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Nut Factor

mikemkc (Mechanical) 
27 Dec 01 23:56 
Sirs,
Does anyone know of a reliable source of information for the "nut factor" or coefficient of friction between silver plated bolts and an austenitic stainless steel part? Closest references I have been able to find are on the order of 0.4, between silver and steel.(details of materials unspecified)
mikemkc 

boo1 (Mechanical) 
28 Dec 01 11:18 
I checked my references and no luck. Try the gear people since they use silver as a antigaulling coating for steel. 

Try MILHDBK60, 1990, http://astimage.daps.dla.mil/docimages/0000/22/90/70455.PD9, p. 28, for coefficient of friction, 0.14. Then using MILHDBK60, 1990, Sect. 100.5, p. 26, Eq. 100.5, or Shigley, Mechanical Engineering Design, 1989, Eq. 819, p. 346, gives torque coefficient (sometimes called "nut factor") of K = 0.185. 

A “nut factor” answer may be more than adequate for your application. However, depending on the degree of accuracy/certainty you need to establish your fastener tension values, approach "nut factor" usage with great caution. The reported ranges, and the ranges of those ranges, vary widely from publication to publication. Almost all of these lists (the responsible, enlightened ones) will emphasize their "reference" nature, and contain strong cautions regarding their use in a particular application without empirical verification (torque/tension testing). A good discussion of nut factor, including some of its limitations and variables, can be found at http://www.fastenal.com/documents/Miscellaneous/Fastenal%20Technical%20Reference%20Guide.pdf"; An excerpt: "The K, or nut factor, not to be confused with the frictional coefficient, can be thought of as a combination of three factors: K1, a geometric factor, K2, a thread friction related factor, and K3, an underhead friction related factor. While there are published tables for K, these will usually vary from publication to publication. For a more detailed analysis it is desirable and often necessary to determine this value experimentally by using a specially designed torquetension load cell." The MILHDBK60 torque/tension formulas are great (like "vonlueke" I recommend and use them) in that they attempt to take into account may of the variables that affect the torque/tension relationship that are completely ignored by more simplified "nut factor" tables (i.e. thread pitch/helix angle, pitch diameter, mean bearing area of the rotating fastener/structure bearing interface, the fact that underhead and thread friction coefficients can be  and usually are  different). Without that additional information (which I didn't see in this thread), I'm not quite sure how vonlueke got from the friction coefficient (not to be confused with nut factor) to the nut factor he mentions in his answer. In additon, the range of coefficient friction values themselves is quite large, and is further affected by even small amounts of supplemental lubrication. Specific to silver plated nuts (from http://www.tcnj.edu/~rgraham/barrett/manual1A.html) "Silver Plating: Since silver tarnishes from normal atmospheric exposure, the silverplated nuts are commonly coated with clear wax to prevent tarnishing. Wax is a good roomtemperature lubricant. Therefore, the normal "dry torque" values of the torque tables should be reduced by 50 percent to allow for this lubricant." Although not noted by Barrett, nut manufacturer’s may also add supplemental lubricants to lots that may otherwise exceed a maximum locking torque requirement, or to help them meet multiplecycle (reuse) locking toque requirements. I have personally seen the variation noted by Barrett in silver plated nuts, and in testing performed on them. This might lead you to want to degrease your nuts to remove any such coating. However if your nut is of the allmetal, "selflocking" variety (the "norm" in the aerospace industry where silver plated nuts find the majority of their usage) and the "locking torque" was set by the nut manufacturer with the coating applied, you run the risk of developing excessive locking torques (reducing the tension "preload" for a given torque and increasing the potential for galling as well  as affecting multiple cycle reuse capabilities). If the coating was applied after the locking torque was set, the effect is the opposite (potential lowering of the locking torque values to the point where vibration resistance, and/or multiplecycle locking torque requirements, may be compromised, etc.). In former scenario you might generate nonconforming hardware by degreasing your parts; the latter scenario could result in the manufacturer shipping you nonconforming hardware. You can see why most users of aerospace fasteners users prohibit modification of fastener lubricants by anyone other than the fastener manufacturer, and require retesting after any such modification. Bottom line: Even without the "wax" variable above, if I needed to know the torque/tension relationship for a given application with any degree of certainty, I would trade one torque/tension test for 100 calculations or "nut factor" tables. Most aerospace companies recognize this and maintain recommended "torques tables" (by diameter) for specific nut/bolt finish/lube combinations based on empirical testing. Note that even testing won't protect you from parttopart and/or lottolot variations in friction coefficients (the overriding factor in the torque/tension relationship), of which the "wax" vs. “no wax” example for silver plated parts above is just a single example. 

Good catch, Kenneth. I should have clarified my post as follows. Try MILHDBK60, 1990, http://astimage.daps.dla.mil/docimages/0000/22/90/70455.PD9, p. 28, for coefficient of friction, mu1 = 0.14. Then, using MILHDBK60, 1990, Sect. 100.5, p. 26, Eq. 100.5, or Shigley, Mechanical Engineering Design, 1989, Eq. 819, p. 346, torque coefficient (sometimes called "nut factor") for mu2 = mu1 becomes K = 0.185. Thanks for your post. By the way, I got the above link from one of your other excellent posts a while back. 

Thanks for the kind words vonlueke. I guess I should have clarified as follows:
I was unable to see how (using MILHDBK60, 1990, Sect. 100.5, p. 26, Eq. 100.5) one could calculate a "nut factor" (even if mu1 = mu2 is assumed) with the information given. The MILHDBK60 torque/tension equation(s) contain(s) variables that I didn't see anywhere in the thread: "L" or lead of the thread helix in inches; either the fastener nominal ("d") or pitch ("d_{2}") diameter; and (if not assumed) the "washer," or "bearing face", diameter ("b"). 

My fault, Kenneth, and good point. I was too cryptic and didn't fully state my derivation and assumptions, as follows. Using MILHDBK60, Eq. 100.5 (Shigley Eq. 819 gives almost exactly the same answer), and using the assumptions stated on the cited page numbers, namely dw = 1.5d and mu2 = mu1, where dw = washer face OD and d = bolt nominal diameter, then for mu1 = 0.14 from the cited table (no wax), the mean K value for typical bolt sizes (4 to 12.7 mm), metric and imperial, coarse and finepitch, is mean1 = 0.185, with standard deviation s = 0.0032. This is mean of 17 bolt sizes and pitches analyzed.
Similarly, for all bolts (d = 1.6 to 38 mm), metric and imperial, coarse and finepitch, 76 bolt sizes and pitches analyzed, the mean value is mean2 = 0.183. I of course placed more emphasis on the most commonly used bolt sizes (for posted AE or ME application), and therefore reported mean1, not mean2.
As an example, evaluating Eq. 100.5 for M8 x 1.25 mm bolt, for dw = 1.5d and mu1 = mu2 = 0.14, gives K = (0.1989 + 0.5810 + 0.7000)/8.00 = 0.1850. Of course the engineer must understand that using theoretical equations and typical values from the cited references merely gives an estimate, and that if a more accurate answer is needed, one should measure the installed fastener with a micrometer and compute torque coefficient K = T*L/(E*A*delta*d), per Shigley, p. 345, para. 2, to test specific combinations and lubricants, where T = installation torque, L = bolt grip length, E = bolt modulus of elasticity, A = bolt crosssectional area, and delta = measured bolt elongation in units of length.
Any insight into how much of that wax typically comes on say an MS210434 nut, and what it typically lowers the above mu1 value to, assuming say an NAS1004 bolt? Thanks. 



