Stress Concentration Factors for Shafts

A. Filleted Transition Regions

Values of fillet radius r

d	rmax
Over 18 to 30	1.6
Over 30 to 50	2.0
Over 50 to 80	2.5
Over 80 to 120	3.0

end of the table 10.2

Values of K _s and K _t

t/r	r/d	K s at s ul (MPa) of	K t at s ul (MPa) of
	0.01	1.55	1.6	1.65	1.7	1.4	1.4	1.45	1.45
	0.02	1.8	1.9	2.0	2.15	1.55	1.6	1.65	1.7
	0.03	1.8	1.95	2.05	2.25	1.55	1.6	1.65	1.7
	0.01	1.9	2.0	2.1	2.2	1.55	1.6	1.65	1.75
	0.02	1.95	2.1	2.2	2.4	1.6	1.7	1.75	1.85
	0.03	1.95	2.1	2.25	2.45	1.65	1.7	1.75	1.9

B. Values of K _s and K _t for Keyed portions of Shafts

s end, MPa	K s for keyseats cut with	K t
End mills	Side mills
	1.60	1.40	1.40
	1.90	1.55	1.70
	2.15	1.70	2.05
	2.50	1.90	2.40

C. Values of K _s and K _t for Splined and Threaded Portions of Shafts

s end, MPa	K s for	K t for
Splined portions	Threaded portions	Parallel-sides splines	Involute splines	Threaded portions
	1.45	1.80	2.25	1.45	1.50
	1.60	2.20	2.45	1.50	1.65
	1.70	2.45	2.65	1.55	2.10
	1.75	2.90	2.80	1.60	2.39

D. Values of K _s/ K_d and K _t/ K_d at Interference-Fit Joints

Shaft diameter d, mm	K s / Kd at s ul, (MPa) of	K t/ Kd at s ul, (MPa) of
	2.5	3.0	3.5	4.25	1.9	2.2	2.5	3.0
	3.05	3.65	4.3	5.2	2.25	2.6	3.1	3.6
100 up	3.3	3.95	4.6	5.6	2.4	2.8	3.2	3.8

In our case the critical section of the shaft is a section where a bearing is mounted so we will use as stress concentrator interference fit. Then from the table 10.2 D.

10.3.6. Determine the surface roughness factor K_F. For that we use Fig.10.3.

Fig. 10.3. Values of K_F: 1 - polished portions; 2 - ground portions;

3 - portions made with finish turning; 4 - portions made with rough turning

It is necessary to note that the portion of the shaft where a bearing is installed should be ground while the shaft portion for a toothed wheel is made with finish turning.

Thus portion of the shaft where a bearing is installed grounded and K_F = 0.9.

Kd 1.0 0.8 0.6 0.4

10.3.7. Determine factor K_d, that takes into account absolute dimensions of the shaft cross-section. For this purpose we use Fig.10.4.

10 15 20 30 40 50 60 70 80 100 150 d, mm

Fig. 10.4. Values of K_d: 1- carbon steels without stress concentrators; 2 – alloy steels without stress concentrators or carbon steels with stress concentrators (K _σ>2); 3 - alloy steels with stress concentrators (K _σ>2).

Thus we have carbon steel without stress concentrators and K_d = 0.82.

10.3.8. Determine safety factors in terms of bending and torsion

;

.

10.3.9. Determine the safety factor of the shaft at the critical section

;

Allowable values of the safety factor [ S ] are given in table 10.3.