ISO 3408 Ball Screw Calculator — L10h Life, Critical Speed & Buckling

ISO 3408 is the international standard that governs the design, rating and acceptance of ball screws. Parts 4 and 5 define the static and dynamic axial load ratings and the rolling-element fatigue life formula L10 = (C_a / F_A)³ × 10⁶ rev — the same formula published in every THK, NSK and Rexroth catalogue. Part 3 defines the accuracy grades (C0–C10) with the travel-error limits engineers use to specify positioning accuracy in CNC machine tools and precision linear drives.

A preloaded double-nut splits the external axial load between two opposed ball tracks following Hertzian contact theory (deflection δ ∝ F^(2/3)). The loaded track carries more than Fa; the opposing track unloads. ISO 3408-5 requires the life to be calculated on the loaded-track equivalent load F_A, not the raw axial load. The opposing track lifts off (preload becomes ineffective) when Fa ≥ 2^1.5 × F_pr ≈ 2.83 × F_pr; above that only the loaded track carries load and F_A = Fa. Using a simple 0.33·F_pr drag allowance instead of the Hertzian split overstates life at light loads.

ISO 3408-3 defines eight grades — C0 through C10 — by their travel error e_t per 300 mm of stroke. C0 (3.5 µm/300 mm) is a master-precision grade used in metrology; C1 (5 µm) and C2 (7 µm) suit precision grinding centres and jig borers; C3 (12 µm) and C5 (23 µm) are standard for CNC machining centres and lathes; C7 (52 µm) and C10 (210 µm) are general-purpose and transport grades. For typical CNC applications specify C3–C5; for sub-10-µm positioning specify C1 or better.

The critical (whirling) speed is the first lateral bending resonance of the screw shaft. Running at or above this speed causes resonance, excessive vibration and premature failure. Operating speed must be kept below 80% of the critical speed. The critical speed is proportional to the root diameter and inversely proportional to the span squared — so doubling the unsupported length reduces the critical speed by a factor of four. For long, high-speed axes the critical speed constraint often governs the screw diameter selection; for short heavy-duty axes, Euler column buckling governs instead.

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