• Structural Engineering and Mechanics
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• 제25권1호
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• pp.1-20
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• 2007

Dynamic behaviors of the contact surface between ball and raceway in a guideway mechanism vary with the applied loads and hence affect the mechanical responses of machine tools. The study aims to investigate the nonlinear characteristics of dynamic behaviors at the rolling contact interface in linear guideway mechanisms. Firstly, analytical method was introduced to understand the contact behaviors based on Hertz contact theory in a point-to-point way. Then, the finite element approach with a three-dimensional surface-to-surface contact model and appropriate contact stiffness was developed to study the dynamic characteristics of such linear guideways. Finally, experiments with modal test were conducted to verify the significance of both the analytical and the numerical results. Results told that the finite element approach may provide significant predictions. The study results also concluded that the current nonlinear models based on Hertz's contact theory may accurately describe the contact characteristic of a linear guideway mechanism. In the modal analysis, it was told that the natural frequencies vary a little with different loading conditions; however, the mode shapes are changed obviously with the magnitude of applied loads. Therefore, the stiffness of contact interface needs to be properly adjusted during simulation which may affect the dynamic characteristics of the machine tools.

• 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.

• 대한조선학회논문집
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• 제44권6호
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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.

• Journal of Mechanical Science and Technology
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• 제19권spc1호
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• pp.422-428
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• 2005

In this paper, the contact force between two colliding bodies is modeled by using Hertz's force-displacement law and nonlinear damping function. In order to verify the appropriateness of the proposed contact force model, the drop type impact test is carried out for different impact velocities and different materials of the impacting body, such as rubber, plastic and steel. In the drop type impact experiment, six photo interrupters in series close to the collision location are installed to measure the velocity before impact more accurately. The characteristics of contact force model are investigated through experiments. The parameters of the contact force model are estimated using the optimization technique. Finally the estimated parameters are used to predict the impact force between two colliding bodies in opening action of the magnetic contactor, a kind of switch mechanism for switching electric circuits.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2000년도 춘계학술발표대회 논문집
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• pp.38-42
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• 2000

In this study, the low velocity impact behavior of the composite laminates has been described by using 3 dimensional nonlinear finite elements. To describe the geometric nonlinearity due to large deformation, the dynamic contact problem is formulated using the exterior penalty finite element method on the base of Total Lagrangian formulation. The incremental decomposition is introduced, and the converged solution is attained by Newton-Raphson Method. The Newmark's constant-acceleration time integration algorithm is used. To make verification of the finite element program developed in this study, the solution of the nonlinear static problem with occurrence of large deformation is compared with ABAQUS, and the solution of the static contact problem with indentation is compared with the Hertz solution. And, the solution of low velocity impact problem for isotropic material is verificated by comparison with that of LS-DYNA3D. Finally the contact force of impact response from the nonlinear analysis are compared with those from the linear analysis.

• Steel and Composite Structures
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• 제49권3호
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• pp.281-291
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• 2023

Due to the fact that the nonlinear low-velocity impact response of graphene platelets reinforced metal foams (GPLRMF) doubly curved shells have not been investigated in the existing works, this paper aims to solve this issue. Using Reddy's high-order shear deformation theory (HSDT), the nonlinear governing equations of GPLRMF doubly curved shells are obtained by Euler-Lagrange method, discretized by Galerkin principle, and solved by the fourth-order Runge-Kutta method to obtain the impact force and central deflection. The nonlinear Hertz contact law is applied to determine the contact force. Finally, the impacts of graphene platelets (GPLs) distribution pattern, porosity distribution form, porosity coefficient, damping coefficient, impact parameters (radius and initial velocity), GPLs weight fraction, pre-stressing force and different shell types on the low-velocity impact curves are analyzed. It can be found that, among the four shell structures, the impact resistance of spherical shell is the best, while that of cylindrical shell is the worst.

• 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.

• Structural Engineering and Mechanics
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• 제62권2호
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• pp.179-196
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• 2017

The paper focuses on dynamic analyses of a series of simply-supported symmetric composite steel-concrete bridges loaded by an ICE-3 train moving at high speeds up to 300 km/h. The series includes five bridges with span lengths ranging from 15 m to 27 m, with repeatable geometry of the superstructures. The objects, designed according to Polish standards valid from 1980s to 2010, are modelled on the bridges serviced on the Central Main Line in Poland since 1980s. The advanced, two-dimensional, physically nonlinear model of the bridge-track structure-high-speed train system takes into account unilateral nonlinear wheel-rail contact according to Hertz's theory and random vertical track irregularities equal for both rails. The analyses are focused on the influence of random track irregularities on dynamic response of composite steel-concrete bridges loaded by an ICE-3 train. It has been pointed out that certain restrictions on the train speed and on vertical track irregularities should be imposed.

• Steel and Composite Structures
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• 제52권6호
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• pp.609-620
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• 2024

The impact problem of imperfect beams is crucial in engineering fields such as water conservancy and transportation. In this paper, the low velocity impact of graphene reinforced metal foam beams with geometric defects is studied for the first time. Firstly, an improved Hertz contact theory is adopted to construct an accurate model of the contact force during the impact process, while establishing the initial conditions of the system. Subsequently, the classical theory was used to model the defective beam, and the motion equation was derived using Hamilton's principle. Then, the Galerkin method is applied to discretize the equation, and the Runge Kutta method is used for numerical analysis to obtain the dynamic response curve. Finally, convergence validation and comparison with existing literature are conducted. In addition, a detailed analysis was conducted on the sensitivity of various parameters, including graphene sheet (GPL) distribution pattern and mass fraction, porosity distribution type and coefficient, geometric dimensions of the beam, damping, prestress, and initial geometric defects of the beam. The results revealed a strong inhibitory effect of initial geometric defects on the impact response of beams.

• 한국항공우주학회지
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• 제30권7호
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• pp.44-50
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• 2002

본 논문에서는 저속충격을 받는 복합재 샌드위치 평판의 동적 거동에 관한 연구를 수행하였다. 접촉 하중의 산출을 위해서 Hertz의 접촉법칙을 새로이 수정하는 방법을 제시했는데, 지수를 줄이는 방법과 심재의 두께방향의 탄성계수의 값을 줄여 등가 탄성계수를 계산하는 방법을 사용했다. 접촉하중을 산출하는 비선형 방정식은 Newton-Raphson 방법을 사용하여 계산하였고, 시간적분에는 Newmark-beta 방법을 사용하였다. 이러한 기법과 18절점 가정변형률 솔리드 요소를 적용하여 저속충격 해석용 유한요소 프로그램을 개발했다. 이 프로그램을 이용하여 다양한 복합재 샌드위치 평판의 저속충격에 대한 동적 거동을 해석하였다. 제안된 접촉법칙을 적용한 해석결과를 분석하여 볼 때, 대부분의 경우에서 접촉하중과 접촉시간이 실험결과와 대체로 일치함을 확인하였다.