The slide rule has long found a useful application in connection with
the gear calculations necessary in screw-cutting, helical gear-cutting,
and spiral gear work.
SINGLE GEARS.—For simple cases of screw-cutting in the lathe it is only
necessary to set the threads per inch to be cut to the threads per inch
in the guide screw (or the pitch in inches in each case, if more
convenient). Then any pair of coinciding values on the two scales will
give possible pairs of wheels.
EX.—Find wheels to cut a screw of 1⅝ threads per inch with a guide
screw of 2 threads per inch.
Setting 1·625 on C to 2 on D, it is seen that 80 (driver) and 65
(driven) are possible wheels.
COMPOUND GEARS.—When wheels so found are of inconvenient size, a
compound train is used, consisting (usually) of two drivers and two
driven wheels, the product of the two former and the product of the two
latter being in the same ratio as the simple wheels. Thus with 60 and 40
as drivers, and 65 and 30 as driven, we have, (60 × 40)/(65 × 30) =
(2400)/(1950) = (2)/(1·625) as before.
With the slide set as above, values convenient for splitting up into
suitable wheels are readily obtainable. Thus, (1600)/(1300);
(2400)/(1950); (4000)/(3250); (4800)/(3900) are a few suggestive values
which may be readily factorised.
SLIDE RULES FOR SCREW-CUTTING CALCULATIONS.—Special circular and
straight slide rules for screw-cutting gear calculations have long been
employed. For compound gears these usually entail the use of six scales,
two on each of the two slides and two on the stock. The upper scale on
the stock may be a scale of threads per inch to be cut, the adjacent
scale (on the upper slide) a scale of threads per inch in the guide
screw. Setting the guide screw-graduation to the threads to be cut, the
lower slide is adjusted until a convenient pair of drivers is found in
coincidence on the central pair of scales, while a pair of driven wheels
are in coincidence on the two lower scales.
Some years ago, a slide rule was introduced by which compound gears
could be obtained with a single slide. Assuming the set of wheels
usually provided—20 to 120 teeth advancing by 5 teeth—the products of 20
× 25, 20 × 30, etc., up to 115 × 120 were calculated. These products
were laid out along each of the two lower scales. The upper scales were
a scale of threads per inch to be cut and a scale of the threads per
inch of various guide screws. Setting the guide screw-graduation to the
threads to be cut, any coinciding graduations on the lower scales gave
the required pairs of drivers and driven wheels.
FRACTIONAL PITCH CALCULATIONS.—The author has long advocated the use of
the slide rule for determining the wheels necessary for cutting
fractional pitch threads, and it is gratifying to find its value in this
connection is now being appreciated. For the best results a good 20 in.
rule is desirable, but with care very close approximations can be found
with an accurate 10 in. rule. In any case a magnifying cursor or a hand
reading-glass is of great assistance.
EX.—Find wheels to cut a thread of 0·70909 in. pitch; guide screw, 2
threads per inch.
To 0·70909 on D, set 0·5 (guide screw pitch in inches) on C. To make
this setting as accurately as possible, the method described on page
112 may be used. Set 10 on C to about 91 on D, and note that the
interval 77–78 on C represents 0·91 of the interval 70–71 on D. Set
the cursor to 78 on C and bring 5 to the cursor. The slide is then set
so that 5 on C agrees with 7·091 on D.
Inspection of the two scales shows various coinciding factors in the
ratio required. The most accurate is seen to be (55 on C)/(78 on D).
These values may be split up into (55 × 50)/(65 × 60) to form a suitable
compound train of gears.