• Title/Summary/Keyword: Hertz Contact Theory

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Pressure Analysis of Sterntube after Bush Bearing Considering Elastic Deflection of Misaligned Journal and Partial Slope of Bearing Bush (탄성 변형된 저어널의 편심과 베어링 부시의 부분경사를 고려한 선미관 후부 베어링의 압력분포 해석)

  • Choung, Joon-Mo;Choe, Ick-Heung
    • Journal of the Society of Naval Architects of Korea
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    • v.44 no.6
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    • pp.666-674
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    • 2007
  • It is very important to estimate static squeezing pressure distributions for lining material of sterntube after bearing at dry dock stage since the maximum squeezing pressure value can be one of the significant characteristics representing coming navigation performances of the propulsion system. Moderate oil film pressure between lining material and propulsion shaft is also essential for safe ship service. In this paper, Hertz contact theory is explained to derive static squeezing pressure. Reynolds equation simplified from Navier-Stokes equation is centrally differentiated to numerically obtain dynamic oil film pressures. New shaft alignment technology of nonlinear elastic multi-support bearing elements is also used in order to obtain external forces acting on lining material of bearing. For 300K DWT class VLCC with synthetic bush of sterntube after bearing, static squeezing pressures are calculated using derived external forces and Hertz contact theory. Optimum partial slope of the after bush is presented by parametric shaft alignment analyses. Dynamic oil film pressures are comparatively evaluated for partially bored and unbored after bush. Finally it is proved that the partial slope can drastically reduce oil film pressure during engine running.

Dynamic Analysis of Engine Valve Train with Flexible Multibody Model Considering Contact between Components (부품간의 접촉을 고려한 유연체모델을 이용한 엔진 밸브트레인의 동특성 해석)

  • Hwang, Won-Gul;Sung, Won-Suk;Ahn, Ki-Won
    • Transactions of the Korean Society of Automotive Engineers
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    • v.19 no.1
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    • pp.125-132
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    • 2011
  • The dynamic characteristics of valve train are responsible for the dynamic performances of engine. We derived the equation of motion for 6 degrees of freedom model of the valve train. Computer model is also developed with flexible multibody model considering contact between components. The simulation results with these two models are compared with experimental results. We investigated the effect of the two spring models, TSDA (Translational Spring Damper Actuator) element and flexible body model, on the valve behavior and spring force. It is found that the dynamic behavior of the two models are not very different at normal operational velocity of the engine. By modeling contact between cam and tappet, the stress distributions of the cam were found. Using stress distribution obtained, contact width and contact stresses of the cam surface were calculated with Hertz contact theory.

Analytical Theory of Ball Bearing Considering Waviness of Rolling Elements (구름요소의 Waviness 를 고려한 볼베어링 해석 이론)

  • 정성원;장건희
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.11 no.7
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    • pp.275-286
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    • 2001
  • The research presents an analytical theory to calculate the characteristics of the bal bearing with waviness in its rolling elements considering the centrifugal force and gyroscopic moment of bal. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. and the waviness of rolling elements is modeled by sinusoidal function to calculate the contact force at each ball. The numerical solutions of governing equation of berating due to waviness are calculated by using the Newton-Raphson method. The accuracy of the research is validated by comparing the contact force. contact angle in case of considering the centrifugal force and gyroscopic moment of bal and the contact force and vibration frequencies in cases of considering waviness with the prior researches respectively. It investigates the stiffness, contact force. displacement and vibration frequencies of the ball bearing considering not only the centrifugal force and gyroscopic moment of ball but also the waviness of the rolling elements.

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A Study on the Vibration and Acoustic Radiation from an Elastic Free- Free Beam due to a Steel Ball Impact (강구의 충돌에 의한 양단자유 보의 진동 및 음향 방사에 관한 연구)

  • 박홍철;이효근;박윤식
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.9
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    • pp.1615-1626
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    • 1992
  • In this study, vibrations and resulting acoustic radiations from an elastic beam impacted by a steel ball were studied theoretically and experimentally. First the transverse vibrations of free-free elastic beams are analysed with modal analysis technique. The impact forces are modeled with the Hertz's theory and the contanct duration is compared with the measured values. Also the calculated beam vibrations are verified with the experimental results. Then the acoustic radiations due to the beam vibration are studied numberically and experimentally. The acousticpressure is calculated assuming the beam has an elliptical cross-section. The predicted acoustic pressure is compared with the measured value. It was found that both the predicted beamvibrations using the Hertz's theory and the estimated acoustic pressure under the assumption of an elliptical cross- section are in very good agreements with the measured values.

Analysis of Particle Packing Process by Contact Model in Discrete Element Method (입자 패킹 공정에 대한 접촉모델별 이산요소법 해석)

  • Lyu, Jaehee;Park, Junyoung
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.18 no.3
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    • pp.59-65
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    • 2019
  • In many industries, particle packing is adopted quite frequently. In the particle packing process, the Discrete Element Method (DEM) can analyze the multi-collision of particles efficiently. Two types of contact models are frequently used for the DEM. One is the linear spring model, which has the fastest calculation time, and the other is the Hertz-Mindlin model, which is the most frequently used contact model employing the DEM. Meanwhile, very tiny particles in the micrometer order are used in modern industries. In the micro length order, surface force is important to decreased particle size. To consider the effect of surface force in this study, we performed a simulation with the Hertz-Mindlin model and added the Johnson-Kendall-Roberts (JKR) theory depicting surface force with surface energy. In addition, three contact models were compared with several parameters. As a result, it was found that the JKR model has larger residual stress than the general contact models because of the pull-off force. We also validated that surface force can influence particle behavior if the particles are small.

Dynamic Wheel/Rail Contact Force due to Rail Irregularities (레일의 상하방향 불규칙성에 의한 차륜과 레일의 동 접촉력)

  • 이현엽
    • Journal of KSNVE
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    • v.8 no.4
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    • pp.616-622
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    • 1998
  • An analytical method has been developed to estimate the dynamic contact force between wheel and rail when trains are running on rail with vertical irregularities. In this method, the effect of Hertzian deformation at the contact point is considered as a linearized spring and the wheel is considered as an sprung mass. The rail is modelled as a discretely-supported Timoshenko beam, and the periodic structure theory was adopted to obtain the driving-point receptance. As an example, the dynamic contact force for a typical wheel/rail system was analysed by the method developed in this research and the dynamic characteristics of the system was also discussed. It is revealed that discretely-supported Timoshenko beam model should be used instead of the previously used continuously-supported model or discretelysupported Euler beam model, for the frequency range above several hundred hertz.

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