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Critical Speed Ball Screw and Lead Screws Formulas and Calculator

Machine Design Formulas and Calculators
Gear Design and Engineering Data

Critical Speed Ball Screw and Lead Screws Formulas and Calculator:

The critical speed is the lowest rational speed that a shaft is in resonance.

n_c = f_c ( d_r / L_c²) 10⁷

Where:

n_c = critical speed (rpm)
d_r = root diameter of screw (mm)
f_c = factor based on end speed support bearings
L_c = unsupported length of screw (mm)

Typical f_c factor (see Ball Screw Design Equations for related images):

Fixed - free = 3.4
Supported - supported = 9.7
Fixed - supported = 15.1
Fixed - fixed = 21.9

Characteristic speed

DN = d_o n_max

and

n_max = DN / d_o

DN = characteristic speed (rpm)
d_o = nominal diameter of the screw (mm)
n_max = maximum allowable rotational speed (typical 60,000 - 150,000 mm/min)

Typical DN values for ball screw return designs are:

• 76,200 mm-RPM (3,000 in-rpm) for Standard external return systems
• 133,300 mm-RPM (5,250 in-rpm) for external returns systems with solid deflectors
• 140,000 mm-RPM (5,510 in-rpm) for internal transfer designs

DN value can be used to deteremine the maximum speed of the screw assembly except for small diameter screws.

Typical Permissible Rotaional Speed Diagram
(Click on image to enlarge)

Related:

• Critical Speeds of Rotating Shafts with Single Loads Equations and Calculators
• Critical Speeds of Rotating Shafts with Single Loads, First Critical Speed
• Critical Speeds of Rotating Shafts and Mass Review
• Ball Screw Support Bearings Review