Road vehicles are subject to random excitation by the unevenness of the road. For a dynamical analysis, vehicle models of the vertical vibrations as well as guideway models of the road unevenness are required. The fundamental dynamics of vehicle suspensions can be already modeled by a quarter car featuring the decoupling of the car body motion and the wheel motion. This suspension model is characterized by five design parameters where two of them, the shock absorber and the tire spring, are highly uncertain due to wear and poor maintenance. For the assessment of the vehicles performance three criteria have to be used: ride comfort, driving safety and suspension travel. These criteria depend on all the five design parameters resulting in a conflict or a pareto-optimal problem, respectively. In this paper, the uncertainties of the parameters are projected into a criteria space in order to support the decision to be made on the basis of a pareto-optimal problem. Simulations with uncertainties support the robust suspension design. It is shown that controlled suspension parameters remain uncertain due to the unpredictable decisions made by the driver.

Disc brakes convert kinetic energy into thermal energy in order to slow down vehicles. During the braking process enormous heat flows and temperature gradients occur in the system. Because heating leads to a change in shape for most materials, it is important to take the temperature and its influence into account during the design process. The interaction between the structure and the heat in disc brakes can be described with methods from thermoelasticity. To simulate thermoelastic behaviour the Finite Element Method is commonly used. The thermal and mechanical domain are taken into account by coupling the equation of motion and the heat equation. However, in transient analysis often the problem occurs of different time scales of the structural and thermal dynamics for many technically relevant materials, like steel. For metallic materials the time constant of structural dynamics is much smaller than those of thermal dynamics. This complicates an efficient transient simulation. In the present work the implementation of a Finite Element Method in thermoelasticity and associated investigations are shown. The method is applied to various parts and load cases. Also different approaches to deal with the different time scales will be shown. Heuristic methods like mass-scaling as well as more mathematically oriented approaches like model order reduction are presented.

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Brake-system dynamics still represents a key question for the understanding and quantification of self-excited vibrations in automotive applications. Conventionally, the dynamics of brake systems is analyzed by using complex eigenvalue analysis, which consists of linearizing the nonlinear equations of motion at a sliding state and solving the quadratic eigenvalue problem there. This method, however, only reproduces the local vibration behavior, tends to overestimate the number of instabilities, and its resulting complex eigenvectors do not provide amplitudes for the vibrations. Thus, in order to overcome these difficulties, alternative methods for the modeling, simulation, and analysis of friction-induced vibrations need to be addressed. In this contribution, as an alternative, a time-domain investigation of an industrial brake system based on elastic multibody systems is proposed. Moreover, since the occurrence of brake squeal is a highly parameter-dependent phenomenon, uncertainties are considered using fuzzy arithmetical methods.

Brake squeal describes noise with different frequencies that can be emitted during the braking process. Typically, the frequencies are in the range of 1 to 16 kHz. Although the noise has virtually no effect on braking performance, strong attempts are made to identify and eliminate the noise as it can be very unpleasant and annoying. In the field of numerical simulation, the brake is typically modeled using the Finite Element method, and this results in a high‐dimensional equation of motion. For the analysis of brake squeal, gyroscopic and circulatory effects, as well as damping and friction, must be considered correctly. For the subsequent analysis, the high‐dimensional damped nonlinear equation system is linearized. This results in terms that are non‐symmetric and dependent on the rotational frequency of the brake rotor. Many parameter points to be evaluated implies many evaluations to determine the relevant parameters of the unstable system. In order to increase the efficiency of the process, the system is typically reduced with a truncated modal transformation. However, with this method the damping and the velocity‐dependent terms, which have a significant influence on the system, are neglected for the calculation of the eigenmodes, and this can lead to inaccurate reduced models. In this paper, we present results of other methods of model order reduction applied on an industrial high‐dimensional brake model. Using moment matching methods combined with parametric model order reduction, both the damping and the various parameter‐dependent terms of the brake model can be taken into account in the reduction step. Thus, better results in the frequency domain can be obtained. On the one hand, as usual in brake analysis, the complex eigenvalues are evaluated, but on the other hand also the transfer behavior in terms of the frequency response. In each case, the classical and the new reduction method are compared with each other.