By the hybrid uncertain model, an optimization design based on reliability and confidence interval is proposed to explore the optimal design for squeal reduction. This review can help analysts to choose right methods and make decisions on new areas of method development. Boundary-value problems with quickly oscillating boundary conditions § 5. Many causes of rotor vibration are so subtle and pervasive that excessive vibration continues to occur despite the use of usually effective design practices and methods of avoidance. The simple shape and common occurrence of disks as machine elements belies a complexity of behavior that can be an important factor in the improvement of modern machine performance. This approach will be demonstrated by two simple examples, a rod with varying material properties and a rectangular plate with a rectangular or circular hole, using a finite element discretization as basis. We obtain closed form approximations for the stability boundaries which give insights in the interaction of different effects which are elsewhere mostly considered in isolated form.
In particular, the brake rotor has to be balanced and has to withstand the high braking loads. The papers in this volume bring together engineers of different background, and it fill gaps between structural mechanics, vibrations and modern control theory. Chapter Twelve Considers The Interaction Between The Structural Dynamics Of Components And Noise, Together With Methods To Improve Sound Quality. Friction-induced vibration and parametric resonance phenomena are areas of research activity that have received considerable attention. The analysis of the dynamic properties of a cutting machine's support structures should be one of the basic steps of a ma- chine tool construction process. Many measures to avoid squeal have been discussed in the engineering community reaching from purely passive measures like the increase of damping, e.
This paper deals with the problem of how to design a rotor such that it is robust against friction induced vibrations using structural optimization. In this case, the maximum of the upper bound of confidence interval of design objective is selected as the objective function, while the minimal value of the probabilistic constraint is selected as the constraint function. The model parameters are chosen rather roughly so that the numerical values of the results will have little practical relevance. Since the early 20th century, many investigators have examined the problem with experimental, analytical, and computational techniques, but there is as yet no method to completely suppress disc brake squeal. Finally the origin and the role of phase shifts between oscillations normal and parallel to the contact surface is clarified with respect to the mode-coupling instability. The regular case and the case of being on the spectrum § 2.
Considering the special conditions of lightweight design rims, a minimal model for safety-relevant self-excited vibrations of brake systems is presented. Realistic modifications are found to be bounded within certain frequency ranges. In this manner, design modifications proposed for conventional disk brakes can easily be tested using this method. For mechanical vibration problems this means that although not everything can be modeled, a way has to be found to obtain a structure which fulfills the requirements. With clear explanations and documentation of the concepts, methods, algorithms, and software available for accounting for wind loads in structural design, it also describes the wind engineer's contributions in sufficient detail that they can be effectively scrutinized by the structural engineer in charge of the design. Brake squeal is still a challenge for design engineers and scientists. The normal forces and the friction couples produced by the rotating sliders are moving loads and are seen to bring about dynamic instability.
Due to cost reasons for the avoidance of brake noise only passive measures are meaningful for a broad industrial range. It replaces the multiple user names and passwords necessary to access subscription-based content with a single user name and password that can be entered once per session. For the validity of the analysis it must therefore be assumed that the initial conditions lie indeed in the basins of attraction of the corresponding attractors. This book discusses the question on how to design a structure such that unwanted self-excited vibrations do not occur. The energy source realizing this kind of steady state motion usually is sufficiently large to maintain the operating conditions, independently of the state of the system. There has been a lot of research going on about these issues and at the same time different methods are being proposed to eliminate or reduce them. Instability of the rotor can yield severe problems, for example in the context of brakes and clutches it causes squeal, in the process of paper calendering the duration of the rollers is decreased substantially.
This book discusses the question on how to design a structure such that unwanted self-excited vibrations do not occur. Brake squeal is still a major issue in the automotive industry due to comfort complaints of passengers and resulting high warranty costs. The results of a numerical example demonstrate the effectiveness of the proposed optimization on reducing squeal propensity of the disc brake systems with hybrid uncertainties. The simulations are validated with measurements on an automotive disc brake. According to classical linear stability analysis see, e. Nonstationary problems with quickly oscillating boundary conditions § 8. The feedback between the vibration modes with the same frequency leads to appearance of the circulation terms in the equations of motion and to instability.
It may be expected that the intuitive picture gained will be of considerable help for practical design purposes. Brake squeal simulation presents different challenges. Emphasis is given on current state-of-the-art methods and concepts in computing methods and their application in engineering practice. The stiffness and mass parameters are determined by an analysis of the null space of a matrix containing the measured receptances. Therefore, a large range of design, active and passive solutions are given.
The rotating speed of the mass—spring— damper slider system studied in these papers is in the subcritical range. Shibboleth is an access management service that provides single sign-on protected resources. This paper presents a multibody system of a brake, which is capable to reproduce the important features of brake squeal. Using this model, the interaction between the pad and the disc is investigated. Each slider is a mass-spring-damper system traveling at the same constant speed around the disk. Therefore an optimization problem is formulated, with the goal to split all eigenfrequencies in the audible range as much as possible in order to make the brake more robust against squeal. The excitation mechanism for squeal is explained by the formulation of a stability problem.
Approximations to the stability boundaries of the system are calculated using a perturbation approach. Pages 5-17 Eigenvalue Placement for Structural Optimization. The paper is compressed in the nip by rollers which sometimes tend to exhibit self-excited vibrations. The occurrence of self-excited vibrations in engineering applications if often unwanted and in many cases difficult to model. Self-excited vibrations in mechanical engineering systems are in general unwanted and sometimes dangerous.