Rotor balancing technology has a unique position in equipment manufacturing industry of the national economy. All rotating machinery, from precision gyro navigator to ordinary wheels of traffic vehicles, from turbine rotors weighing hundreds of tons to light meter rotor with a few grams, and even micro-electromechanical rotor components, from the satellites rotating just a few revolutions per minute to the machine tool main shafts rotating hundreds of thousands per minute, the performance of the rotors is closely related to the quality of balance. Statistics show that the rotor dynamic unbalance is one of main causes of vibration and noise, reducing equipment life and reliability and constraining product quality and performance. Unbalance reduction is a fundamental problem in the process of production, manufacturing and application of the rotating electromechanical products. High-speed balancing technology is a high technology in balancing technologies and provides a guarantee for operation safety and reliability of high-speed rotating machinery. At present, high-speed balancing test has become a routine process for flexible rotors such as steam turbine, generator, turbine compressors and other large rotating machinery. It can be said that high-speed balancing technology plays an important role in reducing the unit vibration and noise, improving the unit working speed and working conditions, ensuring normal and safe operation of units and extending life cycle of rotating machineries.
Compared with low-speed balancing technology, high-speed balancing technology is mainly used in balancing correction and overspeed test of large flexible rotors. As the main process equipment for high-speed balancing, high-speed balancing machines have not only the functions of low-speed balancing machines, but also those of high-speed balancing test, overspeed test and rotor dynamics research and testing. The principle, structure and performance of high-speed balancing machines have special requirements. With the development of engineering technologies, especially computer technologies, balancing technologies including high-speed balancing technology are always evolving dynamically. For example, the circuit technology and computer technology have changed the display mode of electrical measuring unit of balancing machines from the early mechanical measurement (mechanical gauge and phase meter) , electronic measurement (electronic amplifier, filter etc. ) , to micro-controller (embedded system) based electrical measurements. In addition, the digital signal processing technology has also greatly enriched the high-speed balancing technology. The electrical measuring units of modern high-speed balancing machines are no longer simply to measure the unbalance, but also have a wealth of data processing and analysis functions.
At the same time, in order to ensure rotation of the rotor in a state of high security during the test, reduce or eliminate the resistance of air to correctly balancing flexible rotors, the process of high-speed balancing and overspeed test are usually carried out in high-speed balancing and overspeed test chamber. The chamber is usually a separate building structure, which is composed of driving system, explosion-proof vacuum cylinder, gates, vacuum pump room, oil lubrication system, control room, auxiliary room, etc. to ensure smooth and safe running of high-speed rotors and direct monitoring of the system operations.
China had developed the first set of high-speed balancing machine independently which was equipped in a steam turbine plant since the early 1980s. Up to now, many enterprises have equipped high-speed balancing machines with different tonnage to meet the demand of large-scale rotating machinery balancing. Nevertheless, few literatures about high-speed balancing technology and equipment could be found. The aim of this book is to summarize and popularize the high-speed balancing technology.
High-speed balancing technology involves a variety of techniques. We try to give a comprehensive introduction to the principle of high-speed balancing, design of high-speed balancing machines, composition of the high-speed balancing and overspeed test chamber from a system point of view. We also try to allow the readers to have an overall, global understanding on the latest trends of high-speed balancing technology.
This book is divided into five chapters. The chapters are outlined as follows: Chapter one which is authored by Xilin Xu gives a brief description of the basic concept of high-speed balancing technology. Chapter two which is authored by Xilin Xu and Sheping Tian discusses high-speed balancing of flexible rotors. Chapter three which is authored by Yuewu Wang and Sheping Tian describes the machinery of high-speed balancing machines. Chapter four which is authored by Sheping Tian, Jue Yang and Xiaojue Lin presents design of electrical measuring unit. Chapter five which is authored by Yuewu Wang introduces the composition and basic design principles of high-speed balancing and overspeed test chamber. The appendixes which are authored by Zhiqing Zhao and Lin Qin give the technical data sheet of DG and HY-VG Series High-speed Balancing Machines and an introduction to Shanghai Schiak Testing Machinery Co. , Ltd.
This book is not possible without the work of many individuals. The authors would like to acknowledge Mr. Kexiong Fan, chairman and general manager of Shanghai Schiak Testing Machinery Co. , Ltd. He proposed this writing program and gave financial assistance for publication. The authors also acknowledge Mr. Zhiyan Zhou, former chairman of Shanghai Schiak Testing Machinery Co. , and Mr. Weiming Fan, vice president of The Second Industrial Engineering Design & Research Institute, China United Engineering Corporation. Further thanks go to technical staff of Shanghai Schiak Testing Machinery Co. , Ltd. and colleges of Department of Instrument Science and Engineering, Shanghai Jiao Tong University.
The authors also wish to thank Prof. Jin Cheng, Senior engineer Yong Deng, who reviewed the manuscript and made many useful suggestions. Also thanks to Engineer Ronglin Du, Engineer Qiang Guo, Engineer Hao Gu, who read the manuscript from a mechanical engineering point-of-view and provided suggestions for improvement.

Chapter 1 Introduction 1

1.1 A brief introduction to high-speed balancing technology 1

1.2 Rotor and unbalance 3

1.3 Expression of rotor unbalance 9

1.4 Rigid and flexible rotors 11

1.5 Mechanical balance of rotor 13

Chapter 2 High-speed Balancing of Flexible Rotors 15

2.1 Theoretical basis of high-speed balancing 15

      2.1.1 Introduction 15

      2.1.2 Balancing conditions of rigid rotors 16

      2.1.3 Principle of flexible rotor balancing 18

      2.1.4 Balancing conditions of flexible rotors 23

2.2 Flexible rotor balancing 25

      2.2.1 Aims of flexible rotor balancing 25

      2.2.2 Flexible rotor mode shapes 26

      2.2.3 High-speed balancing of flexible rotors 31

2.3 Modal balancing 34

      2.3.1 Computation of unbalance corrections 34

      2.3.2 Procedures for modal balancing 35

      2.4 Influence coefficient balancing 37

2.5 Harmonic component balancing 40

      2.5.1 Procedures for harmonic component balancing 40

      2.5.2 Comparison between influence coefficient balancing and harmonic component balancing 43

Chapter 3 Structural Analysis and Design of High-speed Balancing Machine 45

3.1 Mechanical support 45

3.2 Design of high-speed mechanical support 49

      3.2.1 Principle of mechanical support 49

      3.2.2 Design of complementary stiffness mechanism 52

      3.2.3 Design of axial stiffness and damping mechanism 54

      3.2.4 Dynamic stiffness calculation of the mechanical support 55

      3.2.5 Calculation of natural frequencies of mechanical support 57

      3.2.6 Brief summary 59

3.3 Measurement of performance parameters of mechanical support 60

      3.3.1 Detection of complementary stiffness mechanism 60

      3.3.2 Measurement of natural frequencies of mechanical support 61

      3.3.3 Measurement of dynamic stiffness of mechanical support 63

3.4 Finite element analysis of mechanical support 65

      3.4.1 Analysis of dynamic stiffness of mechanical support 65

      3.4.2 Modal analysis of mechanical support 67

Chapter 4 Design of Electrical Measuring Unit of High-speed Balancing Machine 71

4.1 Basic function and composition of high-speed balancing machine 71

4.2 Sensor and Its selection 74

      4.2.1 Vibration Sensor 74

      4.2.2 Rotational speed sensor 80

      4.2.3 Basic selection principles of the sensors 83

4.3 Circuit design 83

      4.3.1 Programmable gain amplifier 84

      4.3.2 Integration circuit 88

      4.3.3 Filter circuit 91

      4.3.4 A/D converter 101

4.4 Software Design 111

      4.4.1 Basic functions of the software of the electrical measuring unit 111

      4.4.2 Some noteworthy points in software design 113

4.5 Digital signal processing 115

      4.5.1 Estimation algorithm of sinusoidal signal amplitude and phase 116

      4.5.2 Digital filter design 118

4.6 Calibration and test of electrical measuring unit 127

      4.6.1 Sensitivity calibration of mechanical support and sensor 127

      4.6.2 Inspection and evaluation of the electrical measuring unit 128

      4.6.3 Other projects test 128

Chapter 5 High-speed Balancing and Overspeed Test Chamber 129

5.1 Introduction 129

5.2 Drive system 130

      5.2.1 Wo mode of drive system 130

      5.2.2 Determination of power of drive motor 131

      5.2.3 Gearbox and intermediate shaft 133

5.3 Explosion-proof vacuum cylindrical body 135

5.4 Vacuum system 137

5.5 Oil system 139

      5.5.1 Vacuum oil lubrication system 139

      5.5.2 Atmospheric oil lubrication system 141

      5.5.3 Complementary stiffness oil station 142

      5.5.4 Auxiliary oil station 142

5.6 Safety emergency system 143

5.7 The central control monitoring system 143

5.8 Other auxiliary devices 147

Appendix I Technical Data Sheet of DG and HY-VG Series High-speed Balancing Machines 149

Appendix II Introduction to Shanghai Schiak Testing Machinery Co.， Ltd. 151

Index 155

References 157

Sheping Tian was born in July 1967. He received Ph.D. degree from Department of Instrument Engineering, Shanghai Jiao Tong University in 1999. He is currently an associate professor of School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University and the director of SJTU—SSTM Joint Research Center. His research interests include dynamic testing and circuit theory. He has won the Second—Class Science and Technology Progress Award of the Ministry of Machinery Industry for his contribution to piston on—line measurement. He is the author of more than 150 papers and 3 textbooks on electrical circuits, and holds more than ten Chinese patents. He has won the title of outstanding teacher of Shanghai Jiao Tong University for three times.

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