Calculator for fatigue strenght of a drive shaft in bending

Fatigue strength of a SHAFT in BENDING

Shaft diameter d_k

10^-3m

Tensile strength R_p0.2

MPa

Dynamic to static tensile strength ratio σ_e/R_p0.2

Stress concentration factor K_t or K_f

Section modulus for bending S=I/(d_k/2)=(π/32)d_k³

10^-6m³

Maximum bending moment statically loaded Mb=S·R_p0.2

Maximum bending moment cyclically loaded Mb=S·σ_e/K_t

Shaft diameter d_k: Local diameter at the critical area (grooved section).

Endurance strength σ_e: The ratio σ_e/R_p0.2=C_f·C_e/C_m where C_f represent the influence factors listed in eq(3.1), C_e is the ratio of the endurance limit with the ultimate tensile strength as listed in Table 3.1 and C_m is the ratio of the elastic limit and the ultimate tensile strength.

Stress concentration factors: For high strength steel grades and brittle materials the notch sensitivity in not far from unity so Kt=Kf. For ductile materials the lower value of the fatigue stress concentration factor Kf can be applied. It is always save to use the geometrical stress concentration factor Kt which based on (numerical) calculation. Examples of how to limit the stress concentration factor see fig 3.7 and 3.8.