Shaft strength to the FKM guideline

Q: Why is there no minimum safety to enter?

The FKM guideline builds its safety factors in: jD and jges follow from the safety class, the probability of the peak load, the casting factor and the temperature. A point passes when its degrees of utilisation aBK and aSK are at most 1.

The FKM guideline is the German analytical strength assessment for machine components. For a shaft it works with the same nominal stresses as DIN 743, but states the result as degrees of utilisation with explicit safety factors, and it covers finite life and variable loads through an S-N curve and damage accumulation.

Axomek applies the guideline’s nominal stress approach to every shoulder, notch and the most stressed plain section of the shaft. Give it a number of load cycles and a duty cycle, and it shares the cycles over the load cases and accumulates the damage by the Miner rule.

FKM guideline, 7th edition (2020)

Try this example in the app

The shaft module with the drive shaft example switched to the FKM guideline: its material group, safety class and size inputs beside the shaft, and the checks with the fatigue and static safety.

What Axomek calculates

You enter

The shaft, its loads and optionally a duty cycle with time shares, load factors and speeds
FKM material group (quenched and tempered, case-hardening, structural, stainless steel, cast steel, nodular cast iron, wrought or cast aluminium) and the strengths R_m, R_p
Safety class (consequences of failure and inspection, j_F 1.2 to 1.5), probability of the peak load, and casting inspection for cast groups
Load cycles (empty is infinite life) and the damage rule: Miner consistent or Miner elementary, with an optional Miner sum D_m
Notches, roughness, surface treatment, torque amplitude, peak load factor and overload case F1 or F2
Temperature and anisotropy factor K_A, and size constants when the grade is not in the material tables

It calculates

Cyclic degree of utilisation a_BK and static degree of utilisation a_SK at every point
Fatigue safety j_D/a_BK and static safety j_ges/a_SK, with the safety factors j_D and j_ges
Component strengths R_m and R_p at the effective diameter, and the material fatigue strengths σ_W,zd, τ_W,s
Per stress type: K_t, stress gradients, support numbers, K_f, design factor K_WK, S_WK, K_AK, K_BK and S_BK
For a duty cycle: the cycles of each case, the spectrum’s Miner sum and variable amplitude factor K_BK at each point

Method and standards

Component strengths R_m = K_d,m·K_A·R_m,N with the size factor of eq. 1.2.8 and the constants of the material tables (section 5.1); σ_W,zd = f_W,σ·R_m (Table 2.2.1)
Fatigue notch factor K_f = K_t/(n(r)·n(d)), eq. 2.3.2, roughness factor K_R (Table 2.3.6) and surface factor K_V (Table 2.3.8, lower bounds), giving K_WK and S_WK
Mean stress factor K_AK (section 2.4.2) for overload case F2 (constant stress ratio, the default) or F1 (constant mean stress)
Variable amplitude factor K_BK: 1 for infinite life, (10⁶/N)^1/k below the knee, or damage accumulation over the load spectrum with the effective Miner sum of eq. 2.4.41
Utilisation a_BK = σ_a·j_D/S_BK, combined over the stress types, and the static check with S_SK = R_p·n_pl; safety factors from Table 2.5.1
axm verify reproduces the guideline’s worked examples 6.1 and 6.2

Limits

Nominal stress approach only: the local stress approach and the material-mechanics support number are not used
Coating and residual stress factors are 1, and the creep range of the temperature factors (K_Tt) is not covered
Cross bores take K_t from DIN 743-2, as the guideline’s section 5.2 gives none for round bars
K_V is always the lower bound of the table; stainless steel gets no temperature factor above 100 °C

Worked example

The drive shaft example (42CrMo4 +QT, a helical gear passing 525 N·m to a coupling, six notches) switched to the FKM guideline with the default safety class (high consequences, not inspected) and a finite life of 10⁷ load cycles, shared over its duty cycle of Nominal 60 %, Peak 5 % (loads × 1.6) and Part load 35 % (loads × 0.5 at 1200 rpm).

Result	Value
Fatigue utilisation a_BK, over the duty cycle	0.168
Fatigue safety j_D/a_BK	8.93
Safety factor j_D	1.50
K_BK in bending at the gear keyway	1.124
K_f in bending at the gear keyway	2.901
Static safety j_ges/a_SK, worst load case	5.46
Safety factor j_ges	1.51
R_m at the effective diameter	911.3 MPa

A point passes when a_BK ≤ 1 and a_SK ≤ 1. K_BK above 1 is the credit the spectrum gets for its finite life; for a much longer life it falls to 1 and the Peak case alone governs.

The numbers come from the engine: the same commands, run with the axm command line, give them.

The same with the axm command line

axm new ex.axm.json --template drive-shaft
axm apply ex.axm.json {"op":"updateStrength","patch":{"method":"fkm","fkm":{"cycles":10000000}}}
axm solve ex.axm.json --json

Open the example in the app

Questions

Why is there no minimum safety to enter?

The FKM guideline builds its safety factors in: j_D and j_ges follow from the safety class, the probability of the peak load, the casting factor and the temperature. A point passes when its degrees of utilisation a_BK and a_SK are at most 1.

Miner consistent or Miner elementary?

Miner consistent is the guideline’s preference and the default. Miner elementary (eq. 2.4.42) is the more conservative of the two; both use the effective Miner sum of eq. 2.4.41 unless you give D_m.

How does it differ from DIN 743?

Both assess the same sections with the same nominal stresses. The FKM method states the result as degrees of utilisation with explicit safety factors and handles finite life and load spectra; DIN 743 here is an endurance-limit check that takes the worst load case.

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