I am interested in how high-precision screw threads can be made from lower precision parts. As I understand it, one can make threads on a lathe in the following way:
- The workpiece is rotated by some motor, at a not-necessarily fixed speed $\omega$
- The feed rate is set proportional to $\omega$ using gears and the leadscrew
This is illustrated by the diagram below:
Limitations of Precision
It seems like this method limits the accuracy of the machined threads to the accuracy of the leadscrew in the lathe. I would like to know how one can machine threads of higher precision than the leadscrew of the lathe.
It seems that this is possible according to the section making accurate screws in this page, where it is written that:
To produce a screw of a foot or even a yard long with errors not exceeding 1⁄1000th of an inch is not difficult. Professor William A. Rogers of Harvard observatory has invented a process in which the tool of the lathe while cutting the screw is moved so as to counteract the errors of the lathe screw. The screw is then partly ground to get rid of local errors.
So to summarise, my question is:
Suppose you have a lathe, with a not-necessarily-accurate leadscrew. How can you manufacture a leadscrew of higher precision using this lathe?
Or alternatively: what might be the method described by "Professor William A. Rogers"?