Payload Sensitivity in Coupled Bending and Torsional Vibrations in Flexible Beams

摘要

The aim of the report is to analyze the coupling between bending and torsional vibrations in flexible robot arms. The coupling is usually disregarded but it is ultimately present due to the asymmetry of a realistic payload. The author shows that the coupling dramatically changes the system dynamics, most dominantly the mid-frequency range. The kinematic equations are given assuming an Euler-Bernoulli model with Voigt-type of internal damping and with an asymmetric tip body. He also assumes different damping coefficients in bending and in torsional vibrations, respectively. He provides the exact frequency response in the frequency domain, and shows that a finite number of poles of the coupled system are along a circle in the negative half-plane in the s-domain and an infinite number of poles are along the negative real axis. Based on a frequency functions the author provides a sensitivity analysis regarding the payload parameters. A computer package has also been developed to calculate the frequency responses, the sensitivity functions and their pole-zero configurations.