K is determined by using a torque transducer, load cell, and the other hardware like washers and nuts that you are going to use in your joint. You want to make sure your setup is as close to actual production as you can get. You then tighten to 75% of the bolts proof load as measured by the load cell while also measuring torque. That gives you enough information to use the formula to determine K.

K = T/(DP)

T = Torque achieved at 75% of bolts proof load

D = Nominal thread diameter

P = Proof load of bolt

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Using our example above:

111/(.250*2025 = ~.22

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This would be an example setup from work:

https://pieng.com/testing-overview/torque-tension-testing/

If you look at my explanation in this thread, (almost certainly the longest one) the primary factor dictating how much torque you need to apply is friction. The better you control that friction the more accurately the torque you call out gets you to the clamp load required. Unfortunately friction is sometimes hard to control.

One of the other ways you can get an accurate tightening is by turning the fastener the same amount every time. Stretch in the fastener, and therefore clamp load, increases linearly with rotation of the fastener. If the distance between my threads is 1mm and I turn the bolt 360 degrees, I will have stretched my fastener by 1mm.

In practice though the challenge is determining where to start measuring that rotation. Everybody has their on definition and perception of where a thread starts to engage. You need to establish a starting point that is relatively consistent for everybody. That is where the torque comes in.

At lower torque values, the variability in friction has less of an impact on the clamp load you ultimately achieve during tightening. So I can pick a lower torque value, and then once I hit that value I can start counting degrees of rotation. This would get me to roughly the same location every time. This is much more accurate than purely relying on a maximum torque value for joints that have a lot of variability in friction.

Fastener engineer here!

Torque is a means to an end. The end goal is actually to stretch the screw. The screw behaves like a rubber band. As you stretch it out, it wants to return to its original length. As it does so, it squeezes the components you are fastening together. This is typically called clamp load. This clamp load is difficult to measure directly, requiring modifications to include an expensive load cell or ultrasonic measurement. Neither of these are practical in any production environment, and basically impossible at home. Torque on the other hand is really easy to cheaply measure.

What dictates how much clamp load you can get for a given torque is the friction you have to overcome as you tighten and how much clamp load the bolt can sustain. The total load be the proof load of the part and is based on the grade. Friction primarily comes from the contact between the threads and the contact between the underside of the screw's head and your joint components. This friction is also what prevents the screw from coming loose on its own. The amount of friction must be controlled so that you require a consistent amount of torque to reach a consistent amount of clamp load. This is typically done by careful control of the screws finish and application of lubricants.

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There is a pretty simple formula for figuring out approximate torque if you know a few things about the components.

T = KDP

T= torque

K= dimensionless friction value for the entire joint. Takes into consideration the finishes and geometry of all of the components. Can be approximated in non-critical joints, for safety critical should always be experimentally derived.

D= nominal thread diameter

P= clamp load, often 75% of the proof load of the bolt

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If for example I wanted to figure out what torque I should tighten a 1/4-20 grade 5 hex cap screw into a joint that has a matching nut or a tapped hole at least 3/8 deep:

K= .22 (typical for zinc plated parts, would change if using something with significantly different geometry like a flange bolt, different finish, or with lubricant added.)

D= .250 in

P= 2025 lbf (75% proof load)

.22 * .250 * 2025 = 111 in-lb

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One consideration for the DIY at home is that lubrication will often reduce the amount of friction, meaning LESS torque is required to reach the required clamp load. The consequence here is that the torque value your service manual says you should use may actually be enough to damage the threads if you use lubricants that were not originally used during manufacturing.

People are all for helping out 3rd world counties as long is it costs them nothing. Once told their electric rates would have to go up 10% they turn a blind eye.