Device and Measuring Method the Moments of Rolling Resistance Forces on the Contact Spot

Currently, the study of rolling friction is one of the main directions in the study of the laws of contact interaction of solids. The complexity of solving the problems existing in this area is evidenced by the practically vast number of publications, the list of which is constantly growing.

In this paper, attention is paid to studies of the moments of rolling resistance at displacements from the equilibrium position of a ball-shaped body that are substantially smaller than the size of the contact spot. The purpose of the present work is to describe the design of the single-contact pendulum device developed by the authors, in which the physical pendulum, resting on the flat surface of the body under study with only one ball, makes free small stable swings in a vertical plane, as well as in the description of a special measurement technique with high sensitivity and accuracy rolling resistance forces, including adhesion forces and frequency-independent forces of elastic deformations. It is assumed that the adhesion forces can exhibit both dissipative properties and elastic properties, while elastic forces are independent of the strain rate.

The originality of the method of measuring rolling resistance in this paper consists in using the method of nonlinear approximation of the dependence of the amplitude and period of swing of the pendulum on time. The approximation is carried out on the basis of the proposed laws of amplitude decay and period variation, which differ from the usual exponential law.

It is assumed that this approach allows one to evaluate the surface tension of a solid and evaluate the pressure of adhesion forces between the surfaces of the contacting bodies, as well as to establish an analytical form of the moment of rolling resistance. The curves of the dependence of the rolling resistance moment on the swing amplitude of the pendulum are constructed. Experiments were performed for the following pairs of contacting bodies: steel-steel, steel-glass, steel-electritechnical silicon. It was assumed that the pressure at the contact spot did not exceed the elastic limit.

The developed single-ball pendulum device and the proposed measurement procedure open up new wide possibilities for studying the laws of mechanisms of rolling resistance under conditions of microand mesoscale displacements of a rolling body from a state of rest.

1. Cross R. Coulomb’s Law for rolling friction. Amer. J. Phys., 2016, vol. 84, no. 3, pp. 221–230. DOI: 10.1119/1.4938149

2. Cherepanov G.P. The laws of rolling. Physical Mesomechanics, 2019,vol. 22, no. 3, pp. 242–254. DOI: 10.1134/S1029959919030093

3. Popov V.L. Contact mechanics and friction: Physical Principles and Applications. Berlin: Springer, Berlin, Heidelberg, 2017, pp. 231–253. DOI: 10.1007/978-3-662-53081-8

4. Popov V.L. What does friction really depend on? Robust governing parameters in contact mechanics and friction. Physical Mesomechanics, 2016, vol. 19, no. 2, pp. 115–122. DOI: 10.1134/S1029959916020016

5. Bowden F.P., Tabor D. The friction and lubrication of solids. New York: Oxford University Press, 1950, 372 p.

6. Johnson K.L. Contact mechanics. Cambridge university press, 1987, 452 p. DOI: 10.1017/CBO9781139171731

7. Mekid S. A non-linear model for pre-rolling friction force in precision positioning. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2004, vol. 218, no. 4, pp. 305– 312. DOI: 10.1243/1350650041762686

8. Tan X., Modafe A., Ghodssi R. Measurement and modeling of dynamic rolling friction in linear microball bearings. Journal of Dynamic Systems, Measurement, and Control, 2006, vol. 128, pp. 891–898. DOI: 10.1115/1.2362786

9. Amthor A., Zschaeck S., Ament C. High precision position control using and adaptive friction compensation approach. IEEE Transactions on automatic control, 2010, vol. 55, no. 1, pp. 274–278. DOI: 10.1109/TAC.2009.2036307

10. Benditkis R., Necsulescu D.S. Comment on rolling resistance. Technical briefs in J. Tribology, 1994, vol. 116, no. 3, pp. 658–659. DOI: 10.1115/1.2928898

11. Van Spengen W. Merlijn. MEMS reliability from a failure mechanisms perspective. Microelectronics Reliability, vol. 43, no. 7, 2003, pp. 1049–1060. DOI: 10.1016/S0026-2714(03)00119-7

12. Mekid S. Dedicated instruments for nanoengineering education: Integrated nano-manipulation and micro-nanomachining. International Journal of Mechanical Engineering Education, 2019, p. 0306419019846591. DOI: 10.1177/0306419019846591

13. Mekid S., Bashmal S. Engineering manipulation at nano-scale: further functional specifications. Journal of Engineering, Design and Technology, 2019, vol. 17, no. 3, pp. 572–590. DOI: 10.1108/JEDT-09-2018-0165

14. Szoszkiewicz R., Bhushan B., Huey B.D., Kulik A.J., Gremaud G. Adhesion hysteresis and friction at nanometer and micrometer length. Journal of applied physics, 2006, vol. 99, iss. 1, pp. 1–7. DOI: 10.1063/1.2159081

15. Belyiy V.A., Egorenkov N.I., Pleskachevskiy Y.M. Adgeziya polimerov k metallam [Adhesion of polymers to metals]. Minsk: Nauka i tehnika Publ., 1971, 228 p.

16. Mendeleev D.I. Opytnoe issledovanie kolebaniya vesov i vozobnovlenie prototipa ili osnovnoj obrazcovoj russkoj mery massy v 1893-1898 gg. [Experimental research: weight change and the renewal of the prototype or the main exemplary Russian measure of mass in 18931898], L. Gos. nauch.-tekhn. izd-vo, Lenhimsektor, 1931, 302 p.

17. Herbert E.G. Some Recent developments in hardness testing. The Engineer, 1923, vol. 135, pp. 686– 687.

18. Halama R., Podešva J., Suzuki R., Matsubara M., Čech R. Mechanics of Herbert Pendulum Hardness Tester and its Application. Key Engineering Materials. Trans Tech Publications Ltd, 2017, vol. 741, pp. 122–127. DOI: 10.4028/www.scientific.net/KEM.741.122

19. Matsubara M., Sakamoto K. Improved Herbert hardness tester. Experimental Techniques, 2012, vol. 36, no. 3, pp. 73–76. DOI: 10.1111/j.1747-1567.2011.00736.x

20. Suzuki R., Kaburagi T., Matsubara M., Tashiro T., Koyama T. Hardness Measurement for Metals Using Lightweight Herbert Pendulum Hardness Tester With Cylindrical Indenter. Experimental Techniques, 2016, vol. 40, no. 2, pp. 795–802. DOI: 10.1111/ext.12121

21. Kuznecov V.D. Fizika tverdogo tela [Solid state physics: 5 vol.]. Tomsk: Krasnoe znamya Publ., 19371949, vol. 1, 1937, pp. 448–480 (in Russian).

22. Tomlinson G.A. CVI. A molecular theory of friction. The London, Edinburgh, and Dublin philosophical magazine and journal of science, 1929, vol. 7, no. 46, pp. 905–939. DOI: 10.1080/14786440608564819

23. Gilavdary I., Mekid S., Riznookaya N. Microslippage effects in pre-rolling induced by a disturbed and undisturbed pendulum with spherical supports. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2014, vol. 228, no. 1, pp. 46–52. DOI: 10.1177/1350650113498230

24. Gilavdary I., Mekid S., Riznookaya N. A new theory on pure pre-rolling resistance through pendulum oscillations. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2013, vol. 227, no. 6, pp. 618–628. DOI: 10.1177/1350650112465516