Search Results (18)

Flywheel energy storage systems exhibit superior performance in electric vehicle regenerative braking, railway traction power supply, and grid frequency regulation due to their high instantaneous power and fast dynamic response. However, systems supported by conventional mechanical bearings face severe radial structural coupling; unbalanced excitation and gyroscopic effects drastically amplify vibrations during critical speed traversal, undermining operational reliability and engineering scalability. To tackle this challenge, this paper proposes a full-speed vibration suppression scheme for active–passive supported flywheel energy storage systems integrated with a damping ring, combined with an inverse system decoupling controller to eliminate structural coupling, unbalance-induced vibration, and gyroscopic effects. A dynamic model of the integrated system is established using Lagrange’s equations, and four-degree of freedom decoupling expressions are derived to achieve complete radial decoupling. A speed-stage-based control strategy is further developed for full-speed adaptation. Comprehensive simulations validate the scheme’s decoupling performance, vibration suppression efficacy, and robustness. Results demonstrate that the proposed controller achieves full radial decoupling, reducing the average steady-state tracking error by 99.86%. The segmented control enables stable operation across 100–20,000 rpm and cuts critical speed resonance peaks by 81.23%. Compared with pure mechanical and magnetic bearing systems, the integrated active–passive support reduces resonance peaks by 94.72% and 42.25%, respectively. Under current perturbation and parameter variation, the scheme reduces the average steady-state error by 75.89% relative to the coupled system, confirming its strong engineering applicability. Full article

A rotating imperfect ring resonator of the gyroscope is modeled by a rotating thin ring with evenly distributed point masses. The free response of the rotating ring structure at constant speed is investigated, including the steady elastic deformation and wave response. The dynamic equations are formulated by using Hamilton’s principle in the ground-fixed coordinates. The coordinate transformation is applied to facilitate the solution of the steady deformation, and the displacements and tangential tension for the deformation are calculated by the perturbation method. Employing Galerkin’s method, the governing equation of the free vibration is casted in matrix differential operator form after the separation of the real and imaginary parts with the inextensional assumption. The natural frequencies are calculated through the eigenvalue analysis, and the numerical results are obtained. The effects of the point masses on the natural frequencies of the forward and backward traveling wave curves of different orders are discussed, especially on the measurement accuracy of gyroscopes for different cases. In the ground-fixed coordinates, the frequency splitting results in a crosspoint of the natural frequencies of the forward and backward traveling waves. The finite element method is applied to demonstrate the validity and accuracy of the model. Full article

This paper investigates the effect of electrostatic nonlinearity on the rate-sensing performance of imperfect ring-based Coriolis Vibrating Gyroscopes (CVGs) for devices having 8 and 16 evenly distributed electrodes. Mathematical models are developed for CVGs operating in (i) an open loop for a linear electrostatically trimmed device, (ii) a closed loop where a sense force balancing is applied to negate the sense quadrature response, and the effects of electrostatic nonlinearity are investigated for increasing drive amplitudes. The modeling indicates the nonlinear responses for 8- and 16-electrode arrangements are quite different, and this can be attributed to the nonlinear frequency imbalance, which depends on the drive and sense frequency softening as well as the presence of self-induced parametric excitation in the sense response. In open loop the 16-electrode arrangement exhibits much weaker levels of nonlinearity than the 8-electrode arrangement because the nonlinear frequency imbalance is less sensitive to drive amplitude. For devices operating in closed-loop with sense force balancing to ensure the drive and sense responses are in-phase/anti-phase, it is shown that ideal rate-sensing performance is achieved at large drive amplitudes for both 8- and 16-electrode arrangements. Using sense force balancing, rate sensing can be achieved using either the sense response or the required balancing voltage. For the latter, large nonlinear frequency imbalances and low damping levels enhance rate-sensing performance. Full article

This paper presents a design, model, and comparative analysis of two internal MEMS vibrating ring gyroscopes for harsh environmental conditions. The proposed design investigates the symmetric structure of the vibrating ring gyroscopes that operate at the identical shape of wine glass mode resonance frequencies for both driving and sensing purposes. This approach improves the gyroscope’s sensitivity and precision in rotational motion. The analysis starts with an investigation of the dynamic behaviour of the vibrating ring gyroscope with the detailed derivation of motion equations. The design geometry, meshing technology, and simulation results were comprehensively evaluated on two internal vibrating ring gyroscopes. The two designs are distinguished by their support spring configurations and internal ring structures. Design I consists of eight semicircular support springs and Design II consists of sixteen semicircular support springs. These designs were modelled and analyzed using finite element analysis (FEA) in Ansys 2023 R1 software. This paper further evaluates static and dynamic performance, emphasizing mode matching and temperature stability. The results reveal that Design II, with additional support springs, offers better mode matching, higher resonance frequencies, and better thermal stability compared to Design I. Additionally, electrostatic, modal, and harmonic analyses highlight the gyroscope’s behaviour under varying DC voltages and environmental conditions. Furthermore, this study investigates the impact of temperature fluctuations on performance, demonstrating the robustness of the designs within a temperature range from −100 °C to 100 °C. These research findings suggest that the internal vibrating ring gyroscopes are highly suitable for harsh conditions such as high temperature and space applications. Full article

This paper presents the development of an analytical model of an internal vibrating ring gyroscope in a Microelectromechanical System (MEMS). The internal ring structure consists of eight semicircular beams that are attached to the externally placed anchors. This research work analyzes the vibrating ring gyroscope’s in-plane displacement behavior and the resulting elliptical vibrational modes. The elliptical vibrational modes appear as pairs with the same resonance frequency due to the symmetric structure of the design. The analysis commences by conceptualizing the ring as a geometric structure with a circular shape possessing specific dimensions such as thickness, height, and radius. We construct a linear model that characterizes the vibrational dynamics of the internal vibrating ring. The analysis develops a comprehensive mathematical formulation for the radial and tangential displacements in local polar coordinates by considering the inextensional displacement of the ring structure. By utilizing the derived motion equations, we highlight the underlying relationships driving the vibrational characteristics of the MEMS’ vibrating ring gyroscope. These dynamic vibrational relationships are essential in enabling the vibrating ring gyroscope’s future utilization in accurate navigation and motion sensing technologies. Full article

This research presents a comparative analysis of the two important design methodologies involved in developing microelectromechanical system (MEMS) vibrating ring gyroscopes, namely, internal and external ring gyroscopes. Internal ring gyroscopes are constructed with the outside placement of support pillars connected with the semicircular beams that are attached to the vibrating ring structure. The design importance of this particular setting effectively isolates the vibrating ring structure from any external mechanical vibrations, significantly improving the gyroscope’s performance. The internal ring structure provides exceptional precession and reliability, making this design an ideal candidate for harsh conditions, as they can sustain substantial amounts of unwanted and external vibrations without degrading the performance of the gyroscope. On the other hand, external ring gyroscopes include the placement of the support pillars within the vibrating ring structure. This particular design setting is quite convenient in terms of fabrication and provides higher gyroscopic sensitivity. However, this design may lead to coupling of the vibrational modes and potentially compromise the performance of the gyroscope. This research discusses and compares the findings of a modal analysis of the two distinguished design approaches for the MEMS vibrating ring gyroscopes. Full article

Microelectromechanical system (MEMS) inertial sensors are integral components in a variety of smart electronic devices, most notably MEMS vibrating gyroscopes, which are rotational inertial sensors. The applications of MEMS vibrating gyroscopes range from household appliances to GPS and even to military applications. However, the stability and reliability of these MEMS inertial sensors in space applications still pose challenges. In this research study, we introduce a simple design for a vibrating ring gyroscope with eight semicircular support springs connected to outside-placed anchors. The symmetric design structure with semicircular support springs provides higher sensitivity while minimizing mode mismatch. The design and modelling analysis of the vibrating ring gyroscope was conducted using Ansys 2023 R1. The proposed vibrating ring gyroscope has a ring radius of 1000 µm, a 210 µm radius for the semicircular support springs, a ring and support spring thicknesses of 10 µm, and an area of 80 × 80 µm² for the outside-placed anchors. The vibrating ring gyroscope operates at two identical elliptical-shape resonant modes, one for driving resonance frequency and the other for sensing resonance frequency. Both simulated resonance frequencies were measured at 48.78 kHz and 48.80 kHz. The modelled result achieved a mode mismatch of 0.02 kHz, which can be easily rectified with tuning electrodes. Full article

Microelectromechanical system (MEMS) vibrating gyroscope design considerations are always intriguing due to their microscale mechanical, electrical, and material behavior. MEMS vibrating ring gyroscopes have become important inertial sensors in inertial measurement units (IMU) for navigation and sensing applications. The design of a MEMS vibrating ring gyroscope incorporates an oscillating ring structure as a proof mass, reflecting unique design challenges and possibilities. This paper presents a comprehensive design analysis of the MEMS vibrating ring gyroscope from the mechanical, electrical, and damping perspectives. The mechanical design of the MEMS vibrating ring gyroscope investigates the various frame designs of the vibrating ring structure, as well as the various beam structures, including rectangular and semicircular beam structures, which are analyzed using mathematical models and finite element analysis (FEA) simulations that provide an in-depth analysis of the stiffness and deflection of the vibrating structures. The electrical designs of the MEMS vibrating ring gyroscope are analyzed using various electrode configurations, electrostatic actuation, and capacitive detection mechanisms. The design analysis of various forms of damping, including viscous, structural, thermoelastic, and anchor damping, is discussed. The variety of design structures is investigated for MEMS vibrating ring gyroscopes’ mechanical, electrical, and damping performance. Full article

Microelectromechanical system (MEMS) devices have gained tremendous attention in the field of smart electronics applications. A MEMS vibrating gyroscope is a rotational inertial sensor that is exhaustively used in many applications, from GPS, household, smart appliances, and space applications. The reliability of MEMS devices for space applications is a big concern. The devices need to be robust in harsh environments. This paper reports a double-ring MEMS vibrating ring gyroscope with sixteen worm-shaped support springs. The inclusion of the two rings with sixteen worm-shaped springs enhances the sensitivity of the gyroscope. The design symmetry and the worm-shaped springs increase the robustness, mode matching, and gyroscopic sensitivity against harsh environments. The design modeling of the gyroscope is investigated using the ANSYSTM software. The design of the vibrating ring gyroscope incorporates two 10 µm thick rings with an outer ring radius of 1000 µm and an inner ring radius of 750 µm. Both rings are attached with sixteen worm-shaped springs, and a centrally placed anchor supports the whole structure with a radius of 260 µm. The proposed gyroscope operates in two identical wine glass modes. The first targeted resonant mode was recorded at 29.07 kHz, and the second mode of the same shape was recorded at 29.35 kHz. There is a low-mode mismatch of 0.38 kHz observed between the two resonant frequencies, which can be resolved with tuning electrodes. The initial modeling results show a good prospect for the design of a vibrating gyroscope for space applications. Full article

Micro-electromechanical systems (MEMS) vibrating gyroscopes have gained a lot of attention over the last two decades because of their low power consumption, easy integration, and low fabrication cost. The usage of the gyroscope equipped with an inertial measurement unit has increased tremendously, with applications ranging from household devices to smart electronics to military equipment. However, reliability issues are still a concern when operating this inertial sensor in harsh environments, such as to control the movement and alignment of mini-satellites in space, tracking firefighters at an elevated temperature, and assisting aircraft navigation in gusty turbulent air. This review paper focuses on the key fundamentals of the MEMS vibrating gyroscopes, first discussing popular designs including the tuning fork, gimbal, vibrating ring, and multi-axis gyroscopes. It further investigates how bias stability, angle random walk, scale factor, and other performance parameters are affected in harsh environments and then discusses the reliability issues of the gyroscopes. Full article

This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of Young’s modulus was developed via Lagrange’s equations for simulating the dynamical behavior of an imperfect ring-based gyroscope. The dynamical analyses are focused on the effects on the frequency split between two vibration modes of interest as well as the rotation of the principal axis of the 2θ mode pair, leading to modal coupling and the degradation of gyroscopic sensitivity. While both anisotropic Young’s modulus and nonideal deep trench verticality affect the frequency difference between two vibration modes, they have little contribution to deflecting the principal axis of the 2θ mode pair. However, the 4θ variations in the width of both the ring and the supporting beams cause modal coupling to occur and the degenerate 2θ mode pair to split in frequency. To aid the optimal design of MEMS ring-based gyroscopic sensors that has relatively high robustness to fabrication tolerance, a geometrical compensation based on the developed model is demonstrated to identify the geometries of the ring and the suspension. Full article

Disc gyroscope manufactured through microelectromechanical systems (MEMS) fabrication processes becomes one of the most critical solutions for achieving high performance. Some reported novel disc constructions acquire good performance in bias instability, scale factor nonlinearity, etc. However, antivibration characteristics are also important for the devices, especially in engineering applications. For multi-ring structures with central anchors, the out-of-plane motions are in the first few modes, easily excited within the vibration environment. The paper presents a multi-ring gyro with good dynamic characteristics, operating at the first resonant mode. The design helps obtain better static performance and antivibration characteristics with anchor points outside of the multi-ring resonator. According to harmonic experiments, the nearest interference mode is located at 30,311 Hz, whose frequency difference is 72.8% far away from working modes. The structures were fabricated with silicon on insulator (SOI) processes and wafer-level vacuum packaging, where the asymmetry is 780 ppm as the frequency splits. The gyro also obtains a high Q-factor. The measured value at 0.15 Pa was 162 k, which makes the structure have sizeable mechanical sensitivity and low noise. Full article

A new micromachined vibrating ring gyroscope (VRG) architecture with low quadrature error and high-linearity is proposed, which successfully optimizes the working modes to first order resonance mode of the structure. The improved mode ordering can significantly reduce the vibration sensitivity of the device by adopting the hinge-frame mechanism. The frequency difference ratio is introduced to represent the optimization effect of modal characteristic. Furthermore, the influence of the structural parameters of hinge-frame mechanism on frequency difference ratio is clarified through analysis of related factors, which contributes to a more effective design of hinge-frame structure. The designed VRG architecture accomplishes the goal of high-linearity by using combination hinge and variable-area capacitance strategy, in contrast to the conventional approach via variable-separation drive/sense strategy. Finally, finite element method (FEM) simulations are carried out to investigate the stiffness, modal analysis, linearity, and decoupling characteristics of the design. The simulation results are sufficiently in agreement with theoretical calculations. Meanwhile, the hinge-frame mechanism can be widely applied in other existing ring gyroscopes, and the new design provides a path towards ultra-high performance for VRG. Full article

This study presents a new microelectromechanical system, a vibration ring gyroscope with a double U-beam (DUVRG), which was designed using a combination of mathematical analysis and the finite element method. First, a ring vibration resonator with eight double U-beam structures was developed, and 24 capacitive electrodes were designed for drive and sense according to the advantageous characteristics of a thin-shell vibrating gyroscope. Then, based on the elastic mechanics and thin-shell theory, a mathematical stiffness model of the double U-beam was established. The maximum mode resonant frequency error calculated by the DUVRG stiffness model, finite element analysis (FEA) and experiments was 0.04%. DUVRG structures were manufactured by an efficient fabrication process using silicon-on-glass (SOG) and deep reactive ion etching (DRIE), and the FEA value and theoretical calculation had differences of 5.33% and 5.36% with the measured resonant frequency value, respectively. Finally, the static and dynamic performance of the fabricated DUVRG was tested, and the bias instability and angular random walk were less than 8.86 (°)/h and 0.776 (°)/√h, respectively. Full article

This paper analyzes the effect of the anisotropy of single crystal silicon on the frequency split of the vibrating ring gyroscope, operated in the $n=2$ wineglass mode. Firstly, the elastic properties including elastic matrices and orthotropic elasticity values of (100) and (111) silicon wafers were calculated using the direction cosines of transformed coordinate systems. The (111) wafer was found to be in-plane isotropic. Then, the frequency splits of the $n=2$ mode ring gyroscopes of two wafers were simulated using the calculated elastic properties. The simulation results show that the frequency split of the (100) ring gyroscope is far larger than that of the (111) ring gyroscope. Finally, experimental verifications were carried out on the micro-gyroscopes fabricated using deep dry silicon on glass technology. The experimental results are sufficiently in agreement with those of the simulation. Although the single crystal silicon is anisotropic, all the results show that compared with the (100) ring gyroscope, the frequency split of the ring gyroscope fabricated using the (111) wafer is less affected by the crystal direction, which demonstrates that the (111) wafer is more suitable for use in silicon ring gyroscopes as it is possible to get a lower frequency split. Full article