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.
Brake squeal is a self-excited vibration with initially inclining amplitude reaching a limit cycle due to nonlinearities. For a proper simulation of this behavior, it is necessary to know the origin and the influence of the brake system's nonlinearities. It is generally known, that nonlinearities are inherent to the joints [1, 2], complex friction laws [3] and the friction material of the system [4][5][6]. In this work, the influence of friction material and shim nonlinearities on the existence of a limit cycle is investigated. Stiffness and damping characteristics are determined using the chair's owned DCTR [4] test rig. It is shown, how nonlinear characteristics, which are necessary for simulation, are obtained from the performed measurements. They are incorporated in a multiple body model composed of brake disk, pads, shims, carrier and calliper from which the nonlinear equations of motion are derived. For the investigation on the bifurcation behavior, the equations of motion are transformed into normal form. It is then possible to describe the bifurcation behavior with respect to parameter influences. Ultimately, with this information it is possible to show the influence of the investigated nonlinearities on brake squeal.
Squealing automotive brakes are usually not accepted by customers. However, squealing is an omnipresent phenomenon in disc brakes at least in certain operation states. During the development process of new brakes, engineers succeed more or less in covering this phenomenon with tools like using shims, modifying the structure or varying the mounted pads. In 2002 Popp et al. [1] described the pre-conditions for positive work of the friction forces (i.e. excitation of squeal) based on a very simple model. The essential point in this model is a phase shift between the inplane movement of the pad and the friction force. In [2] it was shown that it is possible to suppress actively brake squeal using this approach. Active pads with integrated piezoceramics were used as actuators. The authors of the present paper use multi body brake models for the investigation of the origin of the excitation mechanism by observing the work per period of the friction forces and comparing the results with the classic stability analysis. A measurement technique based on these theoretical investigations is developed for detecting parameter regions (e.g. for the brake pressure and corresponding squealing frequencies) which are suspicious for squeal. Considering two models of the brake, phase shifts between signals and measuring the work of the nonconservative forces are considered with respect to the question of detecting the tendency to squeal. Based on these theoretical results measurement procedures are developed and tested at test rigs at TU Berlin and TU Darmstadt. The results of this procedure coincide with results of state of the art experimental investigations but can be performed much faster. This new procedure yields even more significant results than the ones described in [2].
Due to the maximum rotational speed of modern washing machines (1600 rpm) and the resulting high excitation forces, an appropriate modeling of the dynamical behavior is of interest. As an example, different models of a front‐end loader fabricated by Bosch Siemens Hausgeräte GmbH (BSH) are discussed. Using AUTOLEV, a symbol manipulation tool, the nonlinear and linearized differential equations are derived. Based on those, the dynamical behavior is examined with particular interest in the stability of the solutions. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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