Design and production of sensors, devices and systems

UDC 681.586"326:621.3.088.228

ON NORMALIZING THE TEMPERATURE ERROR OF STRAIN GAUGE SEMICONDUCTOR SENSORS

V. M. Stuchebnikov

For strain gauge sensors of mechanical quantities operating in a wide temperature range, normalizing the additional temperature error using a linear temperature coefficient leads to a significant distortion of the measurement results. The article shows that it is more correct to normalize the temperature error zone in the temperature range in which the sensors are thermally compensated. This is especially important for semiconductor strain gauge sensors with nonlinear temperature dependence of the output signal.

Additional temperature error is an important characteristic of sensors of mechanical quantities, determining the error of their measurement. Therefore, it is always indicated among the main parameters of these sensors. Most manufacturers normalize the additional temperature error using a linear temperature coefficient, that is, as a percentage of the sensor output range of one or ten degrees Celsius (or Fahrenheit in English-speaking countries). In this case, as a rule, it is assumed that the sign of the temperature error can be of any kind, so it is usually indicated as ±y %/°C (or ±y %/10 °C). So it is recommended to normalize the temperature error and regulations IEC (for example,), and after them Russian standards (for example,).

This article discusses the disadvantages of this method of normalizing the additional temperature error of sensors of mechanical quantities, which are especially evident in strain gauge sensors. semiconductor sensors, which today constitute the majority of sensors used for pressure, force, motion parameters, etc. In specific examples, strain gauge pressure sensors based on heteroepitaxial silicon-on-sapphire (SOS) structures, widely used in Russia, are used.

It is quite obvious, firstly, that the specified rationing makes sense only when linear dependence temperature sensor output signal. However, a linear approximation of the temperature dependence of the output signal of a strain gauge sensor with an acceptable degree of accuracy can only be used for sensors with metal strain gauge resistors and/or in a relatively small temperature range. Since semiconductors are characterized by a strong and nonlinear dependence of parameters on temperature, the output signal of semiconductor strain gauge sensors, as a rule, is significant.

strongly nonlinearly depends on temperature, which is especially noticeable when operating in a wide temperature range.

Secondly, this rationing actually disorients the consumer, forcing him to double the real measurement error. The fact is that for specific sensors with a linear temperature dependence of the output signal, the slope of this dependence has a very definite sign, so the signal can only either decrease or increase with temperature. By expressing the normalization of the temperature error in %/°C indicating a certain value and sign, the consumer can actually evaluate and take into account the measurement error, for example, pressure, at a certain temperature; however, if the sign is not determined, then the measurement uncertainty increases greatly.

This is illustrated in Fig. 1. In Fig. 1a shows the case when the measured pressure (proportional to the sensor output signal) decreases linearly with increasing temperature. In this case, at a known temperature "meas", the consumer can take into account the temperature error and bring the pressure measured by the sensor rms to the actual pressure rn, which is normalized at the "normal" temperature "n:

Рн = Rizm - U ("izm - "nX (1)

where y is the slope of the dependence p (") (y< 0). Конечно, при этом, как минимум, сохраняется неопределенность фактического давления, определяемая основной погрешностью датчика (полоса, ограниченная штриховыми прямыми на рис. 1, а).

The situation is completely different when the sign of the temperature error is not determined (see Fig. 1, b). In this case, even at a known measurement temperature, the uncertainty of the measured pressure is Dr = (рн1 - рн2) even without taking into account the main error of the sensor.

Of course, if the measurement temperature is unknown even approximately, and all that is known about it is that it

Rice. 1. Temperature error of pressure measurement with a linear dependence of the sensor output signal on temperature in the case of a negative (a) and uncertain (b) sign of the linear temperature coefficient y

lies within the (max - min) operating temperature range, the resulting pressure measurement uncertainty is

"Рм = (Р2 - Р1) = IУI ("max - "min) (2)

regardless of whether the sign of the slope coefficient of the straight line p(") is known or not.

Let us consider the case of nonlinear temperature dependence of the output signal of a strain gauge transducer (TC). For example, for pressure transformers based on SOS structures, the temperature drift of which is compensated by a circuit with thermally independent resistors, the dependence of the output signal on temperature is close to parabolic. Silicon TCs with diffusion or implanted strain gauges have a similar dependence. Accordingly, the pressure measured by a sensor with such a TP (proportional to the output signal of the sensor) is also not

linearly depends on temperature (Fig. 2), unless special measures are taken to further correct it in electronic circuit, for example, using a microprocessor. In this case, in accordance with the letter of the regulatory documents, if the temperature error is normalized by a linear coefficient, then it is necessary to indicate the maximum (in absolute value) value of the slope + ummax of the tangent to the parabola (thin straight lines in Fig. 2). As a result, the standard total temperature error in the operating temperature range "max..." min should be determined by expression (2):

"Рн = (Р2 - Р1) = 1 Umax _ ("max - "min") (3)

Obviously, this value far exceeds the actual total temperature error (see Fig. 2)

"Rf = (Rn - Rmin). (4)

It follows that with a nonlinear temperature dependence of the sensor output signal, it is meaningless to use the linear temperature coefficient y to normalize the additional temperature measurement error, since within the operating temperature range it changes in magnitude and sign (including passing through zero), and existing rules in the operating manual it is necessary to indicate the maximum (in absolute value) value of Y.

It is for this reason that in MIDA-13P pressure sensors, as a measure of additional temperature error, the temperature error zone is normalized in the operating temperature range "Rf", which is indicated in the sensor passport. Statistical data on the size of the temperature error zone of MIDA-13P sensors are given in the article. It is necessary to say that Gosstandart fully agrees with this approach and all regulatory documents of MIDA sensors are recognized by the State Register of the Russian Federation.

Rice. 2. Determination of the zone of temperature error in pressure measurement for a sensor with a nonlinear temperature dependence of the output signal:

"Рф - actual zone of temperature error; "Рн - standard zone of temperature error when normalizing the temperature error by a linear coefficient of temperature dependence

ZepBOGB & Sysfems No. 9.2004

Rice. 3. Typical temperature dependence of the additional temperature error in pressure measurement with a MIDA-13P sensor, temperature compensated in a 120-degree temperature range (-40...+80 °C)

"Normal" temperature "n = (20 ± 5) °C. With thermal compensation in another temperature range of the same width (for example, 200...320 °C), the temperature dependence of the error has a similar form (but in this case for the given example “normal” temperature should be Tn = (260 ± 5) °C)

Measurement errors in the temperature error zone (along with the linear temperature coefficient) are also allowed by some foreign standards.

A few more points need to be made. Firstly, in sensors with a temperature dependence of the output signal close to parabolic (namely, this is what it is in MIDA pressure sensors), the temperature error zone is minimal when the “normal” temperature “n”, at which the sensor is calibrated and its main error is determined, is in the middle of the operating temperature range (in which temperature compensation of the output signal is carried out).In MIDA-13P sensors this is performed automatically (operating temperature range from -40 to +80 °C, normalization at 20 + 5 °C - see Fig. 3 In high-temperature MIDA-12P sensors, in which the temperature of the measured medium can reach 350 °C, the situation is somewhat more complicated and will be discussed in more detail below.

Secondly, if in the case of a linear temperature dependence, when the operating temperature range is reduced, the total temperature error decreases linearly, then with a parabolic dependence this decrease is quadratic - for example, with a symmetrical reduction in the operating temperature range by half (for example, from -40...+80 ° From to -10...+50 °C) the temperature error zone is reduced by four. This makes it possible to create high-precision pressure sensors operating in a limited temperature range without the use of complex electronics. Thus, in the range of 0...40 °C, the typical temperature error zone of MIDA-13P pressure sensors with a resistive temperature compensation circuit does not exceed 0.2% (see Fig. 3).

Thirdly, if the “normal” temperature at which the main sensor error is determined (usually room temperature) is not in the center of the temperature compensation range, then ignoring the nonlinearity of the temperature dependence of the error

It is clear that after 4 years the question is no longer relevant, but as I understand it, at +23C an error was obtained (25.04/25-1)*100%= +0.16% (in% of URL, which is 25MPa), at +55C it was The resulting error is (24.97/25-1)*100% = -0.12%.

And the sensor error at +23C is normalized as 0.2% of URL, and at +55C it should be 0.2%+0.08%*(55C-23C)/10C = 0.456% of URL.

that is, there cannot be any problems with verification (at +23C we have +0.16% with a tolerance of +/-0.2%, at +55C we have -0.12% with a tolerance of +/-0.456%). At +55C the device even turned out to be more accurate than at normal (+23C) temperature.

That is, there can be no problems with verification (at +23C we have +0.16% with a tolerance of +/-0.2%...

It seems that all the readings taken fit within the basic error , equal in this case to 0.05MPa....

The following question arose: the pressure sensor, which is preparing for type testing for a measuring instrument...

During these tests, the correctness and validity of the MX... proposed by the developer of this sensor must be established, in this case additional sensor error due to temperature changes environment...

The measured values ​​showed that the main error of the tested sensor did not exceed the value of the limits of permissible error proposed by the developer for it - ±0.2% or in absolute values ​​±0.05 MPa, but

the obtained value of the additional error from the temperature change for this sensor exceeded The developer's proposed value for the limits of permissible additional error:

According to the method for calculating the additional temperature error, we obtain:

(24.97-25.04)/(25*0.1*(55-23)) * 100 = -0.0875%, i.e. The sensor does not fit into the additional temperature error!!!

Those. the developer assumed that this type of sensor has additional error from a change in temperature of ±0.08% of URL for every 10°C, and when checking this value on the first sensor it came across, it turned out to be -0.0875%....

Here the question immediately arises as to whether the developer has set the value correctly additional error from a temperature change equal to ±0.08% of URL for every 10°C..., because it is necessary to check not the total error of the sensor at a temperature of +55°C, as you do (imagine what would happen if the obtained value of the main error was at the permissible limit for this sensor...), namely, the parameter which is normalized..., i.e. size changes errors from the corresponding changes temperatures....

Moreover, the measured values ​​make it possible to estimate the additional error from temperature changes only up from the temperature taken as normal +23°C.

It is also necessary to estimate the additional error from temperature changes down from the temperature taken as normal +23°C, i.e. at -40°C, and this change is not 32°C, as up to a temperature of +55°C, but 63°C...., i.e., most likely, the value of the additional error from the temperature change down the result will be even greater than the value obtained for this sensor up (-0.0875%)....

As a rule, the additional error from temperature changes for SI is set to the maximum of the additional errors up And down...., or, in rare cases, two - different...

Therefore, in this case, it is necessary to carry out a series of additional tests on a representative sample of the sensors under consideration in order to establish an adequate additional error for them (for this type of sensor) from temperature changes...

5.2. Errors temperature measurements contact sensors

Errors in temperature measurements are discussed in many monographs and publications, the number of which amounts to hundreds and even thousands. Here we will consider this problem briefly, simplified, schematically based on the most typical measurement situations. The main goal of this consideration is to focus on the correct choice of sensor, meaningful, expedient organization of a measurement experiment that ensures a reduction; inevitable errors, as well as the possibility of their approximate assessment.

We will consider here only errors of thermal origin, caused by various thermophysical characteristics of the sensor and the measured object, as well as the influence on the formation of the temperature field of the sensor not only of the main type of heat transfer, due to which the temperature of the sensitive element of the sensor should be equal to the measured temperature of the object, but also of secondary types of heat transfer, distorting the temperature field of the sensor. These reasons lead to the fact that when measuring stationary temperatures, the steady-state temperature value of the sensor differs from the measured temperature of the object. This difference is the error caused by secondary types of heat transfer.

When measuring non-stationary temperatures, an error is added, which is usually called dynamic, caused by the thermal inertia of the sensor. And secondary types of heat transfer contribute to this error.

In addition, in the presence of external energy sources, in the event of their interaction with the sensor, it is also possible to distort the temperature of the sensor, which is in the nature of additional heating, forming a corresponding sensor error. Such errors include errors caused by the conversion of the kinetic energy of a high-speed gas flow during its braking at the sensor into the enthalpy of the sensor, as well as heating of the sensitive element of the resistance thermometer by the measuring current.

As already noted, the temperature of the surfaces of structural elements is measured using resistance thermometers and thermocouples. The smaller the size of the sensor, the smaller its own heat capacity and thermal resistance, and the smaller the influence of secondary types of heat transfer (in this case, the main heat transfer process is conductive heat exchange between the measured surface and the sensor), the smaller the errors in such measurements.

Consider measuring the temperature of a plate of thickness L 0 flat resistance thermometer. On both sides of the plate, the conditions presented in Fig. 5.3, a. Here α 1 and α 2 are the coefficients of convective heat exchange between the surfaces of the plate and the medium; T 1 And T 2  ambient temperature; T C1 and T C2 is the temperature of the plate surfaces; l d  sensor thickness. Both the sensor and the plate have a relatively finite thickness l d And l 0 , other sizes are unlimited. Thus, it is assumed that the case b) corresponds to the case where the sensor is located on the side opposite to the heating source, the case V) from the side of the heating source, and installing the sensor does not change the heat transfer coefficients α 1 and α 2 .

It is assumed that the temperature measured by the sensor corresponds to the placement of the sensing element in its central section (L D /2).

Let us denote by Λ 0 and Λ d the thermal conductivity coefficients of the plate and sensor, respectively.

When measuring the stationary temperature of a plate, the error has the form:

for the occasion b):

(5.12)

for the occasion V):

(5.13)

Because the L d /Λ d = P d , L 0 / Λ 0 = P 0 thermal resistances of the sensor and plate, respectively, we can rewrite the given error relations in terms of thermal resistances: case b):

(5.14)

(5.15)

When measuring non-stationary temperatures, expressions for steady-state errors under the assumption that the measured surface temperature varies linearly T WITH = T 0 + bτ And α 2 = 0, have the form:

happening b):

(5.16)

happening V):

(5.17)

(5.18)

(5.19)

The assumption that the heat transfer coefficient on the side opposite the heating source is equal to zero means the assumption of adiabatic insulation of the plate, i.e. it is assumed that all the heat entering it is spent on heating it. This case, to a first approximation, is realized when physical insulation of the plate is introduced on the side opposite to the heating source, or at very low heat transfer coefficients (calm air, rarefied environment during flights at high altitudes). It was thanks to this assumption that it was possible to obtain such simple expressions T mouth .

If the plate is thin and its material has a high thermal conductivity coefficient, then Δ T mouth almost independent of thermal resistance plates. Addiction Δ T mouth from α 1 is hyperbolic in nature, a noticeable dependence at small values α 1 and the dependence practically disappears when α 1 >1000 W/m 2 deg. Thus, the error value is mainly determined by the thermophysical parameters of the sensor. These parameters for the main reinforcing materials of surface resistance thermometers are given in Table. 5.4.

Table 5.4

Values ​​of C d, P d for materials reinforcing the surface of resistance thermometers

Let us consider the error in measuring the plate temperature with a thermocouple for the case shown in Fig. 5.4.

P lamina thickness L 0 be in heat exchange with the environment on both sides of the plate. Accordingly, the heat exchange coefficients with the environment α 1 And α 2 and ambient temperature T 1 And T 2 . Radius of thermocouple thermoelectrodes r d , thermal conductivity of thermoelectrodes is assumed to be the same  Λ d .

We consider the influence of a thermocouple as the action of a heat source Qπ R 2 L 0 (R is the radius of the source).

(5.20)

We consider the influence of a thermocouple as the action of a heat source Q, occupying an area in the plate with a volume π R 2 L 0 (R is the radius of the source).

Then the temperature of the plate in the zone remote from the action of the source is

(5.21)

and relative error

(5.22)

Where K 0 (μ ), K 1 (μ ) – modified Bessel functions of zero and first order;

(5.23)

(5.24)

– heat transfer coefficient of thermocouple thermoelectrodes. Here δ from And Λ from– respectively, the thickness and thermal conductivity coefficient of the insulation of thermocouple thermoelectrodes; α d– coefficient of heat exchange between thermoelectrodes and the environment;

(5.25)

Thermocouple errors for the case shown in Fig. 5.4 are limiting. They can be significantly reduced if the thermoelectrodes are first laid along the measured isothermal surface at a sufficient length (the criterion for sufficiency is the ratio l/ r d>50), and then move away from the surface.

Consideration of the errors of the sensor measuring the temperature of the medium will be reduced to the general diagram presented in Fig. 5.5. The medium can be either gas or liquid.

Designations in Fig. 5.5 T Wed– temperature of the measured medium; T d – temperature measured by the sensor; T st– temperature of the sensor body. It is assumed that T Wed > T d > T st > T To α Wed - coefficient of convective heat exchange between the medium and the sensor; ε d , ε st– emissivity coefficients of the sensor surface and wall; q conv , q cond , q glad– convective, conductive y, radiation heat flows (the last two characterize the thermal losses of the sensor for the measurement situation under consideration); V av – free-flow velocity.

To simplify the consideration, the distribution of temperature and velocity of the medium in the line is assumed to be uniform. The sensor is considered as a rod with a uniform distribution of thermophysical characteristics (for real structures, effective values ​​should be taken). The rod is a temperature meter for the medium. In the stationary case, if there were no heat losses from the rod to the colder body (q cond) and losses due to radiation to the colder walls (q rad) and if there were no errors due to braking, then the sensor would measure the temperature of the medium. If the temperature of the medium changes over time, then a dynamic error occurs due to the thermal inertia of the sensor. In reality, sensor errors are formed by the following components:

The combined manifestation of errors caused by conductive heat loss and dynamic heat loss can be called static-dynamic error

(5.27)

With the formulated simplifications, this error

(5.28)

(it is assumed that the temperature at the sensor changes abruptly to T av from the initial value T d (0) = 0). Here

(5.29)

– temperature of convective heating of the sensor;
–specific heat capacity, specific gravity, cross-sectional area of ​​the sensor rod;

(5.30)

– temperature of conductive heat transfer of the sensor rod; A– effective coefficient of thermal diffusivity of the sensor rod; L  rod length.

It can be seen that the presence of a heat sink from the rod to the sensor body leads to the formation of a static error

(5.31)

It can also be seen that the dynamic error decreases in the presence of conductive heat transfer.

In fact, the rate of change in the temperature of the sensor rod

(5.32)

and thermal inertia is the reciprocal of tempo.

Depending on heat transfer conditions and rod structure

, (5.33)

Where ψ(α dk )  coefficient of unevenness of the temperature field of the rod; a dt ,  coefficient of “conductive heat transfer” of the rod; F – thermal factor. Because the

(5.34)

(5.35)

Reciprocal of tempo M called thermal inertia coefficient

ε = 1/M,(5.36)

and addiction ε (a dk )  characteristic curve of thermal inertia.

Thus, the error caused by the joint manifestation of thermal inertia and heat removal depends on the coefficients of convective and conductive heat transfer, the thermal factor Ф and the coefficient of unevenness of the temperature field of the rod ψ(α dk ).

The overall error in measurements increases with increasing heat sink to the body, because in the presence of a heat sink, the more quickly the steady-state temperature value is realized, the more it is distorted by the static error of the heat sink.

Determining the values ​​of static errors and characteristic curves of thermal inertia comes down to finding three parameters that characterize the sensor: α dt , ψ(α dk ) , Φ . Magnitude ψ(α dk ) can be represented in the form

(5.37)

(5.38)

 equivalent of the thermal resistance of the sensor rod. For a rod shape in the form of a plate n = 3, in the form of a cylinder - n = 4, in the form of a ball - n = 5 (strictly valid for conditions of a regular thermal regime of the second kind).

If the rod has a heterogeneous structure - a uniform shell (protective casing) with a core with low thermal conductivity and noticeable thermal resistance, then the limiting value of the coefficient of thermal inertia is determined by the core of the rod (ε ∞ = HF), and the static error is the thermal conductivity of the shell. In this case, the value α dt is easily calculated if you know the geometric dimensions of the shell and the thermal conductivity coefficient of the casing material.

Summary data on the values ​​of static-dynamic parameters of some representative design types of sensors are given in Table. 5.5.

Table 5.5

Static-dynamic parameters of temperature sensors

(5.39)

Where b– rate of temperature change.

The error caused by the radiation heat exchange of the sensor with the walls of the pipeline, which have a temperature lower than the measured temperature of the medium, can be estimated from the following consideration.

If the gas whose temperature is measured is transparent, then the specific heat flux from the sensor to the walls is:

(5.40)

(5.41)

– coefficient of radiant heat exchange between the sensor and the wall ( ε s – black body emissivity coefficient); s d / s st – the ratio of the surface areas of the sensor and the wall exposed to radiation heat exchange.

If we consider the stationary problem of equality of the heat flux supplied to the sensor due to convection and heat loss to the walls due to radiation, then the joint solution of q conv and q rad relative to T d allows you to get a steady value T d And

(5.42)

An effective way to reduce errors caused by radiation losses (by almost an order of magnitude) is to introduce an anti-radiation screen between the sensor and the walls. It is also necessary to keep in mind that at ambient temperatures above plus 500°C, the gas’s own radiation appears, which itself has a shielding effect. Approximately the same effect can be achieved by introducing coatings of the sensitive element of the sensor that have low emissivity coefficients (silver, gold, platinum).

When the flow is decelerated at the sensor, the sensor measures a temperature that exceeds the equilibrium thermodynamic temperature of the gas flow, but does not reach the stagnation temperature value, since the deceleration of the flow at the sensor is incomplete. If Tsr equilibrium thermodynamic temperature of the gas flow, and T*- braking temperature

(5.43)

Where K = c h / c v - ratio of specific heat capacities of gas at constant pressure and constant volume; M =V Wed / V sound  Mach number, i.e. the ratio of the flow speed to the local speed of sound, then

(5.44)

Where r recovery coefficient, characterizing the incompleteness of conversion of the kinetic energy of the flow at the sensor into thermal energy.

Most favorable with from the point of view of the definability and stability of the coefficient of restitution is the longitudinal flow around bodies, in which independence of the coefficient is observed in a wide range of Mach and Reynolds numbers r.

So for a plate thermometer the value r is 0.85. Flow sensitive elements of sensors on a thin-walled tube of small diameter have r = 0.86...0.9, for longitudinally streamlined wire thermocouples r = 0,85... 0,87.

In cross flow around open wire thermocouples r≈ 0.68 ± 0.08.

An effective way to increase the recovery coefficient is to use braking chambers in sensors (an open input with an output hole reduced in area by 25...50 times). With longitudinal flow around a thermocouple in the braking chamber r ≈ 0.98, with transverse r ≈ 0,92... 0,96.

If the working junction of the thermocouple is made in the form of a ball whose diameter exceeds the diameter of the thermoelectrodes, then both in longitudinal and transverse flow r ≈ 0,75.

The correction for determining the static temperature of the flow from the measured equilibrium temperature (or the error if it is not taken into account) has a negative sign and is equal to:

(5.45)

Errors caused by the uneven distribution of temperature across the flow cross section when measured by sensitive elements distributed over the surface require separate consideration.

The role of errors in high-temperature measurements caused by the loss of insulation of reinforcing materials is significant.

For resistance thermometers, the possibility of heating the sensitive element of the thermometer by the measuring current and the associated error, the magnitude of which depends both on the intensity of heat exchange between the thermometer and the environment, and on the thermal resistance and heat capacity of the materials reinforcing the sensitive element, must be taken into account.

When measuring temperature in fields of penetrating radiation, errors due to both instantaneous and integral effects depending on the magnitude of the radiation must be taken into account.

It should be understood that obtaining the information necessary to estimate errors is by no means easier than obtaining basic information. Therefore, they often resort to assessing the maximum error values ​​in order to make sure that they are acceptable.

However, the main thing is to understand the nature of errors and the patterns of their manifestation, since this is the key to the appropriate selection of a sensor and the proper organization of measurements.

The main qualitative characteristic of any instrumentation sensor is the measurement error of the controlled parameter. The measurement error of a device is the amount of discrepancy between what the instrumentation sensor showed (measured) and what actually exists. The measurement error for each specific type of sensor is indicated in the accompanying documentation (passport, operating instructions, verification procedure), which is supplied with this sensor.

According to the form of presentation, errors are divided into absolute, relative And given errors.

Absolute error is the difference between the value of Xiz measured by the sensor and the actual value of Xd of this value.

The actual value Xd of the measured quantity is the experimentally found value of the measured quantity that is as close as possible to its true meaning. In simple terms, the actual value of Xd is the value measured by a reference device, or generated by a calibrator or setter of a high accuracy class. The absolute error is expressed in the same units as the measured value (for example, m3/h, mA, MPa, etc.). Since the measured value may be either greater or less than its actual value, the measurement error can be either with a plus sign (the device readings are overestimated) or with a minus sign (the device underestimates).

Relative error is the ratio of the absolute measurement error Δ to the actual value Xd of the measured quantity.

The relative error is expressed as a percentage, or is a dimensionless quantity, and can also take on both positive and negative values.

Reduced error is the ratio of the absolute measurement error Δ to the normalizing value Xn, constant over the entire measurement range or part of it.

The normalizing value Xn depends on the type of instrumentation sensor scale:

1. If the sensor scale is one-sided and the lower measurement limit is zero (for example, the sensor scale is from 0 to 150 m3/h), then Xn is taken equal to the upper measurement limit (in our case, Xn = 150 m3/h).
2. If the sensor scale is one-sided, but the lower measurement limit is not zero (for example, the sensor scale is from 30 to 150 m3/h), then Xn is taken equal to the difference between the upper and lower measurement limits (in our case, Xn = 150-30 = 120 m3/h ).
3. If the sensor scale is two-sided (for example, from -50 to +150 ˚С), then Xn is equal to the width of the sensor measurement range (in our case, Xn = 50+150 = 200 ˚С).

The given error is expressed as a percentage, or is a dimensionless quantity, and can also take both positive and negative values.

Quite often, the description of a particular sensor indicates not only the measurement range, for example, from 0 to 50 mg/m3, but also the reading range, for example, from 0 to 100 mg/m3. The given error in this case is normalized to the end of the measurement range, that is, to 50 mg/m3, and in the reading range from 50 to 100 mg/m3 the measurement error of the sensor is not determined at all - in fact, the sensor can show anything and have any measurement error. The measuring range of the sensor can be divided into several measuring subranges, for each of which its own error can be determined, both in magnitude and in the form of presentation. In this case, when checking such sensors, each sub-range can use its own standard measuring instruments, the list of which is indicated in the verification procedure for this device.

For some devices, the passports indicate the accuracy class instead of the measurement error. Such instruments include mechanical pressure gauges, indicating bimetallic thermometers, thermostats, flow indicators, pointer ammeters and voltmeters for panel mounting, etc. An accuracy class is a generalized characteristic of measuring instruments, determined by the limits of permissible basic and additional errors, as well as a number of other properties that affect the accuracy of measurements made with their help. Moreover, the accuracy class is not a direct characteristic of the accuracy of measurements performed by this device; it only indicates the possible instrumental component of the measurement error. The accuracy class of the device is applied to its scale or body in accordance with GOST 8.401-80.

When assigning an accuracy class to a device, it is selected from the series 1·10 n; 1.5 10 n; (1.6·10 n); 2·10n; 2.5 10 n; (3·10 n); 4·10n; 5·10n; 6·10n; (where n =1, 0, -1, -2, etc.). The values ​​of accuracy classes indicated in brackets are not established for newly developed measuring instruments.

The measurement error of sensors is determined, for example, when they periodic verification and calibration. With the help of various setters and calibrators, certain values ​​of one or another physical quantity are generated with high accuracy and the readings of the sensor being verified are compared with the readings of a standard measuring instrument to which the same value of the physical quantity is supplied. Moreover, the measurement error of the sensor is controlled both during the forward stroke (increase in the measured physical quantity from the minimum to the maximum of the scale) and during the reverse stroke (decreasing the measured value from the maximum to the minimum of the scale). This is due to the fact that due to the elastic properties of the sensor’s sensitive element (pressure sensor membrane), different rates of chemical reactions (electrochemical sensor), thermal inertia, etc. sensor readings will vary depending on how the force acting on the sensor changes. physical quantity: decreases or increases.

Quite often, in accordance with the verification procedure, the readings of the sensor during verification should be performed not according to its display or scale, but according to the value of the output signal, for example, according to the value of the output current of the current output 4...20 mA.

For the pressure sensor being verified with a measurement scale from 0 to 250 mbar, the main relative measurement error over the entire measurement range is 5%. The sensor has a current output of 4…20 mA. The calibrator applied a pressure of 125 mbar to the sensor, while its output signal is 12.62 mA. It is necessary to determine whether the sensor readings are within acceptable limits.

First, it is necessary to calculate what the output current of the sensor Iout.t should be at a pressure Рт = 125 mbar.

Iout.t = Ish.out.min + ((Ish.out.max – Ish.out.min)/(Rsh.max – Rsh.min))*Рт

where Iout.t is the output current of the sensor at a given pressure of 125 mbar, mA.

Ish.out.min – minimum output current of the sensor, mA. For a sensor with an output of 4…20 mA, Ish.out.min = 4 mA, for a sensor with an output of 0…5 or 0…20 mA, Ish.out.min = 0.

Ish.out.max - maximum output current of the sensor, mA. For a sensor with an output of 0...20 or 4...20 mA, Ish.out.max = 20 mA, for a sensor with an output of 0...5 mA, Ish.out.max = 5 mA.

Рш.max – maximum of the pressure sensor scale, mbar. Psh.max = 250 mbar.

Rsh.min – minimum scale of the pressure sensor, mbar. Rsh.min = 0 mbar.

Рт – pressure supplied from the calibrator to the sensor, mbar. RT = 125 mbar.

Substituting known values we get:

Iout.t = 4 + ((20-4)/(250-0))*125 = 12 mA

That is, with a pressure of 125 mbar applied to the sensor, its current output should be 12 mA. We consider the limits within which the calculated value of the output current can change, taking into account that the main relative measurement error is ± 5%.

ΔIout.t =12 ± (12*5%)/100% = (12 ± 0.6) mA

That is, with a pressure of 125 mbar applied to the sensor at its current output, the output signal should be in the range from 11.40 to 12.60 mA. According to the conditions of the problem, we have an output signal of 12.62 mA, which means that our sensor did not meet the measurement error specified by the manufacturer and requires adjustment.

The main relative measurement error of our sensor is:

δ = ((12.62 – 12.00)/12.00)*100% = 5.17%

Verification and calibration of instrumentation devices must be carried out when normal conditions environment according to atmospheric pressure, humidity and temperature and at rated voltage sensor power supply, since higher or low temperature and supply voltage may lead to additional measurement errors. The verification conditions are specified in the verification procedure. Devices whose measurement error does not fall within the limits established by the verification method are either re-adjusted and adjusted, after which they are re-verified, or, if the adjustment does not bring results, for example, due to aging or excessive deformation of the sensor, they are repaired. If repair is impossible, the devices are rejected and taken out of service.

If, nevertheless, the devices were able to be repaired, then they are no longer subject to periodic, but to primary verification with the implementation of all the points set out in the verification procedure for this type of verification. In some cases, the device is specially subjected to minor repairs () since according to the verification method, performing primary verification turns out to be much easier and cheaper than periodic verification, due to differences in the set of standard measuring instruments that are used for periodic and primary verification.

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