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Abstract MEMS gyroscopes are well known for their outstanding advantages in Cost Size Weight and Power (CSWaP), which have inspired great research attention in recent years. A higher signal-to-noise ratio (SNR) for MEMS gyroscopes operating at larger vibrating amplitudes provides improved measuring resolution and ARW performance. However, the increment of amplitude causes strong nonlinear effects of MEMS gyroscopes due to their micron size, which has negative influences on the performance. This paper carries out detailed research on a general nonlinear mechanism on the sensors using parallel-plate capacitive transducers, which is called the gain nonlinearity in electrostatic actuation. The theoretical model established in this paper demonstrates the actuation gain nonlinearity causes the control-force coupling and brings extra angle-dependent bias with the 4th component for the whole-angle gyroscopes, which are verified by the experiments carried out on a micro-shell resonator gyroscope (MSRG). Furthermore, a real-time correction method is proposed to restore a linear response of the electrostatic actuation, which is realized by the gain modification with an online parameter estimation based on the harmonic-component relationship of capacitive detection. This real-time correction method could reduce the 4th component of the angle-dependent bias by over 95% from 0.003°/s to less than 0.0001°/s even under different temperatures. After the correction of actuation gain nonlinearity, the bias instability (BI) of whole-angle MSRG is improved by about 3.5 times from 0.101°/h to 0.029°/h and the scale factor nonlinearity (SFN) is reduced by almost one order of magnitude from 2.02 ppm to 0.21 ppm.

Abstract The field of levitated optomechanics has experienced significant advancements in manipulating the translational and rotational dynamics of optically levitated particles and exploring their sensing applications. The concept of using optically levitated particles as gyroscopes to measure angular motion has long been explored but has not yet been proven either theoretically or experimentally. In this study, we present the first rotor gyroscope based on optically levitated high-speed rotating particles. The gyroscope is composed of a micrometer-size ellipsoidal vaterite particle that is driven to rotate at MHz frequencies in a vacuum environment. When an external angular velocity is input, the optical axis deviates from its initial position, resulting in changes in the frequency and amplitude of the rotational signal. By analyzing these changes, the angular velocity of the input can be accurately detected, making it the smallest rotor gyroscope in the world. The angular rate bias instability of the gyroscope is measured to be 0.08°/s and can be further improved to as low as 10−9°/h theoretically by cooling the motion and increasing the angular moment of the levitated particle. Our work opens a new application paradigm for levitated optomechanical systems and may pave the way for the development of quantum rotor gyroscopes.

Abstract Singularities ubiquitously exist in different fields and play a pivotal role in probing the fundamental laws of physics and developing highly sensitive sensors. Nevertheless, achieving higher-order (≥3) singularities, which exhibit superior performance, typically necessitates meticulous tuning of multiple (≥3) coupled degrees of freedom or additional introduction of nonlinear potential energies. Here we propose theoretically and confirm using mechanics experiments, the existence of an unexplored cusp singularity in the phase-tracked (PhT) steady states of a pair of coherently coupled mechanical modes without the need for multiple (≥3) coupled modes or nonlinear potential energies. By manipulating the PhT singularities in an electrostatically tunable micromechanical system, we demonstrate an enhanced cubic-root response to frequency perturbations. This study introduces a new phase-tracking method for studying interacting systems and sheds new light on building and engineering advanced singular devices with simple and well-controllable elements, with potential applications in precision metrology, portable nonreciprocal devices, and on-chip mechanical computing.

Abstract High-performance micro-electro-mechanical system (MEMS) gyrocompasses for north-finding systems have been very popular for decades. In this paper, a MEMS north-finding system (NFS) based on virtual maytagging (VM) is presented for the first time. In stark contrast to previous schemes of MEMS-based NFSs (e.g., carouseling, maytagging) and the abandoning rate table, we developed a honeycomb disk resonator gyroscope (HDRG) and two commercial accelerometers for azimuth detection. Instead of the physical rotation of the integrated turntable in traditional NFSs, the vibratory working modes of the HDRG are rotated periodically with electronic control to reduce the uncertainty in the azimuth. After systematically analyzing the principle of NFSs with VM, we designed tests to verify the practicability at the sensor level. A bias instability of 0.0078°/h can be obtained during one day with VM in an HDRG. We also implemented comparative north-finding experiments to further check our strategy at the system level. The accuracy in the azimuth can reach 0.204° for 5 min at 28.2° latitude with VM and 0.172° with maytagging. The results show that without any mechanical turning parts, VM technology makes it possible to develop high-precision handheld MEMS NFSs.

To enhance the performance of micro-hemispherical gyroscopes, achieving low-damage and high-surface-quality trimming is essential. This enables greater stability and reliability for the gyroscopes. Current methods for reducing frequency split often come with drawbacks such as high cost, adverse effects on the Q-factor, or surface damage. In this paper, a chemical etching trimming method is proposed to reduce frequency split in micro-hemispherical resonators. This method allows for trimming with minimal damage, while also being cost-effective and easy to implement. The theoretical basis of this method was analyzed, followed by a simulation to determine the optimal trimming range and location on the resonator. The simulated Q-factor analysis before and after trimming preliminarily validated the method’s low-damage characteristics. Ultimately, the frequency split of the resonator was reduced to below 1 Hz. Additionally, test results of the Q-factor and surface quality before and after trimming further confirmed that chemical etching offers effective low-damage trimming capabilities. The proposed method holds significant potential for improving the performance of micro-hemispherical resonator gyroscopes.

The ultrafast rotation of optically levitated particles has propelled advancements in sensing and precision measurement, while its orientation remains largely unexplored for the spherical shape. Here, we proposed an orientation measurement method for the birefringent rotating particles, which extracts both the azimuthal and polar angles of the optical axis from the polarization of the transmitted laser. A bulk birefringent crystal with a known orientation is measured by this method to verify its effectiveness, and then the orientation of vaterite particles is extracted from the rotational signal. This method paves the way to investigate the orientational dynamics and gyroscope application.

Electromechanical phonon cavity systems offer advantages for solid state implementation, but thus far investigation has been limited to the linear regime. Here, Miao et al demonstrate non-linear operation of an electromechanical phonon cavity system and the drastic difference to the linear regime.

The MEMS gyroscope is one of the basic units of inertial navigation, whose performance and accuracy is noteworthy. Because of the limitations of processing technology and other factors, the relative manufacturing error of MEMS gyroscopes is usually large. Errors directly lead to a frequency mismatch of resonant structures and consequently restrict the performance improvement of the gyroscope. This study proposes a mechanical trimming technique combining the addition and removal of gold in a ring MEMS gyroscope. Firstly, the analysis of the gyroscope dynamics and error model and trimming theory provides theoretical guidance for the trimming process. Secondly, the method of adjusting the mass is investigated, and the ablation threshold of femtosecond laser parameters on gold is analyzed, which provides the process with parameters for the trimming experiment. Finally, the frequency trimming process is conducted in three steps, including the addition of gold spheres and the removal of gold spheres and gold film, which are applicable to the trimming process at different rates of frequency split. The results shows that the proposed method can reduce the frequency split of the gyroscope from 4.36 to 0.017 Hz.

Abstract Whole-angle gyroscopes have broad prospects for development with inherent advantages of excellent scale factor, wide bandwidth and measurement range, which are restrictions on rate gyroscopes. Previous studies on the whole-angle mode are based mostly on the linear model of Lynch, and the essential nonlinearity of capacitive displacement detection is always neglected, which has significant negative effects on the performance. In this paper, a novel real-time calibration method of capacitive displacement detection is proposed to eliminate these nonlinear effects. This novel method innovatively takes advantage of the relationship between the first and third harmonic components of detective signals for calibration. Based on this method, the real-time calibration of capacitive displacement detection is achieved and solves the problems of traditional methods, which are usually related to the vibration amplitude, environmental variations and other factors. Furthermore, this novel calibration method is embedded into a whole-angle control system to restore the linear capacitive response in real time and then combined with a microshell resonator for the first time to exploit the enormous potential of an ultrahigh Q factor and symmetric structure. The effectiveness is proven because the angle drift is reduced significantly to improve the scale-factor nonlinearity by 14 times to 0.79 ppm with 0.0673°/h bias instability and a 0.001°/s rate threshold, which is the best reported performance of the MEMS whole-angle gyroscope thus far. More importantly, this novel calibration method can be applied for all kinds of resonators with the requirement of a linear capacitive response even under a large resonant amplitude.

In capacitive microelectromechanical system (MEMS) devices, the application of dielectric materials causes long-term charging problems in the dielectric layers or substrates, which especially affect the repeatability and stability of high-performance devices. Due to the difficulties of observation and characterization of charge accumulation, an accurate characterization method is needed to study the effect of charge and propose suppression methods. In this paper, we analyze the influence of charge accumulation on the MSRG and propose a characterization method for charge accumulation based on stiffness variation. Experiments are carried out to characterize the charge accumulation in MSRG, and the effect of temperature on the process is also investigated. In the experiment, the charge accumulation is characterized accurately by the variation of the frequency split and stiffness axes. Furthermore, the acceleration of the charge accumulation is observed at high temperatures, as is the higher additional voltage from the charge accumulation.

The vacuum chamber is an important part of microparticle optical levitation technology. The traditional vacuum chamber has a large volume and many peripheral components, which cannot meet the requirements of miniaturization and on-chip optical levitation technology. Therefore, this study proposes a novel microparticle vacuum chamber based on the micro-electro-mechanical system (MEMS) process. This MEMS microparticle vacuum chamber adopts a “glass-silicon-glass” three-layer vacuum bonding process, with a volume of only 15 mm × 12 mm × 1.2 mm, including particle chamber, cantilever resonator chamber, and getter chamber, which can encapsulate microparticles in a tiny vacuum environment and realize optical levitation of microparticles. At the same time, the air pressure in the micro vacuum chamber is monitored by the cantilever resonator, which can provide a miniaturized microparticle chamber with a more accurate vacuum environment for microparticle optical levitation. The research of this paper has significance for promoting the development of miniaturized optical levitation technology.

Ultrafast pulsed lasers can facilitate the manufacturing of complex microstructures. However, previous laser processing applications have focused on static components. Consequently, the application of laser processing in high-performance resonant structures has received less attention. Ultrafast lasers provide a unique opportunity for realizing the structure detachment from the planar fused silica substrates. However, the processing quality has a considerable influence on resonant structures. High-quality and high-efficiency laser manufacturing methods are critical for processing resonant structures. In this study, we demonstrate a method for processing fused silica microstructures based on the femtosecond laser. We studied the influence of different laser parameters on the processing quality and determined the optimal laser parameters suitable for the microstructure. The resonant structure of the butterfly gyroscope was used to verify the manufacturing method. A steepness of 86.6° and a roughness of 653.2 nm were achieved by using the optimized laser parameters. These are expected to provide technical support for the development of high-performance fused silica dynamic devices in the future.

Micro- and nanomechanical resonators play a crucial role in sensing applications. Here, the authors demonstrate electrically tunable modal coupling in capacitive microelectromechanical gyroscopic ring resonators that allows for improving the performance micro/nano-sensors relying on precise control of the degree of modal coupling.

In recent years, the application prospects of high-precision MEMS gyroscopes have been shown to be very broad, but the large temperature drift of MEMS gyroscopes limits their application in complex temperature environments. In response to this, we propose a method that combines mode reversal and real-time multiple regression compensation to compensate for the temperature drift of gyroscope bias. This method has strong adaptability to the environment, low computational cost, the algorithm is online in real time, and the compensation effect is good. The experimental results show that under the temperature cycle of −20~20 °C and the temperature change rate of 4 °C/min, the method proposed in this paper can reduce the zero-bias stability from about 27.8°/h to 0.4527°/h, and the zero-bias variation is reduced from 65.88°/h to 1.43°/h. This method improves the zero-bias stability of the gyroscope 61-fold and the zero-bias variation 46-fold. Further, the method can effectively suppress the zero-bias drift caused by the heating of the gyroscope during the start-up phase of the gyroscope. The zero-bias stability of the gyroscope can reach 0.0697°/h within 45 min of starting up, and the zero-bias repeatability from 0 to 5 min after startup is reduced from 0.629°/h to 0.095°/h.

This paper proposes a new multiple folded-beam disk resonator whose thermoelastic quality factor is significantly improved by appropriately reducing the beam width and introducing integral-designed lumped masses. The quality factor of the fabricated resonator with (100) single crystal silicon reaches 710 k, proving to be a record in silicon disk resonators. Meanwhile, a small initial frequency split of the order-3 working modes endows the resonator with great potential for microelectromechanical systems (MEMS) gyroscopes application. Moreover, the experimental quality factor of resonators with different beam widths and relevant temperature experiment indicate that the dominating damping mechanism of the multiple folded-beam disk resonator is no longer thermoelastic damping.

MEMS gyroscopes play an important role in inertial navigation measurements, which mainly works in n = 2 mode. However, mode matching is the basis for high-precision detection, which can improve the sensitivity, resolution, and signal-to-noise ratio of the gyroscopes. An initial frequency split is inevitably generated during the manufacturing process. There are two methods to eliminate the frequency split and to achieve mode matching for the gyroscopes, which are electrostatic tuning and mechanical trimming, respectively. In this paper, we report a novel ring MEMS resonator and a novel method of mechanical frequency tuning. The most prominent characteristic of the resonator is that 16 raised mass blocks are increased in the circumferential positions of the ring uniformly. This structural design can achieve mass-stiffness decoupling, which means that punching holes on the mass blocks only affects the mass distribution but the stiffness is almost unchanged for the resonator. We verify the mass-stiffness decoupling by way of comparing the simulation with the conventional resonator. In addition, we put up an online tuning platform based on a femtosecond laser and reduce a resonator’s frequency split from 23.3 Hz to 0.4 Hz, which reveals that the frequency split is linearly related to the removed mass. These findings will have a referential significance for other transducers.

Damping asymmetry is one of the most important factors that determines the performance of the hemispherical resonator gyroscope. In this paper, the error mechanism of damping asymmetry in the Whole Angle (WA) mode is investigated, and an adaptive compensation method is proposed to eliminate the angle drift induced by the damping asymmetry. This adaptive compensation approach adopts the recursive least-squares method to identify the damping asymmetry, and the optimal parameters can be calculated through simulation. Furthermore, a self-precession method is applied to make this compensation method available for more occasions. This compensation method is able to automatically complete the compensation process without any angular input or a priori information on damping distribution. According to the experimental results, the angle-dependent bias has been reduced from 0.0316 s−1 to 0.0051 s−1 by this method. The presented method is widely applicable for gyroscopes working in the WA mode, which may be useful for further research on inertial sensors with high accuracy.

In recent years, the optical accelerometer based on the optical trapping force effect has gradually attracted the attention of researchers for its high sensitivity and high measurement accuracy. However, due to its large size and the complexity of optical path adjustment, the optical force accelerometers reported are only suitable for the laboratory environment up to now. In this paper, a miniature optical force dual-axis accelerometer based on the miniature optical system and a particles cavity which is prepared by Micro-Electro-Mechanical Systems (MEMS) technology is proposed. The overall system of the miniature optical levitation including the miniature optical system and MEMS particles cavity is a cylindrical structure with a diameter of about 10 mm and a height of 33 mm (Φ 10 mm × 33 mm). Moreover, the size of this accelerometer is 200 mm × 100 mm × 100 mm. Due to the selected light source being a laser diode light source with elliptical distribution, it is sensitive to the external acceleration in both the long axis and the short axis. This accelerometer achieves a measurement range of ±0.17 g–±0.26 g and measurement resolution of 0.49 mg and 1.88 mg. The result shows that the short-term zero-bias stability of the two orthogonal axes of the optical force accelerometer is 4.4 mg and 9.2 mg, respectively. The main conclusion that can be drawn is that this optical force accelerometer could provide an effective solution for measuring acceleration with an optical force effect for compact engineering devices.

Microrobots have a wide range of applications. The rigid–flexible composite stereoscopic technology based on ultraviolet laser cutting technology is primarily researched for the design and manufacture of microrobots and has been used to fabricate microscale motion mechanisms and robots. This paper introduces a monolithic processing technology based on the rigid–flexible composite stereoscopic process. Based on this process, a split-actuator micro flapping-wing air vehicle with a size of 15 mm × 2.5 mm × 30 mm was designed. We proposed a batch manufacturing method capable of processing multiple micro air vehicles at the same time. The main structure of 22 flapping-wing micro air vehicles can be processed at the same time within the processing range of the composite sheet with an area of 80 mm × 80 mm, and the processing effect is good.

MEMS resonators have become core devices in a large number of fields; however, due to their complex structures, the finite element analysis (FEA) method is still the main method for their theoretical analysis. The traditional finite element analysis method faces the disadvantages of large calculation amount and long simulation time, which limits the development of high-performance MEMS resonators. This paper demonstrates a high-speed and high-accuracy simulation tool based on the artificial neural network, where a multilayer perceptron (MLP) neural network model is constructed. The typical structural parameters of MEMS resonator are used as the input layer, and its performance indicators produced by the finite element analysis method are the output layer. After iteratively trained with 4000 samples, the cumulative error of the neural network decreases to 0.0017 and a prediction network model is obtained. Compared with the finite element analysis results, the structural accuracy error predicted by the neural network model can be controlled within 6%, but its runtime is shortened by 15,000 times. This high-speed and high-accuracy mathematical modeling method can effectively improve the analyzing efficiency and provide a promising tool for the design and optimization of different complex MEMS resonators, which exhibit remarkable accuracy and speed.

A miniature deformable squama mechanics based on piezoelectric actuation inspired by the deformable squama is proposed in this paper. The overall size of the mechanics is 16 mm × 6 mm × 6 mm, the weight is only 140 mg, the deflection angle range of the mechanical deformation is −15°~45°, and the mechanical deformation is controllable. The small-batch array processing of the miniature deformable squama mechanics, based on the stereoscopic process, laid the technological foundation for applying the deformed squama array arrangement. We also designed and manufactured a small actuation control boost circuit and a mobile phone piezoelectric control assistant application that makes it convenient to perform short-range non-contact control of the deformation of the squama. The proposed system arranges the deformed squamae into groups to form the skin and controlls the size and direction of the signals input to each group of the squama array, thereby making the skin able to produce different shapes to create deformable skin.

For micro-electromechanical system (MEMS) resonators, once the devices are fabricated and packaged, their intrinsic quality factors (Q) will be fixed and cannot be changed, which seriously limits the further improvement of the resonator’s performance. In this paper, parametric excitation is applied in a push-pull driven disk resonator gyroscope (DRG) to improve its sensitivity by an electrical pump, causing an arbitrary increase of the “effective Q”. However, due to the differential characteristics of the push-pull driving method, the traditional parametric excitation method is not applicable. As a result, two novel methods are proposed and experimentally carried out to achieve parametric excitation in the push-pull driven DRGs, resulting in a maximum “effective Q” of 2.24 × 106 in the experiment, about a 7.6 times improvement over the intrinsic Q. Besides, subharmonic excitation is also theoretically analyzed and experimentally characterized. The stability boundary of parametric excitation, defined by a threshold voltage, is theoretically predicted and verified by related experiments. It is demonstrated that, when keeping the gyroscope’s vibration at a constant amplitude, the fundamental frequency driving voltage will decrease with the increasing of the parametric voltage and will drop to zero at its threshold value. In this case, the gyroscope operates in a generalized parametric resonance condition, which is called subharmonic excitation. The novel parametric and subharmonic excitation theories displayed in this paper are proven to be efficient and tunable dynamical methods with great potential for adjusting the quality factor flexibly, which can be used to further enhance the resonator’s performance.

Damping asymmetry is one of the most important factors that determines the performance of Coriolis Vibratory Gyroscope. In this paper, a novel damping tuning method for the resonator with parallel plate capacitors is presented. This damping tuning method is based on resistance heat dissipation and the tuning effect is characterized by the control force in Whole-Angle mode. As the damping tuning and stiffness tuning in the resonator with parallel plate capacitors are coupled with each other, a corresponding tuning system is designed. To verify the tuning effects, experiments are conducted on a hemispherical resonator gyroscope with Whole-Angle mode. The damping tuning theories is demonstrated by the testing results and 87% of the damping asymmetry is reduced by this tuning method with a cost of 3% decaying time. Furthermore, the angle-dependent drift in rate measurement after tuning is only 15.6% of the one without tuning and the scale factor nonlinearity decreases from 5.49 ppm to 2.66 ppm. The method can be further applied on the damping tuning in other resonators with symmetrical structure.

Capacitive micromechanical resonators share electrodes with the same bias voltage, resulting in the occurrence of electrostatic coupling between intrinsic modes. Unlike the traditional mechanical coupling, the electrostatic coupling is determined by the structural electric potential energy, and generally, it only occurs when the coupling modes operate in nonlinear regions. However, previous electrostatic coupling studies mainly focus on the stiffness softening region, with little attention on the opposite stiffness hardening condition. This paper presents a study on the electrostatic modal coupling effect in the stiffness hardening region. A novel capacitive micromechanical resonator with different modal nonlinearities is designed and fabricated. It is demonstrated that activating a cavity mode can shift the fundamental resonance of the manipulated mode by nearly 90 times its mechanical bandwidth. Moreover, the frequency shifting direction is found to be related to the manipulated mode’s nonlinearity, while the frequency hopscotch is determined by the cavity mode’s nonlinearity. The electrostatic coupling has been proven to be an efficient and tunable dynamical coupling with great potential for tuning the frequency in a wide range. The modal coupling theory displayed in this paper is suitable for most capacitive resonators and can be used to improve the resonator’s performance.

The butterfly gyroscope is simple to manufacture and it is considered as one kind of MEMS gyroscope with high sensitivity due to its unique structure. In reality, fabrication imperfections result in non-ideal geometries in the resonator, which in turn causes the quadrature error. The quadrature error has a great influence on the performance of the sensors in Micro and Nano scale, such as the zero-rate output (ZRO), the detection resolution and the dynamic range. However, the fact that the mechanical parameters of resonators are unknown (due to fabrication variation, fluctuations with temperature and aging) poses serious challenges. This paper presents a simple, yet effective method of quadrature compensation in butterfly resonator by electrostatic tuning. Theoretical calculation of quadrature error in butterfly gyroscope is carried out, establishing the mathematical model of quadrature compensation. Then, the simulation analysis is conducted to further analyze the mechanism of quadrature error and the method of quadrature compensation. Also, 5 butterfly gyroscopes fabricated on the same silicon wafer are selected for the experiment of quadrature compensation and the ZRO of the butterfly gyroscopes improves up to two orders of magnitude with quadrature cancellation, showing the feasibility of the proposed approach to quadrature compensation in the butterfly gyroscope. Finally, the way to decrease the direct current voltage VT required for suppressing the quadrature error is discussed. What is more, the method is not only suitable for the butterfly gyroscope, but also can be applied to other sensors in the Micro and Nanoscale.

Frequency trimming based on mass and stiffness modification is an important post-fabrication process for micro-shell resonators (MSRs). However, the trimming effects on the quality factor are seldom studied, although they may have great influence on the performance of the resonator. This paper presents a study on the quality factor (Q-factor) variation of trimmed micro-shell resonators (MSR). Thermoelastic damping (QTED) and anchor loss (Qanchor) are found to be the dominant energy loss mechanisms resulting in the reduction of the overall Q-factor, according to finite element method (FEM). The effects of different trimming methods on QTED and Qanchor are studied here, respectively. It is found that trimming grooves ablated in the rim of the resonator can cause a ~1−10% reduction of QTED, and the length of trimming groove is positively related to the reduction of QTED. The reduction of QTED caused by the mass adding process is mainly related to the thermal expansion coefficient and density of the additive and contact area between the resonator and additive masses. Besides, the first and second harmonic errors caused by asymmetrical trimming can cause a 10−90% reduction of Qanchor. Finally, trimming experiments were conducted on different resonators and the results were compared with FEM simulation. The work presented in this paper could help to optimize the trimming process of MSRs.

The multiring disk resonator gyroscope (DRG) has been a candidate for high performance gyroscopes, however nowadays the finite element method (FEM) is the main method for its analysis due to its complex structure. In this paper we propose a new method to mathematically model the DRG for its vibrating modes and lumped parameters based on the component mode synthesis (CMS) method. Firstly, the natural frequencies and the associated mode shapes of the DRG are mathematically modeled and a comparison with the FEM results is conducted. It shows that the mode shapes of DRG obtained by FEM and mathematical modeling are identical and in the full ranges of geometrical parameters, natural frequency error of the simulation, and calculation results are limited in ±15%. It demonstrates the effectivity and feasibility of the mathematical modeling method. Then, based on the calculated natural frequencies and mode shapes, the lumped mass-spring model of the DRG and effects of geometry parameters on the lumped mass-spring parameters are investigated, which can be used on the design of the DRG. This mathematical modeling method can effectively improve the analyzing efficiency of the DRG and the method can also be used on the analysis of other complex multiring-type resonators.

This paper is devoted to discussing the influence of thermal stress on the performance of the Butterfly Vibratory Gyroscope (BFVG). In many gyroscopes, due to the material properties and the fabrication processes, the deformation caused by residual stress or thermal mechanical stress is of great concern since it directly affects the performance. Here, a new stress-released structure was proposed to reduce the deformation to improve BFVG’s performance considering the symmetry of the electrode and the miniaturization of the structure. Its dimensional parameters relate to the effect of thermal stress release and the stiffness characteristics of the BFVG’s oblique beam. The single parameter analysis method was used to explore the influence of the parameters on the effect of thermal stress release to guide the optimal size of the final design. The effect of thermal stress release in the BFVG at the full range temperature was also tested after the fabrication. The results showed that the influence of thermal stress on the BFVG’s performance effectively reduced.

The resonant shells of vibratory cylinder gyroscopes are commonly packaged in metallic caps. In order to lower the production cost, a portion of vibratory cylinder gyroscopes do not employ vacuum packaging. However, under non-vacuum packaging conditions there can be internal acoustic noise leading to considerable acoustic pressure which is exerted on the resonant shell. Based on the theory of the structural-acoustic coupling, the dynamical behavior of the resonant shell under acoustic pressure is presented in this paper. A finite element (FE) model is introduced to quantitatively analyze the effect of the structural-acoustic coupling. Several main factors, such as sealing cap sizes and degree of vacuum which directly affect the vibration of the resonant shell, are studied. The results indicate that the vibration amplitude and the operating frequency of the resonant shell will be changed when the effect of structural-acoustic coupling is taken into account. In addition, an experiment was set up to study the effect of structural-acoustic coupling on the sensitivity of the gyroscope. A 32.4 mV/°/s increase of the scale factor and a 6.2 Hz variation of the operating frequency were observed when the radial gap size between the resonant shell and the sealing cap was changed from 0.5 mm to 20 mm.

A rocking mass gyroscope (RMG) is a kind of vibrating mass gyroscope with high sensitivity, whose driving mode and sensing mode are completely uniform. MEMS RMG devices are a research hotspot now because they have the potential to be used in space applications. Support loss is the dominant energy loss mechanism influencing their high sensitivity. An accurate analytical model of support loss for RMGs is presented to enhance their Q factors. The anchor type and support loss mechanism of an RMG are analyzed. Firstly, the support loads, powers flowing into support structure, and vibration energy of an RMG are all developed. Then the analytical model of support loss for the RMG is developed, and its sensitivities to the main structural parameters are also analyzed. High-Q design guidelines for rocking mass microgyroscopes are deduced. Finally, the analytical model is validated by the experimental data and the data from the existing literature. The thicknesses of the prototypes are reduced from 240 µm to 60 µm, while Q factors increase from less than 150 to more than 800. The derived model is general and applicable to various beam resonators, providing significant insight to the design of high-Q MEMS devices.

It is reported in the published literature that the resonant frequency of a silicon micromachined gyroscope decreases linearly with increasing temperature. However, when the axial force is considerable, the resonant frequency might increase as the temperature increases. The axial force is mainly induced by thermal stress due to the mismatch between the thermal expansion coefficients of the structure and substrate. In this paper, two types of micromachined suspended vibratory gyroscopes with slanted beams were proposed to evaluate the effect of the axial force. One type was suspended with a clamped-free (C-F) beam and the other one was suspended with a clamped-clamped (C-C) beam. Their drive modes are the bending of the slanted beam, and their sense modes are the torsion of the slanted beam. The relationships between the resonant frequencies of the two types were developed. The prototypes were packaged by vacuum under 0.1 mbar and an analytical solution for the axial force effect on the resonant frequency was obtained. The temperature dependent performances of the operated mode responses of the micromachined gyroscopes were measured. The experimental values of the temperature coefficients of resonant frequencies (TCF) due to axial force were 101.5 ppm/°C for the drive mode and 21.6 ppm/°C for the sense mode. The axial force has a great influence on the modal frequency of the micromachined gyroscopes suspended with a C-C beam, especially for the flexure mode. The quality factors of the operated modes decreased with increasing temperature, and changed drastically when the micromachined gyroscopes worked at higher temperatures.

This paper focuses on structural optimization of a Butterfly vibratory gyroscope (BFVG). An oblique suspension beam adopting polygonal cross-section is proposed in order to enhance the sensitivity and robustness. The operation principles of the BFVG are introduced. The suspension beam, which was found to be the key component, is selectively stressed. Varying cross sections of the suspension beam, including parallelogram, pentagon, hexagon, platform of pentagon, L-shaped and convex shapes are compared with each other. In particular, in order to show the advantages of the proposed polygonal cross-section, the convex cross-section is used as a reference. The influence of fabrication imperfections, which includes alignment error, silicon thickness error, etching depth error, upper width error, bottom width error and deep reactive-ion etching (DRIE) verticality error, on the oblique beam’s spindle azimuth angle of the two cross-sections is analyzed. Further, the quadrature error of two cross-sections with a fabrication defect is analyzed. The theoretical arithmetic results suggest that a polygonal cross-section beam is much more stable than a convex cross-section beam in most cases. The robustness of the fabrication imperfection is improved nine-fold and the quadrature error due to fabrication defect is reduced by 70 percent with a polygonal cross-section. It could be a better candidate for BFVG’s oblique beam, which would provide a gyroscope with good robustness and repeatability.

Quality factor is one of the most important parameters for a MEMS resonator. Most MEMS resonators are dominated by thermoelastic dissipation (TED). This paper demonstrates that the TED in a disk resonator that is made of (111) single-crystal silicon is surpassed by clamping loss. The stiffness-mass decoupling design method, combined with reducing the beam width, was used to engineer high QTED. Experiments show that Q of the (111) disk resonator have an upper boundary that is determined by the clamping loss caused by the unbalanced out-of-plane displacement. The origin of the out-of-plane displacement is explained by theory and simulation.

A new approach to improve the performance of a butterfly gyroscope is developed. The methodology provides a simple way to improve the gyroscope’s sensitivity and stability, by reducing the resonant frequency mismatch between the drive and sense modes. This method was verified by simulations and theoretical analysis. The size of the hexagonal section oblique beam is the major factor that influences the resonant frequency mismatch. A prototype, which has the appropriately sized oblique beam, was fabricated using precise, time-controlled multilayer pre-buried masks. The performance of this prototype was compared with a non-tuned gyroscope. The scale factor of the prototype reaches 30.13 mV/ ˚/s, which is 15 times larger than that obtained from the non-tuned gyroscope. The bias stability of the prototype is 0.8 ˚/h, which is better than the 5.2 ˚/h of the non-tuned devices.

This paper reports a dual-butterfly structure gyroscope based on the traditional butterfly structure. This novel structure is composed of two butterfly structures, each of which contains a main vibrational beam, four proof masses, and a coupling mechanism. The coupling mechanism in this proposed structure couples the two single butterfly structures and keeps the driving mode phases of the two single butterfly gyroscopes exactly opposite, increasing the double difference of traditional butterfly gyroscopes to a quad difference, which has the potential advantage of improving bias instability and g-sensitivity. The gyroscope was fabricated using a standard microfabrication method and tested in laboratory conditions. The experimental results show a Q-factor of 10,967 in driving mode and there were two peaks in the frequency responses curve of sensing direction due to unavoidable fabrication errors. Scale factor and bias instability were also measured, reaching a scale factor of 10.9 mV/°/s and a bias instability of 10.7°/h, according to the Allan Variance curve.

This paper reports the design and simulation of a 4 mm2 double differential torsional MEMS accelerometer based on a double-beam configuration. Based on the structure of conventional torsional accelerometers, normally composed of one pair of proof masses and one torsional beam, this work explores the double differential configuration: a torsional accelerometer with two pairs of unbalanced proof masses rotating in reverse. Also, the torsional beam is designed as a double-beam structure, which is a symmetrical structure formed by two torsional beams separated by a certain distance. The device area of the novel accelerometer is more than 50 times smaller than that of a traditional double differential torsional MEMS accelerometer. The FEM simulation results demonstrate that the smaller device does not sacrifice other specifications, such as mechanical sensitivity, nonlinearity and temperature robustness. The mechanical sensitivity and nonlinearity of a ±15 g measuring range is 59.4 fF/g and 0.88%, respectively. Compared with traditional single-beam silicon structures, the novel structure can achieve lower maximum principle stress in critical regions and reduce the possibility of failure when high-g acceleration loading is applied along all three axes. The mechanical noise equivalent acceleration is about 0.13 mg / Hz in the theoretical calculations and the offset temperature coefficient is 0.25 mg/ ℃ in the full temperature range of − 40 ℃ to 60 ℃ .