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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Sun, Tiewei, Min Wang, Xiangsheng Gao, and Yingjie Zhao. "Non-Hertzian Elastohydrodynamic Contact Stress Calculation of High-Speed Ball Screws." Applied Sciences 11, no. 24 (December 18, 2021): 12081. http://dx.doi.org/10.3390/app112412081.

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Анотація:

In order to eliminate the calculation error of the Hertzian elastohydrodynamic contact stress due to the asymmetry of the contact region of the helix raceway, a non-Hertzian elastohydrodynamic contact stress calculation method based on the minimum excess principle was proposed. Firstly, the normal contact stresses of the screw raceway and the nut raceway were calculated by the Hertzian contact theory and the minimum excess principle, respectively. Subsequently, the Hertzian solution and the non-Hertzian solution of the elastohydrodynamic contact stress could be determined by the Reynolds equation under different helix angles and screw speeds. Finally, the friction torque test of the double-nut ball screws was designed and implemented on a self-designed bed for validation of the proposed method. The comparison showed that the experimental friction torque was the good agreement with the simulated friction torque, which verified the effectiveness and correctness of the non-Hertzian elastohydrodynamic contact stress calculation method. Under the large helix angle, the calculation accuracy of asperity contact stress for the non-Hertzian solution was more accurate than that of the Hertzian solution at the contact region of ball screws. Therefore, the non-Hertzian elastohydrodynamic contact stress considering the asymmetry of the raceway contact region could more accurately analyze the wear depth of the high-speed ball screws.

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2

Hanson, M. T., L. M. Keer, and T. N. Farris. "Energy Dissipation in Non-Hertzian Fretting Contact." Tribology Transactions 32, no. 2 (January 1989): 147–54. http://dx.doi.org/10.1080/10402008908981873.

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3

Askari, Ehsan. "Mathematical models for characterizing non-Hertzian contacts." Applied Mathematical Modelling 90 (February 2021): 432–47. http://dx.doi.org/10.1016/j.apm.2020.08.048.

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4

Hooke, C. J. "A Note on the Elastohydrodynamic Lubrication of Soft Contacts." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 200, no. 3 (May 1986): 189–94. http://dx.doi.org/10.1243/pime_proc_1986_200_114_02.

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Анотація:

The clearances in highly loaded non-Hertzian contacts can be calculated directly from the dry contact pressure distribution. This note presents a method of extending the analysis into less highly loaded regions. It is shown that the method accurately predicts the clearance over much of the transition zone for Hertzian contacts and its use in a non-Hertzian situation is illustrated using the contact between a rigid cylinder and an elastomer-lined surface as an example.

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5

Sackfield, A., and D. A. Hills. "The Strength of Some Non-Hertzian Plane Contacts." Journal of Tribology 108, no. 4 (October 1, 1986): 655–58. http://dx.doi.org/10.1115/1.3261296.

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Анотація:

The problem of plane elastic contact between a symmetrical indentor and a half-plane is addressed. The form of the contacting profile of the indentor is represented in terms of Chebyshev polynomials, and the resulting stress-field is deduced, for both static and sliding contact. It is shown that by making the profile somewhat flatter than a cylinder a large load may be sustained without yielding. Practical implications of the result, including profiles needed to attain optimal contact conditions, are discussed.

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6

Ouyang, Wenze, Bin Sun, Zhiwei Sun, and Shenghua Xu. "Anomalous and non-Gaussian diffusion in Hertzian spheres." Physica A: Statistical Mechanics and its Applications 505 (September 2018): 61–68. http://dx.doi.org/10.1016/j.physa.2018.03.034.

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7

Liu, C., and B. Paul. "Rolling Contact With Friction and Non-Hertzian Pressure Distribution." Journal of Applied Mechanics 56, no. 4 (December 1, 1989): 814–20. http://dx.doi.org/10.1115/1.3176176.

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Анотація:

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.

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8

An, Boyang, Daolin Ma, Ping Wang, Jiayi Zhou, Rong Chen, Jingmang Xu, and Dabin Cui. "Assessing the fast non-Hertzian methods based on the simulation of wheel–rail rolling contact and wear distribution." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 234, no. 5 (May 9, 2019): 524–37. http://dx.doi.org/10.1177/0954409719848592.

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Анотація:

This paper aims at assessing several fast non-Hertzian methods, coupled with two wear models, based on the wheel–rail rolling contact and wear prediction. Four contact models, namely Kik-Piotrowski's method, Linder's method, Ayasse-Chollet's STRIPES algorithm and Sichani's ANALYN algorithm are employed for comparing the normal contact. For their tangential modelling, two tangential algorithms, i.e. FASTSIM and FaStrip, are used. Two commonly used wear models, namely the Archard (extended at the KTH Royal Institute of Technology) and USFD (developed by the University of Sheffield based on T-gamma approach), are further utilized for wear distribution computation. All results predicted by the fast non-Hertzian methods are evaluated against the results of Kalker's CONTACT code using penetration as the input. Since the two wear models adopt different expressions for calculating the wear performance, the attention of this paper is on assessing which one is more suitable for the fast non-Hertzian methods to utilize. The comparison shows that the combination of the USFD wear model with any of the fast non-Hertzian methods agrees better with CONTACT+USFD. In general, ANALYN+FaStrip is the best solution for the simulation of the wheel–rail rolling contact, while STRIPES+FASTSIM can provide better accuracy for the maximum wear depth prediction using the USFD wear model.

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9

Ciulli, Enrico, Alberto Betti, and Paola Forte. "The Applicability of the Hertzian Formulas to Point Contacts of Spheres and Spherical Caps." Lubricants 10, no. 10 (September 23, 2022): 233. http://dx.doi.org/10.3390/lubricants10100233.

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Анотація:

Hertzian formulas are commonly used for the evaluation of deformation and pressure distribution of non-conformal and slightly conformal mechanical pairs to estimate component stiffness and durability. For the sake of simplicity, their use is extended even to those cases in which Hertz’s hypotheses do not hold. This paper summarizes Hertz’s theory and compares the results obtained with theoretical and finite element analysis of the point contact of non-conformal and conformal pairs made of spheres, caps, and spherical seats. This study was motivated by the non-Hertzian behavior of a tilting pad bearing ball-and-socket pivot conforming contact observed by the authors in previous experiments. In particular, the displacement and force relation were investigated by varying the geometrical parameters, the materials, the boundary conditions, and the friction coefficient. In the case of non-conformal contact, the parameter variations had negligible effect in agreement with Hertz’s theory while for conformal contact, the cap and seat height and width and the relative clearance were the most influential parameters on the non-Hertzian behavior. These novel results indicate that in conformal pairs, such as for tilting pad bearing ball-and-socket pivots, whenever Hertz’s hypotheses are not satisfied and the assessment of contact stiffness is crucial, Hertzian formulas should not be applied as done in common practice, instead more accurate numerical or experimental evaluation should be made.

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10

MARTIN, RAFAEL GOMEZ, JUAN A. MORENTE, and AMELIA R. BRETONES. "Arrays of hertzian electric dipoles for non-sinusoidal signals." International Journal of Electronics 59, no. 4 (October 1985): 435–38. http://dx.doi.org/10.1080/00207218508920714.

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11

Zhou, M., and W. P. Schonberg. "Smooth Asymmetric Two-Dimensional Indentation of a Finite Elastic Beam." Journal of Applied Mechanics 68, no. 2 (May 31, 2000): 357–60. http://dx.doi.org/10.1115/1.1352068.

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Анотація:

Standard methods of beam indentation analysis use a beam theory solution to obtain the load-displacement relationship and a Hertz solution to calculate local stresses. However, when the contact length exceeds the thickness of the beam point contact can no longer be assumed and Hertzian relations are no longer valid. This paper presents an improved superposition solution technique that uses a true elasticity solution to obtain the load-displacement relationship in non-Hertzian indentation problems.

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12

KIM, SANG-WOO, and SEOCK-SAM KIM. "EFFECT OF FRICTIONAL HEATING ON THE PROPAGATION OF SURFACE CRACK UNDER HERTZIAN CONTACT LOADING." International Journal of Modern Physics B 24, no. 15n16 (June 30, 2010): 2524–29. http://dx.doi.org/10.1142/s0217979210065209.

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In this paper the frictional heating effect on the propagation of surface crack under Hertzian contact loading based on the fracture mechanics is investigated. For the theoretical analysis of this effect, we estimated stress intensity factor of surface crack -tip in shear mode under Hertzian contact sliding friction. Theoretical results showed those thermal loads (Th), Peclet number (Pe) and crack angle (β) are very important factors on the propagation of surface crack under Hertzian contact loading. When thermal load(Th) and Peclet number(Pe) are constant, maximum variable range of stress intensity factor, ΔKII, is located in the range of surface crack angle 130°~150°. Non-dimensional parameter T consisting of thermal load and peclet number for evaluating ceramic wear behavior is introduced.

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13

Xing, Yu, Hua Xu, Shiyuan Pei, Xiaolei Chen, and Xuejing Liu. "A novel non-Hertzian contact model of spherical roller bearings." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 230, no. 1 (May 5, 2015): 3–13. http://dx.doi.org/10.1177/1350650115584428.

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14

Houpert, Luc. "An Engineering Approach to Non-Hertzian Contact Elasticity—Part II." Journal of Tribology 123, no. 3 (July 10, 2000): 589–94. http://dx.doi.org/10.1115/1.1308042.

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Анотація:

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.

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15

Baeza, Luis, Stefano Bruni, Juan Giner-Navarro, and Binbin Liu. "A linear non-Hertzian unsteady tangential wheel-rail contact model." Tribology International 181 (March 2023): 108345. http://dx.doi.org/10.1016/j.triboint.2023.108345.

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16

Bryja, Danuta, and Wojciech Chojnacki. "Two-way Hertzian spring in numerical analysis of coupled train-track system vibrations." Transportation Overview - Przeglad Komunikacyjny 2019, no. 11 (November 1, 2019): 1–11. http://dx.doi.org/10.35117/a_eng_19_11_01.

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Анотація:

The paper presents and compares two methods for simulation the train-track system vibrations, differing in the wheel-rail contact model used. In the first method, two-way Hertzian spring is used, in the second – a non-deformable constraint. In both methods, a flat computational model is assumed, consisting of an Euler-Bernoulli beam resting on a Winkler-type elastic foundation with damping and a set of rail vehicles modeled by dynamic systems with ten degrees of freedom. The results of numerical analysis are presented, in order to determine an influence of the contact constraints’ deformability on the vibration simulations. It is found that the replacement of non-deformable contact constraints by two-way Hertzian springs has no significant effect on track vibration simulations and has a little effect on vibration simulations of vehicle body and bogie. The developed simulation method can be used for numerical studies of the phenomenon of instantaneous detachments of wheels from rails, after minor modifications directed to introduce one-way Hertzian springs (i.e. not carrying tensile forces) being a more accurate contact model.

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17

Xie, G., and S. D. Iwnicki. "A rail roughness growth model for a wheelset with non-steady, non-Hertzian contact." Vehicle System Dynamics 48, no. 10 (October 2010): 1135–54. http://dx.doi.org/10.1080/00423110903410518.

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18

Conry, T. F., S. Wang, and C. Cusano. "A Reynolds-Eyring Equation for Elastohydrodynamic Lubrication in Line Contacts." Journal of Tribology 109, no. 4 (October 1, 1987): 648–54. http://dx.doi.org/10.1115/1.3261526.

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Анотація:

A new Reynolds equation, based on the Eyring theory of non-Newtonian flow, is derived for flow in one dimension. It is shown that this new equation reduces to the traditional Reynolds equation as the Eyring model approaches the Newtonian model in the limit. Numerical solutions are presented for a selected oil at two different temperatures. The central film thickness decreases with increasing dimensionless viscosity parameter and slide/roll ratios. A transition zone is noted through which the ratio of minimum to central film thickness passes as the pressure distribution goes from near Hertzian to a distribution that appreciably deviates from Hertzian.

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19

Magalhães, Hugo, Filipe Marques, Binbin Liu, Pedro Antunes, João Pombo, Paulo Flores, Jorge Ambrósio, Jerzy Piotrowski, and Stefano Bruni. "Implementation of a non-Hertzian contact model for railway dynamic application." Multibody System Dynamics 48, no. 1 (July 17, 2019): 41–78. http://dx.doi.org/10.1007/s11044-019-09688-y.

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20

Liu, Jing, Chenyu An, and Guang Pan. "A vibration model of a rotor system with the sinusoidal waviness by using the non-Hertzian solution." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 236, no. 1 (December 23, 2021): 151–67. http://dx.doi.org/10.1177/14644193211065916.

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Анотація:

The nonlinear contact forces and deformations between the balls and raceways can cause very complex vibration behaviours of rotor systems with the waviness in the support bearings. However, almost all previous works that used sinusoidal waviness took the Hertzian solution as the calculation method, which is not an accurate method based on Johnson’s formulation since the changes in the curvature at the sinusoidal contact surfaces. To overcome this issue, a new dynamic model of a rigid rotor system with the waviness in the support bearings is proposed. To provide a more accurate nonlinear contact force formulation for the sinusoidal waviness profile, the model used the Johnson’s extended Hertzian contact model to replace Hertzian contact model. This model can consider the time-varying curvature between the mating sinusoidal surfaces. The lubricating condition in the support bearing is also considered. A comparative study on the effects of Hertzian contact model, simplified Hertzian contact model, and Johnson's extended Hertzian contact model on the nonlinear vibrations of the rotor system is developed. The effects of the waviness amplitude and orders on the vibrations of the rotor system are discussed. The comparative simulations show that the proposed model can provide a more reasonable approach for predicting the vibrations of the rigid rotor system. Moreover, the simulations give that the nonlinear contact forces in the support bearings can greatly affect the system vibrations.

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21

Snidle, R. W., and H. P. Evans. "A Simple Method of Elastic Contact Simulation." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 208, no. 4 (December 1994): 291–93. http://dx.doi.org/10.1243/pime_proc_1994_208_384_02.

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Анотація:

The note describes an iterative algorithm for calculating contact pressure and areas of contact in nonconforming, two-dimensional, non-Hertzian contacts. In principle the method can be easily extended to three-dimensional problems.

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22

Czyzewski, T., and M. T. Odman. "Analysis of Contact Stress and Deformation in a Trilobe Polygonal Connection." Journal of Engineering for Industry 110, no. 3 (August 1, 1988): 212–17. http://dx.doi.org/10.1115/1.3187871.

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Анотація:

A numerical method for determination of contact stress and deformation in a multilobe connection of shafts and hubs is presented. It relies upon NASTRAN for computation of surface deflections of both members which are then matched by means of relative rotation. Several examples of stress distribution in a trilobe connection and the effects of torque and internal clearance upon maximum pressure, extent of contact, its location and torsional compliance are given. Results discredit the application of well-known Hertzian formulas to this closely conformal non-Hertzian contact and suggest a surprisingly simple approximation. This is the first published solution to the problem of contact in a trilobe connection.

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23

Brusa, E., F. Bruzzone, C. Delprete, L. Di Maggio, and C. Rosso. "Envelope analysis applied to non-Hertzian contact simulations in damaged roller bearings." IOP Conference Series: Materials Science and Engineering 1038, no. 1 (February 1, 2021): 012013. http://dx.doi.org/10.1088/1757-899x/1038/1/012013.

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24

Neubrand, J., C. Bilgen, and H. Weiss. "Rolling wear of tin coatings induced by non-uniform hertzian stress distribution." Surface Engineering 11, no. 2 (January 1995): 133–37. http://dx.doi.org/10.1179/sur.1995.11.2.133.

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25

Sun, Yu, Wanming Zhai, and Yu Guo. "A robust non-Hertzian contact method for wheel–rail normal contact analysis." Vehicle System Dynamics 56, no. 12 (February 21, 2018): 1899–921. http://dx.doi.org/10.1080/00423114.2018.1439587.

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26

Turner, J. A. "Non-linear vibrations of a beam with cantilever-Hertzian contact boundary conditions." Journal of Sound and Vibration 275, no. 1-2 (August 2004): 177–91. http://dx.doi.org/10.1016/s0022-460x(03)00791-0.

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27

Roda-Casanova, Victor, and Francisco Sanchez-Marin. "An adaptive mesh refinement approach for solving non-Hertzian elastic contact problems." Meccanica 53, no. 8 (December 9, 2017): 2013–28. http://dx.doi.org/10.1007/s11012-017-0806-y.

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28

Xie, G., and S. D. Iwnicki. "Simulations of roughness growth on rails – results from a 2D non-Hertzian, non-steady contact model." Vehicle System Dynamics 46, no. 1-2 (February 2008): 117–28. http://dx.doi.org/10.1080/00423110701821767.

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29

Lin, W., C. H. Kuo, and L. M. Keer. "Analysis of a Transversely Isotropic Half Space Under Normal and Tangential Loadings." Journal of Tribology 113, no. 2 (April 1, 1991): 335–38. http://dx.doi.org/10.1115/1.2920625.

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Анотація:

This paper analyzes the response of a transversely isotropic half space subjected to various distributions of normal and tangential contact stresses on its surface. Both the interior displacement and stress fields are given in closed form. Among them, rectangular patch solutions are constructed for application to solutions to non-Hertzian contact problems.

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30

Teutsch, Roman, and Bernd Sauer. "An Alternative Slicing Technique to Consider Pressure Concentrations in Non-Hertzian Line Contacts." Journal of Tribology 126, no. 3 (June 28, 2004): 436–42. http://dx.doi.org/10.1115/1.1739244.

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Анотація:

A new, fast method is presented for the analysis of roller-race contact in roller bearings. Based on a theoretical and implicit load-deflection relationship, an improved slicing technique is developed which accounts for a more accurate representation of the pressure distribution along the line of contact. For validation, the method is compared to literature data and results obtained by FEM analysis. In the course of this, roller profiling and misalignment are considered. Due to its fastness and accuracy, the method has its particular advantages when many contacts have to be evaluated several times, e.g., in static load distribution calculations and dynamic simulations.

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31

Piotrowski, Jerzy, Binbin Liu, and Stefano Bruni. "The Kalker book of tables for non-Hertzian contact of wheel and rail." Vehicle System Dynamics 55, no. 6 (February 24, 2017): 875–901. http://dx.doi.org/10.1080/00423114.2017.1291980.

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32

Riner, Joshua, and Andi Petculescu. "Non-Hertzian behavior in binary collisions of plastic balls derived from impact acoustics." Journal of the Acoustical Society of America 128, no. 1 (July 2010): 132–36. http://dx.doi.org/10.1121/1.3438477.

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33

Liu, C., and B. Paul. "Fully Developed Sliding of Rough Surfaces." Journal of Tribology 111, no. 3 (July 1, 1989): 445–51. http://dx.doi.org/10.1115/1.3261945.

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Анотація:

Given the contact region between two bodies, the normal pressure distribution over the contact region, and the coefficient of friction, we seek to find all combinations of tangential forces and twisting moment (about the normal to the contact surface) for which fully developed sliding impends. As part of the solution we must determine the distribution of the surface tractions (shear stresses) and the location of the instantaneous center (IC) of the impending motion. New closed form solutions of the stated problem are found for circular contact patches with pressure distributions corresponding to (a): a flat stamp; and (b): elastic spheroids with Hertzian pressure distributions. For contact regions other than circular, no closed form solutions are known. We have developed numerical procedures to solve for arbitrary contact patches, with arbitrary distributions of normal pressure, and present carpet plots of tangential force components (Fx, Fy) and IC coordinates for the following cases: flat ellipsoidal stamps; ellipsoidal indenters (Hertzian pressure); and a non-Hertzian, nonelliptical contact of a rail and wheel. Level curves of twisting moment Mz versus tangential force components are provided. Given any two of the three quantities (Fx, Fy, Mz), the algorithms and the plots in this paper make it possible and convenient to find the remaining force or moment which will cause gross sliding to impend, for virtually arbitrary contact regions and arbitrary pressure distributions.

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34

Pop, Nicolae, Spiridon Cretu, and Ana Tufescu. "Non Hertzian Contact Model for Tooth Contact Analysis of Spur Gear with Lead Crowning." Applied Mechanics and Materials 658 (October 2014): 351–56. http://dx.doi.org/10.4028/www.scientific.net/amm.658.351.

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Анотація:

The behavior of the contact surfaces between the gear teeth has a significant influence on the gear service properties. An analytical research concerning this behavior by considering a non Hertzian model was developed. A mathematical model of the surfaces of the teeth flanks for modified involute spur gears with crowning and relieving was presented. The pressure distribution, displacement and contact surfaces were analyzed, on considering the load, material characteristics and geometry of the contact surfaces and using a numerical method.

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35

de Mul, J. M., J. M. Vree, and D. A. Maas. "Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction—Part I: General Theory and Application to Ball Bearings." Journal of Tribology 111, no. 1 (January 1, 1989): 142–48. http://dx.doi.org/10.1115/1.3261864.

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Анотація:

A new, general and consistent mathematical model of highly modular character is presented for calculation of the equilibrium and associated load distribution in rolling element bearings. The bearings may be loaded and displaced in five degrees of freedom. High speed rolling element loading is considered, internal friction is neglected, the material is assumed linearly elastic and the bearing rings are modelled as rigid except for local contact deformation. Either classical Hertzian contact analysis or modern non-Hertzian contact analysis of sophisticated or approximate character is used as applicable. The bearing stiffness matrix is computed analytically and used internally in the iterative bearing equilibrium calculation; its final values may be used for other purposes such as (rotor) dynamics analysis. In Part I, the general theory and application to ball bearings is presented. In Part II, application of the general theory to roller bearings and an experimental verification are presented.

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36

de Mul, J. M., J. M. Vree, and D. A. Maas. "Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction—Part II: Application to Roller Bearings and Experimental Verification." Journal of Tribology 111, no. 1 (January 1, 1989): 149–55. http://dx.doi.org/10.1115/1.3261865.

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A new, general and consistent mathematical model of highly modular character is presented for calculation of the equilibrium and associated load distribution in rolling element bearings. The bearings may be loaded and displaced in five degrees of freedom. High speed rolling element loading is considered, internal friction is neglected, the material is assumed linearly elastic and the bearing rings are modelled as rigid except for local contact deformation. Either classical Hertzian contact analysis or modern non-Hertzian contact analysis of sophisticated or approximate character is used as applicable. The bearing stiffness matrix is computed analytically and used internally in the iterative bearing equilibrium calculation; its final values may be used for other purposes such as (rotor) dynamics analysis. In Part I, the general theory and application to ball bearings is presented. In Part II, application of the general theory to ro´ller bearings and an experimental verification are presented.

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37

Nayak, L. "A Simplified Approach to Predict Elastic Pressure Distribution in Non-Hertzian Contact Stress Problems." Journal of Engineering for Industry 113, no. 2 (May 1, 1991): 218–23. http://dx.doi.org/10.1115/1.2899681.

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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.

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38

Saribay, Zihni B., Robert C. Bill, Edward C. Smith, and Suren B. Rao. "Elastohydrodynamic Lubrication Analysis of Conjugate Meshing Face Gear Pairs." Journal of the American Helicopter Society 57, no. 3 (July 1, 2012): 1–10. http://dx.doi.org/10.4050/jahs.57.032003.

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This paper investigates the nominal elastohydrodynamic lubrication (EHL) characteristics of the conjugate meshing face gears and predicts the mesh efficiency of the pericyclic transmission system. The meshing face-gear tooth geometries and meshing kinematics are modeled. Hertzian contact and the isothermal non-Newtonian lubricant film characteristics of the meshing face-gear pair are investigated. The friction coefficient is calculated with the effects of lubricant behavior and mesh kinematics. Finally, the pericyclic transmission efficiency is calculated as a function of friction coefficient, mesh loads, and mesh kinematics. The Hertzian contact behavior, film thickness, and friction coefficient values are simulated for an example fixed axis face-gear pair rotating at 1000 rpm with 3.4 kN-m torque. The EHL film thickness ranges from 0.1 to 0.25 μm in this example. The average friction coefficient is predicted as 0.05. The efficiencies of three different 24:1 reduction ratio 760 HP pericyclic transmission designs are investigated. The minimum and maximum efficiency in the given design space are 97% and 98.7%, respectively.

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39

Kida, Katsuyuki, Megumi Uryu, Takashi Honda, Edson Costa Santos, and Kenichi Saruwatari. "Changes in Three Dimensional Magnetic Fields of Carbon Tool Steel (JIS-SKS93) under Single Spherical Hertzian Contact." Advanced Materials Research 457-458 (January 2012): 578–85. http://dx.doi.org/10.4028/www.scientific.net/amr.457-458.578.

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Failure of dies and molds is caused by wear and deformation during the metal sheet forming process. Die wear takes various forms, and the contact conditions in die-parts affect the strength of the components. Non-destructive methods that can be related to contact conditions are necessary to study and understand the phenomena caused by the contact stresses. In the present work, a newly developed scanning Hall probe microscope (SHPM) equipped with a GaAs film sensor was used to observe the three-dimensional magnetic fields in tool steel plates before and after contact tests at room temperature in air. It was found that the intensity of three-dimensional magnetic fields is only slightly affected by the spherical Hertzian contact. However, all of the three-dimensional components of the magnetic fields change significantly. The extent of the changes depends not on the distribution of stress under spherical Hertzian contact but on the initial distribution of the magnetic fields.

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40

Ciavarella, M., G. Macina, and G. P. Demelio. "On stress concentration on nearly flat contacts." Journal of Strain Analysis for Engineering Design 37, no. 6 (August 1, 2002): 493–501. http://dx.doi.org/10.1243/030932402320950116.

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Fretting fatigue can severely damage components subjected to oscillatory tangential loads, leading to a dramatic reduction in fatigue life and causing catastrophic ruptures. A conservative approach that can be used when considering the effect of stress concentration induced by fretting is to ensure that the peak stress is smaller than the fatigue limit of the material. However, this depends on details of the geometry as well as loading conditions. In the present work, the contact problem of a flat rounded punch in contact with a half-plane is considered, where a dovetail joint contact geometry is approximated and the classical Hertzian contact is retrieved in the limit. Developing the analytical results given by Ciavarella, Hills and Monno, an approximate Hertzian equivalent solution using Cattaneo superposition is obtained, leading to a simple formula to estimate the maximum tangential stress as a function of the load parameter Q/(f P) and geometric parameter a/b. The accuracy of the formula is checked numerically. The proposed formula gives a maximum error as low as 4 per cent in the case of zero bulk loads. For non-zero bulk loads an analytical solution is possible for the Hertzian case for moderate bulk. This leads to a second general formula containing the three dependencies (geometry, tangential load and bulk stress), which also gives a very good approximation for rounded flat and larger bulk loads, the error being generally well below 10 per cent.

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41

Bruzzone, Fabio, Tommaso Maggi, Claudio Marcellini, and Carlo Rosso. "2D nonlinear and non-Hertzian gear teeth deflection model for static transmission error calculation." Mechanism and Machine Theory 166 (December 2021): 104471. http://dx.doi.org/10.1016/j.mechmachtheory.2021.104471.

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42

Neubrand, J., and H. Weiss. "Dry rolling wear of different materials induced by a non-uniform hertzian pressure distribution." Surface and Coatings Technology 76-77 (December 1995): 462–68. http://dx.doi.org/10.1016/0257-8972(95)02502-2.

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43

Neubrand, J. "Dry rolling wear of different materials induced by a non-uniform hertzian pressure distribution." Surface and Coatings Technology 76-77 (December 1995): 462–68. http://dx.doi.org/10.1016/02578-9729(50)25022-.

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44

Yevtushenko, A. A., and R. B. Chapovska. "Investigation of friction-induced thermal processes for some non-hertzian fast-moving plane contacts." International Journal of Mechanical Sciences 38, no. 10 (October 1996): 1103–16. http://dx.doi.org/10.1016/0020-7403(95)00111-5.

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45

KUZUTA, Masahito, and Takehiko FUJIOKA. "1210 Research on Numerical Method for Non-Hertzian Contact Problem between Wheel and Rail." Proceedings of the Transportation and Logistics Conference 2009.18 (2009): 359–62. http://dx.doi.org/10.1299/jsmetld.2009.18.359.

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46

Li, Peng, Zhaowen Li, Sheng Liu, and Yiren Yang. "Non-linear limit cycle flutter of a plate with Hertzian contact in axial flow." Journal of Fluids and Structures 81 (August 2018): 131–60. http://dx.doi.org/10.1016/j.jfluidstructs.2018.04.014.

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47

Bryant, M. D. "Non-linear forced oscillation of a beam coupled to an actuator via Hertzian contact." Journal of Sound and Vibration 99, no. 3 (April 1985): 403–14. http://dx.doi.org/10.1016/0022-460x(85)90377-3.

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48

Xiaochuan, MA, WANG Ping, XU Jingmang, and FENG Qingsong. "Analysis and Comparison of Different Wheel-rail Non-hertzian Rolling Contact Approaches in Railway Turnout." Journal of Mechanical Engineering 55, no. 18 (2019): 95. http://dx.doi.org/10.3901/jme.2019.18.095.

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49

Vollebregt, E. A. H. "Comments on ‘the Kalker book of tables for non-Hertzian contact of wheel and rail’." Vehicle System Dynamics 56, no. 9 (January 10, 2018): 1451–59. http://dx.doi.org/10.1080/00423114.2017.1421767.

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50

Costa, Kevin D., Alan J. Sim, and Frank C.-P. Yin. "Non-Hertzian Approach to Analyzing Mechanical Properties of Endothelial Cells Probed by Atomic Force Microscopy." Journal of Biomechanical Engineering 128, no. 2 (November 18, 2005): 176–84. http://dx.doi.org/10.1115/1.2165690.

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Detailed measurements of cell material properties are required for understanding how cells respond to their mechanical environment. Atomic force microscopy (AFM) is an increasingly popular measurement technique that uniquely combines subcellular mechanical testing with high-resolution imaging. However, the standard method of analyzing AFM indentation data is based on a simplified “Hertz” theory that requires unrealistic assumptions about cell indentation experiments. The objective of this study was to utilize an alternative “pointwise modulus” approach, that relaxes several of these assumptions, to examine subcellular mechanics of cultured human aortic endothelial cells (HAECs). Data from indentations in 2‐to5‐μm square regions of cytoplasm reveal at least two mechanically distinct populations of cellular material. Indentations colocalized with prominent linear structures in AFM images exhibited depth-dependent variation of the apparent pointwise elastic modulus that was not observed at adjacent locations devoid of such structures. The average pointwise modulus at an arbitrary indentation depth of 200nm was 5.6±3.5kPa and 1.5±0.76kPa (mean±SD, n=7) for these two material populations, respectively. The linear structures in AFM images were identified by fluorescence microscopy as bundles of f-actin, or stress fibers. After treatment with 4μM cytochalasin B, HAECs behaved like a homogeneous linear elastic material with an apparent modulus of 0.89±0.46kPa. These findings reveal complex mechanical behavior specifically associated with actin stress fibers that is not accurately described using the standard Hertz analysis, and may impact how HAECs interact with their mechanical environment.

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