1. 2003 NCSL INTERNATIONAL ANNUAL WORKSHOP AND SYMPOSIUM TAMPA, FLORIDA INAMPUDI L. KOWLINI, Dr. HARISH CHERUKURI, Dr. EDWARD MORSE & Dr. KEVIN LAWTON THE UNIVERSITY OF NORTH CAROLINA at CHARLOTTE THE INFULENCE OF THERMISTORS ON TEMPERATURE MEASUREMENTS

2. ACKNOWLEDGEMENTS NIST NIST Dr. Steve Philips Dr. Steve Philips Dr. Hans Soons Dr. Hans Soons CENTER FOR PRECISION METROLOGY Affiliates CENTER FOR PRECISION METROLOGY Affiliates

3. OVERVIEW Introduction Introduction Research Objectives Research Objectives Experimental Setup Experimental Setup Thermistor Configuration Thermistor Configuration Model Problem Model Problem Numerical Simulations Numerical Simulations Conclusions Conclusions Future Work Future Work

4. INTRODUCTION Temperature variation – with its effect on measuring equipment and workpieces is perhaps the greatest contributor to uncertainty in many dimensional measurements. Temperature variation – with its effect on measuring equipment and workpieces is perhaps the greatest contributor to uncertainty in many dimensional measurements. Non-standard and/or non-uniform temperatures in parts often result in change in shape and size and thus lead to uncertainties in dimensional measurements. Non-standard and/or non-uniform temperatures in parts often result in change in shape and size and thus lead to uncertainties in dimensional measurements. Several factors influence the thermal state of a part during measurements. Several factors influence the thermal state of a part during measurements. Thermal Factors Affecting Measurements

5. THERMAL ISSSUES IN METROLOGY The long-term goals of our research are: develop models to predict soak-out times for parts prior to dimensional measurements. develop models to predict soak-out times for parts prior to dimensional measurements. study the effect of various factors such as cooling conditions, contact conditions, environment, radiation, fixturing on the part temperature. study the effect of various factors such as cooling conditions, contact conditions, environment, radiation, fixturing on the part temperature. develop error budgets for thermal effects on part measurements. develop error budgets for thermal effects on part measurements.

6. Current Research Current Research at UNC – Charlotte: determination of : determination of : convective heat transfer coefficient (h) using a combination of experiments and theory. convective heat transfer coefficient (h) using a combination of experiments and theory. effect of contact conditions on part temperature. effect of contact conditions on part temperature. development of models for soakout time prediction for given parts. development of models for soakout time prediction for given parts.

7. EXPERIMENTAL SETUP Oven to heat the part Keithley 2000 multimeters Data acquisition system Experimental setup at UNC – Charlotte for determining the convective heat transfer coefficient (h)

8. EXPERIMENTAL WORK IN PROGRESS The workpiece is heated in the oven to a predetermined temperature and then allowed to cool. Thermistors attached to the workpiece are used to collect the temperature data until steady-state is reached.

9. THERMISTOR EFFECTS The temperature of the part is influenced by the thermistor. The temperature of the part is influenced by the thermistor. The time constant of the thermistor causes a transient measurement error. The time constant of the thermistor causes a transient measurement error. Contact conditions between the part and thermistor also cause measurement errors. Contact conditions between the part and thermistor also cause measurement errors.

10. MODEL PROBLEM DESCRIPTION The thermistors used to measure the surface temperatures of the workpieces are small surface probes. The thermistors used to measure the surface temperatures of the workpieces are small surface probes. To study their influence on the part temperature, a cylindrical block insulated on the lateral surface is considered. To study their influence on the part temperature, a cylindrical block insulated on the lateral surface is considered. A single thermistor is mounted centrally on one end face of the block. A single thermistor is mounted centrally on one end face of the block. The problem is solved numerically using ANSYS for various conditions of practical interest. The problem is solved numerically using ANSYS for various conditions of practical interest.

11. INFLUENCE OF THERMISTOR ON PART TEMPERATURE Three factors contribute to inaccuracies in part temperature measurements:  Thermistor Calibration  Time Constants of the thermistors  Influence of the thermistor on the test piece temperature.

12. MODEL PROBLEM : THERMISTOR CONFIGURATION The thermistor consists of a spherical bead encompassed by an epoxy layer attached to a stainless steel washer plate. The thermistor model is axisymmetric.  poxy Steel Washer Glass Bead

13. MODEL PROBLEM (Contd…) The thermistor is placed on the cylindrical block, the temperature of which is to be measured. Perfect contact is assumed between the thermistor and the block. The thermal properties of the thermistor are estimated from literature. Figures not drawn to scale

14. NUMERICAL ANALYSIS Temperature-Part Interaction Steady-State conditions Transient conditions Natural Convection Forced Convection Time-Constant Of the thermistor Thermistor response to Time Varying temperature field. The temperature-part interface is studied for various boundary conditions:

15. THERMAL PERTURBATION: STEADY-STATE ANALYSIS With Thermistor T=40C h= 30W/m 2 -K, T ∞ =20C Without Thermistor h= 30W/m 2 -K, T ∞ =20C T=40C

16. NUMERICAL RESULTS Temperature Distribution (Natural Convection) ThermistorComplete System Steel Aluminum

17. NUMERICAL RESULTS LocationWith Thermistor Without Thermistor Perturbation (mK) 139.95539.962-7 239.95739.962-5 LocationSteelAluminum T top 38.93639.598 T center 38.96039.614 T bot 38.99139.634 LocationWith Thermistor Without Thermistor Perturbation (mK) 139.44339.504-71 239.45239.504-52 Table1: Surface Temperature in Steel Block (in C)Table 2: Surface Temperature of Alum. Block (in C) Table 3: Thermistor Bead Temperature (in C)

18. FORCED CONVECTION LocationWith Thermistor Without Thermistor Perturbation (mK) 136.85237.104-252 236.89537.104-209 LocationSteel T top 34.497 T center 34.613 T bot 34.758 Under natural convection conditions, thermistor influence on temperature may be insignificant for many applications. However, for forced convection, this may not be the case. Table 4: Surface Temp. in Steel Block (in C) for h=200W/m2-K Table 6: Bead Temperature (in C) for h=200W/m 2 -K LocationWith Thermistor Without Thermistor Perturbation (mK) 139.44339.504-71 239.45239.504-52 LocationSteel T top 38.936 T center 38.960 T bot 38.991 Table 7: Bead Temperature (in C) for h=30 W/m 2 -K Table 5: Surface Temp. in Steel Block (in C) for h=30W/m2-K Temperatures for Forced Convection case – for Steel Block Temperatures for Natural Convection case – for Steel Block

19. EFFECT OF INSULATING THE THERMISTOR SURFACE LocationWith Thermistor Without Thermistor Perturbation (mK) 139.97739.96215 239.97339.96211 LocationAluminum T top 39.976 T center 39.976 T bot 39.976 How is the temperature of the part affected if the thermistor is insulated? Thermistor: Insulated Block top surface: Convection h=30W/m 2 -K, T ∞ =20C. Block bottom surface: Temperature of 40C is prescribed. Table 8 : Surface temperatures of Aluminum Block (in C) Table 10: Bead Temperature (in C) for h=30 W/m2-K when the glass bead is insulated LocationWith Thermistor Without Thermistor Perturbation (mK) 139.95539.962-7 239.95739.962-5 LocationAluminum T top 39.598 T center 39.614 T bot 39.634 Table 11: Bead Temperature (in C) for h=30 W/m 2 -K when the glass bead is not insulated. Table 9: Surface Temperatures of Aluminum block (in C) Temperatures for the case where the glass bead is insulated Temperatures for the case where the glass bead is not insulated

20. TRANSIENT ANALYSIS Transient Analysis is carried out to study the response of the thermistor to the time-varying temperature field in the block. Transient Analysis is carried out to study the response of the thermistor to the time-varying temperature field in the block. With ThermistorWithout Thermistor h= 30W/m 2 -K, T ∞ =20C Insulated h= 30W/m 2 -K, T ∞ =20C Insulated Initial temperature of the system T 0 =45C

21. TRANSIENT ANALYSIS: RESULTS The temperatures within the bead and at the thermistor-part interface are plotted as functions of time. As evident from the above, the temperature sensed by the thermistor is 0.5C less than the part temperature at early times. However, at late times, the two are essentially the same.

22. TIME CONSTANT OF A THERMISTOR Time Constant of a Thermistor Time Constant of a Thermistor The Thermal Time Constant for a thermistor is the time required for a thermistor to change its temperature by 63.2% of a specific temperature span when the measurements are made in thermally stable environments. The Thermal Time Constant for a thermistor is the time required for a thermistor to change its temperature by 63.2% of a specific temperature span when the measurements are made in thermally stable environments.

23. THERMISTOR TIME CONSTANT ESTIMATION: PROBLEM STATEMENT In order to estimate the Time Constant of the thermistor, the initial temperature of the thermistor is set at 25C and the block at 20C and the system is allowed to equilibrate under insulated boundary conditions. t= 0 Thermistor at 25C Block at 20C All the surfaces are insulated Transient thermal analysis indicates the system reaches steady-state with final temperature being 20.003C.

24. THERMISTOR RESPONSE Simulations indicate a time constant of 0.78sec. Experiments on small surface thermistors indicate effective time constants in the range of 3-5sec, depending on the surface finish and material on which the thermistors were tested. Possible reasons for the discrepancy are inaccurate material properties and boundary/interfacial conditions. So what is the time constant of the thermistor? Temperature is different at different locations within the thermistor. Therefore, no single time constant is possible to estimate. However, one can have a rough estimate of an average time constant by looking at the temperature at various locations within the thermistor.

25. THERMISTOR RESPONSE TO INTERFACE MATERIAL To study the effect of thermistor-part interface contact conditions on the time constant of the thermistor, a thin water film is placed at the interface of washer plate and the base and the combined system is again allowed to equilibrate to a steady-state temperature. The thickness of the water film is varied from 0.05-0.5mm. t= 0 Thermistor at 25C Block at 20C All the surfaces are insulated Water Interface Stainless Steel Washer The film of water produced experimental time constants of the thermistor of 2.5sec and the FEA results produced a range of time constants of 0.8 to 6sec.

26. SENSITIVITY TO EPOXY PROPERTIES Another factor that may have contributed to the large discrepancy between the experimental and numerical estimates of thermistor time constant is the uncertainty in the thermal properties of the epoxy layer. Another factor that may have contributed to the large discrepancy between the experimental and numerical estimates of thermistor time constant is the uncertainty in the thermal properties of the epoxy layer. A survey of the literature indicates that the specific heat of epoxy may range from 300J\Kg-K to 600J\Kg-K. A survey of the literature indicates that the specific heat of epoxy may range from 300J\Kg-K to 600J\Kg-K. The numerical simulations indicate that the time-constant changes from 0.78-1.39 seconds suggesting that the specific heat of epoxy has a significant effect on the time- constant of the thermistor.

27. CONCLUSIONS The discrepancies between experiment and theory in estimating the thermistor time constants are possibly due to lack of accurate material property data and inaccurate modeling of the thermal conditions at the part-base interface. These issues need to be investigated further. The discrepancies between experiment and theory in estimating the thermistor time constants are possibly due to lack of accurate material property data and inaccurate modeling of the thermal conditions at the part-base interface. These issues need to be investigated further. However, present results do indicate that under natural convection conditions, thermistor influence on the part temperature is not very significant. However, present results do indicate that under natural convection conditions, thermistor influence on the part temperature is not very significant. In transient problems, thermistor measurements can be significantly different from the actual part temperature (0.2C to 0.5C difference) at early times. In transient problems, thermistor measurements can be significantly different from the actual part temperature (0.2C to 0.5C difference) at early times.

28. FUTURE WORK The future work in this area will use thermal data collected experimentally to estimate the heat transfer on different surfaces of the part. The future work in this area will use thermal data collected experimentally to estimate the heat transfer on different surfaces of the part. Finally, we will attempt to characterize the contact resistance between the workpiece and fixture elements used to hold the part on the CMM, based on variables such as clamping force and the surface finish of the part. Finally, we will attempt to characterize the contact resistance between the workpiece and fixture elements used to hold the part on the CMM, based on variables such as clamping force and the surface finish of the part. If successful, we will be able to provide guidelines to practitioners for estimating the soakout time needed prior to part measurement, and the dimensional uncertainty that is introduced if it is not possible to wait until the part temperature has stabilized before measurements are taken. If successful, we will be able to provide guidelines to practitioners for estimating the soakout time needed prior to part measurement, and the dimensional uncertainty that is introduced if it is not possible to wait until the part temperature has stabilized before measurements are taken.

29. ?