差压式电容传感器膜片的变形分析与优化设计

doi:10.16183/j.cnki.jsjtu.2021.281

摘要/Abstract

摘要：

为研究差压式电容传感器测量膜片的受压变形,将经典的von Kármán薄板理论应用于受有预张力作用的弹性圆薄板问题,采用同伦分析法给出近似解析解.将求解结果与有限元软件ANSYS的仿真结果进行对比,表明两者吻合度较高.预张力大小对膜片在受压情况下的变形影响较大,从而影响传感器的电容输出特性.利用传感器性能测试验证了预张力对传感器非线性特性的影响.结果表明:选择合适的预张力可以有效提升传感器的线性度,适当降低膜片厚度可以提高输出的灵敏度.分析结果对差压式电容传感器的膜片设计具有重要的参考价值.

关键词: 传感器膜片, 预张力, 变形分析, 同伦分析, 非线性

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

中图分类号:

TH813

赵昭, 雷华明. 差压式电容传感器膜片的变形分析与优化设计[J]. 上海交通大学学报, 2023, 57(3): 264-272.

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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参考文献 17

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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