To produce a stub tooth
gear, standard or nonstandard, certain information is required:
Diametral pitch, pressure angle, major diameter, minor diameter, number
of teeth, and circular tooth thickness, (space width of internals).
FOR
EXAMPLE: 10 D.P., 20° P.A., 30 Teeth,
3.1” O.D., 2.768” R.D.,
.15708” Tooth thickness, .1657” D&F.
At first glance the gear tooth appears stubby, but a standard cutter can
produce this part.The O.D.
of this gear has been reduced, (standard O.D. is 32”).The difference between the standard O.D. and our O.D. is 10” or
.05 on one side.That
difference plus the D&F of the gear, (.1657”) is .2157”.Therefore a standard finishing cutter would work.In cases when the tooth thickness is nonstandard, a standard
cutter can be modified by top=grinding to produce the correct stub
tooth.
FOR
EXAMPLE: Same part as above, except the
tooth thickness is .1520”.The
most accurate way to determine the amount to remove from the tool is to
first cut a sample to measurement over pins.This will give us the tooth thickness we need.Remove the difference of root diameter produced and root diameter
desired from the O.D. of the tool.This can also be determined with nearly the same accuracy without
cutting a sample by dividing the difference of desired tooth thickness
and standard tooth thickness by the tangent of the pressure angle.Reduce the O.D. of the tool by this amount.
FOR
EXAMPLE: .15708”- .1520”= .0051/ TAN
P.A. = .0140”..0140”= Amount of Reduction
THE
INVERSE OF THE INVOLUTE FUNCTION
Θ
IN
DEGREES
INV. Θ
0
0
5
0.00022
10
0.00179
14.5
0.00554
17.5
0.00987
20
0.01490
22.5
0.02151
25
0.02998
30
0.05375
35
0.08934
40
0.14097
45
0.21460
50
0.31909
55
0.46821
60
0.68485
Given the involute of
an angle, there is no simple formula for finding that angle.If you have involute tables, the inverse of the involute can be
found by interpolating between known values, if needed.Without the benefit of tables, the pursuit of the angle can be
achieved with a calculator, the most practical solution is to guess
based on this brief table.
Remember you have involute
(Inv θ) you want θ.
Θ is the Greek letter Theta often used for a given angle
Inv (θ) = Tangent θ-
(θ•π/180)
The function
makes sense only from a range of 0° up to 89°.You should arrive at θ=140° for example.
The involute is a
steadily increasing function; that is, the higher the angle, the
higher the involute and vice versa.
