﻿ 电阻应变式传感器零点温度补偿剖析 Analysis of Zero Temperature Compensation of Resistance Strain Sensor

Journal of Sensor Technology and Application
Vol. 07  No. 02 ( 2019 ), Article ID: 29744 , 11 pages
10.12677/JSTA.2019.72005

Analysis of Zero Temperature Compensation of Resistance Strain Sensor

Zhipeng Yan

Zhonghang Electronic Measuring Instruments Co., Ltd., Hanzhong Shaanxi

Received: Mar. 26th, 2019; accepted: Apr. 10th, 2019; published: Apr. 17th, 2019

ABSTRACT

Zero temperature output is the main performance parameter of the strain sensor. If it is not controlled and compensated, the sensor accuracy is difficult to achieve 0.02% F.S per 10˚C. The main influencing factors of the zero temperature output of the sensor are defined, and the circuit compensation method and algorithm software compensation method are proposed. Through the compensation method, the sensor precision can be up to 0.02% F.S/10˚C, and the algorithm software compensation method can obtain higher precision.

Keywords:Strain Sensor, The Zero Temperature Output, Compensation, Circuit, Algorithm, Precision

1. 引言

2. 影响传感器零点温度输出因素分析

$\frac{\Delta R}{R}=K\epsilon$ (1)

${\epsilon }_{t}=\frac{1}{K}\cdot {\alpha }_{t}\cdot \Delta t+\left({\beta }_{s}-{\beta }_{g}\right)\cdot \Delta t$ (2)

$\frac{\Delta R}{R}=K{\epsilon }_{t}=K\cdot \left[\frac{1}{K}\cdot {\alpha }_{t}+\left({\beta }_{s}-{\beta }_{g}\right)\right]\cdot \Delta t$ (3)

${C}_{t}=\frac{{\epsilon }_{t}}{\Delta t}$ (4)

Figure 1. Diagram of Wheatstone full bridge circuit for strain gage

${U}_{o}={U}_{B}-{U}_{D}=\left[\left(\frac{{R}_{2}+\Delta {R}_{2}}{{R}_{1}+\Delta {R}_{1}+{R}_{2}+\Delta {R}_{2}}\right)-\left(\frac{{R}_{3}+\Delta {R}_{3}}{{R}_{3}+\Delta {R}_{3}+{R}_{4}+\Delta {R}_{4}}\right)\right]×U$ (5)

${R}_{1}={R}_{2}={R}_{3}={R}_{4}=R$ 时，式(5)可简化为

${U}_{o}=\left[\left(\frac{R+\Delta {R}_{2}}{2R+\Delta {R}_{1}+\Delta {R}_{2}}\right)-\left(\frac{R+\Delta {R}_{3}}{2R+\Delta {R}_{3}+\Delta {R}_{4}}\right)\right]×U$ (6)

${U}_{o}=\left[\frac{\Delta {R}_{2}-\Delta {R}_{3}}{2R}\right]×U$ (7)

${U}_{o}=\left[\frac{\Delta {R}_{2}}{R}-\frac{\Delta {R}_{3}}{R}\right]×\frac{U}{2}=\frac{KU}{2}×\left({\epsilon }_{t2}-{\epsilon }_{t3}\right)$ (8)

$\frac{{U}_{o}}{U}=\left({C}_{t2}-{C}_{t3}\right)×\Delta t$ (9)

$\frac{{U}_{o}}{U}=±2×{10}^{-6}×50=±100×{10}^{-6}=±100\text{\hspace{0.17em}}\mu \text{V}/\text{V}$ (10)

3. 传感器零点温度输出电路补偿法

(a) 通用补偿法 (b) 并联电阻补偿法

Figure 2. Diagram of zero temperature drift compensation circuit

${U}_{o}={U}_{B}-{U}_{D}=\frac{{R}_{1}{R}_{3}-{R}_{2}{R}_{4}}{\left({R}_{1}+{R}_{2}\right)\left({R}_{3}+{R}_{4}\right)}×U$ (11)

${R}_{1}={R}_{2}={R}_{3}={R}_{4}=R$ ，并将温度零点补偿电阻Rt串入桥臂电阻R1中，则

$\Delta {U}_{o}={U}_{ot}-{U}_{o}=\frac{R\left(R+\Delta {R}_{t}\right)-{R}^{2}}{\left(R+\Delta {R}_{t}+R\right)2R}×U=\frac{\Delta {R}_{t}}{4R+\Delta {R}_{t}}×U$ (12)

$\Delta {R}_{t}=\frac{4R\Delta {U}_{o}}{U-2\Delta {U}_{o}}$

$\Delta {R}_{t}=\frac{4R\Delta {U}_{o}}{U}$ (13)

$\Delta {R}_{t}={R}_{t}\alpha \Delta t$ (14)

${R}_{t}=\frac{4R\Delta {U}_{o}}{U\alpha \Delta t}$ (15)

${R}_{t}=\frac{4R\Delta {U}_{o}}{U\alpha \Delta t}=\frac{4×350×150×{10}^{-6}}{5×0.004×50}=0.21\text{\hspace{0.17em}}\Omega$

$L=\frac{{R}_{t}S}{\rho }=\frac{0.21×\text{π}×{0.075}^{2}}{1.72×{10}^{-5}}=215.6\text{\hspace{0.17em}}\text{mm}$ (16)

Figure 3. Actual circuit diagram of zero temperature compensation

4. 传感器零点温度输出算法补偿

${U}_{o}={a}_{0}\left(1+\gamma \Delta t\right)$ (17)

${Y}_{o}={b}_{0}\left(1+\beta \Delta t\right)$ (18)

$Y={a}_{0}\left(1+\gamma \Delta t\right)+\lambda {b}_{0}\left(1+\beta \Delta t\right)$ (19)

Figure 4. Diagram of zero temperature compensation sensor model

Figure 5. Zero output curve of the sensor without temperature compensation Which using ZEMIC strain gages

Figure 6. Zero output curve of the sensor without temperature compensation Which using H company strain gages

${U}_{ot}={a}_{0}+{a}_{1}t+{a}_{2}{t}^{2}+{a}_{3}{t}^{3}+{a}_{4}{t}^{4}+\cdots +{a}_{n}{t}^{n}$ (20)

${a}_{n}{t}^{n}+{a}_{\left(n-1\right)}{t}^{\left(n-1\right)}+\cdots +{a}_{4}{t}^{4}+{a}_{3}{t}^{3}+{a}_{2}{t}^{2}+{a}_{1}t+{a}_{0}-{U}_{ot}=0$ (21)

$\begin{array}{l}{t}_{1}+{t}_{2}+\cdots +{t}_{\left(n-1\right)}+{t}_{n}=-\frac{{a}_{\left(n-1\right)}}{{a}_{n}}\\ {t}_{1}{t}_{2}+{t}_{2}{t}_{3}+\cdots +{t}_{\left(n-1\right)}{t}_{n}=\frac{{a}_{\left(n-2\right)}}{{a}_{n}}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}⋮\\ {t}_{1}{t}_{2}{t}_{3}\cdots {t}_{\left(n-1\right)}{t}_{n}={\left(-1\right)}^{n}\frac{{a}_{0}-{U}_{ot}}{{a}_{n}}\end{array}$ (22)

${U}_{Z1ot}=-40-0.65t+0.113{t}^{2}+4.79×{10}^{-3}{t}^{3}-2.36×{10}^{-4}{t}^{4}+2.39×{10}^{-6}{t}^{5}$

${U}_{Z5ot}=34.7-1.71t+0.014{t}^{2}-3.18×{10}^{-5}{t}^{3}-4.51×{10}^{-5}{t}^{4}+6.81×{10}^{-7}{t}^{5}$

${U}_{Z6ot}=34+0.456t-0.092{t}^{2}-4×{10}^{-3}{t}^{3}+2.01×{10}^{-4}{t}^{4}-2.07×{10}^{-6}{t}^{5}$

${U}_{Z8ot}=-22.6+0.85t+0.011{t}^{2}+6.8×{10}^{-4}{t}^{3}-3.1×{10}^{-5}{t}^{4}+3.09×{10}^{-7}{t}^{5}$

${U}_{H1ot}=-37-t+0.044{t}^{2}+4.98×{10}^{-3}{t}^{3}-1.71×{10}^{-4}{t}^{4}+1.49×{10}^{-6}{t}^{5}$

${U}_{H3ot}=58.2-2.22t-0.0356{t}^{2}-6.19×{10}^{-4}{t}^{3}+4.15×{10}^{-5}{t}^{4}-4.4×{10}^{-7}{t}^{5}$

${U}_{H4ot}=17.8-0.86t-2.31×{10}^{-3}{t}^{2}+4.32×{10}^{-4}{t}^{3}-2.48×{10}^{-5}{t}^{4}+3.02×{10}^{-7}{t}^{5}$

${U}_{H7ot}=-9.6-0.85t+0.0243{t}^{2}+1.66×{10}^{-3}{t}^{3}-4×{10}^{-5}{t}^{4}+2.7×{10}^{-7}{t}^{5}$

5. 传感器零点温度输出补偿结果验证

5.1. 电路补偿验证

Table 1. List of uncompensated sensor test data

Table 2. Sensor test results after compensation

5.2. 算法软件补偿验证

(a) ZEMIC应变计样品热输出曲线(b) H公司应变计样品热输出曲线

Figure 7. The thermal output test curves of ZEMIC and H company strain gages

(a) ZEMIC应变计制作传感器ZTC拟合曲线(b) H公司应变计制作传感器ZTC拟合曲线

Figure 8. ZTC fitting curve of aluminum sensors were made by different strain gages

6. 结论

Analysis of Zero Temperature Compensation of Resistance Strain Sensor[J]. 传感器技术与应用, 2019, 07(02): 39-49. https://doi.org/10.12677/JSTA.2019.72005

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