Break loose torque calculation of lock nut against rotating/acceleating bolts?

First of all I would recommend you the documenzt VDI 2230 - "Systematic calculation of high duty bolted joints". The document is bi-lingual (German and English) and among some (german) books the source of my post.

First of all some design 'tips' which ma be useful depending on your application and the tools at hand:

• Use higher tightening torque if possible. The goal of the torque is to get a clamping force bewteen the parts after all. But this is heavily influenced by friction and geometry of the connection.
• You can use loc-tide (or similiar product) to secure the connection. There are several grades of strength an this will certainly prevent slack.
• Use nord-lock washers (or similiar product) since they increase the the loosening torque due to their geometry.
• Avoid normal washers if possible since they increase the number of contact surfaces and hence increase settling in of the connection. In the end this means less clamping force and thus less friction which is preventing your nut from slackening.
• Use a bolt with a smaller shank. They are more flexible and can store more energy in the connection. Better for fatigue and tends less to settling in.
• Use special friction-increasing paste below your mating nut surface. This is used e.g. by cyclists to lower their required tightening torque on carbon frames. YOu can use abrasive powder mixed with bearing grease as well. BUT there may be longterm effects due to the small particles beeing crushed.
• If feasible, drill a hole for a cotter-pin. This only prevents loosing the nut but the connection may slip.
• Use a make-up method other than torquing it up. Good systems stretch the bolt with hydraulics to achieve the neccessary clamping force. The nut is solely put on Ä'hand-tight'. No preload (=clamping) force is lost due to friction in the thread.

If you want to calculate, this requires quite a lot of information. The problem depends on the following parameters:

• angluar acceleration acting on the nut. I would take the peak value since this is conservative.
• rotary moment of interia of the nut. With the peak acceleration this gives you the torque to loosen your bolt.
• geometry of the parts involved. You want your bolt to be flexible and the flange (rotor) to be stiff to make a durable connection.
• Friction coefficients µ of the material pair. This is also influenced by surface coatings and lubrication. There is a HUGEuncertainity connected with this parameter.
• The material and surface finish of nut and rotor. Rough surfaces tend to settle in/relax and reduce the clamping force in the connection after a fewe cylces.