Robust balancing for rotating machines

Abstract

The balancing of rotors divides broadly into two categories: balancing in situ and balancing in a balancing machine. In the latter case, the most common practice is to arrange balance corrections on the rotor such that the net excitations of each of the four in-plane rigid-body modes of the free rotor is zero by deploying balance corrections on two independent planes. In a small proportion of cases, the net excitations of the rst pair of exural modes are also zeroed using a third correction plane. This paper proposes that, when rotors are balanced in a balancing machine (not similar to the machine stator), substantially more utility can be gained from the balancing operation by combining a suitably weighted account of the speci c balancing requirements of the machine with knowledge of the expected machine characteristics than can be achieved by ignoring this knowledge. A single cost function is established based on a numerical model of the machine. Then, depending on circumstances, either the expected value of this cost function or its worst possible value can be minimized.The methods proposed require that relatively detailed knowledge of the distribution of residual unbalance be obtained experimentally. The paper brie y discusses some practical methods for how such information might be extracted. The de nition of the cost function as a matrix quadratic form provides potentially valuable information about the necessary number and the optimal location of balance planes on a given rotor, and methods for determining an optimal set of balance planes are outlined.

Experimental validation of a robust model-based balancing approach

“…Consequently, the success of balancing techniques depends on the accuracy of vibration measurements and the number of uncertainties affecting the rotor vibration responses. Some information on robust balancing for a rotating machine are presented by Garvey et al. (2002), Murthy et al.…”

Generalised analysis of compensating balancing sleeves with experimental results from a scaled industrial turbine coupling shaft

“…Moreover, due of the widespread use of low-speed balancing machines and the difficulties in approximating the balance correction required for high-speed use, a number of alternative balancing methodologies have been proposed based on the assumed modal shape of the shaft, 7 or else underpinned by significant a priori knowledge of the unbalance characteristics. 8 However, due to (typically) unknown imbalance distributions, balancing errors caused by shaft deflection are not adequately catered for across the required operating speed range and many field problems persist where unacceptably high vibrations at the bearings lead to subsequent unit shutdowns and failures.…”

Theoretical investigation into balancing high-speed flexible shafts, by the use of a novel compensating balancing sleeve

“…9 However, because of the unknown imbalance distribution and sometimes the complexity of the shaft geometry, the balancing errors caused by shaft deflection are not adequately catered for across the required operating speed range, 9 and many field problems persist where unacceptably high vibrations at the bearings lead to subsequent engine shut down.…”

“…Also, because of the wide spread use of low-speed balancing machines and the difficulties in approximating the balance correction required for high-speed use, there have been various balance methodologies suggested based on the assumed modal shape of the shaft 8 or else resting upon a significant a priori knowledge of the unbalance. 9 However, because of the unknown imbalance distribution and sometimes the complexity of the shaft geometry, the balancing errors caused by shaft deflection are not adequately catered for across the required operating speed range, 9 and many field problems persist where unacceptably high vibrations at the bearings lead to subsequent engine shut down.…”