CHAPTER 3
SHOULDER FILLETS
The shoulder fillet (Fig. 3.1) is the type of stress concentration that is more frequently
encountered in machine design practice than any other. Shafts, axles, spindles, rotors, and
so forth, usually involve a number of diameters connected by shoulders with rounded fillets
replacing the sharp corners that were often used in former years.
3.1 NOTATION
Definition:
Panel. A thin flat element with in-plane loading
Symbols:
a = semimajor axis of an ellipse
b = semiminor axis of an ellipse
D = larger diameter of circular bar
d = smaller diameter of circular bar; smaller width of thin flat element
df = middle diameter or width of streamline fillet
di = diameter of central (axial) hole
H = larger width (depth) of thin flat element
Hx = depth of equivalent wide shoulder element
h = thickness of a thin flat element
Kt stress concentration factor
Ktl, KtU
= stress concentration factors at I, II
L = length or shoulder width
Figure 3.1 Examples of filleted members: (a) Engine crankshaft; (b) turbine rotor; (c) motor shaft;
(W) railway axle.
Lx = radial height of fillet
Ly = axial length of fillet
M bending moment
P = applied tension force
r = fillet radius
r\ = fillet radius at end of compound fillet that merges into shoulder fillet
YI = fillet radius at end of compound fillet that merges into shaft
T = torque
t = fillet height
cr = stress
"nom = nominal stress
0"max = maximum stress
Tmax = maximum shear stress
Tnom = nominal shear stress
6 angle
3.2 STRESS CONCENTRATION FACTORS
Unless otherwise specified, the stress concentration factor Kt is based on the smaller width
or diameter, d. In tension (Fig. 3.2) K1 = crmax/<jnom, where crnom = P/hd for a thin flat
element of thickness h and <rnom = 4P/ird
2 for a circular bar.
The fillet factors for tension and bending are based on photoelastic values. For torsion
the fillet factors are from a mathematical analysis. A method was given in Peterson (1953)
for obtaining approximate K1 values for smaller r/d values where r is the fillet radius. The
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