CHAPTER 6 CONCLUSION
6.1 Summary of the Research
Through the recent designs for the micromachined accelerometer and the vibrating gyroscope, the capacitive type accelerometer and vibrating ring gyroscope are high potential to be integrated not only for similar structure but the compatible driving and detecting schema.
In theory, the Coriolis force induced by rotation and transportation speed in the rotation frame. By setting the speed, the induced Coriolis force proportionally indicates the rotation rate. Setting the rotation rate to measure the transportation speed is not suitable for microstructure because it is relatively complicated to make a micro rotating structure.
The vibration of a ring can be decoupled into several modes. With proper design of structural size, the first mode and second mode can properly indicates the linear acceleration and rotation rate. Considering the symmetry of support, asymmetry supports is difficult to be analyzed by using simple coordinates. Even under symmetrical arrangement connected to the main ring, it still affects the vibration under acceleration.
Rotational symmetry and mirror symmetry are both required for the structural design.
A simple concept of impedance helps to calculate the natural frequency of the structure, and the corresponding modes are obtained by finite element analysis. The errors between these results are less than 5%.
The drift of natural frequency caused by applying force is slight for microstructure.
The structural design leads to mixed signal contains acceleration and rotation signals. Four loops are required for the detection circuits. The phase locked loop is merged into the driving circuit to obtain high quality factor, and it is useful for determine the damping ratio and the undamped natural frequency of the structure. It is also necessary for detecting rotation rate. Using force-to-rebalance mode of detection could eliminate those noise caused by the different natural frequencies of two vibrating axes. Setting high feedback loop gain helps to eliminate the theoretical error caused by angular acceleration.
The structure is fabricated by using silicon deep etching and anodic bonding technologies. Three sets of process are developed and compared for eliminating the aspect ratio dependent effect that always found after deep silicon etching. Some undesired bonding was found after anodic bonding process. It is possible caused by the strong electrostatic force during the bonding process, and adding an inter layer of metal between the structure and glass substrate eliminates this effect. The primary manufacturing error is the over-etching during deep silicon etching. The sensitivity analysis shows the worst case of the downgrade sensor characteristic is S/N ratio falls to around one-fifth of the designed value.
The applying of anodic bonding also provides a method for the sensor package.
The preliminary test shows that the natural frequency decreases to around 19kHz, which follows the estimation of sensitivities. The electrical test to the structure shows that the fabrication result follows the design in general. However, the existence of large internal resistance may dramatically affect the detected signal. Redesigned the proper interface circuit will greatly improve the sensor performance.
In summary, this dissertation has discussed the development of a micro sensor detecting both linear acceleration and rotation rate. The structural design, electronics analysis, and fabrication are presented. The preliminary test shows that the sensor is highly feasible to be carried out by using micromachining technology.
6.2 Potential Improvement to the Design
For the structural design, the radial vibration along with the primary axis may induce the tangential vibration along with the secondary axis. It may cause undesired quadrature signal to the detection circuit. The possible way is to design a support to transmit only the radial displacement.
The existence of large internal resistance of the structure may seriously affect signal detection of the interface circuit. One possible way is to change the material of the structure. The other way is to design switched capacitor circuit suitable for the structure.
Vertical thin wall structure is manufactured according to the structural and electrical design. Owing to the fabrication difficulty in making deep trench, applying comb appears to offer great potential of improvement.
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Primary Mode
Secondary Mode
x
z y
Figure 2.1 Vibrating beam gyroscope.
y x
z
Ω
Driving vibration Sensing vibration
Ω
Angular rate Figure 2.2 Tuning fork gyroscope.y
proof mass
Ω
x z
Driving vibration Sensing vibration
Ω
Angular rate Figure 2.3 Dual accelerometer gyroscope.Ω
Figure 2.4 Double gimbals vibrating gyroscope.
Input Rotation Drive
Mode Sense
Mode
Figure 2.5 Schematic diagram for z-axis vibrating gyroscope.
Figure 2.6 Z-axis vibrating gyroscope.
z
Tilting mode
Ω
y x
Rotary mode
Driving vibration Sensing vibration
Ω
Angular rate Fixed axisFigure 2.7 Schematic diagram for x-axis vibrating gyroscope.
Figure 2.8 X-axis vibrating gyroscope.
Figure 2.9 Schematic diagram for dual-axis vibrating gyroscope.
Figure 2.10 Dual-axis vibrating gyroscope.
Figure 2.11 Poly-silicon vibrating ring gyroscope (PRG).
Figure 2.12 Vibrating ring gyroscope (Si-VSG).
(a)
(b)
Figure 2.13 Simple pendulum and its projection on: (a) fixed frame; (b) rotating frame.
Moving velocity V
(a) Moving path
Projection
Vy Vx y
x
(b)
Figure 2.14 (a) A particle moves above a rotating frame; (b) the path projection on the rotating frame.
y
Ω
x
r P
P’
V
F
∆r
Figure 2.15 The frame rotates counterclockwise and a particle P moves on it with velocity.
O
X
Y o
Ω
z r R0
R Z
P
y
x
Figure 2.16 The position vector of a point P relative to a rotating system.
y
Ω
F
V
(a)
Ω
M0 M
(b)
Precession axis
ω
Couple axis
Spin axis
ω
z Vx
F
Figure 2.17 (a) The Coriolis force on a rotating disk; (b) the steady precession of a gyroscope.
x y
x y
θ r
v u
(a)
y
x
(b)
x y
(c)
x y
(d)
(e) (f)
y
x
Figure 3.1 (a) The radial displacement u and tangential displacement v for the circular ring; (b) n=0; (c) n=1; (d) n=2; (e) n=3; (f) n=4.
a2
b2
θ 2
2sin b
r+
θ 2
2cos a
r+
(a)
0o
Ω V
(b)
45o
Ω
Coriolis
F
(c)
Figure 3.2 (a) The 2nd mode vibration shapes and its generalized coordinates; (b) the primary mode on 0 degree axis; (c) the secondary
mode result from Coriolis force on 45 degree axis.
Z
Translating and Rotating Coordinate
Figure 3.3 Coordinate system of the sensor.
(b) First mode of vibration
(associated with linear acceleration)
Second mode of vibration (associated with rotation) Original position
Figure 3.4 Motion of the ring, comprising first and second modes of vibration.
a2
(a)
45o
(b)
Figure 3.5 Supports arrangement (a) four supports; (b) eight supports.
Deformed shape
ar
Original shape
(a)
Original shape
Fr
Force response
(b)
Figure 3.6 (a) Structural deformed due to linear acceleration along x-axis;
(b) force response for the force applied at one point positive to x-axis.
45o
Full ring type support Main vibrating ring
Figure 3.7 The vibrating ring gyroscope with symmetry support and symmetry arrangement.
b2
a2
(a) (b)
+Y
-X +X
-Y (c) (d)
Figure 3.8. (a)(b)Scheme for detecting rotation of gyroscope; (c)(d) scheme for detecting linear acceleration of accelerometer.
(a)
(b)
Figure 3.9 Finite element analysis: (a) the part of the structure modeled by quadrilateral shell elements and (b) full view of the meshed structure.
(a) 13628Hz (b) 13651Hz
(c) 22823Hz (d) 43615Hz
Figure 3.10 Mode shape of the structure (a) rotation mode; (b) plane motion mode; (c) 2nd vibration mode; (d) 3rd vibration mode.
Support Ring
Electrode
A’
A Main
Ring
(a)
Support Ring
Electrode
Capacitance
(b)
Figure 4.1 (a) Top view of structure with electrode; (b) detail view of support with electrode.
unreasonable
unstable
2 2
d AV Felectrostatic = −ε
kx F =
stable
d F
Figure 4.2 Intersects of electrostatic force and structure rebalance force.
C C0 +∆
Z
V i Vout
Figure 4.3 The variable capacitor connected to the detection circuit represented by an impedance.
Vi
Vo
(a)
(b)
Figure 4.4 (a) Schematic diagram for detection scheme; (b) output voltage plot for 1n farad (line 1) and 1p farad (line 2).
(a)
(b)
Figure 4.5 (a) Output voltage plot for variable capacitance C2; (b) schematic diagram for detection with stray capacitance.
φ
C2
C1 φ
φ Vi
Vo
2 1 C V C Vo =− i
(a)
φ
φ C2
C1
φ φ
φ Vi
Vo
(b)
Figure 4.6 (a) Basic circuit for switched-capacitor; (b) stray-insensitive design.
C C+∆
R
∆V Vi
(a)
C C+∆
(b)
Figure 4.7 (a) Basic circuit for detection scheme; (b) schematic diagram for capacitive detection circuit.
(a)
(b)
Figure 4.8 (a) Schematic diagram for basic circuit with internal resistance;
(b) output voltage plot shows periodical disturbance.
Rebalancing Loop
for Rotation Rebalancing Loops
for
2 linear acceleration
Main Driving Loop with PLL
Figure 4.9 Schematic overview of control loops and structure.
(a) LF modulator
VCO
Sensing Pole Driving Pole
Phase Lock Loop Module
(b)
Figure 4.10 (a) Schematic diagram of microstructure with PLL driving circuit; (b) Silicon structure etched with RIE and observed with optical
microscope (10 x 5).
(a)
(b)
Figure 4.11 (a) Function block diagram for second order system with PLL;
(b) experiment apparatus setup.
0 0.5 1 1.5
2 3 4 5 6
Log Kvco
Log Kvco