# Publications on the topic of temperature between sliding surfaces

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Hello everybody!

I'm looking for publications (dissertations, articles in journals,... whatever is scientifically based) concerning the temperature between sliding surfaces. I need this information for my own bachelor's thesis and I need to calculate the temperature expected on the contact surface between two bodies. These two bodies will be rubbing against each other at high speed. Body 1 will be some defined steel, Body 2 will consist of the same steel coated with a thin film of some friction-reducing material.

So what I am looking for is in the ideal case some formula, where I can put in my materials' parameters and get the contact temperature. But any publication that's close to this is also welcome.

I have been searching the web of course, but I thought perhaps there might be someone here who has some concrete idea where I could find an answer to my problem.

Thank you for any helpful response!

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Hello everybody!

I'm looking for publications (dissertations, articles in journals,... whatever is scientifically based) concerning the temperature between sliding surfaces. I need this information for my own bachelor's thesis and I need to calculate the temperature expected on the contact surface between two bodies. These two bodies will be rubbing against each other at high speed. Body 1 will be some defined steel, Body 2 will consist of the same steel coated with a thin film of some friction-reducing material.

So what I am looking for is in the ideal case some formula, where I can put in my materials' parameters and get the contact temperature. But any publication that's close to this is also welcome.

I have been searching the web of course, but I thought perhaps there might be someone here who has some concrete idea where I could find an answer to my problem.

Thank you for any helpful response!

You would need to know the the geometry of the steel plate (or make the approximation of an infinite plate in which case thickness is sufficient), the normal force per unit area, the coefficient of friction, the thermal diffusivity of the steel the density of the steel, the initial temperature, the temperature of the surroundings of the steel, and the emissivity of the steel. If the coating you intend to use has a significant effect other than on the coefficient of friction, you will need those parameters as well.

It is fairly easy to calculate the energy per unit area generated as heat by sliding the plate. It is a lot more difficult to calculate the temperature profile through the steel as a function of time and it involves many more variables.

If this is for a bachelor's thesis, should you not have some idea of the basic physics involved and should you not be looking for something of greater depth than a cook book formula (which cannot exist given the dependence of the temperature sought on many parameters) ?

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It's only a very small part of the whole thesis and should therefore be as compact as possible.

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• 1 month later...
...If this is for a bachelor's thesis, should you not have some idea of the basic physics involved and should you not be looking for something of greater depth than a cook book formula?

I had searched for said formula and didn't find it... This may look strange in 21st century but I had to compute by myself the analytic solution for the heat profile, it took me one week.

Even a 5cm-thick book devoted only to the propagation and the diffusion equation didn't mention a solution. But afterwards, I found one in:

Introduction aux transferts thermiques, by Sacadura (in French, sorry)

who uses a Laplace transformation with half-integer powers - I find my solution easier. DrRocket, if you know a third method, please tell the world!

By the way, all analytical solutions suppose that conductivity and capacity are independent of temperature, which is brutally false in a brake. So FEM would be an answer.

As for how heat splits between both materials, that'a a matter of model! People commonly assume a split proportional to sqrt(density*volumiccapacity*conductivity). Their rationale is that contact points share a common temperature. Well, why not.

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If you have no heat transfer in or out, so you are inputting only mechanical energy into the lubricating fluid, and if the lubricant prevents local hot spots and keeps thermal equilibrium in this adiabatic system, then the lubricant will be approximately the same temperature as the plates. You know the resulting enthalpy of the lubricant (the energy content of the material) once you know the horsepower driving the setup and the time it runs. You know the mass of the lubricant, and if there is no change of state, the resulting temperature of the lubricant can be found because you know the resulting enthalpy. Some of the power will go to heating the plates as well, so that will have to be taken into account. The solution is on a macro scale, using elementary thermodynamic principles.

You may be interested in the wet clutch aeration problem, where there is a change of state in the fluid between relatively rotating (rotor-stator as well as counter-rotating cases) metal plates. See e.g. Yuan, et al., "Study on aeration for disengaged wet clutches using a two-phase flow model," J. of Fluids Engineering, vol. 132, 111304 (Nov. 2010).

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The amount of heat stored by any liquid lubricant film would be negligible, and here we're speaking about a solid film.

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