(From: MODEL ENGINEERS'WORKSHOP magazine, 1996)
GEARS. involute form
TOOTH SIZE
There are three methods of defining gear tooth size
Diametral pitch. DP. The number of teeth per one inch of pitch circle diameter.
Module. MOD. The length, in mm, of the pitch circle diameter per tooth.
Circular pitch. CP. The distance between adjacent teeth measured along the are at the
pitch circle diameter
OTHER DEFINITIONS.
Addendum. A. The height of the tooth above the pitch circle diameter.
Centre distance. C. The distance between the axes of two gears in mesh.
Circular tooth thickness.
CTT. The width of a tooth measured along the are at the pitch circle
diameter.
Dedendum. D. The depth of the tooth below the pitch circle diameter.
Outside diameter.OD. The outside diameter of the gear.
Pitch circle dia.PCD. The diameter of the pitch circle.
Pitch point. PP. The point at which the pitch circle diameters of two gears in mesh
coincide. Effectively the diameters at which plain discs would create
the same ratio if relying on friction alone.
Pitch to back. PTB. The distance on a rack between the pitch circle diameter line and
the rear face of the rack.
Pressure angle. PA. The angle between the tooth profile at the pitch circle diameter
and a radial line passing through the same point. See sketch.
Whole depth. H. The total depth of the space between adjacent teeth.
Addendum A = MOD
Centre distance
PCD(g) + PCD(p)
C = ----------------
2
Circular pitch
CP = m x MOD
Circular tooth thickness
CP
CTT = ---------
2
Dedendum
D = H - A
Module
PCD
MOD = ------
N
Number of teeth
PCD
N = -----
MOD
Outside diameter
OD = (N + 2) x MOD
Pitch circle diameter
PCD = N x MOD
Whole depth (finer than 20DP)
H = 2.4 x MOD
Whole depth (20DP and coarser)
H = 2.25 x MOD
Addendum
1
A = ----
DP
Centre distance
PCD(g) + PCD(p)
C = ---------------
2
Circular pitch PI
CP = ------
DP
Circular tooth thickness
CP
CTT = -----
2
Dedendum
D = H - A
Diametral pitch
N
DP = -----
PCD
Number of teeth
N = DP x PCD
Outside diameter
N + 2
OD = -------
DP
Pitch circle diameter
N
PCD = -----
DP
Whole depth (finer than 20DP)
2.4
H = -----
DP
Whole depth (20DP and coarser}
2.25
H = -----
DP
NOTES
1. The pressure angle for commercially available gears is invariably 20 degrees.
Sketch 1 shows, on the left, a 20 degree pressure angle gear, centre 30 degrees,
and right 10 degrees.
2. When two gears are meshed correctly their pitch circle diameters coincide at
the pitch point (PP). A clearance then results between the top of the tooth on one
gear, and the bottom of the gap between two adjacent teeth on the other. The amount
of clearance is the difference between the Addendum and the Dedendum.
That is Clearance = D -- A.
3. When two gears mesh together the larger is called the gear and the smaller the
pinion. That meshed with a rack is also called the pinion.
4. The shape of the space between adjacent teeth varies considerably with the number
of teeth on the gear. Gears having a few teeth have very rounded teeth whilst gears
with a large number of teeth, have almost straight sided teeth. The space between
the adjacent teeth, being that cut by the milling cutter, vary considerably. Therefore,
in theory, a different cutter is required for each number of teeth. In practice, except
for extremely critical applications, a compromise is adopted and 8 different cutters
are required to cut from 12 teeth up to a rack. Table 1 indicates the range of each
cutter. Note, metric cutters(MOD) are numbered in reverse.
5. Gears with small numbers of teeth 11 down to 6 require special consideration. A
detailed book on the subject should be read before cutting gears of that size.
6. Commercially available gears with 16 or less teeth may have a modified tooth form
known as an addendum modification, or corrected gears. These mesh correctly with
standard gears but at a modified centre distance. Consult supplier for details.
7. The tooth shape of the rack is straight sided and with an angle equal to the
pressure angle.
8. Sketch 2 shows 24 tooth gears in the metric sizes MOD2, MOD1 and MOD0.5. These
are very similar to 12DP, 24DP and 48DP The DP gears would be slightly larger.
9. The sketches are approximate representations only. Sketch 2 is nominally
true to size.
10. Table 2 compares the DP and MOD ranges. This table does not imply interchangeability
or mixed usage, though for a few sizes and in a non arduous situation it may be
acceptable if gears are to hand.
11. A pair of gears, adequately lubricated, meshing smoothly, and at the correct centre
distance, should have a transmission efficiency in the order of 97%
Table 1
Cutter number and ranges
DP number MOD number For cutting gears
1 8 135T to rack
2 7 557 to 134T
3 6 357 to 54T
4 5 26T to 34T
5 4 21T to 25T
6 3 17T to 20T
7 2 14T to 16T
8 1 12T to 13T
Table 2
DP and MOD system comparisons
DP MOD DP MOD
standard standard
equivalent equivalent
0. 4 63.5
0.5 50.8
48 0.53
0.6 42.33
40 0.63
0.7 36.29
32 0.79
0.8 31.75
1.0 25.4
24 1.06
1.25 20.32
20 1.27
1.5 16.93
16 1.59
2.0 12.7
12 2.12
3.0 8.47
4.0 6.35
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