TABLE OF CONTENTS Balancing is the technique of correcting or eliminating unwanted inertia forces and moments in rotating machinery. In previous chapters we have seen that shaking forces on the frame can vary significantly during a cycle of operation. Such forces can cause vibrations that at times may reach dangerous amplitudes. Even if they are not dangerous, vibrations increase the component stresses and subject bearings to repeated loads that may cause parts to fail prematurely by fatigue. Thus, in the design of machinery it is not sufficient merely to avoid operation near the critical speeds; we must eliminate, or at least reduce, the dynamic forces that produce these vibrations in the first place.
Production tolerances used in the manufacture of machinery are adjusted as closely as possible without increasing the cost of manufacture prohibitively. In general, it is more economical to produce parts that are not quite true and then to subject them to a balancing procedure than it is to produce such perfect parts that no correction is needed. Because of this, each part produced is an individual case in that no two parts can normally be expected to require the same corrective measures. Thus determining the unbalance and the application of corrections is the principal problem in the study of balancing.
The arrangement shown in Fig. 19.1 a consists of a disk-and-shaft combination resting on rigid rails so that the shaft, which is assumed to be perfectly straight, can roll without friction. A reference system xyz
