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How to Calculate Contact Resistance Between Two Clamped Blocks

Physicists have established the laws of thermodynamics; mechanical engineers know how to design and analyze structures; thermal engineers can predict maximum operating temperatures with impressive accuracy. Yet for all that's understood, for all the success, there are some real-world problems that are very difficult to solve. Calculating the interface resistance between two clamped blocks is one of those problems. Still, a theoretical framework is available, one that culminates in a equation to calculate contact resistance.

Things You'll Need

Automated surface profiler
Microhardness tool
Springs and clamps

Instructions

- 1
  Calculate the harmonic mean thermal conductivity. You'll need to know the thermal conductivity of each of the two materials, but you can find this information from reference materials. Label them k1 and k2. The harmonic mean thermal conductivity is given by
  
  km = k1 x k2 / (k1 + k2).
- 2
  Using a surface profiler, determine the asperity profile for each surface. "Asperity" is just a fancy name for a tiny pinhole. Every surface has some tiny holes in it, and you need to make some measurements about how deep and how steep the asperities are. The depth is put into a measurement called the surface roughness, while the steepness is called the asperity slope. The profiler you use will be able to do these calculations automatically.
- 3
  Calculate the mean asperity slope and the effective surface roughness. The mean asperity slope is given by the square root of the sum of the squares of the individual asperities, and the effective surface roughness is given by the square root of the sum of the squares of the individual surface roughnesses. Mathematically, these equations are:
  
  mean asperity = sqrt (asperity1^2 + asperity2^2);
  
  effective roughness = sqrt (roughness1^2 + roughness2^2).
- 4
  Find the microhardness of each of the two surfaces. You can either find this information in reference materials, or do a microhardness measurement, following the instructions for the microhardness tool.
- 5
  Insert springs between the clamps and one side of the blocks. Measure the difference between the starting length and the compressed length of the springs. Calculate the contact pressure between the two blocks. The force equals the number of springs times the length change of the springs, times the spring constant:
  
  force = number x change in length x spring constant; and the force divided by the contact area is the contact pressure.
- 6
  Calculate the contact resistance. The contact conductance is given by
  
  conductance = 1.25 x km x (mean asperity/effective roughness) x (contact pressure/microhardness). That's the conductance per area, so multiply that by the contact area to get the conductivity. The contact resistance is 1/contact conductance.

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