ELEMENTS OF METRIC GEAR TECHNOLOGY I - SDP/SI · PDF fileThe governing equations become simple...
Transcript of ELEMENTS OF METRIC GEAR TECHNOLOGY I - SDP/SI · PDF fileThe governing equations become simple...
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SECTION 10 TOOTH THICKNESS
There are direct and indirect methods for measuring tooth thickness. In general, there are three methods:
• Chordal Thickness Measurement • Span Measurement • Over Pin or Ball Measurement
10.1 Chordal Thickness Measurement
This method employs a tooth caliper that is referenced from the gear's outside diameter. Thickness is measured at the pitch circle. See Figure 10-1.
sj
hj
q
d
Fig. 10-1 Chordal Thickness Method 10.1.1 Spur Gears
Table 10-1 presents equations for each chordal thickness measurement.
No. Item Example
Circular Tooth Thickness
Half of Tooth Angleat Pitch Circle
Chordal Thickness
Chordal Addendum
Symbol Formula
s
sj
hj
p (–– + 2x tan a )m 290 360 x tan a –– + –––––––– z pz
zm sin q
zm –– (1– cos q) + ha 2
m = 10a = 20°z = 12x = +0.3ha = 13.000s = 17.8918q = 8.54270°sj = 17.8256hj = 13.6657
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2
3
4
Table 10-1 Equations for Spur Gear Chordal Thickness
10.1.2 Spur Racks And Helical Racks
The governing equations become simple since the rack tooth profile is trapezoid, as shown in Table 10-2.
No.
Chordal Thickness
Chordal Addendum
sj
hj
pm pmn ––– or ––– 2 2
ha
m = 3a = 20°sj = 4.7124ha = 3.0000
Item ExampleSymbol Formula
Table 10-2 Chordal Thickness of Racks
NOTE: These equations are also applicable to helical racks.
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10.1.3 Helical Gears
The chordal thickness of helical gears should be measured on the normal surface basis as shown in Table 10-3. Table 10-4 presents the equations for chordal thickness of helical gears in the radial system.
NOTE: Table 10-4 equations are also for the tooth profile of a Sunderland gear.
Table 10-4 Equations for Chordal Thickness of Helical Gears in the Radial System
No. Item Example
1
2
3
4
5
FormulaSymbol
sn
zv
qv
sj
hj
Normal Circular Tooth Thickness
Number of Teeth in an EquivalentSpur Gear
Half of Tooth Angle at Pitch Circle
Chordal Thickness
Chordal Addendum
m = 4at = 20°b = 22° 30' 00"z = 20xt = +0.3ha = 4.7184sn = 6.6119zv = 25.3620qv = 4.04196°sj = 6.6065hj = 4.8350
p (–– + 2xt tan at )mt cos b 2 z––––– cos3 b
90 360xt tan at–– + ––––––––––– zv pzv zv mt cos b sin qv
zv mt cos b –––––––– (1– cos qv) + ha 2
Table 10-5 Equations for Chordal Thickness of Gleason Straight Bevel Gears
m = 4a = 20° S = 90°z1 = 16z2 = 40 z1–– = 0.4 z2 K = 0.0259ha1 = 5.5456 ha2 = 2.4544d1 = 21.8014° d2 = 68.1986°s1 = 7.5119 s2 = 5.0545sj1 = 7.4946 sj2 = 5.0536hj1 = 5.7502 hj2 = 2.4692
Obtain from Figure 10-2(on the following page)
pm – s2
pm––– – (ha1 – ha2) tan a – Km 2
s3
s – ––– 6d2
s2 cos d ha + –––––– 4d
No. Item Example
1
2
4
5
Circular Tooth Thickness Factor(Coefficient of Horizontal Profile Shift)
Circular Tooth Thickness
Chordal Thickness
Chordal Addendum
Symbol
K
s1
s2
sj
hj
Formula
Table 10-3 Equations for Chordal Thickness of Helical Gears in the Normal System
No. Item Example
1
2
3
4
5
FormulaSymbol
sn
zv
qv
sj
hj
Normal Circular Tooth Thickness
Number of Teeth of an EquivalentSpur Gear
Half of Tooth Angle at Pitch Circle
Chordal Thickness
Chordal Addendum
p (–– + 2xn tan an )mn 2 z–––––– cos3 b
90 360xn tan an –– + –––––––––– zv pzv
zv mn sin qv
zv mn –––– (1– cos qv ) + ha 2
mn = 5an = 20°b = 25° 00' 00"z = 16xn = +0.2ha = 6.0000sn = 8.5819zv = 21.4928qv = 4.57556°sj = 8.5728hj = 6.1712
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23
24
Over 25
Circ
ular
Too
th T
hick
ness
Fac
tor,
K
Num
ber o
f Tee
th o
f Pin
ion,
z1
0.7 0.6 0.5 0.4 0.3 0.2 0.1 z1Speed Ratio, –– z2
.110
.100
.090
.080
.070
.060
.050
.040
.030
.020
.010
.000
Fig. 10-2 Chart to Determine the Circular Tooth Thickness Factor K for Gleason Straight Bevel Gear (See Table 10-5)
Table 10-6 Equations for Chordal Thickness of Standard Straight Bevel Gears
No. Item ExampleFormulaSymbol
1
2
3
4
5
6
Circular Tooth Thickness
Number of Teeth of an EquivalentSpur Gear
Back Cone Distance
Half of Tooth Angle at Pitch CircleChordal Thickness
Chordal Addendum
s
zv
Rv
qv
sj
hj
pm ––– 2 z–––– cos d d–––––2cos d 90 –– zv
zv m sin qv
ha + Rv (1 – cos qv)
m = 4a = 20° S = 90°z1 = 16 z2 = 40d1 = 64 d2 = 160ha = 4.0000d1 = 21.8014° d2 = 68.1986°s = 6.2832zv1 = 17.2325 zv2 = 107.7033Rv1 = 34.4650 Rv2 = 215.4066qv1 = 5.2227° qv2 = 0.83563°sj1 = 6.2745 sj2 = 6.2830hj1 = 4.1431 hj2 = 4.0229
Table 10-6 presents equations for chordal thickness of a standard straight bevel gear.
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If a standard straight bevel gear is cut by a Gleason straight bevel cutter, the tooth angle should be adjusted according to:
180° s tooth angle (°) = –––– (–– + hf tan a) (10-1) pRe 2
This angle is used as a reference in determining the circular tooth thickness, s, in setting up the gear cutting machine. Table 10-7 presents equations for chordal thickness of a Gleason spiral bevel gear.
Figure 10-3 is shown on the following page.
The calculations of circular thickness of a Gleason spiral bevel gear are so complicated that we do not intend to go further in this presentation.
10.1.5 Worms And Worm Gears
Table 10-8 presents equations for chordal thickness of axial module worms and worm gears.
No. Item Example
1
2
Symbol
K
s1
s2
Obtain from Figure 10-3
p – s2
p tan an –– – (ha1 – ha2) –––––– – Km 2 cos bm
Formula
S = 90° m = 3 an = 20°z1 = 20 z2 = 40 bm = 35°ha1 = 3.4275 ha2 = 1.6725K = 0.060p = 9.4248s1 = 5.6722 s2 = 3.7526
Circular ToothThickness Factor
Circular Tooth Thickness
Table 10-8 Equations for Chordal Thickness of Axial Module Worms and Worm Gears
sx1
sx2
zv2
qv2
sj1
sj2
hj1
hj2
pmx –––– 2 p(–– + 2xx2 tan a x)mx 2
z2––––– cos3 g
90 360 xx2 tan ax––– + –––––––––– zv2 pzv2
sx1 cos g zv mx cos g sin qv2
(sx1 sin g cos g)2
ha1 + ––––––––––– 4d1
zv mx cos gha2 + –––––––– (1 – cos qv2) 2
No. Item ExampleFormulaSymbol
1
2
3
4
5
Axial Circular Tooth Thickness of WormRadial Circular Tooth Thickness of Worm Gear
No. of Teeth in an Equivalent Spur Gear (Worm Gear)
Half of Tooth Angle at Pitch Circle (Worm Gear)
Chordal Thickness
Chordal Addendum
mx = 3an = 20°zw = 2 z2 = 30d1 = 38 d2 = 90ax = 65 xx2 = +0.33333ha1 = 3.0000 ha2 = 4.0000g = 8.97263°ax = 20.22780°sx1 = 4.71239 sx2 = 5.44934 zv2 = 31.12885 qv2 = 3.34335°sj1 = 4.6547 sj2 = 5.3796hj1 = 3.0035 hj2 = 4.0785
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1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 z1 Speed Ratio, –– z2
Circ
ular
Too
th T
hick
ness
Fac
tor,
K
0.260
0.240
0.220
0.200
0.180
0.160
0.140
0.120
0.100
0.080z = 15z = 16z = 170.060z = 20
0.040z = 25
Over 30
0.020
0
– 0.020
Number of Teeth of Pinion
50
12
1314
1516
45 40 35
1720
2530
50
12
13
14
1516
45
40
35
17
20
25
30
Fig. 10-3 Chart to Determine the Circular Tooth Thickness Factor K for Gleason Spiral Bevel Gears
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Table 10-9 contains the equations for chordal thickness of normal module worms and worm gears.
Table 10-9 Equations for Chordal Thickness of Normal Module Worms and Worm Gears
sn1
sn2
zv2
qv2
sj1
sj2
hj1
hj2
pmn –––– 2 p(––– + 2xn2 tan an)mn 2
z2––––– cos3 g
90 360 xn2 tan an–– + –––––––––––zv2 pzv2
sn1 cos g zv mn cos g sin qv2
(sn1 sin g) 2
ha1 + –––––––– 4d1
zv mn cos gha2 + –––––––– (1 – cos qv2) 2
No. Item ExampleFormulaSymbol
1
2
3
4
5
Axial Circular Tooth Thickness of WormRadial Circular Tooth Thickness of Worm Gear
No. of Teeth in an Equivalent Spur Gear (Worm Gear)
Half of Tooth Angle at Pitch Circle (Worm Gear)
Chordal Thickness
Chordal Addendum
mn = 3an = 20°zw = 2 z2 = 30d1 = 38 d2 = 91.1433ax = 65 xn2 = 0.14278ha1 = 3.0000 ha2 = 3.42835g = 9.08472°sn1 = 4.71239 sn2 = 5.02419 zv2 = 31.15789 qv2 = 3.07964°sj1 = 4.7124 sj2 = 5.0218hj1 = 3.0036 hj2 = 3.4958
10.2 Span Measurement Of Teeth
Span measurement of teeth, sm, is a measure over a number of teeth, zm, made by means of a special tooth thickness micrometer. The value measured is the sum of normal circular tooth thickness on the base circle, sbn , and normal pitch, pen (zm – 1).
10.2.1 Spur And Internal Gears
The applicable equations are presented in Table 10-10.
NOTE: 1 K(f) = –– [sec a √(1 + 2f )2 – cos2 a – inv a – 2f tan a] (10-2) p x where f = z
Table 10-10 Span Measurement of Spur and Internal Gear Teeth
No. Item Example
1
2
Span Number of Teeth
Span Measurement
Symbol Formula
m = 3a = 20°z = 24x = +0.4zmth = 3.78787zm = 4sm = 32.8266
zm
sm
zmth = zK(f) + 0.5 See NOTESelect the nearest natural number of zmth as zm.
m cos a [p (zm – 0.5) +z inv a ] + 2xm sin a
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Figure 10-4 shows the span measurement of a spur gear. This measurement is on the outside of the teeth. For internal gears the tooth profile is opposite to that of the external spur gear. Therefore, the measurement is between the inside of the tooth pro-files.
10.2.2 Helical Gears
Tables 10-11 and 10-12 present equations for span measurement of the normal and the radial systems, re-spectively, of helical gears.
sm
d
Fig. 10-4 Span Measurement of Teeth (Spur Gear)
NOTE: 1 sin2 b K(f, b) = –– [(1 + –––––––––––––)√(cos2 b + tan2 an)(sec b + 2f )2 – 1 – inv at – 2f tan an ] (10-3) p cos2 b + tan2 an
xn where f = z
Table 10-11 Equations for Span Measurement of the Normal System Helical Gears
No. Item Example
1
2
Span Number of Teeth
Span Measurement
Symbol Formula
mn = 3, an = 20°, z = 24b = 25° 00' 00"xn = +0.4as = 21.88023°zmth = 4.63009zm = 5sm = 42.0085
zm
sm
zmth = zK (f, b) + 0.5 See NOTESelect the nearest natural number of zmth as zm.
mn cos an [p (zm – 0.5) + z inv at] + 2xnmn sin an
NOTE: 1 sin2 b ––––––––––––––––––––––––– K(f, b) = –– [(1 + ––––––––––––) √(cos2 b + tan2 an)(sec b + 2f )2 – 1 – inv at – 2f tan an ] (10-4) p cos2 b + tan2 an
xt where f = –––––– z cos b
Table 10-12 Equations for Span Measurement of the Radial System Helical Gears
No. Item Example
1
2
Span Number of Teeth
Span Measurement
Symbol Formula
mt = 3, at = 20°, z = 24b = 22° 30' 00"xt = +0.4an = 18.58597°zmth = 4.31728zm = 4sm = 30.5910
zm
sm
zmth = zK(f, b) + 0.5 See NOTESelect the nearest natural number of zmth as zm.
mt cos b cos an [p (zm – 0.5) + z inv at ] + 2xt mt sin an
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There is a requirement of a minimum blank width to make a helical gear span measurement. Let bmin be the minimum value for blank width. Then
bmin = sm sin bb + Db (10-5)
where bb is the helix angle at the base cylinder,
bb = tan–1 (tan b cos at) = sin–1 (sin b cos an) (10-6)
From the above, we can determine that at least 3mm of Db is required to make a stable measurement of sm.
10.3 Over Pin (Ball) Measurement
As shown in Figures 10-6 and 10-7, measure-ment is made over the outside of two pins that are inserted in diametrically opposite tooth spaces, for even tooth number gears; and as close as possible for odd tooth number gears.
Fig. 10-5 Blank Width of Helical Gear
bmin bb
sm
Fig. 10-7 Odd Number of Teeth
dp
dm
Fig. 10-6 Even Number of Teeth
dp
dm
d
The procedure for measuring a rack with a pin or a ball is as shown in Figure 10-9 by putting pin or ball in the tooth space and using a micrometer between it and a reference surface. Internal gears are similarly measured, except that the measurement is between the pins. See Figure 10-10. Helical gears can only be measured with balls. In the case of a worm, three pins are used, as shown in Figure 10-11. This is similar to the procedure of measuring a screw thread. All these cases are discussed in detail in the following sections. Note that gear literature uses “over pins” and “over wires” terminology interchangeably. The “over wires” term is often associated with very fine pitch gears because the diameters are accordingly small.
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10.3.1 Spur Gears
In measuring a gear, the size of the pin must be such that the over pins measurement is larger than the gear's outside diameter. An ideal value is one that would place the point of contact (tangent point) of pin and tooth profile at the pitch radius. However, this is not a necessary requirement. Referring to Figure 10-8, following are the equations for calculating the over pins measurement for a specific tooth thickness, s, regardless of where the pin contacts the tooth profile: For even number of teeth: d cos f dm = ––––––– + dp (10-7) cos f1
For odd number of teeth: d cos f 90° dm = ––––––– cos (––––) + dp (10-8) cos f1 z
where the value of f1 is obtained from: s dp p inv f1 = ––– + inv f + –––––– – –– (10-9) d d cos f z
When tooth thickness, s, is to be calculated from a known over pins measurement, dm, the above equations can be manipulated to yield:
p dp s = d (––– + inv fc – inv f + ––––––) (10-10) z d cos f
where d cos f cos fc = –––––– (10-11) 2Rc
For even number of teeth:
dm – dp Rc = ––––– (10-12) 2
For odd number of teeth: dm – dp Rc = ––––––––– (10-13) 90° 2 cos (–––) z
In measuring a standard gear, the size of the pin must meet the condition that its surface should have the tangent point at the standard pitch circle. While, in measuring a shifted gear, the surface of the pin should have thetangent point at the d + 2xm circle.
Fig. 10-8 Over Pins Diameter of Spur Gear
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The ideal diameters of pins when calculated from the equations of Table 10-13 may not be practical. So, in practice, we select a standard pin diameter close to the ideal value. After the actual diameter of pin dp is determined, the over pin measurement dm can be calculated from Table 10-14.
Table 10-13 Equations for Calculating Ideal Pin Diameters
NOTE: The units of angles ψ/2 and f are radians.
No. Item ExampleFormulaSymbol
ψ –2
ap
f
dp
p 2x tan a (–– – inv a ) – –––––– 2z z zm cos acos–1 [–––––––––] (z + 2x)m
ψ tan ap + 2
ψ zm cos a (inv f + ––) 2
m = 1a = 20°z = 20x = 0 ψ –– = 0.0636354 2 ap = 20°f = 0.4276057dp = 1.7245
1
2
3
4
Half Tooth Space Angle at Base Circle
The Pressure Angle at the Point Pin is Tangent to Tooth Surface
The Pressure Angle atPin Center
Ideal Pin Diameter
See NOTE dp p 2x tan a––––––– – ––– + inv a + ––––––– mz cos a 2z z
Find from Involute Function Table zm cos aEven Teeth –––––––– + dp cos f zm cos a 90°Odd Teeth –––––––– cos –– + dp cos f z
dp
inv f
f
dm
No. Item ExampleFormulaSymbol
Let dp = 1.7, then:
inv f = 0.0268197f = 24.1350°dm = 22.2941
1
2
3
4
Actual Diameter of Pin
Involute Function f
The Pressure Angle at Pin Center
Over PinsMeasurement
Table 10-14 Equations for Over Pins Measurement for Spur Gears
NOTE: The value of the ideal pin diameter from Table 10-13, or its approximate value, is applied as the actual diameter of pin dp here.
Table 10-15 is a dimensional table under the condition of module m = 1 and pressure angle a = 20° with which the pin has the tangent point at d + 2xm circle.
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Numberof Teeth
z
Coefficient of Profile Shift, x m = 1, a = 20°
––1.62311.64181.65001.6547
1.65771.65981.66141.66251.6635
1.66421.66491.66541.66591.6663
1.66661.66691.66721.66741.6676
10 20 30 40 50
60 70 80 90100
110120130140150
160170180190200
1.63481.65991.66491.66691.6680
1.66871.66921.66951.66981.6700
1.67011.67031.67041.67051.6706
1.67061.67071.67081.67081.6708
1.78861.72451.70571.69671.6915
1.68811.68571.68391.68251.6814
1.68051.67971.67911.67851.6781
1.67771.67731.67701.67671.6764
1.99791.81491.76321.73891.7248
1.71551.70901.70421.70051.6975
1.69511.69311.69141.69001.6887
1.68771.68671.68581.68511.6844
2.26871.93061.83691.79301.7675
1.75091.73921.73051.72371.7184
1.71401.71041.70741.70481.7025
1.70061.69891.69731.69601.6947
2.60792.07181.92671.85891.8196
1.79401.77591.76251.75211.7439
1.73721.73161.72691.72291.7195
1.71641.71381.71141.70931.7074
3.02482.23892.03241.93651.8810
1.84481.81931.80031.78571.7740
1.76451.75671.75001.74441.7394
1.73511.73141.72801.72501.7223
3.53152.43292.15422.02571.9516
1.90321.86911.84381.82421.8087
1.79601.78551.77661.76901.7625
1.75671.75171.74721.74321.7396
– 0.4 – 0.2 0 0.2 0.4 0.6 0.8 1.0
Table 10-15 The Size of Pin which Has the Tangent Point at d + 2xm Circle of Spur Gears
10.3.2 Spur Racks And Helical Racks
In measu ring a rack, the pin is ide-ally tangent with the tooth flank at the pitch line. The equa tions in Table 10-16 can, thus, be derived. In the case of a he-lical rack, module m, and pressure angle a, in Table 10-16, can be sub stituted by normal module, mn, and normal pressure angle, an , resulting in Table 10-16A.
Fig. 10-9 Over Pins Measurement for a Rack Using a Pin or a Ball
dpsj
dmH
pm pm – sj––––––– 2 tan a
No. Item ExampleSymbol Formula pm – sj–––––––– cos a pm – sj dp 1H – ––––––– + ––– ( 1 + –––– ) 2 tan a 2 sin a
dp'
dm
Ideal Pin Diameter
Over PinsMeasurement
1
2
Table 10-16 Equations for Over Pins Measurement of Spur Racks
m = 1 a = 20°sj = 1.5708Ideal Pin Diameter dp' = 1.6716Actual Pin Diameter dp = 1.7H = 14.0000 dm = 15.1774
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Table 10-16A Equations for Over Pins Measurement of Helical Racks
No. Item ExampleSymbolmn = 1 an = 20°sj = 1.5708 b = 15°Ideal Pin Diameter dp' = 1.6716Actual Pin Diameter dp = 1.7 H = 14.0000 dm = 15.1774
dp'
dm
Ideal Pin Diameter
Over PinsMeasurement
1
2
Formula pmn – sj–––––––– cos an
pmn – sj dp 1H – –––––––– + ––– (1 + –––––) 2 tan an 2 sin an
10.3.3 Internal Gears
As shown in Figure 10-10, measuring an internal gear needs a proper pin which has its tangent point at d + 2xm cir cle. The equations are in Table 10-17 for obtaining the ideal pin diameter. The equations for calculating the between pin measurement, dm , are given in Table 10-18.
Fig. 10-10 Between Pin Dimension of Internal Gears
dm
db
d
d + 2xmf
inv ap
inv f
ap
ψ––2
tan ap
Table 10-17 Equations for Calculating Pin Size for Internal Gears
NOTE: The units of angles ψ/2 and f are radians.
No. Item Example
1
2
3
4
Half of Tooth Space Angle at Base Circle
The Pressure Angle at the Point Pin is Tangent to Tooth Surface
The Pressure Angle atPin Center
Ideal Pin Diameter
FormulaSymbol
ψ –2
ap
f
dp
m = 1a = 20°z = 40x = 0 ψ –– = 0.054174 2 ap = 20°f = 0.309796dp = 1.6489
p 2x tan a (––– + inv a) + –––––– 2z z
zm cos acos–1 [–––––––––] (z + 2x)m ψ tan ap – ––
ψzm cos a (–– – inv f)
2
2
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Table 10-18 Equations for Between Pins Measurement of Internal Gears
See NOTE p dp 2x tan a( –– + inv a) – ––––––– + ––––––– 2z zm cos a z
Find from Involute Function Table zm cos aEven Teeth –––––––– – dp cos f zm cos a 90°Odd Teeth –––––––– cos ––– – dp cos f z
dp
inv f
f
dm
No. Item ExampleFormulaSymbol
Let dp = 1.7, then:
inv f = 0.0089467f = 16.9521°dm = 37.5951
1
2
3
4
Actual Diameter of Pin
Involute Function f
The Pressure Angle at Pin Center
Between PinsMeasurement
NOTE: First, calculate the ideal pin diameter. Then, choose the nearest practical actual pin size.
Table 10-19 lists ideal pin diameters for standard and profile shifted gears under the condition of module m = 1 and pressure angle a = 20°, which makes the pin tangent to the pitch circle d + 2xm .
Table 10-19 The Size of Pin that is Tangent at Pitch Circle d + 2xm of Internal GearsNumberof Teeth
z
Coefficient of Profile Shift, x m = 1, a = 20°
––1.46871.53091.56401.5845
1.59851.60861.61621.62221.6270
1.63101.63431.63711.63961.6417
1.64351.64511.64661.64791.6491
10 20 30 40 50
60 70 80 90100
110120130140150
160170180190200
1.47891.56041.59421.61231.6236
1.63121.63681.64101.64431.6470
1.64921.65101.65251.65391.6550
1.65611.65701.65781.65851.6591
1.59361.62841.64181.64891.6533
1.65621.65831.66001.66121.6622
1.66311.66381.66441.66491.6653
1.66571.66611.66641.66661.6669
1.67581.67591.67511.67451.6740
1.67371.67341.67321.67311.6729
1.67281.67271.67271.67261.6725
1.67251.67241.67241.67241.6723
1.72831.70471.69491.68951.6862
1.68391.68221.68101.68001.6792
1.67851.67791.67751.67711.6767
1.67641.67611.67591.67571.6755
1.75191.71541.70161.69441.6900
1.68701.68491.68331.68201.6810
1.68011.67941.67881.67831.6779
1.67751.67721.67681.67661.6763
1.74601.70841.69561.68931.6856
1.68321.68151.68021.67921.6784
1.67781.67721.67681.67641.6761
1.67581.67551.67531.67511.6749
1.70921.68371.67711.67441.6732
1.67251.67211.67181.67171.6716
1.67151.67141.67141.67141.6713
1.67131.67131.67131.67131.6713
– 0.4 – 0.2 0 0.2 0.4 0.6 0.8 1.0
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10.3.4 Helical Gears
The ideal pin that makes contact at the d + 2xn mn pitch circle of a helical gear can be obtained from the same above equations, but with the teeth number z substituted by the equivalent (virtual) teeth number zv. Table 10-20 presents equations for deriving over pin diameters.
Table 10-20 Equations for Calculating Pin Size for Helical Gears in the Normal System
NOTE: The units of angles ψv /2 and fv are radians.
No. Item ExampleFormulaSymbol
1
2
3
4
5
zv
ψv ––2
av
fv
dp
z––––– cos3 b
p 2xn tan an––– – inv an – –––––––– 2zv zv zv cos ancos–1 (–––––––) zv + 2xn
ψv tan av + –– 2
ψvzv mn cos an (inv fv + ––) 2
mn = 1an = 20°z = 20b = 15° 00' 00"xn = +0.4zv = 22.19211ψv –– = 0.0427566 2 av = 24.90647°fv = 0.507078dp = 1.9020
Number of Teeth of an Equivalent Spur Gear
Half Tooth Space Angle at Base Circle
Pressure Angle at the Point Pin is Tangent to Tooth Surface
Pressure Angle at Pin Center
Ideal Pin Diameter
Table 10-21 presents equations for calculating over pin measurements for helical gears in the normal system.
Table 10-21 Equations for Calculating Over Pins Measurement for Helical Gears in the Normal System
NOTE: The ideal pin diameter of Table 10-20, or its approximate value, is entered as the actual diameter of dp.
No. Item Example
1
2
3
4
Actual Pin Diameter
Involute Function f
Pressure Angle at Pin Center
Over Pins Measurement
FormulaSymbol
dp
inv f
f
dm
Let dp = 2, then
at = 20.646896°inv f = 0.058890f = 30.8534dm = 24.5696
See NOTE dp p 2xn tan an–––––––– – –– + inv at + ––––––– mnz cos an 2z z
Find from Involute Function Table
zmn cos atEven Teeth: ––––––––– + dp cos b cos f zmn cos at 90°Odd Teeth: ––––––––– cos –– + dp cos b cos f z
Metric
0 10
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Table 10-22 and Table 10-23 present equations for calculating pin measurements for helical gears in the radial (perpendicular to axis) system.
NOTE: The units of angles ψv /2 and fv are radians.
Table 10-22 Equations for Calculating Pin Size for Helical Gears in the Radial System
No. Item Example
1
2
3
4
5
Symbol
zv
ψv ––2
av
fv
dp
Formula
mt = 3at = 20°z = 36b = 33° 33' 26.3"an = 16.87300°xt = + 0.2zv = 62.20800ψv –– = 0.014091 2 av = 18.26390fv = 0.34411inv fv = 0.014258dp = 4.2190
z––––– cos3 b
p 2xt tan at––– – inv an – ––––––– 2zv zv
zv cos an –––––––– cos–1 ( xt ) zv + 2 ––––– cos b ψv tan av + –– 2
ψvzv mt cos b cos an (inv fv + ––) 2
Number of Teeth of an Equivalent Spur Gear
Half Tooth Space Angle at Base Circle
Pressure Angle at thePoint Pin is tangent toTooth Surface
Pressure Angle at Pin Center
Ideal Pin Diameter
NOTE: The ideal pin diameter of Table 10-22, or its approximate value, is applied as the actual diameter of pin dp here.
See NOTE
dp p 2xt tan at–––––––––––– – –– + inv at + ––––––– mt z cos b cos an 2z z
Find from Involute Function Table
zmt cos atEven Teeth: ––––––––– + dp cos f zmt cos at 90°Odd Teeth: ––––––––– cos –– + dp cos f z
No. Item Example
1
2
3
4
Actual Pin Diameter
Involute Function f
Pressure Angleat Pin Center
Over Pins Measurement
FormulaSymbol
dp
inv f
f
dm
Table 10-23 Equations for Calculating Over Pins Measurement for Helical Gears in the Radial System
dp = 4.2190inv f = 0.024302f = 23.3910dm = 114.793
Metric
0 10
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10.3.5 Three Wire Method Of Worm Measurement
The teeth profile of Type III worms which are most popular are cut by standard cutters with a pressure angle ac = 20°. This results in the normal pressure angle of the worm being a bit smaller than 20°.The equation below shows how to calculate a Type III worm in an AGMA sys-tem. 90° r an = ac – ––– –––––––––– sin3 g (10-14) zw rc cos2 g + r
where: r = Worm Pitch Radius rc = Cutter Radius zw = Number of Threads g = Lead Angle of Worm
The exact equation for a three wire method of Type III worm is not only difficult to comprehend, but also hard to calculate precisely. We will introduce two approximate calculation methods here:
(a) Regard the tooth profile of the worm as a linear tooth profile of a rack and apply its equations. Using this system, the three wire method of a worm can be calculated by Table 10-24.
Fig. 10-11 Three Wire Method of a Worm
dp
dmd
Table 10-24 Equations for Three Wire Method of Worm Measurement, (a)-1
No. Item ExampleSymbol
dp'
dm
Ideal Pin Diameter
Three WireMeasurement
1
2
Formulamx = 2 an = 20°zw = 1 d1 = 31g = 3.691386° ax = 20.03827° dp' = 3.3440; let dp = 3.3dm = 35.3173
pmx––––––2 cos ax
pmx 1d1 – –––––– + dp(1 + ––––) 2 tan ax sin ax
These equations presume the worm lead angle to be very small and can be neglected. Of course, as the lead angle gets larger, the equations' error gets correspondingly larger. If the lead angle is considered as a factor, the equations are as in Table 10-25.
Table 10-25 Equations for Three Wire Method of Worm Measurement, (a)-2
mx = 2 an = 20°zw = 1 d1 = 31g = 3.691386°mn = 1.99585dp' = 3.3363; let dp = 3.3dm = 35.3344
pmn––––––– 2 cos an
pmn 1d1 – –––––– + dp(1 + –––––) 2 tan an sin an
(dp cos an sin g )2
– ––––––––––– 2d1
Ideal Pin Diameter
Three WireMeasurement
No. Item ExampleSymbol
dp'
dm
Formula
1
2
Metric
0 10
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(b) Consider a worm to be a helical gear. This means applying the equations for calculating over pins measurement of helical gears to the case of three wire method of a worm. Because the tooth profile of Type III worm is not an involute curve, the method yields an approximation. However, the accuracy is adequate in practice.
Tables 10-26 and 10-27 contain equations based on the axial system. Tables 10-28 and 10-29 are based on the normal system.
No. Item ExampleFormulaSymbol
See NOTE 1 dp p–––––––––––––– – ––– + inv at mx zw cos g cos an 2zw
Find from Involute Function Table
zw mx cos at –––––––––– + dp tan g cos f
Actual Pin Size
Involute Function f
Pressure Angleat Pin Center
Three Wire Measurement
Let dp = 3.3at = 79.96878°inv at = 4.257549inv f = 4.446297f = 80.2959°dm = 35.3345
dp
inv f
f
dm
1
2
3
4
Table 10-27 Equation for Three Wire Method for Worms in the Axial System, (b)-2
NOTE: 1. The value of ideal pin diameter from Table 10-26, or its approximate value, is to be used as the actual pin diameter, dp. tan an 2. at = tan–1(––––––) sin g
1
2
3
4
5
zv
ψv ––2
av
fv
dp
zw–––––––––– cos3 (90 – g )
p––– – inv an 2 zv
zv cos ancos–1 (–––––––) zv
ψv tan av + –– 2
ψvzv mx cos g cos an(inv fv + ––) 2
Number of Teeth of anEquivalent Spur Gear
Half Tooth Space Angle at Base Circle
Pressure Angle at the Point Pin is Tangent to Tooth SurfacePressure Angle at Pin Center
Ideal Pin Diameter
mx = 2an = 20°zw = 1d1 = 31g = 3.691386°zv = 3747.1491ψv –– = -0.014485 2 av = 20°fv = 0.349485inv fv = 0.014960dp = 3.3382
No. Item Symbol Formula Example
Table 10-26 Equation for Calculating Pin Size for Worms in the Axial System, (b)-1
NOTE: The units of angles ψv / 2 and fv are radians.
Metric
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Table 10-28 shows the calculation of a worm in the normal module system. Basically, the normal module system and the axial module system have the same form of equations. Only the notations of module make them different.
Table 10-28 Equation for Calculating Pin Size for Worms in the Normal System, (b)-3
NOTE: The units of angles ψv /2 and fv are radians.
No. Item ExampleFormulaSymbol
1
2
3
4
5
zv
ψv ––2
av
fv
dp
zw–––––––––– cos3 (90 – g )
p––– – inv an 2zv
zv cos ancos–1 (–––––––) zv
ψv tan av + –– 2
ψvzv mn cos an(inv fv + ––) 2
Number of Teeth of anEquivalent Spur Gear
Half of Tooth Space Angle at Base CirclePressure Angle at the Point Pin is Tangent to Tooth Surface
Pressure Angle at Pin Center
Ideal Pin Diameter
mn = 2.5an = 20°zw = 1d1 = 37g = 3.874288°zv = 3241.792ψv –– = – 0.014420 2 av = 20°fv = 0.349550inv fv = 0.0149687dp = 4.1785
Table 10-29 Equations for Three Wire Method for Worms in the Normal System, (b)-4
No. Item ExampleFormulaSymbol
See NOTE 1 dp p––––––––– – ––– + inv atmn zw cos an 2 zw
Find from Involute Function Table
zw mn cos at ––––––––– + dp sin g cos f
Actual Pin Size
Involute Function f
Pressure Angle at Pin Center
Three Wire Measurement
dp = 4.2at = 79.48331°inv at = 3.999514inv f = 4.216536f = 79.8947°dm = 42.6897
dp
inv f
f
dm
1
2
3
4
NOTE: 1. The value of ideal pin diameter from Table 10-28, or its approximate value, is to be used as the actual pin diameter, dp. tan an 2. at = tan–1(––––––) sin g
10.4 Over Pins Measurements For Fine Pitch Gears With Specific Numbers Of Teeth
Table 10-30 presents measurements for metric gears. These are for standard ideal tooth thicknesses. Measurements can be adjusted accordingly to backlash allowance and tolerance; i.e., tooth thinning.
Metric
0 10
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mm Inch mm InchMeas. Over WirePitch Diameter
No.of
Teethmm Inch mm Inch
Meas. Over WirePitch Diameter
No.of
Teeth
TABLE 10-30 METRIC GEAR OVER PINS MEASUREMENTPitch Diameter and Measurement Over Wires for External, Module Type Gears, 20-Degree Pressure Angle
Module 0.30Wire Size = 0.5184mm; 0.0204 Inch
Module 0.40Wire Size = 0.6912mm; 0.0272 Inch
56789
1011121314
1516171819
2021222324
2526272829
3031323334
3536373839
4041424344
4546474849
5051525354
5556575859
6061626364
6566676869
7071727374
0.07870.09450.11020.12600.1417
0.15750.17320.18900.20470.2205
0.23620.25200.26770.28350.2992
0.31500.33070.34650.36220.3780
0.39370.40940.42520.44090.4567
0.47240.48820.50390.51970.5354
0.55120.56690.58270.59840.6142
0.62990.64570.66140.67720.6929
0.70870.72440.74020.75590.7717
0.78740.80310.81890.83460.8504
0.86610.88190.89760.91340.9291
0.94490.96060.97640.99211.0079
1.02361.03941.05511.07091.0866
1.10241.11811.13391.14961.1654
56789
1011121314
1516171819
2021222324
2526272829
3031323334
3536373839
4041424344
4546474849
5051525354
5556575859
6061626364
6566676869
7071727374
0.32100.3357
0.35260.36740.38420.39910.4157
0.43070.44730.46230.47890.4939
0.51040.52550.54190.55710.5735
0.58870.60500.62020.63650.6518
0.66810.68330.69960.71490.7311
0.74640.76260.77800.79410.8095
0.82570.84100.85720.87260.8887
0.90410.92020.93560.95170.9671
0.98320.99871.01471.03021.0462
1.06171.07771.09321.10931.1247
1.14081.15621.17231.18771.2038
8.154 8.528
8.956 9.333 9.75810.13710.560
10.94011.36111.74312.16312.546
12.96413.34813.76514.15014.566
14.95215.36715.75416.16816.555
16.96917.35717.76918.15818.570
18.95919.37119.76020.17120.561
20.97221.36221.77222.16322.573
22.96423.37323.76424.17324.565
24.97425.36625.77426.16626.574
26.96727.37527.76728.17528.568
28.97529.36829.77630.16930.576
6.115 6.396
6.717 7.000 7.319 7.603 7.920
8.205 8.521 8.808 9.122 9.410
9.72310.01110.32410.61310.925
11.21411.52511.81512.12612.417
12.72713.01813.32713.61913.927
14.21914.52814.82015.12815.421
15.72916.02216.32916.62216.929
17.22317.53017.82318.13018.424
18.73019.02419.33119.62519.931
20.22520.53120.82621.13121.426
21.73122.02622.33222.62722.932
0.24080.2518
0.26440.27560.28810.29930.3118
0.32300.33550.34680.35910.3705
0.38280.39410.40650.41780.4301
0.44150.45380.46520.47740.4888
0.50100.51250.52470.53620.5483
0.55980.57200.58350.59560.6071
0.61920.63080.64290.65440.6665
0.67810.69010.70170.71380.7253
0.73740.74900.76100.77260.7847
0.79630.80830.81990.83190.8435
0.85560.86720.87920.89080.9028
2.000 2.400 2.800 3.200 3.600
4.000 4.400 4.800 5.200 5.600
6.000 6.400 6.800 7.200 7.600
8.000 8.400 8.800 9.200 9.600
10.00010.40010.80011.20011.600
12.00012.40012.80013.20013.600
14.00014.40014.80015.20015.600
16.00016.40016.80017.20017.600
18.00018.40018.80019.20019.600
20.00020.40020.80021.20021.600
22.00022.40022.80023.20023.600
24.00024.40024.80025.20025.600
26.00026.40026.80027.20027.600
28.00028.40028.80029.20029.600
1.500 1.800 2.100 2.400 2.700
3.000 3.300 3.600 3.900 4.200
4.500 4.800 5.100 5.400 5.700
6.000 6.300 6.600 6.900 7.200
7.500 7.800 8.100 8.400 8.700
9.000 9.300 9.600 9.90010.200
10.50010.80011.10011.40011.700
12.00012.30012.60012.90013.200
13.50013.80014.10014.40014.700
15.00015.30015.60015.90016.200
16.50016.80017.10017.40017.700
18.00018.30018.60018.90019.200
19.50019.80020.10020.40020.700
21.00021.30021.60021.90022.200
0.05910.07090.08270.09450.1063
0.11810.12990.14170.15350.1654
0.17720.18900.20080.21260.2244
0.23620.24800.25980.27170.2835
0.29530.30710.31890.33070.3425
0.35430.36610.37800.38980.4016
0.41340.42520.43700.44880.4606
0.47240.48430.49610.50790.5197
0.53150.54330.55510.56690.5787
0.59060.60240.61420.62600.6378
0.64960.66140.67320.68500.6969
0.70870.72050.73230.74410.7559
0.76770.77950.79130.80310.8150
0.82680.83860.85040.86220.8740
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T-100
mm Inch mm InchMeas. Over WirePitch Diameter
No.of
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Meas. Over WirePitch Diameter
No.of
Teeth
TABLE 10-30 (Cont.) METRIC GEAR OVER PINS MEASUREMENTPitch Diameter and Measurement Over Wires for External, Module Type Gears, 20-Degree Pressure Angle
Module 0.30Wire Size = 0.5184mm; 0.0204 Inch
Module 0.40Wire Size = 0.6912mm; 0.0272 Inch
75 76 77 78 79
80 81 82 83 84
85 86 87 88 89
90 91 92 93 94
95 96 97 98 99
100101102103104
105106107108109
110111112113114
115116117118119
120121122123124
125126127128129
130131132133134
135136137138139
140141142143144
1.18111.19691.21261.22831.2441
1.25981.27561.29131.30711.3228
1.33861.35431.37011.38581.4016
1.41731.43311.44881.46461.4803
1.49611.51181.52761.54331.5591
1.57481.59061.60631.62201.6378
1.65351.66931.68501.70081.7165
1.73231.74801.76381.77951.7953
1.81101.82681.84251.85831.8740
1.88981.90551.92131.93701.9528
1.96851.98432.00002.01572.0315
2.04722.06302.07872.09452.1102
2.12602.14172.15752.17322.1890
2.20472.22052.23622.25202.2677
75 76 77 78 79
80 81 82 83 84
85 86 87 88 89
90 91 92 93 94
95 96 97 98 99
100101102103104
105106107108109
110111112113114
115116117118119
120121122123124
125126127128129
130131132133134
135136137138139
140141142143144
1.21931.23531.25081.26681.2823
1.29831.31381.32981.34531.3613
1.37681.39281.40831.42431.4398
1.45581.47131.48731.50291.5188
1.53441.55031.56591.58181.5974
1.61331.62891.64481.66041.6763
1.69191.70781.72341.73931.7549
1.77081.78641.80231.81791.8338
1.84941.86531.88091.89681.9124
1.92831.94391.95981.97541.9913
2.00692.02282.03842.05432.0699
2.08582.10142.11732.13292.1488
2.16442.18032.19592.21182.2274
2.24332.25892.27482.29042.3063
30.96931.37631.77032.17632.570
32.97733.37033.77734.17134.577
34.97135.37735.77136.17736.572
36.97737.37237.77838.17238.578
38.97339.37839.77340.17840.573
40.97841.37341.77842.17442.579
42.97443.37943.77444.17944.574
44.97945.37445.77946.17546.579
46.97547.37947.77548.17948.575
48.97949.37549.78050.17650.580
50.97651.38051.77652.18052.576
52.98053.37653.78054.17654.580
54.97655.38055.77756.18056.577
56.98057.37757.78058.17758.580
23.22723.53223.82724.13224.428
24.73225.02825.33325.62825.933
26.22826.53326.82927.13327.429
27.73328.02928.33328.62928.933
29.23029.53329.83030.13430.430
30.73431.03031.33431.63031.934
32.23032.53432.83133.13433.431
33.73434.03134.33434.63134.934
35.23135.53435.83136.13536.431
36.73537.03237.33537.63237.935
38.23238.53538.83239.13539.432
39.73540.03240.33540.63240.935
41.23241.53541.83242.13542.433
42.73543.03343.33543.63343.935
0.91440.92650.93810.95010.9617
0.97370.98530.99731.00901.0210
1.03261.04461.05621.06821.0799
1.09191.10351.11551.12711.1391
1.15081.16271.17441.18641.1980
1.21001.22171.23361.24531.2572
1.26891.28091.29251.30451.3162
1.32811.33981.35171.36341.3754
1.38711.39901.41071.42261.4343
1.44621.45791.46991.48161.4935
1.50521.51711.52881.54071.5524
1.56441.57611.58801.59971.6116
1.62331.63521.64691.65891.6706
1.68251.69421.70611.71781.7297
30.00030.40030.80031.20031.600
32.00032.40032.80033.20033.600
34.00034.40034.80035.20035.600
36.00036.40036.80037.20037.600
38.00038.40038.80039.20039.600
40.00040.40040.80041.20041.600
42.00042.40042.80043.20043.600
44.00044.40044.80045.20045.600
46.00046.40046.80047.20047.600
48.00048.40048.80049.20049.600
50.00050.40050.80051.20051.600
52.00052.40052.80053.20053.600
54.00054.40054.80055.20055.600
56.00056.40056.80057.20057.600
22.50022.80023.10023.40023.700
24.00024.30024.60024.90025.200
25.50025.80026.10026.40026.700
27.00027.30027.60027.90028.200
28.50028.80029.10029.40029.700
30.00030.30030.60030.90031.200
31.50031.80032.10032.40032.700
33.00033.30033.60033.90034.200
34.50034.80035.10035.40035.700
36.00036.30036.60036.90037.200
37.50037.80038.10038.40038.700
39.00039.30039.60039.90040.200
40.50040.80041.10041.40041.700
42.00042.30042.60042.90043.200
0.88580.89760.90940.92130.9331
0.94490.95670.96850.98030.9921
1.00391.01571.02761.03941.0512
1.06301.07481.08661.09841.1102
1.12201.13391.14571.15751.1693
1.18111.19291.20471.21651.2283
1.24021.25201.26381.27561.2874
1.29921.31101.32281.33461.3465
1.35831.37011.38191.39371.4055
1.41731.42911.44091.45281.4646
1.47641.48821.50001.51181.5236
1.53541.54721.55911.57091.5827
1.59451.60631.61811.62991.6417
1.65351.66541.67721.68901.7008
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ELEMENTS OF METRIC GEAR TECHNOLOGY
T-101
mm Inch mm InchMeas. Over WirePitch Diameter
No.of
Teethmm Inch mm Inch
Meas. Over WirePitch Diameter
No.of
Teeth
TABLE 10-30 (Cont.) METRIC GEAR OVER PINS MEASUREMENTPitch Diameter and Measurement Over Wires for External, Module Type Gears, 20-Degree Pressure Angle
Module 0.30Wire Size = 0.5184mm; 0.0204 Inch
Module 0.40Wire Size = 0.6912mm; 0.0272 Inch
145146147148149
150151152153154
155156157158159
160161162163164
165166167168169
170171172173174
175176177178179
180181182183184
185186187188189
190191192193194
195196197198199
200201202203204
205240280300340
380400440480500
2.28352.29922.31502.33072.3465
2.36222.37802.39372.40942.4252
2.44092.45672.47242.48822.5039
2.51972.53542.55122.56692.5827
2.59842.61422.62992.64572.6614
2.67722.69292.70872.72442.7402
2.75592.77172.78742.80312.8189
2.83462.85042.86612.88192.8976
2.91342.92912.94492.96062.9764
2.99213.00793.02363.03943.0551
3.07093.08663.10243.11813.1339
3.14963.16543.18113.19693.2126
3.22833.77954.40944.72445.3543
5.98436.29926.92917.55917.8740
145146147148149
150151152153154
155156157158159
160161162163164
165166167168169
170171172173174
175176177178179
180181182183184
185186187188189
190191192193194
195196197198199
200201202203204
205240280300340
380400440480500
2.32192.33782.35342.36932.3849
2.40082.41642.43232.44792.4638
2.47942.49532.51092.52682.5424
2.55832.57392.58982.60542.6213
2.63692.65282.66842.68432.6999
2.71582.73142.74732.76292.7788
2.79442.81032.82592.84182.8574
2.87332.88892.90482.92042.9363
2.95192.96782.98342.99933.0149
3.03083.04653.06233.07803.0938
3.10953.12533.14103.15683.1725
3.18833.20393.21973.23543.2512
3.26693.81824.44814.76315.3930
6.02306.33796.96797.59787.9128
58.97759.38159.77760.18160.577
60.98161.37761.78162.17862.581
62.97863.38163.77864.18164.578
64.98165.37865.78166.17866.581
66.97867.38167.77868.18168.578
68.98169.37869.78170.17870.581
70.979 71.381 71.779 72.181 72.579
72.981 73.379 73.782 74.179 74.582
74.979 75.382 75.779 76.182 76.579
76.982 77.382 77.782 78.182 78.582
78.982 79.382 79.782 80.182 80.582
80.982 81.379 81.780 82.180 82.580
82.980 96.982112.983120.983136.983
152.984160.984176.984192.984200.984
44.233 44.535 44.833 45.135 45.433
45.735 46.033 46.336 46.633 46.936
47.233 47.536 47.833 48.136 48.433
48.736 49.033 49.336 49.633 49.936
50.234 50.536 50.834 51.136 51.434
51.736 52.034 52.336 52.634 52.936
53.234 53.536 53.834 54.136 54.434
54.736 55.034 55.336 55.634 55.936
56.234 56.536 56.834 57.136 57.434
57.736 58.036 58.336 58.636 58.936
59.236 59.536 59.836 60.136 60.436
60.736 61.035 61.335 61.635 61.935
62.235 72.737 84.737 90.737102.738
114.738120.738132.738144.738150.738
1.74141.75341.76511.77701.7887
1.80061.81231.82421.83601.8479
1.85961.87151.88321.89511.9068
1.91871.93051.94241.95411.9660
1.97771.98962.00132.01322.0249
2.03682.04862.06052.07222.0841
2.09582.10772.11942.13132.1431
2.15502.16672.17862.19032.2022
2.21392.22582.23762.24952.2612
2.27312.28492.29672.30852.3203
2.33212.34402.35582.36762.3794
2.39122.40292.41472.42662.4384
2.45022.86373.33613.57234.0448
4.51724.75355.22595.69845.9346
58.000 58.400 58.800 59.200 59.600
60.000 60.400 60.800 61.200 61.600
62.000 62.400 62.800 63.200 63.600
64.000 64.400 64.800 65.200 65.600
66.000 66.400 66.800 67.200 67.600
68.000 68.400 68.800 69.200 69.600
70.000 70.400 70.800 71.200 71.600
72.000 72.400 72.800 73.200 73.600
74.000 74.400 74.800 75.200 75.600
76.000 76.400 76.800 77.200 77.600
78.000 78.400 78.800 79.200 79.600
80.000 80.400 80.800 81.200 81.600
82.000 96.000112.000120.000136.000
152.000160.000176.000192.000200.000
43.50043.80044.10044.40044.700
45.00045.30045.60045.90046.200
46.50046.80047.10047.40047.700
48.00048.30048.60048.90049.200
49.50049.80050.10050.40050.700
51.00051.30051.60051.90052.200
52.50052.80053.10053.40053.700
54.000 54.300 54.600 54.900 55.200
55.500 55.800 56.100 56.400 56.700
57.000 57.300 57.600 57.900 58.200
58.500 58.800 59.100 59.400 59.700
60.000 60.300 60.600 60.900 61.200
61.500 72.000 84.000 90.000102.000
114.000120.000132.000144.000150.000
1.71261.72441.73621.74801.7598
1.77171.78351.79531.80711.8189
1.83071.84251.85431.86611.8780
1.88981.90161.91341.92521.9370
1.94881.96061.97241.98431.9961
2.00792.01972.03152.04332.0551
2.06692.07872.09062.10242.1142
2.12602.13782.14962.16142.1732
2.18502.19692.20872.22052.2323
2.24412.25592.26772.27952.2913
2.30312.31502.32682.33862.3504
2.36222.37402.38582.39762.4094
2.42132.83463.30713.54334.0157
4.48824.72445.19695.66935.9055
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ELEMENTS OF METRIC GEAR TECHNOLOGY
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No.of
Teethmm Inch mm Inch
Meas. Over WirePitch Diameter
No.of
Teeth
TABLE 10-30 (Cont.) METRIC GEAR OVER PINS MEASUREMENTPitch Diameter and Measurement Over Wires for External, Module Type Gears, 20-Degree Pressure Angle
Module 0.50Wire Size = 0.8640mm; 0.0340 Inch
Module 0.75Wire Size = 1.2960mm; 0.0510 Inch
5 6 7 8 9
1011121314
1516171819
2021222324
2526272829
3031323334
3536373839
4041424344
4546474849
5051525354
5556575859
6061626364
6566676869
7071727374
0.14760.17720.20670.23620.2657
0.29530.32480.35430.38390.4134
0.44290.47240.50200.53150.5610
0.59060.62010.64960.67910.7087
0.73820.76770.79720.82680.8563
0.88580.91540.94490.97441.0039
1.03351.06301.09251.12201.1516
1.18111.21061.24021.26971.2992
1.32871.35831.38781.41731.4469
1.47641.50591.53541.56501.5945
1.62401.65351.68311.71261.7421
1.77171.80121.83071.86021.8898
1.91931.94881.97832.00792.0374
2.06692.09652.12602.15552.1850
5 6 7 8 9
1011121314
1516171819
2021222324
2526272829
3031323334
3536373839
4041424344
4546474849
5051525354
5556575859
6061626364
6566676869
7071727374
0.60190.6295
0.66110.68890.72030.74830.7795
0.80760.83870.86690.89780.9261
0.95700.98541.01611.04461.0753
1.10381.13441.16291.19351.2221
1.25261.28131.31171.34041.3708
1.39951.42991.45871.48901.5178
1.54811.57691.60721.63601.6663
1.69521.72541.75431.78451.8134
1.84351.87251.90261.93161.9617
1.99072.02082.04982.07992.1089
2.13892.16792.19802.22702.2571
15.28815.990
16.79217.49918.29619.00719.800
20.51321.30322.01922.80523.524
24.30825.02825.81026.53227.312
28.03628.81329.53930.31531.041
31.81632.54433.31834.04634.819
35.54836.32037.05137.82138.552
39.32240.05440.82341.55642.324
43.05743.82444.55845.32546.060
46.82647.56148.32649.06249.827
50.56351.32852.06452.82853.565
54.32955.06655.82956.56757.330
10.19210.660
11.19511.66612.19812.67113.200
13.67614.20214.67915.20415.683
16.20516.68517.20617.68818.208
18.69019.20919.69220.21020.694
21.21121.69622.21222.69823.212
23.69924.21324.70025.21425.702
26.21526.70327.21527.70428.216
28.70529.21629.70630.21730.706
31.21731.70732.21832.70833.218
33.70934.21834.70935.21935.710
36.21936.71037.21937.71138.220
0.40130.4197
0.44070.45930.48020.49890.5197
0.53840.55910.57790.59860.6174
0.63800.65690.67740.69640.7168
0.73580.75630.77530.79570.8147
0.83510.85420.87450.89360.9139
0.93300.95330.97250.99271.0119
1.03211.05131.07151.09071.1109
1.13011.15021.16951.18961.2089
1.22901.24831.26841.28771.3078
1.32711.34721.36651.38661.4059
1.42601.44531.46531.48471.5047
3.750 4.500 5.250 6.000 6.750
7.500 8.250 9.000 9.75010.500
11.25012.00012.75013.50014.250
15.00015.75016.50017.25018.000
18.75019.50020.25021.00021.750
22.50023.25024.00024.75025.500
26.25027.00027.75028.50029.250
30.00030.75031.50032.25033.000
33.75034.50035.25036.00036.750
37.50038.25039.00039.75040.500
41.25042.00042.75043.50044.250
45.00045.75046.50047.25048.000
48.75049.50050.25051.00051.750
52.50053.25054.00054.75055.500
2.500 3.000 3.500 4.000 4.500
5.000 5.500 6.000 6.500 7.000
7.500 8.000 8.500 9.000 9.500
10.00010.50011.00011.50012.000
12.50013.00013.50014.00014.500
15.00015.50016.00016.50017.000
17.50018.00018.50019.00019.500
20.00020.50021.00021.50022.000
22.50023.00023.50024.00024.500
25.00025.50026.00026.50027.000
27.50028.00028.50029.00029.500
30.00030.50031.00031.50032.000
32.50033.00033.50034.00034.500
35.00035.50036.00036.50037.000
0.09840.11810.13780.15750.1772
0.19690.21650.23620.25590.2756
0.29530.31500.33460.35430.3740
0.39370.41340.43310.45280.4724
0.49210.51180.53150.55120.5709
0.59060.61020.62990.64960.6693
0.68900.70870.72830.74800.7677
0.78740.80710.82680.84650.8661
0.88580.90550.92520.94490.9646
0.98431.00391.02361.04331.0630
1.08271.10241.12201.14171.1614
1.18111.20081.22051.24021.2598
1.27951.29921.31891.33861.3583
1.37801.39761.41731.43701.4567
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ELEMENTS OF METRIC GEAR TECHNOLOGY
T-103
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No.of
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No.of
Teeth
TABLE 10-30 (Cont.) METRIC GEAR OVER PINS MEASUREMENTPitch Diameter and Measurement Over Wires for External, Module Type Gears, 20-Degree Pressure Angle
Module 0.50Wire Size = 0.8640mm; 0.0340 Inch
Module 0.75Wire Size = 1.2960mm; 0.0510 Inch
75 76 77 78 79
80 81 82 83 84
85 86 87 88 89
90 91 92 93 94
95 96 97 98 99
100101102103104
105106107108109
110111112113114
115116117118119
120121122123124
125126127128129
130131132133134
135136137138139
140141142143144
2.21462.24412.27362.30312.3327
2.36222.39172.42132.45082.4803
2.50982.53942.56892.59842.6280
2.65752.68702.71652.74612.7756
2.80512.83462.86422.89372.9232
2.95282.98233.01183.04133.0709
3.10043.12993.15943.18903.2185
3.24803.27763.30713.33663.3661
3.39573.42523.45473.48433.5138
3.54333.57283.60243.63193.6614
3.69093.72053.75003.77953.8091
3.83863.86813.89763.92723.9567
3.98624.01574.04534.07484.1043
4.13394.16344.19294.22244.2520
75 76 77 78 79
80 81 82 83 84
85 86 87 88 89
90 91 92 93 94
95 96 97 98 99
100101102103104
105106107108109
110111112113114
115116117118119
120121122123124
125126127128129
130131132133134
135136137138139
140141142143144
2.28612.31612.34522.37522.4043
2.43432.46342.49342.52252.5524
2.58152.61152.64062.67062.6997
2.72962.75882.78872.81782.8478
2.87692.90682.93602.96592.9951
3.02503.05413.08403.11323.1431
3.17233.20223.23143.26123.2904
3.32033.34953.37943.40863.4384
3.46763.49753.52673.55653.5858
3.61563.64483.67473.70393.7337
3.76303.79283.82203.85193.8811
3.91093.94023.97003.99924.0290
4.05834.08814.11744.14724.1764
4.20624.23554.26534.29464.3243
58.067 58.830 59.568 60.331 61.069
61.831 62.570 63.331 64.070 64.832
65.571 66.332 67.072 67.832 68.572
69.333 70.073 70.833 71.573 72.333
73.074 73.834 74.574 75.334 76.075
76.834 77.575 78.334 79.076 79.835
80.576 81.335 82.076 82.835 83.577
84.335 85.077 85.836 86.578 87.336
88.078 88.836 89.578 90.336 91.078
91.836 92.579 93.337 94.079 94.837
95.579 96.337 97.080 97.837 98.580
99.337100.080100.837101.581102.338
103.081103.838104.581105.338106.081
106.838107.582108.338109.082109.838
38.71239.22039.71240.22040.713
41.22141.71342.22142.71443.221
43.71444.22144.71445.22245.715
46.22246.71547.22247.71548.222
48.71649.22249.71650.22350.716
51.22351.71752.22352.71753.223
53.71754.22354.71855.22355.718
56.22456.71857.22457.71858.224
58.71959.22459.71960.22460.719
61.22461.71962.22462.71963.225
63.72064.22564.72065.22565.720
66.22566.72067.22567.72068.225
68.72169.22569.72170.22570.721
71.22571.72172.22572.72173.226
1.52411.54411.56351.58351.6029
1.62291.64221.66221.68161.7016
1.72101.74101.76041.78041.7998
1.81981.83921.85911.87861.8985
1.91791.93791.95731.97731.9967
2.01662.03612.05602.07552.0954
2.11492.13482.15422.17422.1936
2.21352.23302.25292.27242.2923
2.31182.33172.35112.37102.3905
2.41042.42992.44982.46932.4892
2.50862.52852.54802.56792.5874
2.60732.62682.64672.66622.6860
2.70552.72542.74492.76482.7843
2.80412.82372.84352.86302.8829
56.250 57.000 57.750 58.500 59.250
60.000 60.750 61.500 62.250 63.000
63.750 64.500 65.250 66.000 66.750
67.500 68.250 69.000 69.750 70.500
71.250 72.000 72.750 73.500 74.250
75.000 75.750 76.500 77.250 78.000
78.750 79.500 80.250 81.000 81.750
82.500 83.250 84.000 84.750 85.500
86.250 87.000 87.750 88.500 89.250
90.000 90.750 91.500 92.250 93.000
93.750 94.500 95.250 96.000 96.750
97.500 98.250 99.000 99.750100.500
101.250102.000102.750103.500104.250
105.000105.750106.500107.250108.000
37.50038.00038.50039.00039.500
40.00040.50041.00041.50042.000
42.50043.00043.50044.00044.500
45.00045.50046.00046.50047.000
47.50048.00048.50049.00049.500
50.00050.50051.00051.50052.000
52.50053.00053.50054.00054.500
55.00055.50056.00056.50057.000
57.50058.00058.50059.00059.500
60.00060.50061.00061.50062.000
62.50063.00063.50064.00064.500
65.00065.50066.00066.50067.000
67.50068.00068.50069.00069.500
70.00070.50071.00071.50072.000
1.47641.49611.51571.53541.5551
1.57481.59451.61421.63391.6535
1.67321.69291.71261.73231.7520
1.77171.79131.81101.83071.8504
1.87011.88981.90941.92911.9488
1.96851.98822.00792.02762.0472
2.06692.08662.10632.12602.1457
2.16542.18502.20472.22442.2441
2.26382.28352.30312.32282.3425
2.36222.38192.40162.42132.4409
2.46062.48032.50002.51972.5394
2.55912.57872.59842.61812.6378
2.65752.67722.69692.71652.7362
2.75592.77562.79532.81502.8346
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ELEMENTS OF METRIC GEAR TECHNOLOGY
T-104
mm Inch mm InchMeas. Over WirePitch Diameter
No.of
Teethmm Inch mm Inch
Meas. Over WirePitch Diameter
No.of
Teeth
TABLE 10-30 (Cont.) METRIC GEAR OVER PINS MEASUREMENTPitch Diameter and Measurement Over Wires for External, Module Type Gears, 20-Degree Pressure Angle
Module 0.50Wire Size = 0.8640mm; 0.0340 Inch
Module 0.75Wire Size = 1.2960mm; 0.0510 Inch
145146147148149
150151152153154
155156157158159
160161162163164
165166167168169
170171172173174
175176177178179
180181182183184
185186187188189
190191192193194
195196197198199
200201202203204
205240280300340
380400440480500
4.2815 4.3110 4.3406 4.3701 4.3996
4.4291 4.4587 4.4882 4.5177 4.5472
4.5768 4.6063 4.6358 4.6654 4.6949
4.7244 4.7539 4.7835 4.8130 4.8425
4.8720 4.9016 4.9311 4.9606 4.9902
5.0197 5.0492 5.0787 5.1083 5.1378
5.1673 5.1969 5.2264 5.2559 5.2854
5.3150 5.3445 5.3740 5.4035 5.4331
5.4626 5.4921 5.5217 5.5512 5.5807
5.6102 5.6398 5.6693 5.6988 5.7283
5.7579 5.7874 5.8169 5.8465 5.8760
5.9055 5.9350 5.9646 5.9941 6.0236
6.0531 7.0866 8.2677 8.858310.0394
11.220511.811012.992114.173214.7638
145146147148149
150151152153154
155156157158159
160161162163164
165166167168169
170171172173174
175176177178179
180181182183184
185186187188189
190191192193194
195196197198199
200201202203204
205240280300340
380400440480500
4.3536 4.3834 4.4127 4.4425 4.4718
4.5015 4.5308 4.5606 4.5899 4.6196
4.6489 4.6787 4.7080 4.7378 4.7671
4.7968 4.8261 4.8559 4.8852 4.9149
4.9443 4.9740 5.0033 5.0331 5.0624
5.0921 5.1214 5.1512 5.1805 5.2102
5.2396 5.2693 5.2986 5.3284 5.3577
5.3874 5.4167 5.4465 5.4758 5.5055
5.5349 5.5646 5.5939 5.6236 5.6530
5.6827 5.7122 5.7418 5.7713 5.8008
5.8303 5.8599 5.8894 5.9189 5.9485
5.9780 6.0073 6.0369 6.0664 6.0959
6.1255 7.1591 8.3403 8.930810.1120
11.293111.883613.064814.245914.8364
110.582111.338112.082112.839113.582
114.339115.083115.839116.583117.339
118.083118.839119.583120.339121.083
121.839122.584123.339124.084124.840
125.584126.340127.084127.840128.584
129.340130.084130.840131.585132.340
133.085133.840134.585135.340136.085
136.840137.585138.340139.085139.840
140.585141.340142.086142.841143.586
144.341145.091145.841146.591147.341
148.091148.841149.591150.341151.091
151.841152.587153.337154.087154.837
155.587181.842211.843226.843256.844
286.844301.845331.845361.845376.845
73.72174.22674.72175.22675.722
76.22676.72277.22677.72278.226
78.72279.22679.72280.22680.722
81.22681.72282.22682.72283.226
83.72384.22684.72385.22685.723
86.22786.72387.22787.72388.227
88.72389.22789.72390.22790.723
91.227 91.723 92.227 92.724 93.227
93.724 94.227 94.724 95.227 95.724
96.227 96.727 97.227 97.727 98.227
98.727 99.227 99.727100.227100.727
101.227101.724102.224102.724103.224
103.725121.228141.229151.229171.229
191.230201.230221.230241.230251.230
2.90242.92232.94182.96162.9812
3.00103.02053.04043.05993.0798
3.09933.11913.13873.15853.1780
3.19793.21743.23733.25683.2766
3.29623.31603.33553.35543.3749
3.39473.41433.43413.45373.4735
3.49303.51293.53243.55223.5718
3.59163.61123.63103.65053.6704
3.68993.70973.72933.74913.7687
3.78853.80823.82783.84753.8672
3.88693.90663.92633.94603.9656
3.98534.00494.02464.04434.0640
4.08374.77285.56025.95396.7413
7.52877.92248.70989.49739.8910
108.750109.500110.250111.000111.750
112.500113.250114.000114.750115.500
116.250117.000117.750118.500119.250
120.000120.750121.500122.250123.000
123.750124.500125.250126.000126.750
127.500128.250129.000129.750130.500
131.250132.000132.750133.500134.250
135.000135.750136.500137.250138.000
138.750139.500140.250141.000141.750
142.500143.250144.000144.750145.500
146.250147.000147.750148.500149.250
150.000150.750151.500152.250153.000
153.750180.000210.000225.000255.000
285.000300.000330.000360.000375.000
72.500 73.000 73.500 74.000 74.500
75.000 75.500 76.000 76.500 77.000
77.500 78.000 78.500 79.000 79.500
80.000 80.500 81.000 81.500 82.000
82.500 83.000 83.500 84.000 84.500
85.000 85.500 86.000 86.500 87.000
87.500 88.000 88.500 89.000 89.500
90.000 90.500 91.000 91.500 92.000
92.500 93.000 93.500 94.000 94.500
95.000 95.500 96.000 96.500 97.000
97.500 98.000 98.500 99.000 99.500
100.000100.500101.000101.500102.000
102.500120.000140.000150.000170.000
190.000200.000220.000240.000250.000
2.85432.87402.89372.91342.9331
2.95282.97242.99213.01183.0315
3.05123.07093.09063.11023.1299
3.14963.16933.18903.20873.2283
3.24803.26773.28743.30713.3268
3.34653.36613.38583.40553.4252
3.44493.46463.48433.50393.5236
3.54333.56303.58273.60243.6220
3.64173.66143.68113.70083.7205
3.74023.75983.77953.79923.8189
3.83863.85833.87803.89763.9173
3.93703.95673.97643.99614.0157
4.03544.72445.51185.90556.6929
7.48037.87408.66149.44889.8425
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ELEMENTS OF METRIC GEAR TECHNOLOGY
T-105
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Meas. Over WirePitch Diameter
No.of
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TABLE 10-30 (Cont.) METRIC GEAR OVER PINS MEASUREMENTPitch Diameter and Measurement Over Wires for External, Module Type Gears, 20-Degree Pressure Angle
Module 0.80Wire Size = 1.3824mm; 0.0544 Inch
Module 1.00Wire Size = 1.7280mm; 0.0680 Inch
5 6 7 8 9
1011121314
1516171819
2021222324
2526272829
3031323334
3536373839
4041424344
4546474849
5051525354
5556575859
6061626364
6566676869
7071727374
0.19690.23620.27560.31500.3543
0.39370.43310.47240.51180.5512
0.59060.62990.66930.70870.7480
0.78740.82680.86610.90550.9449
0.98431.02361.06301.10241.1417
1.18111.22051.25981.29921.3386
1.37801.41731.45671.49611.5354
1.57481.61421.65351.69291.7323
1.77171.81101.85041.88981.9291
1.96852.00792.04722.08662.1260
2.16542.20472.24412.28352.3228
2.36222.40162.44092.48032.5197
2.55912.59842.63782.67722.7165
2.75592.79532.83462.87402.9134
5 6 7 8 9
1011121314
1516171819
2021222324
2526272829
3031323334
3536373839
4041424344
4546474849
5051525354
5556575859
6061626364
6566676869
7071727374
0.80250.8394
0.88150.91860.96040.99771.0394
1.07681.11831.15591.19711.2349
1.27601.31381.35481.39281.4337
1.47171.51251.55061.59131.6295
1.67011.70831.74901.78721.8278
1.86611.90661.94491.98542.0237
2.06412.10262.14292.18142.2217
2.26022.30052.33902.37932.4178
2.45802.49662.53682.57542.6156
2.65422.69442.73302.77312.8118
2.85192.89062.93072.96943.0094
20.38421.320
22.39023.33224.39525.34226.400
27.35128.40429.35930.40731.365
32.41033.37134.41335.37636.415
37.38138.41839.38540.42041.389
42.42243.39244.42345.39546.425
47.39848.42649.40150.42851.403
52.42953.40554.43055.40756.431
57.40958.43259.41160.43361.413
62.43463.41464.43565.41666.436
67.41768.43769.41970.43871.420
72.43873.42174.43975.42276.440
16.30717.056
17.91218.66619.51620.27421.120
21.88122.72323.48724.32625.092
25.92826.69727.53028.30129.132
29.90530.73431.50832.33633.111
33.93734.71435.53936.31637.140
37.91838.74139.52140.34241.122
41.94342.72443.54444.32645.145
45.92746.74647.52948.34749.130
49.94850.73251.54852.33353.149
53.93454.75055.53556.35057.136
57.95158.73759.55160.33861.152
0.64200.6715
0.70520.73490.76840.79820.8315
0.86150.89460.92470.95770.9879
1.02081.05111.08391.11421.1469
1.17731.21001.24051.27311.3036
1.33611.36671.39921.42981.4622
1.49291.52521.55591.58831.6190
1.65131.68211.71431.74511.7774
1.80821.84041.87121.90341.9343
1.96641.99732.02952.06032.0925
2.12342.15552.18642.21852.2494
2.28152.31252.34452.37552.4075
5.000 6.000 7.000 8.000 9.000
10.00011.00012.00013.00014.000
15.00016.00017.00018.00019.000
20.00021.00022.00023.00024.000
25.00026.00027.00028.00029.000
30.00031.00032.00033.00034.000
35.00036.00037.00038.00039.000
40.00041.00042.00043.00044.000
45.00046.00047.00048.00049.000
50.00051.00052.00053.00054.000
55.00056.00057.00058.00059.000
60.00061.00062.00063.00064.000
65.00066.00067.00068.00069.000
70.00071.00072.00073.00074.000
4.000 4.800 5.600 6.400 7.200
8.000 8.800 9.60010.40011.200
12.00012.80013.60014.40015.200
16.00016.80017.60018.40019.200
20.00020.80021.60022.40023.200
24.00024.80025.60026.40027.200
28.00028.80029.60030.40031.200
32.00032.80033.60034.40035.200
36.00036.80037.60038.40039.200
40.00040.80041.60042.40043.200
44.00044.80045.60046.40047.200
48.00048.80049.60050.40051.200
52.00052.80053.60054.40055.200
56.00056.80057.60058.40059.200
0.15750.18900.22050.25200.2835
0.31500.34650.37800.40940.4409
0.47240.50390.53540.56690.5984
0.62990.66140.69290.72440.7559
0.78740.81890.85040.88190.9134
0.94490.97641.00791.03941.0709
1.10241.13391.16541.19691.2283
1.25981.29131.32281.35431.3858
1.41731.44881.48031.51181.5433
1.57481.60631.63781.66931.7008
1.73231.76381.79531.82681.8583
1.88981.92131.95281.98432.0157
2.04722.07872.11022.14172.1732
2.20472.23622.26772.29922.3307
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ELEMENTS OF METRIC GEAR TECHNOLOGY
T-106
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No.of
Teethmm Inch mm Inch
Meas. Over WirePitch Diameter
No.of
Teeth
TABLE 10-30 (Cont.) METRIC GEAR OVER PINS MEASUREMENTPitch Diameter and Measurement Over Wires for External, Module Type Gears, 20-Degree Pressure Angle
Module 0.80Wire Size = 1.3824mm; 0.0544 Inch
Module 1.00Wire Size = 1.7280mm; 0.0680 Inch
75 76 77 78 79
80 81 82 83 84
85 86 87 88 89
90 91 92 93 94
95 96 97 98 99
100101102103104
105106107108109
110111112113114
115116117118119
120121122123124
125126127128129
130131132133134
135136137138139
140141142143144
2.95282.99213.03153.07093.1102
3.14963.18903.22833.26773.3071
3.34653.38583.42523.46463.5039
3.54333.58273.62203.66143.7008
3.74023.77953.81893.85833.8976
3.93703.97644.01574.05514.0945
4.13394.17324.21264.25204.2913
4.33074.37014.40944.44884.4882
4.52764.56694.60634.64574.6850
4.72444.76384.80314.84254.8819
4.92134.96065.00005.03945.0787
5.11815.15755.19695.23625.2756
5.31505.35435.39375.43315.4724
5.51185.55125.59065.62995.6693
75 76 77 78 79
80 81 82 83 84
85 86 87 88 89
90 91 92 93 94
95 96 97 98 99
100101102103104
105106107108109
110111112113114
115116117118119
120121122123124
125126127128129
130131132133134
135136137138139
140141142143144
3.04823.08823.12693.16703.2057
3.24573.28453.32453.36333.4032
3.44203.48203.52083.56083.5996
3.63953.67843.71833.75713.7970
3.83593.87583.91473.95453.9934
4.03334.07224.11204.15094.1908
4.22974.26964.30854.34834.3872
4.4271 4.4660 4.5058 4.5448 4.5846
4.6235 4.6633 4.7023 4.7421 4.7810
4.8208 4.8598 4.8996 4.9385 4.9783
5.0173 5.0571 5.0960 5.1358 5.1748
5.2146 5.2536 5.2933 5.3323 5.3721
5.4111 5.4508 5.4898 5.5296 5.5686
5.6083 5.6473 5.6870 5.7261 5.7658
77.423 78.440 79.424 80.441 81.425
82.441 83.426 84.442 85.427 86.442
87.428 88.443 89.429 90.443 91.429
92.444 93.430 94.444 95.431 96.444
97.432 98.445 99.432100.445101.433
102.446103.433104.446105.434106.446
107.435108.447109.435110.447111.436
112.447113.436114.447115.437116.448
117.437118.448119.438120.448121.438
122.449123.438124.449125.439126.449
127.439128.449129.440130.450131.440
132.450133.440134.450135.441136.450
137.441138.450139.441140.451141.442
142.451143.442144.451145.442146.451
61.93962.75263.53964.35365.140
65.95366.74167.55368.34269.154
69.94270.75471.54372.35573.144
73.95574.74475.55576.34577.156
77.94578.75679.54680.35681.146
81.95682.74783.55784.34785.157
85.94886.75787.54888.35889.149
89.95890.74991.55892.34993.158
93.95094.75895.55096.35997.150
97.95998.75199.559100.351101.159
101.951102.759103.552104.360105.152
105.960106.752107.560108.353109.160
109.953110.760111.553112.360113.153
113.961114.754115.561116.354117.161
2.43852.47062.50152.53362.5646
2.59662.62762.65962.69062.7226
2.75362.78562.81672.84862.8797
2.91162.94272.97463.00573.0376
3.06873.10063.13173.16363.1947
3.22663.25773.28963.32083.3526
3.38383.41563.44683.47863.5098
3.54163.57283.60463.63583.6676
3.69883.73063.76183.79373.8248
3.85663.88783.91973.95083.9826
4.01384.04564.07684.10864.1398
4.17164.20284.23464.26594.2976
4.32894.36064.39194.42364.4549
4.48664.51794.54964.58094.6126
75.000 76.000 77.000 78.000 79.000
80.000 81.000 82.000 83.000 84.000
85.000 86.000 87.000 88.000 89.000
90.000 91.000 92.000 93.000 94.000
95.000 96.000 97.000 98.000 99.000
100.000101.000102.000103.000104.000
105.000106.000107.000108.000109.000
110.000111.000112.000113.000114.000
115.000116.000117.000118.000119.000
120.000121.000122.000123.000124.000
125.000126.000127.000128.000129.000
130.000131.000132.000133.000134.000
135.000136.000137.000138.000139.000
140.000141.000142.000143.000144.000
60.000 60.800 61.600 62.400 63.200
64.000 64.800 65.600 66.400 67.200
68.000 68.800 69.600 70.400 71.200
72.000 72.800 73.600 74.400 75.200
76.000 76.800 77.600 78.400 79.200
80.000 80.800 81.600 82.400 83.200
84.000 84.800 85.600 86.400 87.200
88.000 88.800 89.600 90.400 91.200
92.000 92.800 93.600 94.400 95.200
96.000 96.800 97.600 98.400 99.200
100.000100.800101.600102.400103.200
104.000104.800105.600106.400107.200
108.000108.800109.600110.400111.200
112.000112.800113.600114.400115.200
2.36222.39372.42522.45672.4882
2.51972.55122.58272.61422.6457
2.67722.70872.74022.77172.8031
2.83462.86612.89762.92912.9606
2.99213.02363.05513.08663.1181
3.14963.18113.21263.24413.2756
3.30713.33863.37013.40163.4331
3.46463.49613.52763.55913.5906
3.62203.65353.68503.71653.7480
3.77953.81103.84253.87403.9055
3.93703.96854.00004.03154.0630
4.09454.12604.15754.18904.2205
4.25204.28354.31504.34654.3780
4.40944.44094.47244.50394.5354
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ELEMENTS OF METRIC GEAR TECHNOLOGY
T-107
mm Inch mm InchMeas. Over WirePitch Diameter
No.of
Teethmm Inch mm Inch
Meas. Over WirePitch Diameter
No.of
Teeth
TABLE 10-30 (Cont.) METRIC GEAR OVER PINS MEASUREMENTPitch Diameter and Measurement Over Wires for External, Module Type Gears, 20-Degree Pressure Angle
Module 0.80Wire Size = 1.3824mm; 0.0544 Inch
Module 1.00Wire Size = 1.7280mm; 0.0680 Inch
145146147148149
150151152153154
155156157158159
160161162163164
165166167168169
170171172173174
175176177178179
180181182183184
185186187188189
190191192193194
195196197198199
200201202203204
205240280300340
380400440480500
5.7087 5.7480 5.7874 5.8268 5.8661
5.9055 5.9449 5.9843 6.0236 6.0630
6.1024 6.1417 6.1811 6.2205 6.2598
6.2992 6.3386 6.3780 6.4173 6.4567
6.4961 6.5354 6.5748 6.6142 6.6535
6.6929 6.7323 6.7717 6.8110 6.8504
6.8898 6.9291 6.9685 7.0079 7.0472
7.0866 7.1260 7.1654 7.2047 7.2441
7.2835 7.3228 7.3622 7.4016 7.4409
7.4803 7.5197 7.5591 7.5984 7.6378
7.6772 7.7165 7.7559 7.7953 7.8346
7.8740 7.9134 7.9528 7.9921 8.0315
8.0709 9.448811.023611.811013.3858
14.960615.748017.322818.897619.6850
145146147148149
150151152153154
155156157158159
160161162163164
165166167168169
170171172173174
175176177178179
180181182183184
185186187188189
190191192193194
195196197198199
200201202203204
205240280300340
380400440480500
5.8048 5.8445 5.8836 5.9233 5.9623
6.0020 6.0411 6.0808 6.1198 6.1595
6.1986 6.2383 6.2773 6.3170 6.3561
6.3958 6.4348 6.4745 6.5136 6.5533
6.5923 6.6320 6.6711 6.7107 6.7498
6.7895 6.8286 6.8682 6.9073 6.9470
6.9861 7.0257 7.0648 7.1045 7.1436
7.1832 7.2223 7.2620 7.3011 7.3407
7.3798 7.4194 7.4586 7.4982 7.5373
7.5769 7.6163 7.6557 7.6951 7.7344
7.7738 7.8132 7.8525 7.8919 7.9313
7.9707 8.0098 8.0492 8.0885 8.1279
8.1673 9.545511.120411.907813.4826
15.057515.844917.419718.994519.7819
147.443148.451149.443150.451151.443
152.452153.443154.452155.444156.452
157.444158.452159.444160.452161.444
162.452163.445164.453165.445166.453
167.445168.453169.445170.453171.446
172.453173.446174.453175.446176.453
177.446178.453179.446180.454181.447
182.454183.447184.454185.447186.454
187.447188.454189.447190.454191.448
192.454193.454194.454195.454196.454
197.454198.455199.455200.455201.455
202.455203.449204.449205.449206.449
207.449242.456282.457302.458342.459
382.459402.460442.460482.460502.461
117.954118.761119.554120.361121.155
121.961122.755123.561124.355125.162
125.955126.762127.555128.362129.156
129.962130.756131.562132.356133.162
133.956134.762135.556136.362137.157
137.962138.757139.563140.357141.163
141.957142.763143.557144.363145.157
145.963146.758147.563148.358149.163
149.958150.763151.558152.363153.158
153.963154.763155.563156.364157.164
157.964158.764159.564160.364161.164
161.964162.759163.559164.359165.159
165.959193.965225.966241.966273.967
305.967321.968353.968385.968401.968
4.64394.67564.70694.73864.7699
4.80164.83294.86464.89594.9276
4.95894.99065.02195.05365.0849
5.11665.14795.17965.21095.2426
5.27395.30565.33695.36865.3999
5.43165.46295.49465.52595.5576
5.58895.62065.65195.68365.7149
5.74665.77795.80965.84095.8726
5.90395.93565.96685.99866.0298
6.06156.09306.12456.15606.1875
6.21906.25056.28206.31356.3450
6.37656.40786.43936.47086.5023
6.53387.63648.89639.5262
10.7861
12.046012.675913.935715.195615.8255
145.000146.000147.000148.000149.000
150.000151.000152.000153.000154.000
155.000156.000157.000158.000159.000
160.000161.000162.000163.000164.000
165.000166.000167.000168.000169.000
170.000171.000172.000173.000174.000
175.000176.000177.000178.000179.000
180.000181.000182.000183.000184.000
185.000186.000187.000188.000189.000
190.000191.000192.000193.000194.000
195.000196.000197.000198.000199.000
200.000201.000202.000203.000204.000
205.000240.000280.000300.000340.000
380.000400.000440.000480.000500.000
116.000116.800117.600118.400119.200
120.000120.800121.600122.400123.200
124.000124.800125.600126.400127.200
128.000128.800129.600130.400131.200
132.000132.800133.600134.400135.200
136.000136.800137.600138.400139.200
140.000140.800141.600142.400143.200
144.000144.800145.600146.400147.200
148.000148.800149.600150.400151.200
152.000152.800153.600154.400155.200
156.000156.800157.600158.400159.200
160.000160.800161.600162.400163.200
164.000192.000224.000240.000272.000
304.000320.000352.000384.000400.000
4.5669 4.5984 4.6299 4.6614 4.6929
4.7244 4.7559 4.7874 4.8189 4.8504
4.8819 4.9134 4.9449 4.9764 5.0079
5.0394 5.0709 5.1024 5.1339 5.1654
5.1969 5.2283 5.2598 5.2913 5.3228
5.3543 5.3858 5.4173 5.4488 5.4803
5.5118 5.5433 5.5748 5.6063 5.6378
5.6693 5.7008 5.7323 5.7638 5.7953
5.8268 5.8583 5.8898 5.9213 5.9528
5.9843 6.0157 6.0472 6.0787 6.1102
6.1417 6.1732 6.2047 6.2362 6.2677
6.2992 6.3307 6.3622 6.3937 6.4252
6.4567 7.5591 8.8189 9.448810.7087
11.968512.598413.858315.118115.7480
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