Nuts (and bolts)

I often wonder why all the tap handles in my new bathroom and kitchen are loose; and why the nut falls off the door of my new wood-burning stove every other day. I am of an age at which new problems seem obviously due to slipping standards, or to the forgetting by callow youth of the wisdom of their elders. So I assume that these loose nuts are symptomatic of some failure of modern workmanship, or of modern materials. I suppose there are several possible explanations, besides 'bad luck'.

Perhaps the coefficient of friction (µ) of common materials has changed? For example, teflon is 10 times 'slippier' than steel, while de-greased steel is some 30% 'grippier' than normal steel [1]. Aluminium grips on aluminium, but not on steel. The oxide layer on materials like aluminium and steel makes a considerable difference to the grip. There is a plethora of data [1] on coefficients of friction, but all-in-all I could not identify in this area a convincing explanation for my loose nuts.

The nuts and bolts that held our bicycles and cars together for half a century before the second world war were defined (pitch, mean diameter, depth of groove) in factions of an inch. Metrication has, of course, minutely changed these linear dimensions to make them fit a metric scheme, and so I wondered if the engineers making the conversions from inches to millimetres had 'rounded' in such a way as to degrade the gripping power. If we define "lead angle" as arctan (lead/(π x mean diameter)) [2], first of all we find lead angle of metric standard bolts curiously variable. A 7 mm diameter bolt (pitch = 1 mm) should, on the face of it, grip appreciable better than the similar sized 6 mm diameter bolt (pitch = 1 mm), and the 4 mm diameter bolt appreciably worse (pitch = 0.7 mm). However, when we compare standard metric bolts with British Standard Whitworth, or American Screw Thread, we find that the new lead angle is significantly less, and should therefore be less prone to work loose.

(Bicycle threads are different. They were (and are) deliberately made with a finer thread, so even with 'amateur' servicing they are less prone to wriggle loose.)

So why then the loose tap handles, fire-door, etc. There is one measurement in the standard metric bolt that is less friendly to security than found in older standard threads, and that is the angle formed by the two sides of the groove. It is now 60º. It was 55 º in the BSW (and was 47.5º in the British Association fine instrument threads). This means that the load, which [a] generates friction and [b] generates the resultant force that causes loosening, is far from 'normal' to the interacting surfaces, but is applied at a glancing angle. I wonder if this is significant.

Wouldn't it be champion if my ruminations on this matter ultimately led to a new international thread standard, and a generation of tap handles that stayed firm indefinitely!

REFERENCES
[1] http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm
[2] "Lead" is the distance of advance up the axis of the bolt for each turn of the helix. See http://en.wikipedia.org/wiki/Lead_(engineering)

Occidentis, MORPETH, UK.