Balancing of rotating masses

In heavy industrial machines such as gas turbines and electric generators, vibration can cause catastrophic failure, as well as noise and discomfort.

In the case of a narrow wheel, balancing simply involves moving the center of gravity to the centre of rotation.

Alternatively, a pair of free-running ball bearing races is substituted for each knife edge, which relaxed the horizontal and parallel requirement.

If a system is initially unbalanced, to avoid the stress upon the bearings caused by the centrifugal couple, counterbalancing weights must be added.

The wheel will not rotate to a preferred position but because some rim mass is offset there is a wobbling couple leading to a dynamic vibration.

Dynamic balancing was formerly the province of expensive equipment, but users with just occasional need to quench running vibrations may use the built in accelerometers of a smart phone and a spectrum analysis application.

This is the method commonly used to dynamically balance automobile wheels with tire installed by means of clip-on lead (or currently zinc) 'wheel weights'.

These off-axis vibration forces may exceed the design limits of individual machine elements, reducing the service life of these parts.

Rotating shaft unbalanced by two identical attached weights, which causes a counterclockwise centrifugal couple Cd that must be resisted by a clockwise couple Fℓ = Cd exerted by the bearings. The figure is drawn from the viewpoint of a frame rotating with the shaft, hence the centrifugal forces.