Some Practical Aspects of Balancing

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1 Journal of NUCLEAR SCIENCE and TECHNOLOGY, 24[11], pp.951~959(november 1987) 951 TECHNICAL REPORT Some Practical Aspects of Balancing an Ultra-Centrifuge Rotor M. Zubair KHAN, M. SULEMAN, M. ASHRAF and A. Q. KHAN Dr. A. Q. Khan Research Laboratories, Kahuta* Received March 2, 1987 Revised June 8, 1987 In this paper the method of balancing centrifuge rotors for initial three modes based on practical experience is presented though, depending on the size of the centrifuge, more than one flexural modes have to be encountered. The object is to provide useful and practical information, as technical information on balancing of centrifuge rotors is hardly available because most of the work is shrouded in the clouds of the so-called secrecy. The rotor is balanced in three stages. Firstly, individual components and sub-assemblies are balanced in traditionally low speed rigid rotor balancing machines. Secondly, the complete rotor is balanced by using modal balancing. Thirdly, the rotor is run in a high speed testing facility and rotor balance quality is checked at the operating speed. During the second and the third stages the rotor is run in its own bearings under vacuum and the data is acquired with the aid of a computer. KEYWORDS: balancing, critical speed, flexural modes, flexible rotor balancing, influence coefficient method, modal balancing, N plane balancing, N+2 plane balancing, rigid rotor balancing, rotors, ultracentrifuges, unbalance I. INTRODUCTION To obtain enriched uranium, there are, at present, two commercially viable methods, ultracentrifuge and gaseous diffusion process. The ultra-centrifuge method is more advanced, and has specific attraction because it consumes comparatively less electric power. The ultracentrifuges are high speed machines and their safe operational speed and the economy of the process are closely related to each other. The high rotational speed demands a high balance quality of the rotating parts, specially the centrifuge rotor which has to pass through multiple critical speeds while going up to or coming down from the operational speed. It is a well known fact that rotor whose operating speed is well below its first critical speed does not exhibit any significant bending and may, therefore, be treated as rigid. In such a rotor, unbalance (a discard between the inertia axis and the axis of rotation) does not change significantly up to the operational speed which means that the change in unbalance remains within permissible limits. Thus, it is balanced at one speed only. If the operating speed is higher than the first critical frequency or is in the vicinity of the first flexural critical speed, the rotor begins to bend at this speed. This class of rotor is known as a flexible rotor. Contrary to the rigid rotor, the state of unbalance in a flexible rotor does not remain constant at such flexural critical speeds. Ultra-centrifuge rotor comes under the class of flexible rotors. The ultra-centrifuge system is illustrated schematically in Fig. 1. The rotor is supported on a pivot-type bearing at lower end and the upper end is supported by a magnetic bearing. The gas tube assembly is located at the centre of the rotor. The casing keeps the surroundings P.O.Box No. 502, Rawalpindi, PAKISTAN. 87

2 952 TECHNICAL REPORT (M.Z. Khan et al.) J. Nucl. Sci. Technol., Fig. 1 Schematic diagram of ultra-centrifuge of the rotor under vacuum. The power to rotate the rotor at very high speed is provided by an electric motor driven by a medium frequency inverter. The ultra-centrifuge rotor is a flexible rotor and, depending upon the size of the rotor, it has to pass through a number of critical speeds while going to or coming down from the operational speed. There are two main techniques for balancing a flexible rotor, viz., influence coefficient(1) and modal(2). Furthermore, modal technique has two different approaches, i.e. (N) plane modal balancing method and (N+ 2) plane modal balancing method. All of these techniques are widely accepted in industry, although there are many modifications of these two main methods(3)(4). II. BALANCING PROCEDURE The balancing procedure adopted in the present work consists of three stages. In Stage 1, the individual components (sub-assemblies, discs, end caps etc.) are treated as rigid. The balancing corrections of sub-assemblies are carried out on a low speed hard bearing balancing machine while the disc-type components are corrected on a vertical balancing machine. In Stage 2, the modal balancing of complete rotor is carried out. The modal balancing technique is one of the earliest approaches to flexible rotor balancing. As defined by ISO (E), the modal balancing is a procedure for balancing of flexible rotors in which balancing corrections are made to reduce the amplitude of vibration in the separate significant principal flexural modes to within specified limits. A different set of weights is sequentially applied to correct the unbalance for each mode shape. The balancing weights are selected in such a way as to leave the lower mode balancing unaffected. The (N) plane modal method of balancing flexible rotors(5)(6) is used for balancing of a flexible rotor having (N) flexual modes in (N) correction planes. The other modal method of balancing flexible rotors(5)(6) is known as the (N+2) plane balancing in which 'N' is the number of flexural modes to be corrected. The later two planes are used for balancing the rotor in rigid mode. For example, a rotor having its operational speed above the first bending critical will be balanced first in two planes as a rigid rotor. Then it should be balanced in three planes, out of which the centre plane is for flexural bending and the remaining two planes are for keeping the rigid mode balancing unaffected. Generally, (N) plane method is used for balancing of centrifuge rotors, but there are some cases where the (N+2) plane balancing method is used. In Stage 3, rotors obtained from Stage 2 (i.e. after modal balancing) are run up to their operating speed in a high speed balance testing facility. Dynamic response of the rotors is monitored at different speeds (i.e. suspension criticals, flexuril criticals, other systems' resonances) during acceleration and deceleration. Rotors having excessive deflections at higher speeds are usually trim balanced for these speeds. 1. Stage 1: Low Speed Balancing on Hard Bearing Horizontal Balancing Machine The centrifuge rotor consists of some disctype components and elastically connected subassemblies, which are themselves rigid. The corn- 88

3 Vol. 24, No. 11 (Nov. 1987) TECHNICAL REPORT (M.Z. Khan et al.) 953 ponents are manufactured and assembled according to strict tolerances. Even then, the distribution of unbalance along the axis of rotor is likely to be random. The distribution may be significantly influenced by the presence of local unbalance arising from tolerances and fits of components and variations in wall thickness of the rotor tube. This can also come from un-straightness of complete rotor, and also from non-perpendicularity of the end discs. In order to avoid the occurrance of large internal bending moments in a centrifuge rotor, the individual components are balanced. These are then assembled keeping in view that at the assembling plane the unbalance weights are nullified. After assembly, the balancing process is repeated for each individual sub-assembly. The sub-assemblies are balanced in two planes on hard bearing force measuring balancing machine. In order to take unbalance measurements, the sub-assembly is rotated on a balancing machine bearings to a pre-selected speed. The magnitude and angular position of the unbalance is indicated on vectormeters. The correction is carried out by addition or removal of masses at each plane. Another test run is conducted to check the residual unbalance. For disc-shaped components, the use of one correction plane is sufficient. The unbalance is checked on vertical balancing machine and the correction is done by removal of mass from the specified location. The stage-wise correction on a low speed balancing machine has proved very effective in minimizing the initial unbalance of the complete rotor. Moreover, it results in reducing the high speed balancing time. 2. Stage 2: Computer-aided Modal Balancing In order to reduce the forced vibrations of a rotor associated with unbalance, and a slight lack of straightness (Before commencing modal balancing, the rotor is straightened to a desired value using a special straightening fixture. Detail description of this apparatus and process is out of scope of this paper.) after assembly, the modal balancing is carried out in its own bearings. 3. Description of Measuring System The computer-aided data acquiring system is illustrated schematically in Fig. 2. In order to measure the relative displacements along the axis of a rotor, non-contact eddy current sensors are mounted in the casing at selected locations. The sensor is connected to the multi-channel measuring system through an oscillator. The vibration amplitude, measured zero to peak in microns by each channel, is displayed on a vibration measuring unit. Transparent glass window in the casing is provided for the photo pick-up Fig. 2 Schematic diagram of computer-aided data acquision and balancing system 89

4 954 TECHNICAL REPORT (M.Z. Khan et al.) J. Nucl. Sci. Technol., to measure the phase angle of displacement and the rotor speed. The rotor speed is displayed on a digital meter. The computer is interfaced with the vibration measuring unit. An on-line programme is used for data acquisition and for some balancing calculations. The data acquired by all the channels for each rotor, before and after its balancing, is stored. The stored data can be printed and displayed for visual observation in the form of a bode diagram which is the amplitude and phase angle as a function of the rotor speed. 4. Selection of Measuring Planes The number and selection of measuring and balancing planes depend on the number and shape of the rotor bending modes which in turn depend on the rotor-bearing dynamic characteristics (the selection of the measuring planes requires basic understanding of dynamic response characteristics of centrifuge rotorbearing system). The system is quite complex, as the top bearing differs from the bottom bearing in characteristics. The top part of the rotor whirls, while the pivot part stays with almost negligible movement. For the purpose of location of the measuring planes, modal analysis was conducted to determine the mode shapes of a rotor. A typical rotor was specifically prepared for the purpose of a balancing example for this paper. The mode shapes determined by modal analysis are similar to those shown in Fig. 3(a)~(c). These are two rigid modes, i.e. translatory and conical rigid modes and one first flexural mode, which are the three initial modes before the operational speed. The position of the measuring planes vertically along the axis Fig. 3 Rigid and flexural modes of typical centrifuge rotor of the rotor is very important, as it should be at the place where maximum deflection of the rotor occurs, i.e. at the anti-nodes. For a typical rotor mentioned above, the locations of the measuring planes are illustrated in Fig. 4 (a). Planes 1 and 5 are for measuring the displacements at rigid mode. Plane 3 is used to measure the displacement at the centre of the rotor for the first flexural mode. Fig. 4 Measuring and correction planes In addition to these three planes, Planes 2 and 4 are provided to check, if desired, the deformation of the rotor up to the operational speed after balancing. of typical centrifuge rotor 5. Location of Correction Planes The correction planes provided for rigid and flexural modes are illustrated in Fig. 4(b). Planes 1 and 5 are used for rigid mode correction. The correction weight for the first flexural mode is added at Plane 3. These planes are examples of a typical centrifuge rotor mentioned above. 6. Balancing by (N) and (N+2) Method The data acquisition and balancing system is illustrated in Fig. 2. The vibration measuring unit indicates the deflection and phase of rotor in all the measuring planes. If the deflection of the rotor, when approaching in the vicinity of the critical speed, exceeds the pre-set limit, the rotor is immediately brought down and, after addition of some trial correction weights, is accelerated again up to the vicinity of the critical speed. The deflections are again checked and 90

5 Vol. 24, No. 11 (Nov. 1987) TECHNICAL REPORT (M.Z. Khan et al.) 955 the data is acquired and stored. The rotor is brought down and correction weights are calculated and added to achieve the desired residual unbalance. The (N) plane balancing procedure is sequentially described below. The data acquisition and balancing system work automatically. An on-line computer programme is used to acquire the data : (1) The rotor under vacuum is rotated slowly and continuously until a change in phase angle and increase in vibration amplitude is observed on the vibration measuring unit. The speed at which these changes are indicated is much lower than the first flexural critical speed of the rotor, and the phase relationship between the three measured vibration signals identifies it as the first translatory rigid mode. If the rotor crosses this mode without excessive deflections then it is allowed to accelerate further and a stage approaches where, again, increase in deflection and change in phase angle occurs. Here the phase angle relationship between the three measured vibration signals identifies the appearance of second rigid mode, i.e. conical rigid mode. Again at this stage if the rotor passes without excessive deflections it is accelerated further until the first flexural mode begins to appear. Figure 3 shows the mode shapes approximately similar to the rigid and flexural modes. In translatory rigid mode the phase angles for all vibration signals are almost the same whereas for conical rigid mode the phase difference between top and bottom signals is about 180d. And for the first flexural mode the central vibration signal is 180d out of phase as compared with top and bottom signals. (2) If the rotor crosses both the rigid modes with little amplitudes and exhibits much higher deflections in the vicinity of first flexural critical speed, then it is brought down to rest. With the help of bode diagram, exact angular location and amplitude of vibration signals at this speed are obtained. (3) An empirical relationship between deflection read-out and correction weight is established by fixing a trial weight in the correction plane and determining the rotor-bearing system response. On the basis of this response the exact amount and phase of the correction weight is determined. (4) The correction weight for first flexural mode is added in central correction plane 3. A test run with this V-mode correction weight is made at exactly the same speed as the previous run, during which the initial deflection amplitude was measured, for determining the expected improvement in rotor response at V-mode. Also the effects of the correction weight on rigid modes are checked. Usually, rigid modes are affected very little whereas for obtaining a better balance quality at flexural speed subsequent runs are carried out. This above mentioned procedure, i.e. (N) plane method of balancing flexible rotors is a useful method and our experience shows that it is valid for almost 80% of the rotors. It gives quite satisfactory results. Rest of the 20% rotors exhibit large deflections either at translatory rigid mode or at conical rigid mode. Usually, translatory rigid mode is more violent than the conical rigid mode. The (N + 2) plane balancing technique is adopted for balancing these rotors and is sequentially described below. (5) The rotor is accelerated under vacuum until significant deflections due to translatory rigid mode begin to appear but before the deflections are too big to strike the surrounding casing the rotor is quickly decelerated to a lower speed. At this speed the rotor truely runs as a rigid rotor without being influenced from any suspension criticals. The amount of deflection and phase angle is obtained from the measuring points 1 and 5 at this speed. Then the rotor is brought to rest and correction weights are applied in the correction planes 1 and 5 according to the measured vibration signals from the top and the bottom points. (6) With these correction weights, the rotor is accelerated to exactly the same speed of previous run, and improvements in deflections at top and bottom are checked. Any 91

6 956 TECHNICAL REPORT (M.Z. Khan et al.) J. Nuci. Sci. Technol., discrepencies in deflection amplitudes and phase angles from the expected values are corrected in the subsequent runs. After achieving the desired rigid balancing, where the deflections at top and bottom should be 3 to 4 times the deflections of a balanced rotor at the operating speed, the rotor is accelerated till it passes safely with the desired vibration amplitudes through both the translatory and the conical rigid modes. Then it is accelerated further until it exhibits excessive deflections due to first flexural mode (V-mode). Balancing for this mode is carried out exactly in the same way as stated in paragraphs '2' to '4', with the exception that the same weight in halves is applied in rigid planes 1 and 5 but directly opposite (i.e. 180d out of phase) to the central weight. After applying this weight set (comprising of 3 weights) for V-mode in correction planes 1, 3 and 5, the rotor is accelerated to exactly the same speed of the previous run. Improvements in the rotor response at flexural speed and any changes at suspension resonances are monitored. Sometimes subsequent runs are needed to acquire the desired balance quality. 7. Stage 3: Over-speed Testing The rotor balanced from stage 2 is tested in a high speed testing facility. The rotor is run up to a higher speed limit than the operating Fig. 5(a)~(c) Rotor response at top (1), central (3) and bottom (5), measuring plane in vicinity of first flexural critical speed ( ª), (I) before and (II) after modal balancing 92

7 Vol. 24, No. 11 (Nov. 1987) TECHNICAL REPORT (M.Z. Khan et al.) 957 speed. The testing facility has almost the same instrumentation as described in stage 2 balancing facility. The rotor is accelerated up to 10% above its operating speed and its deflections at different speeds (suspension criticals, flexural critical, other system's resonances, operating speed) are monitored during acceleration. The rotor is run for 10 min at the overspeed limit and its response is monitored. Then the same monitoring procedure is adopted during deceleration. Normally, the results show that 95% rotors exhibit deflections at different specified speeds within tolerance limits. The rotors which give some excessive deflections at operating speed are trim balanced at the same speed and are again tested in the over-speed testing facility. III. EXAMPLE OF BALANCING The deflections of a newly assembled typical centrifuge rotor in the vicinity of first flexural speed are shown in Fig. 5(a)(1) to 5(c)(I). The rotor was run under vacuum in its own bearings, i.e. in the centrifuge bearings. These figures represent the response of the centrifuge rotor at its top, centre and bottom positions respectively. This is the dynamic state of this centrifuge rotor before modal balancing. Moreover, these bode diagrams indicate that the first (top) and the last (bottom) measuring locations display translatory and conical rigid modes respectively in a clear manner. The flexural V-mode is more pronounced at the 3rd (centre) measuring location. The rotor response shown in these figures Fig. 6(a)~(c) Rotor response at top (1), central (3) and bottom (5), measuring plane near operating speed ((N) method) 93

8 958 TECHNICAL REPORT (M.Z. Khan et al. ) J. Nucl. Sci. Techuol., indicates that the rotor passed through both the rigid modes at 400 and 3,000 rpm with lower vibration amplitudes, but exhibited much higher deflections in the vicinity of flexural V-mode at 5,800 rpm. Therefore, using directly the (N) plane method, a modal correction weight for this V-flexure was applied at the central correction plane 3. The procedure for determining the magnitude and angular location of the correction weight is outlined in Sec. II-6. Two runs were carried out for determining the suitable correction weight. After applying this correction weight, the rotor was run again at the same speed of the initial run, and ensuring sufficient improvement in rotor response at this speed, the rotor was accelerated till it crossed the V-flexural mode. Figures 5(a)~(c) show the rotor response at this stage, i.e. after (N) modal balancing. The dynamic state of this centrifuge rotor before and after modal balancing is compared in Table 1. Table 1 Rotor response at different modes before and after (N) modal balancing The table shows an excellent improvement at V-flexure and a reasonable decrease in vibration amplitudes at the rigid modes. Figures 6(a)~(c) display the dynamic re- Fig. 7(a)~(c) Rotor response at top (1), central (3) and bottom (5), measuring plane at operating speed (N + 2 method) 94

9 Vol. 24, No. 11 (Nov. 1987) TECHNICAL REPORT (M.Z. Khan et al.) 959 sponse of the same centrifuge rotor at the same locations (i.e. top, centre and bottom) when tested in the high speed balance testing facility. The dynamic response of a centrifuge rotor at its top end is of an extremely crucial nature, as the gap between the rotor wall and the surrounding casing at this end is very limited. Figure 6 also shows that the deflections at the centre and the bottom locations are also low. A rotor balanced by using (N+ 2) plane method, as described in Sec. II-6, was tested in a high speed balance testing facility. Figures 7(a) (c) show the dynamic response of this rotor ~ at the top, the centre and the bottom locations. These figures also depict that a rotor balanced with this method also carries almost the same balance quality as with the (N) plane method. IV. SUMMARY (1) The individual balancing of components has proved effective in minimizing the initial unbalance of a complete rotor. About 20 to 30% of the rotors require no correction at the first critical speed. The time to balance the rotor in a high speed balancing facility is reduced. (2) The modal balancing technique for balancing a centrifuge rotor in its own bearings is quite practicable and useful. It also requires less number of balancing runs as compared with the influence coefficient method. (3) The (N) and (N+ 2) plane methods of balancing the flexible rotors are equally effective in producing better balance quality of centrifuge rotors. But (N) plane method is more simple, less time consuming and less susceptible to errors by the operator. (3) The (N+ 2) method gives better reproducibility at high speed conditions and is a little more favourable in a wide range of bearing characteristics. REFERENCES (1) TESSARZIK, J. M., BADGLEY, R. H., ANDER- SON, W. J.: Flexible rotor balancing by the exact point speed influence co-efficient method, Trans. ASME, J. Eng. Ind., 94, 148~158 (1972). ( 2) BISHOP, R. E. D., GLADWELL, G. M. L.: The vibration and balancing of an unbalanced flexible rotor, J. Mech. Eng. Sci., 1 [1], (1959). ( 3) DARLOW, M. S., SMALLEY, A. J., PARKINSON, A. G.: A unified approach to flexible rotor balancing outline and experimental verification, Paper No. c-340/80, IME-1980, Proc. 2nd Int. Conf. on Vibrations in Rotating Machinery, p (1980). ( 4) ZORZI, S. E., Von PRAGENAU, G. L.: Modern rotor balancing emerging technologies, Mech. Eng., ( Dec., 1985). (5) KELLENBERGER, W.: Should a flexible rotor be balanced in (N) or (N + 2) plane, J. Eng, Ind., Trans. ASME, 94, Paper No. 71-Viv-55, p. 548~ 560 (1972). (6) BISHOP, R. E. D., PARKINSON, A. G.: On the use of balancing machines for flexible rotors, ibid., 94, (1972). ( 7) idem: On the isolation of modes in the balancing of flexible shaft, Proc. Inst. Mech. Engineer, 177(161, 407~423 (1963). 95