9781118359419

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Advances in methods of gear design and the possibility of predicting the sound pressure level and life time of gearboxes and perfect instrumentation of test stands allows for the production of a new generation of quiet transmission units. Current literature on gearbox noise and vibration is usually focused on a particular problem such as gearbox design without a detailed description of measurement methods for noise and vibration testing.

Vehicle Gearbox Noise and Vibration: Measurement, Signal Analysis, Signal Processing and Noise Reduction Measures addresses this need and comprehensively covers the sources of noise and vibration in gearboxes and describes various methods of signal processing. It also covers gearing design, precision manufacturing, measuring the gear train transmission error, noise test on testing stands and also during vehicle pass-by tests.

The analysis tools for gearbox inspection are based on the frequency and time domain methods, including envelope and average toothmesh analysis. To keep the radiated noise under control, the effect of load, the gear contact ratio and the tooth surface modification on noise and vibration are illustrated by measurement examples giving an idea how to reduce transmission noise.

Key features:

Covers methods of processing noise and vibration signals
Takes a practical approach to the subject and includes a case study covering how to successfully reduce transmission noise
Describes the procedure for the measurement and calculation of the angular vibrations of gears during rotation
Considers various signal processing methods including order analysis, synchronous averaging, Vold-Kalman order tracking filtration and measuring the angular vibration

Vehicle Gearbox Noise and Vibration: Measurement, Signal Analysis, Signal Processing and Noise Reduction Measures is a comprehensive reference for designers of gearing systems and test engineers in the automotive industry and is also a useful source of information for graduate students in automotive and noise engineering.

Jiri Tuma graduated from the Brno University of Technology, Czech Republic, in 1970 and completed his doctoral studies in 1977. After graduation, he became a researcher in the field of control systems at a research institute and in 1988 began working in the R&D department of an automotive company (Tatra Trucks). He was a member of the team for the introduction of HCR gears in the transmissions. That time, Tatra entered among the top global manufacturers of this type of gears. In 1995, he joined the VSB - Technical University of Ostrava, Faculty of Mechanical Engineering where he became a full professor in 2001. He gives lectures and does research in the field of control systems, signal processing, active vibration control and machine diagnostics. He is the author of more than 200 publications, including a book on signal processing (in Czech) and a chapter of Crocker’s Handbook on noise and vibration control.

Series Preface xi

Preface xiii

Acknowledgements xv

1 Introduction 1

1.1 Description of the TATRA Truck Powertrain System 2

1.2 Test Stands 3

References 5

2 Tools for Gearbox Noise and Vibration Frequency Analysis 7

2.1 Theory of Digitisation of Analogue Signals 7

2.2 Nyquist-Shannon Sampling Theorem 16

2.3 Signal Analysis Based on Fourier Transform 21

2.3.10 Time and Frequency Scales 35

2.3.11 Spectral Unit of Autospectrum 36

2.3.12 Cross-Spectrum 37

2.3.13 Calculation of the Inverse Discrete Fourier Transform 39

2.3.14 Fast Fourier Transform 39

2.3.15 Time Window 40

2.3.16 Calculation of the Signal Power 43

2.3.17 Frequency Weighting 46

2.3.18 Analysis of Random Signals with the Use of Averaging in the Frequency Domain 48

2.4 Zoom FFT 52

2.5 Filtration in the Frequency Domain 55

2.6 Average Power of the Signal 59

References 60

3 Gearbox Frequency Spectrum 61

3.1 Source of Gearbox Noise and Vibration 61

3.2 Spectrum Signature 65

3.3 Low Harmonics of the Shaft Speed 66

3.4 Harmonics of the Fundamental Toothmeshing Frequency and their Sidebands 67

3.5 Subharmonic Components 70

3.6 Ghost (or Strange) Components 71

3.7 Gear Rattle 72

3.8 Periodicity in Signals Measured on a Planetary Gearbox 73

3.9 Spectrum Components Originating from Faults in Rolling Element Bearings 76

References 83

4 Harmonics and Sidebands 85

4.1 Harmonics 85

4.2 Sidebands 87

4.3 Analytic Signal 97

4.4 Cepstrum 111

References 121

5 Order Analysis 123

5.1 Speed Rotation Measurements 124

5.2 Order Analysis Based on External Sampling Frequency 125

5.3 Digital Order Tracking 126

5.4 Frequency Domain Analysis Methods (Multispectral, Slice Analysis) 133

5.5 The Use of Order Spectra for Machine Diagnostics 137

5.6 Averaging in the Time Domain 138

5.7 Time Domain as a Tool for Gear Mesh Analysis 143

References 160

6 Tracking Filters 163

6.1 Interpolation of the Instantaneous Rotational Speed 163

6.2 Quadrature Mixing as a Method for Amplitude and Phase Demodulation 164

6.3 Kalman Filter 168

6.4 Vold-Kalman Order Tracking Filtration 174

References 206

7 Reducing Noise of Automobile Transmissions 209

7.1 Normal Probability Plot 209

7.2 Transmission Error Measurements 210

7.3 Case Study 218

7.4 Gearbox Improvement Aimed at Noise Reduction 226

7.5 Effect of Gear Quality on the Gearbox SPL 230

7.6 Effect of Operation Conditions on the Gearbox Vibrations 231

7.7 Quality Control in Manufacturing 233

References 234

Index 237

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Vehicle Gearbox Noise and Vibration Measurement, Signal Analysis, Signal Processing and Noise Reduction Measures

Vehicle Gearbox Noise and Vibration Measurement, Signal Analysis, Signal Processing and Noise Reduction Measures

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