Input torque balancing using a cam-based centrifugal pendulum: design optimization and robustness

In a companion paper (Input torque balancing using a cam-based centrifugal pendulum: design procedure and example, J. Sound Vib.), the cam-based centrifugal pendulum (CBCP) was introduced as a simple, cam-based, input torque balancing mechanism. The differential equation that governs the CBCP cam design was derived and a methodology for solving it was developed. Furthermore, in a design example, the CBCP was applied to balance the input torque of a high-speed cam-follower mechanism, driving the sley of a weaving loom. The present paper firstly shows how the design parameters for this particular design example can be optimized, so as to obtain a compact and technologically feasible mechanism. The formulation of the optimization problem is based on a parameterization of the CBCP rotor and coupler shape. Because of its nonconvex nature, the optimization problem is solved using a multi-start sequential quadratic programming (SQP) approach. A design chart, based on an exhaustive analysis, is introduced which (i) allows the designer to perform the design optimization in a quick and approximative way, and (ii) gives considerable insight into the behavior of the SQP-algorithm. Secondly, the CBCP is applied to an industrial case study, that is, a weaving loom. The robustness of the CBCP is illustrated by showing that input torque balancing solely the sley movement enhances the overall dynamic machine behavior, despite the presence of the non-balanced shed motion. A particular contribution of this part is the determination of the weaving loom regime behavior in the frequency domain, an approach which is believed to be novel in mechanism literature.