Parameter design of a new thin-diaphragm pressure sensor
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摘要: 利用待测压力与薄膜加速度之间的正比例关系来获取冲击波反射超压峰值的新型测量方法已经得到初步实验验证，该方法具有无需标定、制作简单、成本低廉、测量精度高等优点。为优选薄膜式压力传感器的主要参数，并获取压力测量的不确定度，开展了数值模拟，分析了薄膜厚度、待测压力、拟合参数等因素对压力测量的影响。对薄膜的位移或速度信号进行了拟合处理，获得了冲击起始时刻薄膜的加速度，进而得到了待测压力峰值；将获得的压力与标准压力进行比对，得到了拟合时长、拟合多项式阶次、薄膜厚度等因素的优选值，并获得了薄膜式压力传感器的主要技术指标。另外，开展了激波管比对实验，验证了数值模拟的相关结论。Abstract: In recent years, the new measurement method of shock wave reflection overpressure peak by using the direct proportional relationship between the pressure to be measured and the diaphragm acceleration has been verified by shock-tube verification experiments. This method has the advantages of no calibration, simple fabrication, low cost and high measurement accuracy. In order to optimize the main parameters of the thin-diaphragm pressure sensor and to obtain the uncertainty of pressure measurement, numerical simulations were carried out. Specifically, the numerical simulation based on step pressure was carried out to analyze the influences of diaphragm thickness, pressure to be measured, fitting parameters and other factors on the pressure measurement. The numerical simulation based on blast pressure was carried out to analyze the influence of rapid pressure drop on measurement. The displacement or velocity signal of the thin diaphragm was fitted to obtain the diaphragm’s acceleration value at the beginning of impact, which was further used to calculate the pressure peak to be measured. By comparing the calculated pressure with the standard pressure, the optimum values of fitting time, fitting polynomial degree, diaphragm thickness and other factors were obtained. And the main technical specifications of the thin diaphragm pressure sensor were obtained. In particular, the polynomial fitting method was applied to carry out data processing, which can effectively avoid the model error introduced by linear fitting. This method obviously improved the measurement accuracy of the sensor and was a great improvement. In addition, shock-tube experiments were carried out to verify some conclusions by numerical simulation. In summary, the optimal parameters of the diaphragm pressure sensor were obtained: the thickness of the stainless steel diaphragm is 50－70 µm, velocity data is fitted by second-order polynomial, and fitting time is about 0.8 µs. And the relative error of shock wave reflection overpressure peak measurement can be controlled within 3%. Relevant conclusions can provide references for the popularization and application of the diaphragm pressure sensors.
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图 4 在0.2392 MPa入射压力作用下不同厚度薄膜的表面压力
Figure 4. Surface pressure of thin diaphragms with different thicknesses under the incident pressure of 0.2392 MPa
图 5 在0.2392 MPa入射压力作用下不同厚度薄膜的运动速度
Figure 5. Velocity-time curves of thin diaphragms with different thicknesses under the incident pressure of 0.2392 MPa
图 7 某时刻爆炸产生的压力云图
Figure 7. Explosion shock wave pressure distribution at a certain moment
图 8 爆心距54 mm处的入射冲击波压力和反射冲击波压力
Figure 8. Incident and reflected shock wave pressures at 54 mm away from explosion center
图 9 爆心距54 mm处不同厚度薄膜的运动速度
Figure 9. Movement velocities of thin diaphragms with different thicknesses at 54 mm away from explosion center
图 10 78.05 MPa阶跃压力下30 µm厚薄膜速度数据拟合获取压力的相对误差
Figure 10. Relative errors of pressure obtained from the velocity data of 30-µm-thick diaphragms under the step pressure of 78.05 MPa
图 11 78.05 MPa阶跃压力下90 µm薄膜速度数据拟合获取压力的相对误差
Figure 11. Relative errors of pressure obtained from the velocity data of 90-µm-thick diaphragms under the step pressure of 78.05 MPa
图 12 78.05 MPa阶跃压力下不同厚度薄膜速度数据拟合获取压力的相对误差
Figure 12. Relative errors of pressure obtained from the velocity data of the diaphragms with different thicknesses under the step pressure of 78.05 MPa
图 13 4.619 MPa阶跃压力下不同厚度薄膜速度数据拟合获取压力的相对误差
Figure 13. Relative errors of pressure obtained from the velocity data of the diaphragms with different thicknesses under the step pressure of 4.619 MPa
图 14 20.10 MPa爆炸冲击波下不同厚度薄膜速度数据拟合获取压力的相对误差
Figure 14. Relative errors of pressure obtained from the velocity data of diaphragms with different thicknesses under the shock wave pressure of 20.10 MPa
图 17 厚度10和50 µm薄膜位移数据的二次拟合
Figure 17. Second-order polynomial fitting of displacement data for 10- and 50-µm-thick diaphragms
表 1 不同待测压力下拟合参数的优选值及不同条件下拟合获得的压力与标准压力的相对误差
Table 1. Priority values of fitting parameters under different pressures to be measured and relative errors between the fitted pressures and the standard pressures under different conditions
压力类型 待测压力/MPa 薄膜厚度/µm 拟合起始时刻/µs 速度数据拟合阶次 拟合时长/µs 相对误差/% 阶跃型平台波 0.5107 30～70 0～0.4 1, 2 0.8～1.2 −0.80～0.047 4.619 30～90 0～0.4 2 0.8～1.2 −0.84～0.051 78.05 50～90 0～0.4 2 0.8～1.2 −1.36～1.05 1197 70～90 0～0.1 2 0.6 −2.81～−0.83 爆炸波 20.10 30～90 0～0.1 2 0.8 0.01～1.66 58.55 50～90 0～0.09 2 0.6 −3.18～0.44 
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