Machinery's Handbook, 31st Edition
Critical Speeds
205
Critical Speed Formulas Formulas for Single Concentrated Load
W
W
W
a
b
a
b
1 2
1 2
l
l
l
, , d 1 550 500 2 = Bearings supported l Wl
ab d 2
ab d l 2
W l
Wab l
N
, 387 000 = Bearings supported
, 387 000
N
N
=
Bearings fixed
W
W
W
a
b
1 2
1 2
l
l
l
, , d 3 100 850 2 Bearings fixed l Wl
, d 387 000 2 = One fixed — One free end N l Wl
ab d l 2
Wa l b l 3
N
=
, 775 200
N
=
+ ^ h One-fixed — One supported
Formulas for Distributed Loads—First Critical Speed
Total Load = W
Total Load = W
l
l
l , , , , 2 232 500 4 760 000
l Wl d 2
l Wl d 2
l Wl d 2
, , , 795 200 1 695 500
N
, , 4 979 250 10 616 740 , ,
N
N
=
=
=
l d
l d
l d
N
N
N
1 = One fixed—One free end 2
= Bearings fixed
2 = Bearings supported
1
1
2
N = critical speed, RPM N 1 = critical speed of shaft alone d = diameter of shaft, in inches W = load applied to shaft, in pounds l = distance between centers of bearings, in inches
a and b = distances from bearings to load In calculating critical speeds, the weight of the shaft is either neglected or, say, 1 ∕ 2 to 2 ∕ 3 of the weight is added to the concentrated load. The formulas apply to steel shafts having a modulus of elasticity E = 29,000,000. Although a shaft carrying a number of loads or a dis- tributed load may have an infinite number of critical speeds, ordinarily it is the first critical speed that is of importance in engineering work. The first critical speed is obtained by the formulas given in the distributed loads portion of the table Critical Speed Formulas .
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