Size a ball screw
Drive torque, Euler buckling load with a safety check and the critical bending speed — from axial force, lead, root diameter, unsupported length and the bearing arrangement.
Size a ball screw
Enter load and geometry — results appear immediately.
Sketch
Formulas
M = F · P_h / (2000 · π · η) P = M · n / 9550 I = π · d_r⁴ / 64 F_k = n_L · π² · E · I / L² F_zul = F_k / S n_krit = f_n · (d_r / L²) · 10⁷ n_zul = 0.8 · n_krit
L = bearing distance · E = 210,000 N/mm² (steel) · n_L per arrangement: Fixed–Fixed 4 · Fixed–Supported 2 · Supported–Supported 1 · Fixed–Free 0.25 · f_n: 27.6 / 19.0 / 12.2 / 4.3 (without safety margin; the margin is applied once, in n_zul = 0.8 · n_krit)
Drive
Stability
Without a root diameter there is no stability check — the calculator says so explicitly.
What the model covers
Calculated are the drive torque, the Euler buckling load and the critical bending speed — that is, stability, not service life. The basic rating life L10 = (C_a/F)³ · 10⁶ requires the dynamic load rating from the catalogue and is covered by the bearing life calculator. Also not included: load spectra, the load factor f_w, preload, thermal behaviour and the stiffness of the mounting. n_L is the Euler coefficient of the bearing arrangement, f_n follows from the eigenvalues of the bending beam (catalogue practice); binding are the manufacturer figures for your arrangement and length (ISO 3408, formerly DIN 69051). L is the bearing distance here, i.e. the unsupported length between the bearings or from the fixed bearing to the free end, not the Euler buckling length β·L; the bearing arrangement is contained in the factor n_L. This is on the safe side: we use the full bearing distance rather than, as some manufacturer catalogues do, only the section from the axially loaded bearing to the nut in its least favourable position — treating the nut as a support gives those catalogues higher, less conservative buckling loads. Not verified: the permissible speed factor d₀·n of the nut (manufacturer specification).
Two limits that govern long screws
A ball screw rarely fails on torque. It fails on stability: under compressive load it can buckle, and at high speed it reaches bending resonance. Both limits depend on the same quantity — the unsupported length L between the bearings, and they do so quadratically. Double the unsupported length and the buckling load drops to a quarter.
The buckling load follows the Euler approach F_k = n_L · π² · E · I / L² with the second moment of area I = π · d_r⁴ / 64. L is the bearing distance here, not the Euler buckling length β·L — the bearing arrangement is contained in the factor n_L. Here the leverage sits in the fourth power of the root diameter: 16 instead of 14 mm already gives 70 % more buckling load. The bearing factor n_L ranges from 0.25 (Fixed–Free) to 4 (Fixed–Fixed) — a factor of 16 between the worst and the best arrangement.
The critical speed n_krit = f_n · (d_r / L²) · 10⁷ follows the same logic; at this speed the screw enters bending resonance. The permissible speed is n_zul = 0.8 · n_krit, i.e. 80 % of it; for the axial force our selection guide gives at most 50 % of the buckling load, which corresponds to a safety factor of S = 2. The calculator is preset to S = 2.5 — the stricter value from our configurator practice.
Why the calculator says when it checked nothing
Without a root diameter neither the buckling load nor the critical speed can be determined. In that case the calculator returns only the drive torque and states explicitly that no stability check was performed. That is deliberate: a result without a check otherwise looks exactly like one with — and a missing check is not a passed one.
Frequently asked questions
Which length do I enter as the length L?
The bearing distance, i.e. the unsupported length between the bearing points or from the fixed bearing to the free end — not the total length of the screw, not the stroke and not the Euler buckling length β·L. The calculator accounts for the bearing arrangement through the factor n_L; entering β·L would count it twice. If there is an intermediate support along the travel, take the largest distance between two support points.
Does the buckling check apply under tensile load too?
No. Buckling is a compression phenomenon — a screw in tension does not buckle. With alternating load direction the check must be made for the compression phase, because that is the governing case. The critical speed, by contrast, applies regardless of load direction.
Why is service life missing?
Because it needs a catalogue figure the calculator does not know: the dynamic load rating C_a of your screw. With it, L10 = (C_a/F)³ · 10⁶ revolutions is quickly calculated — the bearing life calculator does exactly that. On top of that comes the load factor f_w (roughly 1.0–1.5 to ISO 3408), which weights shock loads.
What if I need self-locking?
Then a ball screw is the wrong element. Its efficiency is around 90 %, so it back-drives readily — the load runs back without a brake. Where the load has to be held, a trapezoidal screw is the alternative: considerably lower efficiency, but self-locking depending on the lead angle. More in our guide on self-locking.
Note: The calculation tools provided are intended for initial orientation only and do not replace a binding design by qualified engineers. All results must be verified by appropriate engineering calculations before use in safety-related applications. Technische Antriebselemente GmbH accepts no liability for damage arising from the use of the calculation results.
Have the screw and bearing arrangement sized for the calculated load?
Drive torque, buckling load and critical speed are settled — what remains open is the dynamic load rating and with it the service life, the preload, the accuracy class and the stiffness of the mounting. Carry your values into the enquiry and we will size the screw, the nut and the bearings with you.
Related products & guides
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GuideSelf-locking: when is it wanted?
Why a ball screw runs back without a brake — and when the trapezoidal screw is the better choice.
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CalculatorBearing Life Calculator L10
The quantity this calculator deliberately omits: the basic rating life from the dynamic load rating.