Design and modeling of a novel translational and angular micro-electromechanical accelerometer

A continuous model is presented for a combined translational/angular micro capacitive accelerometer. New design includes two rectangular micro-beams, square shaped proof mass and four pairs of parallel capacitors, which are located in an appropriate construction. In order to find the transverse/torsional vibration effects of micro-beams on the proof mass, the Euler-Bernoulli beam theory is used to derive the governing partial differential equations of the problem which are then solved using modal analysis. Effects of squeeze film on the motion of the proof mass, including both spring and dissipative forces/moments, are considered using nonlinear isothermal Reynold's equation. Afterwards, these equations are solved using HPM method. Electrostatic forces/moments of capacitors are also included in the modeling analysis. Finally, the system of two second-order time-dependent differential equations is obtained. Appropriate formulation in order to correlate the output voltages of the system to the actual input accelerations is presented. Furthermore, output responses are precisely calibrated to form input accelerations. Results for different types of inputs are delineated as five case studies. Apart from transient part of the responses, the model predictions for both angular and translational accelerations show reasonably acceptable convergence with input accelerations of the system. Moreover, results revealed that for various combinations of input accelerations, the system presents reasonably accurate output predictions for each one.