This paper derives a stiffness equation for the arbitrarily crowned roller compressed between two plates. The roller is first divided into three parts: two crowned parts and one cylindrical part. The superposition method is introduced to obtain the roller stiffness. Three-dimensional finite element analyses were used to validate the accuracy of the stiffness equation, in which rollers with circular, quadratic, cubic, fourth-order power and exponential profiles were analysed. Comparisons with finite element results indicate that the accuracy of the stiffness equation derived in this paper is acceptable.
JuS. H.ChaK. C.Evaluating stress intensity factors of a surface crack in lubricated rolling contactsInt. J. Fracture, 1999, 96, 1–15.
2.
JuS. H.HorngT. L.ChaK. C.Comparisons of contact pressures of crowned rollersProc. Instn Mech. Engrs, Part J, J. Engineering Tribology, 2000, 214 (J2), 147–156.
3.
NikpurK.GoharR.Deflection of a roller compressed between platesTribology Int., 1975, 8, 2–8.
4.
ReusnerH.The logarithmic roller profile—the key to superior performance of cylindrical and taper roller bearingsBall Bearing J., 1987, 230, 2–10.
5.
NayakL.JohnsonK. L.Pressure between elastic bodies having a slender area of contact and arbitrary profilesInt. J. Mech. Sci., 1979, 21, 237–247.
6.
LundbergG.Elastiche Beruhreng zweier Halbraume (Elastic contact of two half spaces)Forschung AUF dem Gebiete der Ingenieuwesens, 1939, 10, 320.
7.
HorngT. L.JuS. H.ChaK. C.A deformation formula for circular crowned roller compressed between two platesTrans. ASME, J. Tribology, 2000, 122, 405–411.
8.
HollD.Plane-strain distribution of stress in elastic media. Iowa Engineering Experiment Station, Iowa State College, Bulletin, 1941, Vol. 148, p. 39.
9.
HarrisA.Rolling Bearing Analysis, 1984, p. 137 (John Wiley, New York).
10.
DowsonD.HigginsonG. R.Theory of roller bearing lubrication and deformation. In IMechE Proceedings of Convention onLubrication and Wear, 1963, Vol. 19, pp. 216–227 (Institution of Mechanical Engineers, London).
11.
HamrockB. J.Simplified solution for stresses and deformationsTrans. ASME, J. Lubric. Technol., 1983, 105, 171–177.
HoeprichM. R.ZantopulosH.Line contact deformation: A cylinder between two flat platesTrans. ASME, J. Lubric. Technol., 1981, 103, 21–25.
14.
JuS. H.Development of a nonlinear finite element program with rigid link and contact element. Report of the NSC in ROC, NSC-86-2213-E-006-063, 1997, pp. 66–81. This report and program source codes in an executable compressed file nfemnew.exe of MS-DOS can be obtained from the FTP server 140.116.36.4
15.
WilsonE. L.TaylorR. L.DohertyW. P.GhaboussiJ.Incompatible displacement models In Numerical and Computer Method in Structural Mechanics (Eds FenvesS. J.PerroneN.RobinsonA. R.SchnobrichW. C.), 1973, pp. 43–57 (Academic Press, New York).
16.
JuS. H.KungK.-J. S.Mass types, element orders and solving schemes for the Richards equationComputers and Geosci., 1997, 23, 175–187.
17.
JuS. H.RowlandsR. E.A three-dimensional frictional contact element whose stiffness matrix is symmetricTrans. ASME, J. Appl. Mechanics, 1999, 66, 460–467.
18.
JuS. H.HorngT. L.Behaviors of a single crack in multiple bolted jointsInt. J. Solids Structs, 1999, 36, 4055–4070.
