An empirical model for tractive performance of rubber-tracks in agricultural soils

Mathematical models capable of describing the interaction between traction devices and soils have been effective in predicting the performance of off-road vehicles. Such a model capable of predicting the performance of bias-ply tires in agricultural soils was first developed by Brixius [Brixius WW. Traction prediction equations for bias-ply tires. ASAE Paper No. 871622. St. Joseph, MI: ASAE; 1987]. When the soil and vehicle parameters are known, this model uses an iterative procedure to predict the tractive performance of a vehicle including pull, tractive efficiency, and motion resistance. Al-Hamad et al. [Al-Hamad SA, Grisso RD, Zoz FM, Von Bargen K. Tractor performance spreadsheet for radial tires. Comput Electron Agr 1994:10(1):45–62] modified the Brixius equations to predict the performance of radial tires. Zoz and Grisso [Zoz, FM, Grisso RD. Traction and tractor performance. ASAE Distinguished Lecture Series #27. St. Joseph, MI: ASAE; 2003] have demonstrated that the use of spreadsheet templates is more efficient than the original iterative procedure used to predict the performance of 2WD and 4WD/MFWD tractors. As tractors equipped with rubber-tracks are becoming popular, it is important that we have the capability to predict the performance for off-road vehicles equipped with rubber-tracks during agricultural operations. This paper discusses the development of an empirical model to accomplish this goal and its validity by comparing the predicted results with published experimental results.     

Tire inflation and its influence on drawbar characteristics and performance – Energetic indicators of a tractor set

This work deals with the influence of tire inflation on tractive characteristics and performance-energetic parameters of a ploughing set. The test was conducted using two tire sets with different tire pressures under field conditions. Measurements of tractive properties were performed by setting travel speeds to 5, 8, and 10 kph, respectively. The ploughing set was operated at 8 kph, according to the manufacturer’s recommendation. The measurement results were processed graphically and mathematically into the Vehicle Traction Ratio, drawbar power, and slip characteristics. The tire inflation, reduced from 180 to 65 kPa and/or 75 kPa, of tires with wide treads (low-profile) resulted in increase of the front tire footprint by 24.7% and rear tire footprint by 31.1%. This change had a positive impact on the specific tractive fuel consumption that decreased in the range from 3.4% to 16.0%, depending on the travel speed. The results of performed measurements revealed that reducing the tire inflation of appropriate tires can improve the drawbar characteristics and consequently the fuel consumption.     

Traction performance evaluation of a 78-kW-class agricultural tractor using cone index map in a Korean paddy field

The cone index (CI), as an indicator of the soil strength, is closely related to the traction performance of tractors. This study evaluates the traction performance of a tractor in terms of the CI during tillage. To analyze the traction performance, a field site was selected and divided into grids, and the CI values at each grid were measured. The CI maps of the field sites were created using the measured CI. The traction performance was analyzed using the measured traction load. The traction performance was grouped at CI intervals of 400 kPa to classify it in terms of the CI. When the CI decreased, the engine speed and tractive efficiency (TE) decreased, while the engine torque, slip ratio, axle torque, traction force, and dynamic traction ratio (DTR) increased. Moreover, the DTR increased up to approximately 13%, and the TE decreased up to 9%. The maximum TE in the DTR range of 0.45–0.55 was higher than approximately 80% for CI values above 1500 kPa. The DTR and TE results obtained in terms of the CI can help efficiently design tractors considering the soil environmental conditions.     

Evaluation of an empirical traction equation for forestry tires

Variable load test data were used to evaluate the applicability of an existing forestry tire traction model for a new forestry tire and a worn tire of the same size with and without tire chains in a range of soil conditions. The clay and sandy soils ranged in moisture content from 17 to 28%. Soil bulk density varied between 1.1 and 1.4g cm⁻³ with cone index values between 297 and 1418 kPa for a depth of 140 mm. Two of the clay soils had surface cover or vegetation, the other clay soil and the sandy soil had no surface cover. Tractive performance data were collected in soil bins using a single tire test vehicle with the tire running at 20% slip. A non-linear curve fitting technique was used to optimize the model by fitting it to collected input torque data by modifying the coefficients of the traction model equations. Generally, this procedure resulted in improved prediction of input torque, gross traction ratio and net traction ratio. The predicted tractive performance using the optimized coefficients showed that the model worked reasonably well on bare, uniform soils with the new tire. The model was flexible and could be modified to predict tractive performance of the worn tire with and without chains on the bare homogeneous soils. The model was not adequate for predicting tractive performance on less uniform soils with a surface cover for any of the tire treatments.     

Suitability of rubber track as traction device for power tillers

Suitability of using rubber tracks as traction device in power tillers replacing pneumatic tires was studied using an experimental setup consisting of a track test rig for mounting a 0.80 m × 0.1 m rubber track and a loading device for applying different drawbar pulls. Tests were conducted in the soil bin filled with lateritic sandy clay loam soil at an average soil water content of 9% dry basis by varying the cone index from 300 to 1000 kPa. Data on torque, pull and Travel Reduction Ratio (TRR) were acquired using sensors and data acquisition system for evaluating its performance. Maximum tractive efficiency of the track was found to be in the range of 77–83% corresponding to a TRR of 0.12–0.045. The Net Traction Ratio (NTR) at maximum tractive efficiency was found to be between 0.49 and 0.36.Using non-linear regression technique, a model for Gross Traction Ratio (GTR) was developed and it could predict the actual values with a maximum variation of 6% as compared to an average variation of 50% with Grisso’s model. Based on this model, tractive efficiency design curves were plotted to achieve optimum tractive performance of track for any given soil condition.     

Net traction ratio prediction for high-lug agricultural tyre

A study was conducted to determine the accuracy of Wismer-Luth and Brixius equations in predicting net traction ratio of a high-lug agricultural tyre. The tyre was tested on a sandy clay loam soil in an indoor University Putra Malaysia (UPM) tyre traction testing facility. The experiment was conducted by running the tyre in driving mode. A total of 126 test runs were conducted in a combination consisting of three selected inflation pressures (i.e., 166, 193 and 221 kPa) and two wheel numerics (i.e., 19 and 29) representing two extreme types of soil strength under different levels of travel reduction ranging between 0% and 40%. Regression analysis was conducted to determine the prediction equation describing the tyre torque ratio. Marqurdt’s method used by Wismer-Luth for predicting non-linear equation was not found suitable in predicting the torque ratio of the test tyre awing its low coefficient of determination and inadequacy. The logarithmic model was found suitable in torque ration prediction. From analysis of covariance (ANCOVA) the mean effect of travel speed, tyre inflation pressure and wheel numeric on tyre net traction ratio were found to be highly significant, while the interaction of inflation pressure and wheel numeric was not significant. The 193 kPa inflation pressure was found the best, among the three inflation pressures used, in getting higher net traction ratio and higher maximum efficiency. Finally, two models were formulated for tyre net traction ratio; one in terms of wheel numeric and travel speed reduction and the other in terms of mobility number and travel reduction, to describe the tested tyre performance at different soil strengths.     

Tractive characteristics of radial ply and bias ply tyres in a California soil

Four tyres (18.4-38, 18.4R38, 14.9-28, 14.9R28) were tested using the UCD single wheel traction tester. Each tyre was tested at two different inflation pressures and three different vertical loads at each inflation pressure. All tests were conducted in a well tilled Yolo loam soil. A dimensional analysis procedure was used to design and analyse the experiment. Two models were considered: (A) using inflation pressure as a variable, and (B) using tyre deflection as a variable. The effect of tyre type, tyre size, tyre inflation pressure and dynamic load on (1) net traction ratio at 20% slip and (2) average tractive efficiency in the 0–30% slip range were investigated using an ANOVA technique. An estimate of the possible energy savings due to the use of radial ply tyres instead of bias ply tyres in California agriculture was made.     

The tractive performance of a wide, low-pressure tyre compared with conventional tractor drive tyres

The NIAE single-wheel test vehicle was used to compare the tractive performance of a 67 × 34.00-25 tyre at 0.34 bar inflation pressure with that of 20.8–38 radial tyre at 0.6 bar inflation pressure and a similar 18.4–34 tyre at 0.8 bar inflation pressure. All tyres had similar tread patterns and were tested at the same vertical load of 2250 kg. The best performance was achieved by the 20.8–38 tyre. There was little difference in performance between the other two tyres. When compared with empirical predictions of performance derived from previous work, the two narrower tyres were found to perform approximately as predicted, but the performance of the wide, low-pressure tyre was considerably worse than predicted. This was thought to be due to bulldozing, because of the great width and increased wheel-slip caused by deformation of the soft side-wall and also due to the relatively short ground contact area. It was concluded that wide, low-pressure tyres are only suitable for fitting to vehicles requiring a very low draught capability.     

Dynamic load and inflation pressure effects on contact pressures of a forestry forwarder tire

A Trelleborg Twin 421 Mark II 600/55-26.5 steel-reinforced bias-ply forwarder drive tire at inflation pressures of 100 and 240 kPa and dynamic loads of 23.9 and 40 kN was used at 5% travel reduction on a firm clay soil. Effects of dynamic load and inflation pressure on soil–tire contact pressures were determined using six pressure transducers mounted on the tire tread. Three were mounted on the face of a lug and three at corresponding locations on the undertread. Contact angles increased with decreases in inflation pressure and increases in dynamic load. Contact pressures on a lug at the edge of the tire increased as dynamic load increased. Mean and peak pressures on the undertread generally were less than those on a lug. The peak pressures on a lug occurred forward of the axle in nearly all combinations of dynamic load, inflation pressure, and pressure sensor location, and peak pressures on the undertread occurred to the rear of the axle in most of the combinations. Ratios of the peak contact pressure to the inflation pressure ranged from 0 at the edge of the undertread for three combinations of dynamic load and inflation pressure to 8.39 for the pressure sensor on a lug, near the tire centerline, when the tire was underinflated. At constant dynamic load, net traction and tractive efficiency decreased as inflation pressure increased.     

Soil compaction and tires for harvesting and transporting sugarcane

Four tire types (A, block-shape tread; B, rib-shape tread; C, low-lug tread; D, high-lug tread) used to harvest and transport sugarcane were compared regarding the compaction induced to the soil. Tires were tested at three inflation pressures (207, 276, 345 kPa) and six loads ranging from 20 to 60 kN/tire. Track impressions were traced, and 576 areas were measured to find equations relating inflation pressure, load, contact surface and pressure. Contact surface increased with increasing load and decreasing inflation pressure; however, the contact pressure presented no defined pattern of variation, with tire types A and B generating lower contact pressure. The vertical stresses under the tires were measured and simulated with sensors and software developed at the Colombian Sugarcane Research Center (Cenicaña). Sensors were placed at 10, 30, 50 and 70 cm depth. Tire types A and B registered vertical stresses below 250 kPa at the surface. These two tires were better options to reduce soil compaction. The equations characterizing the tires were introduced into a program to simulate the vertical stress. Simulated and measured stresses were adjusted in an 87–92% range. Results indicate a good correlation between the tire equations, the vertical stress simulation and the vertical stress measurement.     

Effects of reduced inflation pressure and vehicle loading on off-road traction and soil stress and deformation state

Field experiments on off-road vehicle traction and wheel–soil interactions were carried out on sandy and loess soil surfaces. A 14 T, 6 × 6 military truck was used as a test vehicle, equipped with 14.00-20 10 PR tyres, nominally inflated to 390 kPa. Tests were performed at nominal and reduced (down to 200 kPa) inflation pressures and at three vehicle loading levels: empty weight, loaded with 3.6 and 6.0 T mass (8000, 11,600 and 14,000 kg, respectively). Traction was measured with a load cell, attached to the rear of the test vehicle as well as to another, braking vehicle. Soil stress state was determined with the use of an SST (stress state transducer), which consists of six pressure sensors. Soil surface deformation was measured in vertical and horizontal directions, with a videogrammetric system. Effects of reduced inflation pressure as well as wheel loading on traction and wheel–soil interactions were analyzed. It was noticed that reduced inflation pressure had positive effects on traction and increased stress under wheels. Increasing wheel load resulted in increasing drawbar pull. These effects and trends are different for the two soil surfaces investigated. The soil surface deformed in two directions: vertical and longitudinal. Vertical deformations were affected by loading, while longitudinal were affected by inflation pressure.     

Laboratory experimental study of tire tractive performance on soft soil: Towing mode,traction mode,and multi-pass effect

Tire tractive performance, soil behavior under the traffic, and multi-pass effect are among the key topics in the research of vehicle off-road dynamics. As an extension of the study (He et al., 2019a), this paper documents the testing of a tire moving on soft soil in the traction mode or towing mode, with a single pass or multiple passes, and presents the testing results mainly from the aspects of tire tractive performance parameters, soil behavior parameters, and multi-pass effect on these parameters. The influence of tire inflation pressure, initial soil compaction, tire normal load, or the number of passes on the test data has been analyzed; for some of the tests, the analysis was completed statistically. A multi-pass effect phenomenon, different from any phenomenon recorded in the available existing literature, was discovered and related to the ripple formation and soil failure. The research results of this paper can be considered groundwork for tire off-road dynamics and the development of traction controllers for vehicles on soft soil.     

The use of soil compaction levels in the selection of field-safe sugarcane transport vehicles

Data was collected for single bundle and nucleus estate trailers aimed at selecting the trailer units that could safely travel in the sugarcane fields without causing detrimental soil compaction. The proportion of trailers carrying loads in excess of established safe axle loads was assessed. Over 60% single bundle trailers traveling in sandy loam and sandy clay loam fields were found not to induce detrimental soil compaction. Nucleus estate trailers, however, were sufficiently loaded to cause significant soil compaction. Working under soil moisture contents of 21.4–27.1% (dry basis), safe loads were found to be payloads of 64.9 and 46.1 kN carried by single bundle and nucleus estate trailers (respectively) on a single axle having two 10 ply 18.4×30 tires with an inflation pressure of 207 kPa.     

Semi-empirical traction prediction equations based on relevant soil parameters

Extensive single-wheel traction tests were conducted in the vicinity of UC Davis campus using four different radial ply tires, two soil types, four soil conditions, three levels of inflation pressures, and three axle loads. Soil sinkage and shear characteristics were also obtained using an instrumented soil test device in every test condition. These field data were analyzed to obtain semi-empirical traction prediction equations for radial ply tires. In general, these prediction equations were able to predict traction equation parameters with less than 25% error.     

Tractive performance of a tread design for improved flexibility

The tractive performance of an 18.4R38 radial-ply tractor tire with increased flexibility in the tread area was compared to that of a standard tread design. Normal soil-tire interface stresses were measured at four locations on the lug surfaces of both tires operating on Decatur clay loam and Norfolk sandy loam soils. There was a tendency for the increased flexibility in the tread area to provide a higher net traction ratio at the same tractive efficiency as the standard tread design, especially on Decatur clay loam soil. The more flexible tread design reduced the magnitude of peak normal contact stresses across the tire width, which may have implications for reducing soil compaction without compromising tractive performance. The more flexible tire reduced the average normal contact stress by approximately 15% in the sandy loam soil and 23% in the clay loam soil for the range of operating conditions investigated.     

Comparison of the tractive performance of a tractor driving wheel during its first and second passes in the same track

The tractive performance of a conventional 13.6–38 tractor driving wheel tyre was measured in 19 different fields using the NIAE Single Wheel Tester. In each field the performance was measured on the undisturbed ground and again in the rut formed by a previous run with the same tyre. The second run simulated the operation of the rear wheels on a four-wheel drive tractor.The performance during the second pass was generally better than during the first pass. On average, the coefficient of traction increased by 7%, rolling resistance reduced by 11% and maximum tractive efficiency increased by 5%. The improvement increased as ground conditions deteriorated but was never large enough to fully explain the differences in performance between two and four-wheel drive tractors previously measured. It is suggested, therefore, that these differences may be primarily due to the greater ease with which power, weight, implement size and working speed can be matched with four-wheel drive tractors.     

Effect of design parameters on the performance of rigid traction wheels on saturated soils

A dimensional analysis was carried out to study the effect of individual wheel parameters, namely the lug angle, lug height, rim width and lug spacing on the traction performance of rigid wheels in saturated soils. The performance of the test wheels was evaluated on the basis of drawbar pull, slip and torque data obtained at different normal loads ranging between 50 and 100 kg (790–980 N). The data were utilized to compute the performance values such as tractive efficiency and overall performance index. Through the regression analysis, the optimum values of lug angle, rim width and lug spacing were found to be 20°, 200 mm and 110 mm respectively for a wheel of 685 mm dia. However, a definite conclusion regarding the optimum value of lug height could not be drawn, though the analysis for higher loads indicated this value as of 38 mm. The wheel parameter most influencing the traction performance of the wheel was found to be the rim width.     

Soil stress and compaction effects for four tractor tyres

Compaction effects and soil stresses were examined for four tractor tyres under three inflation pressures: 67, 100 and 150% of the recommended pressure. The four tyres were 18.4 R 38, 520/70 R 38, 600/65 R 38 and 650/60-38 and they carried a wheel load of 2590 kg. The 650/60-38 was a bias-ply tyre while the other three were radial tyres. Increased inflation pressure significantly increased all measured parameters: rut depth, penetration resistance and soil stress at 20 and 40 cm depth. The 18.4 R 38 caused a greater rut depth and penetration resistance than the other tyres, which did not differ significantly from each other. The soil stress was highest for the 18.4 R 38, followed by the 650/60-38. The low-profile tyres decreased compaction compared with the 18.4–38 tyre, mainly by allowing a lower inflation pressure. The use of low-profile tyres did not reduce compaction if not used at a lower inflation pressure. The bias-ply tyre caused a higher stress in the soil than the radial tyres when used with the same inflation pressure, but the compaction effects in terms of rut depth and penetration resistance were not greater for this tyre than for the radial low-profile tyres.     

Performance prediction of animal drawn vehicle tyres in sand

Four animal drawn vehicle (ADV) tyres of 5.00–19, 6.00–19, 7.00–19 and 8.00–19 sizes were tested in sand under various but controlled conditions in an indoor soil bin. A tyre test carriage with four-bar parallel linkage was developed for accommodating a single wheel of different sizes. Performance tests were conducted at five levels of inflation pressure and load. The sand compaction level was varied in the range of 3.4–4.5 MPa/m and forward speed of the test carriage was maintained at 3.1 km/h. Performance of the tyres 7.00–19 and 8.00–19 was identical and offered less rolling resistance as compared to other tyres. However, their use in camel carts may not be recommended beyond the payload of 6 kN on single wheel with inflation pressure and sand compaction range of 172–379 kPa and 3.4 –4.5 MPa/m, respectively. Based on the experimental results, empirical models were developed to predict the performance of tyres. The accuracy of prediction of the developed empirical models was compared with that of existing semi-empirical approaches. Model with sand mobility number considered relatively simple and convenient to use in the field and yields reasonably good prediction for rolling resistance and sinkage.     

Thrust and slip of a low-pressure tire on compressible ground by the compression-sliding approach

Driving wheels with low-pressure lugged tires are standard propulsion components of wheeled off-road vehicles. Such wheels have been mostly treated in theory as shorter tracks or even as “black boxes”. These procedures, however, appear not to be necessary since an updated theory of thrust generation, based on experiments with double-plate meter, was presented at the 2008 ISTVS Turin conference. This theory is based on the compaction-sliding (CS) concept, which claims that the rearward displacement of soil, a reason for slip, starts as horizontal soil compression by lugs (C-stage at lower thrust), followed by the slide of sheared off soil blocks (S-stage at higher thrust). The thrust in terms of ISTVS Standards equals gross tractive effort minus internal rolling resistance of a tire. The resultant thrust of a tire equals the sum of component thrusts of individual soil segments. The respective technique provides thrust-slip curves, which reflect tire size, loading, inflation pressure and tread pattern design, e.g. tread density, lug angle, pitch, height and tire casing lay-out and thus can be useful notably in assessing the traction properties of new tire designs. Concerning the evaluation of tire traction tests or similar applications, the CS approach offers a simplified version of thrust-slip formula (G-function), which complies with the CS concept and is easy to use.