• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.703-713
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• 2001

Derivation procedures of exact dynamic stiffness matrices of thin-walled straight beams subjected to eccentrically axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of displacement parameters are exactly derived and finally exact stiffness matrices are determined using element force-displacement relationships. The natural frequencies of nonsymmetric thin-walled straight beams are evaluated and compared with analytical solutions or results by thin-walled beam element using the cubic Hermitian polynomials and ABAQU's shell elements in order to demonstrate the validity of this study.

• Transactions of the Korean Society of Automotive Engineers
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• v.10 no.4
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• pp.216-222
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• 2002

Brake Moan is a laud and strong noise occurring at any vehicle speed over 2 mph as a low frequency in below 600Hz. In this study, we targeted to shift the unstable mode that causes the brake moan from the moats frequency range to sufficiently higher frequency range to avoid the moan phenomenon. We simulated the finite element model and found out the nodes in which the brake moan occurs the most and we regarded the boundary and its relationship between the brake pad and the rotor as a spring coefficient k. With the binary set of the spring coefficient k, we finally used genetic algorithm (GA) to get the optimal topology of the brake pad and its shape to avoid the brake moan. The final result remarkably shows that genetic algorithm can be used in topology optimization procedures requiring complex eigenvalue problems.

• Journal of KSNVE
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• v.10 no.5
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• pp.800-805
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• 2000

To determine the modal matrix and modal frequency of engine mount system, we most solve so-called eigen-value problem. However eigen-value problem of engine mount system with hydraulic mount can not be solved by general eigne-analysis algorithm because the properties of hydraulic mount vary with frequency. so in this paper the method for modal analysis of rigid body motions of an engine supported by hydraulic mount is proposed. Natural frequencies and mode shapes of this nonlinear system are obtained by using complex exponential method and Laplace transformation method. In time domain, impulse response functions are calculated by (two-sided) discrete inverse Fourier Transformation of forced frequency response functions achieved by Laplace transformation of the differential equation of motion. Considering the fact that frequency response functions synthesized by modal parameters form proposed method are in good agreement with original FRFs, it is proved that the proposed method is very efficient and useful for the analysis of eigne-value problem of hydraulic engine mount system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.320-325
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• 2006

The phenomenon of squeal in disc brakes has been, and stin is, a problem for the automotive industry. Extensive research has been done in an attempt to understand the mechanisms that cause it and in developing design procedures to reduce it to make vehicles more comfortable. In this paper, the study on squeal noise of disc brake is performed using complex eigen-value analysis, The first part describes the chassis-dynamometer and the testing procedure, and second part explains how the analysis is performed and shows some of the results from typical squeal tests. Finally, to reduce squeal nose of disc brake is investigated by the effects of brake design parameter.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.630-634
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• 2001

Predicting brake squeal noise in design stage can be beneficial to reducing the expense of development. In this paper, the possibility of pre-estimating squeal phenomena of a disc brake system was investigated. To preestimate squeal phenomena, complex eigenvalue analysis was performed for brake system. The evaluation of noise dynamometer test verified the prediction and it corresponded with the result of complex eigenvalue analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.1
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• pp.98-105
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• 2010

Squeal, a kind of self-excited vibration, is generated by the friction between the disc and the friction materials. It occurs at the ending stage of the braking process, and radiates and audible frequency range of 1 kHz to 10 kHz. Squeal is generated from unstability because of the coupling between the translation and rotation of the system. This instability is caused by the follower force and follower force is normal component of the friction force. In this paper modal analysis of wheel brake system was performed in order to predict the squeal phenomenon. It was shown that the prediction of system instability is possible by FEM. A finite element model of that brake system was made. Some parts of a real brake was selected and modeled. Modal analysis method performs analyses of each brake system component. Experimental modal analysis was performed for each brake components and experimental results were compared with analytical results from FEM. To predict the dynamic unstability of a whole system, the complex eigenvalue analysis for assembly modeling of components confirmed by modal analysis is performed. The finite element models of the disk brake assembly have been constructed, and the squeal noise problems have been solved by complex eigenvalue analysis. The complex eigenvalue analysis results compared with real train test.

• Journal of the Korean Society for Railway
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• v.16 no.4
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• pp.253-261
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• 2013

According to the measured results of KTX brake squeal noise in this study, high level brake noise occurred in a wide frequency range, 100~18,000Hz. To identify the sources of the brake squeal noise, unstable vibration modes due to brake disc/pad interaction were analyzed under various conditions by the finite element method. Complex eigenvalues for a brake unit with a disc and four pads were obtained. It was found that the real parts of the complex eigenvalues, that is, unstable vibration modes, were closely related to friction coefficients, pressure on the brake cylinders, elastic moduli of the components, and other conditions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.11
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• pp.930-936
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• 2008

This paper studies the effect of pad at initial stage and wear during braking on the dynamic contact pressure distribution. Wear is influenced by variable factor (contact pressure, sliding speed, radius, temperature) during dynamic braking and variation in contact pressure distribution. Many researchers have conducted complex eigenvalue analysis considering wear characteristic with Lim and Ashby wear map. The conventional analysis method is assumed the pad has smooth and flat surfaces. The purpose of this paper is to validate that wear rate induced by braking is considered for the precise squeal prediction. After obtaining pad wear from experiment, it is incorporated with FE model of brake system. Finally, the comparisons in fugitive nature of squeal will be carried out between the complex eigenvalue analysis and noise dynamometer experiment.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.1 s.94
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• pp.72-80
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• 2005

Recent studies have dealt with brake squeal in terms of the coupled vibration of brake component parts. In this paper, we assemble the mode models derived from FE analysis of the individual components of the drum brake system into the system model by considering the friction interaction of the lining and drum at the interface. The validity of the component models are backed up by the experimental confirmation work. By scrutinizing the real parts of the complex eigen-values of the system, the unstable modes, which may be strong candidate sources of squeal noise, are identified. Mode participation factors are calculated to examine the modal coupling mechanism. The model predictions for the unstable frequencies pointed well the actual squeal noise frequencies measured through field test. Sensitivity analysis is also performed to identify parametric dependency trend of the unstable modes, which would indicate the direction for the squeal noise reduction design. Finally, reduction of the squeal noise tendency through shape modification is tried.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1120-1124
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• 2007

Recently in the automotive brake industry brake squeal noise has become one of the top automotive quality warranty issues. The contact pressure is used to predict friction coupling in the brake squeal analysis. The formulation of friction coupling has performed by nonlinear static analysis prior to the complex eigenvalue analysis. This paper proposes a validation methodology of squeal analysis using modal testing and contact analysis and examines the effect of predicted contact pressure that leads to the discrepancy between unstable complex mode and squeal frequency. This studies compose a three step validation process : examining the modal characteristics of component and assembly loaded contact pressure using modal testing and FEM analysis and verifying the contact pressure distribution using nonlinear static analysis and experiment. Finally, the unstable modes from complex eigenvalue analysis and realistic squeal frequency from the noise dynamometer are investigated.