Shaft Deflection
Two Point Shaft Deflection
Deflection
Sag
L
FA(3L 2 -4A 2 )
5wL 4
δ =
+
A
A
_F_ 2
_F_ 2
48 E I
384 E I
Shaft Unit of measure
Inch
Metric
δ = Total Deflection
in. in.
mm mm
Displacement Angle
Deflection plus Sag
L = Distance between the shaft support
lb./in. 2 N/mm 2
E = Modulus of elasticity I = Shaft moment of inertia
in. 4
mm 4
w = Unit weight of shaft (ref. table below) F = Load applied (including carriage weight)
lb./in.
N/mm
lb. in.
N
A = Distance to end a = Displacement angle
mm deg.
deg.
Inch Shafting
Metric Shafting
Hardened Steel
Stainless Steel
Hardened Steel
Stainless Steel
Shaft Diameter
E I
w
E I
w
Shaft Diameter
E I
w
E I
w
LB•IN. 2
LB•IN. 2
N•mm 2
N•mm 2
LB/IN. 0.0077 0.0138 0.0311 0.0553 0.0865 0.1250 0.1700 0.2220 0.2810 0.3470 0.4200 0.4990 0.6800 0.8880 1.3900 2.0000 3.5500
LB/IN.
N/mm
N/mm
3/16"
1.76E+03 5.60E+03 2.85E+04 9.04E+04 2.21E+05 4.59E+05 8.51E+05 1.45E+06 2.33E+06 3.55E+06 5.20E+06 7.36E+06 1.36E+07 2.33E+07 5.68E+07 1.18E+08 3.72E+08
1.76E+03 5.59E+03 2.84E+04 9.01E+04 2.20E+05 4.57E+05
7.70E-03 1.37E-02 3.10E-02 5.51E-02 8.62E-02 1.24E-01
4 mm 2.54E+06 5 mm 6.22E+06 6 mm 1.29E+07 8 mm 4.10E+07 10 mm 1.00E+08 12 mm 2.08E+08 16 mm 6.57E+08 20 mm 2.54E+09 25 mm 3.92E+09 30 mm 8.14E+09 40 mm 2.57E+10 50 mm 6.28E+10 60 mm 1.30E+11 80 mm 4.12E+11
0.00096 0.00150 0.00217 0.00386 0.00603 0.00869 0.01550 0.02420 0.03780 0.05440 0.09670 0.15100 0.21800 0.38700
2.53E+06 6.19E+06 1.29E+07 4.08E+07 9.96E+07 2.07E+08 6.54E+08 1.60E+09 3.90E+09 8.10E+09 2.56E+10 6.25E+10
0.00096 0.00150 0.00216 0.00384 0.00601 0.00866 0.01540 0.02410 0.03760 0.05420 0.09640 0.15100
1/4" 3/8" 1/2" 5/8" 3/4" 7/8"
–
–
1"
1.45E+06
2.21E-01
1-1/8" 1-1/4" 1-3/8" 1-1/2" 1-3/4"
–
–
3.54E+06
3.46E-01
–
–
7.33E+06
4.98E-01
–
–
– –
– –
2"
2.32E+07
8.85E-01
2 -1/2"
– – –
– – –
3" 4"
Displacement Angle (values calculated on previous page)
± = tan -1 δ A
0.0513"
± = tan -1 0.0504 in. 12 in.
± = 0.240° Displacement Angle 0.240° < 1/2° Allowable = Good Design
12" (A)
146 Round Shaft Technology • pbclinear.com
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