• 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.

• 대한기계학회논문집A
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• 제29권7호
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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.

• Steel and Composite Structures
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• 제27권3호
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• pp.273-283
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• 2018

Nonlinear low velocity impact response of sandwich beam with laminated composite face sheets and soft core is studied based on Extended High Order Sandwich Panel Theory (EHSAPT). The face sheets follow the Third order shear deformation beam theory (TSDT) that has hitherto not reported in conventional EHSAPT. Besides, the two dimensional elasticity is used for the core. The nonlinear Von Karman type relations for strains of face sheets and the core are adopted. Contact force between the impactor and the beam is obtained using the modified Hertz law. The field equations are derived via the Ritz based applied to the total energy of the system. The solution is obtained in the time domain by implementing the well-known Runge-Kutta method. The effects of boundary conditions, core-to-face sheet thickness ratio, initial velocity of the impactor, the impactor mass and position of the impactor are studied in detail. It is found that each of these parameters have significant effect on the impact characteristics which should be considered. Finally, some low velocity impact tests have been carried out by Drop Hammer Testing Machine. The contact force histories predicted by EHSAPT are in good agreement with that obtained by experimental results.

• Steel and Composite Structures
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• 제43권5호
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• pp.533-552
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• 2022

The current article deals with the dynamic stability, and structural improvement of vibrating electrically curved screen on the viscoelastic substrate. By considering optimum value for radius curvature of the electrically curved screen, the structure improvement of the system occurs. For modeling the electrically system, the Maxwell's' equation is developed. Hertz contact model in employed to obtain contact forces between impactor and structure. Moreover, variational methods and nonlinear von Kármán model are used to derive boundary conditions (BCs) and nonlinear governing equations of the vibrating electrically curved screen. Galerkin and Multiple scales solution approach are coupled to solve the nonlinear set of governing equations of the vibrating electrically curved screen. Along with the analytical solution, 3D finite element simulation via ABAQUS package is provided with the aid of a FE package for simulating the current system's response. The results are categorized in 3 different sections. First, effects of geometrical and material parameters on the vibrational performance and stability of the curves panel. Second, physical properties of the impactor are taken in to account and their effect on the absorbed energy and velocity profile of the impactor are presented. Finally, effect of the radius and initial velocity on the mode shapes of the current structure is demonstrated.

• 대한기계학회논문집A
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• 제22권1호
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• pp.198-205
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• 1998

In this paper, the dynamic characteristics of a star type epicyclic gear train have been analyzed. Nonlinear stiffness of a gear pair were obtained considering the bending and shear deformation, Hertz contact deformation, as well as tooth fillet deformation. Nonlinear stiffness coefficients and damping coefficients around the static equilibrium position were obtained by perturbation method. The loci of the planet gears and sun gear were estimated. Tooth meshing forces and bearing reaction forces were calculated. The effects of bearing clearance and oil viscosity on the gear behavior were also analyzed.

• 풍력에너지저널
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• 제14권4호
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• pp.21-28
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• 2023

This study focuses on the analysis of slewing ball bearings in wind turbines. Slewing bearings have an outer diameter of several meters, and hundreds of balls are in contact with the raceway. Due to the large number of balls and raceway contact conditions, it is difficult to accurately analyze contact stresses using general analysis techniques. To analyze the contact stress of a slewing ball bearing, the sub-modeling method is applied, which is a technique that first analyzes the displacement of the entire model and then analyzes the local stress at the point of maximum displacement. In order to reduce the displacement analysis time of the entire ball bearing, the technique of replacing the ball with a nonlinear spring is adopted. The analytical agreement of the simplified model was evaluated by comparing it with a solid mesh model of the ball for three models with different spring attachment methods. It was found that for the condition where a large turnover moment is applied to the bearing, increasing the number of spring elements gives the closest results to modeling the ball with a solid mesh.

• Tribology and Lubricants
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• 제30권2호
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• pp.116-123
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• 2014

The objective of this study is to model and simulate the nonlinear lubrication performance of the sliding part between the piston and cylinder wall in a hydrostatic swash-plate-type axial piston pump. A numerical algorithm is developed that facilitates simultaneous calculation of the rotating body motion and fluid film pressure to observe the fluid film geometry and power loss. It is assumed that solid asperity contact, so-called mixed lubrication in this study, invariably occurs in the swash-plate-type axial piston pump, which produces a higher lateral moment on the pistons than other types of hydrostatic machines. Two comparative mixed lubrication models, rigid and elastic, are used to determine the reaction force and sliding friction. The rigid model does not allow any elastic deformation in the partial lubrication area. The patch shapes, reactive forces, and virtual local elastic deformation in the partial lubrication area are obtained in the elastic contact model using a simple Hertz contact theory. The calculation results show that a higher reaction force and friction loss are obtained in the rigid model, indicating that solid deformation is a significant factor on the lubrication characteristics of the reciprocating piston part.

• 대한조선학회논문집
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• 제42권3호
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• pp.259-267
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• 2005

The effects of hull flexibility on shaft alignment are growing as ship sizes are increased mainly for container carrier and LNG carrier. In order to consider hull flexibility on a propulsion shafting system, standardization of ship service conditions is necessary because hull deformation is continuously variable according to ship service conditions. How to summarize ship service conditions is suggested based on practically applicable four viewpoints : hull, engine, loading and sea status. Effects of the external forces acting on a ship propulsion shafting system are generally commented. Several design criteria regulated by classification societies are pointed at issue which seems to have Insufficient technical background. A qualitative verification is carried out to point out the invalidity of the assumption of effective supporting position. In this work, an elastic nonlinear multi-supporting bearing system is introduced as a key concept of the elastic shaft alignment. Hertz contact theory is proved to be more proper one than projected area method in calculation of the nonlinear elastic stiffness of the bearing, The squeezing and oil film pressure calculations in the long journal bearing like an after stern tube bearing are recognized as a necessary process for elastic shaft alignment design.

• 대한조선학회논문집
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• 제42권5호
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• pp.479-486
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• 2005

The final goal of shift alignment design is that the bearing reaction forces or mean pressures are within design boundaries for various service conditions of a ship. However, it is found that calculated bearing load can be substantially variable according to the locations of the effective support points of after sterntube bearing which are determined by simple calculation or assumption suggested by classification societies. A new analysis method for shaft alignment calculation is introduced in order to resolve these problems. Key concept of the new method is featured by adopting both nonlinear elastic and multi-support elements to simulate a bearing support Hertz contact theory is basically applied for nonlinear elastic stiffness calculation instead of the projected area method suggested by most of classification societies. Three loading conditions according to the bearing offset and the hydrodynamic moment and twelve models according to the locations of the effective support points of sterntube bearings are prepared to carry out quantitative verifications for an actual shafting system of 8000 TEU class container vessel. It is found that there is relatively large difference between assumed and calculated effective support points.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집A
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• pp.576-583
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• 2000

A robust position control using a sliding mode controller is adopted for the stable dynamic walking of the biped. For the biped robot that is modeled with 14 degrees of freedom rigid bodies using the method of the multibody dynamics, the joint angles for simulation are obtained by the velocity transformation matrix using the given Cartesian foot and trunk trajectories. Hertz force model and Hysteresis damping element which is used in explanation of the energy dissipation during contact with ground are used for modeling of the ground reactions during the simulation. By the obtained that forces which contains highly confused noise elements and the system modeling uncertainties of various kinds such as unmodeled dynamics and parameter inaccuracies, the biped system will be unstable. For that problems, we are adopting a nonlinear robust control using a sliding mode controller. Under the assumption that the esimation error on the unknown parameters is bounded by a given function, that controller provides a successful way to preserve stability and achieve good performance, despite the presence of strong modeling imprecisions or uncertainties.