Active control of coupled vibrations in belt drives for power transmission

The development and the results of a methodology for active control of belt vibrations in drivelines that contain elastic belts as power transmission elements are described. The methodology that is presented provides a solution for control of belt vibrations by active control of the torque that acts on a pulley in the belt drive. A new model to describe the dynamic behavior of belt drives has been developed. The nonlinear kinematics of the belt-pulley-assembly are modeled by introduction of scleronomic constraints that define the motion of the belt in the vicinity of the belt entry and exit points on the pulleys. The free belt span is modeled as a beam in finite-element-(FE)-formulation under consideration of the influence of the prestress and of the axial motion of the belt. These features are combined to yield the hybrid belt drive model (HBDM), which provides a state-space representation of the belt drive dynamics under consideration of the operating conditions in conjunction with the geometric arrangement of the driveline and with the dynamic properties of the individual components of the belt drive. Since no experimentally obtained empirical parameters are required to describe the coupling of the degrees of freedom, the HBDM allows to perform analyses of the dynamic behavior of a belt drive in early design stages where no test rigs or prototype parts are available. Based on this model, a linear quadratic regulator (LQR) state-feedback control loop has been designed that is used toreduce the lateral vibration of the free belt spans.