# zbMATH — the first resource for mathematics

A new universal approximate model for conformal contact and non-conformal contact of spherical surfaces. (English) Zbl 1317.74067
Summary: Elastic spherical contact, especially conformal contact, is a widely encountered problem in mechanical design and wear analysis, but corresponding universal methods do not exist. A new approximate universal solution for the normal contact between frictionless spherical surfaces is established by combining analytical and numerical methods. The proposed model is not limited to an elastic half-space and can be universally used to calculate the pressure distribution of conformal and non-conformal contact. The validity and universality of the model were verified by a large number of three-dimensional finite element analyses of different materials and structures. With the new model, users can investigate the complex relationships between key parameters, such as maximum contact pressure, radius of contact region, normal load radii, and radial clearance, and apply this understanding in design and wear analysis of products with spherical contact surfaces, such as bearings.
##### MSC:
 74M15 Contact in solid mechanics
Full Text:
##### References:
 [1] Hertz, H., On the contact of elastic solids, J. Reine Angewandte Mathematik, 92, 156-171, (1882) · JFM 14.0807.01 [2] Zhou, K.; Wei, R., Multiple cracks in a half-space under contact loading, Acta Mech., 225, 1487-1502, (2014) · Zbl 1401.74102 [3] Yoon, J.; Ru, C.Q.; Mioduchowski, A.; etal., Effect of a thin surface coating layer on thermal stresses within an elastic half-plane, Acta Mech., 185, 227-243, (2006) · Zbl 1106.74025 [4] Adams, G.G.; Nosonovsky, M., Contact modeling—forces, Tribol. Int., 33, 431-442, (2000) [5] Argatov, I.I., An approximate solution of the axisymmetric contact problem for an elastic sphere, J. Appl. Math. Mech., 69, 275-286, (2005) · Zbl 1100.74603 [6] Zhupanska, O.I., Contact problem for elastic spheres: applicability of the Hertz theory to non-small contact areas, Int. J. Eng. Sci., 49, 576-588, (2011) · Zbl 1231.74334 [7] Trifa, M.; Auslender, F.; Sidorff, F., Nanorheological analysis of the sphere plane contact problem with interfacial films, Int. J. Eng. Sci., 40, 163-176, (2002) [8] Kulchytsky-Zhyhailo, R.; Kolodziejczyk, W., On axisymmetrical contact problem of pressure of a rigid sphere into a periodically two-layered semi-space, Int. J. Mech. Sci., 49, 704-711, (2007) [9] Chang, L.; Zhang, H., A mathematical model for frictional elastic-plastic sphere-on-flat contacts at sliding incipient, ASME J. Appl. Mech., 74, 100-106, (2007) · Zbl 1111.74350 [10] Giannakopoulos, A.E., Strength analysis of spherical indentation of piezoelectric materials, ASME J. Appl. Mech., 67, 409-416, (2000) · Zbl 1110.74456 [11] Morimoto, T., Iizuka, H.: Conformal contact between a rubber band and rigid cylinders. ASME J. Appl. Mech. 79, 044504, 1-4 (2012) [12] Persson, A.: On the Stress Distribution of Cylindrical Elastic Bodies in Contact. Ph.D. Thesis, Chalmers University, Gothenburg, Sweden (1964) [13] Kovalenko, E.V.: Contact problems for conforming cylindrical bodies. J. Frict. Wear. 4, 35-44 (1995) · Zbl 1300.74038 [14] Ciavarella, M.; Decuzzi, P., The state of stress induced by the plane frictionless cylindrical contact I. the case of elastic similarity, Int. J. Solids Struct., 26, 4507-4523, (2001) · Zbl 1090.74639 [15] Sundaram, N.; Farris, T.N., The generalized advancing conformal contact problem with friction, pin loads and remote loading—case of rigid pin, Int. J. Solids Struct., 47, 801-815, (2010) · Zbl 1193.74105 [16] Sundaram, N.; Farris, T.N., Mechanics of advancing pin-loaded contacts with friction, J. Mech. Phys. Solids, 58, 1819-1833, (2010) · Zbl 1225.74061 [17] Sun, Z.G.; Hao, C.Z., Conformal contact problems of ball-socket and ball, Phys. Procedia, 25, 209-214, (2012) [18] Steuermann, E., On Hertz theory of local deformation of compressed bodies, Comptes Rendus (Doklady) del’Acade ’mie des Sciences del’URSS, 25, 359-361, (1939) · JFM 65.0920.03 [19] Johnson K.L.: Contact Mechanics. Cambridge University Press, New York (1985) · Zbl 0599.73108 [20] Liu, C.S.; Zhang, K.; Yang, L., Normal force-displacement relationship of spherical joints with clearances, ASME J. Comput. Nonlinear Dyn., 01, 160-167, (2006) [21] Goodman, L.E., Keer, L.M.: The contact stress problem for an elastic sphere indenting an elastic cavity. Int. J. Solids Struct. 1, 407 (1965) [22] Wriggers P.: Computational Contact Mechanics. Springer, Berlin (2012) · Zbl 1104.74002 [23] Larissa, G.A.; Johannes, G.; Astrid, S.; Pechstein, A., A two-dimensional homogenized model for a pile of thin elastic sheets with frictional contact, Acta Mech., 218, 31-43, (2011) · Zbl 1300.74038 [24] Kamin’ski, M., Design sensitivity analysis for the homogenized elasticity tensor of a polymer filled with rubber particles, Int. J. Solids Struct., 51, 612-621, (2014) [25] Li, Y.F.; Wang, G.L.; Lu, Z.S.; Shao, D.X., Research on stiffness measurement of spring tubes based on three-dimensional conformal contacts model, J. Phys. Conf. Ser., 48, 701-705, (2006) [26] Fang, X.; etal., Physics-of-failure models of erosion wear in electrohydraulic servovalve, and erosion wear life prediction method, Mechatronics, 23, 1202-1214, (2013) [27] Wu, A.Z.; Andreas, X.S.; Polycarpou, A., An elastic-plastic spherical contact model under combined normal and tangential loading, ASME J. Appl. Mech., 79, 051001, (2012) [28] Vinnik, L.; Bourtchak, G.; Olshevskiy, A., Analysis of parameters of conformal contact for wheel-center and bandage of an innovative wheel, Wear, 265, 1292-1299, (2008) [29] Liu, Y.J.: Boundary Element Method for Moving Contact of 3D Elastic Bodies. Ph.D. Tsinghua University, Beijing, China (2003) [30] Polonsky, I.A.; Keer, L.M., A numerical method for solving rough contact problems based on multi-level multi-summation and conjugate gradient techniques, Wear, 231, 206-219, (1999) [31] Maceri A.: Theory of Elasticity. Springer, Berlin (2010) [32] Khoddamzadeh, A.; etal., Novel polytetrafluoroethylene (PTFE) composites with newly developed tribaloy alloy additive for sliding bearings, Wear, 266, 646-657, (2009) [33] Shen, X.J.; Liu, Y.F.; Cao, L.; Chen, X.Y., Numerical simulation of sliding wear for self-lubricating spherical plain bearings, J. Mater. Res. Technol., 10, 8-12, (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.