Full-field and point strain measurement via the inner surface of a rolling large lug tyre

Vehicle safety and performance can be dramatically improved if force or friction measurement of the tyre-terrain interface is known. Since the tyre-terrain interface is responsible for the majority of forces acting on the vehicle, this region has received a lot of attention in vehicle dynamics. Direct measurement of the tyre-terrain interface is difficult since it is hidden by the tyre and terrain. A lot of research has been conducted on the inside of tyre using accelerometers or strain gauges with research more focussed on passenger car tyres and very little work performed on agricultural tyres with larger lugs. This study performs strain measurements using point measurement, from strain gauges, and full field measurement, using a stereo camera measurement system, of the inside of an agricultural tyre on a drum test rig during vertical and lateral loading. Results show similar trends when compared to results on passenger car tyres, however the mounting of the strain gauge relative to the lug is shown to play a large role in the developed strain. Linear relationships between the applied tyre force and strain were obtained in different direction with R² values above 0.97.     

Parameterisation,validation and implementation of an all-terrain SUV FTire tyre model

This paper focuses on the parameterisation, validation and implementation of an FTire model of a Michelin LTX A/T² 235/85R16 tyre. This tyre is designed for both on- and off-road use and is commonly used on all wheel drive SUVs. Quasi-static laboratory and dynamic field tests were conducted to acquire parameterisation and validation test data for the FTire model. Quasi-static parameterisation tests include acquiring vertical tyre stiffness over a flat plate and cleats, tyre footprint sizes and shapes, longitudinal, lateral and torsional tyre stiffness for various tyre normal loads, as well as vibrational tyre responses. Dynamic parameterisation tests include dynamic cleat test data. An Adams model of the tyre testing equipment is implemented to simulate the FTire model and validate it against dynamic validation test results. Finally, the model is implemented on a fully nonlinear multi-body dynamics model of a Land Rover Defender. It is found that the FTire model is able to predict the lateral tyre behaviour well on a smooth road surface. The vertical and longitudinal tyre behaviour on a smooth road surface and on a rough surface are predicted accurately.     

3D contact patch measurement inside rolling tyres

This paper presents a novel method for capturing the 3D profile of the inside of a rolling off-road vehicle tyre at the tyre-road contact region. This method captures the contact region at all times as the vehicle negotiates obstacles. The system uses a pair of inexpensive digital cameras (capable of capturing up to 300 frames per second) and features a purely mechanical stabilisation system to ensure that the cameras capture the contact region at any wheel speed or vehicle acceleration.The captured images are processed using 3D computer vision techniques using an open source computer vision library called OpenCV. Stereo image pairs are used to create clouds of 3D points showing the profile of the inside surface with good accuracy. Various obstacles were traversed with the deformed tyre profile being compared to the undeformed profile. The system improves on current measurement techniques used to measure the contact patch by capturing a large region of the contact patch, providing full 3D surface geometry, as well as remaining centred on the contact patch irrespective of wheel rotation. The system also enables other imaging techniques to be used such as digital image correlation to determine velocity profiles as well as strain measurements.     

Off-road tyre modelling II: effect of camber on tyre performance

The problem of off-road vehicle tyre-terrain interaction is that it is difficult to model accurately. For an off-road vehicle over medium to firm terrain, the tyre load may be entirely supported by the tips of the lugs, or with a minimum carcass contact with the terrain. In this case, the effect of the lugs should be taken into consideration. The forces at the interface between lugged tyre and the soil, including normal and shear stresses, are discussed in this paper. The multi-spoke tyre model was developed to study the effect of tyre lugs on the forces between tyre and terrain and it has been extended to predict the tyre forces and moments in the case of combined lateral and longitudinal slip for a cambered tyre. The influence of slip angle, camber angle and soil hardness on off-road tyre performance has been investigated. A computer program was developed using MATLAB software. The results were derived as tyre forces and moments in the three directions along the tyre contact length. A comparison between the results of the multi-spoke tyre model of a smooth off-road tyre and an off-road tyre with straight lugs, in the cambered case, has been made. The results indicated that slip angle, camber angle and soil characteristics have a strong effect on off-road tyre performance. The modified mathematical model results help the off-road tyre engineering designers to predict accurate values of tyre forces and moments in this complex case.     

Green’s functions for a loaded rolling tyre

A new formulation to determine the unit impulse response (Green’s) functions of a loaded rotating tyre in the vehicle-fixed (Eulerian) reference frame for tyre/road noise predictions is presented. The proposed formulation makes use of the set of eigenfrequencies and eigenmodes for the statically loaded tyre obtained from a finite element (FE) model of the tyre. A closed-form expression for the Green’s functions of a rotating tyre in the Eulerian reference system as a function of the eigenfrequencies and eigenmodes of the statically loaded tyre is found. Non-linear effects during loading are accounted for in the FE model, while the frequency shift due to the rotational velocity is included in the calculation of the Green’s functions. In the literature on tyre/road noise these functions are generally used to determine the tyre response during tyre/road contact calculations. The presented formulation opens the possibility to solve the contact problem directly in the Eulerian reference frame and to include local tyre softening due to non-linear effects while keeping the computational advantage of describing the tyre dynamics as a set of impulse response functions. The advantage of obtaining the Green’s functions in the Eulerian reference system is that only the Green’s functions corresponding to the potential contact zone need to be determined, which significantly reduces the computational cost of solving the tyre/road contact and since the mesh is fixed in space, a finer mesh can be used for the potential contact zone, improving the accuracy of the contact force calculations. Although these effects might be less pronounced if a more accurate tyre model is used, it is found that using the Green’s functions of the loaded tyre in a contact force calculation leads to smaller forces than in the unloaded case, lower frequencies are present in the response and they decrease faster as the rotational velocity increases.     

Analytical approach for the prediction of steady state tyre forces and moments under different normal pressure distributions

In general, all primary as well as disturbing forces acting on a vehicle (with the exception of aerodynamic forces) are generated at the tyre–road interface. The small size pneumatic tyres presented in this work are mostly used in lightweight vehicles like scooters, motor cycles and 3-wheelers that are extensively used for intercity transportation applications in India and other developing countries. Analytical approach is more advantage than experimental work due to many factors like it involves less cost, minimum time and little effort. Hence, Analytical tyre models are developed based on various normal pressure distributions with tyre contact patch as rectangle at the middle with part of circles at the ends. The tyre longitudinal and lateral force characteristic equations for proposed tyre models are developed. In addition, the equations for self – aligning moment and overturning moment characteristics for all tyre models are also derived. Results of proposed tyre models in the present study are compared with well-established earlier tyre models [4], [5], [6]. From the force and moment characteristics of all tyre models, unsymmetrical trapezoidal pressure distribution tyre model gives better performance than other models due to which better lateral stability of the vehicle can be obtained.     

Determination of dynamic three-dimensional soil-tyre contact profile

A technique for measuring the dynamic three-dimensional contact profile between a tyre and deformable soil has been developed. The method involves measuring incremental lateral arc lengths of the profile at discrete locations along the contact length and fitting the coefficients of a model of soil deformation at the soil-tyre interface to the experimental data using a nonlinear constrained optimization algorithm (SUMT). Two representations of the measured contact area were compared: (i) the two-dimensional surface which is the union of all points on the original undeformed soil surface which undergo deformation by the tyre; (ii) the final three-dimensional deformed surface. Contact area measurements were made for two different sized tyres at two levels of inflation pressure, dynamic load and slip in two different soil conditions. The contact width, length and area predicted by the technique were compared with corresponding values for static contact between a tyre and a rigid surface.     

Digital image correlation techniques for measuring tyre–road interface parameters: Part 2 – Longitudinal tyre slip ratio measurement

Measurement of tyre longitudinal slip-ratio is often estimated from three independent measurements devices namely wheel rotation speed, vehicle speed and tyre rolling radius. This produces an expensive measurement system to indirectly determine the slip-ratio. This paper presents a method by which the slip-ratio is determined from a video camera using digital image correlation techniques. The camera, mounted in such a way that the contact patch region is captured, enables the system to measure the tyre tread speed and ground speed at the contact patch. The slip-ratio is then determined from these two measurements.     

Motion resistance measurements on large lug tyres

Motion resistance of tyres directly contribute to the operational costs of all vehicles. Advances in the design and simulation of large off-road vehicles (construction, mining, agriculture etc.) have increased the need for accurate models of large off-road tyres. Vehicle OEMs use coast down and drawbar pull tests to determine the motion resistance of tyres used. Drum test rigs and motion resistance test trailers can also be used to determine motion resistance. Most research on motion resistance to date have been conducted on passenger car tyres with on-road truck tyres coming into focus. Motion resistance studies on agricultural tyres traversing over deformable terrain have been conducted in the past. However as more off-road vehicle are being used on-road OEMs of off-road vehicle are infesting in motion resistance measurements on non-deformable terrain. This paper compares different methods used to measure the motion resistance of a large lug tyre, as used in agricultural applications, on non-deformable terrain. Some basic considerations that need to be taken into account are the very low longitudinal forces that need to be measured compared to the large vertical load carried by the tyre and tyre operating conditions.     

TRT: thermo racing tyre a physical model to predict the tyre temperature distribution

In the paper a new physical tyre thermal model is presented. The model, called Thermo Racing Tyre (TRT) was developed in collaboration between the Department of Industrial Engineering of the University of Naples Federico II and a top ranking motorsport team. The model is three-dimensional and takes into account all the heat flows and the generative terms occurring in a tyre. The cooling to the track and to external air and the heat flows inside the system are modelled. Regarding the generative terms, in addition to the friction energy developed in the contact patch, the strain energy loss is evaluated. The model inputs come out from telemetry data, while its thermodynamic parameters come either from literature or from dedicated experimental tests. The model gives in output the temperature circumferential distribution in the different tyre layers (surface, bulk, inner liner), as well as all the heat flows. These information have been used also in interaction models in order to estimate local grip value.     

UPM indoor tyre traction testing facility

Universiti Putra Malaysia (UPM) tyre traction testing facility was designed and developed to spearhead fundamental research on traction mechanics with high-lug agricultural tyres on tropical soils. This available facility consists of a moving carriage with a cantilever-mounted tyre that moves in either forward or reverse directions on rails well above a soil tank. The present facility set-up was able to operate in either: (a) towing test mode for tyre motion resistance studies, or (b) driving test mode for tyre net traction and tractive efficiency studies. The test tyre on the moving carriage under the towing test mode was made to rotate and engage onto the soil surface in the tank through a chain drive system. Under the driving test mode, the test tyre on the moving carriage was powered to rotate by a motor and a gearbox system with an additional pull provided by a cable-pulley mechanism connected to a tower with hanging dead weights. All controls on the moving carriage were activated from the main control console. Respective transducers were positioned at various localities within and interfaced to a data acquisition system to measure tyre horizontal and vertical forces, tyre sinkage, tyre speed and motion carriage speed. The data acquisition system was able to receive the measured signals in real time, display on the monitor screen and record into its CPU storage memory. Static calibration tests on various associated transducers showed excellent linearity with coefficients of determination (r²) of close to 1. The developed facility was successfully tested to determine motion resistance and net traction ratios for high-lug agricultural tyre at the recommended inflation pressure on sandy clay loam soil.     

Parameterization and modelling of large off-road tyres for ride analyses: Part 2 – Parameterization and validation of tyre models

Every mathematical model used in a simulation is an idealization and simplification of reality. Vehicle dynamic simulations that go beyond the fundamental investigations require complex multi-body simulation models. The tyre–road interaction presents one of the biggest challenges in creating an accurate vehicle model. Many tyre models have been proposed and developed but proper validation studies are less accessible. These models were mostly developed and validated for passenger car tyres for application on relatively smooth roads. The improvement of ride comfort, safety and structural integrity of large off-road vehicles, over rough terrain, has become more significant in the development process of heavy vehicles. This paper investigates whether existing tyre models can be used to accurately describe the vertical behaviour of large off road tyres while driving over uneven terrain. [1] Presented an extensive set of experimentally determined parameterization and validation data for a large off-road tyre. Both laboratory and field test are performed for various loads, inflation pressures and terrain inputs. The parameterization process of four tyre models or contact models are discussed in detail. The parameterized models are then validated against test results on various hard but rough off-road terrain and the results are discussed.     

车辆纵振路面谱及其应用

对车辆纵振路面谱及其在地面-车辆系统中的应用进行了探讨,计算了行车纵剪力及其作用下的路面应力强度因子．与垂向路面谱相比,纵振路面谱代表的路面等级较高．行车纵剪力为均值等于0的平稳随机过程,在它的作用下,路面荷载型裂纹从上到下扩展的速度明显大于从下往上扩展的速度,扩展速度与力的 4次幂成正比．行车纵剪力对路面的裂纹损伤远远大于轮胎路面压力导致的裂纹损伤．     

高速列车车轮踏面剥离引起的轮轨冲击力学响应有限元模拟

车轮踏面剥离是轨道车辆车轮非圆化损伤的常见形式之一。轮轨滚动接触过程中,车轮踏面剥离会循环冲击钢轨,诱发异常大的轮轨动态相互作用,严重影响高速列车运行平稳性和安全性。基于三维轮轨滚动接触有限元模型,模拟了高速列车车轮踏面剥离引起的轮轨冲击力学响应,分析了轮轨冲击过程中的轮轨接触力/压力、接触斑及黏/滑特性、钢轨表面节点速度分布和应力/应变状态等响应特征,讨论了列车速度、剥离长度和剥离深度等关键参数对轮轨冲击响应的影响。结果发现,车轮踏面剥离引起的轮轨动态垂向接触力随列车速度的提高呈现出先增大后减小的变化趋势,并在列车速度为300 km/h出现最大值,约为轮轨准静态垂向接触力的1.35倍;随着剥离长度的增大,轮轨动态接触力、轮/轨von Mises应力和等效塑性应变均显著增大;随着剥离深度的增大,仅车轮von Mises应力和等效塑性应变显著增大。     

Static Tyre/Road Interaction Modelling

The understanding, modelling and predicting of tyre behaviouralcharacteristics, for both static and dynamic applications, requires theconsideration of many detailed aspects of this seemingly simple component.In order to investigate the problem more fully, computer analysis techniquesare becoming more common than the simplifications associated with analyticalmethods. The finite element method is one such technique that enablesengineers to examine tyre behaviour comprehensively and to predict tyreperformance at the design stage. In this paper, attention is drawn to theproblem of tyre/road interaction modelling. A purely theoretical approach ispresented which gives the analyst more flexibility in changing parameterssuch as inflation pressure, hub load, and material properties thanpreviously developed experimental/numerical techniques. A gap elementformulation is used to model the interaction so that contact patch area,shape and deflection are automatically accounted for under a given load andinflation pressure. Modelling and experimental results are also presented toillustrate the accuracy of the technique.     

Contact of a rigid cylinder indenting an elastic layer sliding over a rigid substrate

Details of the integral transform solution of the state of stress in a layer resting on but sliding over a rigid substrate, in the presence of interfacial friction, is studied. The free surface of the layer is subject to a localised contact, which is represented as a piecewise linear distribution of tractions, using the Bentall–Johnson procedure. The influence functions needed are derived and their properties discussed and compared with those already available for other interface conditions. Lastly, the procedure is applied to the problem of a shrink fit tyre which, under severe tyre/road tangential loading, can be ‘torn’ around the wheel (here, the substrate).