The paper presents a certain method of analysing the dynamics of a belt transmission. A flat transmission model developed by us was presented. For the analysis, it assumed the transmission 5PK belt. A discrete belt model, being a system of rigid beams interconnected with flexible and shock-absorbing elements, was used. To account for the mutual influence between the belt and pulleys, the Kelvin–Voigt contact model was used. The GMS friction model was also implemented, which allows all basic known friction phenomena to be taken into account. For this purpose, the vector of generalized coordinates was expanded with additional sub-systems of coordinates modelling the flexible belt-pulley connection. Moreover, two additional cases of a sudden transmission start were presented: with values of driving and resistance torque not causing a significant slip in the transmission as well as values of torque that cause slip.

A model for the dynamic analysis of a belt transmission using the Dahl friction model

The paper presents a model for dynamic analysis of belt transmission. A twodimensional discrete model was assumed of a belt consisting of rigid bodies joined by translational and torsion spring-damping elements. In the model, both a contact model and a dry friction model including creep were taken into consideration for belt-pulley interaction. A model with stiffness and damping between the contacting surfaces was used to describe the contact phenomenon, whereas a simplified model of friction was assumed. Motion of the transmission is triggered under the influence of torque loads applied on the pulleys. Equations of motion of separate elements of the belt and pulleys were solved numerically by using adaptive stepsize integration methods. Calculation results are presented of the reaction forces acting on the belt as well as contact and friction forces between the belt body and pulley in the sample of the belt transmission. These were obtained under the influence of the assumed drive and resistance torques.

The paper presents the results of measurements of friction forces achieved by forcing slip between a poly-V 5pk belt and the pulley needed to formulate empirical models of dynamic friction. This kind of belt and pulley can be found in automotive industry to drive the alternator and coolant pump in cars. The forces were measured for several cases of assumed preload and two cases of wrap angle. The complicated stick and slip processes are simplified by assuming an average effective dynamic friction coefficient. The results show that the values of friction cannot be described by classic Euler formula. They not only depend on the velocity, but also noticed that can depend on sign of acceleration. Also, some results of the approximation are presented. It is proposed that the assumed norm will be minimised using the Nelder-Mead optimisation method. The measurements and the approximation let assume specified dynamic friction characteristics. The achieved results are applied to the model of a belt transmission. In the paper presented results of simulations of the model of belt transmission.

In this paper it has been presented a research stand that allows to measure static and dynamic friction parameters between the belt and the pulley in a belt transmission. The stand can be rebuilt to three configurations to measure: static friction, the so-called kinetic and dynamic friction characteristics as well as complete belt transmission. It can measure friction parameters of any belts transmissions occurring in cars: flat belts, V-belts or poly-V belts, except toothed belts. In the stand there are build-in torque and force sensors – to measure engine torque and tension of the belt, and rotation and displacement sensors measuring angular velocities of the pulleys and displacement of the slack part of the belt. Finally, some sample results of poly-V belt 5pk, achieved from the research stand are presented.