Ball Screw Torque Calculations

When considering the total torque required for a given screw assembly, you must consider several factors. If Preload is applied to the ball screw assembly, Drag Torque is added to either the Driving Torque or Backdriving Torque.

WHERE:

  • Td = Driving torque (N⋅m)
  • Tp = Drag torque (N⋅m)
  • Tb = Backdriving torque (N⋅m)

NOTE: When determining Total Torque Required, consideration needs to be made for additional motor load such as wipers or seal drag, linear guide drag, proper inertia matching, etc.

Drag Torque (when preload is applied)

Dynamic drag torque is the torque required to rotate the preloaded ball nut relative to the ball screw shaft, or vice versa, in the absence of an external load and any friction torque of the end wipers.

WHERE:

  • Tp = Preload drag torque (N⋅m)
  • Ph = Lead (mm)
  • Fpr = Preload Force (N)
  • β= Lead Angle (deg)
  • B.C.D. = Ball Circle Diameter

Preload Force (Fpr)

Preload is an internal force introduced between a ball nut and screw assembly that eliminates free axial and radial lash. Preloaded assemblies provide excellent repeatability and increased system stiffness.

When considering preload as a percentage of Dynamic Capacity, multiply preload percentage by Ca from the ball nut data tables.

Drag Torque Variation (Tp variation)

Because of natural lead variation and ball thread form tolerancing, Drag Torque can vary significantly and should be considered when preload is applied to a ball nut assembly. The chart below illustrates the expected variation in Drag Torque.

To use the chart below first calculate the S-ratio of the ball screw assembly:

Tp variation

Per ISO 3408 E12  
Tp (N⋅m) SRatio ≤ 40 40 < SRatio ≤ 60 SRatio > 60
T3 T5 T7 T3 T5 T7 T3 T5 T7
< 0.2 - - - - - - - - -
0.2 to 0.4 ±40% ±50% - ±50% ±60% - - - -
0.4 to 0.6 ±35% ±40% - ±40% ±45% - - - -
0.6 to 1 ±30% ±35% ±40% ±35% ±40% ±45% ±40% ±45% ±50%
1 to 2.5 ±25% ±30% ±35% ±30% ±35% ±40% ±35% ±40% ±45%
2.5 to 6.3 ±20% ±25% ±30% ±25% ±30% ±35% ±30% ±35% ±40%
6.3 to 10 ±15% ±20% ±30% ±20% ±25% ±35% ±25% ±30% ±35%

Driving Torque

When rotation is converted into linear motion (Normal Operation), the torque can be obtained from the following formula:

WHERE:

  • Td = Driving torque (N⋅m)
  • F = Axial load (N)
  • Ph = Lead (mm)
  • η1 = Normal efficiency (90%)

Backdriving Torque

When linear motion is converted into rotation (Reverse operation), the torque can be obtained from the following formula:

WHERE:

  • Td = Backdriving torque (N⋅m)
  • F = Axial load (N)
  • Ph = Lead (mm)
  • η2 = Reverse efficiency (80%)

Example

PMBS32×10R-4FW/5/T5/EK/4N/1550/1/S

Preload = 5%
Ca = 36,222 N
Load = 12,000 N
Ph = 10mm Lead
B.C.D. = 32mm

Lead Angle

Drag Torque

Drag Torque Variation (Tp variation)

Driving Torque

Total Torque = 21.443 N⋅m to 21.805 N⋅m

Figure 1