Constructive approach to reduce the influence of temperature on spring suspension eigenfrequencies

Purpose: 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. Design/methodology/approach: 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. Findings: 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%. Originality/value: 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.