Review of Research Advances in Gyroscopes’ Structural Forms and Processing Technologies Viewed from Performance Indices
Abstract
1. Introduction
2. Basic Mechanics Principle and Indices of Gyroscope
2.1. Coriolis Force Effect and Coriolis Acceleration
2.2. Principle of the Resonant Gyroscope
2.2.1. Typical Structure of a Resonant MEMS Gyroscope
2.2.2. Principle of Resonance Detection
- The detection amplitude is directly proportional to the rotation angular velocity of the base (system).
- The mechanical sensitivity of the system is proportional to the amplitude of the driving mode and inversely proportional to the difference in frequency between the driving frequency ωd and the detection frequency ωy.
- Mechanical sensitivity can be enhanced by increasing the driving quality factor, deducing the driving mass, and decreasing the difference frequency.
2.3. Performance Indices of the Gyroscope
2.3.1. Scale Factor
2.3.2. Threshold Value/Resolution
2.3.3. Measuring Range
2.3.4. Zero-Bias Stability
2.3.5. Angle Random Walk (ARW)
2.3.6. Band Width (BW)
2.4. Quantitative Analysis of the Impact of MEMS Gyroscope Structures, Closed-Loop Control, and Phase Alignment Accuracy
3. Research Advances in the Field of Gyroscopes’ Structural Form and Processing Technologies
3.1. Typical Development of Gyroscope
3.1.1. Division of Structural Development Stages
3.1.2. Several Impacts Caused by Structural Evolution
3.2. Performance of Different Structure Forms and Machining Processing in MEMS Gyroscopes
3.2.1. Single-Mass Block Configuration
3.2.2. Dual-Mass-Block Configuration
3.2.3. Quadruple-Mass Block Structure
3.2.4. Ring/Disc Structure
3.2.5. Hemisphere Structure
4. Impacts of Design, Fabrication and Factors on Performance
4.1. Performacne Impacts from Pespective of Design Types
4.2. Performacne Impacts Caused by Certain Factors
4.2.1. Environmental Sensitivity
4.2.2. Sock Resistance
4.2.3. Thermal Stress and Temperature Drift
4.2.4. Other Optimization Technologies
4.3. Fabrication Processes on the Impact of Permormance
4.4. Brief Summary
5. Features and Challenges of Gyroscope Technology
5.1. Typical Characteristics of Gyroscope Research
5.1.1. Multidisciplinary Integration
5.1.2. Statistical Properties of Results
5.1.3. Error and Corresponding Compensation
5.2. Challenges of Gyroscopes Technology
5.2.1. Challenge in Error Reduction Methods
5.2.2. Challenge from the Enhancement of Mechanical Sensitivity
5.2.3. Challenge in Mathematical Modelling of a System
5.2.4. Challenge in Machine, Levelling and Excitation Technologies
5.3. Suggestions for Future Research Directions
6. Conclusions and Perspective
- (i)
- An overview of the modelling principles and processes of gyroscopes based on the Coriolis force and resonance mechanisms lays a theoretical foundation for the research and development of microelectromechanical system (MEMS) gyroscopes. Moreover, the core performance indices of gyroscopes are systematically sorted, providing a standardized evaluation basis for measuring the performance of different gyroscopes and guiding their design and application.
- (ii)
- An in-depth analysis of the evolutionary process of gyroscope designs and the distinctive features of each development stage is performed. On this basis, typical structural forms of various MEMS gyroscopes (such as single-mass-block, dual-mass-block, quadruple-mass-block, ring/disc, and hemispherical structures) are discussed, along with their corresponding processing technologies. The correlations among different structures, processing methods, and gyroscope performance indices are also clarified, revealing how structural innovation and processing progress drive performance optimization.
- (iii)
- From the perspectives of design, fabrication, and other typical factors, analyses are provided to illustrate their impacts on performance, emphasizing the significance and challenges associated with compensation and optimization arising from internal and external influences such as design variations, process deviations, mechanical shock, thermal stress, and temperature drift.
- (iv)
- A summary of the prominent characteristic challenges in gyroscope technologies is as follows:
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Structure Type | Sensitivity (mV/°/s) | Noise Density (°/√h) | Stability Metrics | References |
---|---|---|---|---|
z-axis tuning fork MEMS gyroscope | 21.76 | —— | ZRO: 0.002 (°/s) | [46] |
Dual-Mass System | —— | 0.0414 | Bias stability: 0.415°/h; Bandwidth: 104 Hz | [26] |
Vibratory, doubly decoupled, bulk micromachined | 27.6 (scale factor) | 0.06 | Nonlinearity: <120 ppm; Settling time < 200 ms | [8] |
Doubly decoupled, silicon-glass bonded | —— | 0.316 | Bias instability: 2°/h; ZRO drift: 0.1248°/s | [47] |
Capacitive vibratory, mode-split | —— | 0.068 | Bias instability: 0.9°/h; Phase standard deviation: 0.0004° | [48] |
Tuning fork, comb-driven, silicon-on-insulator (SOI) process | 23 (optimal) | —— | Bias stability: 7.52 × 10−4°/s; Nonlinearity: 0.0062% | [49] |
Vibratory, non-decoupled, dual-mode, custom metal lid | 1.345 | 0.978 | Bias instability: 9.458°/h; ZRO: 0.095°/s | [50] |
Linear vibrating tuning fork MEMS gyroscope | —— | —— | Overshoot: −96%; Settling time: 0.036 s | [51] |
Cavity optomechanical architecture | 122.2 | 0.95 | —— | [52] |
doubly decoupled tuning fork gyroscope | —— | —— | Frequency drift: 0.3 Hz/°C; Standard deviation: 0.027 | [53] |
Control Type | Performance Improvement | Stability Enhancement | Implementation Complexity | References |
---|---|---|---|---|
Self-resonant, AGC, quadrature correction | Coupling force amplitude reduced 105×; ZRO reduced | Improved precision; ZRO: 0.002 (°/s) | GA+Monte Carlo: Medium-high; Adam-LMSD: Medium | [46] |
Closed-loop (no further details) | Bias stability: 2.168–0.415°/h; ARW: 0.155–0.0414°/√h | Bandwidth: 13–104 Hz; Nonlinearity: 660–59.3 ppm | Moderate | [26] |
AGC-PI | Setting time < 200 ms; Amplitude fluctuation < 16 ppm | Nonlinearity < 120 ppm; Threshold: 0.005°/s | Moderate | [8] |
Digital PLLs, PI (LFM vs. AM) | LFM: ZRO drift 0.1248°/s vs. AM: 10.7139°/s | LFM: Nonlinearity 329 ppm vs. AM: 1902 ppm | Moderate | [47] |
MEAM (vs. CEAM), AGC+PLL | Settling time: 45.2 ms; Bias instability improved 2.4× | ARW improved 1.4×; Phase standard deviation: 0.0004° | Moderate-high | [48] |
PI (GA-optimized), Adam-LMS demodulator | Sensitivity: 17.7–23 mV/(°/s); Nonlinearity: 0.0085–0.0062% | Bias stability: 0.0015–7.52 × 10−4°/s | High | [49] |
FTR, PLL, AGC, phase delay correction | ZRO reduced by 755% to 0.095°/s | Bias instability: 9.458°/h; ARW: 0.978°/√h | Moderate-high | [50] |
Adaptive PID vs. classical PID | Overshoot reduced 96%; Settling time: 0.036 s vs. 0.06 s | Similar rise time; faster stabilization | Low | [51] |
Cavity optomechanical detection-based control | Sensitivity up to 122.2 mV/(°/s) | Dual-decoupled structure reduces mode coupling | Low | [52] |
Incremental PID (temperature control) | Frequency drift: 0.3 Hz/°C-stable | Improved frequency stability | Combination of hardware and software, relatively complex | [53] |
Phase Error/Delay (°) | Phase Correction Mechanism | Impact on Performance Metrics | Temperature Range for Correction | References |
---|---|---|---|---|
—— | Quadrature error correction | Coupling force amplitude reduced 105×; ZRO reduced | —— | [46] |
—— | Digital PLLs; phase tracking | LFM mode: ZRO drift 0.1248°/s vs. AM: 10.7139°/s | 10–50 °C | [47] |
0.0004 (phase standard deviation) | Phase-locked loop | Bias instability, ARW improved; phase standard deviation: 0.0004° | —— | [48] |
Phase standard deviation: 0.0004° | PLL, Adam-LMS demodulator | Bias instability improved 2.4×; ARW improved 1.4× | tested under room temperature with 2 °C fluctuation | [49] |
19.419 ± 0.004 | Real-time PLL phase reference adjustment | ZRO reduced by 755% to 0.095°/s; ARW: 0.978°/√h; Bias instability: 9.458°/h | −20 to 70 °C | [50] |
Structure Type | Typical Performance Metrics | Advantages | Limitations | Applications | References |
---|---|---|---|---|---|
Dual-mass gyroscope | Scale factor: 12.5 mV/(°/s); ARW: 3°/h, 0.047°/√h, 0.18°/(h·√Hz), 0.096°/√h, 0.45°/√h, 0.021°/√h, 0.028°/√h, 0.006°/√h; Bias instability: 12°/h, 1.6°/h, 0.2°/h, 0.09°/h, 9.6°/h, 0.29°/h, <0.012°/h; Q-factor: up to 36,000; Bandwidth: 1–100 Hz; Shock resistance: >33,000 g | Vibration decoupling, high Q-factor, reduced environmental sensitivity, differential detection suppresses noise | Requires tuning, trimming, frequency matching; performance optimization still challenging | Automotive and aerospace navigation | [75,76,77,78,79,80,81,82,83,84,85,86,117] |
Quadruple-mass gyroscope (QMG) | Resonant frequency: ~2 kHz; Q-factor: up to 1.2 million; ARW: 26.4°/√h, 0.72°/(h·√Hz), 0.0264°/√h, 0.28°/√h, 0.006°/√h, 0.0005°/√h; Bias instability: 0.12°/h, 5.9°/h, 0.08°/h; Measurement range: ±150°/s | Fully symmetric structure, suitable for FM detection | Requires large sensor area to ensure suspension and mode decoupling | Consumer electronics, tactical-grade sensors | [87,88,89,90,91,92,93,117] |
Ring/disc resonator gyroscope (DRG) | ARW: 6°/√h, 14.4°/√h, 10.4°/(h·√Hz), 27°/√h, 3.6°/(h·√Hz), 0.015°/(h·√Hz), 0.36°/√h, 0.048°/√h, 0.138°/√h, 0.0009°/√h, 0.012°/√h, 0.083°/√h, 0.015°/√h, 0.004°/√h, 0.004°/√h, 0.026°/√h, 0.05°/√h; Bias instability: 10°/s, 0.16°/s, 20°/h, 0.01°/h, 0.08°/h, 0.11°/h, 0.015°/h, 0.87°/h, 0.85°/h, 0.42°/h; Q-factor: up to 650,000; Scale factor: 0.286 mV/(°/s), 39.8 mV/(°/s), 132 mV/(°/s), 98.1 mV/(°/s) | High precision, high Q-factor, stiffness–mass decoupling design, suitable for mass production | Complex design | High-end navigation, aerospace, UAVs | [24,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117] |
Architecture Type | Bias Stability | Angle Random Walk | Notable Performance Advantages | Notable Limitations | References |
---|---|---|---|---|---|
Single-mass, triaxial | —— | —— | Improved navigation with noise modelling | No redundancy | [141] |
Mult-sensor, redundant (orthogonal/cubic/optimal) | >25% reduction | >25% reduction, 3.2×/3.7× reduction | High reliability, error reduction | Hardware complexity, missing data | [142,143,144] |
Dual-mass | 0.09°/h | 0.0096°/√h | High stability, sensitivity | Not Multi-sensor, specialized design | [80] |
9-axis | —— | —— | Static error (0.05°); dynamic error (0.5°) | No architecture detail | [145] |
Design Type | Bias Stability | Angle Random Walk | Environmental Sensitivity | References |
---|---|---|---|---|
Triaxial inertial measurement unit | —— | —— | Field (auto/bike), Global navigation satellite system/inertial measurement unit | [141] |
9-gyroscope, orthogonal | —— | —— | Simulation, fault detection and isolation test | [144] |
6-gyroscope, cubic | >25% reduction | >25% reduction | Field, Global navigation satellite system, stationary/dynamic | [143] |
4/5/6-gyroscope, redundant | —— | Angle random walk 3.2×, rate random walk 3.7× reduction | Swing test, simulation | [142] |
Dual-mass | 0.09 degrees per hour | 0.0096 degrees per root hour | Vacuum, 10 h, temperature/vacuum stabilized | [80] |
—— | —— | Kalman filter output variance ≤ 30% | —— | [147] |
9-axis | —— | —— | static/dynamic, orientation | [145] |
Process Type | Key Parameters | Quality Metrics | Limitations | References |
---|---|---|---|---|
SOG: patterning, anodic bonding, DRIE, CMP | Silicon thickness: 50 μm, roughness: 1.13 nm | Q~12,000, frequency~4 kHz | Lag effect, notching, etch endpoint control | [146] |
SOI, single crystal silicon, digital control | —— | Q~100,000, bias stability 0.18°/h | —— | [156] |
Process Type | Key Parameters | Quality Metrics | Limitations | References |
---|---|---|---|---|
Laser-induced etching (LIE) on fused silica | Etch width 11 μm, temperature 20–70 °C, 10–30 min | Q > 810,000, overload > 15,000 g, 45 MPa | Subsurface cracks, etch control, vacuum requirement | [157] |
Precision machining, polishing, etching | Roundness 0.17 μm, roughness 15.2 nm | Q = 3.11 × 107 | Surface loss, stress, geometry limits | [158] |
Fused silica, hemispherical resonator | Shell radius 10–15 mm, damage layer 0–100 μm | QTED reduction up to 92.5% | Wall thickness nonuniformity | Geometric parameters |
Process Type | Key Parameters | Quality Metrics | Limitations | References |
---|---|---|---|---|
Anodic bonding (silicon to Pyrex) | Bonding after wet etch, pre-DRIE | Well-defined structures, no footing | Wafer misalignment, lapping damage | [146] |
Direct bonding (fused silica) | Resonator to substrate | High process precision | Bonding error, stress | [157] |
Performance Metric | Process Influence | Achieved Results | Limiting Factors | References |
---|---|---|---|---|
Surface roughness | Chemical Mechanical Polishing (CMP), cerium oxide polish | 1.13 nm | Lapping damage, misalignment | [146] |
Subsurface cracks, etch width | Laser-Induced Etching (LIE), ultrasonic, annealing | Etch width 11 μm, crack width 4 μm | Subsurface cracks, etch control | [157] |
Surface roughness | Precision polishing/etching | 15.2 nm | Surface loss, stress | [158] |
Performance Metric | Process Influence | Achieved Results | Limiting Factors | References |
---|---|---|---|---|
Overload, strength | Laser-induced etching (LIE), structure compensation | >15,000 g, 45 MPa | Crack formation, etch uniformity | [157] |
Mechanical performance | DRIE optimization | No notching /footing | Lag effect, endpoint control | [146] |
Performance Metric | Process Influence | Achieved Results | Limiting Factors | References |
---|---|---|---|---|
Q-factor | DRIE/CMP optimization | 10,437–12,058 | Lag effect, etch uniformity | [146] |
Q-factor | Laser-induced etching (LIE), structure compensation | 817,000–819,000 | Subsurface cracks, vacuum | [157] |
Q-factor | Precision machining /polishing | 3.11 × 107 | Surface loss, stress, geometry | [158] |
Q-factor | SOI, digital compensation | ~100,000 | —— | [156] |
Q-factor stability | In situ Joule tuning | ΔQ~150 ppm | Not fabrication- limited | [159] |
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Luo, H.; Su, H.; Tang, Q.; Nisa, F.u.; He, L.; Zhang, T.; Liu, X.; Liu, Z. Review of Research Advances in Gyroscopes’ Structural Forms and Processing Technologies Viewed from Performance Indices. Sensors 2025, 25, 6193. https://doi.org/10.3390/s25196193
Luo H, Su H, Tang Q, Nisa Fu, He L, Zhang T, Liu X, Liu Z. Review of Research Advances in Gyroscopes’ Structural Forms and Processing Technologies Viewed from Performance Indices. Sensors. 2025; 25(19):6193. https://doi.org/10.3390/s25196193
Chicago/Turabian StyleLuo, Hang, Hongbin Su, Qiwen Tang, Fazal ul Nisa, Liang He, Tao Zhang, Xiaoyu Liu, and Zhen Liu. 2025. "Review of Research Advances in Gyroscopes’ Structural Forms and Processing Technologies Viewed from Performance Indices" Sensors 25, no. 19: 6193. https://doi.org/10.3390/s25196193
APA StyleLuo, H., Su, H., Tang, Q., Nisa, F. u., He, L., Zhang, T., Liu, X., & Liu, Z. (2025). Review of Research Advances in Gyroscopes’ Structural Forms and Processing Technologies Viewed from Performance Indices. Sensors, 25(19), 6193. https://doi.org/10.3390/s25196193