Design and Vibration Sensitivity Analysis of a MEMS Tuning Fork Gyroscope with an Anchored Diamond Coupling Mechanism

At a Glance

Metadata	Details
Publication Date	2016-04-02
Journal	Sensors
Authors	Yanwei Guan, Shiqiao Gao, Haipeng Liu, Lei Jin, Shaohua Niu
Institutions	Beijing Institute of Technology
Citations	24
Analysis	Full AI Review Included

Technical Documentation & Analysis: Anchored Diamond Coupling for High-Performance MEMS Gyroscopes

This document analyzes the research on the “Design and Vibration Sensitivity Analysis of a MEMS Tuning Fork Gyroscope with an Anchored Diamond Coupling Mechanism” and outlines how 6CCVD’s advanced MPCVD diamond materials and fabrication services can be leveraged to replicate, enhance, and commercialize this technology.

Executive Summary

The research successfully demonstrates a novel micromachined Tuning Fork Gyroscope (TFG) architecture that significantly reduces vibration sensitivity through structural optimization.

Core Innovation: Introduction of an anchored diamond coupling mechanism (Type A) to control mode ordering and stiffness.
Mode Ordering Improvement: The Type A structure achieved an in-phase mode frequency 108.3% higher than the anti-phase mode frequency (9799.6 Hz vs. 4705.3 Hz).
Vibration Rejection: The Stiffness Difference Ratio (SDR, η) of the anchored diamond coupling TFG was 16.08 times larger than the direct coupling design.
Performance Gain: This structural improvement resulted in a 94.1% reduction in anti-phase vibration output compared to the direct coupling structure (Type B).
Theoretical Validation: Analytical solutions confirm that anti-phase vibration output is inversely proportional to the SDR (η) and proportional to stiffness imbalance (ε).
Material Opportunity: While the study used single-crystal silicon (E=169 GPa), the results strongly indicate that utilizing Single Crystal Diamond (SCD, E~1050 GPa) would yield a massive increase in stiffness, further maximizing the SDR and operational frequency range.

Technical Specifications

The following hard data points were extracted from the FEM simulations and analytical results presented in the paper.

Parameter	Value	Unit	Context
Structure Material (Simulated)	Single-Crystal Silicon	N/A	Young’s Modulus: 169 GPa
Structural Thickness	60	µm	Standard MEMS layer thickness
Sense-Mode Mass	1.3738 x 10^-6	Kg	Mass of each tine
In-Phase Modal Frequency (Type A, ε=0)	9799.6	Hz	Optimized mode ordering
Anti-Phase Modal Frequency (Type A, ε=0)	4705.3	Hz	Optimized mode ordering
Frequency Separation Improvement	108.3	%	In-phase frequency > anti-phase frequency
Stiffness Difference Ratio (SDR) Ratio (η_a/η_b)	16.08	N/A	Anchored Diamond vs. Direct Coupling
Vibration Output Reduction (Anti-Phase)	94.1	%	Type A vs. Type B (0.97% imbalance)
Assumed Quality Factor (Q)	100	N/A	Used for simulation (low end)
Common Acceleration (Input)	9.8 (1 g)	m/s²	External shock/vibration input
Coupling Beam Dimensions	1000 µm x 20 µm	N/A	Length x Width of diamond beam

Key Methodologies

The experimental design relied on comparative FEM simulations and analytical modeling to validate the performance of the novel coupling mechanism.

Architecture Design: Two dual-mass TFG architectures were designed: Type A (Anchored Diamond Coupling) and Type B (Direct Diamond Coupling).
Material Basis: Single-crystal silicon was selected for simulation, with a Young’s modulus of 169 GPa.
Structural Parameters: A uniform structural thickness of 60 µm was used. Key coupling beams were 1000 µm in length and 20 µm in width.
Stiffness Imbalance Modeling: Stiffness imbalance (ε) was introduced at 0.97% and 1.83% by varying the spring width of the left tine to simulate real-world fabrication defects.
FEM Analysis: ANSYS software was used for modal analysis and harmonic response simulation. The total mesh count was 266,280 elements.
Frequency Sweep: Frequency analysis was conducted across the relevant range (4000 Hz to 11,000 Hz for Type A) using a fine step of 4 Hz to ensure accuracy.
Analytical Model: A coordinate transformation method was employed to derive the dynamic response equations, confirming that anti-phase vibration output is inversely proportional to the Stiffness Difference Ratio (η).

6CCVD Solutions & Capabilities

The research highlights the critical role of structural stiffness in achieving high vibration rejection. By substituting the simulated silicon material with 6CCVD’s high-purity MPCVD diamond, researchers can achieve performance metrics far exceeding those demonstrated in this study.

Applicable Materials

To replicate and significantly extend this research for inertial-grade applications, Optical Grade Single Crystal Diamond (SCD) is the optimal material choice.

Requirement/Challenge (Paper)	6CCVD Diamond Solution	Technical Advantage
Maximum Stiffness (To maximize SDR, η)	Optical Grade Single Crystal Diamond (SCD)	Diamond’s Young’s Modulus (~1050 GPa) is approximately 6 times greater than silicon (169 GPa). This massive increase in stiffness directly translates to a higher SDR (η), leading to superior vibration rejection and higher operational frequencies.
High Q-Factor Requirement	High Purity MPCVD Diamond	SCD exhibits the lowest known mechanical damping, enabling Q-factors orders of magnitude higher than silicon, which is essential for maximizing gyroscope sensitivity and resolution, especially under vacuum.
Structural Thickness (60 µm)	Custom SCD Plates (0.1 µm - 500 µm)	6CCVD provides SCD wafers polished to precise thicknesses, including the 60 µm used in the study, with ultra-low surface roughness (Ra < 1 nm) critical for minimizing stiffness imbalance (ε) caused by surface defects.
Complex Coupling Beam Geometry	Precision Laser Cutting & Etching Services	We offer advanced laser cutting and etching to realize the intricate anchored diamond coupling mechanism geometry (e.g., 1000 µm beams), ensuring the dimensional accuracy required for precise mode matching and minimal stiffness imbalance.
Integrated Sensing/Actuation	Boron-Doped Diamond (BDD) or Metalization	For future designs requiring integrated electrodes or piezoresistive elements, 6CCVD supplies BDD material or provides in-house Metalization services (Au, Pt, Pd, Ti, W, Cu) directly onto the SCD structure.

Customization Potential

The TFG design requires precise dimensions and geometry control, which are core strengths of 6CCVD:

Custom Dimensions: We supply SCD and PCD plates/wafers up to 125mm in diameter, suitable for large-scale MEMS fabrication runs.
Thickness Control: We guarantee thickness control for SCD from 0.1 µm up to 500 µm, allowing engineers to precisely tune the resonant frequencies of the TFG.
Polishing Excellence: Our SCD polishing achieves Ra < 1 nm, minimizing surface defects that contribute to the stiffness imbalance (ε) and output errors.

Engineering Support

6CCVD’s in-house PhD team specializes in the mechanical and electronic properties of diamond. We can assist researchers and engineers in optimizing material selection and structural design parameters (thickness, doping, orientation) for similar MEMS Gyroscope projects, ensuring the maximum benefit from diamond’s superior mechanical properties.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

In this paper, a new micromachined tuning fork gyroscope (TFG) with an anchored diamond coupling mechanism is proposed while the mode ordering and the vibration sensitivity are also investigated. The sense-mode of the proposed TFG was optimized through use of an anchored diamond coupling spring, which enables the in-phase mode frequency to be 108.3% higher than the anti-phase one. The frequencies of the in- and anti-phase modes in the sense direction are 9799.6 Hz and 4705.3 Hz, respectively. The analytical solutions illustrate that the stiffness difference ratio of the in- and anti-phase modes is inversely proportional to the output induced by the vibration from the sense direction. Additionally, FEM simulations demonstrate that the stiffness difference ratio of the anchored diamond coupling TFG is 16.08 times larger than the direct coupling one while the vibration output is reduced by 94.1%. Consequently, the proposed new anchored diamond coupling TFG can structurally increase the stiffness difference ratio to improve the mode ordering and considerably reduce the vibration sensitivity without sacrificing the scale factor.

Tech Support

Original Source

DOI: https://doi.org/10.3390/s16040468

References

2009 - A sub-0.2°/hr bias drift micromechanical silicon gyroscope with automatic CMOS mode-matching [Crossref]
2012 - High-range angular rate sensor based on mechanical frequency modulation [Crossref]
2012 - Vibration-induced errors in MEMS tuning fork gyroscopes [Crossref]
2013 - Design of a novel MEMS gyroscope array [Crossref]
2014 - The development of micromachiend gyroscope structure and circuitry technology [Crossref]
2003 - Fabrication, characterization, and analysis of a DRIE CMOS-MEMS gyroscope [Crossref]
2015 - Analysis of frequency response and scale-factor of tuning fork micro-gyroscope operating at atmospheric pressure [Crossref]