A new field balancing method of rotor systems based on holospectrum and genetic algorithm

doi:10.1016/j.asoc.2006.11.012

Applied Soft Computing

Volume 8, Issue 1, January 2008, Pages 446-455

https://doi.org/10.1016/j.asoc.2006.11.012 Get rights and content

Abstract

Field balancing of flexible rotor system is a key technique to reduce turbine vibration in power plants. Traditional balancing methods are generally based on the information from a unidirectional sensor. In fact, the motion of a rotor system is a complex spatial motion, which cannot be objectively and reliably described with just a unidirectional sensor in one bearing section. In order to give an accurate description of rotor vibration responses, multi-sensor fusion instead of a single sensor should be used with the purpose of more comprehensive utilization of information. Based on this theory, the paper presents a new balancing method for rotor systems named the holo-balancing method, which successfully applies the holospectral principle in traditional balancing methods of flexible rotor systems. At the same time, genetic algorithm (GA) optimization and computer simulation are used to simplify balancing process. The new method decreases test number, increases precision and efficiency of field balancing. The principle and detailed procedures of the new method are explained in this paper, and the effectiveness of the new method was validated by field balancing of several 300 MW turbo-generator units.

Introduction

Information science is the most active one in the contemporary era, which developed quickly, and has been seeping through various domains of the national economy. In machine industry, information technology is adopted to improve and expand the function of mechanical products, fully utilize various dynamic information of operating equipments and therefore comprehensively promote the level of manufacturing industry. Information fusion is one of the key techniques informationalizing mechanical products.

A large amount of statistical data indicates that the mass unbalance of the rotors is usually the major cause of excessive vibrations of large capacity turbine. In these huge power plants, a rotor is always consisted of several flexible shafts, which are coupled together by rigid or flexible couplings. Although the shafts would all have been balanced at a high speed in manufactory, after assembled together on-site, their balance conditions change due to coupling-affect between each of them. The field balancing is an ordinary way to reduce shaft vibrations to a given level. In recent decades, the balancing theory has been thoroughly studied, and various balancing techniques have been developed. However, the existing balancing methods are still potential for improvements in accuracy and efficiency. Firstly, nowadays, all general balancing methods (either modal balancing or influence coefficient method) need large numbers of trial runs to obtain the vibration responses of trial weights in different correcting planes. On the other hand, the vibration measurement always depends on a single sensor in one measuring section. This measurement method is based on the assumption that a rotor-bearing system has an equal rigidity in different directions, so considerable errors would occur if obvious difference were found among rigidities. In this case, waveforms in different measuring directions will result in different FFT magnitude spectra, different correction masses, and even contrary balancing projects.

The motion of a rotor system is a complex spatial motion, which cannot be objectively and reliably detected with just one single sensor. The multi-sensors fusion is an effective technique to describe the rotor's spatial motion. Nowadays, to obtain the comprehensive vibration information of a rotor, two mutually perpendicular proximity transducers are mounted in each bearing section to monitor the vibration in large-capacity steam turbo-generator sets, allowing application of the holospectral technique based on the information fusion. The two-dimensional holospectrum is constructed from two FFT spectra of the vibration signals in two mutually perpendicular directions of a bearing section, which synthetically utilizes frequency, amplitude and phase information. If corresponding frequency components in two spectra are combined properly, a series of ellipses, circles or simply straight lines can be obtained. Based on the two-dimensional holospectrum, the three-dimensional holospectrum integrates full information of rotor vibration simultaneously in all bearing sections [1], [2]. Since the frequency, amplitude and phase information is fully utilized, the holospectral technique based on the multi-sensors fusion can improve the balancing accuracy and efficiency [3].

In this paper, the holospectral technique based on conventional FFT spectra and information fusion is applied in the field balancing of a flexible rotor system. A new balancing method for rotor systems named as holo-balancing method is presented. Furthermore, the computer simulation and genetic algorithms (GA) are adopted in this method, which is helpful to simplify the balancing procedure and enhance the balancing accuracy and efficiency.

Section snippets

Holospectral technique

Fig. 1 shows the arrangement of sensors in a 300 MW turbo-generator unit. The rotor vibration can be sensed by two eddy current probes perpendicularly mounted across each bearing section. This paper defines that the phase is the lag angle of key-phasor pulse signal, which is relative to the first forward zero of the vibration waveform.

The vibration components with rotating frequency in the ith measuring section, derived from two mutually perpendicular directions X and Y, can be expressed as $\{\begin{array}{c} x_{i} = A_{i} \end{array}$

Procedure of holo-balancing

Firstly, two proximity transducers have been mounted adjacent to each other perpendicularly in bearing section, monitoring the vibration with key-phasor.

1.
Track a complete field balancing process of a given rotor set, from test runs with loaded or unloaded trial weights and determine the transfer matrices of three-dimensional holospectra R_A, R_B, R_C, …, R_M, which are the characteristic parameters of rotor systems, providing basis for further holo-balancing. The standard form of transfer matrices

Single plane balancing

The case is a single plane balancing of a 300 MW turbo-generator unit, in which the relative shaft vibration in bearing No. 1 is usually up to 270 μm. Since the vibrations in other bearing sections are within the alarm threshold value, balancing was performed only on the shaft of high-pressure cylinder, with purpose to reduce the vibration of bearing No. 1. Table 1 displays all data in balancing process, which were sampled from two perpendicular transducers in one measuring plane, with the

Conclusions

1.
Based on the holospectral technique, this paper presents a new balancing method for rotor systems, named the holo-balancing method, which fully utilizes the information from all sensors. Compared with traditional balancing methods, it reduces errors in balancing calculation due to limited utilization of the information from a unidirectional sensor, and thus improves balancing accuracy.
2.
The presentation of the phase shift ellipse and the initial phase point is the key value of holo-balancing. It

Acknowledgements

The authors acknowledge supports from the National Education Ministry Doctor Foundation of China (No. 9269830, No. 20040698017), and the National Science Foundation of China (No. 50335030, No. 50475084). Special thanks are extended to Puchen Power Plant, Weihe Power Plant, and Shijiazhuang Oil Refinery, who provided the experimental data in the paper.

References (7)

L. Qu et al.
The holospectrum: a new method for rotor surveillance and diagnosis
J. Mech. Syst. Signal Process.
(1989)
B. Xu et al.
The information integration and optimization in flexible rotor balancing
J. Sound Vib.
(2000)
L. Qu et al.
Rotor balancing based on holospectrum analysis principle and practice
China Mech. Eng.
(1998)

There are more references available in the full text version of this article.

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A new field balancing method of rotor systems based on holospectrum and genetic algorithm

Abstract

Introduction

Section snippets

Holospectral technique

Procedure of holo-balancing

Single plane balancing

Conclusions

Acknowledgements

J. Mech. Syst. Signal Process.

J. Sound Vib.

Rotor balancing based on holospectrum analysis principle and practice

China Mech. Eng.