On the eigenfrequencies of a flexible arm driven by a flexible shaft

The simulations of multibody dynamic systems with flexible components are g enerally based on solving the equations of motion by using approximate meth ods. This approach is taken because these systems' closed-form solutions ar e often not directly available. These methods often assume a solution as a finite series in terms of modal functions with time-varying coefficients. T he eigenmodes of the system under study are preferable as the set of the ba sis functions used in these series because such expansions provide greater accuracy with fewer terms. As a consequence, accurate estimation of system eigenfrequencies and eigenmodes is extremely useful (potentially necessary) in the effective modelling and simulation of these systems. In this paper, a new general model consisting of rotor, shaft, hub, beam, and payload, as might be encountered in certain industrial robots, is presented and invest igated. This model is similar in nature to those studied previously by a nu mber of researchers, but it is more general in form. The authors believe th at this model contains a more realistic land higher fidelity) representatio n of the rotor-shaft-hub assembly of this system and its interaction with a flexible beam (arm) and associated payload. Through this model the relativ e influence of seven key dimensionless mass, stiffness and geometric parame ters (ratios) on system eigenfrequencies and modes may be qualitatively and quantitatively investigated. These investigations may include many special cases such as flexible shaft + rigid beam, rigid shaft + flexible beam, ca ntilever-free beam, pinned-free beam, fixed-free shaft, etc. Given the volu me of numerical studies which may be performed to this end, this paper conc entrates on the effect of the two parameters representing the mass and stif fness ratios of the system manipulator on its driveline. (C) 2001 Academic Press.