T = k*Fi*d is the “short form” calculation to determine required installation torque, where T is the target installation torque in in-lbs; Fi is the initial preload; and d is the nominal bolt diameter. Seems like a simple, turn-the-crank calculation at first. The bolt size, d, can be “guesstimated” for an initial design calculation. Initial preload requirement, Fi, may not be known; in which case you can select a torque value from a Torque-Tension chart. Standard chart values for a Grade 5, 3/8-16 UNC hex head capscrew are: 4,940 lbs. preload at 30 lb-ft for k=0.20 dry and 23 lb-ft for k=0.15 lubed. The problem is: which k-value should be used, what does “dry” mean and what constitutes “lubed”?
A U.S. Air Force study identified over seventy-five factors which can combine to affect the resultant torque coefficient, or K-values, of a given bolted joint. The test date below is a good example. This is a data point grouping of ten sample run-ups, all with the same JS2000 fastener topcoat. As you can see, all of the points fell well within the +/- 30% limits, the industry-accepted torque scatter for D-C electric tools.
However, the k-value varied significantly, depending upon the applied torque. T and d are both constants for a particular joint design. Therefore, Fi and k are inversely related [T/d = Fi * k]: if one increases, the other must go down. Note the high k-value at low torques and the lower k-value at high torques. This illustrates that friction increases with higher clamp loads, reducing the maximum preload which can be developed at a given torque value. Therefore, there isn’t any one nut factor which can be used across a wide range of torque values. Thickness and type of fastener coating, length of thread engagement, tolerance of both the external and internal threads, bearing surface conditions, fastener size, thread pitch, etc., all combine to alter the thread and under-head frictions.
Any target torque specification is applicable only for that combination of conditions, coatings and material specified for that particular joint test. This is why I always advise designers to conduct torque-tension testing on the actual joint to confirm k-values. Anything else is just a best-guess, and frequently not even a good one, at that.