No abstract

The “exact” and pole/zero transfer functions are developed for a flexible beam-like single link arm with actuator on one end and payload on the other. This model represents a broader class of actuator hub and payload mass properties than is found in prior literature. The dependence of dynamics on the hub and payload inertia characteristics are studied and graphs are provided to facilitate estimation of poles and zeroes for any similar plant. It is shown that a 10:1 reduction in fundamental frequency and substantial change in the zeroes results from variations in payload through a practical range. Payload rotary inertia is shown to cause a qualitative change in the arm tip zeroes resulting in loss of observability/controllability in some cases. Results provide insight into the two-link problem and it is shown that complex values zeroes may result if the second arm is allowed to “fold back.” Implications to plant modeling and control design are discussed including sensor placement and model order reduction issues. Analytical results are compared to those measured on an experimental arm and show very good agreement in modal frequency and shape.

A fourbar linkage test-bed has been designed, built, and instrumented to measure the effects of dynamic balancing, vibration isolation and system stiffness on the dynamic forces and torques generated at the pivot bearings and on the ground plane. The system was initially designed and modelled using the Aries solids modelling package, the ADAMS dynamic simulation package, program Dynafour, and ANSYS finite element analysis software. The theoretical dynamic forces and accelerations at particular points on the links were calculated in advance, based on the system kinematics and the mass properties of all moving members as defined by the Aries solids modeller. The device was built using accurate NC machining equipment. The finished assembly is instrumented with piezoelectric accelerometers and force transducers. The design allows three bivalent modalities of operation, unbalanced/dynamically balanced, stiff/compliant torque coupling, stiff/compliant motor mounts, all of which may be intermixed in various combinations. The assembly was run under all combinations of modalities and the dynamic forces and accelerations measured and transformed to the frequency domain. The results were subjected to an analysis of variance and compared to those of the theoretical model. The differences were statistically significant in all but a few cases. As expected, the compliances and clearances in the physical model created significantly larger dynamic accelerations, torques and forces on the bearings than was predicted theoretically by a rigid dynamic model. These increased forces will affect bearing and journal wear. This paper reports on the details of this experimental/theoretical study and draws some conclusions relevant to making design decisions applicable to similar mechanical devices. Work is continuing on the theoretical modelling of the system's nonlinearities as well as on measurement of the effects of bearing clearances on the vibration and modal behavior of the physical system.

No abstract