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Design and Analysis of a Novel Fully Decoupled Tri-axis Linear Vibratory Gyroscope with Matched Modes.

Xia D, Kong L, Gao H - Sensors (Basel) (2015)

Bottom Line: With the help of the finite element method (FEM) software ANSYS, the natural frequencies of drive, yaw, and pitch/roll modes are found to be 14,017 Hz, 14,018 Hz and 14,020 Hz, respectively.The cross-axis effect and scale factor of each mode are also simulated.All the simulation results are in good accordance with the theoretical analysis, which means the design is effective and worthy of further investigation on the integration of tri-axis accelerometers on the same single chip to form an inertial measurement unit.

View Article: PubMed Central - PubMed

Affiliation: Key Laboratory of Micro Inertial Instruments and Advanced Navigation Technology of the Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China. xiadz_1999@163.com.

ABSTRACT
We present in this paper a novel fully decoupled silicon micromachined tri-axis linear vibratory gyroscope. The proposed gyroscope structure is highly symmetrical and can be limited to an area of about 8.5 mm × 8.5 mm. It can differentially detect three axes' angular velocities at the same time. By elaborately arranging different beams, anchors and sensing frames, the drive and sense modes are fully decoupled from each other. Moreover, the quadrature error correction and frequency tuning functions are taken into consideration in the structure design for all the sense modes. Since there exists an unwanted in-plane rotational mode, theoretical analysis is implemented to eliminate it. To accelerate the mode matching process, the particle swam optimization (PSO) algorithm is adopted and a frequency split of 149 Hz is first achieved by this method. Then, after two steps of manual adjustment of the springs' dimensions, the frequency gap is further decreased to 3 Hz. With the help of the finite element method (FEM) software ANSYS, the natural frequencies of drive, yaw, and pitch/roll modes are found to be 14,017 Hz, 14,018 Hz and 14,020 Hz, respectively. The cross-axis effect and scale factor of each mode are also simulated. All the simulation results are in good accordance with the theoretical analysis, which means the design is effective and worthy of further investigation on the integration of tri-axis accelerometers on the same single chip to form an inertial measurement unit.

No MeSH data available.


Analysis of the movement in yaw mode. (a) The resultant motion including the undesired rotational movement of the big frame. (b) The desired translational movement.
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sensors-15-16929-f006: Analysis of the movement in yaw mode. (a) The resultant motion including the undesired rotational movement of the big frame. (b) The desired translational movement.

Mentions: After defining the sizes of the frames in different modes, the dimensions of the springs numbered from 1 to 12 shown in Figure 1 should be further discussed and chosen for mode matching. At the beginning, the springs are chosen with their typical values and the structure is analyzed in ANSYS. It is found that the drive and pitch/roll modes can work well with the desired in-plane and out-of-plane translational movements, respectively. However, the yaw mode appears to be a resultant motion of the desired in-plane translational movement and undesired in-plane rotational movement around its center of mass as shown in Figure 6a. To avoid this undesired rotational motion, the dimensions of the springs which affect the yaw mode should be elaborately designed. The desired translational movement of yaw mode is shown in Figure 6b. Taking the rotational movement into consideration, the whole system in yaw mode can be simplified to be a 2-DOF motion system. In this case, the Lagrangian mechanics can be employed to analyze the system [20]. The generalized coordinates can be chosen to be x and θ, where x is the translational displacement of the big frame; θ is the rotational angle of the big frame around its center of mass. The Lagrange function of the 2-DOF system can be expressed as:(14)L=T1+T2+Ty−U7−2U8−2U4−2U9a−2U9b−2U6−2U10where T1 and T2 are the kinetic energies of big frame under translational movement and rotational movement respectively; Ty is the kinetic energy of yaw beam under translational movement; U7, U8, U4, U9a, U9b, U6, U10 are the elastic potential energies of the springs respectively; the coefficients of the elastic potential energies denote the number of different springs respectively.


Design and Analysis of a Novel Fully Decoupled Tri-axis Linear Vibratory Gyroscope with Matched Modes.

Xia D, Kong L, Gao H - Sensors (Basel) (2015)

Analysis of the movement in yaw mode. (a) The resultant motion including the undesired rotational movement of the big frame. (b) The desired translational movement.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4541915&req=5

sensors-15-16929-f006: Analysis of the movement in yaw mode. (a) The resultant motion including the undesired rotational movement of the big frame. (b) The desired translational movement.
Mentions: After defining the sizes of the frames in different modes, the dimensions of the springs numbered from 1 to 12 shown in Figure 1 should be further discussed and chosen for mode matching. At the beginning, the springs are chosen with their typical values and the structure is analyzed in ANSYS. It is found that the drive and pitch/roll modes can work well with the desired in-plane and out-of-plane translational movements, respectively. However, the yaw mode appears to be a resultant motion of the desired in-plane translational movement and undesired in-plane rotational movement around its center of mass as shown in Figure 6a. To avoid this undesired rotational motion, the dimensions of the springs which affect the yaw mode should be elaborately designed. The desired translational movement of yaw mode is shown in Figure 6b. Taking the rotational movement into consideration, the whole system in yaw mode can be simplified to be a 2-DOF motion system. In this case, the Lagrangian mechanics can be employed to analyze the system [20]. The generalized coordinates can be chosen to be x and θ, where x is the translational displacement of the big frame; θ is the rotational angle of the big frame around its center of mass. The Lagrange function of the 2-DOF system can be expressed as:(14)L=T1+T2+Ty−U7−2U8−2U4−2U9a−2U9b−2U6−2U10where T1 and T2 are the kinetic energies of big frame under translational movement and rotational movement respectively; Ty is the kinetic energy of yaw beam under translational movement; U7, U8, U4, U9a, U9b, U6, U10 are the elastic potential energies of the springs respectively; the coefficients of the elastic potential energies denote the number of different springs respectively.

Bottom Line: With the help of the finite element method (FEM) software ANSYS, the natural frequencies of drive, yaw, and pitch/roll modes are found to be 14,017 Hz, 14,018 Hz and 14,020 Hz, respectively.The cross-axis effect and scale factor of each mode are also simulated.All the simulation results are in good accordance with the theoretical analysis, which means the design is effective and worthy of further investigation on the integration of tri-axis accelerometers on the same single chip to form an inertial measurement unit.

View Article: PubMed Central - PubMed

Affiliation: Key Laboratory of Micro Inertial Instruments and Advanced Navigation Technology of the Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China. xiadz_1999@163.com.

ABSTRACT
We present in this paper a novel fully decoupled silicon micromachined tri-axis linear vibratory gyroscope. The proposed gyroscope structure is highly symmetrical and can be limited to an area of about 8.5 mm × 8.5 mm. It can differentially detect three axes' angular velocities at the same time. By elaborately arranging different beams, anchors and sensing frames, the drive and sense modes are fully decoupled from each other. Moreover, the quadrature error correction and frequency tuning functions are taken into consideration in the structure design for all the sense modes. Since there exists an unwanted in-plane rotational mode, theoretical analysis is implemented to eliminate it. To accelerate the mode matching process, the particle swam optimization (PSO) algorithm is adopted and a frequency split of 149 Hz is first achieved by this method. Then, after two steps of manual adjustment of the springs' dimensions, the frequency gap is further decreased to 3 Hz. With the help of the finite element method (FEM) software ANSYS, the natural frequencies of drive, yaw, and pitch/roll modes are found to be 14,017 Hz, 14,018 Hz and 14,020 Hz, respectively. The cross-axis effect and scale factor of each mode are also simulated. All the simulation results are in good accordance with the theoretical analysis, which means the design is effective and worthy of further investigation on the integration of tri-axis accelerometers on the same single chip to form an inertial measurement unit.

No MeSH data available.