Calculation of "Nut Factor", K
Experimental Determination of Friction Coefficients
Just as tabulated values of K are not reliable for application with any assurance of predictable results for a given bolt / nut assembly it is equally true that friction coefficients determined experimentally must be used for comparison purposes and supplemented by torque-angle assembly monitoring to assure proper assembly clamp forces.
The German Norm , DIN 946, provides a practical standard method of evaluation of friction coefficients on screw threads and underhead bearing surfaces. Fastener laboratory testing machines are available for determination of friction coefficients according to DIN 946.
Torque-Tension Coefficient / Nut Factor: K
The basic equation, T= K d F, can be applied to the linear-elastic-clamping zone of the assembly tightening process . The prevailing torque during initial run-down must be subtracted from the total applied torque, a procedure which is usually accurate for all practical purposes. If insufficient torque is applied to tighten beyond the alignment zone the tension estimated for a given assembly will be still be correctly predicted if the overall "K" factor has been accurately guessed.
There are published tables of "K" factors for various combinations of materials, surface finishes, plating, coatings and lubricants. However, actual experience has shown that it is highly unreliable to assume that any given "K" value applies to a specific fastener being assembled. The importance of the torque-angle approach to assembly cannot be overemphasized when you are responsible for the safety and reliability of critical bolted assemblies. It is not uncommon to see variations in friction coefficients of 2:1 or more as the same fastener is repeatedly tightened and loosened. The most practical way to minimize the variation in clamp force for bolted assemblies is to use both torque and angle of turn in your assembly process.
The factor K, often called to as the "nut factor", can be expressed as a combination of three factors:
K1 ( a geometric factor, function of diameter, d and Pitch, P)
K2 ( a thread friction factor, function of Mue_G and pitch dia., d_2)
K3 ( a bearing friction factor, function of Mue_K and D_Km)
Thread /Underhead Friction Coefficient Measurements
In the development of threaded fastener materials, surface finishes, plating, coatings and thread locking adhesives it is necessary to measure and control the friction coefficients on both the threads and underhead regions of the fasteners.
A Torque-Tension Research Head, as illustrated in Figure __, is a special load cell constructed to simultaneously measure both thread torque (pitch torque + thread friction torque) in addition to the tension created as the tightening torque is applied. Special devices such as locknuts, serrated underheads and thread locking adhesives and friction patches can be tested and friction performance standards can be established and maintained through measurements made with the Torque-Tension Research Heads. The Research Head has the capability to fully test for friction coefficients according to DIN 946 .
The average coefficient of friction, Mue_ges,, can be roughly estimated by measuring the change in length of a screw or bolt after application of a given tightening torque. This method can only be applied if there is no yield occurring in the bolt, threads or elsewhere in the joint.
The formula for calculation of the nut factor, K is as follows:
T = K d F : Simplified torque / tension equation
K= (1/d) x [0,159*P + 0,578*d_2*Mue_G) + (D_Km/2)*Mue_K]
d: nominal diameter of the bolt, P: Thread Pitch , d_2: Pitch diameter D_Km: Mean bearing diameter / underhead Mue_G: Thread friction coefficient
Mue_K: Underhead friction coefficient