On static contact of belt and different pulleys

Winter School on Continuous Media Mechanics

Belyaev, A.K.^1 ; Eliseev, V.V.^2 ; Irschik, H.^3 ; Oborin, E.A.^3

Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bolshoy ave., V.O. 61, St.Petersburg

199178, Russia^1

Peter the Great Saint-Petersburg Polytechnic University, Polytechnicheskaya St. 29, St.Petersburg

195251, Russia^2

Institute of Technical Mechanics, Johannes Kepler University, Linz, Austria^3

关键词: Axis of symmetry;    Concentrated contacts;    Contact pressures;    Geometrically nonlinear;    Material coordinates;    Nonlinear boundary value problems;    Shooting methods;    System of ordinary differential equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/208/1/012004/pdf
DOI  :  10.1088/1757-899X/208/1/012004

来源: IOP

【 摘 要 】

The fitting of a looped belt on two pulleys with different radii is considered. A geometrically nonlinear model with account for tension and transverse shear is applied for modeling the belt. The pulleys are considered rigid bodies, and the belt-pulley contact is assumed frictionless. The problem has an axis of symmetry, therefore the boundary value problem is formulated and solved for a half of the belt. The considered part consists of three segments, two contact segments and a free span segment between them. The introduction of a dimensionless material coordinate at all segments leads to a system of ordinary differential equations of fifteenth order. The nonlinear boundary value problem for this system and boundary conditions is solved numerically with the shooting method and the finite difference method. As a result, the belt shape including the rotation angle, the forces, moments and contact pressure are determined. The contact pressure increases near the end point of contact areas, however no concentrated contact forces occur.