Dynamics of Contour Motion of Belt Drive by Means of Nonlinear Rod Approach

Abstract

The contour motion of the belt drive, i. e. the motion with the constant trajectory is addressed. The belt is considered as a closed Cosserat line whose particles have translational and rotational degrees of freedom. The problem is considered in the framework of geometrically nonlinear formulation with no restrictions on the smallness of displacements and rotations. The spatial (Eulerian) coordinate which is the arc coordinate in the actual configuration is introduced. The belt is divided into four segments: two contact segments on the pulleys and two free spans. The friction forces are assumed to obey the Coulomb law. The study is limited to the stationary case with the constant angular velocities of the pulleys and the equations in components are derived for both contact and free spans. In the contact segment two assumptions are employed to eliminate the unknown contact pressure and friction: (i) the full contact i. e. coincidence between the pulley and the belt and (ii) the stick condition i. e. the belt velocity is related to the pulley angular velocity. A nondimensional coordinate is introduced in the segments to obtain the boundary value problem with fixed boundaries. The boundary coordinates of the contact zones are the integration constants of the derived problem along with the other constants. 1 Introduction Friction belt drives were studied extensively as they are interesting from a mechanical perspective. Until recently, one-dimensional models of extensible strings were

Belt–pulley interaction: role of the action line of friction forces

“…In recent related works on the topic (see [2,8]), we find similar formulations with large displacements and rotations. However, the authors of [8] use some simplifying assumptions in the contact segment.…”

“…However, the authors of [8] use some simplifying assumptions in the contact segment. The friction interaction is assumed to occur at the belt's middle axis, whereas in the papers [2,6] it is at the bottom fibers. Shifting the contact forces to the belt's middle axis leads to certain simplifications in the problem formulation, for instance, to constant stretch in the sticking region.…”

Steady state motion of a shear deformable beam in contact with a traveling surface

“…Furthermore, we have demonstrated that the concentrated contact interaction is a limiting case of the distributed sliding friction interaction, when the sliding zone collapses into a single point because of the high friction force. Future finite element solutions for the steady state dynamic problem for a closed belt drive as well as the numerical integration of the boundary value problem similar to [4, 32] will be based on the above theoretical results and techniques of modeling.…”

“…Smallness of the creep (sliding) zones in belt drives at realistic operation conditions makes it desirable to develop an idealized model with perfect adhesion (no-slip condition) on the entire contact surface similar to the previous analysis with the string model [14, 30, 33]. The attempt to extend the static equations to the case of a moving belt [3] and to solve the resulting boundary value problem [4] has not succeeded so far. Trying to solve the problem using various finite element schemes, we arrived at the conclusion that its formulation is probably incomplete without the consideration of concentrated contact forces in the touching points.…”

Measurement of the friction parameters of a belt transmission under heavy load

“…Studies of discrete belt models have been presented in [15,21,22]. Non-discrete belt models can be modelled as an elastic rod (papers [3,4,29]), a string with assumed longitudinal and bending stiffness (papers [9,11,28] and [30]). Of course, regardless of the adopted belt models and models of friction at the belt-pulley contact, there is always a need to adjust the number of coefficients adopted in them, which will ensure the compatibility of these models with the real object.…”