Answer to Question #202728 in Mechanical Engineering for Joe Melwin Raja

Question

Calculate the gears for cutting metric threads of following

pitch. i) 4mm pitch, ii) 5.25 mm pitch. The lead screw of lathe

contains 6 TPI. The lathe is supplied with 20 to 120 teeth in step

of 5and an additional gear wheel of having 127 teeth.

Answer 1

For metric threads,

$\frac{Driver \space teeth}{Driver \space teeth}=\frac{5mp}{127}$

where, n= number of threads per inch i.e TPI

P= Pitch of the thread to be cut

(i) 4mm

$\frac{Driver \space teeth}{Driven \space teeth}=\frac{5mp}{127} =\frac{5*6*4}{127}=\frac{120}{127}Ans$

The gear train will consist of 120 teeth on the spindle gear and 127 teeth on the lead screw

$5.25mm$ Pitch

$\frac{Driver \space teeth }{Driven \space teeth}=\frac{5mp}{127} =\frac{5*6*5.25}{127}=\frac{5*6\frac{21}{4}}{127}$

$=\frac{105*6}{4*127}=\frac{105}{40}*\frac{60}{127} A ns$

Numerators and denominators are multiplying by 10

For 5.25mm pitch, compound gear train to be used with 105 teeth on spindle gear and 127 teeth on the intermediate gear , 60 teeth intermediate gear drives a 40 teeth gear on the lead screw.