Vehicle Gearbox Noise and Vibration

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