 Open Access
 Authors : Raihan Mohammed R , Kiran Teradal , Mukul Karwa , Nikhil N Kumar
 Paper ID : IJERTV10IS080044
 Volume & Issue : Volume 10, Issue 08 (August 2021)
 Published (First Online): 14082021
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Design and Simulation of MEMS based Capacitive Accelerometers for Crash Detection and Airbag Deployment in Automobile
Mr. Kiran Teradal, Mr. Mukul Karwa, Mr. Nikhil N Kumar, Mr. Raihan Mohammed R
PES Institute of Technology, Hosur Road, Bangalore 560100
Abstract: This paper focuses on design and analysis of MEMS based accelerometer to detect accidents and for the deployment of airbags. In the case of a car accident, where there are sudden and strong accelerations, it is necessary to measure as fast as possible their intensity and direction with good accuracy and precision, aiming to reduce the injuries severity to passengers. With the continuous advancements in Micro Electro Mechanical Systems (MEMS) fabrication technology, inertial sensors like accelerometers and gyroscopes can be designed and manufactured with smaller footprint and lower power consumption. Capacitive accelerometers are the most popular and highly researched due to several advantages like high sensitivity, low noise, low temperature sensitivity, linearity, and small footprint. When sudden displacement occurs due to impact the comb gets shock loads or forces and that movement is observed by differential capacitance concept with dielectric as air. The simulations will be carried out on COMSOL while the design will be carried out on COMSOL, the actual theoretical calculation and the simulations are compared in order to get accurate results. The capacitance output obtained is carried to the electronic control unit which sends the impulse signal to air bag system and deployment of air bags takes place.
INTRODUCTION:
Automotive is one of the most emerging area since ages and is constantly under developments. These developments in technology and these advancements are not without responsibilities to assure that the end user is safe and satisfied. The industries primary concerns are improving the performance, safety, and comfort aspects which have become evident over the years with introduction of highly improved standards with every iteration. Passenger safety is a field highly researched on to ensure the survival of a passenger in a car crash. This brings us to the crash detection and air bag deployment systems in the automotive industry. Frontal airbags drastically reduce harm to driver in frontal crashes by almost 30 percent and fatalities of frontseat passengers of age 13 and older by 32 percent (Survey from 2015). NHTSA estimates that as of 2015, a total of 44,869 lives have been saved primarily by frontal airbags (Survey 2017). At the instant of a crash, sensors start to measure severance of the impact. When the crash occurs beyond a set intensity, the sensors signal control unit to inflate the bags with gas within fractions of a second. The reference work analyzes a capacitive accelerometer capable of identifying positive and negative levels of acceleration along three perpendicular directions. However, this project
is referred to a sensor capable of working with accelerations on an XY plane, on which it was built starting from a planar geometry. To understand this type of sensor the technological process with which modern semiconductor integrated circuits are manufactured is extensively used, thanks to which MEMS sensors are able to have dimensions in the order of nano meters. In case of a car accident, it is of utmost requirement that the airbag system reacts as fast as possible from the moment of the impact, in order to avoid fatal injuries. For this reason, it is necessary that the system analyses and give a response within the shortest possible time. The capacitive sensors are basically based on a moving solid body with a certain mass that will move when subjected to acceleration. The movement of the mass is the most important factor, because the small displacements of the structure leads (fingers and proof mass) to a variation of a capacity, as there are parts, called "fingers" that move closer or farther away depending on the direction of acceleration. These displacements are a direct effect of the acceleration on the system. When the capacity produced reaches a certain threshold value, it means that we are in a limit condition in the case under consideration; therefore, the system will react appropriately.
SYSTEM DETAILS

Proof mass: A proof mass or test mass is a known quantity of mass used in a measuring instrument as a reference for the measurement of an unknown quantity. A proof mass that deforms a spring in an accelerometer is sometimes called the seismic mass. This proof mass will have fingers attached to it on either side.

Spring: Thin beams placed in rectangular manner act as springs in the system. It facilitates movement to the proof mass, which in turn moves the fingers. The stiffness of these springs is the key parameter for displacement.

Fingers: Attached to the proof mass, these components are responsible to obtain differential capacitance. They are placed in between dielectric plates, such that a fingergap and an anti finger gap exists between them.

Connecting beams: these are used to connect the proof mass to the springs. 4 connecting beams are used with 2 for each spring.

Dielectric medium: Air is taken as the dielectric
medium.

Anchors: A 100nm square cross section fixed joint, to which the springs are attached.
Density: 2320kg/m3
Fig .1.2.1 Parts of capacitive accelerometer Wa= Width of anchor
W= Width of connecting beam
lf= Length of fingers= Length of static plate l1=l2= Length of spring on either side
lb= Length of connecting beam

Material of component: Polysilicon is chosen as the material of design with following properties:
Working of the System with Key Parameters
It is based on the movement of a proof mass to which are attached mobile fingers whose movement makes a change in capacity, that is calculated between them and the fixed fingers. From the displacement it can be traced back the acceleration value and the capacitive system is used to calculate it.
The instantaneous change in velocity (acceleration) on impact is converted into force on the system by Newtons laws of motion. This force is then responsible for the proof mass to move, which results in the movement of the fingers. A differential capacitance is set up at the gaps between the fingers and the di electric plates. This capacitance produces a voltage which is transferred to the electronic control unit of the vehicle and if it is within the acceptable range causes the airbag to deploy.
The system can be depicted by a springmassdamper setup.
A force F, generated by external acceleration acting on the mass, m, causes a displacement x. The differential equation describing the system response is given by equation:
()=2/2+/+
b is the damping coefficient and K is the spring coefficient, the stiffness.
Displacement
F is both the force that will be induced to the mass of the system by the external acceleration, both the force given by Hookes law that could be
associated to the action of the springs, considering the stationary conditions. K is the springs stiffness
Comparing the equations, displacement x can be given as: x=ma/k (1)
This is the displacement obtained in xdirection for xaxis analysis
The same equation will hold good for ydirection: Displacement y = ma/k. (2)
Capacitance
Capacitance of the system at a single finger between two dielectric plates(electrodes)n is given as
=0 Ã— Ã—/
0 is the dielectric permeabiliy of the vacuum and is worth 8,8541012 F/m, r is the dielectric permeability of the material that separates the armatures, in our case it is taken as 1F/m, considering that there will be only air, A is the total overlap surface between the electrodes and d is the gap from the finger. Finger gapd1 and antifinger gap d2 are taken in the ratio 1:2 respectively. This is done in order to discriminate the displacements in x and y axes. Thus, capacitance will be:
=oH(1/1+1/2)

axis
When acceleration along the xaxis occurs, the capacity between the mobile and fixed fingers varies, because on the right the surface will increase by a factor x, the displacement, which will be added to the overlap length L and on the other side it will decrease, by the same amount.
So, for the two capacities their magnitude is given by:
1=0H (1/1+1/2) (+) Ã—F
2=0H (1/1+1/2) () Ã—F

axis
When acceleration on the yaxis happens, the variation in capacity depends on the displacement that makes the distances d from the fingers vary. The change in capacity will depend on the displacement along the yaxis and further simplified substituting d1=2Ã—d2
1=0H(1/(1) +1/(2+)) Ã— F = 0H (31/(212+12))
Ã—F
2=0H(1/(1+) +1/(2)) Ã— F =0tH (31/ (21212))
Ã—F
A factor F of 6 is taken when 12 fingers are present in total, with 6 fingers contributing to C1 and equally forC2.
A factor F of 8 is taken when 16 fingers are present in total, with 8 fingers contributing to C1 and equally forC2.
Voltage:
The system is initially given a fixed amount of supply voltage, and once the differential capacitance is obtained, an output voltage signal will be sent to the control unit of the vehicle.
Vout = ((C1C2)/ (C1+C2)) Ã—Vs
The following section of the report addresses some of the research work carried out by various researchers in the field of capacitive accelerometers and their extensive utilization for crash detection and airbag deployment. The research papers that were referred to are listed below:
Jesse Kendall, P.E. et.al [1] this paper gives an insight on the airbag deployment criteria and process
D S Dima et.al, 2017[2] this paper provides insight on the crash tests that can help the experts to identify the ranges of accelerations that may appear in various collision types. The correct sensors and data acquisition devices used in crash tests depend by the type of collisions.
Geeta Bhatt et.al, 2019[3] this paper provides insight on the importance of MEMS in the automotive industry along with the various applications in vehicles along with MEMS fabrication.
Vijayakumar S. et.al 2011 [4] this paper depicts the design and analysis of a 2axis MEMS capacitive accelerometer Divya et.aL, 2015[5] this paper provides insight on analysis of 3axis accelerometers using COSMOL.
Gaurav Phulwari et.al, 2017[6] This paper provides insight on the importance of MEMS in the automotive industry and how they are cost effective, compact in size and help prevent major catastrophe.
Mourad Benmessaoud, 2013 [7] Optimization with respect to design parameters are done and variation are studied Giulio Puccioni, 2020 [8] this paper provides insight on the performance of a standard capacitor accelerometer at varying accelerations and also provides insight on the effect of variation of thickness of the capacitive accelerometer.
Zakriya Mohammed 2016 [9] this paper optimizes finger spacing and spring constant and simulation is carried out.
Research Gap
The literature of displacement and stress analysis with respect to 2axis MEMS capacitor accelerometer is scarce and doesnt involve alterations to the accelerometer to improve efficiency. The objective of our project is to design a 2axis MEMS accelerometer and analyze the displacement and stress along the x and y axis. Certain alterations with respect to the design of the accelerometer are done to study the difference in performance.

Objectives To determine the total displacement with respect to acceleration variation(0100g)

To determine the stress on x and yaxis
Theoretical Analysis

W = VPM Ã· LÃ—H
M12F =12Ã—M1F

M2LB = 2Ã—MLB
M2SB = 2Ã—MSB = 4.64Ã—1018 Kg

M tot = MPM + M12F + V2LB + M2SB
Spring Stiffness K= (4Ã—EÃ—WÃ—H3) / (6Ã— (2L1)3+ (2L2)3)
C1=0H (1/1+1/2) (+x) Ã—6
C2=0H (1/1+1/2) (x) Ã—6
1. 1=0H(31/(212+12)) Ã—6
2. 2=0H(31/ (21212)) Ã—6
Table 4.1.1 Result for acceleration in xdirection for the standard design
Acceleration m/s2 
Displacement x (fm) 
C1(*1017 F) 
C2(*1017 F) 
0g 
0 
5.8941 
5.8941 
10g 
3.4 
5.8941 
5.89405 
20g 
6.89 
5.8941 
5.89405 
30g 
10.33 
5.8941 
5.89405 
40g 
13.77 
5.8941 
5.89405 
50g 
17.22 
5.8941 
5.89405 
60g 
20.66 
5.8941 
5.89405 
70g 
24.11 
5.8941 
5.89405 
80g 
27.55 
5.8941 
5.89405 
90g 
31 
5.8941 
5.89405 
100g 
34.44 
5.8941 
5.89405 
Displacement in y axis:
Displacement (ydirection) y = (MÃ—10g)/Ky= (1.129Ã—1016Ã—10Ã—10)/9.74= 1.15 fm
Capacitance produced in y axis:
ydirection for the standard design
Acceleration m/s2 
Displacement y (fm) 
C1(Ã—1017 F) 
C2(Ã—1017 F) 
0g 
0 
5.896764 
5.896764 
10g 
1.32 
5.896763806 
5.896764194 
20g 
2.64 
5.896763611 
5.896764389 
30g 
3.96 
5.896763413 
5.896764584 
40g 
5.29 
5.89676322 
5.89676478 
50g 
6.61 
5.896763026 
5.896764974 
60g 
7.93 
5.896762831 
5.896765169 
70g 
9.25 
5.896762636 
5.896765364 
80g 
10.58 
5.896762441 
5.896765559 
90g 
11.9 
5.896762246 
5.896765754 
100g 
13.22 
5.896762051 
5.896765949 
Table 4.3.1 Result for acceleration in xdirection for thickness (20nm)
Acceleration m/s2 
Displacement x (fm) 
C1(Ã—1017 F) 
C2(Ã—1017 F) 

0g 
0 
2.9483820 
2.9483820 

10g 
24.02 
2.9483822 
2.948381808 

20g 
48.225 
2.9483824 
2.948381616 

30g 
72.34 
2.9483826 
2.948381424 

40g 
96.50 
2.9483828 
2.948381231 

50g 
120.50 
2.9483830 
2.948381040 

60g 
144.50 
2.94838315 
2.94838085 

70g 
168.8 
2.94838335 
2.948380655 

80g 
192.9 
2.94838354 
2.948380463 

90g 
217 
2.94838373 
2.948380271 

100g 
241.135 
2.94838392 
2.948380078 
Table 4.3.2 Result for acceleration in ydirection for thickness(20nm)
Acceleration m/s2 
Displacement y (fm) 
C1(Ã—1017 F) 
C2(Ã—1017 F) 
0g 
0 
2.9487 
2.9487 
10g 
9.285 
2.948698229 
2.948700684 
20g 
18.57 
2.948696445 
2.948701369 
30g 
27.85 
2.948694667 
2.948702053 
40g 
37.135 
2.948692886 
2.948702738 
50g 
46.42 
2.948691117 
2.948703422 
60g 
55.705 
2.94868935 
2.948704106 
70g 
65 
2.94868756 
2.948704792 
80g 
74.25 
2.94868578 
2.948705474 
90g 
83.65 
2.94868401 
2.948706167 
100g 
92.845 
2.94868223 
2.948706844 
Table 4.3.3 Result for acceleration in xdirection for thickness (80nm)
Acceleration m/s2 
Displacement x (fm) 
C1(Ã—1017 F) 
C2(Ã—1017 F) 
0g 
0 
11.793528 
11.793528 
10g 
0.5363 
11.79352802 
11.79352798 
20g 
1.073 
11.79352803 
11.79352797 
30g 
1.61 
11.79352805 
11.79352795 
40g 
2.145 
11.79352802 
11.79352793 
50g 
2.68 
11.79352807 
11.79352791 
60g 
3.22 
11.79352810 
11.79352790 
70g 
3.75 
11.79352812 
11.79352788 
80g 90g 100g 
4.29 4.82 5.36 
11.79352814 11.79352815 11.79352817 
11.79352786 11.79352785 11.79352783 
Table 4.3.4 Result for acceleration in ydirection for thickness (80nm)
Acceleration m/s2 
Displacement y (fm) 
C1(*1017 F) 
C2(*1017 F) 
0g 
0 
11.793528 
11.793528 
10g 
0.144 
11.79352796 
11.79352804 
20g 
0.289 
11.79352792 
11.79352808 
30g 
0.435 
11.79352787 
11.79352813 
40g 
0.579 
11.79352783 
11.79352817 
50g 
0.724 
11.7935278 
11.79352822 
60g 
0.869 
11.79352774 
11.79352826 
70g 
1.014 
11.7935277 
11.79352830 
80g 
1.159 
11.79352766 
11.79352834 
90g 
1.30 
11.79352762 
11.79352838 
100g 
1.448 
11.79352757 
11.79352843 
Table 4.3.5 Result for acceleration in xdirection for thickness(160nm)
Acceleration m/s2 
Displacement x (fm) 
C1(Ã—1017 F) 
C2(Ã—1017 F) 
0g 
0 
23.587056 
23.587056 
10g 
0.0936 
23.58705601 
23.58705599 
20g 
0.187 
23.58705601 
23.58705599 
30g 
0.281 
23.58705602 
23.58705598 
40g 
0.375 
23.58705602 
23.58705598 
50g 
0.47 
23.58705603 
23.58705597 
60g 
0.562 
23.58705604 
23.58705596 
70g 
0.656 
23.58705604 
23.58705596 
80g 
0.75 
23.58705605 
23.58705595 
90g 
0.843 
23.58705605 
23.58705595 
100g 
0.937 
23.58705606 
23.58705594 
Table 4.3.6 Result for acceleration in ydirection for thickness (160nm)
Acceleration m/s2 
Displacement y (fm) 
C1(Ã—1017 F) 
C2(Ã—1017 F) 
0g 
0 
23.5875 
23.5875 
10g 
0.036 
23.58749998 
23.58750002 
20g 
0.072 
23.58749996 
23.58750004 
30g 
0.108 
23.58749994 
23.58750006 
40g 
0.144 
23.58749992 
23.58750008 
50g 
0.180 
23.58749989 
23.58750011 
60g 
0.216 
23.58749987 
23.58750013 
70g 
0.252 
23.58749985 
23.58750015 
80g 
0.288 
23.58749983 
23.58750017 
90g 
0.324 
23.58749981 
23.58750019 
100g 
0.360 
23.58749979 
23.58750021 
4.4 Additional Fingers and Reduction of Dielectric Gap
Table 4.4.1 Displacement for acceleration in xdirection for additional finger and reduced gap
Acceleration (m/s2) 
Displacement (fm) 
0g 
0 
10g 
3.5637 
20g 
7.1274 
30g 
10.691 
40g 
14.254 
50g 
17.818 
60g 
21.382 
70g 
24.946 
80g 
28.509 
90g 
32.0736 
100g 
35.637 
Table4.4.2 Displacement for acceleration in ydirection for additional finger and reduced gap
Acceleration(m/s2) 
Displacement (fm) 
0g 
0 
10g 
1.368 
20g 
2.736 
30g 
4.105 
40g 
5.473 
50g 
6.842 
60g 
8.210 
70g 
9.578 
80g 
10.94 
90g 
12.31 
100g 
13.68 
Table 4.4.3 Capacitance for acceleration in xdirection for additional finger and reduced gap
Acceleration (m/s2) 
C1 (Ã— 1018 F) 
C2(Ã— 1018 F) 
0 
1.5724704 
1.5724704 
10 
1.572470415 
1.572470438 
20 
1.572470430 
1.572470437 
30 
1.572470445 
1.572470435 
40 
1.572470461 
1.572470434 
50 
1.572470476 
1.572470432 
60 
1.572470491 
1.572470431 
70 
1.572470506 
1.572470429 
80 
1.572470521 
1.572470428 
90 
1.572470536 
1.572470426 
100 
1.572470551 
1.572470425 
Table 4.4.4 Capacitance for acceleration in ydirection for additional finger and reduced gap
Acceleration (m/s2) 
C1 (Ã— 1018 F) 
C2(Ã— 1018 F) 
0 
1.5724704 
1.5724704 
10 
1.5724702 
1.5724705 
20 
1.5724701 
1.5724706 
30 
1.5724700 
1.5724707 
40 
1.5724699 
1.5724708 
50 
1.5724698 
1.5724709 
60 
1.5724697 
1.5724710 
70 
1.5724696 
1.5724711 
80 
1.5724695 
1.5724712 
90 
1.5724694 
1.5724713 
100 
1.5724693 
1.5724714 
CHAPTER 5

Design
[All designs are done with a scale of 1nm=1mm]5.1.1 3D model of fixed finger 5.1.2 3D model of proof mass

Design Of Standard Capacitance Accelerometer
The preliminary design was carried out on Solid edge . The design parameters of the standard capacitive accelerometer is taken from one of the research papers that were referred to. The fixed fingers and the proof mass along with fingers and springs were separately designed . The standard design has a total of 12 fingers on the proof mass. The thickness of both the proof mass and the fixed fingers are considered to be 40mm.
5.2.1 Standard capacitive accelerometer

Design Of Capacitance Accelerometer With Reduced Thickness Of 20mm
The thickness of both the proof mass and the fixed fingers are reduced by 20mm with respect to the standard design. There is no variation in any other parameters other than the thickness. The total number of fingers present in this model is 12. The proof mass and the fixed fingers are separately designed and assembled.
5.3.1 Capacitive accelerometer of thickness 20mm

Design Of Capacitance Accelerometer With Increased Thickness Of 80mm
The thickness of both the proof mass and the fixed fingers are increased by 40mm with respect to the standard design. There is no variation in any other parameters other than the thickness. The total number of fingers present in this model is
12. The proof mass and the fixed fingers are separately designed and assembled.
5.4.1 Capacitive accelerometer of thickness 80mm

Design Of Capacitance Accelerometer With Increased Thickness Of 160mm
The thickness of both the proof mass and the fixed fingers are increased by 120mm with respect to the standard design. There is no variation in any other parameters other than the thickness. The total number of fingers present in this model is 12. The proof mass and the fixed fingers are separately designed and assembled.
5.5.1 Capacitive accelerometer of thickness 160mm

Design Of Capacitance Accelerometer With Additional Fingers with same c/s
The fixed fingers and the proof mass along with fingers and springs were separately designed . The standard design has a total of 16 fingers on the proof mass. The thickness of both the proof mass and the fixed fingers are considered to be 40mm. The proof mass and the fixed fingers are separately designed and assembled.
5.6.1 Capacitive accelerometer with additional fingers 5.6.2 Gap between fingers CHAPTER 6 Analysis

Standard model:
Fig 6.1: Load and constraints under structural analysis
The model is scaled as per 1nm=1mm in the simulation process.
The stress analysis is done on the software called ANSYS. First the assembly created on solid edge is converted to a
.igs file which makes it compatible with ANSYS. The assembly is then transferred to ANSYS via the DesignModeler.
After importing the assembly the in the DesignModeler, a face split is performed to separate the proof mass from the fingers and the connecting rods.
The material is selected to be silicon anisotropic for the analysis. The design is then meshed with a size of 50mm.
Fig 6.2: Meshed model in Ansys
The acceleration is set to the proof mass for 10G in the x axis , and a displacement of 0mm is set in the x axis. The Fixed fingers are considered as fixed constraints. The larger springs are also constrained as the analysis is strictly performed for the x axis.
The total deformation analysis is performed and results are obtained for 10G , 30G ,50G ,70G and 100G respectively.
Fig: 6.3 Stress distribution for standard model xaxis simulation AND Fig 6.4: Displacement under xaxis simulation for standard model
Similarly the same procedure is followed for analysis of stress in the y axis. Instead of constraining the larger springs , the smaller springs are constrained. The acceleration is considered to be 10G and the displacement is considered to be 0mm in z axis. The total deformation is analyzed for 10G , 30G , 50G . 70G and 100G respectively.
Fig 6.5: Displacement in yaxis for standard model AND Fig6.6 : Stress displacements in y axis for standard model.

Model with thickness of 20mm: .
Fig 6.2.1 stress for xaxis simulation Fig 6.2.2Displacement for xaxis simulation
Fig 6.2.3 Displacement for yaxis simulation Fig 6.2.4 Stress distribution for yaxis simulation

Model with thickness of 80mm
Fig 6.3.1Displacement for xaxis simulation Fig 6.3.2 Stress distribution xaxis simulation
Fig 6.3.3 Displacement for yaxis simulation Fig 6.3.4 Stress distribution for yaxis simulation

Model with thickness of 160mm:
Fig 6.4.1 Displacement for xaxis simulation Fig 6.4.2Stress distribution for xaxis simulation
Fig 6.4.4 Stress distribution for yaxis simulation Fig6.4.3 Displacement for yaxis simulation

Model with Additional Fingers:
Fig 6.5.1Displacement for xaxis simulation Fig 6.5.2 Stress distribution for xaxis simulation
Fig 6.5.3 Displacement for yaxis simulation Fig 6.5.4 Stress distribution for yaxis simulation

Results:

Result for acceleration in xdirection for the standard design
Acceleration m/s2
Displacement x (fm)
10g 30g 50g 70g 100g
3.91
11.74
19.57
27.40
39.147

Result for acceleration in ydirection for the standard design

Result for acceleration in xdirection for thickness (20nm)
Acceleration m/s2
Displacement y (fm)
10g
33.8
30g
99.6
50g
167
70g
236
100g
338

Result for acceleration in ydirection for thickness (20nm)
Acceleration m/s2
Displacement y (fm)
10g
0.12
30g
1.2802
50g
3.8407
70g
6.4011
100g
8.9616
Acceleration m/s2
Displacement y (fm)
10g
6.7
30g
19.7
50g
33.5
70g
47
100g
68
Acceleration m/s2
Displacement y (fm)
10g
0.12
30g
1.2802
50g
3.8407
70g
6.4011
100g
8.9616
Acceleration m/s2
Displacement y (fm)
10g
6.7
30g
19.7
50g
33.5
70g
47
100g
68

Result for acceleration in xdirection for thickness
(80nm)
Acceleration m/s2
Displacement y (fm)
10g
0.78
30g
2.34
50g
3.6
70g
5.4
100g
9.78

Result for acceleration in ydirection for thickness (80nm)
Acceleration m/s2
Displacement y (fm)
10g 30g 50g 70g 100g
0.076
0.23
0.38
0.52
0.76

Result for acceleration in xdirection for thickness (160nm)
Acceleration m/s2
Displacement y (fm)
10g 30g 50g 70g 100g
0.0768
0.211
0.384
0.53
0.768

Result for acceleration in ydirection for thickness (160nm)

Result for acceleration in xdirection for altered number of fingers
Acceleration m/s2
Displacement y (fm)
10g
3.9
30g
11.74
50g
19.56
70g
27.4
100g
32.67

Result for acceleration in ydirection for altered number of fingers

Acceleration m/s2 
Displacement y (fm) 
10g 
0.69 
30g 
2.07 
50g 
3.45 
70g 
4.8 
100g 
6.9 
Acceleration m/s2 
Displacement y (fm) 
10g 30g 50g 70g 100g 
0.076 0.21 0.34 0.48 0.69 
Conclusion
Capacitance relation to displacement obtained:
C = 0()
generally has a dimension of 40mm thickness.
The analysis conducted indicates that with increase in the thickness of the capacitive accelerometer, the displacement decreases which in turn increases the capacitance induced. With increase in capacitance induced the response time of the airbag control module is reduced, thus increasing the efficiency of accelerometer by increasing the thickness of the capacitive accelerometer also increases the stress induced in the accelerometer. So, we have to compromise with the efficiency of the accelerometer due to the stress produced. The basic standard of capacitive accelerometer available in market
Future Work
The entire work was carried out based on the fingers placed in the lateral position only (along xaxis) even for the yaxis simulations. Thus, one of the major improvements to the model can be the introduction of sensing fingers on the y axis that is along the longitudinal direction as well. This will
Stress analysis:
Stress analysis was carried out to analyze critical points of failure under the action of loads. Thus, what can be inferred from this is that, for application of load in x direction, the maximum stress is concentrated at the point where the fingers are attached to the proof mass. For the yaxis analysis, the stress was observed to be concentrated at the point where the lateral connecting beams are attached to the proof mass.
further enhance the system efficiency particularly for longitudinal analysis.
The work carried out can further be improved and a more idealistic and justified results can be obtained taking into consideration the COMSOL software approach. The model can be taken its true scale and boundary conditions will remain the same as in case of the work carried out above.
Fig 9.1: COMSOL approach static structural
Two primary modules are taken into consideration. One is the solid mechanics module that deals with the static structural analysis of displacement and stress of the body. The next is the Electro Statics Module which deals with determination of differential capacitance at the terminals
required. A reference voltage of 1V is applied to the fixed terminals and the proof mass will be at ground charge condition. This is analyzed under electric potential probe analysis to determine output voltage and maxwell differential capacitances can be obtained in tabulated format.
Fig 9.2: Modules and conditions Fig9.3: System properties
In order to analyze the capacitance produced by the capacitive accelerometer an electrostatics study was conducted in COMSOL. The fixed fingers are given an terminal voltage value of 1V. The proof mass along with the
moveable fingers are grounded. A body load is defined with respect to volume on the proof mass. The fixed constraints are applied on the fixed fingers. A global probe is created to determine the Maxwell capacitance.
Fig9.4 : Electrostatic comsol approach
Thus, through this approach, both static structural and electrostatics can give conclusive evidence on the efficiency of the system, through both static analysis and electrical approach. Dynamic Analysis
Another Approach to obtain precise outputs is the dynamic analysis of te system in time dependent form. Due to lack of system requirements and license of software being limited to
use, this approach was not possible to be done. However, in future prospects, this will definitely enhance the results and give justified outputs for effective efficiency comparison between the models.
However, A transient structural (time variant) approach was carried out in subsets for a time interval of 1s starting from 0.2
seconds in steps of 0.1 /0.15 seconds up to 16 subsets. It was observed that the deformation is more or less the same as in case of static structural, but a very small decrease in deformation was seen half way through the time interval and
the certain small variations of increasedecrease took place, after which, the value increases and maximum value is obtained. Acceleration, displacement and fixed constraints would remain the same as in static structural analysis.
Fig9.5: Transient analysis setup
Fig 9.6: Transient analysis 20nm y axis
Fig 9.7: Transient analysis 20nm x axis
Fig 9.8: Varied finger x axis transient analysis
Fig 9.9: 80nm model transient analysis (xaxis)
Fig 9.10: 160nm model transient analysis (xaxis)
Fig 9.11 Standard model transient analysis
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