Effect of geometric, material and operational parameters on the steady-state belt response for flat belt-drives

Abstract

This thesis presents a comprehensive study of the effects of material, geometric and operational parameters on flat belt-drives steady-state belt stresses, belt slip, and belt-drive efficiency. The belt stresses include: belt rubber shear, normal, axial and lateral stresses; reinforcements tension force; and tangential and normal belt-pulley contact stresses. Belt slip is measured using the driven over driver pulleys’ angular velocity ratio. Each parameter was varied over a range to understand its impact on the steady-state belt-drive response. The material parameters studied are belt axial stiffness and damping, belt bending stiffness and damping, and belt-pulley friction coefficient. The geometric parameters studied are pulley center distance, pulleys diameter ratio, and belt thickness. The operational parameters studied are the driver pulley angular velocity and the driven pulley opposing torque (load).

A high-fidelity flexible multibody dynamics parametric model of a two-pulley belt-drive system was created using a commercial multibody dynamics code. In the model the belt’s rubber matrix is represented using three-dimensional brick elements and the belt’s reinforcements are represented using one dimensional beam elements at the top surface of the belt. An asperity-based Coulomb friction model is used for the friction forces between the pulley and belt. The pulleys are modeled as rigid bodies with a cylindrical contact surface. The equations of motion are integrated using an explicit solution procedure.

Unlike prior models which use one-dimensional truss or beam elements for the belt, the present model uses a three-dimensional belt model which introduces the effect of the thickness of the belt rubber matrix (modeled using brick elements). This enables a more accurate prediction of the belt stresses and slip than prior models. This thesis resolves in more details the complex stick-slip friction behavior of an axially flexible belt coupled with the shear effects of a flexible rubber cushion and at the same time shows the effect of the main system parameters on this stick-slip behavior. Some of the important conclusions of the thesis include: (1) the driver pulley has two distinct contact zones - a negative traction zone and a positive traction zone - while only one traction zone is present over the driven pulley; (2) the width of the negative traction zone on the driver pulley increases with the belt-pulley coefficient of friction and decreases with the belt axial stiffness; (3) the maximum belt tension and normal contact stress occur on the driver pulley and increase with the belt thickness, belt axial stiffness, and coefficient of friction; (4) belt-drive energy efficiency increases with the belt axial stiffness, and decreases with belt thickness, belt bending damping, belt operating speed, and operating torque load. The belt-drive modeling methodology presented in this thesis which enables accurate prediction of the belt stresses and slip can in turn be used to more accurately predict the fatigue life, wear life, and energy efficiency of belt-drives.