# The importance of washers

In a bolted joint, the design of the fasteners is responsible for the proportion of the service load borne by the fastener, and the theoretical ratio of torque or tightening angle to load is influenced strongly by the dimensions of the nuts, bolts and studs and by the coefficient of friction acting between them. Much effort is put into fastener design, but washers are often neglected in terms of design, although they can have a very positive effect on the reliability of the system.

As is widely explained in general mechanical engineering textbooks or specialist fastener books, the amount of the cyclic service load borne by the fastener can be predicted if we know the stiffness of the fastener and the stiffness of the clamped members in a joint. The basics were explained in some RET-Monitor articles first posted in 2009. The ‘Back to Basics Part 2’ article gave the formula for the load coefficient, the calculation of which tells us the proportion of the cyclic service load the fastener will be subjected to.

If you don’t want to subject yourself to some basic maths, we can state one inalienable fact – for a given fastener stiffness, the cyclic service load will be reduced if the stiffness of the clamped members is increased, providing that the joint has sufficient pre-load to resist joint separation. For fixed clamped member geometry, it is unlikely that a change of material to anything stiffer – as in having a greater elastic modulus – will be possible. Not only is it usually impractical, it will often involve far heavier clamped members.

A stiff washer of increased diameter compared to the original part which tightened onto the clamped members (whether this was a nut or washer) will clamp a greater volume of material, and the stiffness of the clamped members will increase as a result. Only in very simple geometry can the effect be easily predicted using ‘pencil and paper’ maths. Engines in general are full of complex structural parts, so the clamped members cannot easily be approximated mathematically by a series of tubes or hollow frusta (truncated cones).

Where geometry is simple enough to be modelled using simple geometric forms, the stiffness of a clamped joint member is usually thought to be most accurately modelled by a frustum rather than a tube. The stiffness of a frustum is a little more complex to calculate than that of a tube; load is known to ‘spread’ to clamp a greater volume than a simple cylinder where material exists for it to spread into. A cone ‘semi-angle’ of 30° is often used, having been adopted from some early studies into joint stiffness (see references), although various studies propose other values.

By clamping a greater volume of material through increasing the outer diameter of the clamped members, the washer leads to a decrease of cyclic load on the bolt or stud. The washer needs to be sufficiently stiff to be able to transmit load to a greater diameter than the head of the bolt or nut which loads it. Thin, flexible washers are of little use for this purpose.

Washers also promote reliability by helping to protect the face of castings or other components from directly having to withstand highly loaded sliding contact as the fastener is tightened.

References

1. Little, R.E., “Bolted Joints: How Much Give?”, Machine Design, November 1967

2. Osgood, C.C., “Saving Weight on Bolted Joints”, Machine Design, October 1979

Written by Wayne Ward