Contact of Flexible Elastic Belt with Two Pulleys

Abstract

The drive belt set on two pulleys is considered as a nonlinear elastic rod deforming in plane. The modern equations of the nonlinear theory of rods are used. The static frictionless contact problem for the rod is derived. The nonlinear boundary value problems for the ordinary differential equations are solved by the finite differences method and by the shooting method by means of computer mathematics. The belt shape and the stresses are determined in the nonlinear formulation which delivers the contact reaction and the contact area. The developed method allows performing calculations for any set of geometrical and stiffness parameters.

Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod

“…4, we discuss the variants of numerical solution of the formulated BVP. Finally, we show the results of numerical work and compare them with the previous results for the extensible model without shear [4] and the model without extension and shear [5]. A special case of different pulleys is studied in [6].…”

“…The pressure is positive, and its maximum equals 14.9 × 10 3 N/m. For considering the shear, there is no lumped boundary reaction force as in the model without shear [4,5]. For comparison, we draw the constant pressure from the equivalent (by the force P) problem without shear, but with tension, see the simpler modelling for this special case in [4].…”

“…[4,5], the first component of force Q 1 is constant in the contact segment, and Q 2 is equal to zero. Besides in the case without shear, we have the lumped contact force at the contact segment boundary.…”

“…The calculation of the belt-pulley interaction can be found in [4,5,21,24,27,28,31]. It should be made with account for transverse shear.…”

“…A way of solving BVP by means of computer mathematics for the system (1) is described in [23]. The algorithms and the results for the belt-pulley contact without shear are presented in [4,5]. The peculiarity of the considered problem is due to the fact that the function r(s) = R(σ ) is unknown in the contact segment because the arc coordinate σ is not yet determined.…”