Slip in the rolling contact of two dissimilar elastic rollers

Bentall, R. H.; Johnson, Kenneth L.

doi:10.1016/0020-7403(67)90043-4

Cited by 100 publications

(20 citation statements)

References 4 publications

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“…The results obtained for free rolling of dissimilar cylinders with normal Hertz tractions, are compared in Figure 6 with Bentall solution [3], the transient e ects disappear after rolling the contact area 1.8 times.…”

Section: Dissimilar Problemmentioning

confidence: 95%

Solving 2D transient rolling contact problems using the BEM and mathematical programming techniques

González

Abascal

2001

Numerical Meth Engineering

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SUMMARYThis work presents a new approach to the transient rolling contact of two-dimensional elastic bodies. A solution will be obtained by minimizing a general B-di erentiable function representing the equilibrium equations and the contact conditions at each time step. Inertial e ects are not taken into account and the boundary element method is used to compute the elastic in uence coe cients of the surface points involved in contact (equilibrium equations). The contact conditions are represented with the help of variational inequalities and projection functions. Finally, the minimization problem is solved using the Generalized Newton's Method with line search. The results are compared with some example problems and the in uence of discretization and integration time step on the results is discussed.

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Section: Dissimilar Problemmentioning

confidence: 95%

Solving 2D transient rolling contact problems using the BEM and mathematical programming techniques

González

Abascal

2001

Numerical Meth Engineering

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“…The regions of violation were found for zinc to be of O(10 −7 )L, where L is the zone width, thereby suggesting that some slip should always be modeled in rolling contact [3,22]. Future efforts based on this analysis will consider such a model.…”

Section: Commentsmentioning

confidence: 99%

Rolling without Slip on a Transversely Isotropic Thermoelastic Half-space

Brock

2004

J Elasticity

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Rolling without slip by a rigid cylinder on a transversely isotropic, coupled thermoelastic half-space at constant subcritical speed is studied. The cylinder is of infinite length, surface heat convection is neglected, and a dynamic steady state of plane strain is treated. The unmixed problem of traction applied to a translating surface strip is addressed first. A robust asymptotic form of the exact transform solution, valid when Fourier heat conduction dominates any thermal relaxation effect, is extracted, and inverted analytically. Use of material characterization and identification of parameters that vanish in the isotropic limit or are invariant under an isothermal-thermoelastic transformation result in compact full-field solutions. These expressions are used to construct analytical solutions that satisfy the mixed boundary value problem and auxiliary conditions of rolling contact. For the hexagonal material zinc, calculations are made for contact zone width and temperature increases near onset of zone yield. (2000): 73B30, 73C25, 73C30, 73C35. Mathematics Subject Classifications

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“…The results will be compared with the corresponding ones obtained using the Carter solution [2]. This problem has also been solved by means of semi-analytic methods by Bentall and Johnson [4] and Kalker [8].…”

Section: Similar Problemsmentioning

confidence: 99%

“…These parameters were the same as those used by Bentall and Johnson [4] and by Nowell and Hills [6] in order to compare our results with theirs. The cited works share the following assumptions: the contact zone is approximated by two half-spaces, the normal tractions and the length of the contact zone have the Hertzian values, and the tangential tractions have no e ect on normal displacements.…”

Section: Dissimilar Problemsmentioning

confidence: 99%