Sommerfeld effect in a single-DOF system with base excitation from motor driven mechanism

Abstract

Sommerfeld effect is a nonlinear phenomenon observed in rotating machinery driven by a non-ideal source. It is characterised by capture at resonance for a finite range of drive power followed by a sudden release. This paper investigates the dynamics of a direct current (DC) motor driven mechanism which excites the base of a vibrating structure. A slotted cam follower mechanism and a scotch yoke mechanism are chosen for the base excitations of a single degree of freedom oscillator. It is shown that the Sommerfeld effect leads to capture-and-escape (jump) through multiple resonance zones, and as a result, some intermediate speed ranges are missed. The critical power/voltage input to escape through all the resonances may exceed that required to escape the primary resonance. Moreover, while increased structural damping makes it easier to escape resonance capture, it reduces the system efficiency at super-critical operating speeds. These are important design considerations for sizing the motor drives of these mechanisms. Analytical predictions for jumps are obtained from a steady-state power balance whereas the transient analysis is performed with the help of Bond Graph (BG) models and MSC-ADAMS software. The transient responses from the numerical models are used to verify the analytical results.