Components: Spindle, nut with ball recirculation, balls
A ball screw converts rotational motion into linear motion—highly efficiently, because it utilizes rolling friction rather than sliding friction. It consists of three main components: the lead screw (a steel cylinder with a ground or rolled spiral groove in accordance with ISO 3408 (DIN ISO 3408), standard diameter 8–80 mm), the nut with ball recirculation (deflection), which sits on the lead screw, bears the load, and returns the balls to the starting point after the load has been applied, and the balls (hardened steel balls, typically 4–10 mm), which roll between the spindle and the nut. A cage to keep the balls spaced apart is not common in standard nuts.
Depending on the design, the return path is routed via a return tube, a return bracket, or an end cap. For the overall design of a linear system, a linear guide is usually added to the ball screw to absorb lateral forces and moments, while the ball screw transmits only the axial force.
Pitch: Feed per revolution
The pitch Ph indicates how far the nut moves linearly during one complete revolution (360°) of the spindle—the key design parameter for force, speed, and precision. A small lead (1–3 mm) delivers a high axial force per Nm of drive torque but little feed per revolution—good for precise positioning; a larger pitch (5–10 mm standard, over 10 mm for high speed) provides more feed per revolution but requires more drive torque per N of axial force.
Efficiency: rolling friction instead of sliding friction
Because balls roll rather than slide, a ball screw achieves an efficiency of 90–98 %—a trapezoidal lead screw, with its sliding friction, only achieves 25–50 %. The efficiency is directly reflected in the drive torque:
M = F · Ph / (2000 · π · η)
M = Drive torque (Nm) · F = Axial force (N) · Ph = Pitch (mm) · η = Efficiency (0…1)
The ball screw calculator uses precisely this formula: it calculates the required drive torque based on the axial force, pitch, and efficiency—and, if the speed n is known, it also calculates the drive power P = M · n / 9550 (in kW).
Mnemonic
Worked example
Given
A ball screw transmits an axial force F = 2,500 N with a lead Ph = 5 mm and an efficiency η = 0.90.
Calculation
- M = F · Ph / (2000 · π · η) = 2,500 · 5 / (2000 · π · 0.90) ≈ 2.21 Nm
For verification: Ball screw calculator (opens in a new tab)
Knowledge check
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