• Title, Summary, Keyword: Hertz Theory

### Calculating the Contact Stress Resulting from Lateral Movement of the Wheel on Rail by Applying Hertz Theory

• 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.

### Torsional Stiffness Analysis of a Cycloid Reducer using Hertz Contact Theory (Hertz 접촉이론을 이용한 사이클로이드 감속기의 비틀림 강성해석)

• Lee S.Y.;Park J.S;Ahn H.J.;Han D.C.
• Proceedings of the Korean Society of Precision Engineering Conference
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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.

### Finite Element Analysis of Hertzian Contact Problem (Hertz 접촉 문제의 유한 요소 해석)

• Ko, Dong-sun;Kim, Hyung-Jong
• 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.

### A mass estimation algorithm for loose part using Hertz theory (Hertz 이론을 이용한 금속파편의 질량추정 알고리즘)

• 김정수;황인구;정철환;박진호;함창식;양재현;이용호
• Proceedings of the Korean Nuclear Society Conference
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• pp.75-75
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• 1999

### The wheel wear prediction of a Korea High Speed Train using a FE-analysis (유한요소해석을 이용한 한국형 고속철도 차량의 차륜 마모 예측)

• Choi Jeong Heum;Han Dong-Chul;Kim Ki-Hwan
• Proceedings of the KSR Conference
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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.

### 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 the Cycloid Drive with Tolerances (공차를 고려한 사이클로이드 감속기의 해석)

• Park J.S.;Lee S.Y.;Ahn H.J.;Han D.C.
• Proceedings of the KSME Conference
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• pp.219.1-219.1
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• 2005

### Dynamic Characteristics of Composite Plates Based On a Higher Order Theory Under Low-Velocity Impact (저속 충격시 고차이론을 이용한 복합 재료 판의 동적 특성)

• 심동진;김지환
• Journal of KSNVE
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• v.8 no.1
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• pp.132-138
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• 1998
• The dynamic response of symmetric cross-ply and angle-ply composite laminated plates under impact loads is investigated using a higher order shear deformation theory. A modified Hertz law is used to predict the impact loads and a four node finite element is used to model the plate. By using a higer order shear deformation theory, the out-of-plane shear stresses, which can be a crucial factor in the failure of composite plates, are determined with significant accuracy. This is accomplished by using a stress recovery technique using the in-plane stresses. The results compared with previous investigations showed good agreement. It can be seen that this method of analyzing impact problems is more efficient than current three dimensional methods in terms of time and expense.

### Study on an efficient modeling for the impact analysis of a flexible body employing Hertzian contact theory (Hertz 접촉이론을 이용한 탄성체의 충돌 해석을 위한 효율적 모델링에 관한 연구)

• Lim, Hong-Seok;Yoo, Hong-Hee
• Proceedings of the KSME Conference
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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.

### Torsional Rigidity of a Two-stage Cycloid Drive (이단 사이클로이드 드라이브의 비틀림 강성)

• Kim, Kyoung-Hong;Lee, Chun-Se;Ahn, Hyeong-Joon
• 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.