The Influence of Pulley Deformations on the Shifting Mechanism of Metal Belt CVT

Abstract

This paper is concerned with the shifting behavior of a metal belt CVT. The calculations are performed for the chain belt case by using a one-dimensional model of the belt: the radial thickness of the belt is neglected. The friction forces are modeled on the basis of the Coulomb friction hypothesis. The deformation of the belt, i.e., the variation of its transversal width, is shown to be negligible with respect to the variation of the local groove width caused by the elastic deformation of the pulleys and by the clearance in the bearings. The particular shape of the deformed pulley is described on the basis of Sattler model (1999) who showed that the variation of the groove angle and that one of the local groove width of the pulley can be easily described by simple trigonometric formulas. The paper shows that the characteristic behavior of the transmission during slow shifting maneuvers, referred to as “creep mode,” is caused by the bending of the pulleys, that is to say for rigid pulleys no “creep mode” can be observed. Moreover, the model shows that increasing the rate of change of speed ratio a transition from the “creep-mode” to the so called “slip-mode” behavior of the variator takes place, as experimentally observed.

RETRACTED: Novel application of continuously variable transmission system using composite recurrent Laguerre orthogonal polynomials modified PSO NN control system

“…In order to reduce system complexity, the torque dynamic equations in the primary drive shaft and the secondary drive shaft of the V-belt CVT shown in Fig. 2 can be simplified as [1][2][3][4][5][6][7][8] …”

“…in which T s l ðF l ðB g Þ; υ a ðv r ; B g Þ; τ a ðv r Þ; ω 2 s Þ [1][2][3][4][5][6][7][8] is the lumped nonlinear external disturbances of the secondary drive side on the wheel; T p ¼ σ s ω s T s =ω p is the drive torque of the primary pulley shaft; T s is the drive torque of the secondary pulley shaft; σ s is the conversion ratio with respective to secondary pulley shaft to primary pulley shaft of V-belt arc length; υ a ðv r ; B g Þ is the rolling resistance; τ a ðv r Þ is the wind resistance; F l ðB g Þ is a braking force; v r is the total wind velocity; B g represents the total frictional coefficient of ground surface; B p and B s represent the viscous frictional coefficients of the PM synchronous motor and the wheel, respectively; J p and J s are the inertias of the PM synchronous motor and the wheel, respectively; ω p and ω s are the speeds of the PMSM and the wheel, respectively. Then using speed ratio and sliding ratio [1][2][3][4][5][6][7][8], the torque equation can be transformed from the secondary pulley side to the primary pulley side.…”

“…In this study the composite recurrent Laguerre orthogonal polynomials modified PSO NN control system is proposed for controlling the V-belt CVT system with many nonlinear dynamics [1][2][3][4][5][6][7][8][44][45][46][47][48]. The composite recurrent Laguerre orthogonal polynomials modified PSO NN control system has good generalization ability and fast learning capability.…”

“…A V-belt continuously variable transmission (CVT) [1][2][3][4][5][6][7][8] usually consists of two springs, which impelled variable radii pulleys, and a chain with belt. To mobilize a vehicle from rest, the primary pulley radius will be smaller than the secondary pulley radius which resulted in torque multiplication transmitted to the secondary drive shaft and in a speed reduction.…”

Control-Oriented Modelling with Experimental Verification and Design of the Appropriate Gains of a PI Speed Ratio Controller of Chain CVTs

“…The clamping force ratio as a function of torque load and traction coefficient is derived in detail. Carbone et al [9] demonstrate that the pulley bending has an important role in the dynamics of the variator. The sliding angle that is one of the main parameters in equilibrium equations varies if the pulley deformation is considered.…”