A modified low-speed balancing method for flexible rotors based on holospectrum

Abstract

Most high-speed rotating machineries operate at a speed higher than their first critical speeds. Since there are two different modal shapes existing in rotors under and over that speed, the most currently used balancing techniques for rotors require two steps to fulfill the balancing purpose. Firstly, a traditional low-speed rigid balancing is performed, and secondly, a high-speed balancing procedure is carried out. This high-speed balancing procedure is very complicated and dangerous; it needs large number of test runs and causes corresponding wastages as well. This paper develops a novel balancing method, called Low-Speed Holo-Balancing (LSHB), which can balance a flexible rotor without test runs at high speeds. The principle of LSHB is mainly based on the holospectrum technique, which will be explained in detail at the end of this paper. Instead of using information from a single sensor, through a multi-sensor fusion a three-dimensional holospectrum is constructed to describe the vibration response of a rotor vividly and accurately. LSHB can easily balance the flexible rotors at lower speeds than the first critical speed, according to the decomposition results of holospectrum. Because LSHB does not need any test runs at or higher than the first critical speed like any other traditional balancing techniques do, the balancing procedure is much safer, and economical. The key points and main operating steps of LSHB will be presented. The experimental results conducted on a flexible-rotor test rig validated the effectiveness of this method.

Introduction

The balancing of flexible rotors is one of the pivotal techniques for high-speed rotating machinery in modern industry. It is obvious that the rotor unbalance is the main source of rotor vibration. In recent decades, it has been studied thoroughly. Various balancing techniques have been developed. In general, since the balance situation of rotor at low speed will be changed at high operating speed, high-speed balancing procedure must be applied for flexible rotors after low-speed balancing. These high-speed balancing methods for flexible rotors fall into two categories: modal balancing and influence coefficient balancing [1], [2], [3], [4]. The influence coefficient balancing method assumes that the rotor response is a linear function of unbalance. It is a data processing method with vector mathematics, which calculates the correction weights by applying the least-squares method or other optimisation methods to solve the over-determined linear equation system. Its disadvantage is that a large amount of test runs are necessary to acquire both the original vibration data and the data of trial weights in multiple correction planes at different speeds. Compared with the influence coefficient method, the modal balancing is a progressive or mode-by-mode balancing method [5], [6], [7], [8]. Different sets of orthogonal weights are calculated and applied for balancing each modal component with the intention of not affecting the previous balance at lower modes. Its disadvantage is that the rotor has to be operated at critical speeds to achieve balance of all modal components below the working speed, so it is dangerous. The traditional low-speed rigid-rotor balancing is also applied for the flexible rotor, but it is only a prelude to later flexible-rotor balancing. This is done to remove the gross unbalances before attempting to approach the first critical speed.

The intention of this paper is to propose a new low-speed balancing method for high-speed rotating machinery running at the speed between the first and second critical speeds. It is not rigid-rotor balancing, but the extension of traditional flexible-rotor balancing methods. The primary goal of this method is that the first two modal components of unbalance can be balanced simultaneously at the speed below the first critical speed. This method is called low-speed holo-balancing (LSHB), by which the satisfactory results can be obtained as that at high speed. Its advantage is that the rotor need not run at high operating speed or critical speeds to achieve satisfactory balance. In this method, the three-dimensional holospectrum [9] (see Appendix A) is used to describe the vibration response of rotor unbalance, which is constructed from vibration information of rotor system in all bearing sections based on the multiple sensor information fusion in data layer. Since the frequency, amplitude and phase information are fully utilised, the three-dimensional holospectrum can ensure the balancing accuracy [10].

The paper includes four sections. To introduce the basic theory, in Section 2 the author first reviews the modal balancing theory, which is the theoretical basis of low-speed holo-balancing. Then, the three-dimensional holospectrum and its decomposition technique are introduced briefly in Section 3, which are the new methods expressing the unbalance responses. Finally, some experiments were carried out to investigate the changing rules of the first two modal components through the first critical speed. Based on all above discussions, we present a low-speed holo-balancing method. In this new method, the rotor modal unbalances and responses are decomposed correspondingly at low speed, and the first two low modal components can be corrected simultaneously at the speed far below the first critical speed. Through a balancing procedure of a symmetrical rotor with LSHB, we acquire a satisfactory result compared with other balancing methods.