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Based on the principle of minimum complementary energy, a theoretical model considering the additional dynamic stiffness caused by the structural deformation of the cord-rubber diaphragm is proposed. The capability of modeling the dynamic stiffness change of the rolling lobe air spring provides guidance for material selection and the design of the diaphragm structure. The directly measured geometric parameters in the proposed model have physical meanings, while the relevant material parameters can be identified by combining the mechanics of composite materials and the Payne effect theory of rubber diaphragm structures. Three air springs with different designs and structures were selected for the indicator test and compared with the theoretical value. The comparison results show that the relative error was less than 3%, which verifies the universality and accuracy of the proposed dynamic stiffness theory of the rubber diaphragm. The results demonstrate that the amplitude-dependent additional stiffness generated by the rubber diaphragm is significant, and the lobe bending moment has the most considerable stiffness contribution to the rolling lobe air spring at low amplitudes. In the end, the changing trend of the entire dynamic stiffness with different design factors is given. The rubber diaphragm stiffness theory of rolling lobe air springs proposed in this paper provides powerful assistance for material selection and shape design for car air springs. [ABSTRACT FROM AUTHOR]

Magnetorheological fluid (MRF) is a widely used smart material that suffers from sedimentation. Since sedimentation is unavoidable, it is crucial to study and improve the redispersibility of MRFs. However, previous redispersibility testing methods have problems, such as complicated operation and low precision. Simultaneously, a simple and effective method is urgently needed for high-precision modeling of MRF sedimentation to test the rheological properties of settled MRFs at different depths. After systematically analyzing the redispersion problem, this paper proposes decoupling the energy required for redispersing settled MRFs into two parts, which are related to different factors. These two parts are the energy required to separate the agglomerated particles (related to the MRF formula) and that to redisperse the settled MRF uniformly vertically against gravity (related to the solid concentration and packing limit). The energy that separates the agglomerated particles is proportional to the shear stress of slowly shearing the corresponding agglomerated samples, i.e., the yield stress. Thus, this paper proposes a simple microdamage quasi-static indentation method to measure the yield stresses of settled MRFs at different depths to characterize the redispersibility of the corresponding MRFs. Herein, this method is applied to study the mechanisms of the influences of surfactants, thixotropic agents, and their networks on the redispersibility of MRFs. The results indicate that a well-dispersed plate-like thixotropic agent network can effectively improve redispersibility, while surfactants with poor compatibility degrade redispersibility. In summary, this redispersibility test method will greatly facilitate studies of MRFs, such as optimizing the formulas and establishing sedimentation models. [ABSTRACT FROM AUTHOR]

Accurate control of the magnetorheological damper (MRD) damping force and current is necessary to realize the effective semi-active suspension control. However, the temperature sensitivity of the magnetorheological fluid makes the MRD force strongly dependent on temperature changes, leading to the problem of the model mismatch and degradation of control effect. In this paper, the experimental study of MRD at different currents and velocities from âˆ'40 °C to 80 °C was implemented. It reveals the characteristic of MRD damping loss at low temperatures and viscous damping reduction at high temperatures. On this basis, a new parametrized hyperbolic hysteresis model with temperature as an independent variable is proposed, providing an accurate description of the viscosity, stiffness, and hysteresis characteristics of the MRD. A simplified temperature-revised inverse model is proposed to calculate the driving current with demanding force. It could improve the accuracy of driving current by 12.79% and demanding force by 18.67%. A process in the loop simulation is implemented to validate the inverse model with a modified non-chattering algorithm. Together with the inverse model, the proposed algorithm could realize continuous current change, reducing the RMS of acceleration by 14% on road of class B. Furthermore, the temperature compensation could improve the control effect by 19.78%. [ABSTRACT FROM AUTHOR]

Material and geometrical parameters of tires involve some degree of uncertainty mainly related to production processes. Accordingly, the associated structural responses are affected by these uncertainties. In this study, a novel theoretical ring model is presented to describe the in-plane and out-of-plane vibrations as well as the steady-state response of tires, and then to evaluate the influence of the uncertainties in structural parameters on the natural frequencies and the sound radiation characteristics under uncertain excitations. The Hamilton principle is applied here to derive the governing equations. The modal superposition method is used to calculate the steady-state response of the tire. In the sound radiation analysis, the in-plane and out-of-plane bending and torsional vibrations under a set of harmonic unit forces and moments are treated as the source of noise generation. On this basis, the generalized polynomial chaos expansion method is then adopted to evaluate the influence of the uncertainty on the natural frequencies and the sound power. To obtain the unknown coefficients of the expansions, the nonintrusive probabilistic collocation method is employed. Moreover, considering the concept of linear independence of vectors, the number of collocation points is reduced. It is applied to investigate the impacts of the elastic and structural uncertainties on the natural frequencies of the tire. This yields an efficient simulation in terms of computational costs. Finally, the distributions of the sound power due to the forced vibration under the random concentrated line forces are given. [ABSTRACT FROM AUTHOR]

Here, the authors propose an energy method to obtain the friction coefficient of a rubber block sliding on self-affine substrates via simulation. Due to the multi-scale property, the rough surfaces are modelled with four harmonic rigid frictionless roads. As the rubber block is a viscoelastic solid, energy dissipation in the contact area results in friction. The authors propose a new simulation method to obtain friction coefficient through energy dissipation. With different loads and sliding velocities, the change law of friction coefficient is calculated. The authors design a test instrument to verify the friction coefficients of rubber on some certain surface. The findings of this research constitute a theoretical basis for safe tire design and tire grip improvements. [ABSTRACT FROM AUTHOR]

Magnetorheological (MR) damper is one of the key technologies in the field of semi-active suspensions. However, the dynamic model and control strategy are not yet well established. A unified MR damper model and its inverse characterization are proposed to investigate MR damper dynamics. First, a novel unified model is proposed to describe the shear term of the MR damper force. This forward unified MR damper model uses one set of parameters to describe all MR force behavior under all currents and velocities, which agrees well with experimental data. Then, an inverse MR model based on the adaptive neuro-fuzzy inference system (ANFIS) technique has been established, where the precise training data are obtained from the proposed unified hysteretic model. A clear step-wise modeling process is proposed to decrease coupling degree of system which can be beneficial to improve inverse modeling efficiency. The inverse MR model is used for a semi-active suspension control, which can obtain the excitation current, exactly tracking the desired damping force computed by suspension control algorithm. Finally, validation of the proposed ANFIS inverse model has been conducted by comparison with three traditional empirical inverse approaches. The results reveal that the ANFIS inverse model could achieve much more tracking capability for the desired damping force and thus contributes to the development of semi-active suspension controllers. [ABSTRACT FROM AUTHOR]

A rigid–elastic coupling theory for the rolling kinematics of tyres, by which the tread slip, the effective rolling radius and the ply steering of the tyres can be analysed, was formulated. The theory demonstrates that, during free-rolling motion, the coupling between the rotational velocity Ω along the wheel axis and the circumferential displacement gradient generates the longitudinal tread slip, and the coupling between the rotational velocity Ω along the wheel axis and the lateral displacement gradient generates the lateral tread slip and the ply steering. Revisiting the tread slip phenomenon using the newly proposed method numerically proves the kinematic mechanism of the rolling friction. It can be found that the effective rolling radius Re increases with increasing inflation pressure and decreases with increasing load; the sensitivity of Re to the inflation pressure is greater than the sensitivity of Re to the load. The good agreement between the theoretical predictions and the test results for the effective rolling radius of the radial tyres of a car is found. The coupling of the displacement gradient and the rigid rolling kinematics causes non-symmetry of the lateral tread slip which, in turn, leads to the ply steering and the residual aligning moment; these depend on the belt and tread design. The proposed theory and approach provide a quick and powerful tool for analysing the tread slip, the effective rolling radius and the ply steering of the tyres under free rolling. [ABSTRACT FROM AUTHOR]

A novel constitutive characterization method for uncured rubber behaviour has been developed in this article. A systematic measuring procedure was designed to fully investigate the uncured rubber complex stress–strain behaviour under different deformation patterns, which integrated three kinds of tests – the uniaxial tensile, the compression test and the shear test. It can be found from the observed behaviour that the uncured rubber has similar but much pronounced non-elastic stress–strain relationship, which is highly non-linear and highly rate dependent. A generalized Maxwell model with modified Yeoh model is developed to constitutively describe the observed phenomena in which parameters are identified by an evolution optimization scheme. Good agreement can be found between the model and the test data. Another finding is that, similar to vulcanized rubber, multi-test data are needed to obtain compatible constitutive models. The test results, findings and the developed model help rubber engineers deeply understand the uncured rubber's mechanical behaviour and provide a base for rubber manufacturing simulation. [ABSTRACT FROM AUTHOR]

A new analytical formula to describe the vertical stiffness of a rolling lobe spring has been established; the equation incorporates the rate of change of the effective area of the spring. Two rolling lobe air springs were studied by performing analytical calculations, and the results were verified by comparisons to finite element simulations and experimental data. The analytical formula can be used to qualitatively predict the vertical stiffness of a rolling lobe air spring. Precise prediction of the value of the vertical stiffness can be obtained using the formula in cases where the reservoir volume is not very large. The influence of geometric parameters on the vertical stiffness of a rolling lobe air spring has been studied using the proposed formula and a guideline for its design has been obtained by plotting a cause–effect chart. [ABSTRACT FROM AUTHOR]

It is well known that the tyre steering torque is highly dependent on the tyre rolling speed. In limited cases, i.e. parking manoeuvre, the steering torque approaches the maximum. With the increasing tyre speed, the steering torque decreased rapidly. Accurate modelling of the speed-dependent behaviour for the tyre steering torque is a key factor to calibrate the electric power steering (EPS) system and tune the handling performance of vehicles. However, no satisfactory theoretical model can be found in the existing literature to explain this phenomenon. This paper proposes a new theoretical framework to model this important tyre behaviour, which includes three key factors: (1) tyre three-dimensional transient rolling kinematics with turn-slip; (2) dynamical force and moment generation; and (3) the mixed Lagrange–Euler method for contact deformation solving. A nonlinear finite-element code has been developed to implement the proposed approach. It can be found that the main mechanism for the speed-dependent steering torque is due to turn-slip-related kinematics. This paper provides a theory to explain the complex mechanism of the tyre steering torque generation, which helps to understand the speed-dependent tyre steering torque, tyre road feeling and EPS calibration. [ABSTRACT FROM PUBLISHER]

As a vehicle travels at moderate/high speeds, tire noise becomes dominant over other sources of vehicle noise. It is a challenging task to determine the spectral characteristics of the tire noise source and even much more challenging to predict the tire pattern noise. This paper proposes a hybrid experimental-numerical method to identify the tire air-pumping noise spectrum and to predict the pattern noise. A special designed test and cut tire are used to obtain the near field tire noise spectrum while the boundary element method (BEM) is used to determine the transfer characteristics between noise source and selected field points. Then, the spectral characteristics of the air pumping source can be identified by combined use of the numerical transfer characteristics and the measured noise of the cut tire by solving the Helmholtz equation. In the end, the proposed approach has been developed into an in-house software and practical tire pattern noise has been investigated successfully. The established model is able to predict the noise at any field point and the good agreement between the predicted results and tests can be found, demonstrating the reasonability of the proposed approach. In addition, an optimization method of tire tread block shift and mold shift, i.e. moving one of the two half molds and/or tread ribs along the circumferential direction to change their relative phases, are proposed based on the developed software. A practical example demonstrates that the proposed approach and in-house code can be used to predict and optimize tire tread pattern noise. [ABSTRACT FROM AUTHOR]

There are two aims for the second part of this paper: verifying the theory presented in the first part through parameter variation and comparison between simulation and experiment, and to study the effect of the belt structure on the cornering properties of radial tyres. Research has been carried out with a passenger car radial tyre and two different kinds of truck or bus radial tyres using both simulation and experiment. This second part of the paper shows that belt structure plays an important role in the generation of tyre forces and moments in addition to the effects of the tread stiffness and friction coefficients. The theory and method presented in this paper opens a new robust way to predict the tyre forces and moments from the tyre design and provides a reliable model for a generation mechanism. [ABSTRACT FROM PUBLISHER]

A new method to describe tyre rolling kinematics and how to calculate tyre forces and moments is presented. The Lagrange–Euler method is used to calculate the velocity and contact deformation of a tyre structure under large deformation. The calculation of structure deformation is based on the Lagrange method, while the Euler method is used to analyse the deformation and forces in the contact area. The method to predict tyre forces and moments is built using kinematic theory and nonlinear finite element analysis. A detailed analysis of the tyre tangential contact velocity and the relationships between contact forces, contact areas, lateral forces, and yaw and camber angles has been performed for specific tyres. Research on the parametric sensitivity of tyre lateral forces and self-aligning torque on tread stiffness and friction coefficients is carried out in the second part of this paper. [ABSTRACT FROM PUBLISHER]