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Dynamic balancing is the process of attempting to align the mass and shaft centerlines so that the rotor will rotate with an absolute minimum of unbalanced centrifugal force. Since there is no such thing as a perfectly concentric rotor with perfectly fitting concentric parts that are supported with perfectly fitting concentric bearings, there will always be some degree of residual unbalance in each rotor. Residual unbalance, sometimes called final unbalance, is the unbalance of any kind that remains after balancing.

Calculations can be performed when balancing a rotor to determine the degree of residual unbalance (this will be covered in Section 2 which will follow). During the 1950’s, a small group of experts active within the balancing field got together and began to formulate discussions on how a set of balance standards could be developed so that one could numerically determine to what quality his rotor is balanced in comparison with other similar rotors.

Several years of intensive study ensued, culminating with this group joining “Technical Committee 108 on Shock and Vibration” of the International Standards Organization (ISO). Later, the group name was changed to

“Sub-Committee 1 on Balancing and Balancing Machies” (ISO TC-108/SC1). Request were made by the committee to groups throughout the world to submit more and more data on balance qualities achieved. Finally, ISO Standard No. 1940 was issued entitled “Balance Quality Requirements of Rigid Rotors” which, after a period of time, was also adopted as “S2.19” by The American National Standards Institute (ANSI). Some of the more important points of this standard are summarized below.

Table VII provides each of the balance quality grades as per ISO1940

delineated by “Balance Quality Grade”. Beside each quality grade G number is a listing of various rotor types, grouped according to these quality grades. As Table VII states, the list of rotor types is meant to include general examples and is not meant to be all-inclusive.

Please note that beside each quality grade number in Table VII is a column entitled “e_per x ω”. It shows that each quality grade number represents the

maximum permissible orbital velocity (e_per x ω) of the center of gravity in mm/sec around the shaft axis (ω) expressed in radians/sec. For example, referring to quality grade G 6.3, this grade allows an orbital velocity of:

6.3 mm/sec, RMS = .248 in/sec, RMS = .351 in/sec peak.

Figure 54 provides the ISO “Permissible Residual Unbalance” bands for each rotor group as a function of the maximum service speed (RPM). This graph is used to establish the actual residual unbalance tolerance (called “U_per”) in terms of lb-in/lb or gram-in/gram. Therefore, this tolerance specifies the permissible residual unbalance per unit of rotor weight (rotor weight includes all portions of a machine which are in fact rotating, not the total weight of the entire machine assembly). For example, a small motor may have a total static weight of 20 lbs. (9 kg), whereas the weight of its rotor alone is only 10 lbs. (4.5 kg). It is the 10 lb. (4.5 kg) rotor weight which should be employed when using these residual unbalance guidelines.

Referring again to Figure 54, note that each of the balance quality grades incorporates four bands except for those in the very upper or lower extremes of the graph. These unofficial bands might be considered (from top to bottom in each grade) as “sub-standard”, “fair”, “good” and “precision”. Therefore, the graph permits some adjustment to individual circumstances within each quality grade.

Importantly, the difference in permissible residual unbalance between the bottom and top edge of each grade is a factor of 2.5. For critical applications,

It is important to point out that the tolerances recommended in Figure 54 apply only to rigid rotors. Recommendations for flexible rotor tolerances are contained in ISO 5343 entitled “Criteria for Evaluating Flexible Rotor Unbalance” which must be read in

conjunction with ISO 1940 and ISO 5406 entitled “The Mechanical Balancing of Flexible Rotors”. Looking again at Figure 54, note that in general, the larger the rotor mass, the greater the permissible unbalance; while the higher the RPM, the lower the allowable residual unbalance. Also, note that when obtaining the residual unbalance from the left-hand vertical axis, it will be expressed in units of (for example) lb-in/lb. As note (2) below Figure 54 states, to obtain this in units of oz-in/lb, multiply by a value of 16. For example, referring to Figure 54, if you had a 10 lb rotor turning at 1000 RPM and wanted to single-plane balance it to the “precision” level of G 2.5 (lowest of the four G 2.5 bands), this would correspond to a permissible residual unbalance of

.00065 lb-in/lb which equals .0104 oz-lb/lb of rotor weight. Therefore, if this were a single-plane problem, the total allowable residual unbalance would be

.0104 X 10 lb = .104 oz/in total in this one plane (had it been a two-plane problem, the permissible residual unbalance would have been .0052 oz-in/plane if this were a symmetric rotor centered between bearings as per note (1) below Figure 54).

Following below will be a discussion on how ISO applies to both single-plane and two- plane problems with standard rotors of symetric design centered between bearings, as well as how it applies to rotors of various other geometries (including overhung rotors).

a. Application of Tolerances to Single-Plane Problems:

A single-plane rotor is normally considered to be “disc shaped” requiring only one correction plane which may be sufficient if the distance between the bearings is large and the disc has small axial run-out. The entire tolerance provided in Figure 54 will be allowed for the single plane. If the couple unbalance (referred to the bearing planes) exceeds one-half the total rotor tolerance, the rotor may require two-plane balance.

b. Application of Tolerances to Two-Plane Problems:

In general, one-half of the permissible residual unbalance is applied to each of the two correction planes provided each of the following three conditions is met:

1) The rotor CG is located within the mid-third of the bearing span; 2) The distance between correction planes is greater than 1/3 of the

bearing span, and the correction planes are between bearings; 3) The correction planes are approximately the same distance from the

TABLE VII

BALANCE QUALITY GRADES FOR VARIOUS GROUPS OF REPRESENTATIVE RIGID ROTORS IN ACCORDANCE WITH ISO 1940 AND ANSI S2.19-1975

c. Application of Tolerances to Special Rotor Geometries

Figure 55 is provided to show how ISO 1940 tolerances can be applied to rotors of special geometries that do not meet each of the three conditions stipulated above in Section b. For example, rotor A at the top of the figure shows a rotor with widely spaced inboard (between bearings) correction planes; rotor B has each of two overhung rotors outboard of each of the bearings; rotor C shows a classic overhung rotor with each of two corrections planes on the single wheel which is outboard of each of its bearings; whereas rotor D is situated between bearings, but away from the bearing span mid-point. Note that permissible tolerances (U_per) are stipulated on Figure 55 for each of these rotor geometries.

Following below are several examples which help illustrate how ISO 1940 tolerances are applied to various rotor types and geometries:

C How to Determine Residual Unbalance Remaining in a Rotor After