9.10 Calculation for types of Gear
Calculation for Standard spur gear
Tooth profile

Description

Full depth tooth

Vocabulary

Modulem

No. of teethZPinionGear
1.5206020°

Rack shift coefficient

αx0.00000.0000Addendum

ha

1.500

1.500

Dedendumhf
h1.875

Tooth depth
Bottom clearancecReference diameterd30.000

90.000Tip (Outside) diameter

da33.000

93.000

Root Diameterdf

26.25086.250Base diameterdbβba28.191

Reference pressure angle

Base helix angle
Centre distance

1.875
3.375
0.375

84.5720° 0’ 0”60.0000
20° 0’ 0”Intermeshing PCD

αw
dw

30.00090.000

Chordal heighth1.546

1.515

Chordal tooth thickness

s2.354

2.356

Sector span of teeth

zmW(3)(7)

11.49130.044

Working pressure angle

Sector spanOver balls or Rollers

dp

2.500

2.500

Over balls or Rollers dimensiondm

33.26893.309Calculation for Standard internal gear
Tooth profile

Vocabulary

Modulem

No. of teeth

zPinion

Gear
120

100
20°

2.250

2.250

0.250

0.250

Reference diameter

αhahf
hc
d20.000

100.000

Tip (Outside) diameterda22.000

98.000

Root diameterdf
α17.500102.500

Pressure angle
Addendum
Dedendum
Tooth depth
Bottom clearanceCentre distanceTransverse contact ratio
Sector span of teeth
Sector span118

Description

Full depth toothεazm
W

1.000

1.000

1.250

1.250

40.000
1.860
(3)

(12)

7.660

35.350Calculation for Normal standard helical gear (based on Centre distance)
Description

Tooth profile
ModuleNo. of teeth
Reference pressure angle
Reference cylinder helix angle
Direction of helix
Rack shift coefficient
Addendum
Dedendum
Tooth depth
Bottom clearance
Reference diameter
Tip (Outside) diameter
Root diameter
Base diameter
Base helix angle
Centre distanceWorking pressure angle
Intermeshing PCD
Chordal height

Chordal tooth thickness
Sector span of teeth
Sector spanOver balls or Rollers
Over balls or Rollers dimension

Vocabularymnz
αβxnhahfhcddadfdb
βba
αwdw

PinionGear
230

Tooth profile
ModuleNo. of teeth
Reference pressure angle
Reference cylindrer helix angle
Direction of helix
Rack shift coefficient
Addendum
Dedendum
Tooth depth
Bottom clearance
Reference diameter
Tip (Outside) diameter
Root diameter
Base diameter
Base helix angle
Centre distance
Normal working pressure angleTransverse working pressure angle
Intermeshing PCD
Shaft angle
Chordal height
Chordal tooth thickness
Sector span of teeth
Sector spanOver balls or Rollers
Over balls or Rollers dimension

60

20°
20° 0’ 0”Right
0.00000
2.000
2.500

Left
0.0000
2.000
2.500
4.500
0.500

63.85167.85158.85159.54018° 44’ 50”
95.7760
21° 10’ 22”

127.701
131.701
122.701
119.081h63.8512.034

127.701
2.017

szm
W
dpdm

3.141(5)27.5723.500
68.8443.141(9)52.1933.500
132.743

Calculation for Normal standard crossed helical gear (Screw gear)
Description

Full depth tooth

Vocabulary
mnz
αβxn
hahf
hcddadf
db
βba
α wn
α wt
dw
∑

Full depth tooth

PinionGear
213
45° 0’ 0”Right
0.0000
2.000
2.500

20°

26
45° 0’ 0”
Left
0.0000
2.000
2.500

4.500
0.500
36.77040.77031.77032.69341°38’ 28”
20° 0’ 0”
27° 14’ 11”
36.77073.53977.53968.53965.386
41° 38’ 28”
55.154390° 0’ 0”

20° 0’ 0”
27° 14’ 11”
73.539h2.034

2.017

szm
Wdpdm

3.141
(5)
27.531
3.500
41.4873.141(9)52.1103,500
78.583119Calculation for Normal worm gear and Worm wheel
Description

Tooth profile
ModuleReference pressure angle
Addendum
Dedendum
Tooth depth
Lead
Reference pitch
Reference cylinder lead angle
Centre distanceType of Worm wheel
No. of thread / No. of teeth
Reference diameter
Outside diameter
Root diameter
Rack shift coefficient
Diameter quotientThroat diameter
Gorge radius
Facewidth
Chordal height
Chordal tooth thickness

Vocabulary

Full depth tooth

Worm gear

mnαhahfhpz
PγaWorm wheel
1.5 (ma=1.5027)
20° (α a=20° 2’ 0”)
1.500
1.875
3.375
4.72094.72093° 26’ 23”
42.500h∗∗∗∗∗∗
1
25.00028.00021.250∗∗∗∗∗∗
16.6366∗∗∗∗∗∗∗∗∗∗∗∗
30.00
1.500

Type I40
60.10865.26056.250-0.0360∗∗∗∗∗∗
63.000
11.00
15.00
1.468

s

2.356

2.316

zw/z2
ddadf
xQ
dTrtb

Calculation for Standard straight bevel gear
Tooth profile
ModuleNo. of teeth
Reference pressure angle
Facewidth
Addendum
Dedendum
Tooth depth
Bottom clearance
Shaft angle
Cone distance
Reference diameter
Pitch angle
Addendum angle
Dedendum angle
Tip angle
Root angle
Outer tip diameter
Inner tip diameter
Pitch apex to crown
Axial facewidth
Tooth thickness
Tooth angle
Angle of material
Angle of material
Chordal tooth thickness

Description

Chordal height
Virtual number of teeth of spur gear(1)Note(1) old gear terms adopted.

120

Full depth tooth

Vocabulary
mz
αbha
hfhc
∑
Red
δ
θaθf
δa
δfda
diX
XbS

PinionGear
1.5

2030.000
26° 33’ 54”

29° 7’ 32”
23° 21’ 56”
32.68322.93929.329
8.744

θxθys

87° 26’ 22”
63° 26’ 6”
2.354

hzv

1.541
22.36120°
101.500
1.8753.375
0.375
90° 0’ 0”33.5412° 33’ 38”
3° 11’ 59”

2.356
190.71(min)40

60.00063° 26’ 6”

65° 59’ 44”
60° 14’ 7”
61.34243.05313.6584.072

87° 26’ 22”
26° 33’ 54”
2.356
1.510
89.443

Calculation for Gleason system Straight bevel gear
Tooth profile
ModuleNo. of teeth
Reference pressure angle
Facewidth
Shaft angle
Working depth
Tooth depth
Cone distance
Reference diameter
Pitch angle
Addendum
Dedendum
Bottom clearance
Addendum angle
Dedendum angle
Tip angle
Root angle
Outer tip diameter
Inner tip diameterPitch apex to crown
Axial facewidth
Tooth thickness
Tooth angle
Material angle
Material angle
Chordal height

Description

Chordal addendum
Virtual No. of tooth of spur gear

Vocabularymzαb∑hwhRedδ
hahfc
θaθf
δa
δfdadiX
XbS

Full depth toothPinion

Gear
1.5

20

30.00026° 33’ 54”
2.018
1.265

θx
θys

3° 55’ 19”
2° 9’ 33”
30° 29’ 13”
24° 24’ 22”
33.60923.43829.0988.638
2.733
187.2 (min)
86° 4’ 41”
63° 26’ 6”
2.729

hzv

2.073
22.36120°
1090° 0’ 0”
3.000
3.332
33.54100.332∑hwhRedδhahfθaθfδaδfdadiX
XbSθxθyzv

2° 9’ 33”
3° 55’ 19”
65° 35’ 38”
59° 30’ 47”
60.87942.65314.1214.135
1.979
187.2 (min)87° 50’ 27”
26° 33’ 54”
1.979

Full depth tooth

Vocabularymz
αbβ60.00063° 26’ 6”
0.983
2.300

0.990
89.443Calculation for Gleason system Spiral bevel gear
Description
Tooth profile
ModuleNo. of teeth
Reference pressure angle
Facewidth
Reference cylinder spiral angle
Hand of spiral
Shaft angle
Working depth
Tooth depth
Cone distance
Reference diameter
Pitch angle
Addendum
Dedendum
Addendum angle
Dedendum angle
Tip angle
Root angle
Pitch apex to crown
Inner tip diameter
Outer cone distance
Axial facewidth
Tooth thickness
Angle of material
Angle of material
Virtual number of teeth of spur gear(1)Note(1) old gear term adopted.

40

Pinion20

左ねじれ30.00026° 33’ 54”
1.714
1.118
3° 24’ 19”
1° 54’ 34”
29° 58’ 13”
24° 39’ 20”
33.06623.05729.2348.678
2.834
86° 35’ 41”
63° 26’ 6”40.681Gear
1.5
20°
10
35° 0’ 0”
90° 0’ 0”
2.550
2.832
33.54140

右ねじれ60.00063° 26’ 6”
0.836
1.996
1° 54’ 34”
3° 24’ 19”
65° 20’ 40”
60° 1’ 47”
60.74842.56114.2524.174
1.878
88° 5’ 26”
26° 33’ 54”
162.724121