Free Lead Screw & Ball Screw Torque Calculator
Size CNC drive motors, calculate driving torque for raising/lowering loads, mechanical efficiency %, linear travel velocity, and back-drive safety.
🔩 Screw Geometry & Drive Specifications
Linear Traverse Speed: 5,000 mm/min (196.8 IPM)
• Self-Locking: NO (Will Back-Drive Under Vertical Load)
• Helix Lead Angle (α): 5.7°
Vertical Z-Axis Warning: Ball screws have near-zero friction ($eta approx 90%$) and will instantly free-fall drop under gravity when motor power is cut! Always equip vertical CNC Z-axes with a powered holding brake or counterweight.
Recommended Tools & Equipment
Tested hardware and components for high reliability
Lead Screw & Ball Screw Kinematics
Lead screws convert rotary motor torque into linear thrust force. Sizing calculations depend on screw diameter, pitch lead, and thread friction:
Governing Equations
Friction Angle: φ = arctan(μ / cos(θ_n))
Driving Torque: T = (F × Lead) / (2π × η) + T_bearing
Efficiency: η = tan(α) / tan(α + φ)
Linear Speed: V = RPM × Lead (mm/min)
Mechanical Power: P = (2π × RPM × T) / 60 (Watts)
Self-Locking vs. Free Backdriving
- Self-Locking (η < 50%): When the lead angle $alpha$ is smaller than the friction angle $phi$, axial loads cannot backdrive the screw. Standard single-start Acme lead screws are naturally self-locking.
- Free Backdriving (η > 50%): Multi-start lead screws and ball screws backdrive effortlessly under light axial force, requiring an active servo brake for vertical applications.
Frequently Asked Questions
What is the difference between screw pitch and screw lead?
Pitch (p) is the distance from one thread crest to the adjacent crest. Lead (L) is the axial linear distance the nut travels in one complete 360° revolution. For single-start screws, Lead = Pitch. For a two-start screw, Lead = 2 * Pitch.
Why do ball screws have virtually zero backlash compared to Acme screws?
Ball screws employ recirculating bearing balls running inside hardened gothic-arch raceways. By using oversized balls or double preloaded nuts, all internal clearances are eliminated (zero mechanical backlash), whereas sliding Acme nuts require clearance to prevent binding.
How does lead angle affect driving torque?
A larger lead (e.g. 10mm vs 5mm) produces higher linear speeds at lower motor RPM, but requires twice as much driving torque from the motor to generate the same axial cutting force (T proportional to Lead).