Critical Speed: Precision Ball Splines

The final factor to verify is the critical speed. The following formula is used to calculate critical speed in r.p.m.

N = Cs × 4.76 × 106 × d


N = Critical Speed (rpm)
d = Root Diameter of Screw (inch)
L = Length Between Bearing Supports (inch)
Cs = 0.36 for one end fixed, one end free
1.00 for both ends simple
1.47 for one end fixed, one end simple
2.23 for both ends fixed

Critical speed can also be affected by shaft straightness and assembly alignment, it is recommended the maximum speed be limited to 80% of the calculated value.

To Use This Chart

  1. Determine the maximum RPM.
  2. Determine the maximum length between bearings.
  3. Determine end fixity.
  4. Find point at which length and speed intersect.
  5. Choose spline direction to the right or above the intersecting point.
Figure 1