Research On Thermoelastic Vibration Modeling For Disk Resonator Gyroscope

The disk resonator gyroscope(DRG)is a new type of solid-state wave gyroscopes,and it becomes the promising alternatives to currently available high-performance gy-roscopes due to its inherent benefits of accuracy,thermal stability,processing,electro-static tuning capability.The optimization of the geometrical parameters can signifi-cantly improve the key performance of the DRG.However,the vibration modal analysis for a DRG by a 3D FE model is computationally expensive due to its complex structure,so it is difficult to use the finite element model for full-parameter optimization.Fortu-nately,the thermoelastic vibration model can be used to rapidly evaluate the impact of variations in structural parameters on vibration characteristics,which can significantly shorten the optimization cycle of the MEMS structures.But the complex structure of DRG also lead to the absence of its thermoelastic vibration model.In this dissertation,the research of the DRG's thermoelastic vibration model is carried out.The researches on the vibration modeling and thermoelastic damping of MEMS resonators are reviewed in this dissertation.Then,the challenges of thermoelastic vi-bration modeling for the DRG are derived,namely,accurately solving two-dimensional thermal-mechanical coupling equations of complex structure;accurately predicting the wave transmission and reflection coefficients at the joints in a DRG;substantially im-proving the efficiency of the thermoelastic vibration model for the DRG.The target of this dissertation is to solve the above three difficulties in thermoelastic vibration modeling for DRG.(1)To establish a thermoelastic vibration modeling for complex structures,the thermoelastic ray tracing method(TERTM)is proposed,which can accurately solve the two-dimensional thermal-mechanical coupling equations of the complex structure and obtain displacement field and temperature field.In order to realize TERTM,the fol-lowing work needs to be carried out:establishing the thermo-mechanical coupling equa-tions of the waveguide component and factoring the two-dimensiona heat conduction equation;using the wave propagation theory to solve the thermo-mechanical coupling equations and establish the thermo-mechanical coupling wave equations;incorporating the thermo-mechanical coupling wave equations into the ray tracing method;establish-ing the thermoelastic vibration model(TEVM);presenting the process of modal analysis and forced response analysis of the TEVM;calculating the thermoelastic damping based on the TEVM.(2)To ensure the accuracy of TEVM for the DRG,the wave transmission and reflection coefficients in TEVM of the DRG need to be accurately calculated.Therefore,a novel C-joint is proposed to replace the conventional ring/beam junction.Based on the C-joint,the wave transmission and reflection coefficients between the rings and spoke can be accurately predicted,because no approximations or simplifications are introduced in the solution process.Meanwhile,the traditional point model is improved based on the TERTM.Then,the improved point model is used to calculate the wave reflection coefficients at the boundary and quantify the elastic wave and temperature wave generated by external excitation.Finally,to verify the soundness of the proposed model,a tentative vibration model for a double ring(the basic element of a DRG)is established by the RTM and compared with the 3D finite element(FE)model.The two models show excellent agreements in natural frequencies,thermoelastic damping,harmonic displacements and temperature field.(3)To improve the efficiency of TEVM for the DRG,the cyclic symmetry bound-ary,which is only applicable to a single physical field,is improved based on TERTM,and TEVM for the DRG is simplified by the improved cyclic symmetry boundary.Af-ter simplification,the number of the waveguide elements included in the TEVM for the DRG is reduced by 87.5%.Meanwhile,it is proved that the TEVM simplified by the improved cyclic symmetry boundary is equivalent to the original model.Then,the simplified TEVM is compressed into a finite double-stranded chain by the substructur-ing method which can reduces the number of circumferential waveguide components by half.Finally,the coupling of all sectors in the finite double-stranded chain can be modeled together into an overall transmission and reflection coefficient matrix by the recursive method,and the final TEVM for the DRG can be obtained.After three sim-plifications,the final TEVM only contains 4 waveguide elements,which means that the efficiency of the TEVM for the DRG is significantly improved.(4)To verify the accuracy and efficiency of the TEVM for the DRG,the TEVM is compared with the 3D FE model,and numerical experiments show that the differences between the resonant frequencies are less than 2.51%,and the differences between the thermoelastic damping are less than 3.50%.In addition,the harmonic displacements and temperature field calculated by the TEVM meet well with the 3D FE model.Then,the running time of modal analysis and the forced response analysis with the 3D FE models,the 2D FE models and the TEVM are calculated,and the results show that the running speed of the TEVM is tens times of that of the other two models.Finally,the structural parameters of the DRGs are rapidly optimized by the TEVM for the DRG.Based on the optimized DRG,the platemaking,processing,packaging,and testing are performed.The thermoelastic damping of operating modal for optimized DRG is decreased by 75%,which is no longer the dominant dissipation mechanism.Moreover,the operating modal becomes the first-order modal of the DRG,and other modals are far separated from the operating modal in the frequency domain.