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Electric motors often include adhesive joints to bond magnets to shells. In this paper, the variability of the frequency response function is assessed with regards to high frequency, finite element modelling and validation. The adhesive bond is used to fix the permanent magnets to the motor shell for the typical PMDC motor as it provides a smoother, more continuous surface than fixings without discontinuity of the magnetic field. To obtain the dynamic response of the motor housing at specified settings of the adhesive layer, which include variations in thickness and stiffness, a finite element model is established in ABAQUS. Given the relative stiffness of the adhesive is lower, this has a significant effect on the overall stiffness of the casing, for a fixed mass and thus the response frequencies and loss factor. When using frequency response functions to couple motors to components, this variability can be significant and thus this work is useful for the e-motor noise optimization at its design stage.

The primary function of windscreen wipers is to remove water and debris from the windscreen, ensuring the driver has a clear view of the road ahead. Predicting wiper performance at the design stage is therefore important to ensure their safe operation. There is hence a need to develop physics-based models of wiper performance that can be used as evaluative tools early in the design stage. This paper presents an analysis of the impact of changing screen curvature on the contact force distribution of a wiper blade and the subsequent effects on the transient dynamics. The contact distributions for three distinct screen curvatures and three loading points are calculated via FEA (finite element analysis) and subsequently analysed via multiple connected mass spring dampers to model the wiper blade lip transient dynamics. By analysing time and frequency domain data for several calculated contact distributions it is found that decreasing the screen curvature reduces the contact force at the centre of the blade, however, increases the amplitude of vibrations and range of frequencies observed. Additionally, it is found that moving the loading point towards the tip of the blade reduces the amplitude of vibrations, a result analogous to that of increasing the screen curvature. Based upon the understanding gained through this work the influence of design criteria on wiper blades can now be assessed, and several suggestions made as to how to reduce windscreen wiper noise.

The concept of the relaxation length is often used to describe a tire's transient response. This paper investigates how the transient response changes under different operating conditions. Through the measurement of tire forces and tire deformations during transient maneuvers performed on an indoor flat-belt tire test machine, experimental data were used to calculate various tire stiffnesses and the associated relaxation lengths using a novel method via optimization. With this methodology, the effects of tire load, inflation pressure, speed, and temperature on these stiffnesses and the relaxation length have been identified. The mechanisms behind these effects are discussed with a particular focus on the influence of temperature.

A new tyre model is developed that can predict the influence of both macroscopic and local flash temperature on tyre force generation. The model comprises two heat-transfer solvers. A macroscopic solver calculates the 3D temperature distribution across the tread and sidewall at a resolution of a few millimetres. A separate flash-temperature solver calculates the local hot-spot temperature distribution at the macro-asperity tyre-road contact interface at a resolution of micrometres. The two heat-transfer solvers are coupled with a structural model for the calculation of tyre forces and the sliding speed distribution along the contact patch. The sliding speed distribution feeds into the flash-temperature model and the local coefficient of friction is found as a function of sliding speed, flash temperature, normal pressure, road roughness and the complex modulus of rubber. The proposed tyre model is the first to include the effect of a changing macroscopic temperature distribution on the build-up of the local flash temperature. And to account for road-tread conduction at the macro-asperity contact interface. The model is applicable for identifying the friction envelope and optimum temperature range for tyres on roads with known roughness. This is important in motorsport where knowledge of grip offers a competitive advantage.

Modal testing is routinely applied to tyres for the identification of structural parameters and prediction of their vibration response to excitations. The present work focuses on the more demanding case of modal testing with the aim of constructing a full mathematical model of a tyre, appropriate for use in a generic time-based simulation. For this purpose, the less common free–free boundary condition is employed for the wheel, while the tyre belt is excited in all three directions, namely radial tangential and lateral. To improve efficiency, a novel partial identification method is developed for the mode shapes, whereby measured and predicted frequency responses are matched around distinct resonance peaks, while eliminating the effect of out-of-band modes. Axial symmetry of the tyre requires high purity mode shapes to avoid angular dependency of the tyre’s response. For this reason, experimental mode shapes are digitally filtered and combined with their orthogonal counterparts. Processed data reveal apparent repetition of selected mode shapes, and this is attributed to rim deflection.

Tire modal testing is frequently used for validation of numerical tire models and identification of structural tire model parameters. Most studies focus primarily on in-plane dynamic tire behavior and adopt the approach of the fixed boundary condition at the wheel center. Here, an identification method of in-plane tire dynamics was developed for the case of a free tire-rim combination. This particular case is important when the aim is to construct a full tire model, capable of predicting ride and noise, vibration, and harshness involving the whole vehicle, all from modal testing. Key attributes of the proposed approach include ease of implementation and efficient processing of measurements. For each type of excitation, i.e., radial and tangential, both radial and tangential responses were recorded. Compounding of the corresponding radial/tangential eigenvectors, which, in the context of the present work, refers to expressing the motion of the tire belt as a combination of the radial and tangential responses, results in smooth mode shapes that were found to agree with those published in other analytical and experimental studies.

This article presents a minimal parameter vehicle simulation model to predict the vertical suspension loads expected during abusive driving manoeuvres, such as a kerb strike event. Impulsive suspension loads are applied to tyre and suspension elements under such conditions. In particular, the aim is to specifically study the reactions of jounce bumper–rebound stop and tyre characteristics. For this purpose, a vehicle in-plane pitch dynamics model with 7 degrees of freedom suffices. Non-linear and hysteretic characteristics of the bump-stop elements are included through a new parametric map concept, based on displacement and velocity-dependent hysteresis. Furthermore, a static tyre model is described, tailored to predict the radial stiffness against penetration of an edge with a flat-type rigid body geometry. The tyre model is derived on the basis of classical membrane theory and represented in terms of only a few input parameters. Model validation is supported through experiments at both component and system levels.

The aim of this article is to assess the influence of the tyre/road contact interface on driveline vibrations. The mode shapes of a vehicle driveline are obtained and analysed, initially using three tyre models: a simple torsional spring, linear slip, and relaxation length-based models. Additionally, a fully transient load- and slip-dependent non-linear relaxation length model is incorporated into the driveline to determine the dynamic response on different surfaces. Simulations of pull-away manoeuvres on various surfaces are carried out. The halfshaft torque in each case is analysed and conclusions drawn on the effect of tyre dynamics on the frequency and intensity of driveline vibrations. In order to investigate the influence of higher-frequency tyre dynamics, a model incorporating tyre belt inertia is simulated for the same cases. It is found that the higher-order dynamics introduced by the tyre belt result in additional frequencies in the response, as well as differences in response amplitude. Using the non-linear relaxation length and belt inertia models it is observed that low-μ surfaces promote driveline vibrations at higher and more numerous frequencies compared with the typical shuffle response observed on a high-μ surface. It is shown that this frequency migration can be physically explained by considering the effect of decoupling between driveline and vehicle on low-μ surfaces. It is also shown that the observed frequencies can be predicted by appropriately modified linear models.

The analysis of the in-plane deformation of the tyre in relation to the frictional contact between the road and the tread is a crucial first step in the understanding of its contribution to the longitudinal dynamics of a vehicle. In this work, the physical mechanism of the generation of the two-dimensional contact pressure distribution for a non-rolling tyre is studied. Towards this aim, a physical tyre model is constructed, consisting of an analytical ring under pretension, a non-linear sidewall foundation, and a discretised foundation of viscoelastic elements representing the tread. Tread behaviour is examined first, with focus on the development of shear micro-slip. The tread simulation is enhanced with the combination of radial and tangential tread elements and the benefits of such an approach are identified. Subsequently, the contact of the complete model is examined by implementing an algorithm for transient simulations in the time domain. The effects of the imposed vertical load and sidewall non-linearity on the contact stress and strain fields are identified. The modelling approach is validated by comparison with published experimental results. The physical mechanism that couples the torsional and horizontal/vertical deformations of the carcass with the frictional forces at the tread is identified and discussed in detail. The proposed modelling approach is found appropriate for the description of the development of the two-dimensional contact pressure field as a function of the frictional potential of the contact.

In-plane tyre modal behaviour determines the response of tyres to ride excitations and braking/traction manoeuvres. In many studies, the interest is limited to relatively low frequencies and a detailed investigation into the ability of models to accurately simulate higher-order responses is unnecessary. In cases where an in-plane model is to be used for the generation of the contact deformation and stresses, or where modal reduction methods are implemented, a detailed knowledge of the modal response is desirable. The present work forms a study on the ability of a number of frequently used modelling approaches to generate realistic modal data throughout a wide frequency range. The analytical ring on elastic foundation model is used as a benchmark throughout the paper. Its predictions are compared with those of two discretised models, namely a truss- and a beam-based model. The sensitivity of the ring's response to a number of physical parameters is discussed. The results are used to inform the comparison between the analytical ring and the discretised models, providing explanations for any discrepancies observed. The limited applicability of the truss model is pointed out, while the accuracy of the beam-based model is enhanced by a circumferential inextensible string element. Both the ring and the enhanced beam models are further improved with the addition of a nonlinear string-based sidewall that accounts for the change in sidewall stiffness with inflation pressure. The findings may offer a reference when setting up in-plane models, including the stage of planning modal tests for parameter identification.

Transient tyre characteristics can have significant influence in vehicle handling, particularly in anti-lock braking system (ABS), which involves wheel speed oscillations as a result of rapid changes in wheel brake pressure. Hitherto, ABS studies have been conducted mostly with straight-line motion. Relatively simple vehicle models have been used which cannot capture the interactions between non-linear handling dynamics and tyre behaviour. This article takes such interactions into account, using a non-linear 14-degrees-of-freedom vehicle model in combination with three different single-point contact tyre models with transient characteristics. They include a stretched-string-based model, a modified stretched-string model, and a contact mass model. The particularly demanding situation of combined cornering/ABS braking is investigated. It is shown that although all tyre models are of similar bandwidth (maximum frequency ≈ 15 Hz), the simple string tyre model fails to cope with the non-linearities involved in combined braking/cornering and predicts greater braking distances than the two more enhanced tyre models.

The two-dimensional, frictional tyre-road contact interaction is investigated. A transient contact algorithm is developed, consisting of an analytical belt model, a non linear sidewall structure and a discretized viscoelastic tread foundation. The relationship between the magnitude/shape of the predicted two-dimensional pressure distribution and the corresponding belt deformation is identified. The effect of vertical load and the role of sidewall non linearity are highlighted. The modal expansion/reduction method is proposed for the increase of the computational efficiency and the effect of the degree of reduction on the simulation accuracy is presented. The qualitative results are physically explained through the participation of certain modes in the equilibrium solution, offering directions for the application of the modal reduction method in shear force oriented tyre models.

The paper aims to quantify the influences of non-steady state tyre behaviour and suspension damping on the instantaneous response of a vehicle to handling manoeuvres. The influences of such parameters cannot be determined using steady state tests. In the present work, a recently developed methodology is employed, which has been applied in the past to simple transient handling studies. Here, the approach is applied to more demanding situations and the effects of tyre lags and suspension damping are directly related to the under-steer, over-steer, or neutral-steer character of the vehicle under test. To distinguish between the effects of tyre force lags, tyre non-linearities, and combined tyre—vehicle non-linearities, an increasingly complex approach is adopted, which involves the implementation of a linear bicycle model, a non-linear bicycle model, and a ten-degrees-of-freedom (10DOF) non-linear vehicle model. In all cases, tyre-force lags are simulated using the relaxation length concept. The 10DOF vehicle model is validated against experimental measurements and forms the basis for fully non-linear studies. It is shown that even inherently under-steering vehicles may initially over-steer as a result of the delayed response of tyres. Finally, it is demonstrated that the proposed approach captures the effect of suspension damping and some problems are discussed regarding its application.

The paper attempts to provide an integrated framework for the objective assessment of the transient handling responses of non-linear vehicles. The ultimate aim of the proposed framework is the characterization of such responses as neutral or under/over-steering. A new methodology is employed, which has previously been applied for the classification of the transient response of linear vehicles. The success of the proposed method is judged based on its robustness, the consistency of the results, and their practical implications. Furthermore, the results are compared with the findings of traditional approaches for the characterization of the steady-state and transient handling behaviour. The corresponding discussion reveals the agreement between the approaches, but also highlights the slightly different definition of the neutrally steering vehicle, as perceived by the proposed method.

This article suggests a new methodology for the objective assessment and quantification of the response of a vehicle subjected to transient-handling manoeuvres. For this purpose, a non-dimensional measure is defined, namely the normalized yaw impulse. This measure appears in two variations. In its general or dynamic form, it represents the difference between the yaw moment due to the front-tyre forces and the yaw moment due to the rear-tyre forces, divided by the sum of the aforementioned yaw moments. By employing a linear, two-degree-of-freedom bicycle model, it is shown that the general form of the normalized yaw impulse can be written as a function of the steer angle and the forward, lateral and yaw velocities of the vehicle. This form is referred to as the kinematic yaw impulse. It is demonstrated that the combined application of the dynamic and kinematic expressions of the yaw impulse not only facilitates the explicit assessment and quantification of the transient behaviour of a vehicle, but also reveals the influence of parameters such as the yaw moment of inertia, which traditionally leave the steady-state behaviour unaffected.

An analysis of the mechanism of tyre contact force generation under transient conditions is presented. For this purpose, two different versions of a brush model are used, both with inertial and viscoelastic properties. The first model consists of independent bristles, while the second, with a more realistic scenario, introduces viscoelastic circumferential connections between the sequential bristles, which affect the lateral degrees of freedom. Friction between the tyre and the ground follows an experimentally verified stick-slip law. For the model with independent bristles, the state of each bristle at any instant of time depends only on the state of the same bristle at a previous time step. In the second model, the instantaneous state depends on the state of the same bristle at the preceding time step, as well as on the state of the two adjacent bristles at the same time. Simulation results reveal the differences between the two models and most importantly show how transient friction force generation may differ substantially from steady state predictions. The findings suggest that transient tyre behaviour should not be attributed solely to the contributions of the flexible belt and carcass. On the contrary, the observed transience in the neighbourhood of the contact patch should also be taken into account.

The close relationship between tyre contact mechanics and low-frequency driveline dynamics is examined in this chapter. First, a dynamic model of a typical rear wheel drive driveline is developed. The model is then used to demonstrate the shuffle error state. Focus is subsequently moved to tyre–road interaction. A number of frequently used tyre modelling approaches are presented, initially for steady state operation and then for the investigation of low bandwidth transient responses. Such responses are treated by integrating a simple steady state tyre model with the relaxation length concept. Finally, the influence of tyre dynamics on shuffle is investigated by implementing a linear transient tyre model into the driveline model. Simulation results demonstrate the strong dependency of the rate of attenuation of shuffle oscillations on forward speed. It is shown that capturing such effects depends greatly on the tyre model of choice.

This paper presents a detailed 4×4 off-road vehicle modelling method, based on a multi-physics approach. A full drivetrain system including all aspects of rotational inertial dynamics, friction, damping and stiffness properties is integrated with a fourteen-degrees-of-freedom vehicle model including body dynamics, kinematics, suspension and wheel dynamics as well as the terramechanical phenomena between tyres and soft soils. The interaction between all these modules is implemented in the MATLAB/SIMULINK/SimDriveline environment. The concepts of modularity, flexibility, and user-friendliness were emphasized during model development. The model is developed in order to provide design engineers with the capability to investigate effects of component selection and to develop control systems and automatic optimization processes for off-road 4×4 vehicles. While the modelling approach can be used for a wide variety of operating conditions, the present work focuses on the analysis of the contribution of different aspects on the off-road traction of 4×4 vehicles.Copyright © 2006 by ASME

A comprehensive computer model is devised for the simulation of AWD off-road vehicle dynamics. Particular attention has been paid to the modelling of various visco-lock devices, including the viscous couplings and visco-lock limited-slip differentials. These devices are represented by fully parameterised physical models which capture the torque transmission mechanism represented by various thermodynamic, hydrodynamic, structural and mechanical modules. The characteristics of these devices can easily be altered so that comparisons can be made between different types. In addition, the influence of a wide range operating conditions, vehicle design parameters and tyre characteristics can also be made over various deformable soils.