369. A Simplified Technique for Measurement of Product of Inertia

Paper

Abstract

This paper was presented at the Twenty-second Annual National Conference of the Society of Aeronautical Weight Engineers at St. Louis, Missouri, April 29-May 1, 1963. This paper presents a technique developed by Douglas Aircraft Company, INC. for measurement of POI (product of inertia). The method is used to dynamically balance missile control fins. Derivation of equations, discussion of hardware design and general test procedures are included.
The POI of an object is a mass distribution property which can be measured only when the object has angular motion. Any system used in measuring this property must produce angular acceleration and/or velocity on the test body. The angular motion, in this case, is caused by rotation of the test body as a pendulum. A bifilar pendulum system was selected to provide the angular motion because of the necessary restraints provided by the supporting linkage.
Harmonic motion occurs as the bifilar pendulum oscillates. Thus, the angular accelerations and velocities vary sinusoid ally according to the natural frequency of the pendulum. Turning moments are induced about each of two horizontal axes because of the angular velocity, angular acceleration, and the POI of the test body. These turning moments cause pertabations in the pendulum motion.
Adjustable counterweights added to the system induce turning moments opposite to those caused by the test body. The resulting pertabation in the motion of the pendulum system is visually observed and the counterweights are adjusted until the pertabations no longer occur. The system, therefore, is dynamically balanced; the POI of the counterweights is equal and opposite to that of the test body. The POI of the test body can be readily calculated from the mass and geometry of the counterweights. This technique is advantageous because:
A. POI of the test object may be measured with essentially the same test apparatus that is used in locating cg (center of gravity) and measuring moment of inertia.
B. Measuring instrumentation for POI test is not required.
C. A simple test procedure permits unskilled personnel to conduct the testing.
This approach may be used as a relatively simple and inexpensive method for dynamically balancing test objects if a high degree of precision is not required. It is concluded that there are many useful applications of this technique for measurement of POI.