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35 O PULLEYS.
Stepped Pulleys.
Stepped pulleys, or cone pulleys, as they are usually called,
may be considered as several pulleys of different diameters cast
together. Their proportions and sizes are calculated to get the
required changes of speed, and the belt must have practically
the same tension on all the different changes.
Frequently it is required to have both pulleys of the same size,
in order that they may be cast from the same pattern. In such
cases the shaft of constant speed (usually a counter-shaft) must
be run at a velocity equal to the square root of the product
of the fastest and the slowest speed of the shaft of changeable
speed (which usually is a spindle in a lathe or a similar machine).
For convenience, in the following formulas we will call the
driver, which is the shaft of constant speed, a counter-shaft, and
the shaft of changeable speed, a swindle.
The number of revolutions of the counter-shaft per minute
is calculated by the formula
:
N=\/ F X S
N = Number of revolutions of the counter-shaft per
minute.
F = Number of revolutions of the spindle per minute,
when run at its fastest speed.
6* — Number of revolutions of the spindle per minute, when
run at its slowest speed.
The diameter of either the largest or the smallest step is
then obtained by choosing one diameter and calculating the
other by the formula :
D = d X N d — D X n
.N
D = Diameter of largest step on spindle.
d — Diameter of smallest step on counter-shaft.
11 = Slowest number of revolutions of the spindle per
minute.
N = Revolutions of the counter-shaft per minute.
The intermediate steps may be obtained by drawing a
straight line, a &, and constructing steps within the angle
formed by the line a b and the center line (see Fig. 2). The sum
of the diameters of the two opposite steps will then be equal,
and this is the way in which stepped pulleys may primarily be laid
out, whether both pulleys are of the same size or not. After-
wards the diameters will have to be slightly changed, in order
to give the belt the same tension on any of the different steps,
as explained further on.
Example 1.
A pair of stepped pulleys, for four changes of speed, both
pulleys of the same size, are to be used on a milling machine
spindle and its counter, the fastest speed to be 250 revolutions,
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