In this paper we present analytical expressions for determining the stiffness of cantilevers with fillets and tappers. We consider the unavoidable fillet due to the feature size limitation of lithography that rounds acute vertices, and the intentional tapper that is often used for reducing stress concentrations or can be used to reduce the effect of fillets. Previous compact models have not included the stiffness contributions from fillets. However, although fillets are small, they can measurably affect the performance of MEMS by affecting deflection or resonance frequency by their second most significant digit. We extend the well-known analytical beam model to include fillets. To our knowledge, this is the first analytical model of a filleted cantilever. In addition to the typical model parameters of beams, our model also includes process variation overcut and fillet radius of curvature, which are key parameters for MEMS designers. Our analytical solution is within 0.01% of finite element analysis.
A Compact Cantilever Model That Includes Fillets
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Chigullapalli, A, & Clark, JV. "A Compact Cantilever Model That Includes Fillets." Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition. Volume 9: Micro- and Nano-Systems Engineering and Packaging, Parts A and B. Houston, Texas, USA. November 9–15, 2012. pp. 221-230. ASME. https://doi.org/10.1115/IMECE2012-89214
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