# Radial engagement

When we talk about the engagement of a male and female threaded fastener, it is commonly in the context of the length of engagement, which is often specified in order to prevent damage to the female thread by stripping or fatigue. However, there is usually no discussion of radial thread engagement.

The amount of radial thread engagement is referenced to the pitch of the thread and the nominal diameter, and is controlled by varying the inner diameter of the female thread. It is usual to provide a female thread that is weaker in terms of shear strength than the male – in this case the nut will strip, rather than the thread on the bolt. Provided that the major (outside) diameter of the male thread remains at a certain size, the load required to strip the female thread should be unaffected.

However, this assumes that the male and female thread axes remain parallel and concentric, and this is not always the case. Where there is excessive lateral play (clearance) in a thread, the result can be that the axes are not coincident. In this case, the assumptions about thread-stripping strength are no longer valid, and if too large a pilot drill is used along with a male thread towards to lower end of the tolerance range for thread class, the thread axes can become so far displaced from one another that they become disengaged on one side.

The formula used to define radial thread engagement calculates maximum possible engagement height based on the pitch of the thread and the thread angle. If the male and female threads were perfectly sharp and were an exact fit, 100% engagement height would be the pitch x cos 30° (the semi-angle of the thread). To allow for a radius root in the male thread, 60° threads allow the female thread to be truncated by 25% of the engagement height – that is, the maximum theoretical engagement is 0.75 x 0.866 x pitch (cos 30° = 0.866) = 0.6495P

The percentage engagement is the ratio of the actual overlap of the thread radially to this 0.6495P, which is:

% radial engagement = 100 x (nominal radius – pilot hole radius) ÷ 0.6495P

It is easier to calculate by multiplying the top and bottom of the formula by 2, so that we then have the calculation in terms of diameter, for which we will have data to hand, and this is the formula you might find in texts on the subject:

% radial engagement = 100 x (nominal diameter – pilot hole diameter) ÷ 1.299P

For an example of M10 x 1.25P, the nominal diameter is 10 mm, the pilot is 8.8 mm and the pitch is 1.25mm Therefore the percentage engagement is 100 x (10 – 8.8) ÷ (1.299 x 1.25) = 73.9%

The figure of around 75% engagement is typical for 60° threads, and small changes make a large difference to the result. In the previous example, if the pilot hole is adjusted to 8.9 mm, the engagement changes to 67.7%

In production engineering there is an incentive to use a lower thread engagement, and figures as low as 50% are typical. Two reasons for this are lower production costs and faster production, as the amount of metal removal is reduced, as is the tapping torque.

There are reasons for us to be wary of this practice though. First, it increases the effective contact diameter of the threads, and will give a higher tightening torque for a given load. If we have specified a tightening procedure based on the assumption of 75% engagement, we may have less pre-load than expected. Second, by increasing the pilot hole diameter, we are decreasing the shear area of the male thread, making it more prone to strip.

Written by Wayne Ward