Tire-soil Interaction Model Research Articles

Data-Driven Modeling of Tire-Soil Interaction with POD-Based Model Order Reduction

Abstract A data-driven model capable of predicting time-domain solutions of a high-fidelity tire-soil interaction model is developed to enable quick prediction of mobility capabilities on deformable terrain. The adaptive model order reduction based on the proper orthogonal decomposition (POD), for which the high-dimensional equations are projected onto the reduced subspace, is utilized as the basis for predicting the time-domain tire-soil interaction behavior. The projection-based model order reduction, however, requires many online matrix operations due to the successive updates of the nonlinear functions and Jacobians at every time step, thereby hindering the computational improvement. Therefore, a data-driven approach using a Long Short Term Memory (LSTM) neural network is introduced to predict the reduced order coordinates without the projection and time integration processes for computational speedup. With this model, a hybrid data-driven/physics-based off-road mobility model is proposed, where four separate LSTM-POD data-driven tire-soil interaction models are integrated into the physics-based multibody dynamics (MBD) vehicle model through a force-displacement coupling algorithm. By doing so, the individual data-driven tire-soil interaction model can be constructed efficiently, and the MBD and LSTM models are assembled as a single off-road mobility model and analyzed with existing off-road mobility solvers. The predictive ability and computational benefit of the proposed data-driven tire-soil interaction model with the POD-based model order reduction are examined with several numerical examples.

Effect of Soil Properties and Powertrain Configuration on the Energy Consumption of Wheeled Electric Agricultural Robots

Agricultural emissions can be significantly reduced with smart farming, which includes moving away from large conventional tractors to fleets of compact wheeled electric robots. This paper presents a novel simulation modeling approach for an ATV-sized wheeled electric agricultural robot pulling an implement on deformable terrain. The 2D model features a semiempirical tire–soil interaction model as well as a powertrain model. Rear-wheel drive (RWD), front-wheel drive (FWD), and all-wheel drive (AWD) versions were developed. Simulations were carried out on two different soils to examine the energy consumption and tractive performance of the powertrain options. The results showed that energy consumption varies the least with AWD. However, RWD could provide lower energy consumption than AWD with light workloads due to lower curb weight. However, with the heaviest workload, AWD had 7.5% lower energy consumption than RWD. FWD was also found to be capable of lower energy consumption than AWD on light workloads, but it was unsuited for heavy workloads due to traction limitations. Overall, the results demonstrated the importance of taking the terrain characteristics and workload into account when designing electric agricultural robots. The developed modeling approach can prove useful for designing such machines and their fleet management.

Parameters collaborative optimization design and innovation verification approach for fuel cell distributed drive electric tractor

Fuel cell distributed drive electric tractors (FCDET) are one of the necessary means to achieve truly green agriculture. However, low traction efficiency, poor control coordination, and excessive energy consumption are the main reasons hindering the industrialization of FCDET. This paper proposed a parametric collaborative optimization design method and innovative verification system that considers the drive system and energy system. Based on the tractor plowing operating conditions, a 7-DOF coupled dynamics model of the distributed drive system and a tire-soil interaction model were established, and the key component selection and parameter matching were completed. On the drive system optimization level, the front and rear wheelside transmission ratios are optimized based on a multi-island genetic algorithm (MIGA). On the energy system optimization level, the globally optimal power distribution ratio is found based on the dynamic programming algorithm (DP). A complete experimental prototype verification system is constructed based on the MATLAB/Simulink-NI PXI joint simulation platform, physical prototype test bench, and real vehicle multi-index test platform. The results show that the average efficiencies of the optimized drive and energy system are increased by 0.38 % and 3.82 %, the total energy consumption (total hydrogen consumption) is reduced by 25.40 % and 15.39 %, respectively. The maximum fault-free operating time is 5.5h, the average traction power is 21.07 kW, and the average traction force is 10610 N in the all-wheel drive mode. The experimental results fully demonstrate that the electric tractor with the fuel cell distributed drive system as the core can meet the verification of multiple indicators. This study can provide a new theoretical basis and technical verification method for the optimal design and system control of fuel cell distributed drive electric tractors.

Load characteristics analysis of tractor drivetrain under field plowing operation considering tire-soil interaction

The drivetrain of a tractor is prone to fatigue failure under heavy load plowing operations. The load variation of its transmission shafting is affected by the "machine-soil" interaction environment, especially the tire-soil interaction. Therefore, a load transfer model of a tractor plowing operation composed of a drivetrain model, tire-soil interaction model, and tractor dynamics model was established, to analyze the load characteristics of the transmission shafting. For verifying the proposed model, the field plowing process was carried out experimentally. The driving wheels and shafting were discussed as influenced by the slip rate variation in the tire-soil interaction model. The fitting distribution characteristics of cycle average and range of transmission shafting in the rain-flow domain were obtained. The results showed that the established model can accurately simulate the speed and dynamic load characteristics of the tractor plowing operation. The driving wheel loads increased with the increase of slip rate except for the motion resistance. When the slip rate exceeded 25 %, loads of the transmission shafts changed steadily. The reliability of fit R2 of the statistical distribution for transmission shafting load was greater than 0.94. The mean and variance of rear-drive half shaft torque were the largest, where fatigue failure was more likely to occur. The above theoretical model and results provide practical guidance for structural optimization design, fatigue durability analysis and reliability loading test of the tractor drivetrain.

Reduced Order Modeling of Deformable Tire-Soil Interaction With Proper Orthogonal Decomposition

AbstractIn this study, model order reduction of high-fidelity off-road mobility models is explored to address the computational intensity of nonlinear finite element deformable tire–soil interaction models. To this end, a model order reduction procedure for the tire–soil interaction model is developed with the proper orthogonal decomposition (POD), and it is integrated into the off-road mobility simulation framework, leveraging high-performance computing. The POD is, however, limited in that the modes are dependent on snapshot data collected during the running of a full order model, limiting the modes to being accurate only for the specific scenario from which they were collected. Due to this limitation, a method of mode adaptation through interpolation on a tangent space of the Grassmann manifold is investigated to allow modes to be predicted for cases in which a full order model has not been run. It is demonstrated by several numerical examples that the POD modes are effective at retaining predictive accuracy while reducing computational time. The results show that adapted POD modes are more capable of characterizing the behavior of the model than modes produced at a different value of the simulation parameter. The POD-based reduced order modeling approach is further extended to the full vehicle simulation on deformable terrain through the co-simulation coupling algorithm by leveraging the high-performance computing technique.

Embedding aircraft system modeling to ATM safety assessment techniques: The runway excursion safety case for runway strips with reduced strength

Several concepts were developed over the last years to fit safety assessment (SA) techniques to ATM operational needs. Quantitative SA models proved to achieve robust results if reliable data for hazard modeling and corresponding target levels of safety are available, inducing much effort in historic incident data gathering. Meanwhile, we consider hazard probability determination as a reliable mathematical process whereas consequence modeling as second risk component remains mainly a subjective technique. This paper presents an analytic approach to link a mechanical model of a representative critical aircraft part called TSIM (Tire-Soil Interaction Model) to an FEM (Finite Element Method) tire stress simulation to study critical aircraft part failures (here the landing gear) at high detail level during a hazardous condition. In doing so, we can show to significantly and robustly increase the transparency for allocating a severity category to a given hazard compared to current categories based on EASA and other international standards. The research also shows that risk-based aircraft part certification reveals weaknesses in data and setting of target levels of safety (TLS) as a risk considered to be acceptable in non-nominal situations. We apply the developed concept to a runway excursion scenario where the infrastructure is considered non-compliant to EASA/ICAO regulations.

Finite element modeling of the interaction of a treaded tire with clay-loam soil

In the present study, a treaded tire-soil interaction model was developed and its results were validated with laboratory data. In the laboratory test plaster molding was used to obtain contact area and contact volume. Experimental and FEM modeling results for output parameters such as the contact area, contact volume, and rolling resistance showed close agreement. Increasing soil moisture significantly decreased the maximum contact pressure transmitted to soil due to an increase in tire-soil contact area. Also, increasing soil moisture, increased the effect of stress on the soil, which, in turn, increased soil deformation in each layer and consequently the total soil sinkage. In all three levels of moisture tested in this study, an increase in vertical load and tire inflation pressure increased the tire-soil contact volume. At a constant soil moisture level, tire inflation pressure variations affected compaction at the top-soil layers and did not affect compaction changes in the sub-layers. Moreover, variations of the vertical load on the tire changed compaction at the top and sub-soil layers significantly.

Hierarchical Multiscale Modeling of Tire–Soil Interaction for Off-Road Mobility Simulation

A high-fidelity computational terrain dynamics model plays a crucial role in accurate vehicle mobility performance prediction under various maneuvering scenarios on deformable terrain. Although many computational models have been proposed using either finite element (FE) or discrete element (DE) approaches, phenomenological constitutive assumptions in FE soil models make the modeling of complex granular terrain behavior very difficult and DE soil models are computationally intensive, especially when considering a wide range of terrain. To address the limitations of existing deformable terrain models, this paper presents a hierarchical FE–DE multiscale tire–soil interaction simulation capability that can be integrated in the monolithic multibody dynamics solver for high-fidelity off-road mobility simulation using high-performance computing (HPC) techniques. It is demonstrated that computational cost is substantially lowered by the multiscale soil model as compared to the corresponding pure DE model while maintaining the solution accuracy. The multiscale tire–soil interaction model is validated against the soil bin mobility test data under various wheel load and tire inflation pressure conditions, thereby demonstrating the potential of the proposed method for resolving challenging vehicle-terrain interaction problems.

Improved tire-soil interaction model using FEA-SPH simulation

The purpose of this paper is to predict the rolling resistance of a free rolling off-road truck tire (size 315/80R22.5) over several soils. The soils are modelled using Smoothed-Particle Hydrodynamics (SPH) in the software package “Pam-Crash”. The soil models are calibrated using data obtained from published pressure-sinkage and shear-strength tests. The truck tire used in this study was modelled using Finite Element Analysis (FEA) and validated in previous studies. The tire-soil interaction algorithm is implemented in Pam-Crash software package to capture node-symmetric node-to-segment contact with edge treatment. The rolling resistance coefficient is computed from simulations and then validated against physical measurements. The rolling resistance coefficient is calculated for different terrains, such as dry sand, dense sand, clayey soil and hard surface. In addition, the rolling resistance is also computed for various tire inflation pressures and applied vertical loads. The research results presented in this paper will be further used for soil mixing-layering investigation.

Physics-Based Deformable Tire–Soil Interaction Model for Off-Road Mobility Simulation and Experimental Validation

A physics-based deformable tire–soil interaction simulation capability that can be fully integrated into the monolithic multibody dynamics computer algorithm is developed by extending a deformable tire model based on the flexible multibody dynamics approach to off-road mobility simulations with a moving soil patch technique and it is validated against test data. A locking-free nine-node brick element is developed for modeling large plastic soil deformation using the multiplicative finite strain plasticity theory along with the capped Drucker–Prager failure criterion. To identify soil parameters including cohesion and friction angle, the triaxial compression test is carried out, and the soil model developed is validated against the test data. In addition to the component level validation for the tire and soil models, the tire–soil interaction simulation capability developed in this study is validated against the soil bin mobility test results. The tire forces and rolling resistance coefficients predicted by the simulation model agree well with the test results. It is shown that effect of the wheel loads and tire inflation pressures is well captured in the simulation model. Furthermore, it is demonstrated that the moving soil patch technique, with which soil behavior only in the vicinity of the rolling tire is solved to reduce the soil model dimensionality, leads to a significant reduction in computational time, thereby enabling use of the high-fidelity physics-based tire–soil interaction model in the large-scale off-road mobility simulation.

Statistical modeling and comparison with experimental data of tire–soil interaction for combined longitudinal and lateral slip

The interaction of a tire with a soft terrain has multiple sources of uncertainties such as the mechanical properties of the terrain, and the interfacial properties between the tire and the terrain. These uncertainties are best characterized using statistical methods such as the development of stochastic models of tire–soil interaction. The quality of the models can be assessed via statistical validation measures or metrics. Although validation of stochastic tire–soil interaction models has recently been reported with good results, it involves longitudinal slip only without considering lateral slip which can occur simultaneously with longitudinal motion. This paper presents results of the validation of a simple stochastic tire–soil interaction model for the more complicated case of combined slip. The statistical methods used for validation include the development of a Gaussian process metamodel, the calibration of model parameters using the approach of the maximum likelihood estimate in conjunction with new test data. The validation of the calibrated model, when compared with test data, is obtained using four validation metrics with good results.

Numerical analysis of the effect of tire characteristics, soil response and suspensions tuning on the comfort of an agricultural vehicle

The paper focuses on the numerical investigation of riding comfort of an agricultural vehicle. The analysis is carried out combining a multi-body model of a tractor with a tire–soil interaction model. The multi-body model schematizes the tractor through several rigid bodies representing the chassis, the cabin, the seat and the tires. Model parameters (masses, suspension parameters) were identified by means of full scale tests on a four-post test-rig. Tire–soil interaction model allows computation of the forces exchanged at the contact interface considering soil deformability and the 3D tread design. Several simulations were performed considering the vehicle running at constant speed over a deformable soil; different combinations of suspensions parameters were analyzed to determine their effect on driver comfort evaluated in terms of vertical acceleration on the seat. In addition, the analysis was completed with four different scenarios coupling two different tires with two different soils.

Vehicle–soil interaction: Testing, modeling, calibration and validation

Although many studies have been conducted on different aspects of tire–soil interaction, little work has been done focusing on the uncertainties involved such as those of the mechanical properties of soil and the interfacial properties between the tire and soil. Even less, if any, work has been done on the validation of stochastic tire–soil interaction models using rigorous statistical methods. In this paper, a statistical framework, along with new vehicle–soil interaction test data, is used to build a stochastic metamodel from a simple physically-based tire–soil interaction model, to calibrate model parameters with uncertainties, to predict model responses with uncertainties, and to validate the models using four validation metrics: one local metric that measures the differences between test and model at each instant of time, and three global metrics that measure these differences but over the entire time period of vehicle motion. Results in using the metrics indicate that the models performed well.

Three dimensional finite element model of soil compaction caused by agricultural tire traffic

Most of the finite element models of soil compaction do not represent the tire, only the effect of a uniform ground stress is distributed on a soil area with a preset form. It constitutes an oversimplification of the problem and it would yield erroneous contact conditions, because the tire–soil contact stress distribution is the result of simultaneous tire and soil deformation. This research was carried out with the objective of developing a model, valid for soil compaction simulation caused by agricultural tire traffic that allows research factors that cause soil compaction of a Rhodic Ferralsol soil. The tire was developed as a unique solid layer, which represents its mean properties with a linear elastic constitutive model. Predictions of deflection and tire contact area in rigid surface were compared with experimental results and the tire model was validated. A three dimensional model of the soil was created and the soil properties were represented with an Extended Drucker Prager material model. ABAQUS/STANDARD 6.8-1 code was used to develop the tire–soil interaction model. A tire traffic experiment was carried out at a soil bin to two soil water conditions, tire inflation pressures and tire load. Triaxial and direct shear tests were used to obtain soil properties and constitutive parameters. Predictions were compared with experimental results to verify the validity of the model in each soil water content. Simulated and observed stresses after wheel traffic under different inflation pressures and tire loads agree well. The model predicts the effect of inflation pressures, ground pressure and tire load on the stresses on the contact and the soil profile, it can be used in both teaching and research. The model was used to predict the depth at which soil compaction was produced for each combination of tire inflation pressure and tire load, and the relationship between the tire inflation pressure, contact stress and tire load with soil compaction. The model showed that magnitudes of vertical stresses transmitted to soil are independent to water content and that more soil compaction in wet soils depends on the less yield stresses in those conditions. Besides, the good agreement of the model with experimental results demonstrates the validity of using the Extended Drucker Prager model to represent the mechanical response of the Rhodic Ferralsol soil.

Investigation of Tire-Soil Interaction with Analytical and Finite Element Method#

This article is devoted to the modeling of tire–soil interaction with the analytical and finite element method (FEM). Different from the traditional tire–soil interaction models in which the contact between tires and soils is described by nonlinear springs in the normal direction, the new analytical model added dampers accounting for the soil damping effects. A nonlinear three-dimensional tire–soil interaction model with the FEM, which takes into consideration the tire treads and belt/carcass layers, was validated by measuring tire vertical stiffness and contact stress. The conversion of the Modified Drucker-Prager/Cap soil model to the analytical soil model was demonstrated as well. The simulations for investigating the dynamic behavior of a bias tire running on the soft soil were performed. Good agreement was observed based on the simulation results obtained from these two tire–soil interaction models. However, experimental validation is necessary before the models can be further applied in the prediction of off-road vehicle dynamics.

Tire-soil interaction model for turning (steered) tires

A review of the experimental information on the development of lateral forces on tires traveling at an angle to their center plane is presented and the usefulness of the consideration of the lateral forces for the development of an analytical model is evaluated. Major components of the lateral force have been identified as the forces required to balance the tractive force and the drawbar pull vectorially. The lateral forces are generated by the shear stresses developing in the contact area and the horizontal component of the normal stresses acting on the in-ground portion of the curved side walls of the tire. The tire-soil interaction model for steady state straight travel has been expanded to include the necessary algorithms for the calculation of these lateral forces. The pattern of tractive force-slip and longitudinal-lateral force relationships is in general agreement with experiments.