Modeling MEMS accelerometer anchor velocity during package drop with a discrete impact model and a transfer function

Abstract

During everyday use, devices containing MEMS sensors (e.g., smartphones, watches, drones, cars) are accidentally dropped, impacted or endure shocks from the environment. However, as they can hardly be repaired or replaced, impact resistance should be ensured during the entire life-cycle of the sensor.

The simplest drop impact case is the so-called package drop, that is, the sensor package falling on a floor. It is usually modeled with explicit finite element method (FEM) because of the complex geometry of the package and the various materials it includes. While an analytical model encompassing package effects is elusive, a discrete model with parameters fitted to FEM results is presented.

The proposed model consists of two parts: an impact model gives the velocity of the package center of gravity, while a discrete transfer function turns it into an anchor velocity estimate. This in turn can be used as a kinematic constraint in an FEM simulation of the sensor structure, to evaluate its impact robustness. It is shown that a two degrees-of-freedom Kelvin–Voigt impact model with additional spring can adequately model the package drop for reasonable drop heights. Moreover, the transfer function gives an estimation of the anchor movement that fits the FEM solutions with $R^2>0.75$ for different drop heights and floor materials, while having a computational time of less than a second instead of hours.