RU2444700C1 - Method to adjust strain gauges with bridge measuring circuit by multiplicative temperature error with account of non-linearity of temperature characteristic of gauge output signal - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: method consists in identification of the rating of a thermally dependent resistor R_α, for the specified temperature resistance coefficient, sec, and the rating of the thermally independent resistor R_s, which shunts the inlet resistance of the bridge circuit, based on the condition of compensation of the multiplicative temperature error. Besides, resistors R_α and R_s are installed into an output diagonal of the bridge circuit operating for load resistance of R_L≤2 kOhm. For this purpose the rating of the output resistance of the bridge circuit R_out is identified, as well as its temperature resistance coefficient α_r ⁺ and α_r ^- for two temperature ranges, Δt⁺=t⁺-t₀ and Δt^-=t^--t₀, where t₀, t⁺, t^- - accordingly the normal temperature and extreme points of temperatures of the gauge working temperature range. Bridge circuit temperature coefficient of frequency α_∂0 ⁺ and α_∂0 ^- for two temperature ranges of gauge operation at R_L≥500 kOhm and non-linearity of bridge circuit temperature coefficient of frequency (Δα_∂0=α_∂0 ⁺-α_∂0 ^-) in the temperature range from t⁺ to t^-. If identified α_r ⁺, α_∂0 ^- and Δα_∂0 are in the area of complete compensation of the multiplicative temperature error, ratings of R_α and R_s resistors are calculated. Rates values R_α and R_s are set into the output diagonal of the bridge circuit.

EFFECT: higher accuracy of set-up.

1 tbl, 3 dwg

Description

The invention relates to measuring equipment and can be used to configure strain gauge sensors with a bridge measuring circuit for a multiplicative temperature error.

A known method of compensating for the multiplicative temperature error of a bridge circuit (see "Designing sensors for measuring mechanical quantities" edited by E.P. Osadchy, 1979), which consists in installing a temperature-dependent compensation resistor R _α and a thermally independent resistor in the power supply circuit of the bridge measuring circuit R _W , shunting the input resistance of the bridge circuit, and calculating their ratings through the physical characteristics of the elements that make up the sensor.

However, the use of this method when configuring sensors does not take into account the non-linearity of the sensor output signal from temperature.

In this case, the additional temperature error from non-linearity of the sensor output signal from temperature reaches significant values.

The non-linearity of the output signal from the temperature is determined by three factors:

- the value of the temperature coefficient of resistance (TCS) of strain gauges and its non-linearity in temperature;

- the value of the temperature coefficient of strain sensitivity (TCR) of strain gauges and its non-linearity in temperature;

- the value of the temperature coefficient of the elastic modulus (TCMU) of the material of the elastic element and its non-linearity in temperature.

T.O. depending on their ratio, the non-linearity of the sensor output signal can be either increasing or decaying.

The expression for TCS strain gages has the form [see “Theory, calculation and the basics of designing sensors of mechanical quantities”, V.A. Tikhonenkov, 2000]:

- температурный коэффициент удельного сопротивления материала тензорезистора;Where

- temperature coefficient of resistivity of the material of the strain gauge;

ρ is the resistivity of the material of the strain gauge;

- температурный коэффициент линейного расширения материала тензорезистора (ТКЛР);

- temperature coefficient of linear expansion of the strain gauge material (TLCR);

l is the length of the strain gauge.

In accordance with expression (1), the TCS of the strain gage has a decaying character, that is, it will decrease with increasing temperature, since its TEC for structural materials always has a positive value.

The expression for the temperature coefficient of strain sensitivity (TCR) of the strain gauge has the form [see “Theory, calculation and the basics of designing sensors of mechanical quantities”, V.A. Tikhonenkov, 2000]:

- температурный коэффициент теплоемкости материала тензорезистора;Where

- temperature coefficient of heat capacity of the strain gauge material;

C _ν is the heat capacity of the material of the strain gauge.

In accordance with expression (2), the TFC of the strain gage will increase, that is, it will increase with increasing temperature, however, the strain gages assembled in the bridge circuit can lead to both increase and decrease of the TFC of the bridge circuit, depending on the arm of the strain gauge installation.

The expression for the multiplicative temperature sensitivity has the form [see “Theory, calculation and the basics of designing sensors of mechanical quantities”, V.A. Tikhonenkov, 2000]:

where η _e - TCMU of the material of the elastic element (RE);

α _∂ - TFC of strain gauges;

ΔU _oyt - increment of the output signal when exposed to temperature;

U _n - the output signal of the sensor at a load R _n > 500 kOhm.

For all structural materials, TCMU has a negative value and a decreasing character with increasing temperature, which, in accordance with expression (3), leads to a decrease in the multiplicative error with increasing temperature.

Denoting expression (3) by a current-protective coefficient of strain gauges α _∂ , taking into account the resistance of the measuring power circuit (internal resistance of the power source and an additional resistor used to adjust the sensitivity of the bridge circuit), the output signals when the sensor is in idle mode (load resistance more than 500 kOhm) without exposure and when exposed to temperature will have the form [see “Theory, calculation and the basics of designing sensors of mechanical quantities”, V.A. Tikhonenkov, 2000]:

where E is the EMF of the power source;

R _in - input impedance of the bridge circuit;

R _i is the resistance of the sensitivity adjustment of the bridge circuit;

- суммарное относительное изменение сопротивления тензорезисторов от измеряемого параметра;

- the total relative change in the resistance of the strain gages from the measured parameter;

α _∂ - TFC of strain gauges;

α _r - TCS input resistance of the bridge circuit.

An analysis of expression (5) shows that the use of a bridge measuring circuit also leads to the appearance of an additional nonlinearity of the output signal as a function of temperature when there is a temperature dependence of the input resistance of the bridge circuit and the TFC of the strain gauges:

- with decreasing α _r with increasing temperature, the output signal will have a fading character;

- with increasing α _∂ with increasing temperature, the output signal of the sensor will have an increasing character;

- with decreasing α _∂ with increasing temperature, the output signal of the sensor will have a fading character.

Thus, if α _r and α _∂ have the same character of change in temperature (decreasing), then the sensor will have a decreasing character of the output signal when the temperature changes (negative non-linearity), and when α _r is affected, it is less than the effect of α _∂ , when the latter will have increasing nature of the temperature, the sensor will have an increasing nature of the output signal when the temperature changes (positive non-linearity).

The analysis shows that the non-linearity of the output signal of the sensor when the temperature changes is explained by the change in the total temperature coefficient of strain sensitivity (TFC) of the bridge circuit α _∂о when the temperature changes. The change in the total DC current factor of the bridge circuit is determined by both the change in the input current transformer resistance from the temperature α _r and the change in the current transformer factor of the strain gauges α _∂ . The analytical expression for calculating the total DC link bridge circuit can be determined from the expression [see “Theory, calculation and the basics of designing sensors of mechanical quantities”, V.A. Tikhonenkov, 2000]:

Substituting expressions (4) and (5) into equation (6) and making simple mathematical transformations, we obtain:

Воспроизводимые в процессе изготовления α_r находятся в пределах (0,1-10)·10^-4 1/°С и α_∂ - в пределах (1-10)·10^-4 1/°С.Expression (7) allows us to quantitatively estimate the nonlinearity regions of the general DC coupling of the bridge circuit, i.e. determine the sign of the nonlinearity of the output signal when the temperature changes from the ratio of α _r and α _∂ . Since the nonlinearity of the TCS of the input resistance of the bridge circuit from the temperature Δα _r and the nonlinearity of the TFC of the bridge circuit from the temperature Δα _∂o are of the same order, it can be assumed that the change in α _∂о with temperature

Reproducible in the manufacturing process, α _r is in the range (0.1-10) · 10 ^-4 1 / ° С and α _∂ is in the range (1-10) · 10 ^-4 1 / ° С.

To assess the effect of the non-linearity of the TCD strain gages on the temperature error, we consider an example of compensation of the multiplicative temperature error in accordance with the prototype and determine the obtained temperature sensitivity after compensation from the presence of non-linearity of the TCD bridge circuit.

Example

Determine the temperature sensitivities at the extreme values of the temperature range of operation of the sensor with an equal-arm bridge measuring circuit, in which:

- resistance of strain gages R ₁ = R ₂ = R ₃ = R ₄ = 1000 Ohms;

- resistance of a temperature-dependent resistor R _α = 500 Ohms (obviously greater than necessary to compensate for the multiplicative temperature error);

- TCS input resistance of the bridge circuit in the extreme values of the temperature range are respectively equal

,

;- TKH strain gages in extreme values of the temperature range are respectively equal

,

;

- TCS of a temperature-dependent compensation resistor R _α is temperature independent and is equal to α _к = 4 · 10 ^-3 1 / ° С;

- the total relative change in the resistance of the strain gages at the nominal value of the measured parameter

- temperature range of operation of the sensor 20 ± 100 ° C;

- supply voltage of the bridge circuit U _n = 10 B.

Decision

Define in accordance with the prototype the nominal value of the compensation resistor R _W , for a given R _α , expressing it from the formula (see "Designing sensors for measuring mechanical quantities" edited by EP Osadchy, 1979)

To determine the temperature sensitivities in the extreme values of the temperature range of operation of the sensor, we calculate in accordance with (4) and (5) the deviations of the output signals at a normal temperature of 20 ° C and temperatures Δt ⁺ = + 100 ° C and Δt ^- = -100 ° C.

The total input resistance of the bridge circuit when using a shunt resistor is:

TCS total input resistance of the bridge circuit can be determined by the formula [see “Theory, calculation and the basics of designing sensors of mechanical quantities”, V.A. Tikhonenkov, 2000]:

Then the temperature sensitivities in the extreme values of the temperature range of operation of the sensor [see “Theory, calculation, and design fundamentals of sensors of mechanical quantities”, V.A. Tikhonenkov, 2000]

The calculation results show that the method of compensating for the multiplicative error given in the prototype gives a high degree of compensation only in the temperature range for which the compensation chain R _α , R _{W was} calculated (within ± 1 · 10 ^-4 1 / ° С). In the presence of non-linearity of the DC circuit of the bridge circuit, which is typical for all types of strain gages, the temperature sensitivity at the other extreme point of the temperature range is 2 times higher than the permissible value.

To consider the influence of the nonlinearity of the general TFC of the bridge circuit α _∂о on additional temperature errors, it is necessary to evaluate the change in α _∂о taking into account the sign, taking into account the change in the parameters α _r and α _∂ at extreme values of the temperature range of the sensor from expression (7):

where α ⁺ _∂о and α ^- _∂о - respectively TFC of the bridge circuit at extreme positive t ⁺ and negative t ^- temperature;

и

- соответственно ТКЧ тензорезисторов и ТКС входного сопротивления датчика при крайней положительной температуре t⁺;

and

- respectively, the TCC of the strain gauges and the TCS of the sensor input resistance at an extremely positive temperature t ⁺ ;

и

- соответственно ТКЧ тензорезисторов и ТКС входного сопротивления датчика при крайней отрицательной температуре t^-.

and

- respectively, the TCC of the strain gages and the TCS of the input resistance of the sensor at extreme negative temperature t ^- .

а

где Δα_r - нелинейность ТКС входного сопротивления от температуры. Так как α_∂ имеет как возрастающий, так и убывающий характер с ростом температуры, то для случая когда α_∂ имеет возрастающий характер, примем

а

где Δα_∂ - нелинейность ТКЧ тензорезисторов от температуры, а для случая когда ад имеет убывающий характер -

а

Примем крайние значения рабочего температурного диапазона t⁺=120°С, а t^-=-80°С (пределы изменения температуры Δt⁺=+100°С и Δt^-=-100°С), тогда, изменяя значения всех параметров, входящих в последнее выражение, можно определить области существования общей нелинейности ТКЧ мостовой цепи при изменении температуры.Since a _r has a decaying character with increasing temperature, we take

but

where Δα _r is the nonlinearity of the TCS input resistance versus temperature. Since α _∂ has both increasing and decreasing character with increasing temperature, for the case when α _∂ has an increasing character, we take

but

where Δα _∂ is the non-linearity of the DTC of the strain gages against temperature, and for the case when hell has a decreasing character -

but

We take the extreme values of the operating temperature range t ⁺ = 120 ° С, and t ^- = -80 ° С (the limits of temperature change are Δt ⁺ = + 100 ° С and Δt ^- = -100 ° С), then, changing the values of all parameters included in the last expression, it is possible to determine the region of existence of the general nonlinearity of the DC-link circuit of a bridge circuit with temperature.

Due to the fact that in order to ensure the possibility of adjusting the sensitivity of the sensor to the nominal value, in the manufacturing process its sensitivity is performed (10-15)% higher than the nominal value, and the sensitivity is adjusted by including an additional resistor in the power circuit, the nominal value of which is within 50-200 ohms. Therefore, in the calculation we take the resistor R _i = 100 Ohms. Let us determine the effect of α _r and α _∂ at R _in = 1000 Ohms on the general nonlinearity of the DC circuit of the bridge circuit with a change in temperature in the ranges of their reproducible characteristics during the manufacturing process.

Figure 1 shows the dependence of the overall nonlinearity of the DC circuit of the bridge circuit from the DC circuit of strain gauges at five values of the TCS of the input resistance of the bridge circuit α _r = (1,3,5,8,10) × 10 ^-4 1 / ° С in accordance with the expression (8 ) In this case, each value of the TCS of the bridge circuit corresponds to four realizations, each of which corresponds to one of the values Δα _∂ = (- 5; 0; 3; 5) × 10 ^-6 1 / ° С. All implementations are straight lines, which are located left to right as Δα _∂ values increase.

An analysis of the results shows:

- with an increase in the TCS of the input resistance of the bridge circuit, the general non-linearity of the DC-link circuit of the bridge circuit shifts to the negative side, that is, it becomes damped, despite the increasing character of the non-linearity of the DC link of strain gauges;

- for α _∂ = 1.0 · 10 ^-4 1 / ° С, the general non-linearity of the TFC of the bridge circuit becomes negative in the entire range of non-linearity of the TFC of strain gauges even with the TCS of the input resistance of the bridge circuit more than α _r = 6 · 10 ^-4 1 / ° FROM;

- the total TFC of the bridge circuit increases with the growth of the TCS of the bridge circuit and exceeds the TCR of the strain gauges;

- with a positive general non-linearity of the TFC of the bridge circuit, the non-linearity is within the non-linearity of the TFC of the strain gages, and with a negative one it can exceed the non-linearity of the TFC of the strain gauges by several times, that is, with an increase in the TCS of the input resistance, the bridge circuit additionally compensates for the TCC of the strain gauges;

- with the decreasing nature of the TCF of the strain gauges, the general nonlinearity of the TCF of the bridge circuit is always negative, that is, with increasing temperature, the TCI of the bridge circuit will have a decaying character.

- with the growth of the TFC of the strain gauges, the general nonlinearity of the TFC of the bridge circuit shifts to the positive side, that is, the TFC of the bridge circuit becomes more increasing;

- the general non-linearity of the DC current factor of the bridge circuit increases with the increase of the DC voltage gages of the strain gauges and increases from α _∂ ⁺ = 2.0 · 10 ^-4 1 / ° С exceeds the non-linearity of the DC voltage gages of the strain gages;

- the total TFC of the bridge circuit (α ⁺ _∂о ) increases with the growth of the TFC of the strain gauges, but does not exceed its value, that is, the bridge circuit itself partially compensates for the TFC of the strain gauges;

- with a simultaneous increase in the TCS of the input resistance of the bridge circuit and the TFC of the strain gauges, there is a mutual compensation of their influence on the general nonlinearity of the TFC of the bridge circuit;

- TFC of strain gauges has a greater effect on the overall temperature nonlinearity of the TFC of the bridge circuit than the TCR of the input resistance, and as a result, α _r and α _∂ become more positive (increasing) with the same increase;

- if the TCS of the input resistance of the bridge circuit increases faster than the TFC of the strain gauges, then the temperature nonlinearity of the TCR of the bridge circuit becomes negative, that is, it will have a damping characteristic.

In accordance with the considered example, there are two areas of general nonlinearity of the DC coupler of a bridge circuit:

- positive, determined by the increasing nonlinearity of the TCF of the bridge circuit α _∂о = (0.0-10.0) × 10 ^-4 1 / ° С, the compensation of which is possible by increasing the nonlinearity of the TCS input resistance of the bridge circuit;

- negative, determined by the TCS of the input resistance, the influence of which on the non-linearity of the _{DC current factor of the} bridge circuit exceeds the influence of the positive nonlinearity of the _{DC current transformer of} strain gauges or when both characteristics have a damped character α _∂o = (0.0-20.0) × 10 ^-4 1 / ° С.

T.O. Although the method of compensating for the multiplicative temperature error described in the prototype can significantly reduce this error, it is applicable only in cases with a linear temperature characteristic of the output signal, which requires the development of a method for compensating for the multiplicative error taking into account the nonlinearity of the temperature characteristic of the sensor output signal (full compensation of the multiplicative temperature errors).

The invention consists in the following.

The problem to which the claimed invention is directed is to develop a method for tuning strain gauge sensors with a bridge measuring circuit based on a multiplicative temperature error, which would improve the accuracy of compensation for a multiplicative temperature error during the setup process.

The technical result consists in increasing the accuracy in the process of tuning strain gauge sensors with a bridge measuring circuit by a multiplicative temperature error.

The technical result is achieved by the fact that to configure strain gauge sensors with a bridge measuring circuit based on a multiplicative temperature error, taking into account the non-linearity of the temperature characteristic of the sensor output signal, the value of the thermally dependent resistor R _α for a given TCS α _k and the value of the thermally independent resistor R _w , shunting the output resistance of the bridge circuit, from the condition for compensation of the multiplicative temperature error. Moreover, the resistors R _α and R _W set in the output diagonal of the bridge circuit operating on the load resistance R _n ≤2 kOhm. To do this, determine the nominal output resistance of the bridge circuit R _o and its TCS α _r ⁺ and α _r ^- for two temperature ranges, Δt ⁺ = t ⁺ -t _o and Δt ^- = t ^- -t _o , where t _o , t ⁺ , t ^- - respectively, the normal temperature and extreme temperature points of the operating temperature range of the sensor. The DCT of the bridge circuit α _∂o ⁺ and α _∂o ^is _determined for two temperature ranges of operation of the sensor at R _n ≥500 kOhm and the nonlinearity of the DCT of the bridge circuit (Δα _∂o = α _∂o ⁺ -α _∂o ^- ) in the temperature range from t ⁺ to t ^- . The finding of α _r ⁺ , α _∂o ⁺ and Δα _∂о in the region of existence of full compensation of the multiplicative temperature error is revealed. If the defined α _r ⁺ , α _∂o ⁺ and Δα _∂o are in the specified area, then the values of the thermally dependent resistor R _α and the thermally independent resistor R _W are calculated. Set the calculated values of R _α and R _W in the output diagonal of the bridge circuit.

The method is as follows.

The thermally dependent resistor R _α and the thermally independent resistor R _W are installed in the output diagonal of the bridge circuit operating on the load resistance R _n ≤2 kOhm. The output voltage of the sensor on the load resistance, when a thermally dependent resistor R _{α is} included in the output diagonal of the bridge circuit, will look like [see “Theory, calculation and the basics of designing sensors of mechanical quantities”, V.A. Tikhonenkov, 2000]:

where U _xx is the output voltage of the bridge circuit in idle mode (at the load resistance R _n > 500 kOhm);

R _n - load resistance (input resistance of the normalizing Converter);

R _o - the output resistance of the bridge circuit.

When a thermally dependent resistor R _{α is} included in the output diagonal of the bridge circuit and a thermally independent resistor R _{w is} installed in parallel with the bridge circuit output resistance, expression (9) takes the form:

Under the influence of temperature on the considered circuit, provided that the load resistance is thermally independent, expression (10) takes the form:

where α _∂o - _DCB bridge circuit, determined by (6) at R _n > 500 kOhm;

α _r - TCS output resistance of the bridge circuit;

α _to - TCS thermally dependent resistance R _α .

Then the TFC of the bridge circuit operating on the load resistance R _n ≤2 kOhm (TFC of the sensor), in accordance with (6), will look like:

The condition for compensation of the multiplicative error will be the equality to zero of the TFC of the sensor at the load α _∂n = 0, i.e.

, то естьThe condition for compensation of the non-linearity of the temperature characteristic of the sensor output signal will be the equality of the TFC of the sensor at the load at the extreme values of the temperature range of operation of the sensor

, i.e

To fully compensate for the multiplicative temperature error of the sensor, the calculation of the values of the compensation resistors R _α and R _W must be carried out by solving the system of equations (13) and (14):

To ensure the effectiveness of the compensation resistor R _α, set to the output diagonal of the bridge circuit, the load resistance value R _n must not exceed the value of 2 · R _O, R unnecessarily increase _n> 2 · R _O R _α will require tens of kOhm value, which will lead to a significant drop in the sensitivity of the sensor.

To determine the areas of complete compensation of the multiplicative temperature error of the sensor by the considered circuit, we will calculate the values of the compensation resistors R _α and R _w by solving the system of equations (15) for the circuit parameters considered in the previous example with some refinements

R _o = 1000 Ohms, R _n = 2000 Ohms;

- TCS output resistance of the bridge circuit α _r ⁺ is in the range (0-10) · 10 ^-4 1 / ° C;

- nonlinearity of the TCS output resistance of the bridge circuit

Δα _r = -5.0 · 10 ^-6 1 / ° C;

- TFC bridge circuit α _∂о ⁺ is in the range (0-20) · 10 ^-4 1 / ° C;

- the nonlinearity of the _DC- link circuit of the bridge circuit Δα _∂о is within

(-20-10) · 10 ^-6 1 / ° С.

A graphic image of the zones of complete compensation by the considered circuit according to the results of the above calculations is presented in FIG. 2.

Analysis of the above results allows us to draw the following conclusions:

- full compensation of the non-linearity of the temperature characteristic and the temperature error of the sensor can be carried out in the region of negative non-linearity values from Δα _∂о = -0.2 · 10 ^-6 1 / ° С to Δα _∂о = -12 · 10 ^-6 1 / ° С ;

- all areas of full compensation for the considered non-linearity values have overlapping, which allows a smooth transition with non-linearity compensation in the considered zones.

To determine the areas of change of the compensation resistors in the zones of full compensation, we will calculate them by solving the system of equations (15) in the entire range of changes in the TCS of the output resistance of the bridge circuit from α _r = 0,0 · 10 ^-4 1 / ° С to α _r = 10, 0 · 10 ^-4 1 / ° С.

The calculation results are presented on the graph of the change in the compensation resistors (see Figure 3).

Thus, the use of a compensation circuit for output circuits using a thermally dependent resistor R _α and a shunt resistor R _w installed parallel to the output impedance of the bridge circuit, and analysis of the calculation results allow us to state that:

- the zone of full compensation of negative non-linearity in the direction of low values of TFC of the bridge circuit reaches Δα _∂о = -0.1 · 10 ^-6 ;

- the range of variation of the resistor R _α is from 0.0 to 1000 Ohms for all values of the TCS output resistance and TFC bridge circuit;

- the range of variation of the thermally independent resistor R _W is from 33.0 Ohms to 1.0 MOhm for all values of the TCS output resistance and TFC bridge circuit;

- the change in the values of the resistances R _α and R _W has a damping character with a toast TKCh bridge circuit;

the change in the temperature-dependent resistor R _α for α _r = 0,0 · 10 ^-4 1 / ° С and α _∂о = 10,0 · 10 ^-4 1 / ° С with increasing non-linearity is in the range from 748 Ohms to 992 Ohms, which is less than 25%, and decreases with increasing TCS of the output resistance (at α _r = 0.0 · 10 ^-4 1 / ° С and α _∂о = 10.0 · 10 ^-4 1 / ° С, the change was from 678 Ohms up to 750 Ohms, which is less than 10%);

- a change in the thermally independent shunt resistor R _W for α _r = 0,0 · 10 ^-4 1 / ° С and α _∂о = 10,0 · 10 ^-4 1 / ° С with increasing non-linearity is in the range from 324 Ohms to 40384 Ohms , which is more than 99% of the maximum value, and slightly decreases with increasing TCS of the output resistance (at α _r = 0,0 · 10 ^-4 1 / ° С and α _∂о = 10,0 · 10 ^-4 1 / ° С the change ranged from 38 ohms to 1634 ohms, which is less than 98%).

Thus, the range of TCS of the output resistance α _r ⁺ , TFC of the bridge circuit α _∂o ⁺ and its nonlinearity Δα _∂o , for which full compensation of the multiplicative temperature error is possible, is presented in table 1:

Table 1 TKS R _out α _r ⁺ · 10 ^-4 , 1 / ° С Non- _{linearity of the DC} circuit of the bridge circuit Δα _∂o · 10 ^-4 , 1 / ° С TCC bridge circuit α _∂о · 10 ^-4 , 1 / ° С 0 0 > 0.69 -0.05 ... -0.2 > 0 3.0 0 > 1.28 -0.05 ... -0.2 > 0 5,0 0 > 1.91 -0.05 ... -0.2 > 0 8.0 0 > 2.91 -0.05 ... -0.2 > 0 10.0 0 > 3.59 -0.05 > 1.76 -0.1 ... -0.2 > 0

Let us consider an example to confirm the possibility of full compensation of the multiplicative temperature error by a circuit consisting of a thermally dependent resistor R _α , a thermally independent resistor R _W , shunting the output resistance of the bridge circuit installed in the output diagonal of the bridge circuit operating at a low resistance load R _n ≤2.0 kOhm.

Example

Make full compensation of the multiplicative temperature error of the strain gauge sensor with an equal-arm bridge measuring circuit, having characteristics in accordance with the earlier considered example, differing only in the TCS and TFC parameters of the bridge circuit, selected in accordance with the restrictions on the area of existence of full compensation (see Table 1):

- TCS of the output resistance of the bridge circuit α _r ⁺ = 8.0 · 10 ^-4 1 / ° С;

- nonlinearity of the TCS output resistance of the bridge circuit

Δα _r = -5.0 · 10 ^-6 1 / ° C;

- TCC bridge circuit α _∂o ⁺ = 1.5 · 10 ^-4 1 / ° С;

- non-linearity of the _DC circuit of the bridge circuit Δα _∂о = -5.0 · 10 ^-6 1 / ° С.

Decision

We believe that the bridge circuit is balanced, because the resistance of all shoulders is equal. Then, solving the system of equations (15), it is possible to determine the values of the compensation elements R _α and R _W :

The real roots of the solution of the system of equations are

R _α = 64.3222 Ohms and R _W = 608.7311 Ohms.

To evaluate the accuracy of full compensation of the multiplicative temperature error by the considered circuit, it is necessary, in accordance with equations (10) and (11), to calculate the sensor output signals at a load at normal temperature and extreme temperatures of the sensor operating range:

- at a normal temperature of 20 ° C

- at a temperature of + 120 ° C

- at a temperature of -80 ° C

The temperature sensitivity of the sensor in different temperature ranges can be defined as:

- in the positive temperature range Δt ⁺ = + 100 ° С

- in the negative temperature range Δt ^- = -100 ° С

не превышает 3,5·10^-4 % от предельно допустимого значения температурной чувствительности.Thus, the accuracy of the compensation of the multiplicative temperature error does not exceed 2.5 · 10 ^-4 % of the maximum permissible value of the temperature sensitivity (S _ktdop = 1 · 10 ^-4 1 / ° С), and the accuracy of the compensation of the temperature non-linearity of the output signal

does not exceed 3.5 · 10 ^-4 % of the maximum permissible value of temperature sensitivity.

The proposed method for full compensation of the multiplicative temperature error showed a high accuracy of compensation, which depends only on the accuracy of manufacturing compensation resistors and the accuracy of determining the physical characteristics of strain gauges.

Claims (1)

A method for tuning strain gauge sensors with a bridge measuring circuit based on a multiplicative temperature error taking into account the non-linearity of the temperature characteristic of the sensor output signal, which consists in determining the value of the thermally dependent resistor R _α for a given TCS α _k and the value of the thermally independent resistor R _w , shunting the input resistance of the bridge circuit, from the condition multiplicative error compensation temperature, characterized in that the resistors R _α and R _w is set to an output diagonal Mostovo circuit operating at the load resistance R _n ≤2 ohms, which define the nominal bridge circuit output impedance R _O and TCR and α _r ⁺ α _r ^- two temperature ranges, Δt ⁺ = t ⁺ -t _o and Δt ^- = t ^- -t _o , where t _o , t ⁺ , t ^- are the normal temperature and extreme temperature points of the operating temperature range of the sensor, determine the output voltage U ⁺ _output , U ^- _output , U _output with a load resistance of R _n > 500 kOhm, extreme points and the normal temperature of the operating temperature range of the sensor, respectively, calculate TKH bridge _∂o chain α ^+, α _∂o ^- by the formula:

,
and the nonlinearity of the DC circuit of the bridge circuit (Δα _∂o = α _∂о ⁺ -α _∂о ^- ) in the temperature range from t ⁺ to t ^- , it is found that α _r ⁺ , α _∂о ^- and Δα _{∂о are the} regions of the existence of full compensation in according to table 1:

and if certain α _r ⁺ , α _∂o ^- and Δα _∂o are in the specified area, then the values of the thermally dependent resistor R _α and the thermally independent resistor R _{W are} determined by solving the system of equations:

and set the calculated values of the thermally dependent resistor Rα and the thermally independent resistor R _W in the output diagonal of the bridge circuit operating on a low-impedance load R _n ≤2 kOhm.

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