• Title/Summary/Keyword: Hertzian contact Theory

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A Study on the Shape Design of Wheel-Rail for Rolling Stock (철도차량용 휠과 레일의 형상설계에 관한 연구)

  • Seong, Gi-Deuk;Yang, Won-Ho;Jo, Myeong-Rae;Heo, Seong-Pil
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.23 no.11 s.170
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    • pp.2033-2039
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    • 1999
  • One of the main causes of severe wear or crack initiation in wheel and rail is the contact stress due to wheel-rail contact. In this paper, the shape design based on more reasonable contact stress analysis rather than a general Hertzian contact theory is investigated in order to reduce the contact stress. The optimal design is performed using the simple 2-D finite element model and its results are verified by 3-D finite element analysis.

Determination of Flexible Tool Path in Curved Surface Finishing Based on Contact Analysis (곡면 다듬질에서 접촉해석에 근거한 유연공우 경로 설정)

  • Cho, Sung-San;Lee, Seung-Yeong;Ryu, Yong-Kyoon
    • Journal of the Korean Society for Precision Engineering
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    • v.17 no.11
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    • pp.69-74
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    • 2000
  • Roughness of curved surfaces finished with flexible tools depends on the tool/work contact pressure and area. In this study, non-Hertzian closely conforming elastic contact theory is employed to analyze the tool/work contact and to generate a tool path producing a constant pressure at initial contact points. Finishing experiments on curved surfaced are conducted using the tool path. For comparison, curved surface finishing is also performed along the tool path producing a constant tool/work interference depth. It is demonstrated that the tool path of constant contact pressure improves the finished surface roughness.

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Nonlinear Vibration Analysis of Porous Thin Plate with Wire Impact Damping (와이어 충돌감쇠를 갖는 다공성 박판의 비선형 진동 해석)

  • 김성대;김원진;이부윤;이종원
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2001.11a
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    • pp.341-348
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    • 2001
  • In this study, nonlinear vibration analysis of the cylindrical orthotropic porous thin plate under V-shaped tension distribution with wire impact damping is considered. We make dynamic model of the plate under the tension using commercial FEM code and reduce the number of its degrees of freedom using dynamic condensation. The dynamic model of wire is obtained as lumped mass model from string equation. And then we analyze the nonlinear vibration of the plate including the impact phenomenon between the plate and the wire using the reduced mass and stiffness matrices of the plate and lumped model of the wire. The contact phenomenon between them can be described by impact contact elements composed of contact stiffness coefficients from Hertzian contact theory and contact damping coefficients from restitution coefficient between them. And we discussed the results of nonlinear vibration analysis for variations of their design parameters.

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Experimental Study on Simple Dimensionless Parameter in Higher Pair (점접촉에서 단무차원매개변수에 관한 실험적 연구)

  • 김경모
    • Journal of the Korean Society of Safety
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    • v.9 no.3
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    • pp.34-40
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    • 1994
  • It is important to have exact informations on the real contact mechanism between spheres and rough plates under various normal loads, sphere diameters and combined surface roughnesses. Most previous papers have proposed the questions of the errors which might be incurred when the Hertzian theory is used to calculated the contact deformation and the contact pressure of practical higher pair. So, this study investigates the real contact deformation between a rough sphere and a rough plate by three experimental methods far from any assumptions and theorems. The soot coating method among them is used successfully. Accordingly, this study presents the simple dimensionless parameter to predict such errors to occur in the design of high pair members and to govern the real mechanism of two-body higher pair.

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Vibration Analysis and Its Application of a Linear Motion Guide Supported by Rolling Ball Bearings (볼 베어링을 이용하는 직선 운동 가이드의 진동 해석 및 응용)

  • Choi Jae Seok;Yi Yong-sub;Kim Yoon Young;Lee Dong Jin;Lee Sung Jin;Yoo Jeonghoon
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.7 s.238
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    • pp.955-963
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    • 2005
  • This research investigates dynamic characteristics of a linear motion (LM) guide through a experimental result and theoretical analysis. The stiffness in the LM guide is determined by the preloading due to the minus clearance between the ball bearing and the contact surface and it can be derived by Hertzian contact theory and the nonlinear motion of equation. The vibration analysis is performed using Lagrange equations and its result agrees with the experiment result. Using the sensitivity analysis on design parameters such as the contact angles of ball bearings and the eccentricity of mass center, the variation of the natural frequencies can be predicted.

Experimental Verification of Analysis Model of the Shadow Mask with Damping Wires (댐핑 와이어를 갖는 새도우 마스크의 해석모델에 대한 실험적 검증)

  • 김성대;김원진;이종원
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.05a
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    • pp.460-465
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    • 2002
  • The nonlinear vibration of the CRT shadow mask is analyzed in consideration of the V-shaped tension distribution and the effect of wire impact damping. The reduced order FEM model of the shadow mask is obtained from dynamic condensation for the mass and stiffness matrices. Damping wire is modeled using the lumped parameter method to effectively describe its contact interactions with the shadow mask. The nonlinear contact-impact model is composed of spring and damper elements, of which parameters are determined from the Hertzian contact theory and the restitution coefficient, respectively. The analysis model of the shadow mask with damping wires is experimentally verified through impact tests of shadow masks performed in a vacuum chamber. Using the validated analysis model of the shadow mask with damping wires, the‘design of experiments’technique is applied to search fur the optimal damping wire configuration so that the vibration attenuation of the shadow mask is maximized.

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Experimental Verification of Analysis Model of the Shadow Mask with Damping Wires (댐핑 와이어를 갖는 새도우 마스크의 해석모델에 대한 실험적 검증)

  • 김성대;김원진;이종원
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.12 no.9
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    • pp.731-737
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    • 2002
  • Nonlinear vibration of the CRT shadow mask with impact damping wires is analyzed in consideration of the mask tension distribution and the effect of wire impact damping. A reduced order FEM model of the shadow mask is obtained from dynamic condensation of the mass and stiffness matrices, and damping wire is modeled using the lumped parameter method to effectively describe its contact interactions with the shadow mask. The nonlinear contact-impact model is composed of spring and damper elements, of which parameters are determined from the Hertzian contact theory and the restitution coefficient, respectively. The analysis model of the shadow mask with damping wires is experimentally verified through impact tests of shadow masks performed in a vacuum chamber.

Nonlinear Vibration Analysis of Thin Perforated Plate with Wire Impact Damping (와이어 충돌감쇠를 갖는 다공성 박판의 비선형 진동 해석)

  • 김성대;김원진;이부윤;이종원
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.12 no.8
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    • pp.639-647
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    • 2002
  • The nonlinear vibration of the thin perforated plate is analyzed in consideration of the V-shaped tension distribution and the effect of wire impact damping. The reduced order FEM model of the tension plate is obtained from dynamic condensation for the mass and stiffness matrices. Tension wire is modeled using the lumped parameter method to effectively describe its contact interactions with the plate. The nonlinear contact-impact model is composed of spring and damper elements, of which parameters are determined from the Hertzian contact theory and the restitution coefficient, respectively. From the evaluation of the computational accuracy and computation time for the deduced impact stiffness and damping coefficient, we determined proper values for the simulation works, accounting for the computational accuracy as well as the computational efficiency. Finally we discussed the results of nonlinear nitration analysis for variations of their design parameters.

Prediction of Rolling Noise of Korean Train Express Using FEM and BEM (FEM과 BEM을 이용한 한국형 고속전철의 전동소음 예측)

  • 김관주
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2001.11b
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    • pp.555-564
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    • 2001
  • Wheel-rail noise is normally classified into three catagories : rolling, squeal and impact noise. In this paper, rolling noise caused by the irregularity between a wheel and rail is analysed as follows: The irregularity between the wheel and rail is assumed as combination of sinusoidal profiles. Wheel-rail contact stiffness is linearized by using Hertzian contact theory, and then contact force between the wheel and rail is calculated. Vibration of the rail and wheel is calculated theoretically by receptance method or FEM depending on the geometry of wheel or rail for the frequency range of 100-5000Hz, important for noise generation. The radiation caused by those vibration is computed by BEM. To verify this analysis tools, rolling noise is calculated by preceding analysis steps using typical roughness data and it is compared with experimental rolling noise data. This analysis tools show reasonable results and used for the prediction of KTX rolling noise.

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Study on the Rolling Noise Model Using an Analysis of Wheel and Rail Vibration Characteristics (철도 차륜 및 레일 진동 특성 해석을 통한 전동 소음 모델 연구)

  • Jang, Seungho;Ryue, Jungsoo
    • Journal of the Korean Society for Railway
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    • v.16 no.3
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    • pp.175-182
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    • 2013
  • Rolling noise is an important source of noise from railways; it is caused by wheel and rail vibrations induced by acoustic roughness at the wheel/rail contact. To reduce rolling noise, it is necessary to have a reliable prediction model that can be used to investigate the effects of various parameters related to the rolling noise. This paper deals with modeling rolling noise from wheel and rail vibrations. In this study, the track is modeled as a discretely supported beam by regarding concrete slab tracks, and the wheel vibration is simulated by using the finite element method. The vertical and lateral wheel/rail contact forces are modeled using the linearized Hertzian contact theory, and then the vibration responses of the wheel and rail are calculated to predict the radiated noise. To validate the proposed model, a field measurement was carried out for a test vehicle. It was found that the predicted result agrees well with the measured one, showing similar behavior in the frequency range between 200 and 4000 Hz where the rolling noise is prominent.