# Converting torque applied to a bolt into the linear force exerted by the bolt

by Morganjs1
Tags: applied, bolt, converting, exerted, force, linear, torque
 P: 3 Hello all, I have an experiment set up where I need to compress some material using some G clamps. I have a torque wrench which I can use to tighten up the gclamp to a known torque but am having trouble converting this to the linear force that will actually be applied to the material. I've been looking at some mechanics of screws + bolts but have yet to locate a formula to tell me how much torque I need to apply to get a given force output. Any help would be greatly appreciated. The last formula I found is this: T = (C x D x P x A) / (no of screws) T = torque per screw (Nm) C = torque coefficient; generalized values for copper/mild steel (0.36 dry, 0.18 lubricated) D = nominal screw size (m) P = desired Pressure (force per unit area) (N/sq m) A = surface area (sq mm)
 Sci Advisor PF Gold P: 2,248 Predicting preload on a bolt based on applied torque can be a tricky subject, as you have no doubt determined. Because calculation of a bolt's preload is such a black art, most applications I have designed that have a specific force requirement usually use a spring and a shoulder bolt that compresses the spring to a precise length. It's possible to guess at what torque might be required for a given force, but in many applications guessing at what the force might be and directly controlling force can be the difference between a design working or failing. Here is a website I found a while ago that has a detailed method for calculating bolt preload, however the accuracy of those calculations will depend on the measured accuracy of the numbers used. http://www.torqueleader.com/Support_.../Torque_Values
PF Gold
P: 2,248
For what its worth, Federal Standard H28 (FED-STD-H28) has this to say on the subject:

 Quote by FED-STD-H28 Tests in numerous laboratories have shown that satisfactory torque-tension relationships may be established for a given set of conditions, but that the change of any one variable may alter the result. Changes such as indeterminate friction, a change in the surface roughness of the bearing surfaces or of the threads, or a change lubrication will drastically affect the friction and thus the torque-tension relationship. Thus, it must be recognized that a given torque will not always produce a definite stress in the bolt but will probably induce a stress that lies in a stress range that is satisfactory.

The federal standard also states that the best way to determine a precise preload is to direclty measure the change in length of the bolt with strain gauges, whenever the geometry allows you to do so.

 Sci Advisor P: 5,095 Converting torque applied to a bolt into the linear force exerted by the bolt The relationship between torque and preload is soooo tricky. It is, on the surface, easy to calculate, however, the infamous coefficient of friction rears it's ugly head and makes things easy to mess up (the method of calculating is easy because a standard starting point for the coefficient of friction is assumed to be a statistically acceptable number). It is quoted in many references (Bickford, et al) that preload on a bolt, when determined via the torque method, can be off by as much as 25% even with proper precautions being taken. It simply is not an accurate method. The best way to measure clamping force is to measure the stretch in the fastener. There's no way around it. I would say in your case that you get some pressure sensitive film and do some trials with your fasteners/clamps. That way you may be lucky enough to get to the clamp force you want.
 P: 3 Thanks for the responses. I don't need a super accurate measure of the force I'm exerting on my samples, I just need to know that I'm in the region of 30kN. I'll look into some pressure sensitive film as that sounds like the easiest option. Just to clarify in my mind, when referring to friction in these formulae, what is the friction assumed to be between?
 Sci Advisor P: 5,095 The friction is in a couple of places. There is friction in the thread interface and there is a friction force between the head of the bolt/nut and the clamped material face. The kicker is that the frictional forces increase with load. As a side note, for your attempts to correlate the torque and preload, make sure to lubricate the threads with a drop or so of oil. That is an assumed condition for the standard calculations.
 P: 1,127 If you need accuracy, back the sample with a load cell. If you need only an approximate value, make sure you use the lowest coefficient of friction threads you can get. Steel with rolled threads, well-lubricated, is the best simple solution (I would assume about 0.2 friction coefficient). In this instance, the required torque would be about 0.2F*screw pitch (using appropriate units for the pitch). The preload formulas are not very useful for this case since what you want is essentially a simple machine.
 P: 3 Thankyou to everybody for the help. I think I'll have to perform some measurements of the applied force using a load cell or pressure sensitive film, and try to get a specific torque to force correlation for my specific situation.
 P: 1 Hi, I have set up a test rig with a load cell to test the load applied by a bolt on a surface......however i would like to back up my testing with some research. there seems to be very limited research done on this topic. any pointers on where to go would be greatly appreciated. cheers Uni student

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