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Proposed multi-degree of freedom (multi-DoF) microelectromechanical systems (MEMS) gyroscope design with 3-DoF drive mode and 2-DoF sense mode oscillators.
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This paper presents microfabrication process-driven design of a multi-degree of freedom (multi-DoF) non-resonant electrostatic microelectromechanical systems (MEMS) gyroscope by considering the design constraints of commercially available low-cost and widely-used silicon-on-insulator multi-user MEMS processes (SOIMUMPs), with silicon as a structura...
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... the integration of the proposed MEMS gyroscope with readout electronics is discussed in detail. Figure 1 shows the proposed multi-DoF MEMS gyroscope design with a 3-DoF drive mode and 2-DoF sense mode oscillators. The drive and sense masses are connected to each other using serpentine-shaped mechanical springs. ...
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... the proposed multi-DoF MEMS gyroscope, this implies that in comparison to traditional multi-DoF MEMS gyroscope designs reported in the literature, the sense mass cannot be completely enclosed within another mass due to the requirement of anchor part for the fixed parallel sensing plates. Thus, for the proposed MEMS gyroscope, the anchor for the fixed parallel sensing plates attached to mass m 3b, is provided by routing the silicon fixed beams from one side of the outer mass m 1 as shown in Figure 1. are considered for the proposed multi-DoF MEMS gyroscope design are discussed below. ...
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... the proposed multi-DoF MEMS gyroscope, this implies that in comparison to traditional multi-DoF MEMS gyroscope designs reported in the literature, the sense mass cannot be completely enclosed within another mass due to the requirement of anchor part for the fixed parallel sensing plates. Thus, for the proposed MEMS gyroscope, the anchor for the fixed parallel sensing plates attached to mass m3b, is provided by routing the silicon fixed beams from one side of the outer mass m1 as shown in Figure 1. ...
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... frequency response of the 3-DoF drive mode oscillator. Figure 10 shows the frequency response of the 2-DoF sense mode oscillator. At the first resonant frequency, the displacement in the mass í µí± was dynamically amplified with an amplification ratio of 1.85. ...
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... in the flat operational region between the two resonant peaks, there was an amplified displacement in the mass í µí± with respect to mass í µí± with an average amplification ratio of nearly 2.6. The frequency response results shown in Figures 9 and 10 show that the most suitable operational frequency region was between the resonant frequencies of 1.707 kHz and 3.329 kHz with a bandwidth of 1.622 kHz for the propose MEMS gyroscope design. ...
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... analyze the dominant air damping mechanism for the proposed MEMS gyroscope, a detailed FEM-based analysis was carried out in the DampingMM module of CoventorWare. Figure 11a,b shows the effect of oscillation frequency on the slide film and squeeze film air damping respectively at room temperature and pressure conditions and the relative Figure 10 shows the frequency response of the 2-DoF sense mode oscillator. At the first resonant frequency, the displacement in the mass m 3b was dynamically amplified with an amplification ratio of 1.85. ...
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... analyze the dominant air damping mechanism for the proposed MEMS gyroscope, a detailed FEM-based analysis was carried out in the DampingMM module of CoventorWare. Figure 11a,b shows the effect of oscillation frequency on the slide film and squeeze film air damping respectively at room temperature and pressure conditions and the relative Figure 10 shows the frequency response of the 2-DoF sense mode oscillator. At the first resonant frequency, the displacement in the mass m 3b was dynamically amplified with an amplification ratio of 1.85. ...
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... in the flat operational region between the two resonant peaks, there was an amplified displacement in the mass m 3b with respect to mass m 3a with an average amplification ratio of nearly 2.6. The frequency response results shown in Figures 9 and 10 show that the most suitable operational frequency region was between the resonant frequencies of 1.707 kHz and 3.329 kHz with a bandwidth of 1.622 kHz for the propose MEMS gyroscope design. Figure 10 shows the frequency response of the 2-DoF sense mode oscillator. ...
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... frequency response results shown in Figures 9 and 10 show that the most suitable operational frequency region was between the resonant frequencies of 1.707 kHz and 3.329 kHz with a bandwidth of 1.622 kHz for the propose MEMS gyroscope design. Figure 10 shows the frequency response of the 2-DoF sense mode oscillator. At the first resonant frequency, the displacement in the mass í µí± was dynamically amplified with an amplification ratio of 1.85. ...
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... in the flat operational region between the two resonant peaks, there was an amplified displacement in the mass í µí± with respect to mass í µí± with an average amplification ratio of nearly 2.6. The frequency response results shown in Figures 9 and 10 show that the most suitable operational frequency region was between the resonant frequencies of 1.707 kHz and 3.329 kHz with a bandwidth of 1.622 kHz for the propose MEMS gyroscope design. ...
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... analyze the dominant air damping mechanism for the proposed MEMS gyroscope, a detailed FEM-based analysis was carried out in the DampingMM module of CoventorWare. Figure 11a,b shows the effect of oscillation frequency on the slide film and squeeze film air damping respectively at room temperature and pressure conditions and the relative Figure 10. The frequency response of the 2-DoF sense mode oscillator. ...
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... analyze the dominant air damping mechanism for the proposed MEMS gyroscope, a detailed FEM-based analysis was carried out in the DampingMM module of CoventorWare. Figure 11a,b shows the effect of oscillation frequency on the slide film and squeeze film air damping respectively at room temperature and pressure conditions and the relative Figure 10. The frequency response of the 2-DoF sense mode oscillator. ...
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... analyze the dominant air damping mechanism for the proposed MEMS gyroscope, a detailed FEM-based analysis was carried out in the DampingMM module of CoventorWare. Figure 11a,b shows the effect of oscillation frequency on the slide film and squeeze film air damping respectively at room temperature and pressure conditions and the relative contribution of both the viscous and elastic/spring damping forces. The results show that for the oscillation frequency in the range of 6 kHz, the viscous damping force was the main energy dissipation mechanism and effect of the elastic/spring force of air damping is negligible. ...
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... results were also verified by the Equation (12), since the squeeze number value for the MEMS gyroscope, at 6 kHz and room temperature and pressure was only 0.005. Figure 11c shows that with the higher values of oscillation frequency, the elastic/spring air forces became dominant and increased linearly with the oscillation frequency, while the viscous damping forces decreased. The FEM results presented in this section thus show that for the proposed MEMS gyroscope the main damping force will be viscous air damping. ...
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... results were also verified by the Equation (12), since the squeeze number value for the MEMS gyroscope, at 6 kHz and room temperature and pressure was only 0.005. Figure 11c shows that with the higher values of oscillation frequency, the elastic/spring air forces became dominant and increased linearly with the oscillation frequency, while the viscous damping forces decreased. The FEM results presented in this section thus show that for the proposed MEMS gyroscope the main damping force will be viscous air damping. ...
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... mismatch can be explained by the assumption that, in the analytical formulation, ideal sensing plate edge conditions were assumed while the simulation results from the DampingMM module of CoventorWare also accounted for the non-ideality of the sensing plate edges which leads to a more accurate and relatively higher value of damping coefficient [37]. Figure 11. Effect of oscillation frequency on (a) squeezed film air damping for frequency up to 6 kHz (b) slide film air damping for frequency up to 6 kHz (c) squeezed film air damping for frequency up to 10 MHz. Figure 11. ...
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... of oscillation frequency on (a) squeezed film air damping for frequency up to 6 kHz (b) slide film air damping for frequency up to 6 kHz (c) squeezed film air damping for frequency up to 10 MHz. Figure 11. Effect of oscillation frequency on (a) squeezed film air damping for frequency up to 6 kHz (b) slide film air damping for frequency up to 6 kHz (c) squeezed film air damping for frequency up to 10 MHz. ...
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... effect of temperature and pressure variations on the MEMS gyroscope was analyzed through FEM simulations in the DampingMM module of CoventorWare in the form of the energy loss function (1/Q air ). Figure 12 shows that effect of change in temperature in the range of −40 • C to 100 • C on energy loss is negligible for the fixed values of atmospheric pressure at 1 kPa and 101 kPa. However, the energy loss function values were strongly dependent on the variation in the device operating pressure conditions. ...
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... effect of temperature and pressure variations on the MEMS gyroscope was analyzed through FEM simulations in the DampingMM module of CoventorWare in the form of the energy loss function (1 í µí± ⁄ ). Figure 12 shows that effect of change in temperature in the range of −40 °C to 100 °C on energy loss is negligible for the fixed values of atmospheric pressure at 1 kPa and 101 kPa. However, the energy loss function values were strongly dependent on the variation in the device operating pressure conditions. ...
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... addition to energy loss factor, the effect of varying temperature and pressure values on the frequency response of the absorber mass (í µí± ) in the drive mode and sense mass í µí± in the sense mode was analyzed through FEM simulations. Figure 13a,b shows that the effect of temperature variations, in the range of −40 °C to 100 °C, was negligible on the response amplitude of the absorber mass both in the drive and sense direction. Figure 14a,b shows the effect of change in the operating air pressure, for 1 kPa and 101 kPa, on the frequency response of the absorber mass in the drive direction and sense mass in the sense direction. ...
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... 13a,b shows that the effect of temperature variations, in the range of −40 °C to 100 °C, was negligible on the response amplitude of the absorber mass both in the drive and sense direction. Figure 14a,b shows the effect of change in the operating air pressure, for 1 kPa and 101 kPa, on the frequency response of the absorber mass in the drive direction and sense mass in the sense direction. The results show that the displacement amplitude at resonance peaks was significantly increased by decreasing the operating air pressure. ...
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... in the flat operational region between the resonant peaks, both in the drive and sense mode, there is a negligible change in the displacement amplitude of the masses. The results in Figures 13 and 14 show that the proposed MEMS gyroscope is robust against both the operating temperature and air pressure variations in the flat operating region between the resonant peaks in the drive and sense mode. In addition to energy loss factor, the effect of varying temperature and pressure values on the frequency response of the absorber mass (m 3 ) in the drive mode and sense mass m 3b in the sense mode was analyzed through FEM simulations. ...
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... addition to energy loss factor, the effect of varying temperature and pressure values on the frequency response of the absorber mass (m 3 ) in the drive mode and sense mass m 3b in the sense mode was analyzed through FEM simulations. Figure 13a,b shows that the effect of temperature variations, in the range of −40 • C to 100 • C, was negligible on the response amplitude of the absorber mass both in the drive and sense direction. Figure 14a,b shows the effect of change in the operating air pressure, for 1 kPa and 101 kPa, on the frequency response of the absorber mass in the drive direction and sense mass in the sense direction. ...
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... 13a,b shows that the effect of temperature variations, in the range of −40 • C to 100 • C, was negligible on the response amplitude of the absorber mass both in the drive and sense direction. Figure 14a,b shows the effect of change in the operating air pressure, for 1 kPa and 101 kPa, on the frequency response of the absorber mass in the drive direction and sense mass in the sense direction. The results show that the displacement amplitude at resonance peaks was significantly increased by decreasing the operating air pressure. ...
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... in the flat operational region between the resonant peaks, both in the drive and sense mode, there is a negligible change in the displacement amplitude of the masses. The results in Figures 13 and 14 show that the proposed MEMS gyroscope is robust against both the operating temperature and air pressure variations in the flat operating region between the resonant peaks in the drive and sense mode. . Effect of operating temperature variations on the frequency response of (a) drive mass í µí± and (b) sense mass í µí± . ...
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... silicon, the values of B and T 0 are estimated as 15.8 MPa and 317 K respectively [39]. Figure 15 shows Young's modulus value for the silicon for the operating temperature range of −40 • C to 100 • C for the proposed MEMS gyroscope. The results show that, for the desired operating temperature range for the MEMS gyroscope, the effect of temperature on stiffness variations is negligible. ...
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... analyze the effect of the operating temperature in the range of −40 • C to 100 • C on the thermal deformation in the MEMS gyroscope, an FEM-based thermal analysis was carried out. The thermal deformation results in Figure 16a show that at 100 • C there was structural expansion in the MEMS gyroscope with a maximum value of 4.66 µm in the mechanical suspension beams. Figure 16b shows that at −40 • C, the mechanical structure contracted and maximum deformation in the mechanical springs was 3.21 µm. ...
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... thermal deformation results in Figure 16a show that at 100 • C there was structural expansion in the MEMS gyroscope with a maximum value of 4.66 µm in the mechanical suspension beams. Figure 16b shows that at −40 • C, the mechanical structure contracted and maximum deformation in the mechanical springs was 3.21 µm. Although the deformation in the mechanical springs was high, the maximum expansion and contraction in the drive and sense mass was very low, with a maximum value of 0.4 µm at 100 • C and 0.27 µm at −40 • C. In the electrostatic comb drive actuator, attached to a mass m 1 , the net effect of thermal deformation in the comb drives and hence on the electrostatic force is negligible due to symmetric deformation of the mass m 1 . ...
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... analyze the effect of the operating temperature in the range of −40 °C to 100 °C on the thermal deformation in the MEMS gyroscope, an FEM-based thermal analysis was carried out. The thermal deformation results in Figure 16a show that at 100 °C there was structural expansion in the MEMS gyroscope with a maximum value of 4.66 μm in the mechanical suspension beams. Figure 16b shows that at −40 °C, the mechanical structure contracted and maximum deformation in the mechanical springs was 3.21 μm. ...
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... thermal deformation results in Figure 16a show that at 100 °C there was structural expansion in the MEMS gyroscope with a maximum value of 4.66 μm in the mechanical suspension beams. Figure 16b shows that at −40 °C, the mechanical structure contracted and maximum deformation in the mechanical springs was 3.21 μm. Although the deformation in the mechanical springs was high, the maximum expansion and contraction in the drive and sense mass was very low, with a maximum value of 0.4 μm at 100 °C and 0.27 μm at −40 °C. ...
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... the electrostatic comb drive actuator, attached to a mass í µí± , the net effect of thermal deformation in the comb drives and hence on the electrostatic force is negligible due to symmetric deformation of the mass í µí± . To get more detailed information on the thermal deformation and its effect on the capacitive sensing plates, a deformation path is added in the FEM analysis along with the sense mass í µí± , as shown in Figure 17a. The results of the expansion and contraction along this path at −40 °C and 100 °C are shown in Figure 17b,c, respectively. ...
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... get more detailed information on the thermal deformation and its effect on the capacitive sensing plates, a deformation path is added in the FEM analysis along with the sense mass í µí± , as shown in Figure 17a. The results of the expansion and contraction along this path at −40 °C and 100 °C are shown in Figure 17b,c, respectively. The results show that the deformation due to temperature did not remain constant throughout the length of the sense mass and it was minimized at the center and increased on either side. ...
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... decrease in the initial gap results in the decrease in the maximum pull-in voltage value and maximum input angular rate measurement. To get more detailed information on the thermal deformation and its effect on the capacitive sensing plates, a deformation path is added in the FEM analysis along with the sense mass m 3b , as shown in Figure 17a. The results of the expansion and contraction along this path at −40 • C and 100 • C are shown in Figure 17b,c, respectively. ...
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... get more detailed information on the thermal deformation and its effect on the capacitive sensing plates, a deformation path is added in the FEM analysis along with the sense mass m 3b , as shown in Figure 17a. The results of the expansion and contraction along this path at −40 • C and 100 • C are shown in Figure 17b,c, respectively. The results show that the deformation due to temperature did not remain constant throughout the length of the sense mass and it was minimized at the center and increased on either side. ...
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... effect of change in structural layer thickness with 25 µm ± 1 µm was studied and its effect on the resonant frequency change and capacitance change was analyzed. Figure 18a shows that the effect of change in resonant frequency due to thickness tolerance of ±1 µm resulted in nearly 2% change in resonant frequency from the nominal values. Figure 18b shows that thickness tolerances result in a capacitance change variation of nearly 3.1% from the nominal values. ...
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... 18a shows that the effect of change in resonant frequency due to thickness tolerance of ±1 µm resulted in nearly 2% change in resonant frequency from the nominal values. Figure 18b shows that thickness tolerances result in a capacitance change variation of nearly 3.1% from the nominal values. These results show that the proposed MEMS gyroscope is robust against the microfabrication process tolerances. ...
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... effect of change in structural layer thickness with 25 μm ± 1 μm was studied and its effect on the resonant frequency change and capacitance change was analyzed. Figure 18a shows that the effect of change in resonant frequency due to thickness tolerance of ±1 μm resulted in nearly 2 % change in resonant frequency from the nominal values. Figure 18b shows that thickness tolerances result in a capacitance change variation of nearly 3.1 % from the nominal values. ...
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... 18a shows that the effect of change in resonant frequency due to thickness tolerance of ±1 μm resulted in nearly 2 % change in resonant frequency from the nominal values. Figure 18b shows that thickness tolerances result in a capacitance change variation of nearly 3.1 % from the nominal values. These results show that the proposed MEMS gyroscope is robust against the microfabrication process tolerances. ...
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... actuation voltage of 80 V DC and 5 V AC was applied to the electrostatic actuator with a frequency of 2.5 kHz, which results in an oscillation amplitude of 0.22 µm in the mass m 3 . For this oscillation amplitude and with a rotation of 50 rad/s in the z-axis, a Coriolis force of 1.943 µN was generated in the y-axis Figure 19a,b shows the input rotation and drive mass displacement, respectively. Figure 19c shows the y-axis displacement in the mass m 3b corresponding to an induced Coriolis force with an amplitude of 0.114 µm. ...
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... this oscillation amplitude and with a rotation of 50 rad/s in the z-axis, a Coriolis force of 1.943 µN was generated in the y-axis Figure 19a,b shows the input rotation and drive mass displacement, respectively. Figure 19c shows the y-axis displacement in the mass m 3b corresponding to an induced Coriolis force with an amplitude of 0.114 µm. Assuming the linear relation between the input rotation and induced Coriolis force and hence sense mass displacement, the mechanical sensitivity for the proposed MEMS gyroscope was 0.00228 µm/rad/s. ...
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... G is the gain with a value of 2, V2P25 and V re f are set to 2.25 V, ∆C is the change in capacitance and C F is the feedback capacitor with a nominal value of 2.8 pF. The value of C F can be changed according to the sense capacitance range to make the output voltage reside within the desired range of 0.5 V to 4 V. Figure 21 shows the effect of variation in the C F on the output voltage of MS 3110 IC for the proposed MEMS gyroscope. The graph shows that for the MEMS gyroscope, for smaller values of C F , the output voltage is higher than the upper limit of 4 V for the same input capacitance change. ...
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... í µí°º is the gain with a value of 2, í µí±2í µí±25 and í µí± are set to 2.25 V, Δí µí° ¶ is the change in capacitance and í µí° ¶ is the feedback capacitor with a nominal value of 2.8 í µí±í µí°¹. The value of í µí° ¶ can be changed according to the sense capacitance range to make the output voltage reside within the desired range of 0.5 V to 4 V. Figure 21 shows the effect of variation in the í µí° ¶ on the output voltage of MS 3110 IC for the proposed MEMS gyroscope. The graph shows that for the MEMS gyroscope, for smaller values of í µí° ¶ , the output voltage is higher than the upper limit of 4 V for the same input capacitance change. ...
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... Among the microdevices developed are accelerometers, which are used as sensors in air bags for the automotive sector [1,2]; microgrippers for microwires manipulation, useful for example in materials research; microfibers and microdevices used in microelectronics and photonics development, research, and innovation [3,4]. Microgrippers have been developed for the acquisition of biological samples in the biomedical sector [5][6][7], gyroscopes that allow rotation on the screens of mobile devices, find applications in GPS and mobile systems, that means, they are widely used in navigation and communication systems [8,9]. Acoustic or pressure diaphragms are applied in sound auxiliary devices or to monitor variables such as temperature, pressure, and hydration levels, among other medical applications [10,11]. ...
This paper provides the design of aluminum grippers based on the geometry of a microgripper created in silicon. The values of the parameters used in the first scaled gripper were obtained experimentally, which allows to adjust the conditions considered in the numerical analysis , making the modeling more accurate. The numerical analysis allows to know the grippers performance, in such a way that scaling, modifications , and even integrations can be made in complex systems. The use of a gripper with 4 arms integrated into a like-cobot structure is also validated , which allows to propose its use in intelligent manufacturing, when considering the manipulation of tiny objects, on a micro and millimeter scale. The thermal performance of the grippers allows the use of waste thermal energy for their operation, making it useful for the energy purposes of Smart Cities.
... In this section, we compare the performance characteristics of previously reported high-precision micro-opto-electro-mechanical systems (MOEMS) gyroscopes to our novel dual-frame optomechanical gyroscope architecture incorporating an integrated photonic crystal cavity. As summarized in Table 3, three earlier frame-type MEMS gyroscope designs utilized an electrostatic comb drive actuator and displacement sensor [39,42,43]. ...
... In this section, we compare the performance characteristics of previously reported high-precision micro-opto-electro-mechanical systems (MOEMS) gyroscopes to our novel dual-frame optomechanical gyroscope architecture incorporating an integrated photonic crystal cavity. As summarized in Table 3, three earlier frame-type MEMS gyroscope designs utilized an electrostatic comb drive actuator and displacement sensor [39,42,43]. However, these approaches exhibited limitations associated with electronic noise introduced by the driving and sensing methods employing different operating modes. ...
Micro-gyroscopes based on the Coriolis principle are widely employed in inertial navigation, motion control, and vibration analysis applications. Conventional micro-gyroscopes often exhibit limitations, including elevated noise levels and suboptimal performance metrics. Conversely, the advent of cavity optomechanical system technology heralds an innovative approach to micro-gyroscope development. This method enhances the device’s capabilities, offering elevated sensitivity, augmented precision, and superior resolution. This paper presents our main contributions which include a novel dual-frame optomechanical gyroscope, a unique photonic crystal cavity design, and advanced numerical simulation and optimization methods. The proposed design utilizes an optical cavity formed between dual oscillating frames, whereby input rotation induces a measurable phase shift via optomechanical coupling. Actuation of the frames is achieved electrostatically via an interdigitated comb-drive design. Through theoretical modeling based on cavity optomechanics and finite element simulation, the operating principle and performance parameters are evaluated in detail. The results indicate an expected angular rate sensitivity of 22.8 mV/°/s and an angle random walk of 7.1 × 10−5 °/h1/2, representing superior precision to existing micro-electromechanical systems gyroscopes of comparable scale. Detailed analysis of the optomechanical transduction mechanism suggests this dual-frame approach could enable angular vibration detection with resolution exceeding state-of-the-art solutions.
... The fabrication techniques used in MEMS production combine the capabilities of the techniques that are utilized in the IC domain with the processes of micromachining such as surface micromachining, bulk micromachining, Lithographie Galvanoformung Abformung (LIGA), high-aspect-ratio micromachining (HARM) to wafer bonding and molding, etc. [30]. MEMS CAP Inc., USA, is one of the famous companies that provides MEMS fabrication facilities for researchers through multiusers MEMS procedures (MUMPs) including several standard fabrication procedures such as MetalMUMPs [35], PolyMUMPs [36], SOIMUMP [37], and PiezoMUMPs [38], whereas there are hundreds of other fabs in the global who are fabricating MEMS devices, just to mention some, including SilTerra [39][40][41], Infineon [42], CEA-LETI [43,44], CSEM [45], TSMS [46,47], and Bosh [48,49]. ...
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... In the research of non-resonant gyroscopes, researchers often ignore the influence of the Coriolis force on the frequency response of the sense mode for convenience. Bukhari et al. [3] investigated a multi-DoF gyroscope with an incomplete 2-DoF sense mode system. On the one hand, the results revealed the advantages of large resonant peaks spacing and wide bandwidth. ...
... Dynamical equations of the fully decoupled 3-DOF gyroscope are deduced as follows: Figure 1a describes the dynamical model of the micro-gyroscope with an incomplete 2-DOF sense mode system. An incomplete 2-DOF system means that it is based on the principle of dynamic vibration absorber [3]. In order to realize the arbitrary adjustment of the resonant peaks spacing, a complete 2-DOF sense mode system is constructed by adding a spring k y3 as shown in Figure 1b, where, k y11 , k y12 , k y2 , and k y3 represent the equivalent spring stiffness of the micro-beams of the sense mode; c y1 and c y3 represent the damping coefficients of the sense mode. ...
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In this paper, we use the nonlinear hardening stiffness of drive mode deal with the contradiction between gain and bandwidth of the linear micro-gyroscope, to improve the bandwidth and gain in sense direction. Firstly, in order to adjust the distance between two resonant peaks, we changed an incomplete two-degree-of-freedom(2-DoF) sense mode system of the micro-gyroscope into a complete 2-DoF system. Afterward, according to the given nonlinear coefficient of stiffness of drive mode, the structure size of driving micro-beams was designed to obtain a nonlinear micro-gyroscope with controllable stiffness. Finally, we investigated the effects of peaks spacing, damping, and driving nonlinearity on gain and bandwidth, and the nonlinear micro-gyroscope was optimized by orthogonal experiment method and response surface method. The results reveal that the peaks spacing has a great influence on the gain and bandwidth of both linear and nonlinear micro-gyroscopes. The larger the peaks spacing, the lower the gain, but higher gain can be achieved when the resonant frequency of the drive mode is close to the lower-order resonant frequency of the sense mode. Driving nonlinearity leads to the response peak of the Coriolis force to have a hardening characteristic, thus forming a wide platform in the sense direction. Hardening of the response peak of the Coriolis force allows the micro-gyroscope to obtain a higher gain while the bandwidth of the sense mode is also greatly improved. In addition, parameter optimization can make the gain and bandwidth of the micro-gyroscope optimal. When the peaks spacing is small and the nonlinear stiffness coefficient is about 1012.2, under the premise that the gain is basically constant, the bandwidth of the sense mode increases about 1.76 times compared with the linear gyroscope. Damping can suppress the influence of nonlinearity in a micro-gyroscope system. Within a certain range, the frequency response of the nonlinear micro-gyroscope tends to be a linear system with the increase in damping, resulting in narrower bandwidth and lower gain.
... Capacitive sensors with good stability, high speed and adaptability of extreme environments are widely adopted to measure the displacement of motion targets [9][10][11][12]. Chapman et al. carried out research on the measurement of rotary axis error motions using a cylindrical capacitive sensor (CCS) with multiple electrodes of large sense area [13][14][15]. ...
As a key indicator reflecting the working accuracy of rotary functional units, the error motions of the precision shafting are very necessary to be measured. In this paper, the main error sources for the error motion measurement of a precision shafting using a T-type capacitive sensor were investigated. The theoretical modeling error due to the approximate simplification for the output capacitance expressions was firstly analyzed. By means of the 3D-FEA method, the influence of fringe effects was subsequently investigated. Finally, the analysis of electrode installation errors was emphasized on the tilt error of the cylindrical electrode and coaxiality error of the fan-shaped electrode by establishing mathematical models and numerical simulation. Based on the theoretical analysis and simulation results, the methods of decreasing the approximate error and the nonlinear error caused by fringe effects were subsequently proposed; for the installation errors, the tilt error of cylindrical electrode only makes the solution of phase angle have a certain deviation and has almost no effect on solving the radial displacement, especially for the measurement range less than 0.1 mm; the measurement of the rotor tilt displacement was basically not affected by the coaxiality error of the fan-shaped electrode.
... For each simulation run in the design matrix, the computed values of squeeze number and Reynolds number are in the range of 10 −3 thus air compressibility and inertial damping effects are ignored. A detailed description of modelling of thin film air damping effects in capacitive sensing combs is given by the authors in [40,41]. ...
This paper presents a systematic and efficient design approach for the two degree-of-freedom (2-DoF) capacitive microelectromechanical systems (MEMS) accelerometer by using combined design and analysis of computer experiments (DACE) and Gaussian process (GP) modelling. Multiple output responses of the MEMS accelerometer including natural frequency, proof mass displacement, pull-in voltage, capacitance change, and Brownian noise equivalent acceleration (BNEA) are optimized simultaneously with respect to the geometric design parameters, environmental conditions, and microfabrication process constraints. The sampling design space is created using DACE based Latin hypercube sampling (LHS) technique and corresponding output responses are obtained using multiphysics coupled field electro–thermal–structural interaction based finite element method (FEM) simulations. The metamodels for the individual output responses are obtained using statistical GP analysis. The developed metamodels not only allowed to analyze the effect of individual design parameters on an output response, but to also study the interaction of the design parameters. An objective function, considering the performance requirements of the MEMS accelerometer, is defined and simultaneous multi-objective optimization of the output responses, with respect to the design parameters, is carried out by using a combined gradient descent algorithm and desirability function approach. The accuracy of the optimization prediction is validated using FEM simulations. The behavioral model of the final optimized MEMS accelerometer design is integrated with the readout electronics in the simulation environment and voltage sensitivity is obtained. The results show that the combined DACE and GP based design methodology can be an efficient technique for the design space exploration and optimization of multiphysics MEMS devices at the design phase of their development cycle.
... The design presented in this paper is optimized using the SOI-MUMPs process, which is a commercially available microfabrication process with the structural thickness of 25 of silicon. In comparison to nickel, silicon is more thermally stable, in a range of 40° to 100° [18]. ...
... However, this robustness is a trade-off with the sensitivity, as the sensitivity of non-resonant MEMS gyroscopes is lower due to operation in the flat region between two resonant peaks where the oscillation amplitude is low. To increase the oscillation amplitude in non-resonant MEMS gyroscopes, different approaches based on the dynamic amplification have been implemented [8][9][10], but the sensitivity and resolution of the non-resonant MEMS gyroscopes are generally low compared to resonant MEMS gyroscopes. ...
... The drive and sense mode natural frequency values and corresponding mode shapes for the proof mass system and electrostatically coupled 3-DoF WCRs system are obtained through FEM simulations in the CoventorWare software. In the analysis, density of 2500 kg/m 3 , Young's Modulus of 169 GPa and Poisson ratio of 0.29 are used for the silicon structural layer [10]. Fig. 5 (a) and (b) shows the drive and sense mode shapes for the MEMS gyroscope with resonant frequency values of 2832.46 ...
This paper presents a novel design for a high resolution microelectromechanical systems (MEMS) technology based resonant gyroscope using the mode-localization effect in weekly coupled resonators (WCRs) as a mechanism for sensing the input angular rate. The design consists of a single proof mass with two three degree-of-freedom (3-DoF) WCRs systems attached on either side. The MEMS gyroscope is designed according to the microfabrication constraints of the foundry process, silicon-on-insulator multi-user MEMS process (SOIMUMPs). The shift in the resonance frequency values, amplitude ratios of the WCRs, and amplitude ratios difference of two sets due to electrostatic stiffness perturbation, corresponding to the input angular rotation, are discussed as an output metric for the measurement of angular rate. The results show that the amplitude ratio difference as an output metric allows to achieve a linear output response and large dynamic range in comparison to the shift in the amplitude ratio and resonance frequency in 3-DoF WCRs in a single set. The dynamic range and resolution of the MEMS gyroscope in terms of maximum allowed resonators amplitude and noise floor is discussed. The proposed MEMS gyroscope design has a sensitivity of 62830 ppm/°/s based on a difference in the amplitude ratios of resonators in two 3-DoF WCRs systems and a dynamic range of ±100 °/s. The resolution of the MEMS gyroscope is 31.09 × 10-6 °/s which is significantly higher than existing MEMS gyroscopes and is comparable to traditional bulky ring laser gyroscopes. This high resolution makes the proposed MEMS gyroscope design suitable for use in applications such as earth rotation rate measurement for gyrocompassing and high precision robotics.
... Different structural parameters like beam lengths, comb drive parameters, and rigid plate dimensions have been optimized using FEA simulations to achieve a higher sensitivity from the device. Although most of the available 4 DoF systems consists of 2 drive and 2 sense mode resonant frequencies 4 DoF design presented in [7] has 3 drive mode frequencies. There is only one sense mode in this electro thermally actuated vibratory gyroscope. ...
In this paper, design and simulation of a Multi DoF (Degree of Freedom) Vibratory Gyroscope is presented. Most of the available gyroscopes are vibratory gyroscopes due to their design and fabrication simplicity. But the performance of these devices is highly sensitive to device operating conditions, fabrication imperfections, and environmental effects. As a solution to this, Multi DoF vibratory gyroscopes have been introduced. The Multi DoF system proposed here consists of 2 DoF drive and sense mode vibrations. During the design procedure of the system, structural parameters are optimized to obtain a constant amplitude flat operational frequency region with a wider bandwidth. In addition to that Dynamic Amplification increases the sensitivity. Drive mode forced vibration is actuated electrostatically and suspension structure was chosen to minimize the quadrature error. The device uses capacitive sensing to measure angular velocity. Further, SOI(Silicon on Insulator) based fabrication process is proposed to fabricate the 4 DoF vibratory gyroscope.
