1. Use of Air Showers to Reduce Soaking Time for High Precision Dimensional Measurements Ted Doiron, Donna McLaughlin, Ann Schneider Engineering Metrology Group Precision Engineering Division National Institute of Standards and Technology

2. Thermal Expansion There are three major sources of uncertainty: the thermometer calibration, temperature gradients, and the assumed CTE. Thermometer Uncertainty CTE Uncertainty Temperature Gradient The first term is small if the Master and Gage are nearly the same length. The second term can be small if you are near 20 °C or know the Master Gage CTE well. The third term can be surprisingly large. Gradients of 0.1 °C can often be found between gages on the same platen.

3. Radiation Left graph shows the thermal response of two 16 inch gage blocks when illuminated by a 40 W fluorescent light. The right graph shows the same experiment with the blocks wrapped in aluminized Mylar. The wrapping lowers the response, slows it down, and eliminated the differential heating.

4. Scale of Problem At NIST the uncertainty for 500 mm gage blocks calibrated by mechanical comparison is less than 0.2 µm. If the master block and customer block differ in temperature by as little as 0.030 °C we will have a thermal error larger than our uncertainty. In practice, our uncertainty depends on keeping the temperature difference between the master and test blocks below 10 mK. To understand the precautions used to get long end standards to a constant temperature with temperature differences below 10 mK, we need to understand the mechanisms for heat transfer.

5. Four Mechanisms for Heat Transfer Contact Conduction: The blocks are set on the same steel platen of the comparator, which allow heat to flow through mechanical contact. Conduction/The blocks are in contact with the air which Free Convection transfers heat by conduction. Even in still air, the temperature difference between the air and part causes some convection. Forced Convection Fan pulls or pushes air past part. Radiation:All bodies emit and absorb radiation, for room temperature the light is primarily infrared.

6. Heat Transfer Equation Here T is the temperature of the object, T s is the temperature of the environment, A is the area of contact and h is a constant that depends on the details of the heat transfer mechanism. Even when there are two or more types of heat transfer involved, the heat transfer follows the equation closely with some effective “h”.

7. Heat Transfer Coefficient The effective heat transfer coefficients vary significantly. The different heat transfer modes are quite different, but secondary effects from surface geometry, orientation, emissivity, temperature difference and air speed also cause wide variation within each mode. Heat Transfer Mechanismh in W/(m 2 -K) Mechanical Contact100 - 4,000 Free Convection of Gasses5 – 30 Forced Convection of Gasses50 - 150 Radiative Transfer1 - 10

8. Thermal Relaxation Here T 0 is the initial temperature, t 0 is the initial time and τ is the relaxation time that depends on the thermal transfer (h), area, density of the body (ρ), heat capacity (C p ) and volume of the gage. Although there are more than one heat transfer mechanisms at work, we expect that the approach to equilibrium for a gage block will be very similar to an exponential decay, and the soaking time needed dependent only on the initial temperature and the decay time, τ.

9. Soaking Time, τ τeτe τ 10 The equation says that after a time of τ the temperature difference between the gage and room will be reduced by a factor of 1/e or 37%. Often the relaxation time is given as the time needed to reduce the difference by 90 %, and we will denote this as τ 10.

10. Planck’s Radiation Law All bodies give off electromagnetic waves, the distribution for a black body is given by Planck’s Law. The higher the temperature the longer the wavelengths that are emitted. Knowing the distribution will give us the temperature.

11. Emissivity Real bodies do not completely absorb all incident light (blackbody). Emissivity is the ratio of the intensity of light of a wavelength emitted from a real body to the intensity of light of the same wavelength from a black body. When the emissivity is not equal to 1, the temperature recorded by the sensor will be low.

12. Infrared Camera and Temperature The camera used in these studies was a FLIR Merlin infrared camera based on a Indium-Antimonide (InSb) detector cooled by an internal Sterling Cooler. The system has a spectral range of 1.5 – 5.0 µm and an array format of 320 x 256 pixels and a sensitivity of about 20 mK. A number of experiments were done to quantify the accuracy and precision of the system. The use of data averaging allows a usable precision of a few mK.

13. Emissivity Targets A large number of different target materials were put on an aluminum plate. The plate temperature was changed and different types of lighting were used to find targets that were easy to use and high emissivity in the range of the camera’s sensor.

14. Target Tests These graphs show the apparent temperature of two targets when exposed intermittently with a 500 W incandescent light. A true black body would show no change.

15. Scale Check Plot shows the change in a gage block temperature as measured with a high accuracy thermistor thermometer and the infrared camera using electrical tape as the target. The difference shows that the emissivity of the tape is over 0.9. The scale is nearly the same but with an offset.

16. Soaking Time Experiments Each of the 500 mm gage blocks have three strips of tape as the thermometry target. The fan can be seen in the background and the anemometer extends horizontally from the right side of the picture. The white board is insulated to keep the heat sources on the table from being seen by the infrared camera.

17. These are the first and last frames of a thermal video movie. You can create windows and extract the average temperature in the window as a function of time.

18. Results The data for the graph is taken from the “spots” that the software can superimpose on the image from the camera, which can be added before or after recording. The spikes are courtesy of a cameo appearance by Bryon Faust in the field of view of the camera

19. Results This slide shows the change in temperature of a 20 inch gage block warmed to over 30 °C and set on either a steel box parallel or the wooden table. You can see that the steel on steel gives a slightly faster response.

20. Results This logarithmic plot shows that the exponential decal model works very well, and the addition of the fan has a dramatic effect.

21. Results This shows that the difference between the wooden table and steel box become negligible with enough air flow. Convection dominates the heat transfer at 1 m/s.

22. Results - Final In still air, soaking times for gage blocks over 3 hours is unnecessary. With even modest air velocity the time for a gage to come to equilibrium in the environment is dramatically lower. When a fan is used the soaking time never reaches an hour, even for gages that are initially quite far from 20 °C.