Non-driven Micromechanical Gyroscopes and Their Applications (eBook)

Zhang Fuxue is director of the research center for sensor technology, doctoral tutor of Beijing Information Science and Technology University. His research mainly engaged in level posture sensor, accelerometer and micro mechanical gyro. In the recent 10 years, he mainly researches on vehicle driven gyroscope. The author has won: The State Technological Invention Award; The National Science and Technology Progress Award. He has 50 invention patents which includes 18 foreign patents and published 23 books. The book “Piezoelectricity” won the second prize of National Excellent Book in 1988. The book “Robot technology and its application” won the Chinese Book Award in 2002. The book “Modern Piezoelectric Science” won the second prize of Electronic Science and Technology Annual in 2008.

Preface 5
About the Book 7
Contents 8
Author’s Introduction 13
Non-driven Mechanical Gyroscopes 15
1 Operating Theory of a Non-driven Mechanical Gyroscope 16
1.1 Characteristics of a Flying Aircraft 16
1.2 Motion Equation for the Sensitive Elements in a Non-driven Mechanical Gyroscope 22
1.3 Performance of the Gyroscope as the Aircraft Rotates With a Constant Angular Velocity 29
1.4 Choice of System Scheme for a Non-driven Mechanical Gyroscope 32
1.5 Dynamic Performance Regulation of the System 40
1.6 Stability of a Non-driven Mechanical Gyroscope with Negative Velocity Feedback 48
1.7 Technical Performance of a Non-driven Mechanical Gyroscope 69
2 Precision of a Non-driven Mechanical Gyroscope with Negative Velocity Feedback 71
2.1 Measurement Precision of a Constant Angular Velocity Rotating Around The Horizontal Axis 71
2.2 Regulation of a Non-driven Mechanical Gyroscope 92
3 Performances of Non-driven Mechanical Gyroscope in the Condition of an Alternating Angular Velocity 97
3.1 Performance of Non-driven Mechanical Gyroscope in the Condition of an Angular Vibration 98
3.2 Output Signal of Non-driven Mechanical Gyroscope in the Condition of an Angular Vibration 112
3.3 Measurement Accuracy of the Harmonic Angular Velocity for the Aircraft 117
3.4 Performance of Non-driven Mechanical Gyroscope in a Circumferential Vibration 141
4 The Operating Errors of a Non-driven Mechanical Gyroscope 148
4.1 Error Caused by Static Unbalance of the Framework 148
4.2 Error Caused by Angular Vibration and Circumferential Vibration 152
4.3 Error Caused by Imprecise Installation 154
4.4 Error Caused by Change of Environmental Temperature 157
Non-driven Micromechanical Gyroscopes 162
5 The Micromechanical Accelerometer and the Micromechanical Gyroscope 163
5.1 The Micromechanical Accelerometer 163
5.1.1 Basic Principle, Technology Type and Applications of a Micromechanical Accelerometer 163
5.1.2 The Working Principle of a Micromechanical Accelerometer 166
5.1.3 The Micromechanical Accelerometer Manufactured by a Bulk Micromachining Process 167
5.1.4 The Micromechanical Accelerometer Manufactured by a Surface Micromachining Process 171
5.1.5 Force Feedback 176
5.1.6 The Resonant Micromechanical Accelerometer 178
5.2 The Micromechanical Gyroscope 181
5.2.1 The Structural Basis of a Micromechanical Gyroscope 181
5.2.2 The Basic Principle of a Micromechanical Gyroscope 183
5.2.3 Frequency Bandwidth 186
5.2.4 Thermal Mechanical Noise 189
5.2.5 Types of Micromechanical Gyroscope 190
6 The Working Principle of a Non–Driven Micromechanical Gyroscope 197
6.1 The Structure Principle 197
6.2 The Dynamic Model 198
6.2.1 The Mass Vibrational Model 198
6.2.2 The Solution of the Angular Vibrational Equation 203
6.3 Analysis and Calculation of Kinetic Parameters 206
6.3.1 Torsion Stiffness of the Elastic Supporting Beam 206
6.3.2 Parameter Calculation of the Flexible Joints 207
6.3.3 The Damping Coefficient of Angular Vibration for the Vibrating Element 209
6.3.4 Relationship Between the Angular Vibration Natural Frequency, the Angular Vibration Amplitude and the Measured Angular Velocity 211
6.4 Signal Detection 212
6.4.1 The Relationship Between the Output Voltage and The Swing Angle 213
6.4.2 Signal Processing Circuit 215
6.5 ANSYS Simulation and Analogy 220
6.5.1 Modal Analysis 220
6.5.2 Frequency Response Analysis 221
7 Error of a Non-driven Micromechanical Gyroscope 223
7.1 Motion Equations of a Vibratory Gyroscope 223
7.2 Error Principle of a Vibratory Gyroscope 234
7.3 Error Calculation of a Non-driven Micromechanical Gyroscope 240
7.4 Error of a Non-driven Micromechanical Gyroscope 243
8 Phase Shift of a Non-driven Micromechanical Gyroscope 246
8.1 Phase Shift Calculation of a Non-driven Micromechanical Gyroscope 246
8.2 Phase Shift of a Non-driven Micromechanical Gyroscope 250
8.3 Feasibility of Adjusting the Position to Compensate the Phase Shift of the Output Signal 252
8.4 Characteristic Calculation of a Non-driven Micromechanical Gyroscope in the Angular Vibration Table 256
9 Static Performance Test of a Non-driven Micromechanical Gyroscope 260
9.1 Performance of the Prototype of a Non-driven Micromechanical Gyroscope 260
9.1.1 Temperature Performance of the Prototype 260
9.1.2 Performance of the Prototype 263
9.1.3 Temperature Stability of the Prototype 265
9.2 Performance of a CJS-DR-WB01 Type Silicon Micromechanical Gyroscope 266
9.3 Performance of a CJS-DR-WB02 Type Silicon Micromechanical Gyroscope 267
9.4 Performance Test of CJS-DR-WB03 Type Silicon Micromechanical Gyroscope 267
Applications of Non-driven Micromechanical Gyroscopes 291
10 Signal Processing 292
10.1 Inhibiting the Influence of a Change in Rolling Angular Velocity of the Rotating Body on the Stability of the Output Signal 292
10.1.1 Influence of a Change in Rolling Angular Velocity of the Rotating Body on the Output Signal 292
10.1.2 Method for Inhibiting the Influence of a Change in Rolling Angular Velocity on the Output Signal 292
10.1.3 Validation of Inhibiting Influence Method 295
10.2 The Attitude Demodulation Method of a Micromechanical Gyroscope Based on Phase Difference 299
10.2.1 Study of the Phase Difference Between the Output Signal and the Reference Signal of the Gyroscope 299
10.2.2 Factors Influencing Phase Difference 307
10.2.3 Phase Difference Compensating Method 314
10.3 Posture Demodulation of the Rotating Body Based on the Micromechanical Gyroscope 317
10.3.1 Demodulation Method 317
10.3.2 Simulation Experiment 328
11 Applications in the Flight Attitude Control System 331
11.1 Calculation Method Design and Software Creation 331
11.1.1 Calculation Method and Software 331
11.1.2 Computer Software Design 331
11.2 Influence Connected Motion (Angular Vibration) as Three Axes Move Simultaneously 335
11.3 DSP Digital Output of the Gyroscope 336
11.3.1 Hardware Circuit Design 336
11.3.2 Algorithm and Software Realization 337
11.3.3 Test Results 340
11.4 Attitude Sensing System for Single Channel Control of the Rotating Flight Carrier 343
11.5 Three Channels Attitude Sensing System of the Rotating Flight Carrier Through the Rectangular Coordinate Transformation 346
11.6 Attitude Sensing System of the Rotating Flight Carrier Through the Polar Coordinate Transformation 350
11.6.1 Method for Obtaining the Transverse Angular Velocity Relative to the Rotating Coordinate System of the Rotating Flight Carrier 352
11.6.2 Method for Obtaining the Rolling Angular Velocity Relative to the Coordinate System of the Quasi-Rotating Flight Carrier 354
11.6.3 Method for Obtaining the Pitch Angular Velocity and the Yaw Angular Velocity Relative to the Coordinate System of the Quasi-Rotating Flight Carrier 356
11.7 Applications in the Non-rotating Flight Carrier 357
References 359