Critical speed for a leadscrew

Description

The critical speed is the speed that excites the natural frequency of the screw. For a steel leadscrew or steel ballscrew, the critical speed is approximately
Furthermore the running speed for a leadscrew (or ball screw) is typically limited to, at most, 80% of the calculated critical speed.
Constant C values for steel leadscrew or steel ballscrew, depending on the ends:
C = 0.36 for one end fixed, one end free
C = 1.00 for both ends simple
C = 1.47 for one end fixed, one end simple
C = 2.23 for both ends fixed

Related formulas

Variables

NCritical speed (rpm)
drSmallest (root) diameter of the leadscrew (in)
CConstant for steel leadscrew or steel ballscrew depending on the end of the leadscrew (rpm*in)
LLength between bearing supports (in)