Unbalance is defined as an unequal distribution of mass causing the mass axis to differ from the bearing axis. During rotation, the unequal mass along with the radial acceleration due to rotation create a centrifugal force. This results in force on the bearings and/or vibration of the bearings.
Balancing is a procedure in which the mass distribution of a rotor is assessed and if necessary, adjusted via addition or subtraction of weight to ensure that the vibration of the journals and/or forces on the bearings are within specified limits. Vibration is a mechanical movement where an object oscillates about an equilibrium point. It commonly produces unwanted sound and wastes energy. Vibration in rotating equipment can greatly reduce the life of the equipment and the bearings. Before studying the basic principles of balancing, one must keep in mind that there are many causes of vibration other than unbalance. In some cases, balancing may result in only a partial or temporary reduction in vibration, while in other cases balancing is the only effective course of action. Mechanical unbalance, which produces a force at 1 X RPM, has been found to be one of the most common causes of machinery vibration, present to some degree on nearly all rotating machines.
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Unbalance is often defined as simply the unequal distribution of the weight of a rotor about its rotating centerline. Causes of unbalance include the following:
In summary, all of the above causes of unbalance can exist to some degree in a rotor. However, the vector summation of all unbalance can be considered as a concentration at a point termed the "heavy spot." Balancing is the technique for determining the magnitude and location of this heavy spot so that an equal amount of weight can be removed at this location, or an equal amount of weight added directly opposite.
The amount of unbalance in a rotating workpiece is expressed as the product of the unbalance mass (ounces, grams, etc.) and its distance from the rotating centerline (inches, centimeters, etc.).
Where U is the unbalance, m is the magnitude of the mass, and e is the eccentricity in the disc (or the distance from the center point of the mass to the axis of rotation). Thus, the units for expressing unbalance are generally:
For example, one ounce inch of unbalance would be a heavy spot of one ounce located at a radius of one inch from the rotating centerline.
Rotors are classified into two groups. Whether or not a rotor is classified as rigid or flexible depends on the relationship between the rotating speed (RPM) of the rotor and its natural frequency. When the natural frequency of some part of a machine is also equal to the rotating speed or some other exciting frequency of vibration, there is a condition of resonance. The rotating speed at which the rotor itself goes into bending resonance is called a "critical speed."
As a general rule, rotors that operate below 70% of their critical speed are considered rigid and, when balanced at one speed will be balanced at any other normal operating speed below 70% of its critical speed. Rotors that operate above 70% of their critical speed will actually bend or flex due to the forces of unbalance and, thus are called flexible rotors.
A flexible rotor balanced at one operating speed may not be balanced when operating at another speed. This is because as the rotor bends or deflects, the weight of the rotor is moved out away from the rotating centerline creating a new unbalanced condition, known as whip. This new unbalance can be corrected by re-balancing in the two end planes; however, the rotor would then be out of balance at slower speeds where there is no deflection. The only solution to insure smooth operation at all speeds is to make the balance corrections in the actual planes of unbalance. Typical machines which contain flexible rotors are steam and gas turbines, multistage centrifugal pumps, compressors, and paper rolls.
The International Standard ISO 1940/1 "Balance Quality Requirements of Rigid Rotors" is a widely-accepted reference for selecting rigid rotor balance quality. This standard sets a level of unbalance to be acceptable based on the type of rotor and its operating speed. To determine the balance quality requirement of your rotor, please reference our Technical Literature, Balance Quality Requirements of Rigid Rotors.
While the ISO determines a standardized qualification for balancing, the unbalance tolerance, or amount of unbalance allowed in a product can easily be determined by the manufacturer. The best way to determine an acceptable balance tolerance is to experiment with a batch of rotors. Balance the rotors to reduce unbalance to a minimum. Then slowly add unbalance until the performance becomes unacceptable. Keep in mind that more unbalance can lead to premature bearing failure or excessive vibration. Pick a balance tolerance within this range that is cost effective and achievable with little lost time.
Static unbalance is a condition of unbalance where the central principal axis is displaced parallel to the rotating centerline. It can be detected by placing the rotor at its point of rotation on each end. The heavy side of the rotor will swing to the bottom. A part is considered statically balanced when it does not rotate regardless of the position in which it is placed.
When testing a rotor that is symmetrically supported between identical bearings, identical vibration amplitude and phase readings will be measured at the bearings / end of shaft if the unbalance is truly static. This does not apply for rotors which are mounted in an overhung configuration.
Static unbalance can be corrected by adding or removing weight in only one correction plane. In the figure to the right, the balance correction weight in scenario A is added as one singular weight addition in the same plane as the unbalance. This will result in a well balanced rotor. In scenario B, the static unbalance is corrected by placing the correction weights in-line at opposite ends of the rotor. This method is typically used when it is not possible to add a single correction weight at the center portion of the rotor. This results in a statically balanced rotor; however, during faster rotations, there is an increased chance of bending moments.
Scenario C shows an unacceptable attempt of balancing a rotor. The correction weight was added in a different plane than the one containing the rotor center of gravity. The rotor may be considered statically balanced, due to the fact that no heavy spot would swing to the bottom if the rotor were suspended and allowed to spin freely; however, when the rotor is rotated, the original heavy spot and correction weight, being located in different planes, produce moments of inertia which cause the central principal axis to intersect the rotating centerline, thus creating another type of unbalance.
Couple unbalance exists when two unbalances exist 180 degrees apart, but in different planes. This condition of unbalance has a central principal mass axis intersecting the rotating centerline. Unlike static unbalance, couple unbalance cannot be detected by allowing the rotor to spin freely. In fact, during the process of static balancing, one can add the weight in the wrong plane, as seen in the Methods of Fixing Static Unbalance, Figure C. When the weight is added disproportionately, a coupled unbalance is created. Couple unbalance can only be detected when the part is rotating and can be identified by comparing the bearing or shaft vibration amplitude and phase readings at each end of the rotor.
Readings from a rotor experiencing couple unbalance will reveal equal amplitudes of vibration with phase readings which differ by 180 degrees. Again, this method of detecting the type of unbalance does not apply to overhung rotors.
Correction of couple unbalance requires that weight be added or subtracted within two correction planes. In only very few cases will a rotor have true static or true couple unbalance. Normally, an unbalanced rotor will have some of each type. Combinations of static and couple unbalance are further classified as quasi-static or dynamic unbalance.
Dynamic unbalance is the most common type of unbalance and is defined simply as unbalance where the central principal axis and the rotating centerline do no coincide or touch. This type of unbalance exists whenever static and couple unbalance are present, but where the static unbalance is not in direct line with either couple component. As a result, the central principal axis is both tilted and displaced from the rotating centerline.
Generally, a condition of dynamic unbalance will reveal comparative phase readings which are neither the same nor directly opposite one another. This type of unbalance can only be solved by making weight corrections in a minimum of two planes.
Once the heavy spot is located, it can be corrected by either adding mass to the rotor on the opposite side as the heavy weight or removing weight from the heavy location.
Methods of adding weight include bolting or welding weights onto the rotor, etc. Removing weight from the rotor can be done by drilling, grinding, milling, etc.
If the location of weight addition / removal is unaccessible, the unbalance vector can be split such that the correction can be made via two accessible additions / removals instead.
One important reason for balancing is that the forces created by unbalance are detrimental to the life of the machine - the rotor, the bearings, and the supporting structure. The amount of force created by unbalance depends on the speed of rotation and the amount of unbalance.
In the figure to the right, an unbalance is represented by a heavy spot, W, located at some radius, R, from the rotating centerline. If the unbalance weight, radius and machine RPM are known, the centrifugal force, F, can be generated:
Example: If an unbalance of 1 ounce exists 3 inches from the rotating centerline on a rotor that operates at 2,000 RPM, the centrifugal force can be calculated as follows.
While 1 ounce is a small amount of weight, simply revolving the rotor at 2,000 RPM can produce 69.4 pounds-force. As speeds increase, the force increases. Thus, for a very high speed machine, a relatively small unbalance weight can produce a tremendous amount of force.