Measurement of soil parameters useful in predicting tractive ability of off-road vehicles using an instrumented portable device

An instrumented portable device that measures soil sinkage, shear, and frictional parameters in situ was developed to investigate the complexity of soil-traction device interaction process. The device was tested to determine its ability to measure soil frictional and shear characteristics. Extensive laboratory tests were conducted using dry and moist Capay clay and Yolo loam soils. In addition, field tests were also conducted in a Yolo loam field located at the UC Davis Agricultural Experiment Station. The Cohron sheargraph was also tested under the same laboratory experimental conditions to determine adhesion, soil-metal friction, cohesion, and angle of internal friction of soil. The analysis of experimental data indicated that soil adhesion and soil-metal friction were found to be functions of the intercept and slope values of cone torque versus cone index plot (r² = 0.94 and 0.95, respectively). Moreover, soil cohesion was found to be related to adhesion by the constrained adhesion relationship, and soil angle of internal friction was proportional to soil-metal friction as reported by Hettiaratchi [7] and [8]. These results imply that a simpler device consisting of a rotating cone can be developed to measure soil frictional and shear characteristics. Preliminary results showed that the soil parameters determined using this device predicted the maximum net traction developed by four different radial ply tires tested by Upadhyaya et al. [18] under similar soil conditions quite well. These results indicate that the parameters obtained from the device could be useful in obtaining traction related parameters of a soil-tractive device interaction process.     

An overview of methods to convert cone index to bevameter parameters

This paper reviews experimental methods for the conversion of cone index measurements to bevameter parameters in support of vehicle soil/tire/track interactions for two general soil types, sand and lean clay. The accurate prediction of traction, motion resistance, and sinkage of tire/tracks off-road requires estimates of soil strength. Equipment used in the measurement of soil strength to support predictions of off-road mobility include the bevameter and the cone penetrometer. The portability of the cone penetrometer and rapid estimates of spatial/temporal variability in all terrain conditions make it an invaluable tool. The bevameter, a less portable tool, is used for the mechanical analysis of soils. The bevameter measures parameters defining soil strength in terms of cohesive modulus of soil deformation (k_c), frictional modulus of soil deformation (k_φ), exponent of soil sinkage (n), cohesion (c), angle of internal friction (φ), and the plate pressure at 1 in. (2.54 cm) of penetration (K) (Bekker, 1969). The field of terramechanics would greatly benefit from having the ability to convert cone penetrometer data in areas where bevameter parameters are difficult to collect. That ability to convert from cone index to bevameter parameters could be used for the large sets of existing cone index data to support determination of traction and motion resistance. This paper examines those methods for converting cone index to bevameter plate penetration parameters k_c, k_φ, and n.     

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.     

Determination of the soil pressure distribution around a cone penetrometer

The objective of this paper was to investigate the pressure distribution around a cone penetrometer using a pressure sensing mat under laboratory conditions. The investigation was conducted under (1) constrained conditions using cylindrical split pipe molds and (2) unconstrained conditions using a soil box. These tests were conducted in Capay clay and Yolo loam soil containing two different moisture conditions and two compaction levels.In the constrained tests, a maximum radial pressure of 111 kPa was observed in the Capay clay soil with 3.4–4.3% d.b. moisture content and three blows of compaction (cone index value of 2040 kPa) when using the 41 mm diameter split pipe mold. These pressure levels decreased to 82 and 22 kPa, respectively, when 65 and 88 mm diameter molds were used. In both the Capay clay and Yolo loam tests, the average radial pressure and average cone index values showed similar trends.In the unconstrained tests, a maximum pressure of 9.0 kPa was observed in the Capay clay with 4.5% d.b. moisture content and three blows of compaction (cone index value of 550 kPa) at a horizontal distance of 25.4 mm from the vertical axis of the cone penetrometer and minimum pressure levels in the range of 0.2–0.3 kPa when the horizontal distance of the penetrometer was in the range of 56.8–66 mm. The pressure levels are much smaller than the ones obtained in the constrained tests and may suggest that the pressure distribution under field conditions is small at a distance of 25.4 mm or higher from the tip of the cone.The experimental data were statistically analyzed to identify significant factors. The results of the analysis for the constrained test indicated that the mold diameter and number of blows significantly increased the pressure readings within the soil mass. Increasing the mold diameter led to a decrease in the average radial pressure and increasing the number of blows contributed to an increase in the average radial pressure. In the unconstrained test, the average radial pressure distribution at a given point were significantly influenced by the horizontal distance of the point from the vertical axis passing through the center of the penetrometer shaft, soil type, and soil moisture content. Higher pressure values were obtained in the Capay clay tests compared to the Yolo loam tests. In all cases, the pressure levels were greater for the drier soil than for the moist soil.     

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.     

The effect of dynamic impact and water potential on some surface soil properties

A direct shear test with a superimposed impact was used to simulate the action of a track on the soil surface and to study the effect on soil surface properties. Results showed that impact increased bulk density, reduced saturated hydraulic conductivity and decreased cone penetrometer resistance. An impact plus shear treatment reduced the residual shear strength to approximately 60 kPa compared with 85 kPa for a shear only treatment. Water tension also greatly influenced the changes measured with the order of greatest change being −5>−10>−60>t-100>−300 kPa. The results are discussed with respect to soil trafficability and soil structural change with vehicle passage.     

Out-of-plane deflections of metallic and composite pin-loaded coupons

The projection shadow moiré technique was employed to determine an out-of-plane contouring history of aluminum, [(+45/–45)]_3S , [(0/90₃,0] _S and [(0/90/+45/–45)]_2S fiberglass epoxy pin-loaded specimens experimentally. The contouring interval was limited to 0.0254 mm by experimental concerns. Qualification of the projection shadow moiré optical arrangement was initially accomplished by the out-of-plane contouring of a clamped, centrally loaded, circular aluminum plate. Experimental results indicate significant out-of-plane displacements in the bearing region of the coupon at load levels well below ultimate. Effects of material anisotropy could be seen in the fiber-oriented shape of the displacement contours. Comparisons with three-dimensional finite-element results indicate that experimental out-of-plane contours were significantly larger than their finite-element counterparts in the region above the pin for the [(+45/–45)]_3S , [(0/90)₃, 0] _S laminates. These deviations increased with increasing pin-load level. These variations could be attributed to linear-elastic through-thickness moduli assumptions as well as through-thickness finite-element mesh coarseness.     

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.     

Effect of inflation pressure on tractive performance of bias-ply tires

This study was to investigate the effect of inflation pressure on the tractive performance of bias-ply tires for agricultural tractors. Traction tests were conducted at velocities of 3, 4, and 5.5 km h⁻¹ under four different surface conditions using a 13.6–28 6PR bias-ply tire as driving the wheel of the test tractor. When the inflation pressure was reduced from 250 to 40 kPa by a decrement of either 30 or 50 kPa depending upon the test surfaces, some of the test results showed that the traction coefficient and tractive efficiency were increased maximally by 14 and 6%, respectively, at 20% slip. However, such improvements in traction were not statistically consistent enough to find any rules regarding the effect of inflation pressure of bias ply tires on the tractive performance of tractors.     

Overland transport technology and environment: A series of public lectures presented at Carleton University, Ottawa, Canada

The demand for Canada's natural resources and their wide distribution in remote areas have prompted development of off-road transport technology in that country. New requirements for compatibility of off-road transport systems with environmental features has also stimulated innovation. In the light of these concepts, the Faculty of Engineering at Carleton University sponsored a series of public lectures in 1971–1972. These lectures form the main subject of this special issue of the Journal of Terramechanics.     

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.     

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.     

Comparisons of different procedures of pre-compaction stress determination on weakly structured soils

Compaction is an important component of soil degradation. In this regard, the pre-compaction stress (σ_pc) concept is considered useful in mechanized agriculture nowadays. When the external forces exceed the internal strength (σ_pc) of soil, soil structure and soil physical quality will deteriorate. This concept was introduced at first for confined consolidation of non-structured, homogenized and saturated subsoils in civil engineering, though it is also suitable for agricultural conditions where the topsoil and subsoil are considered and both are often structured, heterogeneous and unsaturated. The best method for predicting σ_pc is by the plate sinkage test (PST) in the field, but it is expensive and time-consuming. This study was conducted to find an alternative laboratory method besides the confined compaction test (CCT) for predicting σ_pc. The CCT may not be a good method, especially at higher water contents, and for soils with low organic matter content, because of low sharpness of the critical region on the stress–strain curves. The study was performed on five soil types with a range of soil textures and organic matter content from central Iran using three loading types and three pF (i.e. Log [soil matric suction in cm]) values of 2.3, 2.7 and 2.9 with two replicates. Loading types consisted of CCT, the semi-confined compaction test (SCCT) and the kneading compaction test (KCT) at three maximum (or pre-compaction) stresses of 200, 400 and 600 kPa. The experiment was a completely randomized factorial design. The aim was to determine how accurately each loading type test could predict σ_pc of soil pre-compacted by one of the other methods. The applied combinations of CCT–SCCT, SCCT–CCT and KCT–CCT mean that the soil was pre-compacted by the first loading type and evaluated by the second one. The results showed that σ_pc and the sharpness of the σ_pc region were significantly affected by loading types as well as the soil conditions. The sharpest σ_pc region was observed in SCCT and the least sharp in CCT with the overall order being CCT–SCCT > SCCT–CCT > KCT–CCT. The sharpness of the σ_pc region was reduced for the soil samples with higher water content and coarser texture. Regardless of the soil and loading conditions, the prediction by SCCT was consistently more accurate than by CCT. The prediction of σ_pc by SCCT was more precise in comparison with CCT especially at higher stresses and soil water contents. However, the prediction of σ_pc by SCCT was very accurate at pF values of 2.7 and 2.9, and with low σ_pc values, when compared with the actual values of the σ_pc. For the clay soil at a pF value of 2.3, no pre-compaction region (i.e. zero σ_pc) could be determined by CCT at a maximum axial stress of 600 kPa. This was because of the incompressibility of soil water at this near-saturated soil condition at high stress. However, the sharpness of the critical region in SCCT was high enough to predict σ_pc satisfactorily. There was no significant difference between the combinations of SCCT–CCT and KCT–CCT in predicting σ_pc. The SCCT is a compromise method that lies between CCT and PST. SCCT has the advantage of using a limited and definite soil volume that can be modeled as a soil element. Marginal effects of disturbance caused by coring/sampling as well as pre-test sample preparation seem to have minor effects on the stress–strain curve determined by SCCT in comparison with CCT. Moreover, the soil volume needed for this test is the same as for CCT.     

A large deformation theory for rate-dependent elastic–plastic materials with combined isotropic and kinematic hardening

We have developed a large deformation viscoplasticity theory with combined isotropic and kinematic hardening based on the dual decompositions F=F^eF^p [Kröner, E., 1960. Allgemeine kontinuumstheorie der versetzungen und eigenspannungen. Archive for Rational Mechanics and Analysis 4, 273–334] and [Lion, A., 2000. Constitutive modelling in finite thermoviscoplasticity: a physical approach based on nonlinear rheological models. International Journal of Plasticity 16, 469–494]. The elastic distortion F^e contributes to a standard elastic free-energy ψ^(e), while , the energetic part of F^p, contributes to a defect energy ψ^(p) – these two additive contributions to the total free energy in turn lead to the standard Cauchy stress and a back-stress. Since F^e=FF^p-1 and , the evolution of the Cauchy stress and the back-stress in a deformation-driven problem is governed by evolution equations for F^p and – the two flow rules of the theory.We have also developed a simple, stable, semi-implicit time-integration procedure for the constitutive theory for implementation in displacement-based finite element programs. The procedure that we develop is “simple” in the sense that it only involves the solution of one non-linear equation, rather than a system of non-linear equations. We show that our time-integration procedure is stable for relatively large time steps, is first-order accurate, and is objective.     

Liquid–crystalline nematic polymers revisited

A new model for nematic polymers is proposed, based on the probability ψ(u,u,t) for a macromolecule to be oriented along direction u while embedded in a u environment created by its neighbours. The potential of the internal forces is written Φ(u,u) accordingly. The free energy contains a contribution ν Φ + k_BT ln ψ where the brackets mean an average over the probability distribution, while ν is the (uniform) polymer number density. An equation is derived for the time-evolution of the order parameter S = uu − I/3, together with an expression for the stress tensor. These two results offer a generalization of the Doi Model in so far as they include a distortional energy, analogue to the Frank elastic energy for low molecular mass nematics. Extending the Maier–Saupe variational procedure, we specify the way that the internal potential Φ(u,u) must be written for it to favour non-zero values of the order parameter, while giving a penalty to situations with gradients of the order parameter. The result is quite different from the potential proposed a decade ago by Marrucci and Greco (their Φ depends on u only), while it has a clear connection with the so-called Landau-de Gennes (LdG) tensor models, which are based on a free-energy depending on the order parameter and its gradients.     

A review on traction prediction equations

A variety of methods, ranging from theoretical to empirical, which have been proposed for predicting and measuring soil-vehicle interaction performance are reviewed. A single wheel tyre testing facility at Indian Institute of Technology, Kharagpur, India, was used to check the applicability of the most widely used traction models, for tyres used in Indian soil conditions. Finally, the coefficients of traction prediction equations developed by Brixius [16] were modified to fit traction data obtained from the testing of the tyres in the Indian soil conditions.     

Effect of inflation pressure on motion resistance ratio of a high-lug agricultural tyre

A single wheel tyre facility at University Putra Malaysia (UPM) was used to check the validity of Wismer–Luth and Brixius equations in predicting the motion resistance ratio of a high-lug agricultural tyre and to investigate the effect of inflation pressure. A Bridgestone 5-12, 4 ply, lug M was tested on sandy-clay-loam soil. The experiments were conducted by running the tyre in towing mode. Three inflation pressures (i.e., 166, 193 and 221 kPa) were investigated and wheel numerics ranging between 0 and 70. The analysis of covariance (ANCOVA) revealed that both inflation pressure and wheel numeric have significant effects on tyre motion resistance ratio. Regression analysis was also conducted to determine the closeness of fit for Wismer–Luth’s and Brixius’ equations in predicting the motion resistance ratio of the tested tyre. Finally, three new logarithmic models for tyre motion resistance were formulated. The advantage of reducing tyre inflation pressure from 221 (nominal pressure) to 193 kPa on the motion resistance ratio of the high-lug agricultural tyre was pronounced. However, the tyre’s motion resistance ratio deteriorated with further reduction in tyre inflation pressure from 221 (nominal pressure) to 166 kPa.     

Dynamic mode I perturbation solution for a moving crack unsteadily

Rice et al. (Journal of Mechanics and Physics of Solids42, 813–843) analyze the propagation of a planar crack with a nominally straight front in a model elastic solid with a single displacement component. Using the form of Willis et al. (Journal of the Mechanics and Physics of Solids43, 319–341), of dynamic mode I weight functions for a moving crack, we address that problem solved by Rice et al. in the 3D context of elastodynamic theory. Oscillatory crack tip motion results from constructive-destructive interference of stress intensity waves. Those waves, including system of the dilatational, shear and Rayleigh waves, interact on each other and with moving edge of crack, can lead to continuing fluctuations of the crack front and propagation velocity.     

Modélisation du comportement thermique d'un outil de fraisage : approche par identification de système non entierThermal modelling of a milling tool: a noninteger system identification approach

In this work we present an experimental apparatus devoted to the thermal characterisation of a milling tool. The experimental device used thermistors, one for each insert. Each thermistor is located at a point in the tool close to the tip of the insert. The heat flux in each insert is expressed according to the temperature at the sensor from a non-integer model. The parameters of the model are identified from transient evolutions measurements of the temperature on the sensor and on the cutting edge. An application shows the difference in the behaviour of each insert during machining from the estimated heat fluxes. To cite this article: J.-L. Battaglia et al., C. R. Mecanique 330 (2002) 857–864.     

Fractal model for virgin compression of pure clays

The well-known linear relation between the void ratio and the logarithm of pressure for the one-dimensional consolidation has widely incorporated into elastoplastic constitute equation of soils, however, it is not at all straight line for more compressible clays and has several physically unaccepted properties. The compression of clays is explained by fractal theory, and is seen as a balance between the vertical pressure and repulsive force between clay plates. The distance between clay plates depends on the structure formation of the clay flocculation and clay surface. The structure formation of the clay flocculation and clay surface can be modeled by fractal approach. A new formulation of one-dimensional virgin compression of pure clays, expressed by the linear function of ln ν–ln p or ln e–ln p, is proposed based on the fractal model for clay structure. The linear function of ln ν–ln p is suitable to express the virgin compression of the extremely high plasticity clays up to the high pressure of 5000 kPa. For low plasticity clays, the virgin compression satisfies with the linear relationship of ln e–ln p at the pressure higher than 100 kPa. These too are show to be in satisfactory agreement with experimental data. The gradient of the plots of ln ν–ln p and ln e–ln p is related to the fractal dimensions of clay structure, the fundamental material parameters for the first time.