• Transactions of the Korean Society of Automotive Engineers
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• v.18 no.3
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• pp.127-132
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• 2010

Eigensolutions associated with self-excited vibration of disc brake system can be obtained by complex eigenvalue analysis. The eigenvalue sensitivity to change in contact stiffness can be used to demonstrate stability criteria and eigenvalue veering. Dynamic instability on eigenvalue loci with respect to the variation of contact stiffness is found to be related to mode interaction between two adjacent modes. This modal interaction can be effectively shown by mode shape visualization. This paper presents the methodology to construct the mode shape of disc brake system where a disc and two brake pads are coupled with contact stiffness.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.10
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• pp.1074-1080
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• 2009

A method for determining the geometric stability characteristics of a brake corner module (BCM) is presented. Since disc brake "squeal" noise typically occurs at unstable resonant frequencies of a system, the likelihood of disc brake squeal for a particular design can be determined. Finite element methods are used to derive complex eigenvalue for a brake corner module. Some unstable modes calculated by finite element methods correspond to squeal noise data. Through kinetic energy participation analysis for each part of BCM, we can efficiently predict squeal noise data.

• 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.

• Steel and Composite Structures
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• v.48 no.3
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• pp.293-303
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• 2023

In this paper, geometrically nonlinear free vibration analysis of Mindlin viscoelastic plates with various geometrical and material properties is studied based on the Von-Karman assumptions. A novel solution is proposed in which the nonlinear frequencies of time-dependent plates are predicted according to the nonlinear frequencies of plates not dependent on time. This method greatly reduces the cost of calculations. The viscoelastic properties obey the Boltzmann integral law with constant bulk modulus. The SHPC meshfree method is employed for spatial discretization. The Laplace transformation is used to convert equations from the time domain to the Laplace domain and vice versa. Solving the nonlinear complex eigenvalue problem in the Laplace-Carson domain numerically, the nonlinear frequencies, the nonlinear viscous damping frequencies, and the nonlinear damping ratios are verified and calculated for rectangular, skew, trapezoidal and circular plates with different boundary conditions and different material properties.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.3
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• pp.325-331
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• 2013

In this study, a complex eigenvalue analysis is implemented to verify the unstable mode of a brake system using ABAQUS software. The component participation factors and component modal participation factors are used to analyze the total contributions from each component and each component mode to a particular unstable system mode. This study shows that the 1.4-kHz unstable system mode comes from mode coupling between the 2nd nodal diametric mode and 3rd lateral axial mode (LAM) in the baseline model. A sensitivity analysis with a linking index is performed to prevent the mode coupling of the component modes. This linking index analysis shows the optimum mass loading position to move away the natural frequency of the 3rd LAM, which contributes to the unstable mode. Finally, a complex eigenvalue analysis is implemented with mass loading in the tie bar position, and no unstable system mode is generated in the low-frequency range (below 2 kHz).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.597-600
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• 2004

A two-degree-of-freedom out-of-plane model with contact stiffness is presented to describe dynamical interaction between the pad and disc of a disc brake system. It is assumed that the out-of-plane motion of the system depends on the friction force acting along the in-plane direction. Dynamic friction coefficient is modelled as a function of both in-plane relative velocity and out-of-plane normal force. When the friction coefficient depends only on the relative velocity, the contact stiffness has the role of negative stiffness. The results of stability analysis show that the stiffness of both pad and disc are equally important. Complex eigenvalue analysis is conducted for the case that the friction coefficient is also dependent on the normal force. The results further verify the importance of the stiffness. It has also been found that increasing the gradient of friction coefficient with respect to the normal force makes the system more unstable. Nonlinear analysis is also performed to demonstrate various responses. Comparing the responses with experimental data has shown that the proposed model may qualitatively well represent a certain type of brake noise.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.10a
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• pp.546-552
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• 2012

This paper is a study on squeal noise simulation under the consideration of temperature and pressure dependent material properties of friction material. For this, data of pressure and temperature dependent material properties of lining is achieved by using lining data base and exponential curve fit. Complex eigenvalue analysis is performed for predicting squeal noise frequency and instability and chassis dynamo test is performed for achieving squeal noise frequency, sound pressure level, occurrence temperature & pressure. Initial multi models are composed for considering complex interface conditions such as pad ear-clip, piston-housing and guide pin-torque member. The simulation result of base models is compared with the test result. Squeal noise simulation under the consideration of temperature and pressure dependent material properties of friction material is performed and analyzed using multi models. And additional condition is disc material property variation. Entire simulation conditions are combined and analyzed. Finally, this paper proposes direction of the warm squeal noise model.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.10a
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• pp.264-270
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• 2011

The goal of this study is a stability evaluation through eigenvalue and rotor dynamics analysis of the vacuum pump. The vacuum pump used is a roots type pump, one of the dry middle vacuum pumps, is necessary at the procedure to produce semiconductor and display. The eigenvalue evaluation is solved by numerical analysis through using Modal test and 2D 3D models. Both the experiment and the analysis result are similar, the analysis result using 2D is more oculate the 3D model comparing with test result. So rotor dynamic evaluation is performed through using 2D model. Rotor dynamic evaluation used the campbell diagram and root locus map which were acquired by complex eigenvalue analysis. And we checked minimum clearance of vacuum pump composition between two rotors through unbalance response analysis. Thus, vacuum pump, the target object of this study, was evaluated to be operated stably.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.8 s.113
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• pp.830-839
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• 2006

The phenomenon of squeal noise in the disk brake system has been, and still is, a. problem for the automotive industry. Extensive research has been carried out in an attempt to understand the mechanism that causes squeal noise and In developing design procedures to reduce squeal noise to make vehicles more comfortable. In this paper, the study on the analysis of squeal noise is performed by using computer aided engineering to design the anti-squeal noise disk brake system. The first part describes the chassis dynamometer and the testing procedure, and second part explains the finite element model and the complex eigenvalue analysis. Finally, it is shown that the proposed squeal noise analysis could be useful to investigate the design parameters that affect the squeal noise characteristics.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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• pp.129-139
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• 2000

The problem of eigenvalue and eigenvector is obtained from a V-notched crack in pseudo-isotropic dissimilar materials by the traction free boundary and the perfect bonded interface conditions. The complex stress function is assumed as the two-term William's type. The eigenvalue is solved by a commercial numerical program, MATHEMATICA to discuss stress singularities for V-notched cracks in pseudo-isotropic dissimilar materials. The RWCIM(Reciprocal Work Contour Integral Method) is applied to the determination to eigenvector coefficients associated with eigenvalues. The RWCIM algorithm is also coded by the MATHEMATICA.