An important form of vibration experienced by rotating machinery in a wide range of applications is that due to inherent unbalance. Rotating machinery may incorporate either rigid or flexible shafts and balancing procedures for both cases are discussed, but emphasis is given to a review of techniques for the high-speed balancing of flexible shafts. Reference is also made to the main International Standards in the field.
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References
1.
BishopR. E. D.ParkinsonA. G.Vibration and balancing of flexible shafts. Appl. Mech. Rev., 1968, 21, 439–451.
2.
RiegerN. F.Balancing of rigid and flexible rotors. Shock and vibration monograph SVM-12, 1986, Naval Research Laboratory, Washington, D. C.
3.
Proceedings of IMechE Conference on Vibrations in rotating systems, 1972 (Institution of Mechanical Engineers, London).
4.
Proceedings of IMechE Conference on Vibrations in rotating machinery, Cambridge, 1976 (Mechanical Engineering Publications, London).
5.
Proceedings of Second IMechE International Conference on Vibrations in rotating machinery, Cambridge, 1980 (Mechanical Engineering Publications, London).
6.
Proceedings of Third IMechE International Conference on Vibrations in rotating machinery, York, 1984 (Mechanical Engineering Publications, London).
7.
Proceedings of Fourth IMechE International Conference on Vibrations in rotating machinery, Edinburgh, 1988 (Mechanical Engineering Publications, London).
8.
Proceedings of International Conference on Rotordynamics, Rome1982 (International Federation for the Theory of Machines and Mechanisms).
9.
Proceedings of Second International Conference on Rotordynamics, Tokyo, 1986 (International Federation for the Theory of Machines and Mechanisms).
10.
Proceedings of Third International Conference on Rotordynamics, Lyon, 1990 (International Federation for the Theory of Machines and Mechanisms).
11.
ISO 1925: 1990 Mechanical vibration—balancing—vocabulary [BS 3851: 1990].
12.
ISO 5406: 1980 The mechanical balancing of flexible rotors [BS 5265: Part 2: 1981].
13.
JeffcotH. H.The lateral vibration of loaded shafts in the neighbourhood of a whirling speed—the effect of want of balance. Phil. Mag., 1919, 37, 304–315
14.
BishopR. E. D.The vibration of rotating shafts. J. Mech. Engng Sci., 1959, 1, 50–65.
15.
BishopR. E. D.GladwellG. M. L.The vibration and balancing of an unbalanced flexible rotor. J. Mech. Engng Sci., 1959, 1, 66–77.
16.
ISO 1940/1: 1986 Mechanical vibration—balance quality requirements of rigid rotors—Part 1 [BS 6861: Part 1: 1987].
17.
ISO 5353: 1983 Criteria for evaluating flexible rotor balance [BS 5265 Part 3: 1984].
18.
ParkinsonA. G.The balancing of flexible rotors. Proceedings of IUTAM Symposium on Dynamics of rotors, Copenhagen, 1974, pp. 413–435 (Springer-Verlag, Berlin, 1975).
19.
ParkinsonA. G.An introduction to the vibration of rotating flexible shafts. Bull. Mech. Engng Educ., 1967, 6, 47–62.
20.
BishopR. E. D.ParkinsonA. G.On the isolation of modes in the balancing of flexible shafts. Proc. Instn Mech. Engrs, 1963, 177, 407–426.
21.
ParkinsonA. G.BishopR. E. D.Residual vibration in modal balancing. J. Mech. Engng Sci., 1965, 7, 33–39.
22.
MooreL. S.DoddE. G.Mass balancing of large flexible rotors. GEC J., 1964, 31, 74–83.
23.
ParkinsonA. G.JacksonK. L.BishopR. E. D.Some experiments on the balancing of small flexible rotors: Part I—Theory. J. Mech. Engng Sci., 1963, 5, 114–128.
24.
ParkinsonA. G.JacksonK. L.BishopR. E. D.Some experiments on the balancing of small flexible rotors: Part II—Experiments. J. Mech. Engng Sci., 1963, 5, 133–145 (Also reply to discussion, J. Mech. Engng Sci., 1963, 5, 388–390).
25.
BishopR. E. D.Unbalanced and initially bent shafts. Engineering, 1960, 190, 735–736.
26.
NicholasJ. C.GunterE. J.AllaireP. E.Effect of residual shaft bow on unbalance response and balancing of a single mass flexible rotor, Part I: Unbalance response. Trans. ASME, J. Engng Power, 1976, 98, 171–181.
27.
NicholasJ. C.GunterE. J.AllaireP. E.Effect of residual shaft bow on unbalance response and balancing of a single mass flexible rotor, Part II: Balancing. Trans. ASME, J. Engng Power, 1976, 98, 182–189.
28.
ParkinsonA. G.DarlowM. S.SmalleyA. J.Balancing flexible rotating shafts with an initial bend. AIAA J., 1984, 22, 683–689.
29.
MooreL. S.Balancing on large turbine rotors. Trans. Inst. Marine Engrs, 1969, 81, 105–115.
30.
FedernK.Fundamentals of systematic vibration elimination. VDI Ber., 1957, 24, 9–24.
31.
KellenbergerW.Balancing flexible rotors on two generally flexible bearings. Brown Boveri Rev., 1967, 54, 603–617.
32.
KellenbergerW.Should a flexible rotor be balanced in N or (N + 2) planes?Trans. ASME, J. Engng Industry, 1972, 94, 548–560.
33.
BishopR. E. D.ParkinsonA. G.On the use of balancing machines for flexible rotors. Trans. ASME, J. Engng Industry, 1972, 94, 561–576.
34.
LundJ. W.TonnesenJ.Analysis and experiments on multiplane balancing of a flexible rotor. Trans. ASME, J. Engng Industry, 1972, 94, 233–242.
35.
TessarzikJ. M.BadgleyR. H.Experimental evaluation of the exact point-speed and least-squares procedures for flexible rotor balancing by the influence coefficient method. Trans. ASME, J. Engng Industry, 1974, 96, 633–643.
36.
DarlowM. S.SmalleyA. J.ParkinsonA. G.Demonstration of a unified approach to the balancing of flexible rotors. Trans. ASME, J. Engng Power, 1981, 103, 101–107.
37.
DrechslerJ.A combination of modal balancing and the influence coefficient method. Proceedings of World Congress on Theory of machines and mechanisms, Newcastle-upon-Tyne, 1975, pp. 81–86 (Institution of Mechanical Engineers).
38.
IwatsuboT.The balancing of flexible rotors (theoretical relation of each balancing method and accuracies). Bull. JSME, 1980, 23, 2096–2103.
39.
GiersA.Comparison of the balancing of a flexible rotor following the methods of Federn-Kellenberger and Moore. VDI Ber., 1971, 161, 29–34.
40.
ParkinsonA. G.The role of rigid body balancing for flexible shafts. International Conference on Rotordynamics, Tokyo, 1986, pp. 109–112 (International Federation for the Theory of Machines and Mechanisms).
41.
SaitoS.AzumaT.Balancing of flexible rotors by the complex modal method. Trans. ASME, J. Vibr., Acoustics, Stress and Reliability in Design, 1983, 105, 94–100.
42.
MeachemW. L.TalbertP. B.NelsonH. D.CooperriderN. K.Complex modal balancing of flexible rotors including residual bow. J. Propulsion, 1988, 4, 245–251.
GnielkaP.Modal balancing of flexible rotors without test runs—an experimental investigation. J. Sound Vibr., 1983, 90, 157–172.
45.
MortonP. G.Modal balancing of flexible shafts without trial weights. Proc. Instn Mech. Engrs, Part C, 1985, 199, C1, 71–77.
46.
FujisawaF.ShiohatoK.SatoK.ImaiT.ShoyamaE.Experimental investigation of multi-span rotor balancing using least squares method. Trans. ASME, J. Mech. Des., 1980, 102, 589–596.
47.
ParkinsonA. G.BishopR. E. D.Vibration and balancing of rotating continuous shafts. J. Mech. Engng Sci., 1961, 3, 200–213.
48.
BauerP.Field balancing of rotating machinery. Power, 1983, October, S1–S16.
49.
ChevalierR.Balancing of highly flexible shaft lines on their critical bending speeds. Third International Conference on Rotordynamics, Lyon, 1990, pp. 257–261 (International Federation for the Theory of Machines and Mechanisms).
50.
BachschmidN.FrigeriC.Some results on the twice-per-revolution balancing of generators. Energia Elettrica, 1982, 59, 49–54.
51.
BishopR. E. D.ParkinsonA. G.Second order vibration of flexible shafts. Phil. Trans. (A), 1965, 259, 1–31.
52.
SharpR. S.Analysis of a self-balancing system for rigid rotors. J. Mech. Engng Sci., 1975, 17, 186–189.
53.
HedayaM. T.SharpR. S.Analysis of a new type of automatic balancer. J. Mech. Engng Sci., 1977, 19, 221–226.
54.
BovikP.HogforsC.Autobalancing of rotors. J. Sound Vibr., 1986, 111, 429–440.
55.
Van de VegteJ.Balancing of flexible rotors during operation. J. Mech. Engng Sci., 1981, 23, 257–261.
56.
GosiewskiZ.Automatic balancing of flexible rotors, Part I: Theoretical background. J. Sound Vibr., 1985, 100, 551–567.
57.
GosiewskiZ.Automatic balancing of flexible rotors, Part II: Synthesis of system. J. Sound Vibr., 1987, 114, 103–119.
58.
BishopR. E. D.On the possibility of balancing rotating flexible shafts. J. Mech. Engng Sci., 1982, 24, 215–220.
59.
VanceJ. M.Rotordynamics of turbomachinery, 1980 (John Wiley, New York).
60.
LalanneM.FerrarisG.Rotordynamics prediction in engineering, 1990 (John Wiley, Chichester).
61.
ISO 1940: 1973 Balance quality of rotating rigid bodies [BS 5265: Part 1: 1979].
