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354 PULLEYS.
Stepped Pulleys for Back=Geared Lathes.
On machinery having changeable reducing gearing, such as
lathes, milling machines, etc., it is frequently the aim of the
designer to arrange the speed of the counter and the diameters
of the different steps of the cone pulley in such proportions that
the same ratio of speed will be maintained on each step and also
from the slowest speed, with back gears out, to the fastest
speed, with back gears in. When the ratio of the back gearing
is given, the ratio of speed for each step will be obtained by the
formula
:
m
S = \/~R
S = Ratio of speed for each step.
m = Number of changes of speed on the cone pulley.
R = Reduction of speed by the back gearing.
Example.
The back gearing of a lathe reduces its speed 8 times. The
cone pulley has 5 changes of speed. The largest diameter of
cone pulley on the spindle is 10>£ inches. The cone pulley on
the counter-shaft is to be of the same size as the cone pulley on
the spindle, and an even ratio of speed is to be maintained
throughout the whole range of the ten changes of speed.
The slowest speed, when back gears are in, is 6 revolutions per.
minute. Calculate the speed of the counter-shaft, the speed of
the spindle for each change, and the diameter of each step on
the cone pulley of the spindle.
Solution
:
The ratio of speed for each step will be
:
5 log. 8
= 0.90309
= Q lg062
V 8 5 5
The corresponding number is 1.516.
With back gears in, the speed of spindle :
On first cone is 6 revolutions per minute.
On second cone is 6 X 1.516 = 9 revolutions per minute.
On third cone is 9 X 1.516 = 14 revolutions per minute.
On fourth cone is 14 X 1.516 = 21 revolutions per minute.
On fifth cone is 21 X 1.516 = 32 revolutions per minute.
With back gears out, speed of spindle
:
On first cone will be 6X8= 48 revolutions per minute.
On second cone will be 9X8= 72 revolutions per minute.
On third cone will be 14 X 8 = 112 revolutions per minute.
On fourth cone will be 21 X 8 = 168 revolutions per minute.
On fifth cone will be 32X8 = 256 revolutions per minute.
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