How to Calculate Lead Screw Maximum Load, Speed & More

Load Requirements of Lead Screws

In order to properly incorporate a lead screw into a design, load requirements must be taken into account. Maximum load values for the nuts are listed in the tables in our linear component catalog sections:

Linear Components - Inches      Linear Components - Metric

These numbers are based on the shear of the nuts and does not take shaft buckling into account (see Max. Column Load formula below). Wherever possible, nuts should be positioned so as to be put in tension, pulling the load. This eliminates the need for buckling considerations. Listed below are some helpful formulas to assist in proper lead screw selection.

Maximum Column Load Formula

Formula: (F) = K x C X 106 x d4 /D2

Where:

 K = End support factor

•  .025 one end fixed, other free (Figure 9.1)
•  1.00 simple supports both ends (Figure 9.2)
•  2.00 one end fixed, one simple (Figure 9.3)
•  4.00 both ends fixed (Figure 9.4)

 C = Material factor

• 13.4 for Stainless Steel screws
• 4.8 for Aluminum screws
• d = Root diameter of the screw
• D = Length between the nut and the support bearing

If the screw is supporting the load weight in a vertical orientation, its diameter and pitch should be selected accordingly, to prevent buckling or excessive deflection.

Torque to Move a Load Formula

Formula: (T) = (F x L) / (2 x M x E)

Where:

• F = Load
• L = Lead
• E = Efficiency (consult Berg Engineering Department for efficiency values)
• M = Coefficient of friction for thread interface

When the lead screw is in a vertical (rather than horizontal) orientation you may also need to account for the force of gravity acting on the load.

Formula for Drive Horsepower (Linear)

Use the following equation to calculate horsepower requirements for a drive motor used to move a load along a lead screw:

Horsepower (HP) = Torque (in. lbs.) x RPM / 63,025

Different types of motors can be used to drive linear movement along a lead screw, including stepper motors, servo motors, AC induction motors, DC motors and brushless DC motors. Hydraulic or pneumatic actuators may be used in applications where an electric motor isn’t suitable (due to the operating environment or load requirements).

Calculate RPM of a Lead Screw Formula

Critical speed of a lead screw shaft is the maximum safe RPM (rotational speed) before the screw becomes dynamically unstable (when the forced frequency of the rotating screw corresponds to its natural frequency).

Lead screw critical speed in RPM is governed by the following equation:

Critical Screw Speed (N) = K x C X 106 X d/D2 

Where:

• K = End support factor
  • 0.36 one end fixed, other free (Figure 9.1) 
  • 1.00 simple supports both ends (Figure 9.2) 
  • 1.47 one end fixed, one simple (Figure 9.3) 
  • 2.23 both ends fixed (Figure 9.4) 
• C = Material factor 
  • 4.5 for stainless steel screws 
  • 1.6 for aluminum screws 
• d = Root diameter of the screw 
• D = Distance between the nut & the support bearing

This formula calculates critical velocity of a lead screw regardless of screw orientation (horizontal, vertical, etc).

Lead Screw Efficiency

Lead screw efficiency is how well the screw transforms torque (rotational force) into linear motion. Use the following equation to calculate lead screw efficiency, or consult the Berg engineering department for efficiency values.

E = tan(ha) / tan(ha + arctan(M)) x 100

Where:

• E = Efficiency (expressed as a percentage)
• ha = helix angle (degrees)
• M = coefficient of friction for thread interface

Lead screw efficiency is mainly affected by the helix angle (aka lead angle) and lead distance (the axial distance the nut travels in a complete revolution: lead distance = pitch x number of starts). The efficiency of a lead screw can also be affected by orientation: you may need to consider the force of gravity on vertical screws.

Find high-precision and precision lead screw assemblies manufactured by WM Berg or request technical assistance with lead screw design calculations.