An analytical method for calculating the natural frequencies of spatial compliant mechanisms. (September 2022) - Platl, Vivien; Zentner, Lena
Abstract: Compliant mechanisms are becoming increasingly important in both research and industry. The design and the static analysis of such mechanisms has made much progress in recent years, yet comparatively little research has been done on their dynamic behaviour. The aim of this paper is to advance the dynamic analysis of spatial compliant mechanisms by pursuing the calculation of their natural frequencies. So far, their determination is only possible with time-consuming 3D-FEM simulations or via pseudo-rigid-body models and Lagrangian equations. An analytical method is developed to simplify and accelerate the calculation of the natural frequencies of compliant mechanisms. The method is integrated into an algorithm on which a graphical user interface is developed to allow the design and calculation of the system in the most time efficient and intuitive way. The results are verified by 3D-FEM simulations and validated through an experiment. The evaluation shows good agreement with the reference models. The results of this paper allow a reliable and efficient calculation of natural frequencies and serve to facilitate further work regarding the dynamic analysis of compliant mechanisms. Highlights: Analytical method and algorithm for free vibration of spatial compliant mechanisms. Calculation tool for natural frequencies of spatial compliant mechanisms. Open source software to calculate eigenfrequencies of spatial compliant mechanisms. Transfer matrix method for fast calculation of spatial compliant mechanisms. Transfer matrix method based on Bernoulli-beams for eigenfrequency calculation.