# Determine acclimation time for metals

## Main Question or Discussion Point

A little background: Inspection room is kept at 20 C +/-2 C. Temperature gauge is accurate to +/-.5 C. Outside ambient temperature where parts are kept can vary from 5 C to 38 C. One part in particular is a rotor made of 4340 steel, ~2350mm long, average diameter of 115mm, and weighs ~ 650lbs. There are lengths that are in the 2000mm range with a +/-.100mm tolerance and diameters in the 120mm range with tolerances of +/-.013mm that I have to accurately measure. Typically, we allow the rotors to acclimate for 24 hours but because of "schedules" they want me to figure out how to reduce the acclimation time. Any help is appreciated.

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Merlin3189
Homework Helper
Gold Member
The rotor's rate of change of temperature is proportional to the difference in temperature between it and the environment. Its temperature approaches the air temp ever more slowly, until it falls within your ±2 C range.

The rate constant would be very difficult to calculate for anything but a very simple shape, so would be best determined experimentally. If the room temp is cycling, as it probably is due to the air conditioning, that adds complication. Some data on temp and time for actual rotors would help you see how long it is really taking. (Plotting the log of temperature should linearise the graph to help you estimate rates.) Collecting some data seems like a good starting point.

Presumably you can't change the room temperature to help the process? If you could, then you could increase the temperature difference until the rotor was near the target, then return it to normal. But that would be another difficult calculation and need some experimentation.

The easest way to improve the rate might be to install fans to ensure good air circulation around the rotor. That helps the rate of heat transfer between the rotor and the air. Also the hot rotor will locally heat that part of the room, so that its environment is not as cold as the rest of the room. Reducing that effect keeps the cooling rate at its best.

Asymptotic
Thank you for that info, it's much appreciated. If time allows, I will experiment with a scrap rotor we have laying around and use all methods you mentioned, thanks.

mfb
Mentor
Based on the thermal expansion coefficient given here and with the more critical length (0.1mm over ~2000 mm), your temperature should be within +- 4 K assuming the length is exact at the right temperature.

Convection and conduction (with things in contact to the rotor) can both be important, and difficult to model. The thickest parts will need the longest time to get close to the room temperature.

Baluncore
2019 Award
Typically, we allow the rotors to acclimate for 24 hours but because of "schedules" they want me to figure out how to reduce the acclimation time.
How would I repeat the process as quickly as possible? Firstly; I would thermally insulate the rotor and measure the temperature with surface contacts at 9 points. That would be at three points separated by 120° around the rotor, near each end and in the middle. The average of those will be an initial temperature estimate. From that difference temperature and the heat capacity of the rotor material, compute the heat needed to warm it to 20°. Secondly; transfer it quickly to an insulated empty bath, add a known mass of hot water or melted ice water calculated to bring the rotor to exactly 20°.

Since the heat is removed along the length and all faces, the average temperature at depth and along the length will rapidly approach the target value. It may not be necessary to reach thermal equilibrium in depth or along the length since, once the thermal energy has been transferred, any thermal stresses will tend to cancel a length variation between the ends.

Maybe the insulated jacket used during measurement could be the bath used later. A stretchy neoprene wetsuit material that fits the rotor would position the embeded thermometer probes to contact the rotor, and then the fluid to be pushed in and through the jacket later. The temperature probes will show when the bath is sufficiently close to 20°. Measuring the length during the acclimation process will identify how close the temperature needs to be.

Tom.G
A less involved method would be to temperature stabilize the scrap rotor at 38°C to 40°C then take dimensional and temperature measurements at time intervals (1 hour?) until the measurements no longer change. That generated chart will also tell you the worst case stabilization time for various initial temperatures.

Cheers,
Tom

Asymptotic
Baluncore
2019 Award
A less involved method would be to temperature stabilize the scrap rotor at 38°C to 40°C then take dimensional and temperature measurements at time intervals (1 hour?) until the measurements no longer change.
Why stabilise at 40° when it is just as easy to stabilise the rotor at 20°, then note that it does not change dimensions. It appear you are estimating the cooling time constant while unnecessarily heating the thermally stabilised inspection room, a process that cannot be applied to every quick turn around job.

Dimensions are proportional to temperature, but there can still be thermal gradients within or along the article being measured that do not significantly affect the measurements. It is the total thermal energy content that needs to be quickly stabilised to avoid the long time constant and overnight acclimation.

Tom.G
Why stabilise at 40° when it is just as easy to stabilise the rotor at 20°, then note that it does not change dimensions.
Perhaps I wasn't clear enough that the 38°-40° soak would take place outside the inspection room.

The point was to establish the time constant of a rotor (the scrap rotor) and also to build a calibration table for the rotors in general. That way the production items could be scheduled for needed stabilization time, perhaps depending on their temperature upon arrival in the inspection room.

Depending on their product flow, I agree there could be a problem if the rotors have been stored at a given temperature and transferred to another temperature before arrival at inspection. But so far, that is unknown to us.

Is there a fallacy in that approach?

Baluncore
2019 Award
Is there a fallacy in that approach?
No fallacy, maybe at cross-purposes. While measuring the time constant will be interesting, it will depend on the convection environment. For example, the acclimation could be accelerated by using fans to direct the temperature stable contact air onto the rotor. To speed the production process we need to reduce the asymptotic time constant you are measuring, which should make your measurement redundant.

The accelerated acclimation process I am considering would employ a stretchy insulated sock, with inbuilt sensors, that could be applied to any rotor in the class. The production process would be;
1. Weigh the rotor. Identify rotor material and look up the thermal capacity per kg of rotor material.
2. Put rotor in the sock, remove slack folds to exclude air with a zipper or spiral cord.
3. Measure initial temperature on all sensor channels.
4. Compute temperature change needed, then the energy required to reach 20°.
5. Prepare the volume and temperature of water needed for injection into the sock.
6. Inject the water. Sensors will show temperature passes thru the target temp as water spreads.
7. Watch as temperature fall back into the target temperature window.
8. Drain the (now close to 20°) water from the sock, remove the sock.
9. Verify the surface temperature with IR thermometer. Make the dimensional measurements.

That process makes it possible to cut acclimation time since a known thermal energy transfer will be from the water contact, all inside the insulated sock, which will also minimise disturbance of the measurement room temperature.