K) 52 The performance of a track shoe should be evaluated from the standpoint of the entire vehicle traction. The vehicle traction is obtained by summing the traction of each shoe, which is a function of soil diSplacement. The soil diSplacement of each shoe is a function of the slip of the vehicle and the position of the Shoe on the track. For simplicity it is assumed that the vertical load is the same on all shoes along the track. Assume that n shoes are contacting the ground between front idler and Sprocket as shown in Fig. 28. The traction of the ith shoe is given by: The momentary traction of the entire track is calculated by: Hi(Ji) (23) The average traction of the vehicle during the time t is given by the general equation 1: / Tdt — = 2_____ T t In this case t is chosen equal to the time.tmax in which one shoe travels from the front idler to the drive sprocket t max _ O. Tdt T = ——~ (24) t max 53 Fig.28 Slip of vehicle 77// Fig.32 Behavior of a triangle shoe 54 where tmax = L/vO V 0 Track speed Using the relations: dx 6.13:?!" 0 xi = j L Ji max Equation (24) is transformed in the following way: max t {1 1. H j. dt = 0 i=1 i 1 t max T Due to the continuity of the track this can be shown to be equal to: J 71... 1. Pix... 1.- x j j. = 0 i=1 i 1 i = o 1=1 i i 1 L Jmax jjmax H(J)dJ = n. 0 = nfi Jmax Jmax where' H=j l / H(J)dJ max 0 55 H is interpreted as the average traction as one shoe travels from the front idler to the sprocket with slip conditions giving maximum soil deformation jmax at the sprocket. The entire traction of track is obtained by multi- plying H by the number of track shoes. H is given by the area under the curve divided by the maximum displacement. The result of the calculation for all cases is presented in Table 4. The value of sinkage given on the data sheets con— sists of initial static sinkage due to own weight and added weight and slip sinkage. In this study slip sinkage was considered important. Slip sinkage was obtained by subtracting the initial sinkage from the total value at the point to be considered. The values at j = 14 cm ob— tained in this manner are listed in Table 5 for all cases. Comparison of Single Models The difference of soil deformation among models is clearly observed in Fig. 21. Model C does not show significant sinkage, while Model A is digging down.. There is excessive sinkage with Model B. Model G is causing large amount of soil deformation, which gives. much traction, but sinkage is similar as for Model A. On the other hand the soil deformation is small with Model C. It is interesting to note that Model C gives more traction than Model A and B which show more soil deformation than A. Model D does not Show significant 56 TABLE 4.~-Average traction H in kg for jmax = 14 cm. v kg 5.8 10.9 16.0 21.1 A 13.9 20.2 23.2 25.3 P, B 10.9 18.1 21.6 24.9 g c 12.9 19.2 24.4 32.0 .3 D 20.4 23.1 30.5 ng E 10.5 9.7 13.1 F 17.7 20.2 26.0 G 29.8 31.0 37.2 ! A-O 9.6 9.2 7.5 A-S 15.6 16.1 16.1 .3 A-2s 14.1 19.1 20.6 EB—o 7.2 8.3 8.3 .5 B-S 11.0 14.6 12.5 ‘5' 8-28 14.0 19.6 18.9 c-s 15.3 19.1 19.9 c-2s 19.9 20.4 23.2 “The values refer to the second shoe. V = twice value for two shoes. 57 TABLE 5.—-Sinkage in cm at J = 14 cm. V kg 5.8 10.9 16.0 21.1 A -3.5 -1.4 0.1 0.4 B -2.5 0.8 4.6 7 H g c -4.0 —2.1 -1.7 -0.6 2 D -0.8 0.5 1 0 (D H b0 E 1.9 2.9 3.5 C: H W F 0 1.0 1.2 G -3.1 —0.4 0 V kg 21.8 32.0 42.2 A-O 0.1 0.9 1.7 A-S -o.5 0.2 1.1 H A—2s -1.1 0.4 0.7 Q) 8 B—O 1.0 . 2.2 3.2 2 ‘E B-S 0.7 3.5 5.0 5* B-2S 0.6 2.8 4.9 c—s —1.4 —0.2 0 c-2s —2.0 —0.4 0 l. The values indicate the change in sinkage from the start of shoe movement = slip sinkage. 2. Negative values = the shoe rose. 58 sinkage compared with Model B, which indicates that the extra plate is effective in reducing sinkage. This fact is also confirmed by comparing Model F with Model E. Fig. 22 explains the differences of soil deformation among Models A, B, and C. With Model A the soil over the shoe does not contribute to resistance force. The soil in front of the raised edge of Model C is still resisting the shoe. It might be the reason that there is a tendency to rise up with Model C. Model B shows small initial sinkage, but it digs down as the displacement develops. Fig. 29 was made from Table 3, which shows the comparison of the maximum horizontal force between different models. With small vertical loads, there is not much difference except for the special models E and G. At higher loads, however, C and D both showed more traction than A. There was about 30% increase with C. B also showed high traction at V = 21.1 kg, but because of ex— treme sinkage the stem must have caused considerable ef- fect and the true value must have been somewhat less. It is interesting to note that Model F, which had no grouser, showed more traction than A. This indicates that a similar failure pattern to that of A is developed under the plane plate. F is also significantly better than B. Model G proved that grouser height gives great ef- fect to traction in this soil condition. Consideration, however, must be made for the fact that the width of shoe 59 50 30— J