A Compact Device for Measuring Rigid-Body Properties Based on Five Unscaled Modes

Abstract

This article describes a new method and device for measuring the rigid-body properties of mechanical structures (the inertia tensor, the center of gravity coordinates, and optionally the mass). The setup consists of a platform constrained from underneath by soft coil springs and supported at its center by a 5-DOF air bearing mechanism. Following a random push by hand, laser distance sensors measure the platform’s free vibrations. The rigid-body properties are then obtained by fitting a numerical model to the free vibration signals. The model’s key components (a mass matrix, a stiffness matrix, and a kinematic transformation matrix) are obtained by calibration. Together with the unknown rigid-body properties, the three matrices define the natural frequencies and unscaled mode shapes, which are fitted to the sensor signals directly in time domain. A prototype of the device is presented and its accuracy is evaluated in an extensive series of tests. Advantages over previous methods include a faster and simpler procedure, higher accuracy, lower frequencies, and an unlimited work space.