Nonlinear Dynamical System Model for Drive Mode Amplitude Instabilities in MEMS Gyroscopes

Abstract

The requirements pertaining to the reliability and accuracy of micro-electromechanical gyroscopic sensors are increasing, as systems for vehicle localization emerge as an enabling factor for autonomous driving. Since micro-electromechanical systems (MEMS) became a mature technology, the modelling techniques used for predicting their behaviour expanded from mostly linear approaches to include nonlinear dynamic effects. This leads to an increased understanding of the various nonlinear phenomena that limit the performance of MEMS sensors. In this work, we develop a model of two nonlinearly coupled mechanical modes and employ it to explain measured drive mode instabilities in MEMS gyroscopes. Due to 3:1 internal resonance between the drive mode and a parasitic mode, energy transfer within the conservative system occurs. From measurements of amplitude response curves showing hysteresis effects, we extract all nonlinear system parameters and conclude that the steadystate model needs to be expanded by a transient simulation in order to fully explain the measured system behaviour.2019 IEEE.Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Validating the Critical Point of Spontaneous Parametric Downconversion for Over 600 Scanning MEMS Micromirrors on Wafer Level

“…Our model for the critical amplitude given in equation ( 6) can be applied to any oscillatory MEMS sensor or actuator with a fitting frequency match that also fulfils the conditions of separable fast and slow time scales as well as high quality factors. Here, similar coupling mechanisms for resonant systems, such as four-wave mixing or three-wave mixing effects of different origins are also conceivable [25]. Due to the versatility of the developed method, it can also be applied to high-Q oscillatory systems outside of the MEMS domain.…”

Thermoelastic damping in MEMS gyroscopes at high frequencies

“…Therefore, a positive ∆f allows to obtain mode-matched operation despite process tolerances. Furthermore, shifting the eigenfrequencies of the spurious modes away from 1f drv , 2f drv and 3f drv avoids internal resonances which can deteriorate the sensor's performance (Nabholz et al, 2019). Mathematically the optimization problem is written as…”

“…Especially in automotive applications, where gyroscopes operate in safetycritical systems, device reliability is of utmost importance. Functionality has to be ensured under various harsh environmental conditions 3 and the sensor signal stability has to be maintained despite many adverse linear and nonlinear effects 4,5 . Most importantly, sensors have to withstand temperatures ranging from −40 ∘ C to +120 ∘ C and should be insensitive against external vibrations 2 .…”

Thermoelastic Damping in MEMS Gyroscopes at High Frequencies

“…Especially in automotive applications, where gyroscopes operate in safety-critical systems, device reliability is of utmost importance. Functionality has to be ensured under various harsh environmental conditions [3] and the sensor signal stability has to be maintained despite many adverse linear and nonlinear effects [4,5]. Most importantly, sensors have to withstand temperatures ranging from −40 °C to 120 °C and should be insensitive against external vibrations [2].…”