Deformation Analysis and Optimal Design of Membrane for Differential Pressure Capacitance Sensor

doi:10.16183/j.cnki.jsjtu.2021.281

Abstract

Abstract:

The compression deformation of the measuring membrane of the differential pressure capacitance sensor is studied. The classical von Kármán thin plate theory is applied to the elastic circular thin plate subjected to pretension, and the approximate analytical solution is given by adopting the homotopy analysis method. The results are compared with the simulation results of the finite element software ANSYS, which shows that they have a high degree of agreement. The magnitude of pretension has a great influence on the deformation of the membrane under compression, thus affecting the capacitance output characteristics of the sensor. The effect of pretension on the nonlinear characteristic of the sensor is verified by the sensor performance test. The results suggest that the linearity of the sensor can be effectively improved by selecting the appropriate pretension, and the sensitivity of the output can be improved by appropriately reducing the membrane thickness. The analysis results have an important reference value for the design of membrane of differential pressure capacitance sensors.

Key words: sensor membrane, pretension, deformation analysis, homotopy analysis, nonlinearity

CLC Number:

TH813

ZHAO Zhao, LEI Huaming. Deformation Analysis and Optimal Design of Membrane for Differential Pressure Capacitance Sensor[J]. Journal of Shanghai Jiao Tong University, 2023, 57(3): 264-272.

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S₀	Q	m	M	c	E_min	计算时间/s
[0, 40]	[0, 400]	2	110	-0.1	(0, 10^-20)	0.07
[0, 150]	[0, 1 000]	2	300	-0.04	(0, 10^-20)	0.11
[0, 700]	[0, 4 200]	4	700	-0.01	(0, 10^-20)	0.35
[0, 1 500]	[0, 19 000]	10	5000	-0.001	(0, 10^-20)	8.00

q/kPa	N₀/ (N·m^-1)	ω₀/mm		结果偏差/%
q/kPa	N₀/ (N·m^-1)	FEM	HAM	结果偏差/%
100	20 000	0.257 76	0.257 60	0.06
100	0	0.644 18	0.642 88	0.20
10	2 000	0.192 92	0.192 45	0.24
10	0	0.295 53	0.295 38	0.05
1	200	0.109 05	0.108 64	0.38
1	0	0.132 99	0.132 96	0.02

h/ mm	q_max/ Pa	Q_max	δ= 5%		δ= 1%
h/ mm	q_max/ Pa	Q_max	S₀	N₀/ (N·m^-1)	S₀	N₀/ (N·m^-1)
0.02	500	1 372.32	289	489.3	514.6	871.3
0.03	500	271.08	93.3	533.1	168.5	962.9
0.04	500	85.77	40.6	549.9	74.9	1 014.5
0.05	500	35.13	20.5	542.3	39.1	1 034.4

h/mm	δ= 5%			δ= 1%
h/mm	低压端灵敏度/(pF·Pa^-1)	高压端灵敏度/(pF·Pa^-1)	非线性误差/%	低压端灵敏度/(pF·Pa^-1)	高压端灵敏度/(pF·Pa^-1)	非线性误差/%
0.02	0.039 4	-0.016 8	0.86	0.018 3	-0.011 3	0.15
0.03	0.030 8	-0.015 0	0.94	0.015 1	-0.010 0	0.17
0.04	0.025 8	-0.013 7	0.95	0.013 2	-0.009 1	0.18
0.05	0.022 4	-0.012 6	0.94	0.011 7	-0.008 4	0.18

传感器参数	数值	传感器参数	数值
a/mm	15	H₁/mm	0.32
h/mm	0.02	H₂/mm	0.34
b/mm	10.5	N₀/(N·m^-1)	840