GB2140923A - Resistance thermometer testing - Google Patents

Abstract

In a method for testing the characteristics of a resistance thermometer comprising a resistance element and a support for the resistance element, the support being intended to contact a material the temperature of which is to be sensed, a formula is derived representative of the thermometer's heat transfer function, the formula being of second or higher order and including constants representative of at least the thermal resistance of the support, the thermal capacitance of the support, the thermal resistance of the boundary layer between the support and its surroundings, and the thermal capacitance of the boundary layer between the support and its surroundings. A heating current is passed through the resistance element for a limited period to heat the thermometer. Variations with time of the resistance of the element as its temperature varies are monitored, and the formula constants are calculated such that the formula fits the monitored variations in resistance, the calculated constants being a measure of the characteristics which they represent in the formula.

Description

SPECIFICATION Resistance thermometer testing The present invention relates to resistance thermometers, and in particular to a method and apparatus for detecting changes in he characteristics of such thermometers.

Resistance thermometers are widely used to obtain temperature measurements in for example industrial or experimental processing equipment. In particular, platinum resistance thermometers which comprise a platinum resistance element supported inside a sheath filled with a suitable fluid or solid can give a measurable response to very small temperature changes of tor example 0.0001"C. The thermometers are often used in closed loop systems, for example systems intended to maintain the temperature of a bath of fluid constant, the thermometer output controlling the supply of heat to the bath.

The use of a resistance thermometer in a closed loop system requires a considerable amount of information about its frequency response in order to achieve an optimum response of the system and avoid undesirable behaviour like overshoot or even instabilities. In addition it is desirable to increase the rate of response of the thermometer.

The heat transfer, from the fluid in which the thermometer is immersed to the resistance element itself, determines the dynamic response of the thermometer, i.e. the way in which the output of the thermometer follows any change in the fluid temperature. This heat transfer can be affected by changes within the thermometer itself, e.g. deterioration of the sheath filler, and by changes external to the thermometer, e.g. a build up of contaminants on the sheath or the failure of a stirrer provided to agitate the fluid. It is thus necessary to periodically check the dynamic response of the thermometer if the system of which it forms a part is to operate efficiently.

Once a platinum resistance thermometer has been installed in process equipment, it is highly undesirable to have to periodically remove it from that equipmet for testing because the equipment is put out of action, the thermometer which is delicate can be damaged during handling, and the test cannot truely reproduce the actual working conditions of the thermometer in any event. Accordingly efforts have been directed to achieving reliable in situ testing of resistance thermometers.

It has been proposed to achieve in situ testing by shelf-heating, that is passing a heating current through the resistance element, and then monitoring the output of the resistance element after the heating current is terminated. This method does enable an approximation to the actual thermometer time constant to be derived, and enables changes in the time constant resulting from factors internal to the resistance thermometer (e.g. damage to the thermometer structure) to be distinguished for factors external to the resistance thermometer (e.g. failure of a stirrer normally agitating the fluid around the thermometer).This method does not make it possible however to identify the cause of any internal changes which affect the time constant, or to detect internal damage to the thermometer which does not significantly affect the time constant but might result in premature failure of the thermometer. It would be very useful to be able to identify internal faults in platinum resistance thermometers, whether immediately after manufacture during routine post-manufacture checks, or after the installation of the thermometers in process plants so that faulty thermometers can be discarded and methods of manufacture improved to avoid faults developing.

Usually, a single value for the time constant of the thermometer is supplied by the manufacturer in accordance with a British Standard Specification or its equivalent in other countries. However, this information is not enough for some applications because firstly, it assumes that the thermometer can be modelled as a first order system (one single pole) with a dead zone, and secondly, the conditions under which the test is carried out in the manufacturer's laboratory are very different from those in which the thermometer will work.

It has been shown previously that in order to represent the dynamic response of a platinum resistance thermometer at least a second order model is required. No attempt has been made however to use such a second order model to obtain data representative of the internal condition of a resistance thermometer. It is an object of the present invention to obtain the transfer function of a thermometer in terms of a second or higher order thermal model in such a way that information about the thermometer itself and its operating conditions is obtained, and to use the information obtained to improve the response of the thermometer in terms of its overall time constant.

According to the present invention, there is provided a method for testing the characteristics of a resistance thermometer comprising a resistance element and a support for the resistance element, the support being intended to contact a material the temperature of which is to be sensed, wherein a formula is derived representative of the thermometer's heat transfer function for heat generated by passing current through the resistance element, the formula being of second or higher order and including constants representative of at least the thermal resistance of the suport, the thermal capacitance of the support, the thermal resistance of the boundary layer between the support and its surroundings, and the thermal capacitance of the boundary layer between the support and its surroundings, a heating current is passed through the resistance element for a limited period to heat the thermometer, variations with time of the resistance of the element as its temperature changes as a result of the passage of the heating current are monitored, and the formula constants are calculated such that the formfula fits the monitored variations in resistance, the calculated constants being a measure of the characteristics which they represent in the formula.

The resistance variations may be monitored after termination of the heating current, or during the period when the heating current is flowing.

The thermometer may comprise a resistance element housed within but spaced from a sheath, the sheath being intended to contact the material the temperature of which is to be sensed. The space between the element and the sheath may be filled with for example cement. The constants in such a case represent the thermal resistance and capacitance of the filler, the thermal resistance between the sheath and its surroundings, and the thermal capacity of the sheath. The thermal capacity of the sheath may be negligible if for example it is a thin metal cylinder, but where the thermometer is housed in a robust so-called "well" to protect it from damage the thermal capacity of the sheath may be substantial.

The invention also provides an apparatus for putting into effect the above method, comprising means for passing a heating current through the resistance element for a limited period to heat the thermometer, means for monitoring the variations with time of the resistance of the element as its temperature changes as a result of the passage of the heating current, and means for calculating the formula constants such that the formula fits the monitored variations in resistance.

The invention enables the identification of particular faults in the structure of a resistance thermometer to be detected without removing it from its working position. in addition, the invention enables the detection of certain manufacturing faults during routine production testing which faults would previously not have been detected. Furthermore, an accurate knowledge of the thermometer's characteristics enables the frequency and time response of the device to be compensated to advantageous effect.

The invention is further described below and with reference to the accompanying drawings, in which: Figure 1 shows the typical step response of a platinum resistance thermometer; Figure 2 is a simplified longitudinal sectional view of a cylindrical platinum resistance thermometer; Figure 3 is a schematic representation of the thermal circuit of the thermometer of Figure 2; Figure 4 is a graphical representation of a self heating input step; Figure 5 is a graphical representation of the response of the thermometer of Figure 2 to the heating input step of Figure 4; and Figures 6 and 7 are graphical representations of the frequency response and time response respectively of the thermometer of Figure 2.

Figure 1 represents the response of a platinum resistance thermometer to a step input, i.e. a sudden change in the temperature it is monitoring. The time constant of such a thermometer is usually defined from the step function response as the time taken for the output to reach 63.2% of its final value. Thus in the illustrated example the time constant would be Tc. In fact this definition assumes a very simplified model for the thermometer but nevertheless it would be advantageous to be able to reduce Tc.

The initial step in implementing the present invention requires the derivation of a formula based on a model of the thermal system represented by the thermometer. For example, if we are concerned with a platinum resistance thermometer operating in a fluid in which the temperature gradient in the axial direction is negligible, there is no heat flow in that direction and the heat transfer problem becomes a two dimensional one. This is usually the case when the thermometer is operating in a fluid of turbulent characteristics.

Furthermore, if the sheath of the thermometer and the sensing element itself are considered as two concentric cylinders, as in the case illustrated in Figure 2, the problem is reduced to a uni-dimensional one in cylindrical coordinates. The following description assumes a thermometer structure as shown in Figure 2, that is a cylindrical metal (e.g. stainless steel) sheath 1, a coaxial platinum resistance element 2, and a cement filler 3 occupying the space between the sensing element and the sheath.

It is well known that the differential equation describing the distribution of temperatures and heat flow in a solid including the effects of stored thermal energy in the solid is satisfied by a model which consists of a thermal RC circuit with series thermal resistances and shunt thermal capacitances.

A precise model obviously requires the use of distributed parameters. However, for most practical applications a lumped parameter model is adequate. It corresponds mathematically to the replacement of a differential equation by an equation of finite difference.

Figure 3 represents a notional thermal circuit corresponding to a thermometer having the physical structure of Figure 2 sensing the temperature of a fluid. The constant components of the thermal circuit represent the following physical characteristics: R1 & C1: Thermal resistance and capacitance of the material used to support the sensing element Thermal resistance of the boundary layer of the fluid.

C2: Thermal capacitance of the sheath.

Tf: Fluid temperature.

To: Sensing element temperature.

Q: Heat flow due to self heating.

The thermal resistances of metallic components of the thermometer can be ignored when compared with those of the cement 3 and the fluid surrounding the sheath 1 so that the thermal resistances of the sheath and sensing element can for practical purposes be ignored and are thus not taken into account in the model.

Also, as the sensing element is a coil of very thin platinum wire, it has a negligible mass and its thermal capacitance is ignored for the purposes of the model. The thermal capacitance of the support and of the boundary layer also make small contributions to C2.

The resulting model clearly is a second order system and represents the dynamics of the thermometer of Figure 2 with a high degree of approximation. Its response to an input step function reproduces the shape of Figure 1 including its apparent dead zone.

The above-described simplified model can be used in the dynamic analysis of a resistance thermometer.

In platinum resistance thermometers the transfer functions to be considered are: The self heating transfer function (resulting from passing heating current through the resistance element): Gl(s)= R(s)/Q(s) The external heating transfer function: G2(s) = R(s)/T(s) where all variables are measured from their equilibrium values and expressed as Laplace transforms].

R(s) : sensor output, T(s) : temperature of the surrounding medium, Q(s) : heat flow produced by self heating.

Any change of the temperature in the sensing element will be reflected as an immediate and almost proportional change in its resistance, so the actual transfer functions become: G1 (s) = k * (To(s)/Q(s)) G2(s)= k*(To(s)/T(s)) where K is a real coefficient and To(s) is the temperature of the sensing element.

Considering the simplified form of Figure 3, it can be shown that the transfer functions in terms of the parameters of the circuit are:

Then, the transfer function G2(s) has no zeroes and its poles are the same as for G1 (s). Thus if the poles of G1(s) can be identified, the transfer function G2(s) will be known except for a real coefficient.

Consider now the thermometer of Figure 2 operating in a fluid of constant temperature and suppose that a high current has been passing through the resistance element for a relatively long time and then is suddenly removed. This is equivalent to having an input step in the place of Q(s) as indicated in Figure 4, a step which goes from some positive value to zero.

The transfer function G1(s) can be expressed in a more compact notation as: s+a1 Gi(s) = k1 s+a, (s+p2) where p1 and P2 are the roots of the denominator polynominal, k, = k/C" and a, = R, +R2 R 1 R2C2 The Laplace transform of the response when the input is as described is: To(s) = k1 s+a1 O s(s+p1) (s+p2) By expanding To(s) in partial fractions: To(s) = Bo + B1 + B2 s s+p1 s+p2 If the initial conditions are considered: B0 = Tf;B1 = - k1(a1-p1) Q. B = - k1(a1-p2) P1(P1 P2) 2 p2(p2-p1) In the time domain: To(t) = Bo+B1e-p1t + B2e -p2t....................................(1) Figure 5 shows the kind of response which is observed at the output of the thermometer.

In any practical thermometer which can be modelled as described, the two poles are well separated from each other. This allows their identification as well as that of Bo, B1, B2 by using curve fitting techniques for example least squares techniques.

Once the parameters have been identified, the following equations can be obtained after manipulation of the equation 1 and the initial conditions of the circuit: C1 = Q/So ........................................ 2 R1 = 1/(p1 x p2 x C1 x M) 3 R2 = R1 - (B1 + B2)/Q.............................. 4 C2 = M/R2 5 where So = B1 x p, + B2 x P2 ............................................. 5a M = (p1 + P2)/(P1 x P2) + C1 x (B1 + B2)/Q ......................... 5b Q is given by the exciting current used for the self heating test and the value of the resistance of the thermometer just after the high current is removed.

Equations 2 to 5 provide a complete set of parameters for the thermal circuit.

In order to obtain the overall time constant of the system (defined as the time necessary for the sensor to reach 63.2% of the final output when the input is a step), the response to a unitary step is constructed from the transfer function G2(s).

The Laplace transform of that response can be obtained by multiplying G2(s) by 1/s: k2 To(s) = (s+p1) (s+p2) 5 which, expanded in partial fractions gives: To(s) - A0 + A1 + A2 s s+p1 S+p2 where:

A0 = 1 A1 = p2/(p1 - p2)............................................... 6 A2 = -p1/(p1 - p2) and, in the time domain:: To(t) = 1 + A1e-P't + A2e-P2t Now, consider the case in which p2 p1. In this case, the term in To(t) containing p2 decays more quickly than the term containing p1. Then, after enough time, To(t) can be approximated by: To(t) = 1 + A1e-P't and the time constant is given by: 1 p2-p1 Tc=--1n(0.368 P1) " 7 P1 P2 In a practical implementation of the method of the invention, an instrument is programmed to pass a current on 50mA through the thermometer resistance element for a duration of 120 seconds. After that time, the current is reduced to 1 mA which is used to measure resistances without introducing significant self heating errors in the measurement and a number of readings are taken in rapid succession.The first reading is taken 0.075 seconds after removing the high current and the others with a sampling period of 0.52 seconds.

When the last reading has been taken, the instrument waits for a further 120 seconds to allow the thermometer to reach the surrounding fluid temperature and another reading is taken which corresponds to "Tf" (or "Bo" in the model).

With the measured data the instrument produces a double exponential curve fitting which defines equation 1. Next, by using equations 2 to 5 the thermal model is completed.

The actual time response to a unitary step and its corresponding time constant are calculated by using relations 6 and equation 7.

Once the value of the actual resistance of the thermometer is measured, if some previous readings are known and if enough information about the frequency response is available, digital filtering is possible in order to provide a faster response of the system.

A possible configuration for the filter consists of a single pole and a single zero. The zero cancels the low frequency pole of the thermometer and the pole limits the bandwidth of the system to reduce high frequency noise. Furthermore, if the pole is selected to coincide with the high frequency pole of G2(s), the resulting system will have a damping factor near or equal to unity, there will be no overshoot and the time constant will be reduced.

Figure 6 is a Bode plot showing the response of the system with and without such compensation.

It can be shown that with this configuration a reduction in the overall time constant of the system is achieved. This reduction depends on the separation of the original poles according to the following equation: Tc1=-2.14Tc2 r 1 8 r 1n(0.368 r-1) r where Tc2 is the time constant of the system without compensation, Tc1 is the time constant with compensation, risthe ratio P2/P1 and r > 1.

Equation 8 indicates that for the improvement to be effective the minimum value of r is 1.467. In this case the time constant is reduced by 32%.

For the design of the digital filter the "point to point" transformation can be used. This consists in assigning poles and zeroes in the z plane to poles and zeros in the s plane, i.e. any root (pole or zero) at s = -a is transformed to a root at z = e-aTs. Ts is the sampling period of the system.

After the transformation has been applied and a constant term is used to compensate the difference existing between to compensate the difference existing between the gain of the digital filter and that of the analogue one, the transfer function in terms of z transform for the compensator becomes: 1 - 1ePlTs 1 = k3 1 - z-le-PZT" 1 1 - e-P2 k3 = 1 - The following equation forthe digital filter is obtained: y(k) = k3.u(k) -k3e-P'TsBu(k-1) + e-P2Tsylk-1) This equation means that it is necessary to store the previous input and output values and to perform three multiplications and two additions to obtain the actual output value.

Several tests were performed in order to assess the validity of the above described method. They included: 1) Measurement of the time constant of platinum resistance thermometers by conventional methods and by the above described method.

2) Validity of the model.

3) Digital compensator.

To gain control over the internal parameters, a thermometer was built. It was made from a 4mm wide PLATFILM device in a copper tube of 6mm diameter. The PLATFILM device comprises a film of platinum on a ceramic substrate, The following table shows the results of these tests including the errors after comparing the time constants obtained by the two methods. Results of the "home made" thermometer are also indicated. The space inside the sheath was filled with air.

The tests were performed in an oil bath at 30"C with stirring.

TIME CONSTANT time constant (seconds) thermometer conventional self error type method heating E12382/11139 17.55 17.01 -3% E 12382/16276 18.37 18.69 +2% E 13540 22.95 20.14 -12% BSE712F460082 5.83 5.92 +2% Home Made 21.40 20.01 -6% All of the thermometers with the exception of the last one were manufactured and supplied by ROSEMOUNTENGINEERING CO. PLC.

The highest error in the determination of time constants occurs when the thermometers are PLATFILM type (types E 13540 and "home made") which incorporate a film of platinum on a substrate. This is due to the presence of a third pole introduced by the mass of the sensing element and substrate which in PLATFILM devices can no longer be ignored. In this case constants representative of the thermal resistance and capacitance of the sensing element mass must be included if an accuracy better than 13% is required.

To assess the validity of the selected model the following experiments were performed: a) Thermometer type El 2382 No. 11139 was tested in two different liquids at the same temperature (21"C) and without stirring. The results were: Parameter Water Oil Difference R1 3.532 3.489 C1 0.944 0.951 +0.7% R2 1.947 3.622 +86% C2 6.522 6.641 +1.8% As expected, the change in the type of fluid (different thermal conductives and different densities) introduced a very important change in the resistance R2 which in the model is associated with the thermal resistance of the fluid boundary layer. The small changes in other parameters might be due to random errors in the measurements or to the use of a simplified model.

b) The surface of the thermometer (same as in previous experiment) was covered with layers of plastic tape. For each layer one test was performed in a bath of water at ambient temperature with stirring, and the results are: Parameter No plastic type One layer Two layers R1 3.533 3.468 3.740 C1 1.224 1.054 0.958 R2 0.695 2.187 2.815 C2 4.607 5.304 6.402 As in the previous experiment, no important changes are produced in R1 and C1. R2 is increased with every new layer of plastic tape because of the very low thermal conductivity of this material. C2 is also increased because of the mass added to the sheath.

c) Athermometer (type BSE712-F4-6008-2 No 14076) was exposed to a bending stress at about 2 cm from its end without visibly apparent damage. Self heating tests were performed before and afterthe bending and the results were: Parameter Before After Difference R1 8.576 9.998 +16.6% C1 0.225 0.222 -1.3% R2 5.468 5.370 -1.8% C2 0.487 0.501 +2.9% X-ray photographs taken before and after the experiment revealed that a fracture in the cement which supports the sensing element was produced by bending the thermometer.

This test demonstrates that the resistance R1 of the model in fact represents the thermal resistance introduced by the cement in the thermometer.

d) The "home made" thermometer was modified by filling the spce inside the sheath with silicone grease.

The following table shows the results of tests performed in both cases: Parameter Air Silicone Difference R1 11.80 2.36 -80% C1 0.59 0.92 +56% R2 3.75 1.47 -61% C2 2.58 8.92 +246% The time constants determined by the self heating test and by the standard test were: Thermometer standard test self heating difference Air 21.4 s 20.01 s -6.5% Silicone 19.3 s 16.72 s -13% The silicone grease did not improve the overall time constant of the home madethermometerto a great extent because although the resistance R1 was reduced, the capacitance C1 was increased by a similar amount.

The test for the digital compensator consists of observations of the step responses without and with the compensator. The thermometer used was tye E12382 No. 16276 for which a previous self heating test had determined its poles to be: P1 = 0.068 and p2 = 0.287 rad/seconds.

The resulting step responses are shown in Figure 7, from whih Tc1 = 18.1 seconds and Tc2 = 6.66 seconds.

If equation 8 is used to predict Tc, the following result is obtained (r = p2/p1 = 4.22): Tc = 7.23 seconds. As observed, there is a difference of 8.56%, which is due to the uncertainty in the curves and the approximations made in the development of the model.

Thus, the self heating test described above offers a reliable way to obtain relevant information about the thermometer in its operating conditions without having to remove it from its normal operating environment.

Even disconnection from the normal measuring instrument is not necessary because the same instrument which is used to measure the resistance value and to calculate the temperature is also used for this test.

A test can, for example, be carried out at defined time intervals and the results automatically can be taken into account according to pre-programmed decisions.

In PLATFILM type thermometers, the presence of three poles and the fact that two of them are very close together, invalidate the two pole model and make curve fitting difficult, but the freuqency compensation is still valid because the low frequency pole which introduces most of the delays is still well defined.

The early detection of faulty thermometers is possible even if the fault is not large enough to be observed in normal, operating conditions.

The use of the compensator allows a faster temperature measurement and the possibility of using the system in closed-loop applications.

Claims (9)

1. A method for testing the characteristics of a resistance thermometer comprising a resistance element and a support for the resistance element, the support being intended to contact a material the temperature of which is to be sensed, wherein a formula is derived representative of the thermometer's heat transfer function for heat generated by passing current through the resistance element, the formula being of second or higher order and including constants representative of at least the thermal resistance of the support, the thermal capacitance of the support, the thermal resistance of the boundary layer between the support and its surroundings, and the thermal capacitance of the boundary layer between the support and its surroundings, a heating current is passed through the resistance element for a limited period to heat the thermometer, variations with time of the resistance of the element as its temperature changes as a result of the passage of the heating current are monitored, and the formula constants are calculated such that the formula fits the monitored variations in resistance, the calculated constants being a measure of the characteristics which they represent in the formula.

2. A method according to claim 1, wherein the resistance variations are monitored after termination of the heating current.

3. A method according to claim 2, wherein the resistance variations are monitored during the period when the heating current is flowing.

4. A method according to claim 1, wherein the thermometer to be tested comprises a resistance element housed within but spaced from the sheath, and a filler which occupies the space between the resistance element and the sheath, and wherein the constants represent the thermal resistance and capacitance of the filler, the thermal resistance between the sheath and its surroundings, and the thermal capacity of the sheath.

5. An apparatus for putting into effect the method according to claim 1, comprising means for passing a heating current through the resistance element for a limited period to heat the thermometer, means for monitoring the variations with time of the resistance of the element as its temperature changes as a result of the passage of the heating current, and means for calculating the formula constants such that the formula fits the monitored variations in resistance.

6. An apparatus according to claim 5, wherein the monitoring means comprises means for sampling the resistance ofthe element at predetermined intervals after termination of the heating current.

7. An apparatus according to claim 6, comprising a digital filter to provide a faster system response.

8. A method for testing the characteristics of a resistance thermometer substantially as hereinbefore described with reference to the accompanying drawings.

9. An apparatus for testing the characteristics of a resistance thermometer substantially as hereinbefore described with reference to the accompanying drawings.