تجزیه و تحلیل حساسیت پارامتر ساختاری شتاب سنج های از نوع معلق و پل

The paper deals with the analytical estimation of bandwidth and device sensitivity of cantilever- and bridge-type monolithic piezoresistive and capacitive accelerometers using different beam models and of their design sensitivity due to the change of geometrical parameters. Using a simplified two-beams model, closed-form formulae have been derived to give the relationship between the rates of length, width and thickness of the beams and the lowest eigenfrequency characterizing the bandwidth as well as the physical sensitivity of the accelerometers. By means of symbolic derivation, a structural design sensitivity analysis has been carried out to obtain information for the optimal selection of the geometrical parameters.

Silicon-based accelerometers are typical monolithic sensors [1]. Its simplest form consists of a thin cantilever carrying a large seismic mass (Fig. 1). The view of the cross-section shows the cantilever fixed on its left end. The right end is free — the edge of the frame (as thin line) is beyond the cantilever. It is also possible to suspend the mass from both sides as a bridge (Fig. 2). Both configurations can be used for measuring acceleration. Full-size image (6 K) Fig. 1. Cantilever-type accelerometer. Figure options Full-size image (6 K) Fig. 2. Bridge-type accelerometer. Figure options In piezoresistive sensors, the piezoresistive element is formed in the cantilever or in the bridge. The bandwidth of an accelerometer is given by its first (lowest) natural frequency. The higher is the first natural frequency, the highest signal frequency can be measured. Damping effects are neglected. In real elastic structures, damping slightly diminishes the natural frequency and hinders an infinite amplitude in resonance cases. The device sensitivity is defined as the relative change of resistance per unit of acceleration g equation(1) where ΔR/R=Kε. The factor K depends on the orientation of the piezoresistor relative to the crystal and its doping level, while the strain ε is linear function of the stresses. In most cases of MEMS, the main contribution is the normal direction, therefore ε can be approximated by the σm, normal stress in the place of the piezoresistive element equation(2) where E is the Young’s-modulus of the material. Combining and , and introducing Kp=K/E, the physical sensitivity of the device is equation(3) which means that the device sensitivity of a piezoresistive accelerometer is proportional to the normal stress in the place of the piezoresistor. In capacitive accelerometers, one-plate of the capacitor is stationary, i.e. connected to the housing and the other plate is attached to the seismic mass. Due to acceleration, the mass deflects, consequently changing the distance between the two-plates. In analogy to the piezoresistive sensor, the sensitivity S is defined as the relative change of capacitance per unit of acceleration equation(4) where C=ε0A/d0 is the rest capacitance (when no input signal is applied) and ΔC=C′−C, a nonlinear function, since the capacitance C′ is inversely proportional to the distance between the electrodes. For bridge-type sensors equation(5) where ε0 is the free-space permittivity, d0 the gap at rest between the plates, and zm the vertical deflection of the middle of the movable capacitor plate. Thus, using Δd=d0−zm, the device sensitivity of a capacitive sensor is equation(6) The aim of structural design in several applications is to achieve large bandwidth and high sensitivity of the sensor. A correctly designed accelerometer should have large bandwidth ensuring a large range of flat frequency response [2].

Structural parameter sensitivity analysis has been carried out to investigate the effect of dimension changes on the bandwidth and device sensitivity of cantilever- and bridge-type accelerometers. The device has been modeled by two-elastic beams. Using Rayleigh’s energy principle, estimation for the lowest natural frequency could be obtained making possible the analytical parameter sensitivity analysis. The selection of geometrical parameters has opposite effects on bandwidth and device sensitivity. The study of their rate functions show that high device sensitivity can be achieved by selecting large width and thickness ratios of the seismic mass over the bridge once an appropriate length ratio has been determined ensuring the minimum necessary bandwidth.