Gordon E. Hines and Michael J. Myers

Hines Industries, Inc., Ann Arbor, Michigan

Note: This article assumes an understanding of the basics of balancing.

1.0 Establishing Realistic Tolerances

There is a misconception that balance problems in a motor can be cured by balancing the armature to a tighter balance specification. Unless other sources of unbalance are also considered, this only raises the cost of balancing the armature, slows production, and in some cases, still ends up with noisy out of balance assemblies. What should be done is to take care of the real problems, and not expect the armature balancing machine to work miracles.

The reasons for balancing an electric motor are to make it run smoothly and quietly, and to assure longevity of the motor bearings. In order for this to happen, the motor’s rotating components must be balanced. A question that arises is "How well does the armature have to be balanced?" In other words, "How good is good enough?" The specifications for "good enough" is known as the balance tolerance.

It is important to realize that balancing the motor’s armature is only one step in the balancing process. Just as a chain is no stronger than its weakest link, it is equally important to consider the balance of every rotating component attached to the armature, and also to consider how each of them is attached. A perfectly balanced component that is mounted off-center will create unbalance.

Vacuum cleaner fans are often made with an oversize hole. A balanced fan can move to one side, and this causes unbalance. The fan may also be held in place with an unbalanced pressed-fit washer used as a retainer, or with a nut that may be out of balance or have threads with run off-center. The motor shaft may have run-out, meaning that even if the fan, washer, and nut were all in balance, the run-out would generate unbalance.

Too much emphasis is often placed on making a "tight" unbalance tolerance for the motor armature, ignoring other design consideration.

2.0 Static And Dynamic Balance

Generally speaking, if most of the mass of a rotor is concentrated in a disc that is 5 to 10 times as large in diameter as in thickness, static balance will be sufficient. Rotors that have their mass distributed along their axis should be dynamically balanced. In the gray area between the extremes, each case must be examined individually.

If an armature has a particularly short stack, so that the correction planes are close together, it makes sense to do only "single-plane" (static) balancing. It is unlikely that this type of armature would have a significant amount of "two-plane" (couple) unbalance.

The sum of the forces at the bearing planes due to static unbalance is equal to the force of static unbalance at the correction plane. If the correction plane is reasonably centered between the bearings, half of the sum appears at each bearing. If the correction plane is nearer to one bearing, a larger fraction of the force appears at that bearing. Making a static unbalance correction at a single "correction plane" location will have a direct effect on the static unbalance as measured at the armature support bearings.

A typical unbalanced armature usually has "dynamic" unbalance. Dynamic unbalance is a combination of "static" and "couple" unbalance. Dynamic unbalance can only be corrected by making two corrections to the armature, in two "correction planes". This will not have a direct effect on the vibration at the bearing planes. The force at the bearings, due to couple unbalance, is reduced by the ratio of the correction-plane-spacing to the bearing-spacing. In other words, if the correction planes are close together, and the armature support bearings are further apart, an unbalance correction at the correction planes will have a smaller effect on the unbalance as measured at the support bearings. An armature with the bearing planes six inches apart, and a 3 inch long stack, might be corrected with a correction mill making two cuts two inches apart on the stack. The force at the bearings due to this much couple unbalance measured at the correction planes will be equal to 1/3 of the force at the bearings due to the same couple unbalance measured at the bearing planes. In other words, 0.003 ounces of unbalance at the correction planes (2 inches apart) will result in a 0.001 ounces of unbalance at the bearing planes (six inches apart).

Figure 01

One way around this confusion is to establish balance tolerances at the bearing planes. Another way is to separate the dynamic unbalance in the armature into static unbalance and couple unbalance. In the example given above, one would impose a couple tolerance of three times the static tolerance at the correction planes. These two methods are equivalent. Either method can be used. In these days of computer based balancing machines, it is simple to have the computer calculate the unbalance correction amounts at the correction planes, and the unbalance at the bearings for comparison with a tolerance.

The apparent change in couple unbalance as the planes are moved about is because couple unbalance causes a "twisting" force that causes the axis of spin to wobble about a point on the shaft that is somewhere between the two bearings. As the planes are moved closer together, the "lever arm" for the couple decreases, and a larger couple amount is required to produce the same wobble effect.

3.0 Causes Of Motor Unbalance

The best way to minimize balance problems, is to minimize the initial unbalance which will need to be corrected. Unbalance in a small electric motor can be split into two categories, unbalance that is created BEFORE the armature is balanced, and unbalance that is created AFTER the armature is balance.

3.1 Unbalance before the armature is balanced.

The following causes of armature unbalance occur before the armatures is balanced.

3.1.1 Eccentricity of the laminations

Eccentricity in the laminations which make up an armature stack can cause unbalance. To minimize the unbalance, sometimes the laminations are randomly placed, and sometimes they are split into three of four groups oriented as shown below.

Figure 02Figure 03

3.1.2 Runout

If the bearing surfaces on the shaft are not concentric, this will create unbalance equal to the weight of the part multiplied by the amount of eccentricity between the workpiece’s mass centerline and its geometric centerline.

Figure 04

3.1.3 Shaft Straightness

If the armature shaft is bent, the mass of the armature stack may be off-center, resulting in unbalance. If the bearing spacing in the balancing machine is different from what it will be in the end product, the axis of rotation in the balancing machine may not be the same as the axis of rotation in the end product. It is good practice to use the same bearing spacing in the balancer, as in the end product.

Figure 05

3.1.4 Winding Irregularities

If the wires are longer on one side of the armature than the other, this will result in unbalance. This can be caused by winding tension variations. There can be "loose" wires, or a "bump" can develop in the winding pattern, increasing the length of all the wires that go over that bump.

Figure 06

3.1.5 Non Uniform Trickle Impregnating

If the epoxy resin on the armature is not applied uniformly, this can result in unbalance.

Figure 07

3.2 Unbalance after balance the armature

The following causes of unbalance can occur after the armature is balanced.

3.2.1 Adding a Component – Eccentricity

If there is eccentricity in the armature (or components placed on the armature), this can cause unbalance. All too often there are loose tolerances on components that get mounted to an armature. Unbalance is created by not holding the "fits and clearances" for these parts tightly enough. If there is excess clearance, any part, even a perfectly balanced part, mounted off-center, will generate an unbalance equal to its weight multiplied by the distance that it is off-center.

In particular, this applies to fans that are rigidly mounted to an armature. When mounting a cooling fan on an armature, if the minimum clearance is 0.0002", and the maximum is 0.002" the centerline of the fan can shift almost 0.001 inches on a loose fit condition. If a 10 ounce fan is balanced separately on a collet so that it is balanced while running on-center, and then mounted on this shaft, the fan will create 10 x 0.001 or 0.01 ounce inches of unbalance.

Figure 08

In this case, it is not reasonable to balance either the fan or the armature to 0.001 ounce inches (and less reasonable to specify a tighter balance tolerance on both), rather than fixing the problem of excess clearance by specifying tighter dimensional tolerances on the fit of the fan to the shaft. 3.2.2 Adding a component – Defective Parts

It is possible for defective parts to cause unbalance. If the parts such as fans or locating washers are made with their hole off-center, this can generate a significant amount of unbalance, depending on the weight of the part.

Figure 09

4.0 Process Control

It is important to establish reasonable balance tolerances, both of the individual motor components, and of the completed motor assembly.

4.1 Motor Components

If the balance tolerance of individual motor components is set too tightly, it will increase their balancing time. If the balance tolerance of individual motor components is set too loosely (or if the workpiece dimensional tolerances are too loose), this may result in a large amount of unbalance in the assembled motor. Even if it is possible to physically correct such a large amount of unbalance, this is undesirable, as the large amount of material that must be removed will lower the electrical efficiency of the motor. If the manufacturing process is not kept under control, the motor design may need to have windings and/or laminations added, to make up for what is being taken away in the balancing operation.

4.2 Motor Assemblies:

If the tolerance of the complete motor assembly is set too tightly, it will be more difficult to balance the armature, the balancing operation will take more time, which will reduce the production rate, and increase cost. If the tolerance is set too loose, the end product may have too much vibration.

4.3 Production Rate:

Production line clearances and tolerances need to be controlled so that a motor component to be balanced, will have less unbalance than can be corrected in a single correction pass. Modern day automatic balancing machines such as those built by Hines Industries can typically make a 95 percent unbalance correction in a single pass. This means that to balance a part to a given unbalance tolerance level in a single pass, the initial unbalance should be no more than twenty times the unbalance tolerance. More than that, will usually take (at least) two correction passes. This is one reason why some balancing machines that are rated at processing 600 parts per hour, can only produce 300 balanced parts per hour.

4.4 Other Considerations

Vibration can be caused by problems other than unbalance. Non-uniform windings on the armature, or an eccentric shaft will generate more electrical "pull" on one side of the motor than the other.

5.0 Establishing A Balance Tolerance

The International Standards Organization (ISO) has developed standards, for use in establishing a balance tolerance for different applications. To follow the ISO guidelines, it is necessary to know the following three things about the part to be balanced:

  1. – the general type classification
  2. – the approximate maximum service speed of the workpiece
  3. – the weight (mass) of the workpiece

5.1 Type Classification – "G" Grades

A small electric motor in a non vibration-sensitive application does not need to be balanced to the same level as a small high-speed motor powering a precision instrument. The ISO has developed a grading system, crating a "G" grade for G-0.4 to G-4,000 for different product applications. For armatures, we normally deal with G-1, G-2.5, and G-6.3.

Figure 1 shows the three ISO grades that are usually used in establishing an unbalance tolerance in electric motor armatures.

Grade G-6.3 is used for "small electric armatures, often mass produced, in vibration insensitive applications.

Grade G-2/5 is used for small electric motors which need to run more smoothly.

Grade G-1 is used for small electric motors with special requirements, which need to run even more smoothly.

5.2 Operating Speed

The second step is to evaluate the approximate maximum service speed of the workpiece. For each "G" level, the faster a part turns, the smaller the permissible vibration displacement must be. What this means, is that armatures that spin at higher speeds need to be balanced to finer balance tolerance levels. The "x-axis" in Figure 1 shows the maximum service speed, in RPM. 5.3 Maximum Displacement - eper

The third step in establishing a balance tolerance for a workpiece is to locate the point where the appropriate rotor classification line intersects the maximum service speed line (see Figure 1). The "y-axis" will then give the f displacement this is known as the "eper".

5.4 Maximum Unbalance – uper

The maximum amount of unbalance in units such as "ounce-inches" or "gram centimeters" is known as the uper. To calculate the unbalance tolerance, multiply the maximum permissible displacement (eper) by the weight of the workpiece.


= (m) (eper)


uper = Permissible Unbalance

(unbalance tolerance)

in ounce inches

m = weight of workpiece in ounces

eper = permissible eccentricity

(mass center displacement)

in inches

The following formulas can be used with the eper value in (thousandths of an inch) obtained from Figure 1 to calculate an unbalance tolerance based on the maximum permissible displacement:

To convert eper into ounce-inches of unbalance:
(eper) (weight, oz.)
= unbalance in gram-centimeters

To convert eper into gram-inches of unbalance:
(eper) (weight, oz.) (28.35)
= unbalance in gram-centimeters

To convert eper into gram-centimeters of unbalance:
(eper) weight, oz.) (28.35 (2.54)
= unbalance in gram millimeters

5.5 Establishing the Balance Tolerance:

ISO 1940 recommends two methods of allocating uper to correction planes: simplified approximate methods and general methods:

5.5.1 Simplified Approximate Methods

If the workpiece meets the following criteria, section recommends allocating ½ of uper to each plane: the center of gravity of the workpiece is in the mid-third of the bearing span; the distance between the correction planes is greater than one third of and less than the bearing span; the correction planes are essentially equidistant from the center of gravity of the rotor.

If the correction planes are not essentially equidistant from the center of gravity, section describes a method of allocating a proportion of uper to each plane, allowing the plane closer to the center of gravity a larger proportion. The ratio between the tolerances at the correction planes must not exceed 0.7:0.3 (no more than 0.8 uper in the plane closer to the center of gravity, no less than 0.3 uper in the plane farther from the center of gravity)

If the distance between the correction planes is smaller than 1/3 the bearing span, the effect of couple unbalance is reduced. Consequently, section describes a method of allocating separate couple and static unbalance tolerances. In this case, as the distance between correction planes decreases relative to the distance between bearing planes, the couple unbalance tolerances increase. In fact, if the planes are close enough, the couple unbalance tolerance for each plane may easily exceed uper itself. On the other and, the tolerance for the arbitrarily selected static unbalance plane is assigned a proportion of uper depending upon the distance between this plane and the farthest bearing. As the distance between the static plane and the farthest bearing increases with respect to the total bearing span, the smaller the proportion of uper assigned to that plane.

5.5.2 General Methods

Section 7.3.3 of ISO 1940 offers two methods of allocating uper to the correction planes. The first method ( applies to all rotors. The second method ( applies to the specific case of rotors where the distance between the correction planes is smaller than the bearing span. Both these methods require some decision-making, which assumes some knowledge of how balance affects the workpiece in its service application.

Section involves calculating unbalance tolerances by determining (somewhat arbitrarily) two ratios: "k", a ratio of permissible unbalance at a reference plane to uper, and "R", a ratio of permissible unbalance in one plane to that in the other plane. After factoring in the plane locations, spacing and bearing span, the lowest unbalance obtained from four separate equations is allocated to the two planes using one of the ratios.

Section addresses the particular problem of workpieces where correction planes are significantly closer together than the bearing span. To accommodate this problem, section makes two suggestions: allocate uper to the correction planes in the same ratio as the permissible dynamic bearing load is allocated to the bearings; measure the unbalance at the service bearings. Remember that as the distance between correction planes decreases, the effect of couple unbalance (unbalance 180 degrees out of phase in two planes) on the service bearings also decreases. However, the distance between planes does not change the effect of static unbalance on the bearings. Consequently, using the methods in, one can measure static unbalance just as easily, couple unbalance more easily, and evaluate the effect of unbalance on the service bearings in proportion to the permissible dynamic bearing loads.

6.0 Effective Balancing

It is not cost effective to balance an armature to an extremely fine tolerance, and then mount add-on components that were not balanced to a similar degree of accuracy, or to mount add-on components without selecting appropriate fits and clearances to control the unbalance that will be caused by the add-on part not being held concentric with the armature.

Balancing the armature to a finer tolerance than necessary will not make up for unbalance created by mounting less precise components to the armature.

Figure 10