Microsystems Technology based inertial sensors offer important advantages in low-invasive measurement of spatial motion with sub-micron accuracy. Their successful implementation hinges upon achieving very low distortion and noise at the low end of the frequency spectrum. Of particular importance is the Vibration Rectification Error (VRE) — an apparent shift in the signal bias that occurs when inertial sensors are subjected to vibration. A common approach to the reduction of VRE is assuring a highly symmetrical mechanical structure of sensors. Furthermore, a low cross-axis sensitivity is desirable. In accelerometers these properties are achieved by employing multiple flexures supporting the seismic mass. However, this may lead to mechanical over-constraining and multiple local equilibria rather than a single global one. Multiple equilibria combined with the nonlinearity of flexures create conditions for chaotic behavior, which can greatly degrade the sensors’ performance. We investigate representative architectures of high performance servo accelerometers, study the impact of over-constraining, and develop comprehensive dynamic models accounting for the presence of this condition. Given the complexity of spatial motion of the proof mass and resulting deformations in the flexures, we employ computer aided generation of constitutive, symbolic and scaleable models of the investigated sensors. We illustrate analytical investigations with numerical simulations and experimental results.
Stochastic dynamic models and Chebyshev splines