How to Calculate a Specific Pressure by Applied Bolt Torque?

Forgive me if this is incorrect. I would think that the torque applied to the bolts would give you the basic pressure between the copper block and processor.

This may be of help.

http://euler9.tripod.com/fasteners/preload.html See link on threads within.

You may be able to calculate it, but a better way may be to measure it. There is a pressure-sensitive film-based product that will have lighter or darker color shades according to how much pressure is applied. You can even get a few free samples to see if it will work. You simply put the film between the (CPU and the heat sink in your case) and do several different torque settings.

You send the samples in to the company and they are analyzed (I think that part will cost you). Now you have a set of torques with corresponding pressures.

The name of the company is Sensor Products, Inc. This tells how it works.

Company website is here. (Disclaimer) There are probably similar products from other vendors out there as well.

Good luck!

In light of Lyn's post you could use it to find the optimal torque to be used.

Thanks for the replies so far

To the best of my knowledge you only have a couple of things that affect getting the most out of the thermal interface material and that's application - contact and pressure.

The contact needs to be across the whole area between the two (no air ingress) and the pressure needs to be high without distorting either the copper block or the pcb and as a consequence the top of the processor. High pressure results in a very thin layer of TIM which is desirable because it functions as a filler of imperfections in the mating surfaces but can allow almost direct contact too.

What I call high pressure, in this instance, probably falls in the region of 50-100 psi, higher is likely to damage the pcb.

I have seen the pressure sensitive material but never used it before.

I might consider that or a tool/gauge that measures the pressure but was hoping that someone would have knowledge of a nice spreadsheet that would be reasonably accurate for this purpose. .....

Most heatsink vendors and manufacturers of devices that require heatsinks have torque recommendations on their websites.

This might work

You problem is how to measure accurately torque on the bolts.

It is proven using torque to calculate bolt clamping force is not accurate.

Pressure sensitive firm maybe the most accurate and cost effective.

You asked a mechanically iffy question, that nobody solves the way the question was posed.

IF dissimilar metals + PC board needs to be pushed together, a split or wavy washer will provide specific pressure, while flexing and differing thermal expansions do their thing. A thermal interface layer, or messy grease aids in heat transfer.

The split or wavy washer maintains near constant pressure at 10%: at 10 mm diameter 1mm radial movement is allowed. That is from the top of my head. You may find, that bigger than expected bolts are needed for the desired pressure. These washers are NOT torqued down.

Well, You can get an estimate by calculating the slope of the threads (axial length of one thread turn divided by one thread diameter), then

force = torque x friction coefficient of bolt / slope x diameter

There are several of these numbers that are not easy to get, although there is always the old tried and true, namely, put a known weight on a bolt, and measure the torque needed to lift it. Repeated measurements with different weights on a graph should give you as good accuracy as you want.

Total force /total contact area = average pressure

assuming the surface areas match and do not distort.

Oops. Should be slope is axial length of one turn / pi x diameter.

Not sure what you mean by that. Slope = thread pitch/thread length (circumference). For metric bolts pitch is typically D/8, so slope = D/(8*pi*D) = 1/(8*pi).

Usual assumption is that only 10% of applied torque T causes bolt tensile force F, 90% being lost in friction. If bolt radius = R, F = 0.1*T/(R*slope) = 0.1*T/(D/2/(8*pi)) = 0.1*T*2*8*pi/D ~ 5*T/D. Rearranging gives a common formula for torque, T = 0.2*F*D. In consistent units of course, if you want to mix ft.lb torque with inch dia., or Nm torque with mm dia., extra factors needed.

Cheers..........Codey

A CPU is very brittle and the plastic heat transfer paste or membrane(both of which are usually filled with silver/high heat conductivity particles in such high ratio that they touch at many points to give a max conductivity path - as best they can) is made to fill the gap under modest torque (usually a spring clip prevents excess pressure on the die).

Once you have a continuous thin film of heat transfer paste/membrane of the required minimum thickness you are done. If the heat sink flat is bowed = bad, if there is an air gap trapped = bad. Usually these pastes or membranes are made to extrude under the spring pressure so the die flat and the heat sink flat meet the required separation.

if I understood your question, you want to know how to calculate the contact pressure of the plates from the torque on the bolts, but not how to measure it. An approximate assessment could be obtained using a simulation via CAE. If you are not a user of this tool, you can request these services externally.

Gentlemen, thank you for your insightful replies.

I have ordered some of the pressure film and the "Hang a known weight...." method described is so simple but I did not think of it.

I will attempt to calculate using this info posted then hang the weight then armed with the results try the film