1. Comb Driven Double Ended Tuning Fork
Studies of the
Comb Driven Double Ended Tuning Fork
(CDDETF)
Wayne Huang
March 2005

2. The focus of my research is about the vibrations of the CDDETF (comb driven double ended tuning fork.)

3. The purpose of modal analysis is two fold:
1) Understand the stability of the modes shapes

4. Modal analysis suggests that the current excitation mode is stable with respect to perturbations in gap length of the comb drive.

5. Disclosure filed on 02/25/’05
The purpose of modal analysis is two fold:
2) Develop temperature compensation techniques for the CDDETF. (One of the technique realized is patentable.)
Disclosure filed on 02/25/’05
United States Patent &
Trademark Office
Dual Mode Solution

6. 2-D view of the complete sensing system
The full temperature compensation technique involves not only the CDDETF, but also the bonding and boundary conditions.
2-D view of the complete sensing system
CDDETF
Bonding
Steel Substrate
(x1,y1)
(x2,y2) y
force x
moment
Heat Input
The displacement between (x1,y1) and (x2,y2) due to the applied force and moment is affected by the temperature gradient (caused by the heat input) in the steel.

7. Therefore, a complete system model is necessary for achieving complete temperature compensation.
 Bonding
 Strain Transfer
 Heat Transfer
 Boundary Conditions
 Natural Expansion
 Strain
 Temperature Gradient
 CDDETF
(mechanical aspect completed)
Displacement
Strain

8. The CDDETF needs to be temperature compensated because its resonant frequency depends on on both temperature and strain.
Frequency
Surface of constant
frequency
Temperature changes the elastic modulus and the dimensions of the CDDETF.
Axial Strain induces
stress in the tines

9. There are several methods to achieve temperature compensation for the CDDETF.
methods for Resonators
1. Two Resonators
method
2. Dual Mode
method (Patentable)
3. Differential-
Pair method

10. The operating principle behind the two resonators method is to use two functions to determine .
Anchored on
both sides  T 
Look-up table 1 T
Anchored on
one side,
“free” on the
other side f2 F2 T
Look-up table 2

11. The look up table is generated in Ansys, and the results confirm with the Cosserate model and measurements from the prototype.
Prototype
Cosserat
Model
FEM
Resonant Frequency (KHz)
217
216
225
Strain Sensitivity (Hz/με) 39 34 42
Thermal Sensitivity (Hz/oC) 7
101* 11
* No compensation was made for the thermal expansion of the substrate.

12. The operating principle of the dual mode method is similar to the two resonator solution.
1st operating mode f1 F1
F1=f1(,T) T 
Look-up table 1
, T
2nd operating mode f2 ? F2
F2=f2(,T) T 
Look-up table 2

13. Finding the 2nd mode of operation is not trivial, but we have identified one that works.
Mechanical Requirements:
1) Enough sensitivity to temperature or strain
2) Cause a sufficiently large change in capacitance
3) Symmetric motion
Mathematical Requirements:
The system of equations F1=f1(,T) and F2=f2(,T) is guaranteed to have a unique solution only if,
1) They are linear functions of strain and temperature, and 2) they are independent from each other.

14. Does not cause a sufficiently large  capacitance This mode works!
The feasibility of several possible candidates were investigated, including:
3rd harmonic mode
“Flapping” mode
Does not cause a sufficiently large
 capacitance
This mode works!

15. A frequency sweep suggests that the 3rd harmonic mode does not cause a large change in capacitance, but the flapping mode does.
Bar: Measured frequency
Circle: Modal analysis result in Ansys
Flapping Mode
1st Harmonic
3rd harmonic mode
4.5MHz

16. Simulation shows that the “flapping mode” also satisfies the mathematical requirement.

17. Experiments were performed to confirm the result from Ansys.
Notice that the noise level is relatively large for the flapping mode. This is because it doesn’t cause a large change in capacitance.

18. An sample calculation of temperature compensation is shown here.

19. Development of the full temperature compensation technique is under way.
The model of the entire system is not trivial due to the different length scales involved in the system.
Si Substrate
Si Substrate
CDDETF
5000m
200m
26,000 m
Steel
Bond
40m

20. Future work for the next six month is shown here.
1. Optimize the CDDETF so that the amplitude of flapping mode can be maximized.
2. Characterize the stability of mode shapes with respect to temperature and strain.
3. Develop analytical model for the flapping mode.
4. Develop the FEM model of the entire system.