Question

The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line. The pitch $p = 4$ mm and the included angle of the thread is $60^\circ$. The diameter of the best size wire is ____________ mm (round off to 2 decimal places).

Hint:

For a 60° metric thread, the best wire diameter depends only on pitch: $d = \frac{p}{2} \sec 30^\circ$.

Answer 1

Correct Answer: 2.29

For metric (60°) threads, the best size wire touches the flanks exactly at the pitch line. The formula for best wire diameter in a 60° thread is: \[ d_w = \frac{p}{2} \sec\left(\frac{\theta}{2}\right) \] where pitch \(p = 4\) mm and \(\theta = 60^\circ\). Thus, \[ d_w = \frac{4}{2} \sec 30^\circ = 2 \times \frac{1}{\cos 30^\circ} = 2 \times \frac{1}{0.866} \] \[ d_w \approx 2.309\ \text{mm} \] Rounded to 2 decimals: \[ \boxed{2.31\ \text{mm}} \quad (\text{acceptable range } 2.29 \text{–} 2.33) \]