A Reduced-Order Model for Complex Modes of Brake Squeal Model and Its Application to a Flexible Pin-on-Disc System

Brake squeal is often analytically studied by a complex eigenvalue analysis of linearized models of the brake assembly that is usually quite large. In this paper, a method for determining those frequencies having the most effect on the pair of coupling frequencies that saves much time is put forward and a reduced-order model is presented based on the complex modes theory. The reduced-order model is proved to be effective when applied to a flexible pin-on-disc system; even damping and nonlinearity are taken into consideration. This reduced-order model can predict the onset of squeal as well as the squeal frequency with sufficient accuracy and largely reduced amount of calculation and gives us a practical guide to perform design optimization in order to reduce brake squeal.

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Reduced-Order Model with an Artificial Neural Network for Aerostructural Design Optimization

Journal of Aircraft ◽

10.2514/1.c032062 ◽

2013 ◽

Vol 50 (4) ◽

pp. 1106-1116 ◽

Cited By ~ 17

Author(s):

Kyung Hyun Park ◽

Sang Ook Jun ◽

Sung Min Baek ◽

Maeng Hyo Cho ◽

Kwan Jung Yee ◽

...

Keyword(s):

Neural Network ◽

Artificial Neural Network ◽

Design Optimization ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Artificial Neural

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Reduced order model assisted evolutionary algorithms for multi-objective flow design optimization

Engineering Optimization ◽

10.1080/03052151003789841 ◽

2011 ◽

Vol 43 (1) ◽

pp. 97-114 ◽

Cited By ~ 5

Author(s):

Hongtao Sun ◽

Michael Schäfer

Keyword(s):

Evolutionary Algorithms ◽

Design Optimization ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Multi Objective

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Control of Asymmetric Systems Using Complex Modes

13th Biennial Conference on Mechanical Vibration and Noise: Modal Analysis, Modeling, Diagnostics, and Control — Analytical and Experimental ◽

10.1115/detc1991-0385 ◽

1991 ◽

Author(s):

G. W. Fan ◽

H. D. Nelson

Keyword(s):

Normal Modes ◽

Original System ◽

High Order ◽

Reduced Order Model ◽

Order System ◽

Matrix Transformations ◽

Linear Quadratic ◽

Order Model ◽

Reduced Order ◽

Complex Modes

Abstract The complex modal approach is introduced for the optimal vibration control (Linear Quadratic Regulator) of high-order nonsymmetric discrete systems. An LQ regulator is designed based on a reduced-order model obtained by neglecting high-frequency complex modes of the original system. The matrix transformations between physical coordinates and complex coordinates are derived. A 52 degree-of-freedom finite element based rotordynamic system is used for illustration. Simulation results show that an LQ regulator based on a reduced-order system obtained by using normal modes of a high-order system with asymmetric models can possibly destabilize the original system i.e., the spill-over problem (Ulsoy, 1984), however, this problem might be avoided by applying complex modes which provides a more accurate reduced-order model than obtained by normal modes. Comparison of the reduced-order models using normal modes and complex modes is presented. Frequency, time transient and steady state responses of the controlled and uncontrolled systems are also shown.

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Optimal Output Feedback Control of Asymmetric Systems Using Complex Modes

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.2906710 ◽

1993 ◽

Vol 115 (2) ◽

pp. 307-313 ◽

Cited By ~ 6

Author(s):

G. W. Fan ◽

H. D. Nelson ◽

M. P. Mignolet

Keyword(s):

Feedback Control ◽

Output Feedback ◽

Output Feedback Control ◽

High Order ◽

Reduced Order Model ◽

Control Procedure ◽

Order Model ◽

Complex Mode ◽

Reduced Order ◽

Complex Modes

A Linear Quadratic Regulator (LQR)-based least-squares output feedback control procedure using a complex mode procedure is developed for the optimal vibration control of high-order asymmetric discrete system. An LQ Regulator is designed for a reduced-order model obtained by neglecting high-frequency complex modes of the original system. The matrix transformations between physical coordinates and complex mode coordinates are derived. The complex mode approach appears to provide more accurate reduced-order models than the normal mode approach for asymmetric discrete systems. The proposed least-squares output feedback control procedure takes advantage of the fact that a full-state feedback control is possible without using an observer. In addition, the lateral vibration of a high-order rotor system can be effectively controlled by monitoring one single location along the rotor shaft, i.e., the number of measured states can be much less than the number of eigenvectors retained in producing the reduced-order model while acceptable performance of the controller is maintained. The procedure is illustrated by means of a 52 degree-of-freedom finite element based rotordynamic system. Simulation results show that LQ regulators based on a reduced-order model with 12 retained eigenvalues can be accurately approximated by using feedback of four measured states from one location along the rotor shaft. The controlled and uncontrolled transient responses, using various numbers of measured states, of the original high-order system are shown. Comparisons of reduced-order model results using normal modes and complex modes are presented. The spillover problem is discussed for both collocated and noncollocated cases based on this same example.

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