Fully coupled MEMS gyroscope simulations with Quanscient Allsolve

Expert contributors for this post

Dr. -Ing.  Abhishek Deshmukh
Application Engineering Team Lead

Key takeaways

• MEMS gyroscopes are essential sensors for measuring angular velocity in applications like consumer electronics, automotive systems, and robotics.

• Simulating MEMS gyroscopes helps engineers understand key performance indicators such as eigenfrequencies and quality factors

• Quanscient Allsolve enables multiphysics simulations that capture mechanical, thermal, and damping phenomena in one environment

• The study explores how parameters such as beam width, proof-mass geometry, and ambient pressure influence drive and sense modes

• Combined damping effects, anchor loss, squeeze-film damping, and thermoelastic damping, can be simulated together to approach real-world performance

Introduction

Micro-electromechanical systems (MEMS) form the backbone of many modern devices, from smartphones and drones to vehicle stability systems and navigation equipment. Among them, MEMS gyroscopes are critical components for detecting angular velocity using the Coriolis effect. These sensors measure rotation by translating mechanical motion into electrical signals and are valued for their small size, low cost, and high precision.

Despite their ubiquity, MEMS gyroscopes are complex devices to design and optimize. Their performance depends on subtle mechanical and environmental factors, geometry, material properties, packaging, and air damping, all of which interact in nonlinear ways. Simulation plays a crucial role in understanding and optimizing these effects before fabrication.

The work presented here focuses on simulating a MEMS gyroscope based on a classical design developed at Draper Laboratory. The goal is to analyze its drive and sense modes, extract key performance indicators (KPIs) such as eigenfrequencies and quality factors, and demonstrate how engineers can iterate through design variations efficiently using Quanscient Allsolve.

What is value add with Quanscient Allsolve?

Quanscient Allsolve integrates mechanical, thermal, acoustic, and fluid effects in a single environment. For MEMS devices, this is particularly valuable because multiple damping and coupling phenomena interact simultaneously. Allsolve allows engineers to:

• Run full finite element simulations that incorporate multiple physical effects without manually coupling separate tools

• Conduct parametric studies and geometric sweeps efficiently in the cloud

• Extract key performance metrics such as eigenfrequencies and quality factors directly from the simulation results

• Combine damping effects, such as anchor loss, squeeze-film, and thermoelastic, into a unified simulation

The emphasis here is on accuracy and iteration speed. Instead of simulating a single static design, Allsolve enables users to explore many geometric and environmental variations quickly, making it a practical tool for real-world MEMS development.

Case example

MEMS gyroscope simulation

The case study focuses on a MEMS gyroscope structure inspired by an early Draper Laboratory design. The model represents a typical vibratory gyroscope with proof masses, beams, and comb electrodes. The goal is to study both drive mode (in-plane oscillation) and sense mode (out-of-plane oscillation induced by the Coriolis effect).

In a functioning device, the comb electrodes would apply an electrostatic drive force to sustain oscillation, while sense electrodes detect the resulting displacement. However, this study focuses on the mechanical domain only, no electrostatics are simulated, to isolate and understand the structural behavior and associated damping mechanisms.

Simulation objective

The main objective of the simulation is to perform eigenmode (modal) analysis to determine the natural frequencies and mode shapes for both the drive and sense modes of the MEMS gyroscope. This analysis provides insight into how the device behaves under excitation and how it responds to rotational motion in each vibration mode.

In addition, the study focuses on extracting key performance indicators (KPIs) such as eigenfrequencies and quality factors (Q factors) under varying design and environmental conditions. These metrics quantify the system’s energy losses, sensitivity, and operational bandwidth, offering a clear understanding of how different configurations influence overall performance.

The effect of changes in geometry and damping mechanisms on the gyroscope’s performance is also analyzed. Modifications in structural parameters, such as beam width or proof-mass hole size, directly impact the resonance frequencies and mode coupling. Similarly, damping mechanisms like anchor losses, squeeze-film damping, and thermoelastic damping determine how energy dissipates within the system and how the gyroscope maintains stability and sensitivity.

Finally, the combined impact of multiple damping mechanisms is investigated. In real-world operation, these effects coexist and interact, influencing the gyroscope’s sensitivity and bandwidth in complex ways. Fully coupled simulations that include all damping phenomena simultaneously provide the most realistic representation of device behavior and are essential for accurate performance prediction and optimization.

The broader modeling goal is to give designers the ability to iterate rapidly testing different designs, extracting performance metrics, and identifying the optimal geometry and operating conditions.

The model

The simulated MEMS gyroscope is composed of a proof mass suspended by beams anchored to a substrate. The structure includes comb electrodes fixed on the substrate, although their electrostatic effects are not modeled here. The mesh generated in Allsolve uses layered elements, which are well suited for thin, planar geometries typical of MEMS devices.

Two primary vibration modes are analyzed:

• Drive Mode: In-plane oscillation of the proof masses, where they move along the plane of the substrate.

• Sense Mode: Out-of-plane motion perpendicular to the substrate, induced by Coriolis forces when the gyroscope experiences rotation.

Each mode has its own resonant frequency and quality factor, both of which determine sensitivity and bandwidth. A high quality factor (Q) generally implies lower energy loss and higher sensitivity, while a lower Q allows broader bandwidth but reduced sensitivity.

Key results

Eigenmode and frequency analysis

Initial simulations identified distinct drive and sense modes with separate eigenfrequencies. These frequencies shift when key geometric parameters are modified.

Geometric parameter sweeps

Two geometric studies were performed:

• Etch-Hole Dimension Sweep: The square holes within the proof mass were varied. Increasing the hole size reduced the effective mass, pushing both mode frequencies higher.

• Beam Width Variation: The beam width on either side of the proof mass was varied. As beam width increased, the frequencies of drive and sense modes converged. This is often desirable because closer mode frequencies can enhance Coriolis coupling, improving sensitivity.

These parametric sweeps demonstrate how easily Allsolve handles geometry-driven KPI extraction. Designers can visualize how specific parameters influence system dynamics and choose trade-offs accordingly.

Anchor loss simulation

The gyroscope is anchored to the substrate, which in reality is not perfectly rigid. Some of the oscillation energy leaks from the anchors into the substrate, causing anchor losses. Simulations show that anchor losses can significantly reduce the Q factor, especially for the sense mode. In the studied geometry, the sense mode exhibited a Q factor several orders of magnitude lower than the drive mode due to greater energy leakage.

Drive mode | Freq: 39 kHz | Q-factor = 7.18834e+07

Sense mode | Freq: 47.76 kHz | Q-factor = 51262.4

Squeeze-film damping

When a MEMS gyroscope operates in air, a thin layer of air lies between the proof mass and the substrate. As the proof mass oscillates, this air film is compressed and released, dissipating energy, a phenomenon known as squeeze-film damping.

Simulations including this effect revealed:

• Q factors decrease as air pressure increases, reflecting stronger viscous damping.

• Squeeze-film damping dominates at low frequencies (in the kilohertz range).

• At high frequencies, viscous effects become negligible, and Q factors stabilize.

This insight helps designers select operating frequencies or packaging pressures to achieve desired bandwidth and sensitivity trade-offs.

Drive mode | Freq: 39 kHz | Q-factor = 23030.01

Sense mode | Freq: 47.76 kHz | Q-factor = 552.91

Controlled ambient pressure

By adjusting the pressure in the device package, it’s possible to tune the Q factor. A high Q factor corresponds to a narrower bandwidth, while lower Q provides a flatter frequency response and broader sensing range. This is a practical design knob for engineers: by controlling the packaging pressure, they can optimize the gyroscope for either high sensitivity or wide bandwidth.

Thermoelastic damping

Another important damping mechanism is thermoelastic damping (TED). Real materials expand and contract with temperature changes, dissipating mechanical energy as heat. For silicon, the common material in MEMS, its coefficient of thermal expansion varies with temperature, even becoming negative under certain conditions.

Simulations incorporating temperature-dependent thermal expansion revealed significant changes in Q factors over a wide temperature range (−60 °C to 120 °C). In low Earth orbit applications, where temperatures can fluctuate dramatically, this effect becomes critical. The study showed that both drive and sense mode Q factors can change by orders of magnitude depending on temperature, underscoring the need for thermomechanical simulations in early design stages.

Navarro, Pablo. (2022). Fine Tuning of a Directly Cooled Silicon Crystal for 0 Slope Errors. 10.13140/RG.2.2.18451.25127/1. 

Combined damping effects

In real-world devices, anchor losses, squeeze-film damping, and thermoelastic damping occur simultaneously. Allsolve enables fully coupled simulations where all these effects interact within a single model.

In the combined simulation (2.4 million degrees of freedom, solved in about 10 minutes using 21 core-hours), the following insights were obtained:

• Dominant Mechanism: Squeeze-film damping contributed the most to energy loss in both drive and sense modes at 100 Pa ambient pressure.

• Thermoelastic Contribution: Notable primarily in the drive mode.

• Anchor Loss: Still present but smaller compared to the viscous damping contribution.

A comparison between the fully coupled simulation and the traditional inverse-sum approximation (where Q factors from separate damping mechanisms are combined mathematically) revealed that the two approaches differ significantly.
For the drive mode, the coupled simulation predicted a Q factor nearly half that estimated from the inverse-sum method, while for the sense mode, it predicted a higher Q factor. This suggests interplay and partial compensation between damping mechanisms, effects that can only be captured by a fully coupled multiphysics simulation.

Drive mode | Freq: 39 kHz | Q-factor = 9867.36

Sense mode | Freq: 39 kHz | Q-factor = 716.51

Key benefits demonstrated

Rapid, high-fidelity analysis

The combined damping simulation with millions of degrees of freedom completed in minutes. This demonstrates that complex MEMS models can be solved efficiently in the cloud without compromising accuracy.

Parametric design exploration

Allsolve’s parametric tools allow engineers to perform geometric sweeps and visualize KPIs like frequency and Q factor in real time. This replaces manual, repetitive workflows with systematic exploration.

Accurate multiphysics coupling

The observed differences between fully coupled and simplified damping models show the importance of capturing real physical interactions. Engineers can rely on results that align more closely with experimental behavior.

Environmental and material insight

By including temperature-dependent material properties and environmental conditions like pressure, the simulation reflects true operating scenarios, from consumer electronics to aerospace environments.

Scalability and flexibility

The simulation setup scales easily for different geometries and parameter ranges, enabling efficient optimization loops or integration with reduced-order modeling workflows.

Other benefits of Quanscient Allsolve related to MEMS gyroscopes simulation

Beyond the gyroscope example, the same modeling approach can be extended to other MEMS devices such as resonators, microphones, and sensors. Allsolve’s core advantages for MEMS simulation include:

• Layered Mesh Generation: Efficient handling of thin-film geometries typical in MEMS manufacturing.

• Multiphysics Integration: Structural, thermal, and fluidic domains are solved together without external coupling scripts.

• Cloud Computation: Parallelized simulations allow high-resolution meshes and multiple design iterations without local hardware constraints.

• Reduced-Order Model (ROM) Compatibility: Simulation-derived KPIs (e.g., Q factors, frequencies) can feed into reduced-order models for large-scale design optimization.

• Design Iteration and Reproducibility: Consistent workflows and automated parametric studies help maintain reproducibility across design versions.

These features reduce the friction between concept and verification, letting engineers explore the design space thoroughly before fabrication.

Conclusion

This study of a MEMS gyroscope simulation demonstrates how Quanscient Allsolve enables a comprehensive understanding of device performance through full multiphysics analysis. Accurate eigenmode and damping analysis are crucial steps in optimizing MEMS gyroscopes, as they determine how the device responds to mechanical excitation and how energy is dissipated within the system.

The results show that geometric variations, such as changes in beam width or proof-mass hole size, have a direct impact on mode frequencies and coupling strength between the drive and sense modes. These parameters define how effectively the gyroscope converts mechanical motion into measurable signals.

In addition, environmental and packaging effects, including anchor losses, squeeze-film damping, and thermoelastic damping, play a significant role in determining the quality factor (Q) and overall sensitivity. Each of these damping mechanisms contributes differently under varying operating conditions, making their combined analysis essential.

By performing fully coupled simulations, Allsolve reveals the complex interactions between different damping effects that simplified or decoupled models fail to capture. This comprehensive approach ensures more accurate predictions of real-world behavior.

Finally, the high computational efficiency of Allsolve allows engineers to explore numerous design variations in a short period of time. This capability supports rapid iteration, making it practical to test and refine multiple design concepts until an optimal configuration is achieved.

The results demonstrate that realistic, combined-effect simulations are both feasible and informative. For MEMS designers, this approach bridges the gap between idealized models and real-world performance, allowing better understanding and optimization of devices before fabrication.

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