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For an ideal frictionless screw, required torque equals axial force times lead divided by the circumference factor.
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Formula
T in N·m; F in N; p in m/revolution
| Symbol | Meaning | Unit |
|---|---|---|
| Ideal drive torque | N·m | |
| Axial load force | N | |
| Lead per revolution | m |
T=\frac{F p}{2\pi}The relation follows from work equality per revolution: 2πT=Fp. It assumes frictionless motion, constant load and negligible bearing losses. Real threads need more torque because of flank and bearing friction and may be self-locking. For a multi-start thread, p is lead per revolution, not spacing between adjacent threads.
The relation follows from work equality per revolution: 2πT=Fp. It assumes frictionless motion, constant load and negligible bearing losses. Real threads need more torque because of flank and bearing friction and may be self-locking. For a multi-start thread, p is lead per revolution, not spacing between adjacent threads.
For an ideal frictionless screw, required torque equals axial force times lead divided by the circumference factor.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Ideal torque of a lead screw” and check its unit and magnitude.
For F=1,000 N and a 5 mm lead, ideal torque is about 0.80 N·m.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: T in N·m; F in N; p in m/revolution.
Formula cluster
For an ideal frictionless screw, required torque equals axial force times lead divided by the circumference factor.
For F=1,000 N and a 5 mm lead, ideal torque is about 0.80 N·m.
Understand ideal force-to-torque conversion in a screw drive.
Here is how to work through a typical Ideal torque of a lead screw (T = Fp/(2π)) task step by step:
Task
Work through the numerical example for “Ideal torque of a lead screw” and check its unit and magnitude.
Solution path
For F=1,000 N and a 5 mm lead, ideal torque is about 0.80 N·m.
One revolution turns the screw through 2π radians and supplies rotational work 2πT. The load moves through lead p and receives work Fp. Equating these gives T=Fp/(2π) when friction losses are absent. This is the frictionless work-balance limit; real screw torque must include thread and bearing friction. Application: Understand ideal force-to-torque conversion in a screw drive. The numerical example For F=1,000 N and a 5 mm lead, ideal torque is about 0.80 N·m anchors the idea in a concrete measurement case.
p is the axial travel per complete revolution, called the lead. For a single-start thread it equals pitch; for multiple starts it is an integer multiple. Use travel per revolution in the work balance, not spacing between adjacent threads. This is the frictionless work-balance limit; real screw torque must include thread and bearing friction. The corresponding units are T in N·m; F in N; p in m/revolution. For F=1,000 N and a 5 mm lead, ideal torque is about 0.80 N·m. This checks that the reference quantities are compatible.
Thread flanks, nut face and bearings create friction, so input torque must exceed the ideal work balance. Self-locking and lubrication also change efficiency and backdrivability. Real drives require suitable friction geometry, material pairing and operating conditions rather than a generic correction factor. This is the frictionless work-balance limit; real screw torque must include thread and bearing friction. Scope: The relation follows from work equality per revolution: 2πT=Fp. It assumes frictionless motion, constant load and negligible bearing losses. Real threads need more torque because of flank and bearing friction and may be self-locking. For a multi-start thread, p is lead per revolution, not spacing between adjacent threads. A practical application is Understand ideal force-to-torque conversion in a screw drive.
Write the quantity and unit from the variable list next to every value: T in N·m; F in N; p in m/revolution. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For F=1,000 N and a 5 mm lead, ideal torque is about 0.80 N·m. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. This is the frictionless work-balance limit; real screw torque must include thread and bearing friction.
The background states this starting condition: The relation follows from work equality per revolution: 2πT=Fp. It assumes frictionless motion, constant load and negligible bearing. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. This is the frictionless work-balance limit; real screw torque must include thread and bearing friction.
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Curated exam set for "Ideal torque of a lead screw":
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Which formula describes Ideal torque of a lead screw?
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How do you rearrange Ideal torque of a lead screw for Base equation for the target quantity?
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Which common mistake happens with Ideal torque of a lead screw?
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