Closure to “Discussion of ‘Influence of Surface Waviness and Roughness on the Normal Pressure Distribution in the Hertzian Contact’” (1987, ASME J. Tribol., 109, pp. 469–470)

1987 ◽  
Vol 109 (3) ◽  
pp. 470-470
Author(s):  
J. Seabra ◽  
D. Berthe
Keyword(s):  
Pressure Distribution ◽  
Normal Pressure ◽  
Hertzian Contact ◽  
Surface Waviness

Influence of Surface Waviness and Roughness on the Normal Pressure Distribution in the Hertzian Contact

1987 ◽  
Vol 109 (3) ◽  
pp. 462-469 ◽  
Author(s):  
J. Seabra ◽  
D. Berthe
Keyword(s):  
Surface Roughness ◽  
Contact Problem ◽  
Pressure Distribution ◽  
Variational Formulation ◽  
Virtual Work ◽  
Normal Pressure ◽  
Hertzian Contact ◽  
Surface Waviness ◽  
Normal Contact ◽  
Surface Imperfections

Contact stresses are one of the most important parameters in the analysis of a contact problem found for instance, in the design of gears and roller bearings. In this work the influence of geometrical surface imperfections on the normal pressure distribution in the contact is studied. A variational formulation based on the principle of complementary virtual work is used to solve the normal contact problem. The normal contact between two elastic half-spaces is considered, as the contact surface is small when compared to the dimensions of the contacting bodies. Results are presented to determine the influence of surface roughness, wavelength, and amplitude on the normal pressure distribution.

Mechanical analysis of spherical roller bearings due to surface waviness

2016 ◽  
Vol 232 (4) ◽  
pp. 639-656 ◽  
Author(s):  
Yu Xing ◽  
Hua Xu ◽  
Xuejing Liu ◽  
Hui Xi ◽  
Shibin Wang
Keyword(s):  
Contact Angle ◽  
Mechanical Analysis ◽  
The Self ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Surface Waviness ◽  
Characteristic Frequencies ◽  
Roller Bearings ◽  
Runge Kutta Method ◽  
Proposed Model

This work presents a theoretical model to research the vibration due to surface waviness of spherical roller bearings (SRBs), taking account of the self-aligning feature and the external axial load. The surface waviness is described by cosinoidal functions. The self-aligning features, including the variation law of the self-aligning contact angle and the interaction with the external loads, are introduced into the non-Hertzian contact model. The nonlinear equations are solved by Runge–Kutta method and the proposed model is validated by comparing with the results of the published references. The results show more characteristic frequencies will be excited under the self-aligning operating condition, whereby the improved equations proposed in this paper are recommended to instead of the previous ones to predict characteristic frequencies of the waviness vibration in an SRB. In addition, these characteristic vibrations caused by waviness are obviously influenced by the magnitude and the direction of the self-aligning contact angle. A proper pretightening load should be chosen according to the self-aligning feature or else it will lead to hidden dangers. The radial clearance and the waviness amplitude can both highlight the effect of waviness. And the vibration caused by a larger radial clearance may be fiercer than the vibration due to waviness.

Rolling Contact With Friction and Non-Hertzian Pressure Distribution

1989 ◽  
Vol 56 (4) ◽  
pp. 814-820 ◽  
Author(s):  
C. Liu ◽  
B. Paul
Keyword(s):  
Pressure Distribution ◽  
Numerical Technique ◽  
Contact Region ◽  
Three Dimensional ◽  
Contact Problems ◽  
Rolling Contact ◽  
Sliding Contact ◽  
Hertzian Contact ◽  
Limiting Case ◽  
Large Spin

A numerical technique has been developed to deal with three-dimensional rolling contact problems with an arbitrary contact region under an arbitrary pressure. Results of this technique are checked against existing solutions for cases of Hertzian contact. A solution for a case of non-Hertzian contact is also presented. This numerical technique works satisfactorily for cases with small spin creepage. For cases of large spin creepage, we utilize a recent work (by the authors) for the limiting case of fully developed sliding contact.

An Engineering Approach to Non-Hertzian Contact Elasticity—Part II

2000 ◽  
Vol 123 (3) ◽  
pp. 589-594 ◽  
Author(s):  
Luc Houpert
Keyword(s):  
Pressure Distribution ◽  
Analytical Solutions ◽  
Curve Fitting ◽  
Numerical Solutions ◽  
Companion Paper ◽  
Hertzian Contact ◽  
Line Contact ◽  
Correction Factors ◽  
Analytical Development ◽  
Single Radius

Roller/race misalignment and deformation are used for calculating analytically the pressure distribution along the roller/race contact and the final roller/race load and moment. Use is made of the surface crowns and race undercuts for calculating contact dimensions with their possible truncations at large misalignment or loads. The pressure distribution is not symmetrical when misalignment occurs. This analytical development was possible by using a slicing technique in which the local roller/race geometrical interference was calculated in each slice of the contact. A mix of point and line contact Hertzian solutions developed in a companion paper “Part I” is used for obtaining the final load per slice. The final analytical solutions (load, moment and pressure) are successfully compared to two numerical solutions described briefly. The analytical model has been slightly fine-tuned using correction factors obtained by curve-fitting for matching the results to the numerical ones. In the curve-fitting, the single radius profile and multi-radius profile are distinguished.

scholarly journals SIMULATION OF A SINGLE THIRD-BODY PARTICLE IN FRICTIONAL CONTACT

2020 ◽  
pp. 537
Author(s):  
Qiang Li
Keyword(s):  
Boundary Element Method ◽  
Stress Distribution ◽  
Pressure Distribution ◽  
Tangential Stress ◽  
Frictional Contact ◽  
Normal Pressure ◽  
Contact Interface ◽  
Third Body ◽  
Rigid Particles ◽  
Force Moment

Contact of a single third-body particle between two plates is simulated using the Boundary Element Method. The particle is considered as deformable, and the Coulomb’s law of friction is assumed at the contact interface. The normal pressure distribution and tangential stress distribution in contact as well as the macroscopic force and force moment are calculated. Several movement modes are shown to be possible: rolling, rotation, or sticking during the loading. It is found that, differing from rigid particles, the state of particle may change during the loading. The particle may stick to the plates initially, but rotation may occur when the load becomes larger. Examples with the same and different coefficients of friction are presented to show kinematics of particle. The method can be further applied to simulation of multiple third-body particles.

Simulation of Fretting Wear in Halfplane Geometries: Part 1—The Solution for Long Term Wear

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
D. A. Hills ◽  
A. Sackfield ◽  
R. J. H. Paynter
Keyword(s):  
Pressure Distribution ◽  
Oscillatory Shear ◽  
Fretting Wear ◽  
Hertzian Contact ◽  
Final Configuration ◽  
State Of Stress ◽  
Long Time

The final configuration of a cylindrical Hertzian contact, subject to oscillatory shear and undergoing wear, is studied. It is assumed that wear has proceeded for a long time, so that the final, modified contact is wholly adhered. It is shown that the extent of the final contact corresponds to that of the initial adhered region and the pressure distribution, and state of stress at the new contact edge are all derived, so that the environment in which cracks nucleate is well described.

A Simplified Approach to Predict Elastic Pressure Distribution in Non-Hertzian Contact Stress Problems

1991 ◽  
Vol 113 (2) ◽  
pp. 218-223 ◽  
Author(s):  
L. Nayak
Keyword(s):  
Numerical Methods ◽  
Pressure Distribution ◽  
Contact Stress ◽  
Normal Load ◽  
Hertzian Contact ◽  
Two Dimensional ◽  
Simple Method ◽  
Simplified Approach ◽  
Design Engineers ◽  
Hertzian Contact Stress

An approximate but simple method to predict elastic pressure distribution in non-Hertzian contact stress problems has been developed using the two-dimensional Hertz relations and experimentally observed footprint shapes. Predicted pressures have been compared with results available from other numerical methods and are found to be quite satisfactory. The method has been applied to determine pressure distribution in wheel-rail contact under the normal load only. Because of its simplicity and reasonably accuracy in predicting pressure it can be readily used by industrial design engineers for many practical problems of contact mechanics.

scholarly journals Using Homemade Pressure Device to Improve Plantar Pressure—A Case Study on the Patient with Lower Limb Lymphedema

2021 ◽  
Vol 11 (20) ◽  
pp. 9629
Author(s):  
Jong-Chen Chen ◽  
Yao-Te Wang ◽  
Ying-Sheng Lin
Keyword(s):  
Lower Extremity ◽  
Pressure Distribution ◽  
Plantar Pressure ◽  
Normal Pressure ◽  
University Hospital ◽  
Lower Extremity Edema ◽  
Foot Pressure ◽  
Entire Study ◽  
Before And After ◽  
Sole Of The Foot

Feet play a very important and indispensable role in people’s lives. Patients with lymphedema often suffer from collapsed (or even deformed) foot arches as a result of lower extremity edema. This result will change the normal pressure distribution on the soles of their feet, which will affect their mobility and physical health. When the patient does not know that the distribution of pressure on the sole of the foot has changed significantly, the deformation of the sole of the foot will become severe. In response to this problem, this research team hopes to use a set of self-made sensor insoles to help to understand the plantar pressure points in different situations or actions. The subject invited in this study was a patient with lower extremity edema. The entire study was carried out with the consent of the patient, the guidance of the physician and the approval of the Ethics Committee of National Taiwan University Hospital (No: 201805068 RINB, date: 18 June 2018). This study uses this self-made sensor insole to analyze the plantar pressure distribution of the patient before and after the operation of lower extremity edema. The results show that the operation can effectively improve the high foot pressure in the center and rear of the foot area during different sports (standing, walking and biking). This not only increases its stability when standing and walking, but also significantly and effectively improves its walking speed and step distance.

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