Features of an elastic wheel motion along a curvilinear and rectilinear trajectory with a slip

The results of the study of the motion of an elastic wheel as an integral mechanism along a curvilinear and a rectilinear trajectory with a slip on the ground plane having a high adhesion coefficient are presented. The previous researches analysis has shown that the most complete theory of wheel skidless rolling without slipping on elastic pneumatics was formulated by Keldysh V. M. who proposed the equation for calculating the curvature of the motion trajectory. Due to the difficulty of this equation coefficients determining, its use is currently limited. In this paper, the dependences for determining the components of the equation of the elastic wheel motion trajectory curvature have been proposed. According to the shimmy theory, during an elastic wheel rolling along a curvilinear trajectory, the rim turn and its lateral displacement relative to the tire-ground contact patch occur simultaneously. The rim turn causes tire body torsion, and the lateral displacement causes the elastic wheel moving with a slip angle. It is established that the absolute value of the tire body torsion angle is equal to the slip angle, and their values depend on the trajectory curvature, on the tire-ground contact patch longitudinal axis, and on the existence of traction there. The condition, under which the tire body energy distribution on the rim relative rotation and on its lateral displacement during the movement along a curved trajectory is uniform, has been determined. The experimental confirmation of the hypothesis of uniform distribution of the energy supplied to the elastic wheel during its movement along a curvilinear trajectory on the rim relative turning and its lateral displacement has been obtained. When the elastic wheel moves along a rectilinear trajectory with a slip, only the rim lateral displacement occurs, this displacement is accompanied by a cornering force applied in the center of the tire-ground contact patch and by the tire alining torque relative to the vertical axis passing through the contact patch geometric center. The energy consumption for the rim lateral displacement during the wheel rolling along a rectilinear trajectory with a slip has been also determined. The results of the research can be useful to professionals improving the wheeled vehicles performance characteristics, including maneuverability, handling, and road stability.

Three-dimensional contact stresses of a slick solid rubber tyre on a rigid surface

The main aim of this paper is to quantify the three-dimensional contact stresses imposed by a single slow-moving (or rolling) slick solid rubber tyre on a relatively rough contact surface, such as stiff asphalt concrete or airport concrete surfacing layers. The results indicated the tyre-contact patch of a slick solid rubber tyre to be of rectangular shape for a vertical tyre loading range between 20 kN and 100 kN. The rectangular tyre contact shape was confirmed with static paper prints, as well as an electronically measured contact patch with the stress-in-motion pad device. The study included load calibration using a mass load scale, and a stress-in-motion device. These were used with an existing full-scale accelerated pavement test device, referred to as the heavy vehicle simulator. In addition, simplistic multi-layer linear elastic modelling was used to quantify differences between stress and strain responses of two types of two relatively 'stiff' based pavements, such as an asphalt concrete base and Portland cement concrete base, on similar subbase and subgrade layers. Notable differences were obtained, which could potentially influence further detailed studies on the performance of full-scale slick solid rubber tyres on typical multi-layered pavements.

Wind turbine main-bearing lubrication – Part 2: Simulation based results for a double-row spherical roller main-bearing in a 1.5 MW wind turbine

This paper is the second in a two-part study on lubrication in wind turbine main-bearings. Where “Part 1” provided an introductory review of elastohydrodynamic lubrication theory, this paper will apply those ideas to investigate lubrication in the double-row spherical roller main-bearing of a 1.5 MW wind turbine. Lubrication is investigated across a “contact conditions dataset” generated by inputting processed loads, obtained from aeroelastic simulations, into a Hertzian contact model of the main-bearing. From the Hertzian model is extracted values of roller load and contact patch dimensions, along with the time rate-of-change of contact patch dimensions. Also included in the dataset are additional environmental and operational variable values (e.g. wind speeds and shaft rotational speeds). A suitable formula for estimating film thickness within this particular bearing is then identified. Using lubricant properties of a commercially available wind turbine grease, specifically marketed for use in main-bearings, an analysis of film thickness across the generated dataset is undertaken. The analysis includes consideration of effects relating to starvation, grease thickener interactions and possible dynamic EHL effects. Results show that the modelled main-bearing would be expected to operate under mixed lubrication conditions for a non-negligible proportion of its operational life, indicating that further work is required to better understand lubrication in this context and implications for main-bearing damage and operational lifetimes. Key sensitivities and uncertainties within the analysis are discussed, along with recommendations for future work.

Development of the scheme and method for measuring the characteristics of the friction areas in the car wheel contact

The aim of the research is to develop and implement a scheme and method for measuring the characteristics of static and sliding friction areas in the contact patch of an elastic wheel with a solid support when they appear, exist and disappear. The characteristics are understood as: the relative location of static and sliding friction in relation to the vector of the translational speed of the wheel axis; their size and location in the contact patch when they appear, spread and disappear; the values of the moments on the wheel, corresponding to the appearance, spread and disappearance of static and sliding friction. A scheme and a method for measuring these characteristics have been developed and implemented. The measurements are indirect. It has been experimentally established that, in the general case, the geometric center of static friction in the contact patch moves towards the moment acting in the plane of the wheel rotation relative to the rotation axis by an amount proportional to the moment. The maximum value of this displacement according to the moment that is maximum in terms of sliding conditions, and is one third of the contact patch length for all types and conditions of a solid support. The research results are valid for elastic wheels with a radial stiffness not exceeding 12000000 N/m, the main plane of which is perpendicular to the reference plane. The research results can find application in design modeling of stability and controllability of vehicles.

Theoretical Tire Model for Wear Progress of Tires with Tread Pattern Considering Two-Dimensional Contact Patch

ABSTRACT A new theoretical tire model for the wear progress of tires with tread block pattern is developed considering a two-dimensional contact patch. In the model, the wear energy is calculated from the shear force and pressure distribution in a two-dimensional contact patch that are changed with not only shear forces in a contact patch but also with the wear and irregular wear of tires. The fore–aft shear force in a contact patch consists of six mechanisms related to slip ratio, camber, contact between a tire and a road, barrel deformation of a loaded block, rolling resistance, and a rolling tire with rounded crown shape, whereas the lateral shear force consists of three mechanisms related to slip angle/camber, contact of a tire with rounded crown shape, and barrel deformation of a loaded block. The heel and toe irregular wear and the progress of irregular wear under pure slip condition qualitatively agree with the conventional knowledge of tire engineers. The expected wear energy is introduced to predict the wear progress under combined slip condition in the wear course. Using the vehicle dynamics to predict the tire force history, a histogram of external forces is obtained by transforming from it. Calculating wear energies by changing slip angle and slip ratio, the relation between external forces and the wear energy is expressed as the response surface. Multiplying the wear energy by the histogram, the expected wear energy distribution in a block is calculated. Assuming that the worn depth is proportional to the expected wear energy, the wear progress is predicted.

Comprehensive Grounding Performance Evaluation of Tires Based on the Analytic Hierarchy Process

ABSTRACT The contact patch between tire and road surface has a direct impact on tire grounding performance. Acquiring tire grounding performance either by testing or simulation is not only time intensive but comes at a high cost. This paper proposes an effective means of evaluating tire grounding performance based on the tire-ground contact pressure distribution. This paper adopts fifteen characteristics to describe the tire-ground contact patch in which twelve structural schemes were designed for a certain type of tire. By using the simulation test method, the grounding performance characteristics such as grip performance, rolling resistance, wear performance, and the tire footprint characteristics were obtained. Correlation analysis was used to explore the relationship between tire grounding performance and footprint characteristics. Based on the correlation analysis and expert judgement, the analytic hierarchy process (AHP) model for comprehensive grounding performance evaluation of a tire was constructed. Then judgment matrix of the AHP model was established, and the consistency or otherwise of the judgment matrix was verified. The model was then used to evaluate and predict the four design schemes of tires. The evaluation results were in good agreement with the simulation test results, which shows that the construction method of the tire comprehensive grounding performance evaluation system proposed in this paper is practical. It is also evident that grounding performance evaluation of a tire based on the tire footprint is feasible.

A Strategy for Fine Mesh Resolution in Contact Mechanics

To obtain detail in elastic, frictional contact problems involving contact many — at least tens, and more suitably hundreds [1] — of nodes are necessary over the contact patch. Generally, this fine discretization results in intractable numbers of system equations that must be solved, but this problem is greatly mitigated when the elasticity of the contacting bodies is represented by elastic compliance matrices rather than stiffness matrices. An examination of the classical analytic expressions for the contact of disks — an example of smooth contact — shows that for most standard engineering metals, such as brass, steel, or titanium, the pressures that would cause more than one degree of arc of contact would push the materials past the elastic limit. The discretization necessary to capture the interface tractions would be on the order of at least tens of nodes. With the resulting boundary integral formulation would involve several hundreds of nodes over the disk, and the corresponding finite element mesh would have tens of thousands. The resulting linear system of equations must be solved at each load step and the numerical problem becomes extremely difficult or intractable. A compliance method of facilitating extremely fine contact patch resolution can be achieved by exploiting Fourier analysis and the Michell solution. The advantages of this compliance method are that only degrees of freedom on the surface are introduced and those not in the region of contact are eliminated from the system of equations to be solved.

Theoretical Tire Model Considering Two-Dimensional Contact Patch for Force and Moment

ABSTRACT The new theoretical tire model for force and moment has been developed by considering a two-dimensional contact patch of a tire with rib pattern. The force and moment are compared with the calculation by finite element method (FEM). The side force predicted by the theoretical tire model is somewhat undervalued as compared with the FEM calculation, while the self-aligning torque predicted by the theoretical tire model agrees well with the FEM calculation. The shear force distribution in a two-dimensional contact patch under slip angle predicted by the proposed model qualitatively agrees with the FEM calculation. Furthermore, the distribution of the adhesion region and sliding region in a two-dimensional contact patch predicted by the theoretical tire model qualitatively agrees with the FEM calculation.