  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 steady-state model needs to be expanded by a transient simulation in
order to fully explain the measured system behaviour.
