Stationary Tire Research Articles

A cylindrical shell model with distributed springs for a rotating tire

In a companion paper (Vol. 248, Article 108227), we demonstrated the dependence of tire parameters on the modal characteristics of a stationary tire. For a more realistic scenario, when tire rotation is considered, the modal characteristics are veered due to centrifugal, Coriolis, and gyroscopic effects. In this paper, we study the forced vibration response of a rotating tire and also consider the effect of static load on modal characteristics. The tire tread is modeled as a cylindrical shell and the sidewall is modeled using distributed springs in axial, circumferential, and radial directions. The tire inflation pressure is accounted for, which generates pre-stresses in the tire belt in circumferential and axial directions. The material model incorporates an orthotropic composite structure of the tire with multiple stacked layers of steel belt reinforcing. The governing equations of motion of the rotating shell are derived and further reduced to the corresponding eigenvalue problem. Galerkin’s projection with orthogonal basis functions is used to obtain the natural frequencies and associated mode shapes. For the forced vibration, the tire is excited by a harmonic point load at a fixed location, and the response is calculated by superimposing the basis functions of the free vibration problem. The analytical model predictions are compared against the computation finite element (FE) model developed in ABAQUS® and experimental modal testing results. To understand the effects of rotation on wave propagation, dispersion relations were obtained, and the wave number spectrum of the rotating tire was compared with that of the stationary one. Finally, to understand the dependence of natural frequencies on tire rotation and normal load, Campbell diagrams and frequency response functions (FRFs) were obtained from the proposed model. The model shows a fairly good agreement with experimental results and FE simulations.

Influence of tire dynamics on a braking process with ABS

This article analyzes the influence of the proper modeling of the anti-lock brake system control loop components. Both the use of a stationary tire model and not considering the delays due to measurement, estimation, and actuation tend to be overlooked. Therefore, this affects the efficiency of the control algorithms developed through simulation. Thus, this work proposes to analyze the influence of the modeling of the components by performing experimental tests on a flat-track test bench. These tests demonstrate the need for taking these effects into account.

Research on mechanism and evolution features of frequency split phenomenon of tire acoustic cavity resonance

The acoustic cavity resonance inside the tire–wheel assembly is known to contribute to audible noise in the passenger compartment of vehicles. To obtain control methods of tire acoustic cavity resonance, its characteristics and producing mechanism need to be clarified first. In this article, the finite element model of a tire coupled with acoustic medium in the tire cavity is constructed. The Euler method is introduced to study the modal characteristics of tire cavity under the influence of tire inflation pressure, load, and tire rotation velocity. Frequency splitting phenomena under four separate conditions (stationary tire without load, stationary tire with load, rotating tire without load, and rotating tire with load) are simulated and analyzed. The slope change of the resonance frequency as a function of rotation speed is found to be close to the reciprocal of tire radius which can be explained by a model of wave propagation in a ring-shaped channel with moving media inside the ring. The obtained function of the slope change can help determine the frequency variation range under different vehicle velocity, structure load, and tire inflation pressure, which can then help to control the cavity resonance energy and provide a more comfortable driving experience.

Theoretical Analysis for Tire Cavity Resonance inside Deformed Stationary Tire

Theoretical Analysis for Tire Cavity Resonance inside Deformed Stationary Tire

Numerical method for simulating tire rolling noise by the concept of periodically exciting contact force

For the numerical simulation of tire rolling noise, an important subject is the extraction of normal velocity data of the tire surface that are essential for the acoustic analysis. In the current study, a concept of periodically exciting contact force is introduced to effectively extract the tire normal velocity data. The ground contact pressure within contact patch that is obtained by the static tire contact analysis is periodically applied to the whole tread surface of stationary tire. The periodically exciting contact forces are sequentially applied with a time delay corresponding to the tire rolling speed. The tire vibration is analyzed by the mode superposition in the frequency domain, and the acoustic analysis is performed by commercial BEM code. The proposed method is illustrated through the numerical experiment of 3-D smooth tire model and verified from the comparison with experiment, and furthermore the acoustical responses are investigated to the tire rolling speed.

Numerical simulation of radiation noise of 3-D smooth tire using the rebound excitation force at the bending front

This paper is concerned with the numerical prediction of the vibration-induced radiation noise of main grooved smooth tire. The tire body is to be vibrated by the ground impact force at the bending front within the contact patch, which becomes a main source of tire radiation noise. Tire radiation noise is a physical phenomenon associated with rolling tire so that its numerical prediction virtually requires the structural vibration data in the state of rolling. But, such vibration data are not only highly time consuming to obtain, but the rolling tire model is not applicable to commercial acoustics software. Hence, in the current study, the structural vibration data is obtained by applying the rebound excitation force which is obtained by the dynamic rolling analysis to the stationary tire model. The vibro-acoustic analysis is analyzed by combining the finite element and boundary element methods. The present method is illustrated through the numerical experiment and verified from the comparison with the experiment.

Antemortem radiological imaging findings in a fatal tyre blast injury due to shock wave: a case report

Fatal tyre blast injuries are rare and occur due to primary blast injury from shock wave or due to dislodged iron-locking rim. We report here the radiological imaging findings in a case of fatal injury caused by shock wave from the stationary truck tyre blast.

Static Tire/Road Stick–Slip Interactions: Analysis and Experiments

Tire/road interactions play a critical role in safe operation of ground vehicles. This paper presents the modeling, analysis, and experimental studies of stick-slip interactions between the stationary tire and the firm road. A semi-analytical model is first proposed to predict the normal force distribution on the tire contact patch. A beam-spring network modeling approach is then used to capture and compute the friction force and rubber deformation distributions on the contact patch during a stick-to-slip transition. To validate the contact models and analyses, a pressure-sensitive, electric conductive rubber sensor is embedded inside the tire rubber layer to extract the 3-D forces on the contact patch. Both the analytical and experimental results show that the friction force and rubber deformation distributions are dependent on the contact normal force distribution and the tire structural properties. The understanding and modeling of the static stick-slip interactions presented in this paper provide new knowledge and methods for studying dynamic tire/road interactions and flexible thin-layer/rigid contacts in other mechanical systems.

Aerodynamic and aero noise of stationary tire

The characteristics of aerodynamic and aero noise of stationary tire are investigated using computational fluid dynamics (CFD) and wind tunnel tests. A positive lift coefficient of almost 0.27 was found at all tested Reynolds numbers, while the drag coefficient was twice as large. The averaged pressure coefficient computed agrees with the measured, while the separation point predicted by numerical simulation is brought forward. The aero-noise numerical results using hybrid method based on large eddy simulation (LES) and FW-H formulations compares well with results from the wind tunnel test for total sound pressure level and noise spectra. Due to the defects of turbulence model and limited computer resources, the agreement of noise spectra for some test points in the frequency above 600 Hz is not the best. Sound energy of sound source and sound energy radiated from sound source are nearly proportional to the fourth power and sixth power of wind speed, respectively. At the simulated speeds, about 2.7% of sound energy comes from quadrupole sources, while 97.3% of sound energy comes from the dipole sources, which is the first time a quantitative description has been given. It should be pointed out that due to the different phases of dipole and quadrupole, the contribution of quadrupole to radiation is different at the receivers.

DAMPING ANALYSIS WITH RESPECT TO ROLLING SPEED BY ANALYTIC SOLUTION OF A FLEXIBLE RING MODEL AND ITS FREQUENCY RESPONSE FUNCTION DERIVATION BY MODAL SUMMATION METHOD

In this research, a modal approach has been adopted to analyze the dynamic characteristics of the rolling tire by a ring model. Previously, most of the researchers focused on the changes in natural frequencies with respect to the rotational speed (in global coordinate) only. In this research, the change in the damping has also been taken into account by including a damping term in the ring model equations. The bi-orthogonal property which is used to obtain the Frequency Response Functions (FRFs) of a rotor/bearing system described in Cartesian coordinate has been applied to the ring model described in cylindrical coordinate to obtain the FRFs. The obtained damping values and FRFs from the analytic model are then compared with experimental results. Moreover, the physical meanings of the results are analyzed, based on experimental data of a stationary tire and a rolling tire at 60 km/h and 100 km/h.

A waveguide finite element aided analysis of the wave field on a stationary tyre, not in contact with the ground

Although tyre/road noise has been a research subject for more than three decades, there is still no consensus in the literature as to which waves on a tyre are mainly responsible for the radiation of sound during rolling. Even the free vibrational behaviour of a stationary (non-rotating) tyre, not in contact with the ground, is still not well understood in the mid- and high-frequency ranges. Thus, gaining an improved understanding of this behaviour is a natural first step towards illuminating the question of which waves on a rolling tyre contribute to sound radiation. This is the topic of the present paper, in which a model based on the waveguide finite element method (WFEM) is used to study free wave propagation, on a stationary tyre, in the range 0–1500 Hz. In the low-frequency region (0–300 Hz), wave propagation is found to be rather straightforward, with two main wave-types present. Both have cross-section modes involving a nearly rigid motion of the belt. For higher frequencies (300–1500 Hz) the behaviour is more complex, including phenomena such as ‘curve veering’ and waves for which the phase speed and group speed have opposite signs. Wave-types identified in this region include (i) waves involving mainly sidewall deformation, (ii) belt bending waves, (iii) a wave with significant extensional deformation of the central belt region and (iv) a wave with a ‘breathing’ cross-section mode. The phase speed corresponding to found waves is computed and their radiation efficiency is discussed, assuming free-field conditions. In a future publication, the tyre model will be used in conjunction with a contact model and a radiation model to investigate the contribution of these waves to radiated sound during rolling.

Tyre/road interaction noise—A 3D viscoelastic multilayer model of a tyre belt

Vehicle noise is an increasing local environmental problem. For cars, above a steady speed of 40km/h the noise produced by the interaction of the tyres with the road surface is the dominant noise source.In order to be able to predict this noise, the vibration characteristics of a stationary tyre must be determined. A multilayer viscoelastic cylindrical representation of the tyre belt, located between the sidewalls of the tyre and excluding the tread, is provided which yields the displacement and velocity response of the tyre belt when excited in the radial or tangential directions for a wide range of excitation frequencies, using only data from the design process.This model includes a representation of an air cavity and sidewalls and the response of the tyre belt is determined in both the frequency–wavenumber and time–spatial domains. The model can then be used to determine the noise of a tyre rolling on a rough road.

The identification of tyre induced vehicle interior noise

Sound transmission into a vehicle is classified as either airborne or structure borne sound. From the point view of noise control, the reduction of noise transferred by different paths requires different solutions. Coherence function analysis is often used to identify transmission paths. However it can be difficult to separate the airborne from structure borne components. The principle of acoustic reciprocity offers a convenient method for overcoming this difficulty. The principal states that the transfer function between an acoustic volume velocity source and an acoustic receiver is independent of a reversal of the position of source and receiver. The work done on this study involves exciting a stationary tyre and measuring the surface velocity of the tyre at a number of discrete points. The acoustic transfer functions between each point on the tyre and a receiver point are measured reciprocally. Two sets of measurements are then combined to yield a measure of the sound pressure due to a point force on the tyre via the acoustic transmission path only. This technique also provides information on the relative contributions of various regions of the tyre wall to the resultant noise. Also the sound radiation characteristics, the horn effect, and resonance at the wheel housing are identified through the reciprocal measurement.

Elastic Multi-layered Analysis Using DE-Integration

In classical mechanics, solutions to various solid mechanics problems have very well been established. The most famous one is the Boussinesq solution for the case of concentrated vertical load acting on the surface of a semi-infinite body. However, in engineering problems like foundation, road or airport pavement design, solutions to a multi-layered system are required. Furthermore, simple but accurate and flexible solution approach which can be extended to multi-layered systems with various boundary conditions is of great necessity for engineering design. Authors of this paper have already analyzed various types of loads acting simultaneously or separately on the surface of the pavement structure. A pavement is modeled as a multi-layered elastic structure on the surface of which circular wheel loads act. In general, a wheel load is assumed to exert a vertical surface load due to the weight of the vehicle while braking or accelerating the vehicle would exert horizontal surface load [1]. Moreover, when large-sized vehicles like trucks and trailers turn on sharp corners wheels may exert turning (torsional) load on the pavement surface [2]. Finally, a rolling or stationary tire on the surface of a pavement system generates not only vertical load but also centripetal shear load due to the fact that the wheel can not freely expand due to surface frictional force [3]. This centripetal shear load causes an increase in tensile stress at the surface of a pavement structure. Theoretical analysis utilizes the principle of superposition and the solution is given by summing up the solution of the various loads considered. In the

Effects of rotation on the dynamics of a circular cylindrical shell with application to tire vibration

For the purpose of understanding the effects of rotation on wave propagation within a tire’s treadband, the vibration of an inflated, circular cylindrical shell, rotating about a fixed axis has been considered here. The equations of motion of the rotating shell are formulated in a fixed reference frame (i.e., Eulerian co-ordinates). By assuming wave-like solutions for the free vibration case, the natural frequencies and corresponding wave-like basis functions can then be obtained. A natural frequency selection procedure is introduced that can be used to associate each of the basis functions with a single natural frequency. The basis functions are then superimposed to represent the forced response of the system when driven by a point harmonic force at a fixed location in the reference frame. By using the procedure described here, the coefficients of the basis functions can be obtained directly by solving an uncoupled ordinary differential equation. Finally, the resulting forced responses are presented in both the spatial and wave number domains, and the wave number spectrum of the rotating shell is compared with that of a stationary shell. Based on the results presented here, it is suggested that at typical rotational speeds it may be possible to use a stationary tire analysis to predict the characteristics of a rotating tire after performing a simple kinematic compensation.

ON THE HORN EFFECT OF A TYRE/ROAD INTERFACE, PART I: EXPERIMENT AND COMPUTATION

Near the tyre/road contact area, the road surface and the tyre belt form a horn-like geometry, which provides a significant amplification mechanism for sound sources. Measurements have been carried out on a stationary tyre placed on a plane surface in an otherwise anechoic chamber. Following the reciprocal theorem a microphone was placed in the road surface near the contact patch and a white noise source was used in the far field. The amplification by the horn effect can then be determined as a function of frequency for an array of microphone positions relative to the contact patch and the centre of the tyre. These experimental measurements show that the horn effect is responsible for about 10–20dB increase in noise level. The amplification function shows a distinct interference pattern for higher frequencies and is independent of the longitudinal source position for low frequencies and source positions close to the contact patch. Numerical calculations using the indirect boundary element method have been carried out. These show excellent agreement with the measurements in the frequency regime of the BEM, i.e., up to 2500 Hz. The dependence of the horn effect on primary geometrical parameters such as the effect of the radius of curvature of the shoulders, the load and the width of the tyre has been investigated experimentally and numerically. The broad features of the horn effect are given by the cylindrical geometry of the tyre. The rounded edges of the tyre tend to increase the levels of the minima and shift them to higher frequencies, while slightly decreasing the levels of the maxima. Shape variations due to load can be accounted for by correcting the source distance to the edge of the formed contact patch. The amplification at low frequencies increases with width, the results collapsing onto a single curve as a function of the dimensionless width ω / λ.

Influence of Flexibility Properties and Friction Laws on Tyre Behaviour

The paper presents an analysis of tangential interaction between flexural properties of tyres and frictional properties of the tyre-road interface. Using simple models to represent tyre structure and friction, the traction-slip characteristics are derived for various situations of practical interest: a standing tyre subjected to monotonic and oscillatory loading, a stationary rolling tyre and especially that of the transition from standing to steady rolling. To gain deeper insight into the requirements for modelling flexural and the complex friction properties, the study examines the influence of the normal pressure profile, tyre structural properties and friction in the contact region on the overall and detailed characteristics of tyre traction. The analysis presented serves as a basic framework for modelling the complex tyre-road interactions such as that encountered in the snap-start problem of road vehicles.

Two-dimensional experimental analysis of tire vibration

This paper presents an experimental analysis of the velocity response of a treadless tire in the two-dimensional wave-number domain. The out-of-plane velocity response was measured on a stationary tire using a Doppler laser vibrometer for a two-dimensional 2-cm by 2-cm grid of points over the frequency band from 70 to 1500 Hz. From the data, three distinct regions of behavior can be identified: simple standing wave patterns, waveguide behavior, and nearly cylindrical wave propagation. Using 2-D wave-number reduction techniques, the measured spatial velocity distribution at each frequency was transformed into 2-D wave-number space. Different wave types in the tire carcass can be identified including the dominant flexural and in-plane waves (due to Poisson’s strain). At frequencies below the ring frequency of the tire cross section, a qualitative comparison is made to published results for 2-D dispersion curves of cylinders. At higher frequencies, a comparison is made in the wave-number domain, to a coupled plate model of the tire carcass and models of wave behavior in inhomogeneous plates. A qualitative explanation of the behavior of the tire is identified from the comparisons.

Identification of the airborne component of tyre-induced vehicle interior noise

The dominant noise generation mechanism of a tyre below 1 kHz is the tyre wall vibration caused by collisions between the tread blocks and the road. This paper is concerned with the identification of the transmission path of this tyre noise into a vehicle. A stationary tyre is excited by an electrodynamic shaker and a description of surface velocity is obtained. A reciprocity technique is used to measure the transfer functions which describe the transmission of sound from points on a tyre wall to a point inside a vehicle. The combination of these measurements offers a means of separating airborne noise from structure-borne noise while, at the same time, providing information on the relative contribution of various regions of this vibrating tyre surface to vehicle interior noise.

Measurement of Stress Paths under Agricultural Vehicles and their Interpretation in Critical State Space

Soil behaviour depends on the stress state of the soil and for the application of some soil compaction models, including the critical state model, knowledge of the stress path or the relationship between the generalized deviatoric stress q and the mean normal stress p is required. Stress paths under agricultural vehicles commonly used in the Australian cotton industry were measured using a soil stress state transducer, and found to be dependent on the horizontal and vertical position of the transducer relative to the tyre. The paths were interpreted in terms of critical state soil mechanics and were in agreement with expected and observed changes in void ratios under a tyre. Stress paths observed in a heavy clay field soil traced the Hvorslev surface, along a constant volume plane due to the near-saturated and incompressible nature of the soil. However, stress paths obtained in soil bins filled with unsaturated and compressible lighter textured soil appear to trace the Roscoe surface along a constant stress ratio plane. The stress path alone is not sufficient to predict soil behaviour; a knowledge of the initial conditions indicated by for example the preconsolidation stress is essential. The magnitude and direction of the major principal stress under a moving tyre were determined. It was shown that the horizontal and shear stress components of the stress state under a stationary tyre are much smaller than those under a moving tyre. An increase in speed had only a small effect on the magnitudes of the stresses and stress paths. Similar results were found for an increase in the draught force, generated by pulling a small cultivator.