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416 STRENGTH OF GEAR TEETH
If the small pitch diameter of a bevel gear is less than two-
thirds of the large pitch diameter the strength should not be cal-
culated by these tables. In such cases use formula on page 411.
Note : The large pitch diameter of a bevel gear is obtained
simply by calculating the same as for a spur gear, but the small
pitch diameter may be obtained either by a scale drawing ( see
Fig. 11, page 398) or by trigonometrical calculations.*
Important : When calculating the strength of gear teeth
for machinery where the motion is intermittent or in alternate
direction or where the load is variable, and where the gears con-
sequently are exposed to variable strain and shocks, as for
instance in punching machines, geared pumps, air compressors,
rolling mill machinery, etc. , the strength of the gear teeth must
always be calculated according to the maximum and never
according to the average load or horse-power. For additional
safety it may in such cases be advisable not to make use of table
No. 56 or 57 but to use formulas (see pages 409-412) and take the
value of s smaller than what is given in table No. 55. Be very
careful in all such calculations, never jump at conclusions, but
always check results by what experience has taught to be service-
able in common practice.
Inspecting these tables we see that the horse-power a gear
can transmit with safety does not increase in the same ratio
as the speed ; for instance, doubling the speed of a gear from
i2oo feet to 2400 feet a minute will increase its horse-power
less than 50 per cent.
We also become aware of the fact that if we do not change
the diameter of a gear, its strength will not increase in propor-
tion to the size of the teeth.
For instance: Assuming a gear 5 inches pitch diameter,
cut 6 pitch, it will have 30 teeth, and its strength given in
the table, at 100 feet linear speed, is 2564 divided by 6, which
gives 427 pounds.
If this gear had been larger in diameter so that it could
have been cut with 30 teeth, 4 pitch, instead of 30 teeth, 6 pitch,
its strength would have been increased from:
-~- =427 pounds, to
—— = 641 pounds,
or in the ratio of 4 to 6, which is a gain of 50 per cent; but if
we keep the same diameter and increase the pitch from 6 to
4, the gear will have 20 teeth instead of 30 teeth and its
strength at the same speed is 2262 divided by 4 which is 566
pounds. Although the pitch is increased 50 per cent the strength
is increased only about 32 per cent.
* A very good book on the subject is "Formulas in Gearing," by Brown
& Sharpe Mfg. Co.. Providence, R.I. Also see "Machinery and ita
supplement Engineering Edition, New York, Feb 1910.
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