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04CVT-32 Analysis of self-induced vibrations in a pushing V-belt CVT Wolfram Lebrecht Institute of Applied Mechanics, Technical University of Munich Friedrich Pfeiffer, Heinz Ulbrich Institute of Applied Mechanics, Technical University of Munich Copyright © 2004 SAE International ABSTRACT Although there exist different types of CVT-systems, in this paper only the metal V-belt CVT is considered. As it The paper will focus on investigations which were made is shown in Figure. 1.1 such a system consists of two during a cooperation project with an important supplier of sets of pulleys and the belt that runs inside of the two V- gears. In some working points of a pushing V-belt CVT pulleys. In this case the power transmission is very an unexplainable noise occurs. To find out the reason of complicated because the transmitted torque results in this phenomena a simulation model is built up which the compression force between the elements and the contains an elastic model of the pulley sheaves as well ring tension. Additionally there are sveral types of as a detailed description of the belt. With this model different contacts: element-element, element-ring, investigations are made but the results do not include the element-pulley and ring-ring. expected vibration so far. An analytical approach is used At the institute of Applied Mechanics of the Technical the calculate possible eigenfrequencies of the belt. University of Munich a two-dimensional model was Together with the belt forces from the simulation model it developed to analyse the complex dynamical behaviour is shown that the eigenfrequencies of the belt are in the of a pushing V-Belt CVT. same range as the measured frequencies of the noise. In the next step the simulation model is extended by a 2 MECHANICAL MODEL non-constant friction law. Investigations show that if the friction coefficient in the contact between pulley and The multibody system of the gear described above elements decreases with the relative velocity, the belt consists of two movable and two fixed sheaves and a could be excited by the friction-contact. force transmitting belt like in Figure. 2.1. 1 INTRODUCTION Continuously variable transmissions are an interesting alternative to conventional concepts like manual or automatic transmissions. Due to a stepless variable speed ratio they have the potential to be an ideal intersection between the engine and the power train. Figure 2.1 Metal pushing V-belt 2.1 PULLEY SET – A belt CVT-system contains a driving and a driven pulley. One sheave of each pulley is axially movable by a hydraulic cylinder forcing the belt to a pretended radius. With a controller the piston pressures pdr , pdn are affected to adjust the speed ratio Figure 1.1 model of a metal V-Belt CVT and the pulley thrust. The boundary conditions are given by the external excitation (torque M, or angular velocity ω ), the control pressure p and the belt contact forces fi . A CVT-system with its different components offers a (2) diversified frequency spectrum which has to be taken into account in the mathematical model. To reduce the At steady state the axial components of the contact calculation time, frequencies above a defined limit are forces fi,ax are balanced with the spring prestress Fc and eliminated by calculating their degrees of freedom with a the piston force composed by a rotation independent part quasi-static formulation. This section is divided into two Appand a rotation dependent part Fω. The tilting δx, δy is parts: In the first part the dynamical degrees of freedom calculated by equation (3), using a stiffness of tilting cδ . are introduced and in the second part we will focus on the quasi-static degrees of freedom which are used to describe the deformation of the elastic bodies. 2.1.1 Rigid-body model – The global dynamics of the pulleys can be de

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