textbook-type problem - response to heating one side of slab 2

[electricpete]

I'm sure the answer to this one lies in a textbook but I don't have the knowledge/time to work through it... maybe someone can help get me started.

The idealized problem: Start with a slab of steel 2"x3"x1" at uniform temperature. Suddenly start adding heat uniformly accross one of the 2"x3" faces. We measure temperature at the opposite face and see that temperature increases linearly from 70F to 180F over a period of 18 minutes. What is the temperature at the side where heat is applied at this time?

The real-world problem - Tilting-pad radial bearing pad on top of vertical motor. Geometry of a single pad as described above except slightly curved. Heat is generated by friction at the inner face (toward runner) and temperature is sensed by thermocouple tip at opposite face. We started motor and saw the linear increase 70F to 180F over 18 minutes at which point the motor was secured and temperature increased another 5F before decreasing. We opened the bearing and saw melted babbit and overheated oil stains. Obviously temperature at inner surface was much higher than the measured 185 to cause this damage.

My intuition says we must have had a problem with our temperature measurment (probe not in full contact with the bearing). The other explanation is that we didn't see the full temperature due to measuring at opposite side of the pad from heat. Which do you believe and can you help me prove it one way or the other? Thx.

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[electricpete]

One more piece of info - To melt babbit I think the local temperature has to get in the neighborhood of 400F. (I'm open to comments on this piece of info as well.

I realize there is some delay and some reduction in temperature measured at opposite face but I didn't think it would be sensing 180F when actual temperature at heated face approached 400F

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[quark]

If we neglect losses, there can be a simple solution. Atleast, this will give you maximum possible temperature at the other end.

If m is the mass of plate in Kgs then the rate of heat flowing into the plate will be Q(kJ/sec) = m(kg)xC(kJ/Kg C)xdT(C)/t(sec) (dT is centigrade equivalent of 110F and t is 1080sec)

Using conductivity equation Q = kA(T1-T2)/d, where k is thermal conductivity of material in W/mK, A is area of exposure in m², T1 and T2 are temperatures of hot and cold ends in K, and d is thickness of plate in meters, you can obtain T1 for any T2.

Q = 0.9574x0.163285x61/1080 = 0.0088kJ/sec

0.0088kJ/sec = 0.024kW/m.K x 0.00387x(T1-82.22)/0.0254
or T1 = 2.4+82.22 = 84.62⁰C or 183.56F

Don't worry, somebody will help us.


Regards,

 

[quark]

Data I considered.

Thermal conductivity of babbitt - 24W/m.K
Density - 9730kg/cu.mtr
Specific heat - 0.163285kJ/kg.K

Regards,

 

[sailoday28]

This is a transient problem and boundary conditions must be considered with:
1)As a first approach a one dimensional solution.
2) The outer boundary insulated.
For the inside bounary
3a) a step (or linear)change from an initial temperature to the babbit melting temp.
3b)Estimating and using heat flux generated from failure of the lube oil film.

Based on the above type approach, determine if the transient temp on outside surface is near that of measured temperatures.

 

[chicopee]

Melting point of babbit ranges from 358 to 479 deg F depending on the alloy number.
The real question s/b what caused this type of bearing to fail? Was it run dry before it got a shot of belated lubricant?

 

[pmover]

electricpete,

i concur with chicopee . . .

by all means, investigate why bearing temperature is excessive (check with bearing/equipment mfg). excessive bearing temperatures result from excessive temperatures due to excessive loads, poor lubrication, misalignment, etc. - many to mention.

good luck!
-pmover

 

[electricpete]

Thx guys. Understanding the failure is of course my primary interest. I have accumulated a lot of info and probably too much to go into here so I'd prefer to focus on the heat transfer question here. A few tidbits:

This is a vertical motor with upper thrust and guide bearing immersed in a water-cooled oil bath. Pumping action of motion of the rotating parts creates oil flow through the radial bearing. Convection driven by temperature difference between oil at bearing and oil at cooling coil creates oil flow throught the thrust bearing. It is quite a bit different than the Kingsbury Brand design. I hesitate to mention bearing OEM.

The apparent obvious smoking gun here is that the motor OEM made a modification which inadvertantly starved the radial bearing of oil flow. Prior to the modification, bearing had been inspected/run and there was no damage and stabilized temperatures while running. Immediately after the modification we had this unstable increasing temperature and found this damage.

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[electricpete]

For completeness, I think flow through thrust pads is a combination of temperature-driven flow as well as centrifugal force drive due to fact that oil tends to rotate at some speed between the rotating thrust runner and stationary pads. Not relevant to the problem which applies to radial pads.... just wanted to correct my mistatement.

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