The Dynamics of the Mechanical Variable Speed Drives of the Friction-Wheel Type

Mechanical variable speed drives are widely used as a manipulating device in speed and tension control systems of running arns and fabrics. In spite of the importance of the knowledge of their dynamics in the analysis and synthesis of these control systems, very few investigations have been published until now.As a part of the authors' study about the feed control system, they have taken up the mechanical variable speed drive of the friction-wheel type, and have analyzed its dynamics both theoretically and experimentally.<BR>In theoretical investigation, it is assumed that the slip in the direction of rolling at the rolling contact is exclusively dependent upon the tangential force in that direction according to K. L. Johnson. This dependence is determined through experiments to avoid the theoretical complexity of the rolling contact phenomena. The results of the analysis of the dynamics based on this expermental analysis are compared with those of the experiments of a mechanical variable speed drive of the friction-wheel type. The following is a summary of the results thus obtained : <BR>(1) The dynamics of the mecanical variable speed drive is descrived by a set of non-linear ordinary differential equations. By means of approximate linearisation at the vicinity of the set point, it is transformed into a set of linear equations. The transfer functions between the angular displacement of the handle which changes the revolutions of the output shaft and the angular velocity of the output shaft are found to be expressed by a rational fraction. The denominator and the numerator are both second order polynomials for a variable speed drive using a pair of friction wheels. For a variable speed drive using two pairs of friction wheels, the denominator is a third order polynomial and the numerator is of the second order.<BR> (2) The single contact type variable speed drive is used for the experiment. The theoretical dynamics of the variable speed drive derived on the basis of the statical experiments about the slip at the contactbetween the friction wheels are proved to be in fairly good coincidene with the experimental ones, thus the validity of the theory being accertained.<BR> (3) The dynamics of the mechanical variable speed drive tested here are greatly affected by the change in the set-point angular velocity and the set-point torque of the driven shaft.