• 한국자동차공학회논문집
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• 제19권1호
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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.

• 한국음향학회지
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• 제6권3호
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• pp.5-16
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• 1987

본 논문에서는 충격으로 인한 점탄성층을 가진 경계가 고정된 원형 평판으로부터의 음압복사에 대해 이론적, 실험적으로 연구한다. 층을 가진 평판의 운동을 모우드 해석법과 회전 관성효과와 전단력에 의한 변형을 고려한 Mindlin 의 평판이론으로부터 구한 고유치를 이용하여 구한다. 탄성구와 평판사이의 접촉력은 Hertz 이론으로 구하고 평판의 진동으로부터 복사되는 음압은 Rayleigh integral에 의해 구한다. 또한 층을 가진 평판으로부터 복사되는 음의 파형과 발생되는 음을 감소시키는 방법을 예측한다.

• 한국공간구조학회논문집
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• 제11권3호
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• pp.77-83
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• 2011

복합적층판은 다른 금속재료에 비해 높은 비강도, 비강성 등의 우수한 역학적 특성을 지니므로 최근 다양한 분야에서 사용하고 있다. 그러나 이러한 복합적층판은 일반 금속재료에 비해 충격에 약하다는 단점이 있다. 이 점을 해결하기 위한 연구는 많은 연구자들에 의해 다양하게 시도되고 있다. 본 연구는 복합적층판에 초기응력을 도입하여 충격거동 특성을 파악한다. 고전적인 이론식인 Hertz의 접촉법칙과 실험식인 Sun과 Tan의 압입법칙을 포함한 유한요소프로그램을 이용하여 복합적층판의 초기응력에 의한 충격거동 특성을 조사한다.

• 소음진동
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• 제11권2호
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• pp.336-345
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• 2001

This research presents a nonlinear model to analyze the ball bearing nitration due to the waviness in a rigid rotor supported by multi-row ball bearings. The waviness of a ball and each races is modeled by the superposition of sinusoidal function, and the position vectors of inner and outer groove radius center are defined with respect to the mass center of the rotor in order to consider five degrees of freedom of a general rotor-bearing system. The waviness of a ball bearing is introduced to these position vectors to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. Numerical results of this research are validated with those of prior researchers. The proposed model can calculate the translational displacement as well as the angular displacement of the rotor supported by the multi-row ball bearings with waviness. It also characterizes the nitration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing. and the sideband frequencies resulting from the waviness interaction.

• 대한기계학회논문집A
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• 제33권11호
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• pp.1217-1224
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• 2009

This paper presents a finite element (FE) analysis of the torsional rigidity of a two-stage cycloid drive. The cycloid disk makes contact with a number of pin-rollers simultaneously and eccentric shafts transmit not only torque of the spur gear stage to the cycloid disk, but also that of the cycloid disk to the output disk. Contacts between the disk and pin-rollers are simplified as linear spring elements, and the bearing of eccentric shaft is modeled as a rigid ring that has frictional contact to the disk and an elastic support. FE analysis for an ideal solid cycloid drive was performed and verified by a theoretical calculation. Accurate contact forces were then estimated by iterating between FE analysis for contact forces and Hertz theory calculations for nonlinear contact stiffness. In addition, torsional rigidity of the cycloid drive is analyzed to show that the bearing and nonlinear Hertz contact theory should be considered in analysis and design of a cycloid drive, which was verified with experiments. Finally, the effects of contact stiffness, bearing stiffness and cycloid disk structural stiffness according to the cycloid disk rotation on the torsional rigidity were investigated.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 I
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• pp.297-303
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• 2001

This research presents an analytical model to characterize the ball bearing vibration due to the waviness in a rigid rotor supported by multi-row ball bearings considering centrifugal force and gyroscopic moment of ball. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. The waviness of ball and races is modeled by the superposition of sinusoidal function and it is introduced to position vectors of race curvature center to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. The accuracy of this research is validated by comparing with the results of the prior researches. It characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing resulting from the waviness interaction.

• 소음진동
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• 제8권4호
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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.

• 한국소음진동공학회논문집
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• 제16권5호
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• pp.441-451
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• 2006

It is known that ball bearings mounted in housing or on shaft are playing a key role to keep it running smoothly. The roundness of a housing bore on which bearing outer ring is mounted with interference has directly affected the running accuracy of bearing. The running accuracy of bearing, therefore, can extend the significant influence to the rotating machinery as well. In this paper, bearing's vibration and fatigue life considering raceway roundness of ball bearing before and after mounted in housing bore are theoretically estimated. To perform analysis, a simple three degrees of freedom model was proposed and then Newton-Raphson iterative method was introduced to be utilized in the analysis. The results show that the vibration magnitude of ball bearing fitted into housing unit is appeared considerably larger than the one of its pre-assembling. And theoretical $L_{10}$ life which ninety percent of the bearing population will endure decreased in about fifty percent.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.112-118
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• 2005

Ball bearings which were fitted between housing and shaft play an important role in rotating shaft system smoothly, Therefore bearing's running accuracy has significant influence on that of rotating machinery. Manufacturing accuracy of bearings as well as that of shaft and housing is main factor to affect bearing running accuracy In this paper, bearing's vibration and fatigue life considering raceway roundness of ball bearing before and after being fitted into housing are theoretically estimated. To perform analysis, a simple three degrees of freedom model was proposed and then these analysis was conducted utilizing the Newton-Raphson iterative method. The results show that vibration magnitude of ball bearing fitted into housing is considerably larger than before assembly, and bearing's theoretical L$_{10}$ fatigue life that ninety percent of the bearing population will endure decreased in about fifty percent.

• 대한기계학회논문집A
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• 제35권8호
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• pp.855-861
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• 2011

본 연구에서는 극박 압연 이론과 6 단 압연기 수식 모델을 이용하여 압연 후 판 형상 예측에 대하여 제안하였다. 폭 방향에서 롤 사이의 접촉 압력과 판과 워크롤 사이의 압연하중은 6 단 압연기의 형상학적 구조와 경계조건을 이용한 수식모델을 통하여 계산된다. 그리고 압연 방향의 압연하중 분포는 Fleck 의 극박 압연 이론을 이용하여 계산하였다. 워크롤의 3 차원 탄성 변형량은 폭 과 압연방향의 압력분포에 의하여 계산된다. 이때, 3 차원 판 형상은 워크롤의 탄성변형에 의하여 얻어진다. 또한 3 차원 판 형상은 극박 압연 실험과 유한요소해석을 통하여 검증하였다.