Krzysztof Kubas

One of the problems occurring at the stage of creating belt transmission models is determining the tribological properties at the belt-pulley interface. These properties depend on the manufacturer and, most importantly, on the materials and technological processes used during the belt production. The article presents the research results of 5PK belts from various manufacturers used in belt transmissions of the alternator and air conditioning compressor pump, i.e. FEAD (Front Engine Accessory Drive) systems. The main goal of the research was to check whether these belts would differ in their tribological properties. Belts from ten different manufacturers were subjected to experiments. The research was divided into two stages. First, the values of the friction coefficients of the belt fragment were determined when trying to force it to move around the pulley. Subsequently, an analysis was conducted to establish the relationship between the belt slip installed in the transmission and the resistance torque in all the cases under consideration. As shown in the work, belts from various manufacturers differ in both the surface layer structure interacting with the pulley and the values of friction and slip coefficients. Finally, a simplified model was proposed to analyze the dynamics of belt transmissions, using research results presented in this work.

This article presents the results of measurements of a belt transmission with a poly-V belt 5PK, most often used in the industry, especially in industrial drives, agricultural machines and in the automotive industry. The main goal of the works was to obtain the dependence of the belt slip value on the measured, relatively high values of resistance torque. For this purpose, a series of measurements were made using a specialised research stand consisting of two alternating current motors and attached pulleys. It considered four cases of the value of the belt pre-tensioning force. In each of the cases, while making the measurements, the resistance of the passive pulley was increased, resulting in increasing values of belt slip. Finally, the achieved courses were approximated. The obtained results will be used to develop empirical models of friction at the belt-pulley interface. They can also be useful for belt manufacturers to make better belts, especially those subjected to higher loads.

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.

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.

The article presents a method of discretising a belt used in a transmission model with any number of pulleys and tensioning rollers and any direction of wrapping the pulleys or rollers. The positions of the discretising points are formulated in a global coordinate system. The method allows for arbitrary placement of pulleys and tensioning rollers. It also consequently allows to calculate the length of the belt, resulting from the geometry of the transmission, and the length of the belt, resulting from the coordinates of the discretising points that lie on its circumference. The method presented here allows to estimate the number of points that would provide satisfactory accuracy of the belt’s curvature surrounding the individual pulleys and rollers. In the paper presented comparison between two proposed ways of estimating. Designated points can be used as input data to analyse the belt dynamics with the belt modelled as rigid elements connected to one another by translational or rotational spring-damping elements.

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

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.

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.