A Hybrid Model for Predicting Steering Brake Squeal Based on Multibody Dynamics and Finite Element Methods

In recent years, the problem of automotive brake squeal during steering braking has attracted attention. Under the conditions of squealing, the loading of sprung mass is transferred, and lateral force is generated on the tire, resulting in stress and deformation of the suspension system. To predict the steering brake squeal propensity and explore its mechanism, we established a hybrid model of multibody dynamics and finite element methods to transfer the displacement values of each suspension connection point between two models. We successfully predicted the occurrence of steering brake squeal using the complex eigenvalue analysis method. Thereafter, we analyzed the interface pressure distribution between the pads and disc, and the results showed that the distribution grew uneven with an increase in the steering wheel angle. In addition, changes in the contact and restraint conditions between the pads and disc are the key mechanisms for steering brake squeal.

On the interrelation of equilibrium positions and work of friction forces on brake squeal

Brake noise, in particular brake squeal, is a permanent topic both in industry and academia since decades. Nonlinearities play a decisive role for this phenomenon. One nonlinear effect widely ignored so far is that the brake can engage multiple equilibrium positions with severe consequences on the noise behavior. In fact in an automotive disk brake, the essential elements carrier, caliper and pad are elastically coupled with each other and their behavior is nonlinear that multiple equilibrium positions are possible. The engaged equilibrium position depends, for example, on the initial conditions, external disturbances, and the transient application of the brake pressure, and in consequence configurations with or without self-exciting characteristics of the friction forces result. Obviously, a self-exciting characteristic of the friction force is a necessary precondition for the occurrence of squeal. The authors recently published some corresponding results (Koch et al. FU Mech Eng, 2021. https://doi.org/10.22190/FUME210106020K) demonstrating that for same operating parameters with respect to brake pressure (i.e., brake torque), rotational speed and temperature the engaged equilibrium position has decisive influence whether squeal occurs or not. While in Koch et al. (2021) it has just been detected whether there is squeal or not, the excitation characteristic of the friction forces becomes, beside the engaged equilibrium position, the additional focus in the present paper. Therefore, a work criterion already successfully applied in earlier publications for squeal tendency is considered. For the experimental application of the work criterion, accelerometers have to be mounted. The accelerometers’ location to be applied can be determined in the chosen setup by the camera system anyway necessary for the measurement of the engaged equilibrium position. With this refined setup, it is possible to specify the states squeal, close to squeal and far from squeal. The test series again demonstrate the decisive influence of the engaged equilibrium position (for constant operation parameters) on the occurrence of the respective state. These findings can have consequences for simulations (consideration of multiple equilibrium positions in models and respective linearization with consequences on system’s eigenvalues), but also for the design (avoidance of equilibrium positions suspicious for squeal) and experimental setups (determination of special positions) of brakes.

Optimal Design of Brake Disc Structures for Brake Squeal Suppression

Aiming at the brake squeal problem of automobile disc brakes, an optimization design method of brake disc structure based on the weighted brake squeal tendency coefficient is proposed. This method is based on the brake squeal complex modal finite element model of a certain disc brake. Based on the validity of the model verified by the bench test, the single-sided disc surface height of the brake disc, the height of the radiating rib, the elastic modulus and the disc are selected. The four key structural parameters of the cap height are used as design variables. Taking the weighted braking squeal tendency coefficient proposed in this paper as the optimization target, the response surface method and the central composite test design are combined to construct a weighted braking squeal tendency coefficient response surface model, and use multi-island genetic algorithm to optimize the model. The results show that the optimization design method proposed in this paper can greatly improve the optimization efficiency while effectively reducing the screaming tendency of the disc brake in the full frequency band, so as to achieve the purpose of improving the NVH performance of the disc brake and improving the comfort of the car.

Light duty automotive drum brake squeal analysis using the finite-element method

The method presented in this work intends to analyze drum brake design parameters of a light duty automotive drum brake system. The main objective of this work is to correlate brake materials and unstability parameters to identify which condition will effectively reduce squeal propensity. The methodology involves (a) the finite-element method of the brake components, namely, drum, shoes, and frictional linings, (b) static calculations to get a pre-stress state around which (c) is computed the complex eigenvalues of the system. Hence, positive real parts indicate dynamic instabilities which are explored by varying parameters, namely, the modulus of elasticity of the materials and the friction coefficient at the contact of the shoes with the drum. According to calculations, it was observed that there exist a given range of values for Young’s modulus and friction coefficient that are favorable to reduce drum brake squeal occurrence. In addition, the method proposed delivered results that match with brake squeal literature.

DISC BRAKE SQUEAL ANALYSIS USING NONLINEAR MATHEMATICAL MODEL

Many academics have examined the disc brake squeal problem with experimental, analytical, and computational techniques, but there is as yet no method to completely understand disc brake squeal. This problem is not fully understood because a nonlinear problem. A mathematical model was created to understand the relationship between brake disc and pad thought to cause the squeal phenomenon. For this study, two degree of freedom model is adopted where the disc and the pad are modeled. The model represents pad and disc as single degree of freedom systems that are connected together through a sliding friction interface. This friction interface is defined by the dynamic friction model. Using this model, linear and nonlinear analyzes were performed. The stability of the system under varying parameters was examined with the linear analysis. Nonlinear analysis was performed to provide more detailed information about the nonlinear behavior of the system. This analysis can provide information on the size of a limit cycle in phase space and hence whether a particular instability is a problem. The results indicate that with the decrease in the ratio of disc to pad stiffness and disc to pad mass, the system is more unstable and squeal noise may occur.

ON MODELS WITH WOBBLING DISK FOR BRAKE SQUEAL

Among many mathematical models of disk brakes for the explanation of brake squeal, models with wobbling disk have their own advantage over planar models. Applying a recently developed matrix form of Euler equations in rigid body dynamics, the equations establishment process can now be performed with almost all popular computing software. Furthermore, the presented models are more generalized in terms of damping, in-plane vibration, and unsymmetrical mounting.

Light duty automotive duplex drum brake squeal analysis using the finite element method

The brake system creation is an important achievement for automotive production. However there is a secondary response of this system, its noise emission. Brake noise researches started in 1920’s and since then several causes were identified. In addition, many kinds of noises, their frequency range and characteristics were detected. Between these, the squeal is the noise that most concerns the automotive industry by reason of high warranty costs and environmental impact. The squeal noise occurs as a result of three mechanisms that are the stick-slip, the sprag-slip and the modal coupling and these are connected to material parameters of the brake components. This paper proposes a correlation between material and stability parameters of a light duty automotive duplex drum brake to indicate the influence of this on brake squeal. The results suggest that friction coefficient is the most influential parameter and its restrain does make possible to maintain squeal level under emissions regulations.