Question

To measure the effective diameter of an external metric thread (included angle is ${60}^{\circ }$) of 3.5 mm pitch, a cylindrical standard of 30.5 mm diameter and two wires of 2mm diameter each are used. The micrometer reading over the standard and over the wires are 16.532 mm and 15.398 mm respectively. The effective diameter (in mm) of the thread is

• A. $29.366$
• B. $30.397$
• C. $33.336$
• D. $26.397$

Answer 1

The correct option is B $30.397$

$\text{Correction = Actual value - Measured value correction}$

$=(30.5+2+2)-16.532$

$\text{= 17.968 mm}$

$\text{(To be added in measured value)}$


$M_{actual}=M_{measured}+correction$

$=15.398+17.968$

$M_{actual}=33.366mm$

$M=T+2d_w$

$T=M-2d_2=M-4$

$T=29.366mm$

$PCD=T+2x$

$x=\frac{d_w}{2}(1-cosec\alpha )+\frac{P}{4}cot\alpha$

$2\alpha ={60}^{\circ },\alpha ={30}^{\circ },P=3.5mm$

$x=\frac{2}{2}(1-cosec30)+\frac{3.5}{4}cot30$

$x=-1+1.5155=0.5155mm$

$PCD=T+2x$

$=29.366+2\times 0.5155=30.397mm$