Question

A non standard thread of pitch $3.175mm$ is to be cut on a lathe having lead screw of pitch $6mm$. A change gear set provdied with the lathe has one gear each with the following number of teeth: $20,30,40,50,60,70,80,90,100,110,120,127.$ The correct pairs of change gears $(a/b\times c/d)$ for machining the given thread are (assuming that transmission ratio of the rest of the kinematic train between the late spindle and lead screw is equal to 1)

• A. $\frac{127}{30}\times \frac{20}{80}$
• B. $\frac{127}{40}\times \frac{20}{120}$
• C. $\frac{127}{30}\times \frac{30}{120}$
• D. $\frac{127}{50}\times \frac{30}{80}$

Answer 1

The correct option is B $\frac{127}{40}\times \frac{20}{120}$

$\text{Gear ratio}=\frac{\text{Pitch of job threads}}{\text{Pitch of lead screw theras}}$

$=\frac{3.175\times 40}{6\times 40}=\frac{127}{240}\to \text{not possible}$

$=\frac{127}{40}\times \frac{1\times 20}{6\times 20}=\frac{127}{40}\times \frac{20}{120}$