For a better understanding of balancing, it is necessary to have an understanding of its terminology and its fundamental concepts.
The center of mass is the point about which the total mass of a rigid body is equally distributed. It is useful to assume that all the mass is concentrated at this one point for simple dynamic analyses. A force vector that acts through this point will move the body in a straight line, with no rotation, according to Newton’s second law of motion. The sum of all forces acting on a body, cause a body to accelerate at a rate, a proportional to its mass.
CENTER OF GRAVITY
For normal commercial balancing applications, the mass center and the center of gravity occur at the same point. This does not hold true for applications involving a non-uniform gravitational field, however, the scale of most balancing applications is very small with respect to gradients in the earth’s gravitational field and the terms are synonymous.
AXIS OF ROTATION
The axis of rotation is the true centerline of rotation – the instantaneous line about which a part rotates. It is also referred to as the shaft axis or the geometric axis. The axis of rotation is generally determined by geometric features on the rotor or by its support bearings. The quality of the mounting datums greatly influence the ability to balance a part. Non-circular surfaces, non-flat surfaces, irregular or loose bearings all allow or cause variations in the position of the rotation axis. Any variation of the axis appears to be motion of the mass center with respect to the axis and contributes to non-repeatability.
A particle made to travel along a circular path generates a centrifugal force directed outward along the radial line form the center of rotation to the particle. As the particle rotates about the center point, so does the centrifugal force. With rigid bodies the unbalance remains the same although an increase in speed causes an increase in force. The increased force will in turn cause increased motion depending on the stiffness of the shaft or the shaft supports. Force increases exponentially as the square of the change in speed. Twice the speed equates to four times the force and four times the motion.
MOMENT AND COUPLE
A couple is a system of two parallel forces, equal in magnitude and acting in opposite directions. A couple causes a moment or torque proportional to the distance between the parallel forces. Its effect is to cause a twisting or turning motion.
WEIGHT AND MASS
The units of weight and mass are often used interchangeably and somewhat loosely in balancing. This is generally acceptable provided the balance computer displays units that are consistent or easily converted to those of the weights in use or the scale used to make the weights. The distinction between weight and mass becomes an issue when calculating unbalance force. It should be understood that weight and force have the same units; Newtons (N) in the metric system and pounds (lbs) in the English system. Mass has the units of grams (g) or kilograms (kg) in the metric system and slugs in the English system.