• International Journal of Railway
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• v.6 no.4
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• pp.148-154
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• 2013

This article has tried to review the maximum contact stresses in the contact area of the wheel and rail as a result of lateral movement of the wheel on rail by taking advantage from Hertz theory. Since wheel movement on rail is accompanied by lateral movement due to wheel profile conisity, so the contact point of wheel and rail is not constant and the contact stresses are therefore changeable in every single moment. Since the shape of rail profile and rail inclination, wheel diameter and the mechanical properties of the wheel and rail are effective on the stresses of contact area, these parameters have been studied by applying Hertz theory. This article aims to calculate the contact stresses in different parts on the wheel surface by using Hertz theory.

• Journal of Industrial Technology
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• v.28 no.A
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• pp.81-88
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• 2008

Generally, Hertz theory is used to analyze the contact problem of two bodies. It is simple derivation of solution in the contact part. And calculation time is short Moreover, it can mean well that many wear occurs relatively. However, material property becomes plastic deformation when large perpendicular pressure acts on a small contact surface product. In this case, Hertz theory is inapplicable. Therefore this thesis carried the finite element analysis in consideration of material elasticitystrain and the shape of the geometric from contact point. And it compared with Hertz theory that change of the contact surface and contact pressure.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.816-821
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• 2005

The cycloid reducer has very high efficiency, high ratios, high stiffness and small size, in comparison with a conventional gear mechanism, which makes it an attractive candidate for limited space and precision application such as industrial robot. There are several publications on analysis and design of the cycloid reducer, however, it was assumed that the contact stiffness of pin rollers and cycloid disk is constant regardless of their contact geometry. Moreover, the torsional stiffness of the cycloid reducer couldn't be calculated due to the assumption. In this paper, we present a new procedure of calculating torsional stiffness of the cycloid reducer using Hertz contact theory. First, conventional force analysis of the cycloid reducer is briefly reviewed. Then, iterative numerical calculation procedure of the contact stiffness is proposed based on the Hertz contact theory where the contact stiffness depends on the contact force. In addition, total torsional stiffness of the cycloid reducer is estimated considering its rolling element bearing stiffness. The torsional stiffness of the cycloid reducer is dominated by the rolling element bearing stiffness since the contact stiffness of the cycloid disk is too large.

• Proceedings of the KSR Conference
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• 2005.05a
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• pp.409-414
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• 2005

It is difficult to apply the Hertz theory to the wheel-rail contact problem which has the complicated geometric form and plastic deformation. Therefore, we perform the elastic-plastic FE analysis and compare the results with those of Hertz theory. Kalker's simplified theory of rolling contact is used to discretize the contact patches and calculate local traction and slip. The wear volumes are calculated using Archard wear equation.

• Structural Engineering and Mechanics
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• v.25 no.1
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.11
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.383-388
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• 2008

A modeling method for the impact analysis of plate structures employing Hertzian contact theory is presented in this paper. Since local deformation as well as bending deflection of the plate occurs due to the collision, it has to be considered for the impact analysis. When the coefficient of restitution is employed for the impact analysis, the local deformation is not considered. For more accurate and reliable impact analysis, however, the local deformation should be considered. The effects of the location of collision and the collision mass on the impact duration time and the contact force magnitude are investigated through numerical studies employing Hertzian contact theory.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.838-843
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• 2008

Since thickness deformation and lateral deflection often occurs during the collision of flexible bodies, they should be considered simultaneously in the impact analysis. The thickness deformation, however, cannot be considered in beam/shell theory since the thickness is assumed to be constant in the theory. So, solid elements are employed to estimate the thickness deformation. However, the CPU time increases significantly if solid elements are employed. In the present study, a modeling method for the impact analysis of a flexible body employing Hertzian contact theory is presented. The efficiency and the accuracy of the modeling method are discussed with some numerical examples.

• Tribology and Lubricants
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• v.4 no.2
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• pp.28-35
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• 1988

A general and efficient algorithm is proposed for the analysis of the frictionless elastic contact problems. It utilizes a simplex-type algorithm with a modified entry rule and incoporates finite element method to obtain flexibility matrices. The algorithmic solution is compared with the Hertzian solution for the contact problem between two cylinders to prove its accuracy and the contact problem between pin and piston rod is solved and compared with the numerical results of Frankavilla and Zienkiewicz to demonstrate the generality and effectiveness of the suggested algorithm. The contact problem between mating involute gear teeth at the worst load position is considered. The computed contact stress is smaller than the result of Hertz's theory applied to the contact between two kinematically equivalent discs and the contact area is larger than that of Hertz's theory.

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.5
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• pp.148-156
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• 2000

In this paper, we investigate contact characteristic of wheel-rail interface for rolling stock using the finite element method. Contact stress distribution due to the rail mounting slope is obtained in order to reduce the contact stress. Stress analysis of the rail, firstly, is performed one subjected to elliptical pressure based on Hertz theory. Secondly, we perform stress analysis of the rail subjected to contact stress obtained by this study. Results for the maximum shear stress, its location and the principal shear stress distribution are compared.