Microelectromechanical systems (MEMS) gyroscopes are widely used in consumer and automotive applications. They have to fulfill a vast number of product requirements which lead to complex mechanical designs of the resonating structure. Arriving at a final design is a cumbersome process that relies heavily on human experience in conjunction with design optimization methods. In this work, we apply node-based shape optimization to the design of a MEMS gyroscope. For that purpose, we parametrize the coordinates of the nodes of the finite element method (FEM) mesh that discretize the shapes of the springs. We then implement the gradients of the mechanical eigenfrequencies and typical MEMS manufacturability constraints, with respect to the design parameters, in a FEM code. Using gradient-based optimization we tune the gyroscope's frequency split and shift spurious modes away from the first three multiples of the gyroscope's drive frequency while manufacturability constraints are fulfilled. The resulting optimized design exhibits novel geometrical shapes which defy any human intuition. Overall, we demonstrate that shape optimization can not only solve optimization problems in MEMS design without required human intervention, but also explores geometry solutions which can otherwise not be addressed. In this way, node-based shape optimization opens up a much larger space of possible design solutions, which is crucial for facing the ever increasing product requirements. Our approach is generic and applicable to many other types of MEMS resonators.

翻译：微机电系统（MEMS）陀螺仪广泛应用于消费电子和汽车领域。它们必须满足大量的产品要求，这导致了谐振结构复杂的机械设计。达成最终设计是一个繁琐的过程，严重依赖于人工经验并结合设计优化方法。在本工作中，我们将基于节点的形状优化应用于MEMS陀螺仪的设计。为此，我们对离散化弹簧形状的有限元法（FEM）网格节点坐标进行参数化。随后，我们在FEM代码中实现了机械特征频率及典型MEMS可制造性约束相对于设计参数的梯度计算。通过基于梯度的优化方法，我们在满足可制造性约束的同时，调整了陀螺仪的频率分裂，并将杂散模态移离陀螺仪驱动频率的前三倍频。最终得到的优化设计呈现出违背人类直觉的新颖几何形状。总体而言，我们证明了形状优化不仅能够在无需人工干预的情况下解决MEMS设计中的优化问题，还能探索其他方法无法处理的几何解决方案。通过这种方式，基于节点的形状优化开辟了更大的可能设计解空间，这对于应对日益增长的产品要求至关重要。我们的方法具有通用性，可应用于许多其他类型的MEMS谐振器。