How is the r.pm. of lathe machine varies with variation in diameter of cylinderical job

Also give the reason?

You want a constant cutting speed for the smoothest work . For the same RPM a larger diameter piece will have a higher rim speed than a smaller diameter.

A circumference of a circle is C = 3.14 * diameter

So for example, a 3" diameter piece will turn at 3* 3.14 * 60 rev/ minute = 565.2 inches a minute

A 6" diameter piece will be 6 * 3.14 * 60 rpm = 1130.4 inches a minute.


For the 6" piece to turn properly you would have to slow the lathe down to 30 rpm to get same rim speed as the 3" diameter piece. Then the 6" diameter piece would turn at 565.2 inches/min also

The type of steel used in the cutting tools determines how much heat they can take before the metal starts to break-down. The amount of heat generated is based on the feet-per-minute surface speed of the work. So, to keep the surface speed the same, the larger the work piece diameter, the slower the rpm of the lathe.

Usually, you want the tool to move at a constant linear speed with respect to the material. So as the diameter gets smaller, the RPM gets bigger in proportion. Each time you half the diameter, you double the speed.

But don't get too carried away with that. At zero radius, that would predict infinite RPM.

No. the RPM does not depend on the diameter of the work piece.
The surface feet per minute does depend on RPM.