Shaft Deflection
Dual Point Shaft Deflection
L
A
A
Deflection plus Sag
_W_ 2
_W_ 2
Displacement Angle
δ = Deflection L = Distance between the shaft support (in.) E = Modulus of elasticity (lbf/in. 2 ) (30 • 10 6 ) I = Shaft moment of inertia (in. 4 ) S = Unit weight of shaft; reference the table below W = Load applied (including carriage weight) (lbf)
WA(3L 2 -4A 2 )
5SL 4
δ =
+
48 EI
384 EI
A = Distance to end (in.) a = Displacement angle
Inch Shafting
Metric Shafting
Steel Shaft EI (LBF/IN. 2 ) 5.75 x 10 3 2.91 x 10 4 9.20 x 10 4 2.25 x 10 5 4.66 x 10 5 8.63 x 10 5 1.47 x 10 6 2.36 x 10 6 3.60 x 10 6 5.26 x 10 6 7.46 x 10 6 1.38 x 10 7 2.36 x 10 7 1.19 x 10 8
Steel Shaft
Shaft Diameter
S (LBF/IN.)
Shaft Diameter
EI
S
1.45 x 10 4 7.34 x 10 4 2.32 x 10 5 5.66 x 10 5 1.38 x 10 6 2.87 x 10 6 9.06 x 10 6 2.21 x 10 7
1/4" 3/8" 1/2" 5/8" 3/4" 7/8"
0.014 0.031 0.055 0.086 0.125 0.170 0.222 0.281 0.348 0.420 0.500 0.681 0.890 2.003
8
0.022 0.050 0.088 0.138 0.216 0.311 0.552 0.863
12 16 20 25 30 40 50
1"
1-1/8" 1-1/4" 1-3/8" 1-1/2" 1-3/4"
2" 3"
Displacement Angle (values calculated on previous page)
± = tan -1 δ A
0.0513"
± = tan -1 0.0513 in. 12 in.
± = 0.2449° Displacement Angle 0.2449° < 1/2° Allowable = Good Design
12" (A)
146 Round Shaft Technology • pbclinear.com
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