Shaft Calculation per DIN 743

The standard states S_min = 1.2 for both verifications. This value only covers the uncertainty of the calculation method. In practice, higher values of 1.5 to 2.0 are agreed depending on how well the loads are known and the consequences of a failure - the minimum safety factor is therefore adjustable in the calculator.

Both verifications are mandatory and address different failure modes: the dynamic verification compares the stress amplitudes with the component fatigue strength (fatigue fracture after many load cycles), the static one compares the maximum stresses with the component yield limit (permanent deformation at peak load). At high mean loads the static verification often governs.

The one that actually sits at the cross section being verified - the calculation always covers one location of the shaft, never the whole shaft. Shaft shoulder: step in diameter with a fillet, d is the small diameter, D the large one, r the fillet radius. Circumferential groove: undercut or round groove in an otherwise continuous diameter, D is the outer diameter, d the groove root, r the groove root radius. For the same geometry the groove is the sharper notch, because the notch root is constricted from both sides. Transverse hole: lubrication or pin hole across the shaft, r is the hole radius, and the nominal stresses follow from the net section moduli. Keyway: hub seat with a groove, without a radius input. Interference fit: hub seat without a key, also with the seat diameter only. Plain shaft: notch-free section, for example the free shaft end or the span between two notches. Where several notches meet, calculate each cross section separately and take the least favourable one; superimposed notches are not covered by DIN 743.

The cases describe how the mean stress behaves when the load increases. Case 1: the mean stress stays constant, only the amplitude grows. Case 2: the ratio of mean stress to amplitude stays constant, both grow together. Case 2 is usually more critical and therefore the conservative choice when in doubt - the calculator defaults to case 2.

Tabulated material properties apply to the 16 mm reference diameter. Larger cross sections harden less thoroughly during quenching and tempering, so the strength drops. The technological size factor K1 captures this via the effective diameter d_eff - with different factors for tensile and yield strength. Forgetting K1 is the most common mistake in DIN 743 calculations.

Only when the properties were determined on the finished component in its final condition - for example by a hardness test on the quenched and tempered part converted to tensile strength, or by a tensile test on a specimen taken from it. Two things then belong together: enter your measured value in the σB and σS fields, and tick the box. The tick alone only says that no second conversion from the reference diameter takes place (K1 = 1) - if the table values for 16 mm still stand alongside it, you are claiming that your component is as strong as a 16 mm specimen. That is on the unsafe side, because on a large shaft one usually measures less. An inspection certificate for the material, a value measured on the blank or a hardness figure from the data sheet are not sufficient: they say nothing about the through-hardening of your cross section. The option matters - for a quenched and tempered steel with d_eff = 50 mm, K1 = 0.87 for tensile strength and 0.80 for yield strength apply otherwise - which is why the statement and its justification appear in the verification PDF.

Simply enter its properties. The σB and σS fields always sit below the selection and initially show the values of the chosen table row; as soon as you change one of them, the selection switches to “Free (own values)” and the calculator uses your figures. Pick the matching material group as well, because it decides how steeply K1 reduces the properties with the effective diameter - case-hardening and nitriding steels are only reachable this way. You do not have to enter the three fatigue limits: the calculator derives them from the tensile strength per DIN 743-3 (σzdW = 0.4·σB, σbW = 0.5·σB, τtW = 0.3·σB) - the same ratios every row of the table observes. Do check whether your data sheet value applies to the 16 mm reference diameter (then leave the box unticked and K1 converts) or was measured on the component (then tick it).

The roughness factor K_F requires the mean roughness depth Rz in µm, not the arithmetic mean roughness Ra. Entering Ra would give far too favourable results. Typical values: polished 1, ground 4, fine-turned 10, turned 25, mill scale 200 µm. For keyways and interference fits the calculator sets K_F = 1 because the reference roughness is already contained in the experimental fatigue notch factor.

There is no closed-form stress concentration formula for keyways. DIN 743 instead uses experimentally determined fatigue notch factors that depend only on the tensile strength of the component and are converted from the 40 mm specimen diameter to the component diameter with the size factor K3. The nominal stresses are formed with the full circular cross section. With two keyways in the same cross section, the fatigue notch factor increases by a factor of 1.15.

Choose the notch case interference fit and enter the seat diameter only. Here too there is no stress concentration factor: the notch effect does not arise from a geometry of the shaft but at the end of the hub seat, where the force flow enters the hub, and it already contains the fretting load in that run-in zone. DIN 743 gives an experimental value that depends only on the tensile strength at the component: β_σ ≈ 2.7·(σ_B(d)/1000 N/mm²)^0.43 and β_τ ≈ 0.65·β_σ, referred to the 40 mm specimen diameter and converted via K3. The value stays below that of the keyway - a hub seat without a groove is the milder notch. Two limits: it applies to a plain, non-stepped shaft, and the table in the standard covers 400 to 1200 N/mm². If the hub sits directly against a shaft shoulder, verify the shoulder instead - the press fit changes its notch effect only slightly.

For the cross section that carries no notch at all and can still be the critical one - the free shaft end, the span between two notches, or the location with the largest bending moment on a small diameter. The fatigue notch factor there is 1 by definition, since β is defined as the ratio of the fatigue strength of the unnotched specimen to that of the component. Size and roughness keep acting unchanged; they stand separately in K2 and K_F. There is no form factor and no support factor. Without this case you would have to invent a notch just to be able to calculate the plain cross section at all.

Not separately, but combined into one figure per verification. The normal stresses from tension/compression and bending are added because they act in the same direction; the shear stress from torsion enters quadratically: S_D = 1/√((σ_zda/σ_zdADK + σ_ba/σ_bADK)² + (τ_ta/τ_tADK)²), and S_F likewise with the maximum stresses and the component yield limits. Each direction is first referred to its own tolerable value, and only these utilisations are combined. Two consequences: the overall safety factor is always below that of every single direction, and the Haigh diagram shows only the governing direction, not the overall result. The mean stresses are combined beforehand via the distortion energy hypothesis into the equivalent mean stress σ_mv = √(σ_m² + 3·τ_m²); loading is assumed to be in phase.

Red means the check is not satisfied: S_D or S_F is below the selected minimum safety factor S_min. This applies even when the factor is still above 1.0 and neither fatigue fracture nor yielding occurs numerically - the wording next to it distinguishes the two cases (“below S_min” versus “not OK”). Amber is used only just above S_min, that is satisfied without appreciable reserve. Green means satisfied with reserve. The colour therefore follows the verification, not the distance to fracture.

DIN 743 applies to non-welded steel shafts and axles at −40 to +150 °C in a non-corrosive environment, under tension/compression, bending and torsion (assumed in phase). The endurance limit refers to 10⁷ load cycles. Transverse shear, buckling and residual stresses are not covered explicitly by the method.