Loading...

“Static and Dynamic Analysis of Vibrating Ring Gyroscopes based on the Strain Gradient Theory”

Karimzadeh, Ali | 2018

869 Viewed
  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 50835 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Ahmadian, Mohammad Taghi; Firoozbakhsh, Kikhosro; Rahaeifard, Massuod
  7. Abstract:
  8. Vibrating ring gyroscopes (VRG) as MEMS devices are employed to micro scale systems for determination of the rotation rate and rotation speed of them. It is experimentally approved that micro scale structures behaves differently in comparison to macro scale systems, Therefore higher order continuum theories are required for modeling and analysis of these systems. In addition to that there is no comprehensive investigation on the dynamic performance of ring gyroscopes in the literature, In view of this in the present research the static and dynamic analysis of vibrating ring gyroscopes based on the strain gradient theory and the proposed finite element model of the gyroscope is performed. The governing equations of motion of extensional and in-extensional micro-rings based on the Euler-Bernoulli and Timoshenko beam theories are derived.Utilizing the Galerkin method, the finite element model of micro-rings, rotating rings and ring gyroscopes (ring with eight stiffeners embedded inside the ring) are implemented. Results indicate that based on the strain gradient theory when the ring thickness is in order of material length scale parameter the system becomes stiffer, hence the resonant frequency of the system is significantly higher than the classical theory. Comparing the presented analytical and numerical frequencies of rotating ring shows excellent agreement between them and the previously reported experiments. Utilizing the proposed complete finite element model of the gyroscope, the static behavior and natural frequencies of the system under electrostatic DC voltage are investigated. Results indicate that the obtained mode shapes are slightly different from the mode shapes previously reported in the literature. Two different orientations for the actuation electrodes of the micro-ring gyroscope (namely one electrode in direction and two electrodes in & direction) are considered. Results reveals that static deflection is higher and pull-in phenomena take place under lower voltage for & orientation of electrodes in comparison with orientation. In addition to that the frequency split occurs in higher voltages for & orientation.Implementing a hybrid finite element-finite difference method, the dynamic behavior of the ring gyroscope reveals that angular velocity affects the vibrational behavior of the gyroscope and it should be kept low enough in order not to change the device behavior ( ). The AC voltage frequency and amplitude should be large enough to precisely capture the angular velocity and small enough in order that the gyroscope operates in linear working range. Therefore in this research an appropriate work range is inquired and proposed for the ring gyroscopes in which the device operates in linear zone and the sense response is measurable. Finally using the Rayleigh-Ritz method a simpler model of vibrating ring gyroscope is presented and compared with FEM model. Good agreement shows that for simpler investigations, this simpler model is applicable
  9. Keywords:
  10. Finite Element Modeling ; Strain Gradient Theory ; Static Analysis ; Dynamic Behavior ; Microgyroscope ; Electrostatic Voltage

 Digital Object List