Counterweight balancing for reducing machine frame vibration : a convex optimization framework

This paper focusses on reducing, through counterweight addition, the vibration of an elastically mounted, rigid machine frame that supports a linkage. In order to determine the counter-weights that yield a maximal reduction in frame vibration, a non-linear optimization problem is formulated with the frame kinetic energy as objective function and such that a convex optimization problem is obtained. Convex optimization problems are nonlinear optimization problems that have a unique (global) optimum, which can be found with great efficiency. The proposed methodology is successfully applied to improve the results of the benchmark four-bar problem, first considered by Kochev and Gurdev. For this example, the balancing is shown to be very robust for drive speed variations and to benefit only marginally from using a coupler counterweight. Copyright © 2006 by ASME.status: publishe