College of Mechanical Engineering and Automation, National University of Defense Technology, Changsha, Hunan Province, 410073, China.
Sensors (Basel). 2011;11(1):296-309. doi: 10.3390/s110100296. Epub 2010 Dec 29.
It is reported in the published literature that the resonant frequency of a silicon micromachined gyroscope decreases linearly with increasing temperature. However, when the axial force is considerable, the resonant frequency might increase as the temperature increases. The axial force is mainly induced by thermal stress due to the mismatch between the thermal expansion coefficients of the structure and substrate. In this paper, two types of micromachined suspended vibratory gyroscopes with slanted beams were proposed to evaluate the effect of the axial force. One type was suspended with a clamped-free (C-F) beam and the other one was suspended with a clamped-clamped (C-C) beam. Their drive modes are the bending of the slanted beam, and their sense modes are the torsion of the slanted beam. The relationships between the resonant frequencies of the two types were developed. The prototypes were packaged by vacuum under 0.1 mbar and an analytical solution for the axial force effect on the resonant frequency was obtained. The temperature dependent performances of the operated mode responses of the micromachined gyroscopes were measured. The experimental values of the temperature coefficients of resonant frequencies (TCF) due to axial force were 101.5 ppm/°C for the drive mode and 21.6 ppm/°C for the sense mode. The axial force has a great influence on the modal frequency of the micromachined gyroscopes suspended with a C-C beam, especially for the flexure mode. The quality factors of the operated modes decreased with increasing temperature, and changed drastically when the micromachined gyroscopes worked at higher temperatures.
据已发表的文献报道，硅微机械陀螺的谐振频率随温度升高呈线性下降。然而，当轴向力较大时，谐振频率可能会随温度升高而升高。轴向力主要是由结构和衬底热膨胀系数不匹配引起的热应力引起的。本文提出了两种带有倾斜梁的微机械悬浮振动陀螺，以评估轴向力的影响。一种采用自由端固定（C-F）梁悬浮，另一种采用两端固定（C-C）梁悬浮。它们的驱动模态是倾斜梁的弯曲，传感模态是倾斜梁的扭转。建立了两种类型的微机械陀螺的谐振频率之间的关系。采用 0.1 毫巴的真空对原型进行封装，并获得了轴向力对谐振频率影响的解析解。测量了微机械陀螺工作模态响应的温度相关性能。由于轴向力引起的谐振频率温度系数（TCF）的实验值为驱动模态的 101.5 ppm/°C 和传感模态的 21.6 ppm/°C。轴向力对采用 C-C 梁悬浮的微机械陀螺模态频率有很大影响，特别是对弯曲模态。工作模态的品质因数随温度升高而降低，当微机械陀螺在较高温度下工作时，其变化很大。
