Thread errors and effect of pitch error

(a) Errors in threads

1. Pitch errors: progressive (the pitch increases or decreases uniformly), periodic (the error repeats every revolution, e.g. due to an eccentric lead screw), drunken thread (the helix is irregular within each turn), and irregular.
2. Flank angle errors: the thread angle is incorrect, or one flank is inclined differently from the other.
3. Major and minor diameter errors: wrong depth and root form.
4. Effective (pitch) diameter errors: the diameter at which the thread width and the gap width are equal is wrong.

Effect: a pitch error or an angle error makes the bolt (external thread) behave as if it had a larger effective diameter, so it may not assemble with the nut (internal thread). Contact then occurs only at a few points on the flanks, so the load-carrying area drops, and the thread wears quickly and can strip. To compensate, the effective diameter of the bolt must be reduced (or that of the nut increased), which uses up part of the tolerance.

(b) Numerical

Because of a pitch error $\delta P$, the flanks of the bolt and nut interfere. The bolt behaves as if its effective diameter were larger, so the virtual (functional) effective diameter is increased by

$$\delta E = \delta P\,\cot\frac{\alpha}{2}$$

For $\alpha = 60^\circ$: $\cot 30^\circ = 1.732$

$$\delta E = 1.732 \times 0.03 = 0.052\ \text{mm}$$

Virtual effective diameter $= 18.350 + 0.052 = 18.402$ mm.

For Whitworth ($\alpha = 55^\circ$): $\cot 27.5^\circ = 1.921$

$$\delta E = 1.921 \times 0.03 = 0.0576\ \text{mm}, \quad E_{virtual} = 18.350 + 0.058 = 18.408\ \text{mm}$$

Answer: increase = 0.052 mm (metric), virtual effective diameter = 18.402 mm; for Whitworth 0.058 mm (18.408 mm).