Natural frequency and frequency response are two important indicators for the performances of resonant microelectromechanical systems (MEMS) devices. This paper analytically and numerically investigates the vibration identification of the primary resonance of one type of folded-MEMS comb drive resonator. The governing equation of motion, considering structure and electrostatic nonlinearities, is firstly introduced. To overcome the shortcoming of frequency assumption in the literature, an improved theoretical solution procedure combined with the method of multiple scales and the homotopy concept is applied for primary resonance solutions in which frequency shift due to DC voltage is thoroughly considered. Through theoretical predictions and numerical results via the finite difference method and fourth-order Runge-Kutta simulation, we find that the primary frequency response actually includes low and high-energy branches when AC excitation is small enough. As AC excitation increases to a certain value, both branches intersect with each other. Then, based on the variation properties of frequency response branches, hardening and softening bending, and the ideal estimation of dynamic pull-in instability, a zoning diagram depicting extreme vibration amplitude versus DC voltage is then obtained that separates the dynamic response into five regions. Excellent agreements between the theoretical predictions and simulation results illustrate the effectiveness of the analyses.
To realize high efficiency, low/no damage and high precision machining of tungsten carbide used for lens mold, a high frequency ultrasonic vibration cutting system was developed at first. Then, tungsten carbide was precisely machined with a polycrystalline diamond (PCD) tool assisted by the self-developed high frequency ultrasonic vibration cutting system. Tool wear mechanism was investigated in ductile regime machining of tungsten carbide. The cutter back-off phenomenon in the process was analyzed. The subsequent experimental results of ultra-precision machining with a single crystal diamond tool showed that: under the condition of high frequency ultrasonic vibration cutting, nano-scale surface roughness can be obtained by the diamond tool with smaller tip radius and no defects like those of ground surface were found on the machined surface. Tool wear mechanisms of the single crystal diamond tool are mainly abrasive wear and micro-chipping. To solve the problem, a method of inclined ultrasonic vibration cutting with negative rake angle was put forward according to force analysis, which can further reduce tool wear and roughness of the machined surface. The investigation was important to high efficiency and quality ultra-precision machining of tungsten carbide.
This paper attempts to qualitatively identify the static pull-in position, pull-in voltage, and fundamental frequency of one-electrode microresonators from a physical perspective. During theoretical derivation, a generalized one-degree-of-freedom (1-DOF) model in nondimensional form derived using the differential quadrature method (DQM) is first introduced and then transformed for frequency normalization. Based on the deduced formulas, the upper and lower bounds of the static pull-in position and pull-in voltage are both deduced through mathematical proof. To distinguish the monotonic and nonmonotonic behavior of the fundamental frequency versus direct current (DC) voltage, a critical condition decided only by cubic stiffness is then determined. For the first time, two extreme static positions, as well as the corresponding fundamental frequencies and DC voltages to identify different frequency behaviors are derived, and their variations versus cubic stiffness are then discussed and verified. During the simulation process, a high-order DQM and COMSOL 2D model are both applied for numerical analyses. Guided by nondimensional results, typical behaviors with specific physical parameters are examined in detail. Results demonstrate that the curve tendencies between all the qualitative results and quantitative numerical simulations in dimensional form agree well with each other, implying the possibility of using 1-DOF model to qualitatively discuss physical parameters effects on the system statics and dynamics.
To resolve the problem of lacking tools to sustain the Top-Down decomposition of parameters and multi-level parametric drive modeling based on skeleton, the technology of product multi-level parametric design is put forward. This technology takes product control parameters and constraint relationships as the core. The technology of product decomposition modeling is studied to obtain the control parameters and constraint relationships. The product multi level parametric skeleton modeling technology is studied to obtain skeleton constraint model based on the technology of product decomposition modeling. A new product instance can be obtained rapidly by changing control parameters of the skeleton constraint model.
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