BIZOMAT MAKEOS · Power Transmission
Lead Screw Input Torque
What torque is needed to drive this axial load through a lead screw?
Calculate the torque needed to drive a steady axial load through a lead screw or ball screw at a known overall efficiency.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Axial load | N | Total axial load to be moved, including gravity load on a vertical axis and process forces. |
| Screw lead (travel per revolution) | mm | Travel per revolution (pitch × number of starts). |
| Overall screw efficiency (as a fraction) | fraction 0–1 | Overall efficiency as a fraction from 0.01 to 1, from the screw manufacturer for this screw, nut material and lubrication. Enter 0.3 for 30%. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Axial load
- What it is
- The total force along the screw axis that the nut must push or pull: process force, friction in the guides, and the weight of the load on a vertical or inclined axis.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Input torque is directly proportional to the axial load.
- Get it right
- On a vertical axis include the full weight of the moving parts (mass times standard gravity, in newtons); it is easy to leave out.
What this means: Screw lead (travel per revolution)
- What it is
- The axial travel of the nut for one full turn of the screw: thread pitch times the number of starts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.01 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Input torque is directly proportional to lead: a coarser lead needs more torque but moves faster.
- Get it right
- A multi-start screw has a larger lead than its pitch; use the lead, or the torque will be too low.
What this means: Overall screw efficiency (as a fraction)
- What it is
- The share of input work that reaches the load as useful axial work, after thread friction and nut losses, written as a fraction. It depends on the screw type, nut material and lubrication.
- Units and format
- Enter a number in fraction 0–1: fraction 0–1. The form accepts 0.01 fraction 0–1 to 1 fraction 0–1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 fraction 0–1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Input torque is inversely proportional to efficiency: halving it doubles the torque.
- Get it right
- Type a fraction, not a percent: 0.3 means 30 %. Take it from the screw manufacturer for this screw and nut.
Method and formulas
- Frictionless torque (N·m) = axial load (N) × lead (mm) / 1,000 / (2π).
- Input torque = frictionless torque / efficiency.
- Example: 2,000 N, 5 mm lead and efficiency 0.3 give 2,000 × 0.005 / (2π × 0.3) = 5.305165 N·m; the frictionless torque is 1.591549 N·m.
Limitations
- Steady motion only: acceleration torque, support bearing and seal drag, and preload torque are excluded.
- Back-driving and load holding are not checked. Whether a screw can be back-driven depends on its thread friction and lead angle; a brake may be needed on vertical axes.
- No certification or drive selection is implied.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a motor or gearbox for a screw axis
- Compare lead screw and ball screw torque
- See how lead and efficiency change torque
Who it is for
- Design engineers
- Maintenance engineers
What you get
- Input torque at the entered efficiency (N·m)
- Frictionless torque at efficiency 1 (N·m)
Interpreting the result
- Lead screws commonly have much lower efficiency than ball screws, so the same load needs more torque and generates more heat.
Before relying on the result
- Use the manufacturer’s efficiency for the actual screw, nut and lubrication, not a generic figure.
- Add acceleration and drag torque and apply the drive manufacturer’s service factor before sizing a motor.
References
- Budynas R. G. and Nisbett J. K., Shigley’s Mechanical Engineering Design, 10th edition (McGraw-Hill, 2015), chapter 8, section on the mechanics of power screws. Topic reference; no source tables or recommended settings are reproduced.
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