Machinery's Handbook, 31st Edition
Centrifugal Force
195
h
R Mn R 60 2 2 2 π ^
2
R Mv = = 2
=
2
. 001097
MRn
F
If the rate of rotation is expressed as n 1 = revolutions per second, then F = 39.48 MRn 1 2 ; if it is expressed as ω radians per second, then F = MR ω 2 . Calculating Centrifugal Force.— In the ordinary formula for centrifugal force, F = 0.000341 WRn 2 ; the mean radius R of the flywheel or pulley rim is given in feet. For small dimensions, it is more convenient to have the formula in the form: . F Wrn 02842 10 2 4 # = − in which F = centrifugal force, in pounds; W = weight of rim, in pounds; r = mean radius of rim, in inches; n = number of revolutions per minute. In this formula let C = 0.000028416 n 2 . This, then, is the centrifugal force of one pound, one inch from the axis. The formula can now be written in the form, F WrC = C is calculated for various values of the revolutions per minute n , and the calculated val ues of C are given in Table 5. To find the centrifugal force in any given case, simply find the value of C in the table and multiply it by the product of W and r ; the four multiplications in the original formula given are thus reduced to two. Example: A cast-iron flywheel with a mean rim radius of 9 inches is rotated at a speed of 800 revolutions per minute. If the weight of the rim is 20 pounds, what is the centrifugal force? Solution: From Table 5, for n = 800 revolutions per minute, the value of C is 18.1862. Thus, . . F WrC 20 9 18 1862 3273 52 pounds # # = = = Using metric SI units, 0.01097 n 2 is the centrifugal force acting on a body of 1 kilo gram mass rotating at n revolutions per minute at a distance of 1 meter from the axis. If this value is designated C 1 , then the centrifugal force of mass M kilograms rotating at this speed at a distance from the axis of R meters is C 1 MR newtons. To simplify calculations, values for C 1 are given in Table 6. If it is required to work in terms of millimeters, the force is 0.001 C 1 MR 1 newtons, where R 1 is the radius in millimeters. Example: A steel pulley with a mean rim radius of 120 mm is rotated at a speed of 1100 rpm. If the mass of the rim is 5 kg, what is the centrifugal force? From Table 6, for n = 1100 rpm, the value of C 1 is 13,269.1. Thus, . . , . . F C MR 0001 0 001 13 269 1 5 120 7961 50 N 1 1 # # # = = = Centrifugal Casting.— The centrifugal casting of metals is an old art. This process has become important in such work as the manufacture of paper-mill rolls, railroad car wheels, and cast-iron pipe. The centrifugal casting process has been successfully applied in the production of non-metallic tubes, such as concrete pipe, in the production of solid castings by locating the molds around the rim of a spinning wheel, and to a limited extent in the production of solid ingots by a largely similar process. Hollow objects such as cast- iron pipe are cast by introducing molten metal into a spinning mold. If the chilling of the metal is extremely rapid, for example in casting cast-iron pipe against a water-cooled chilled mold, it is imperative that a movable spout be used. The particular feature that determines the field of application of hot-mold centrifugal casting is the ability to produce long cast shapes of comparatively thin metal.
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