Torsional vibration reduction of rotating shafts for multiple orders using centrifugal double pendulum vibration absorber

Abstract

Centrifugal Pendulum Vibration Absorbers (CPVAs) reduce the torsional fluctuations of rotating shafts at fixed vibration order by changing the natural frequency in accordance with the excitation frequency. Attenuation of multiple orders is necessary in the case of the rear wheel drive vehicle and cylinder deactivation applications for achieving refined vehicle performance. Single pendulum vibration absorbers attenuate only one vibration order at a time and the pendulum length must be reduced for higher orders in the order of (1/n2) times the distance between the center of rotation and pivot point to attenuate nth order vibration. Use of single pendulum absorbers for reducing higher orders has limitations due to manufacturing inaccuracies and occurrence of wear of joints over prolonged usage which reduces the effectiveness of absorber in reducing the torsional vibration. In this study, a centrifugal double pendulum vibration absorber (CDPVA) is proposed to make the design easy for higher orders by deploying two pendulums in series. The CDPVA is designed to attenuate the fundamental excitation order (n) and its second harmonic (2n) without significant reduction in the pendulum length hence making the design robust for prolonged usage. The mass and length values of the double pendulum are tuned to match the two natural frequencies correspond to the fundamental and second harmonic order of the torsional vibration excitation. Torsional springs are used at the pivot joints of the double pendulum to counteract the gravitational effects at low speeds and the influence of spring stiffness on the natural frequencies is analyzed. The nonlinear second order equations of motion of pendulum masses and rotor are solved analytically using method of multiple time scales and the stability characteristics of pendulum motion are analyzed at the excitation frequencies with different torque levels. Numerical simulation of complete nonlinear equations is carried out and the analytical results are compared with the simulation results. The designed CDPVA for 2nd and 4th order is tested on a 4-cylinder the rear wheel drive vehicle and considerable reduction is achieved in the torsional vibration of the drive shaft and also in the vibration levels at seating locations. The proposed methodology helps in designing the CDPVAs for attenuating the torsional vibration of multiple higher orders yet avoiding impacts in low speed operation.