A substrate energy dissipation mechanism in in-phase and anti-phase micromachined z-axis vibratory gyroscopes

This paper analyzes energy dissipation mechanisms in vacuum-operated in-phase and anti-phase actuated micromachined z-axis vibratory gyroscopes. The type of actuation is experimentally identified as the key factor to energy dissipation. For in-phase devices, dissipation through the die substrate is the dominant energy loss mechanism. This damping mechanism depends strongly on the die attachment method; rigid die attachment minimizes the loss of energy at the cost of reduced vibrational and stress isolation. For anti-phase actuated devices, dissipation through the substrate is suppressed and immunity to external vibrations is provided. However, even in anti-phase actuated devices fabrication imperfections introduce structural non-symmetry, enabling dissipation of energy through the die substrate due to momentum imbalance. Based on the experimental investigation, an analytical model for energy dissipation through the die substrate is proposed and used to study the effects of the actuation type, die attachment and fabrication imperfections. The limiting Q-factor for in-phase devices is generally below 20 × 103 while Q-factors much higher than 100 × 103 can be achieved with balanced anti-phase actuated gyroscopes. (Some figures in this article are in colour only in the electronic version)