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Lead Screw Drive Torque & Efficiency Calculator (Acme / Ball Screw)

Lead screws and ball screws convert rotary motor torque into high-thrust linear motion in 3D printers, CNC linear actuators, and scissor jacks.

Axial force resisting or driving the screw in Newtons (5000 N ≈ 510 kgf / 1124 lbf).

Mean thread pitch diameter in mm (approx outer diameter minus half pitch).

Linear travel distance per 360° revolution in millimeters (Lead = Pitch × Starts).

Coefficient of friction (Bronze nut on steel Acme ≈ 0.15; Plastic nut ≈ 0.10; Ball screw ≈ 0.005).

Thread profile flank angle.

Calculated Result
11.87 N·m

Lifting Drive Torque

Torque Required to Raise Load

11.87 N·m

Torque to Lower Load

3.72 N·m

Drive Mechanical Efficiency

33.5%

Screw Lead Angle (λ)

4.55°

Self-Locking Safety

Self-Locking (Will not back-drive under gravity)

Calculation Breakdown

  1. 1. Helix Lead Angle Calculationtan(λ) = Lead / (π · d_m) = 5 mm / (π · 20 mm) = 0.0796 ⇒ λ = 4.55°
  2. 2. Flank Angle Friction CorrectionFor ACME-29, effective friction μ_eff = 0.15 / cos(14.5°) = 0.155
  3. 3. Input Drive Torque CalculationT_raise = (F · d_m / 2) · tan(λ + φ) = (5000 N · 0.02 m / 2) · tan(4.55° + φ) = 11.87 N·m (33.5% efficiency)

Drive Torque & Mechanical Efficiency

Interactive visualization based on your current inputs

Value
0.08.4172534Raising Torque (N·m)Lowering Torque (N·m)Efficiency (%)Lead Angle (°)MetricValue

What Is the Lead Screw Drive Torque & Efficiency Calculator (Acme / Ball Screw)?

Lead screw torque calculations determine the motor torque required to drive linear actuator screws under high axial thrust loads.

How Does the Lead Screw Drive Torque & Efficiency Calculator (Acme / Ball Screw) Work?

Treats thread engagement as an inclined wedge wrapped around a cylinder with normal forces magnified by thread flank angles.

Lead Screw Drive Torque & Efficiency Calculator (Acme / Ball Screw) Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

T_{raise} = \frac{F \cdot d_m}{2} \tan(\lambda + \phi), \quad T_{lower} = \frac{F \cdot d_m}{2} \tan(\phi - \lambda), \quad \eta = \frac{\tan\lambda}{\tan(\lambda + \phi)}

Raising torque accounts for lead angle lambda and flank-corrected friction angle phi. Self-locking occurs when friction angle exceeds lead angle (phi > lambda).

How to Use the Lead Screw Drive Torque & Efficiency Calculator (Acme / Ball Screw)

  1. Enter axial load in Newtons.
  2. Specify pitch diameter and screw lead in mm.
  3. Enter thread friction coefficient and thread geometry.

Step-by-Step Example Calculation

20mm Acme Screw with 5mm Lead Lifting 5 kN Load

Input Values:

axialLoadNewtons:5000
meanDiameterMm:20
screwLeadMm:5.0
frictionCoefficient:0.15
threadType:acme-29
Worked Steps: Lead angle is 4.55°. Raising torque is 11.75 N·m at 33.7% efficiency. The screw is safely self-locking (will not fall under load).

Understanding Your Result

Raising Torque (N·m): Torque needed to lift or advance against load.

Lowering Torque: Torque needed to retract.

Efficiency (%): Percentage of motor energy converted into linear thrust work.

Self-Locking: Safety assessment against catastrophic back-driving.

Factors That Affect the Result

  • Higher lead increases linear speed but requires more torque; lower friction boosts efficiency but eliminates self-locking.

When Should You Use This Calculator?

  • CNC machine Z-axis drive sizing, motorized standing desks, electric linear actuators, and heavy equipment jacks.

Assumptions & Limitations

  • Excludes thrust bearing collar friction (typically adds ~10-15% additional torque in real mechanical assemblies).

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard Shigley mechanical engineering power screw formulation.

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