Solving Friction & Heat Generated: Analytical Modeling

[alpha754293]

What is the best way to solve for friction, and in particular, heat generated due to friction (Qfric), analytically?

The first presumption is that is a sliding contact (the domain can be either 2D or 3D, it doesn't really matter yet at this point).

One model is to have two rectangles sliding along each other, and to be able to test for feasibility for calculating friction.

The other is two cylinders (or circles) rotating in same and opposite directions, but at different angular velocities.

I haven't been able to find the correlation or a way to calculate Qfric easily or readily.

Based on physics, force due to friction = coeff. of friction * normal force.

Ff = uN

Based on thermodynamics, heat (transferred) = specific heat capacity at constant pressure (Cp) * (T_high - T_low).

Q = Cp * delta(T)

Any ideas or suggestions?

I have access to the following tools to help me try and solve (and eventually simulate) this piece of the problem:

MATLAB
COMSOL
Ansys CFX
Ansys Mechanical

Other things that might be important to note: I don't have experimental data that I am trying to simulate (yet) therefore; the materials are arbitrarily selected as steel (for both surfaces). I don't know the coefficient of friction (yet) but I can probably look that up.

The surfaces do not have any type of lubricating material (i.e. dry surface on dry surface) because analytically, the introduction of any fluid (I think) makes it harder to solve.

 

[berkeman]

The easiest way to figure out the heat is from the work done -- force X distance. The force is the mu*N friction force, and the distance depends on the geometry, etc.

 

[alpha754293]

The easiest way to figure out the heat is from the work done -- force X distance. The force is the mu*N friction force, and the distance depends on the geometry, etc.

But see, the only way that I (currently) know how to solve for work from a thermo/fluids standpoint, is the integral of pressure with respect to change in volume.

In a 2D case, there is no dV.

And that the only way that I can think of relating it back to thermo with regards to heat is by the first law of thermodynamics:

q - w = (change in enthalpy) + (change in kinetic energy) + (change in potential energy)

 

[PerennialII]

I may be missing something, but how about building it around integrating the surface frictional shear stress & the related relative slip path (pretty much like above but the way many contact modeling software work on it) over the domain of interest/the whole contact surface?

 

[alpha754293]

I may be missing something, but how about building it around integrating the surface frictional shear stress & the related relative slip path (pretty much like above but the way many contact modeling software work on it) over the domain of interest/the whole contact surface?

So, would that be:

closed surface integral (friction shear stress) dA

where ds is the relative slip path f(x,y)? (which translates to dx dy)

So, would that give me friction force, or frictional work? And how would I relate that back to heat?

Q - W = 0 change in enthalpy + 0 change in KE + 0 change in PE?

 

[PerennialII]

I was thinking of expressing the rate of frictional energy dissipation as

$$P_{friction}= \tau \cdot \dot{\gamma}$$

(shear stress * slip rate)

And the amount of energy released on a surface under contact would then be

$$q=\eta f P_{friction}$$

where f would specify how much of the heat goes to either side of the contact (0.5 if nothing else known) and $\eta$ is a factor specifying how much of the dissipated energy turns out as heat (so 1 if nothing else known).

It's essentially a typical gap heat generation model which is used for example when solving related coupled problems numerically.

 

[alpha754293]

I was thinking of expressing the rate of frictional energy dissipation as

$$P_{friction}= \tau \cdot \dot{\gamma}$$

(shear stress * slip rate)

And the amount of energy released on a surface under contact would then be

$$q=\eta f P_{friction}$$

where f would specify how much of the heat goes to either side of the contact (0.5 if nothing else known) and $\eta$ is a factor specifying how much of the dissipated energy turns out as heat (so 1 if nothing else known).

It's essentially a typical gap heat generation model which is used for example when solving related coupled problems numerically.

Hmm...that's very interesting. I've never seen that equation before. I will have to sit and ponder on it for a bit. Thank you!

 

[dimensionless]

You could calculate the energy that is lost to friction. This is simply $$E_{friction} = N\mu \Delta x$$. This is essentially what berkeman was saying. Some portion of this energy is transferred into sound and EM waves, although I don't know how significant this portion is. If your not in a vacuum, then some of the heat would be transferred to air.