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Posted by Mark Kelly (M ) on October 27, 2006 at 07:08:49

One of my favourite websites is TribologyABC.com, source of many useful calculators and much help with the design of bearings. I recently bought the associated book "Advanced Engineering Design" and am steadily ploughing through it.

On reading the section on frictional heating in a ball on surface contact I realised that the same calculation could be brought to bear on the chestnut regarding the heating effect of a diamond stylus on vinyl. The appropriate calculator is 5.5 on the website.

If we use appropriate values for the diamond / vinyl interface, making worst case assumptions where values are hard to determine, we can calculate a temperature rise for contact patch of the vinyl surface. The answer comes out to about 10oC. No, that's not a typo, that's 10 degrees celsius or 18 degrees Fahrenheit.

The 24 hour rule is dead. Don't start with the stuff about slow recovery after deformation, it's called stress creep and the recovery time is proportional to the creep strain which in turn is proportional to the stress duration, so the recovery period is of the same order of magnitude as the stress period.

For those who want to check my results, I used the following values:

Thermal conductivity diamond = 1000 W/mK.

Thermal conductivity PVC = 0.16 W/mK

Thermal diffusivity PVC = 1.2 x 10^-7 m^2/s

H (Hardness of interface) = 1 GPa (the hardness of the softer material dominates)

F = 15 N (1.5 g VTF)

V = 0.5 m/s

mu = 0.4 (a reasonable value for PVC/ diamond)

Assumed radius of contact patch = 70 um (deliberately large as the frictional coefficient of polymer materials increases as the contact pressure decreases, in contrast with classic solid bodies where the two are independent. This is why wide tyres work.)

By the way since we are working with a soft polymer Ar is roughly equal to An and it is easy to throw the calculator out of whack by giving values which would make Ar > An (which is impossible). AFAICS this does not affect the accuracy the model.

Mark Kelly

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