Vibration-induced errors in MEMS tuning fork gyroscopes

Abstract This paper analyzes potential causes of vibration-induced error in ideal MEMS tuning fork gyroscopes. Even though MEMS gyros are known to be highly susceptible to mechanical vibration, the mechanisms responsible for generating vibration-induced errors are not well understood. We focus on the tuning fork gyroscope (TFG) design that is known to be relatively immune to vibration because of its differential operation and common-mode rejection. Our analysis, however, demonstrates that even an ideal TFG cannot completely eliminate vibrations in special situations because of vibration-induced asymmetry and nonlinearity. We identify three major causes of error that arise from (1) capacitive nonlinearity at the sense electrode, (2) asymmetric electrostatic forces along sense direction at the drive electrodes, and (3) asymmetric electrostatic forces (i.e., drive-electrode capacitance) along drive direction at the drive electrodes. The occurrence conditions and characteristics of each cause are analyzed. The effects of the causes on three classes of TFG gyro designs are analyzed and compared both qualitatively and quantitatively using dynamic analysis and simulation. Interestingly, in our simulation conditions, one TFG design (denoted as Type-DD) is less sensitive to vibration (>99% reduction) than the other two TFG designs (denoted as Type-CP and Type-DS). The reason for this difference is that Type-DD gyroscopes are immune to the dominant cause of error afflicting Type-CP and Type-DS designs. Our analysis also demonstrates that the most critical error-generation condition is vibration along with the sense direction of gyroscopes (denoted as sense-direction vibration) because of its contribution to all causes of error.

[1]  F. Ayazi,et al.  The resonating star gyroscope , 2005, 18th IEEE International Conference on Micro Electro Mechanical Systems, 2005. MEMS 2005..

[2]  Robert Kazinczi,et al.  Environment-induced failure modes of thin film resonators , 2002 .

[3]  Tao Jiang,et al.  Detection capacitance analysis method for tuning fork micromachined gyroscope based on elastic body model , 2006 .

[4]  Tayfun Akin,et al.  Symmetrical and decoupled nickel microgyroscope on insulating substrate , 2004 .

[5]  F. Ayazi,et al.  High Performance Matched-Mode Tuning Fork Gyroscope , 2006, 19th IEEE International Conference on Micro Electro Mechanical Systems.

[6]  Gary K. Fedder,et al.  Integrated Microelectromechanical Gyroscopes , 2003 .

[7]  T. Akin,et al.  An SOI-MEMS tuning fork gyroscope with linearly coupled drive mechanism , 2007, 2007 IEEE 20th International Conference on Micro Electro Mechanical Systems (MEMS).

[8]  S. Sherman,et al.  Single-chip surface-micromachined integrated gyroscope with 50/spl deg//hour root Allan variance , 2002, 2002 IEEE International Solid-State Circuits Conference. Digest of Technical Papers (Cat. No.02CH37315).

[9]  Steven W. Shaw,et al.  Nonlinear Dynamics and Its Applications in Micro- and Nanoresonators , 2010 .

[10]  David A. Horsley,et al.  Parametrically amplified MEMS magnetometer , 2009, TRANSDUCERS 2009 - 2009 International Solid-State Sensors, Actuators and Microsystems Conference.

[11]  Toshiyuki Tsuchiya,et al.  Polysilicon vibrating gyroscope vacuum-encapsulated in an on-chip micro chamber , 2001 .

[12]  C. Painter,et al.  Experimental evaluation of a control system for an absolute angle measuring micromachined gyroscope , 2005, IEEE Sensors, 2005..

[13]  Sang Won Yoon,et al.  Vibration Isolation and Shock Protection for MEMS. , 2009 .

[14]  G.A. Geen.  Progress in integrated gyroscopes , 2004, IEEE Aerospace and Electronic Systems Magazine.

[15]  J. Frech,et al.  Decoupled microgyros and the design principle DAVED , 2001, Technical Digest. MEMS 2001. 14th IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.01CH37090).

[16]  F. Ayazi,et al.  High-frequency capacitive disk gyroscopes in (100) and (111) silicon , 2007, 2007 IEEE 20th International Conference on Micro Electro Mechanical Systems (MEMS).

[17]  Josephus Hulshof,et al.  Amplitude saturation of MEMS resonators explained by autoparametric resonance , 2010 .

[18]  T. Braman,et al.  Designing Vibration and Shock Isolation Systems for Micro Electrical Machined Based Inertial Measurement Units , 2006, 2006 IEEE/ION Position, Location, And Navigation Symposium.

[19]  A. A. Kazaryan.  A Thin-Film Piezoelectric Pressure Sensor , 2002 .

[20]  K. Najafi,et al.  A HARPSS polysilicon vibrating ring gyroscope , 2001 .

[21]  B.E. Boser,et al.  An integrated, vertical-drive, in-plane-sense microgyroscope , 2003, TRANSDUCERS '03. 12th International Conference on Solid-State Sensors, Actuators and Microsystems. Digest of Technical Papers (Cat. No.03TH8664).

[22]  A.A. Trusov,et al.  Multi-Degree of Freedom Tuning Fork Gyroscope Demonstrating Shock Rejection , 2007, 2007 IEEE Sensors.

[23]  A.A. Trusov,et al.  Anti-Phase Driven Rate Gyroscope with Multi-Degree of Freedom Sense Mode , 2007, TRANSDUCERS 2007 - 2007 International Solid-State Sensors, Actuators and Microsystems Conference.

[24]  Seonho Seok,et al.  A study on resonant frequency and Q factor tunings for MEMS vibratory gyroscopes , 2004 .

[25]  Andrei M. Shkel,et al.  Micromachined rate gyroscope architecture with ultra-high quality factor and improved mode ordering , 2011 .

[26]  A.P. Pisano,et al.  Dual axis operation of a micromachined rate gyroscope , 1997, Proceedings of International Solid State Sensors and Actuators Conference (Transducers '97).

[27]  Yong-Soo Oh,et al.  Wafer level vacuum packaged de-coupled vertical gyroscope by a new fabrication process , 2000, Proceedings IEEE Thirteenth Annual International Conference on Micro Electro Mechanical Systems (Cat. No.00CH36308).

[28]  S. Sherman,et al.  Single-chip surface micromachined integrated gyroscope with 50°/h Allan deviation , 2002, IEEE J. Solid State Circuits.

[29]  A. Kourepenis,et al.  Error sources in in-plane silicon tuning-fork MEMS gyroscopes , 2006, Journal of Microelectromechanical Systems.

[30]  A. Shkel.  Type I and Type II Micromachined Vibratory Gyroscopes , 2006, 2006 IEEE/ION Position, Location, And Navigation Symposium.

[31]  M. Palaniapan,et al.  Modal Coupling in Micromechanical Vibratory Rate Gyroscopes , 2006, IEEE Sensors Journal.

[32]  Farrokh Ayazi,et al.  Micromachined inertial sensors , 1998, Proc. IEEE.

[33]  Guohong He,et al.  A single-crystal silicon vibrating ring gyroscope , 2002, Technical Digest. MEMS 2002 IEEE International Conference. Fifteenth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.02CH37266).

[34]  Rajesh Rajamani,et al.  The development of a MEMS gyroscope for absolute angle measurement , 2005, IEEE Transactions on Control Systems Technology.

[35]  A.H. von Flotow,et al.  Linear control design for active vibration isolation of narrow band disturbances , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[36]  F. Ayazi,et al.  A Mode-Matched Silicon-Yaw Tuning-Fork Gyroscope With Subdegree-Per-Hour Allan Deviation Bias Instability , 2008, Journal of Microelectromechanical Systems.

[37]  S.J.C. Dyne,et al.  The vibration environment on a satellite in orbit , 1993 .

[38]  Sang Won Yoon,et al.  Vibration Sensitivity of MEMS Tuning Fork Gyroscopes , 2007, 2007 IEEE Sensors.

[39]  Chan-Shin Chou,et al.  In-plane free vibration of a single-crystal silicon ring , 2008 .

[40]  Stewart McWilliam,et al.  ANISOTROPY EFFECTS ON THE VIBRATION OF CIRCULAR RINGS MADE FROM CRYSTALLINE SILICON , 1999 .

[41]  Hyoungho Ko,et al.  A planar, x-axis, single-crystalline silicon gyroscope fabricated using the extended SBM process , 2004, 17th IEEE International Conference on Micro Electro Mechanical Systems. Maastricht MEMS 2004 Technical Digest.

[42]  B. Murmann,et al.  Effects of Mechanical Vibrations and Bias Voltage Noise on Phase Noise of MEMS Resonator Based Oscillators , 2006, 19th IEEE International Conference on Micro Electro Mechanical Systems.

[43]  Noel C. Perkins,et al.  Analysis and wafer-level design of a high-order silicon vibration isolator for resonating MEMS devices , 2010 .

[44]  J. Bernstein,et al.  A micromachined comb-drive tuning fork rate gyroscope , 1993, [1993] Proceedings IEEE Micro Electro Mechanical Systems.

[45]  A. Shkel,et al.  Inherently robust micromachined gyroscopes with 2-DOF sense-mode oscillator , 2005, Journal of Microelectromechanical Systems.

[46]  Roger T. Howe,et al.  Performance comparison of integrated z-axis frame microgyroscopes , 2003, The Sixteenth Annual International Conference on Micro Electro Mechanical Systems, 2003. MEMS-03 Kyoto. IEEE.

[47]  F. S. VanVleck,et al.  A Technique for Determining Stability Regions for the Damped Mathieu Equation , 1974 .

[48]  M. W. Putty.  A Maicromachined vibrating ring gyroscope , 1994 .

[49]  Wenhua Zhang,et al.  Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor , 2002 .

[50]  A. Witvrouw,et al.  A 10 μm thick poly-SiGe gyroscope processed above 0.35 μm CMOS , 2007, 2007 IEEE 20th International Conference on Micro Electro Mechanical Systems (MEMS).

[51]  Dong-Il Cho,et al.  Surface/bulk micromachined single-crystalline-silicon micro-gyroscope , 2000, Journal of Microelectromechanical Systems.

[52]  Sung Kyu Ha,et al.  Dynamic analysis of a resonant comb-drive micro-actuator in linear and nonlinear regions , 2005 .

[53]  Farrokh Ayazi,et al.  A Sub-0.2$^{\circ}/$ hr Bias Drift Micromechanical Silicon Gyroscope With Automatic CMOS Mode-Matching , 2009, IEEE Journal of Solid-State Circuits.

[54]  Sung-Hoon Choa,et al.  A high yield rate MEMS gyroscope with a packaged SiOG process , 2005 .