One of the problems encountered by developers of inertial systems, such as gyroscopes and accelerometers, is the critical dependence of the eigenfrequencies of elastic suspensions (ES) on temperature when using substrates for sensors made of dielectric materials, such as borosilicate glass. The internal stresses arising in the ES caused by the difference in the temperature coefficients of linear expansion (TCLE) lead to deformation of the sensor and complication of the electronic part of the sensor. The purpose of this paper is to approach for in-plane and out-of-plane ES are considered that allow for minimization of the influence of internal stresses on eigenfrequencies.,Analytical, finite element and experimental results are considered. The temperature coefficient of thermal expansion, the Young’s modulus and the Poisson ratio are given as a function of temperature. The shape of the spring elements (SEs) and the construction of the elastic suspension are the main topics of focus in this study. The authors’ out-of-plane ES based on a meander-like spring element implemented via finite element modeling show good agreement with the experimental results.,Meander-like SEs have been developed that have lower temperature errors in comparison with traditional types of SEs. The main contribution to the change in the eigenfrequency from temperature is made by internal stresses that arose from the deformation of the bonded materials with different TCLE. The change of eigenfrequency from the temperatures that were calculated by finite element method did not exceed 0.15%, however, in practice, the scatter of the obtained characteristics for different samples showed a change of up to 0.3%.,This study shows a way to design and optimize the structure and theoretical background for the development of the microelectromechanical systems (MEMS) inertial module combining the functions of gyroscope and accelerometer. The obtained results will improve and expand the manufacturing technology of MEMS gyroscopes and accelerometers.

中文翻译：

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减少温度对弹簧悬架特征频率影响的建设性方法

惯性系统（例如陀螺仪和加速度计）的开发人员遇到的问题之一是，在使用由介电材料（例如硼硅酸盐玻璃）制成的传感器基板时，弹性悬架 (ES) 的特征频率对温度的关键依赖性。由线性膨胀温度系数 (TCLE) 的差异引起的 ES 中产生的内应力导致传感器变形和传感器电子部分的复杂化。本文的目的是考虑平面内和平面外 ES 的方法，以最大限度地减少内应力对特征频率的影响。考虑了分析、有限元和实验结果。热膨胀温度系数，杨氏模量和泊松比作为温度的函数给出。弹簧元件 (SE) 的形状和弹性悬架的构造是本研究的主要焦点。作者基于通过有限元建模实现的曲折状弹簧元件的平面外 ES 与实验结果非常吻合。, 与传统类型的 SE 相比，已经开发出具有更低温度误差的曲折状 SE . 由温度引起的特征频率变化的主要贡献是由具有不同 TCLE 的粘合材料变形引起的内应力造成的。通过有限元方法计算的温度的特征频率变化不超过 0.15%，然而，在实践中，不同样品所得特性的离散度变化高达0.3%。,本研究为结合陀螺仪功能的微机电系统(MEMS)惯性模块的开发提供了一种设计和优化结构和理论背景的方法和加速度计。获得的结果将改进和扩展MEMS陀螺仪和加速度计的制造技术。