Tire Balance - The Physics of Dynamic Balance

The Physics of Dynamic Balance

Mathematically, the moment of inertia of the wheel is a tensor. That is, to a first approximation (neglecting deformations due to its elasticity) the wheel and axle assembly are a rigid rotor to which the engine and brakes apply a torque vector aligned with the axle. If that torque vector is not aligned with the principal axis of the moment of inertia, the resultant angular acceleration will be in a different direction from the applied torque. Whenever a rotor is forced to rotate about an axis that is not a principal axis, an external torque is needed. This is not a torque about the rotation axis (as in a driving or braking torque), but is a torque perpendicular to that direction. If the rotor is suspended by bearings, this torque is created by reaction forces in the bearings (acting perpendicular to the shaft). These reaction forces turn with the shaft as the rotor turns, at every point producing exactly the torque needed to keep the wheel rotating about the non-principal axis. These reaction forces can excite the structure to which they are attached. In the case of a car, the suspension elements can vibrate giving an uncomfortable feel to the car occupants. In practical terms, the wheel will wobble. Automotive technicians reduce the wobble to an acceptable level when balancing the wheel by adding small weights to the inner and outer wheel rims. Balancing is not to be confused with wheel alignment.