Balancing of High-Speed Machinery

The mass balancing of high-speed rotors is an integral part of the study and practice of rotordynamics. As is implied by the name, rotordynamics is concerned with the dynamics of rotating machinery. In this context, dynamics refers to harmonic motion, or vibration. Any machine with rotating components is considered to be a rotating machine. The great majority of commercial machinery falls into this category. Rotating machines range in size from small gyroscopes weighing only a few ounces to large rock tumblers weighing several tons. Other examples of rotating machines are household electric motors, internal combustion engines, gas turbine engines, steam turbines, electric generators, industrial compressors and power transmission systems, to name just a few.

In recent years, the trend in the design of rotating machinery has been toward reduced weight and increased operating speeds, with the objective of increasing operating efficiency and thus reducing cost. However, these more efficient designs result in increased rotor flexibility and are, in general, more susceptible to a variety of undesirable rotordynamic phenomena. In particular, increased rotor flexibility substantially complicates rotor balancing requirements. Control of rotor vibration is necessary to maintain reasonable noise levels and to ensure operator, and consumer safety, and machinery survival. In general, the operating expense of rotating machinery is a direct function of the success with which rotor vibrations are controlled.

While the necessity of rotor balancing was demonstrated by Jeffcott in his classic paper [68], published in 1919, the first significant contributions to the rotor balancing literature did not appear until about 1930. Prior to the 1950s, the balancing literature was concerned with the balancing of rigid rotors and, in a few cases, very simple flexible ones. There is no documentation during this period of any systematic balancing procedure using more than two balancing planes. The first flexible rotors of significance to be built were steam turbine rotors. Initially, these rotors were balanced using simple, rigid-rotor procedures. However, as these rotors became more flexible, and were often operated supercritically, the existing balancing procedures became inadequate. This led to the development of a number of balancing methods specifically designed for flexible rotors.

Rotor balancing methods may be separated into two categories: rigid rotor balancing and flexible rotor balancing. These generic titles refer to whether or not rotor flexibility is taken into account. That is, flexible rotor balancing procedures take into account rotor flexibility, while rigid rotor balancing procedures do not. Many flexible rotor balancing methods are suitable for balancing rigid rotors. However, rigid rotor balancing methods are, in general, not effective for balancing flexible rotors. Unfortunately, in practice, the use of rigid rotor balancing methods with flexible rotors is not unusual. The result is, at best, an extremely inefficient and costly balancing process and, at worst, a presumably well-balanced rotor which, at its operating speed, is actually very poorly balanced and potentially destructive. Specific rigid and flexible rotor balancing methods are discussed in considerable detail in this and the following several chapters.

Modal balancing procedures are characterized by their use of the modal nature of rotor response. In general, modal balancing procedures are highly developed, but are largely intuitive in nature. They seek to balance the rotor, one mode at a time, with a set of masses specifically selected not to disturb previously balanced, lower modes. This chapter includes the analytical background and typical procedures for modal balancing.

The assumption that rotor response is proportional to unbalance is basic to virtually all balancing methods for both rigid and flexible rotors. Even for systems where substantial nonlinearity is observed, this assumption can be satisfied by balancing in a stepwise fashion with sufficiently small steps to approximate linear behavior. An additional assumption inherent in most balancing methods, and of particular import to influence coefficient balancing, is that the effect of individual unbalances can be superposed to give the effect of a set of unbalances. This has been generally accepted as a fact for unbalances that are not excessively large. The premise behind influence coefficient balancing is that based on these two assumptions a rotor can be characterized from a set of individual trial mass runs. This characterization can be used to define a combination of these masses which will eliminate, or minimize, the synchronous rotor response due to unbalance. The analytical development and implementation procedures for influence balancing are presented in this chapter. A method for identifying and eliminating non-independent balancing planes is also presented.

The Unified Balancing Approach has been designed to incorporate the advantages of both the influence coefficient and modal balancing methods, while eliminating the disadvantages of both methods. That is, the Unified Balancing Approach uses a modal method of applying correction masses in modal sets using data derived in an empirical manner and requiring a minimum of prior knowledge of the dynamics of the rotor. Essentially, the technique involves the calculation of modal trial mass sets. Generally, these modal trial mass sets are determined such that they affect the mode of interest while not having any effect on the lower modes that have already been balanced. However, using the appropriate data, if available from previous tests, a modal trial mass set can be constructed that will have no effect on any general set of modes (hereafter referred to as the unaffected modes), which can include modes above and below the mode being excited. In general, the number of planes required for the modal trial mass set is one more than the number of modes which must not be affected. In addition, the Unified Balancing Approach is not restricted to planar modes. In this chapter, the theoretical development of the Unified Balancing Approach is presented along with the step-by-step procedure required for its implementation.

In order to evaluate the true merits of any balancing method, it is necessary to apply it to actual hardware. To be credible, a balancing method must have, in addition to theoretical appeal, demonstrated practical appeal. That is, it is necessary to demonstrate both effectiveness and usability in an actual hardware application. Consequently, modal balancing, influence coefficient balancing and the Unified Balancing Approach were compared experimentally in a test program involving a supercritical power transmission shaft test rig.

The least desirable feature of most flexible rotor balancing procedures is the considerable number of trial mass runs required. This is of particular importance in the balancing of machines which require a substantial stabilization time during start-up. Using an adaptation of the principle of reciprocity, it is possible to significantly reduce the required number of trial mass runs for certain rotors when using either influence coefficient balancing or the Unified Balancing Approach. This may be applied to the more empirical forms of modal balancing, as well. When applied to flexible rotor balancing, the principle of reciprocity states that, given two rotor axial locations, A and B, at which both balancing planes and vibration sensors are located, the influence coefficient relating the vibration level at A to the unbalance at B is identical to that relating the vibration level at B to the unbalance at A. This is true even in the presence of damping. This chapter begins with a theoretical discussion of the principle of reciprocity and its application to flexible rotor balancing. The particular means by which reciprocity can be applied to improve the influence coefficient and Unified Balancing Approach procedures are then described in detail. Results of a numerical study to verify this application of reciprocity and to investigate any possible limitations are also discussed, along with the results of a similar experimental study using two substantially different tests rotors.