Page 532 - Dynamics of Mechanical Systems

0593_C15_fm Page 513 Tuesday, May 7, 2002 7:05 AM

15

Balancing

15.1 Introduction
As with stability, balancing is a subject of great interest to engineers and to designers of
mechanical systems — particularly in the design of rotating machinery. Unlike stability,
however, balancing is a more applied subject, although balancing procedures can be rather
detailed and technical. In what follows, we will discuss fundamental concepts of balancing.
Readers interested in more detail or in more technical aspects should consult references
at the end of the chapter or in an engineering library.
In classical dynamical analyses of machines and mechanical systems, the machines or
systems are generally modeled as ideal bodies with perfect geometry and uniform mass
distribution — and, specifically, with no imbalance. In reality, of course, it is impossible
to manufacture ideal bodies. Even with modern technologies, there will be variations in
geometry and variations in mass distribution. Often, these variations are insignificant and
unimportant. With high-speed and high-precision machines, however, even minor varia-
tions in geometry and mass distribution can have significant and deleterious effects upon
the function and life of a machine. This is especially the case with high-speed rotating
bodies. A variation in geometry or in mass distribution away from the ideal is referred to
as an imbalance.
Because imbalances often lead to instability, particularly with rotating equipment, a
technology of balancing has arisen which is intended to counter or eliminate the imbal-
ances. Indeed, balancing technology has become an integral part of modern manufacturing
processes for a wide variety of products ranging from rotors to propellers, automobile
wheels, and bowling balls. In the following sections, we will briefly explore the funda-
mentals of balancing and will restrict our attention to rotating bodies. Initially, we will
study static balancing and then go on to dynamic balancing.

15.2 Static Balancing
Consider a rotor consisting of a cylindrical shaft together with a circular disk D mounted
on S as in Figure 15.2.1. Let A–A be the axis of rotation. Ideally, with perfect geometry,
we would expect the mass center G of such a system to lie on axis A–A. In a physical
system, however, even with precision machining and careful fabrication, G will not lie
exactly on A–A. Instead, G will generally be a small distance δ away from A–A. Figure
15.2.2 depicts an end view of the rotor showing G and a point O on the axis A–A.

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