Design of a MEMS Gyroscope, actuated by the pressure difference

1. Thermal Gyroscope
Study of Various MEMS Gyroscopes design, there advantages and Simulation of Thermal Gyroscope on COMSOL
Nemish Kanwar
2012A4PS305P
Akershit Agarwal
2012A4PS340P
Varun Prabodh Sharma
2012A4PS294P
Submitted to
Dr N N Sharma
11/16/2014

2. Table of Contents
1.
Abstract
2
2.
History
2
3.
MEMS Gyroscopes
4
4.
About Various MEMS Gyroscope Designs
4
5.
Application
8
6.
Principle
9
7.
Design
10-12
8.
Modification
13
9.
Model
14-16
10.
COMSOL Simulation Result
17-18
11.
Results
19-20
12.
Conclusion
20
13.
References
21
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3. Abstract
Gyroscopes are attracting a lot of research these days, and MEMS gyroscopes are expected to make a huge impact on the market in the near future. They have found automotive applications such as vehicle stability control, navigation assist, and roll-over detection in high-end cars, where cost is not a major factor. Examples of consumer applications are 3D input devices, robotics, platform stability, camcorder stabilization, virtual reality, and more. With cost prohibitive existing designs, new models must be studied.
This report is intended to study various existing MEMS gyroscope designs, and to propose a modified design simulation of the thermal gyroscope. COMSOL has been used to create the simplified model and to simulate the effects of angular rate on the pressure difference. Hence, the device’s sensitivity and applicability have been obtained. The study is not expected to be conclusive, since it is only for a particular design based on thermal principles, and further research is recommended.
A Brief History of Gyroscope
In order to discuss MEMS gyroscopes we must first understand gyroscopes in general and what role they play in science. Technically, a gyroscope is any device that can measure angular velocity. As early as the 1700s, spinning devices were being used for sea navigation in foggy conditions. The more traditional spinning gyroscope was invented in the early 1800s, and the French scientist Jean Bernard Leon Foucault coined the term gyroscope in 1852. In the late 1800s and early 1900ís gyroscopes were patented for use on ships. Around 1916, the gyroscope found use in aircraft where it is still commonly used today. Throughout the 20th century improvements were made on the spinning gyroscope. In the 1960s, optical gyroscopes using lasers were first introduced and soon found commercial success in aeronautics and military applications. In the last ten to fifteen years, MEMS gyroscopes have been introduced and advancements have been made to create mass-produced successful products with several advantages over traditional macro-scale devices.
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4. Traditional Gyroscopes
Usually, when one talks about gyroscopes, most people think of heavy spinning disks, tops or bicycle wheels. However, a number of devices are based on the gyroscope’s principle that look nothing like the mechanical gyroscope.
Gyroscopes function differently depending on their type. Traditional spinning gyroscopes work on the basis that a spinning object that is tilted perpendicularly to the direction of the spin will have a precession. The precession keeps the device oriented in a vertical direction so the angle relative to the reference surface can be measured.
Optical gyroscopes are most commonly ring laser gyroscopes. These devices send two lasers around a circular path in opposite directions. If the path spins, a phase shift can be detected since the speed of light always remain constant. Usually the rings are triangles or rectangles with mirrors at each corner. Optical gyroscopes are a great improvement to the spinning mass gyroscopes because there is no wear, greater reliability and smaller size and weight. 3

5. MEMS Gyroscopes
Even after the introduction of laser ring gyroscopes, a lot of properties were desired. MEMS vibrating mass gyroscopes aimed to create smaller, more sensitive devices. Many types of MEMS gyroscopes have appeared in the literature, with most falling into the categories of tuning-fork gyros, oscillating wheels, Foucault pendulums, and wine glass resonators. Conventional (non-MEMS) spinning wheel gyros are common, but levitation and rotation of a MEMS device with no springs has not yet been commercialized.
About Various MEMS Gyroscope Designs
1. Tuning Fork Gyroscopes
Tuning fork gyros contain a pair of masses that are driven to oscillate with equal amplitude but in opposite directions. When rotated, the Coriolis force creates an orthogonal vibration that can be sensed by a variety of mechanisms. The Draper Lab gyro uses comb-type structures to drive the tuning fork into resonance. 4

6. The first working prototype of the Draper Lab comb drive tuning fork gyro is shown here in an SEM image. Due to the superior mechanical properties of single-crystal silicon, a much better performance was achieved using single-crystal silicon with the dissolved wafer process.
Rotation causes the proof masses to vibrate out of plane, and this motion is sensed capacitively with a custom CMOS ASIC. The technology has been licensed to Rockwell, Boeing, Honeywell, and others.
The resonant modes of a MEMS inertial sensor are extremely important. In a gyro, there is typically a vibration mode that is driven and a second mode for output sensing. In some cases, the input and output modes are degenerate or nearly so. If the I/O modes are chosen such that they are separated by ~10%, the open-loop sensitivity will be increased due to the resonance effect. It is also critical that no other resonant modes be close to the I/O resonant frequencies.
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7. 6
2. Vibrating-Wheel Gyroscopes
Many reports of vibrating-wheel gyros also have been published. In this type of gyro, the wheel
is driven to vibrate about its axis of symmetry, and rotation about either in-plane axis results in
the wheel's tilting, a change that can be detected with capacitive electrodes under the wheel.
The vibrating wheel gyro made by Bosch Corp., with capacitive sensing under the wheel, can be
used to detect two in-plane rotational axes.
It is possible to sense two axes of rotation with a single vibrating wheel. A surface micro-machined
polysilicon vibrating wheel gyro has been designed at the U.C. Berkeley Sensors and
Actuators Center.
This polysilicon surface micro-machined vibrating wheel gyro was designed at the Berkeley
Sensors and Actuators Center. The potential for combining the mechanical resonator and sense
and drive electronics on a single chip permits extreme miniaturization.
3. Wine Glass Resonator Gyroscopes. A third type of gyro is
the wine glass resonator. Fabricated from fused silica, this device
is also known as a hemispherical resonant gyro. Researchers at
the University of Michigan have fabricated resonant-ring gyros in
planar form. In a wine glass gyro, the resonant ring is driven to
resonance and the positions of the nodal points

8. The Silicon Sensing Systems gyro is fabricated from single-crystal silicon with metal added for higher conductivity. This device measures 29 by 29 by 18 mm and is used to stabilize the Segway Human Transporter.
Analog Devices has been working on MEMS gyros for many years, and has patented several concepts based on modified tuning forks. The company has recently introduced the ADXRS family of integrated angular rate-sensing gyros, in which the mass is tethered to a polysilicon frame that allows it to resonate in only one direction. Capacitive silicon sensing elements inter- digitized with stationary silicon beams attached to the substrate measure the Coriolis-induced displacement of the resonating mass and its frame.
The iMEMS ADXRS angular rate-sensing gyro from Analog Devices integrates an angular rate sensor and signal processing electronics onto a single piece of silicon. Based on the Coriolis Effect, it’s very low noise output makes it a good choice for GPS receivers, where critical location information is required during temporary disruptions of GPS signals.
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9. These devices are based on a vibrating rod that is typically oriented out of the plane of the chip. They are therefore challenging to build with planar fabrication tools, but recent advances in MEMS technology allow very high aspect ratio MEMS that make it possible to fabricate the pendulum without hand assembly of the rod.
Application
• Space Orientation: The Oscillation can also be used and controlled in vibrating structure gyroscope for the positioning of spacecraft such as Cassini-Huygens
• Automotive: Automotive yaw rate sensors detect error in predicted yaw response in a car in conjunction with Steering wheel sensor. Advanced systems are able to detect rollover of a car
• Entertainment: Different gaming companies like Nintendo, Sony employ gyroscope to make controllers for providing good gaming experience to its customers
• Cameras: Image Stabilization System on Camera and Videos employ Vibratory Gyroscope
• Industrial Robotics: Vibrations in Robots are detected via MEMS gyroscopes, this helps robot to work with more precision
With gyros costing as little as $10.00 per sensed axis, they should soon claim a sizeable market share.
Summary
MEMS inertial sensing is an established industry, with performance-to-cost rapidly improving each year. Gyroscopes and angular accelerometers are entering the marketplace and will soon make many non-MEMS components obsolete. They should also open up new applications due to their small size and weight, modest power consumption and cost, and high reliability.
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10. Principle
The operating principle of the Thermal MEMS gyroscope is the deflection of a current of moving hot fluid by the Coriolis force. The Coriolis force refers to the appearance of an object in rectilinear motion being deflected from its course if observed from a rotating frame of reference. The Coriolis force is sometimes referred to as a “fictitious” force, since it disappears when the physics of the situation are described within an inertial frame of reference. 퐹푐표푟푖표푙푖푠=2푚(휔ሬሬ⃗×푉ሬ⃗)
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11. Design
In this device, 2 heaters are placed on the opposite side of device and are switched on/off alternatively. This creates an oscillating flow of fluid within the sensor, from Heater-On to Heater-Off. This flow is deflected in the y-direction due to Coriolis force which is directly proportional to x-velocity of fluid. Shown below is the plot of velocity vector represented by arrow 10

12. This deviation of air flow results in Temperature gradient between sensor 1 and sensor 2 as shown below
The temperature difference is plotted for different angular velocity of device 11

13. Periodically reversing the direction of air flow by changing the point of heat influx, helps cancel out the effect of linear acceleration, which needs to be filtered out to get pure rotation effect. In the device frame, the Coriolis force direction reverses when the velocity changes direction for same rotation-sense. If acceleration was linear and not a rotation, the temperature difference would not fluctuate in sign, and this difference can be noticed by the electronics in order to filter out the effect.
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14. Modification
• We have modified our model in terms of feasibility in the practical model. In the given model there was no inlet and outlet for the fluid which would continuously raise its temperature. Hence we have given an inlet and an outlet for the fluid.
• We have given constant velocity and removed the heaters.
• Instead of temperature sensors we are measuring the pressure difference using pressure sensors.
• Due to the rotation of the body the air is deflected on one side and we get a higher pressure on the side where it deflects and lower on the other side.
In this manner we can judge in which direction the body rotates.
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15. Our Model
For the simulation, a cubic volume of air was taken as the domain of study. The following model was made on COMSOL Multiphysics version 4.3:
Geometry
Units
Length unit
μm
Angular unit
deg
Materials
Air [gas] was taken as the material from the Material Browser inbuilt into COMSOL. This would be the easiest material to obtain when considering cost. 14

16. Properties of Material
Property
Material
Property Group
Density
Air [gas]
Basic
Dynamic Viscosity
Air [gas]
Basic
Laminar Flow was assumed, and the results confirmed that this was the right choice of physics.
Equations
These did not have to be modified, since the correct physics (laminar flow) was chosen.
Boundary Conditions
Inlet
Normal Inflow Velocity
1 μm/s
Outlet 15

17. Pressure
0 Pa
Volume Force
Coriolis force is a body-force or volume force, acting on each moving point in the non-inertial frame It acts in y direction for x direction velocity and z axis of rotation. Since this is not an inbuilt function, we had to apply the equation for coriolis force in the body-force section. We have negleced the y-velocity in the force calculation since it is much less than the x direction velocity, as observed in the simulation.
x
0
y
2*1.15[kg/m^3]*omega[1/s]*u
z
0
Mesh
Normal mesh has been used, with element size varying from 0.03 to 0.1micro-m
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18. COMSOL Simulation Results:
Velocity Distribution:
Evidently, the velocity profile is shifted towards the Coriolis force direction, as expected.
Line Graph
Corresponding points have been chosen on opposite ends of the block, in the y direction. Since the force direction is y, the pressure at the point of higher y is expected to be higher. The two pressures are measured, and knowledge of velocity and pressure-difference gives us the magnitude of rotational velocity at that instant.
X=0.5 y=0.01 z=0.5 = Blue
X=0.5 y=0.99 z=0.5 = Green
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19. The pressure difference increases linearly with increase in omega.
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20. Result
Line Plots at P1: x=0.5 y=0.01 z=0.5 P2: x=0.5 y=0.99 z=0.5
The following data was obtained from COMSOL (휔,푃푟푒푠푠푢푟푒 푎푡 푃1 푎푛푑 푃2)
1.00E+08
2.00E+08
3.00E+08
4.00E+08
5.00E+08
6.00E+08
7.00E+08
8.00E+08
9.00E+08
1.00E+09
8.74E-05
-4.62E-05
-1.72E-04
-2.90E-04
-3.97E-04
-4.91E-04
-5.70E-04
-6.28E-04
-6.60E-04
-6.58E-04
3.74E-04
5.25E-04
6.81E-04
8.42E-04
1.01E-03
1.18E-03
1.36E-03
1.55E-03
1.76E-03
1.97E-03
Using Matlab, The data Pressure difference was plotted for different angular velocity
And plot was also made for Omega v/s pressure difference and a correlation was found 19

21. Conclusion
Correlation between ω and ΔP was found out to be
ω=3.8e11*ΔP-2.3e7
The slope is too high, and the sensitivity is expected to be too low to be of practical importance. Apart from this, additional sensors will be required to correct for velocity fluctuations. This is likely to drive up the cost of the device. However, if the sensing method is changed, and an independent oscillation driving mechanism is added, the sensitivity can be made high enough to become practical. Cost cannot be estimated without solving these problems first. 20

22. References
1. Aaron Burg,Azeem Meruani,Bobsand Heinrich,Michael Wickmann, MEMS Gyroscope and there applications
2. Nilgoon Zarei, Thermal MEMS Gyroscope Design and Characteristics Analysis, B.Sc., Shiraz University, 2009
3. Rui Feng, Jamal Bahari, John Dewey Jones, Albert M. Leung, MEMS thermal gyroscope with self-compensation of the linear acceleration effect, Elsevier ,30 September, 2013
4. Steven Nasiri, A Critical Review of MEMS Gyroscopes Technology and Commercialization Status, 2013
5. History of the Gyroscope, http://www.gyroscopes.org/history.asp
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