ON THE EIGENFREQUENCIES OF A FLEXIBLE ARM DRIVEN BY A FLEXIBLE SHAFT
β Scribed by O. KOPMAZ; K.S. ANDERSON
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 283 KB
- Volume
- 240
- Category
- Article
- ISSN
- 0022-460X
No coin nor oath required. For personal study only.
β¦ Synopsis
The simulations of multibody dynamic systems with #exible components are generally based on solving the equations of motion by using approximate methods. This approach is taken because these systems' closed-form solutions are often not directly available. These methods often assume a solution as a "nite series in terms of modal functions with time-varying coe$cients. The eigenmodes of the system under study are preferable as the set of the basis 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 e!ective 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 investigated. This model is similar in nature to those studied previously by a number of researchers, but it is more general in form. The authors believe that this model contains a more realistic (and higher "delity) representation of the rotor}shaft}hub assembly of this system and its interaction with a #exible beam (arm) and associated payload. Through this model the relative in#uence of seven key dimensionless mass, sti!ness and geometric parameters (ratios) on system eigenfrequencies and modes may be qualitatively and quantitatively investigated. These investigations may include many special cases such as #exible shaft#rigid beam, rigid shaft##exible beam, cantilever}free beam, pinned}free beam, "xed}free shaft, etc. Given the volume of numerical studies which may be performed to this end, this paper concentrates on the e!ect of the two parameters representing the mass and sti!ness ratios of the system manipulator on its driveline.
π SIMILAR VOLUMES
A mathematical model for a #exible arm undergoing large planar #exural deformations, continuously rotating under the e!ect of a hub torque and supported by a #exible base is developed. The position of a typical material point along the span of the arm is described using the inertial reference frame
In a recent article [1], Pun and Semercigil successfully applied a joint variable stiffness control (VSC) scheme to a one-link flexible arm. A standard finite element method was used to discretize the continuous system and produce global matrices. The Newmark-b method was applied to integrate the gl