Ball Screw Efficiency⚠ unverified
Mechanical / Power Screws · Return the typical efficiency of a ball screw
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| eta | η | — | 0.9 | Efficiency value to return (dimensionless). Default is 0.9 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | η | — | Ball screw efficiency (dimensionless) |
The science & history
Understanding the Parameters
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Efficiency $\eta$ — for a ball screw this is high (0.90–0.98) and, importantly, nearly independent of lead angle, unlike a sliding screw whose efficiency swings strongly with lead. The high, flat efficiency comes from rolling contact: the effective friction coefficient of a ball–race contact is ~0.001–0.005, an order of magnitude below sliding thread friction.
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The self-locking consequence — because friction is so low, a ball screw is not self-locking ($\mu < \tan\lambda$ almost always): a suspended load will back-drive the screw. Ball-screw systems therefore need a brake or a worm/irreversible stage to hold a load — the direct price of their high efficiency (the opposite trade-off to a self-locking Acme jack).
Derivation (Approaching a Proof)
The registry formula does nothing, but ball-screw efficiency follows from the same power-screw efficiency relation as a sliding screw (Power Screw Efficiency), simply with a tiny effective friction:
$$\eta = \frac{\tan\lambda\,(1 - \mu_{\text{eff}}\tan\lambda)}{\tan\lambda + \mu_{\text{eff}}}.$$
For rolling contact the effective friction $\mu_{\text{eff}}$ is on the order of $0.003$–$0.01$ instead of the $0.1$–$0.2$ of sliding threads. With $\mu_{\text{eff}} \ll \tan\lambda$, the expression collapses to $\eta \approx 1 - \mu_{\text{eff}}/\tan\lambda$, which for typical leads gives $\eta \approx 0.9$–$0.95$ and is only weakly sensitive to $\lambda$. Physically, the balls roll rather than slide along the race, so almost no energy is lost to sliding friction — the same reason a rolling-element bearing is far more efficient than a plain bearing. A more complete model also adds small losses from ball recirculation, preload drag, and seal friction, which is why real efficiency is ~90 %+ rather than 99 %.
Dimensional check. $\eta$ is dimensionless (pass-through). ✓
History and Development
Ball screws were patented in the late 19th century but became widespread with mid-20th-century machine tools and, famously, automotive recirculating-ball steering gears. Their high efficiency, low wear, and precision (with preload eliminating backlash) made them the enabling technology for CNC and servo linear motion. The trade-off — no self-locking — is managed with brakes.
Related Concepts: Power Screw Efficiency, Power Screw Torque raise, Torque Lower Load, Preload For Backlash, Screw Lead Angle
Notes: Pass-through placeholder (returns the input; no computation) — see registry note. Real ball screws ≈ 0.90–0.98, and are not self-locking (need a brake to hold a load).