Something you might want to consider is that measuring torque is only a proxy for actual bolt preload, and honestly not a very accurate one. When assembling a bolted joint, the goal is to preload the fastener to a defined stress value. This elastic deformation creates the clamping force that the fastener uses to hold whatever you're attaching together.
Measuring this preload directly is challenging, and requires more expensive, high-precision equipment. It is often not feasible to do this kind of direct measurement. What is easy to measure, however, is the installation torque. So the T = KDP equation is an empirically derived way to relate torques and bolt preload. The fastener resists turning for two reasons - firstly, turning is applying a force to a fastener via the geometry of the threads. Secondly, the friction between the bolt or nut head, and the mounting surface also resist turning. So theoretically, if you can determine your frictional forces perfectly, you can determine the amount of force that goes into stretching the bolt, based on the materials and geometry. Of course, in reality, it is quite difficult to determine actual installation friction (environmental factors can affect it quite a bit - humidity, temperature, cleanliness of surfaces, etc). This is where the nut factor comes in - while people have attempted to determine an engineering basis, it's primarily determined empirically, by testing various fastener joints and measuring the true preload with some of the fancier equipment I mentioned above. The empirical nut factor came first, before anyone tried to derive a real formula for it.
So to summarize, the reason friction affects preload, is that the installation torque is applied to two different things - stretching the fastener, and turning the fastener against its mounting surface. If you need more torque simply to turn the fastener, that means less torque goes to preloading. There are methods of preloading fasteners that don't require turning or torquing at all - hydraulic bolt stretchers, and preheating a fastener before installation to preload it by the shrinking cooling.
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It is clearly very important to ensure that there is as much friction as is needed between fasteners. However, how do you go about ensuring that its actually enough? The main method of verifying this is through the use of torque. Torque is a measure of the rotational force that a material is subjected to. When you install a fastener using higher levels of torque, its likely to be exposed to more friction. This in turn means that you will benefit more from all the above.
However, you need to be careful with this, since having too much torque is also associated with a few problems. The most important one is the fact that the fastener may end up becoming damaged, and will then become loose. In addition to that, when the torque surpasses the plastic limits of the metal, its likely to lead to breaking of the shafts of fasteners such as steel socket head cap screws and Inconel hex head cap screws.
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Other measures you can take include making sure that you use washers during the installation of the fasteners. You may also need to pay attention to the guide holes through with the fasteners are used. When the guide holes are of the right size, its much easier to maintain the right amount of friction, which will in turn ensure that the fasteners stay in place for long.
All in all, friction is something that you should pay attention to when installing fasteners. Using the tips above, you can then get the most out of it without compromising the structural integrity of the fasteners in question.
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