10.2 Calculation for Bevel gear strength
Calculation formula of Bending strength for Bevel gear JGMA 403-01 (1976)
Calculation formula of Surface durability (Pitting resistance) for Bevel gear JGMA 404-01 (1977)
1. Application range (common)

1.1 This standard applies to Bevel gears (1) for powertransfer used in the general industrial machinerywith the following range.
Outer transverse module : 1.5 ～ 25 mm
Outer pitch diameter:	Below 1,600 mm (ForStraight bevel gear)		Below 1,000 mm (For
Spiral bevel gear)
Outer circumferential velocity : Below 25 m/s
Revolving velocity: Below 3,600 min-1
Shaft angle: 90°
Mean spiral angle: Below 35°
Facewidth
For Maximum Facewidth, choose the smaller
value from either 0.3 times of Cone distance or 10
times of Outer transverse module. However for
Zerol® Bevel gear, it is 0.25 times of Outer cone
distance.
Ⓡ mark is Gleason Works Trademark.

2 Definition

2.1 Bending strength
Bending allowable load of Bevel gear is stipulated as
Nominal allowable tangential load on the Mean pitch
circle based on Allowable tooth root bending stressfor each gear when transferring power during operation.
2.2 Surface durability
Surface durability of Bevel gear is stipulated as load
capacity that is necessary to provide sufficient safety
to the gear against progressive pitting.
Therefore, Allowable load on Bevel gear flank is stipulated as Allowable tangential load on the Mean pitch
circle based on Surface durability for each gear whentransferring power during operation.

3. Basic formula

For calculating gear strength, conversion formulas are
related to calculating Nominal tangential load on the
Reference pitch circle. Nominal power and torque areas follows.

Tooth profile
Normal reference pressure angles are 20 °, 22.5°
and 25°.

3.1 Nominal tangential load on the Mean pitch circle
Ftm(kgf)

Accuracy
Accuracy of Bevel gear is defined in JIS B1704 class
1 to 6.

HerebyP : Nominal power (kW)υ m : C ircumferential velocity (m/s) on the Mean
pitch circle
dm : Mean pitch diameter (mm)n : Revolving velocity (min-1)

Note (1)	This standard is for Straight, Spiral and Zerol
bevel gears.
1.2.1. U
 se this standard for calculation of Bending ofBevel gear for Allowable load as defined abovein 1.1 and to determine gear dimensions basedon Tooth root bending stress.
1.2.2 T his standard used for calculation of tooth flankof allowable load for Straight, Spiral bevel gears
and determines gear dimension based on Hertz
stress of tooth flank.

Ftm =102 P 1.95 × 106 P=. .................................................. (1)
ȣm
d mn

d mn
.............................................................................. (2)19100
d m = d − bsinį ........................................................................ (3)ȣm =Herebyd : Pitch diameter (mm)
δ : Pitch angle (°)
Or Ftm =2000T. ....................................................................... (4)dmHerebyT : Nominal torque (kgf・m)
3.2 Nominal power P (kW)P=

Ftm ȣm
= 5.13 × 10−7 Ftm d m n ........................................... (5)
102

137

3.3 Nominal torque T (kg・m)
T=
Or T =

Ftm d m. ........................................................................... (6)
2000
974 P
............................................................................. (7)n4. Calculation formula for gear strength

4.1 Calculation for Bending strength
When calculating Bending strength, use Nominal
tangential load on the Mean pitch circle as reference.
Therefore Nominal tangential load on the Mean pitch
circle should be equal or less than Allowable tangential load on the Mean pitch circle calculated by Allowable tooth root stress. That is to say,
Ftm ҇ Ftmlim ............................................................................... (8)4.1.2 C alculation for Tooth root bending stress is asfollow.

σ F = Ftm

YFYεYβYCRe§ KMKVKO · KR¨¸
0.85cos β m mb Re − 0.5b © KLKFX ¹ . ........ (11)4.2 Calculation for Tooth root strength
Nominal tangential load on the Mean pitch circle
is necessary as reference for calculating Surface
strength. Therefore, Nominal tangential load on the
Mean pitch circle should be equal or below Allowabletangential load on the Mean pitch circle, which is derived from calculating Allowable Hertz stress. Therefore,
Ftm ҇ Ftmlim . ........................................................................... (12)HerebyFtm

HerebyFtm: Nominal tangential load on the Mean pitch
circle (kgf)
Ftmlim : Nominal allowable tangential load (kgf ) on
the Mean pitch circle is selected from its
smaller value from either pinion or gear.
On the other hand, Tooth root stress obtained from
Nominal tangential load on the Mean pitch circle
should be equal or lesser than Allowable Tooth root
bending stress.
Thereforeı F ҇ ı Flim ................................................................................ (9)HerebyσF: Tooth root stress (kgf/mm 2) from Nominal
tangential load on the Mean pitch circle.
σ F lim : Allowable Tooth root bending stress (kgf/mm2): Nominal tangential load on the Mean pitch
circle (kgf)
Ftmlim : C alculate Allowable tangential load (kgf )on the Mean pitch circle by selecting thesmaller Allowable tangential load (kgf) fromeither pinion or gear.
On the other hand, Hertz stress based on Nominal
tangential load on the Mean pitch circle should beequal or less than Allowable hertz stress.
Thereforeσ H ҇ σ Hlim ............................................................................. (13)HerebyσH: H ertz stress (kgf/mm 2) from Nominal tangential load on the Mean pitch circle
σ Hlim : Allowable hertz stress (kgf/mm2)
4.2.1 Calculation for Allowable tangential load on the
Mean pitch circle is as follow.
2

4.1.1 C alculation for Allowable tangential load on the
Mean pitch circle is as follow.
Ftmlim = 0.85cos β m σ Flim mb

1
Re − 0.5b
×
Re
YFYεYβYC§ KLKFX · 1¨¸..................................................... (10)© KMKVKO ¹ KR

Herebyβ m : Mean spiral angle (°)
m : Outer transverse module (mm)b : Facewidth (mm)
Re : Cone distance (mm)YF : Form factor
Yε : Load distribution factor
Yβ : Spiral angle factor
Yc : Cutter diameter influence factor
KL : Life factor
KFX : Dimension factor for Tooth root stress
KM : Load distributed factor for Tooth trace
Kv : Dynamic factor
K0 : Overload factor
 eliability factor for Tooth root bending damage
KR : R138§ σ Hlim · d 1 Re − 0.5b
u2•b
Ftmlim = ¨
¸
2
1
M
cos
δ
e
u
+1
Z
R
©
¹
2

� KHLZLZRZVZWKHX �
1
1
��
��
2
ZH Z ε Zβ�� K Hβ KVKO CR. .................. (14)Herebyd1 : Outer pitch diameter for pinion (mm)b : Facewidth (mm)u : Gear ratio
Re : Cone distance (mm)
ZH : Zone factor
ZM : Elasticity factor
Zε : Contact ratio factor
Zβ : Spiral angle factor for Surface durability
KHL : Life factor for Surface Durability
ZL : Lubricating oil factor
ZR : Roughness factor
ZV : Lubricating speed factor
ZW : Work hardening factor
ZHX : Dimension factor for Surface durability
KHβ : Face load for contact stress for Surface durability:
Dynamic
factorKV

KO : Overload factor
CR : Reliability factor for Surface durability

Herebyδ : Pitch angle (°)
x=

σH =

cos�1Ftm u 2 + 1
Re
ZHZM Z ε Zβ×d 1b
u 2 Re − 0.5b KHLZLZRZVZWKHX

K Hβ KVKO CR . ......................................... (15)5 Calculation method for factors

5.1 Calculation method for factors based on Bending(tooth root) strength of Bevel gear.
Factors used in calculation formulas for Bending(tooth root) strength as mentioned above are stipulated as follows.
5.1.1 Facewidth b
Facewidth b is stipulated as Facewidth on Pitch cone.
For different Facewidth, use narrower side from either
pinion or gear as Effective facewidth.
5.1.2 Form YF
Obtain Form factor from Fig. 1 and 2.
(a) R efer to Table 1, items 5 and 6 where Normal reference pressure angle is 20°.
Use Form factor graphs in Fig. 2 and 3 to obtain primary value of YFO (Value of Form factor by Rack shift).
Then obtain Revision factor C using Horizontal rackshift from Fig. 1.
YF=CYF0................................................................................. (16)
Calculate YF from formula YF=CFY0. However, Tooth
profile with no Horizontal rack shift to be YF=YF0.
a.1 Refer to Table 1 for lists of Form factor chart.
Calculate Virtual number of teeth of spur gear Zυ andRack shift coefficient x using following formula.
zυ =z............................................................... (17)cosδ cos3 β m

h a − ha 0
. ........................................................................ (18)m

Herebyha : Outer addendum (mm)hao : Refer to Table 1 for Reference profile addendum (mm)m : Outer transverse module (mm)a. 2. For Bevel gear with tip of cutter with γ about 0.375
mm, constant 0.85 to be changed to 1.0 in theformulas for Allowable tangential load and Bending stress. (Refer to 4.1.1 of standard σ F lim).
a. 3. Calculate Horizontal rack shift coefficient K in Fig.
1 using the following formula.

K=2( ha − ha 0)tan α n ½1­® s − 0. 5 π m −¾ ........................ (19)cos β mm¯¿Hereby		s : O uter transverse circular thickness(mm)		ha, hao and m : Same as formula (14).
However the above formula for K is inapplicable for
an Isothermal full depth gear tooth.
Fig. 1 Revision factor base on Horizontal Rack shift
1.6
1.5
1.4
Revision coeﬃcient C

4.2.2 Calculation for Hertz stress is as follow.

1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
- 0.3

- 0.2

- 0.1

0

0.1

0.2

0.3

Horizontal rack shift coeﬃcient K

Table 1. Table for Form factor
Transverse reference profile (Transverse tooth thickness : 0.5π m)
Item No.

Normal reference
pressure angle
αnTooth depth(heel)h

Addendum(heel)
hα 0Dedendum(heel)
hf0

Bottom clearance(heel)
c

Cutter tip radius(normal)
r

2
4

20°

1.888m0.850m1.038m2.188m1.000m1.188m1.888m0.850m1.038m1.788m0.800m

0.988m1.888m0.850m1.038m1.788m0.800m

0.988m0.188m

0.12m

6
8
9
10

22.5°
25°

25°
30°
35°
0°

5
7

βm
15°
20°

1
3

Mean spiralangle

0.188m

0.12m

35°
0°

0.188m

0.12m

35°
0°

139

Fig. 2 Form factor graph (No.6)
4.1

Reference pressure angle  n = 20°
Addendum ha0 = 0.850m

4.0

Dedendum hf 0 = 1.0338m
3.9

Cutter tip radius r = 0.12m
Spiral angle  m = 35°

3.8
- 0.4

3.7
- 0.3

3.6

3.6

- 0.2
3.5

3.5

- 0.1

3.4

3.4

3.3

3.3

3.2

Form factor YF0

3.7
x = - 0.5

3.2

x=0

3.1

3.1

3.0

3.0
0.1

2.9

2.9

2.8

2.8
0.2

2.7

2.7
2.6

2.6
0.3

2.5

2.5
0.4

2.4

2.4
2.3

x = 0.5

2.3
2.2

2.2

2.1

2.1

2.0

2.0

1.9

1.9

1.8

1.8

1.7

12

13

14

15

16

17

18 19 20

25

30

35

Virtual number of teeth of spur gear Z

140

40 45 5060

80 100200 400

1.7∞

Fig. 3 Form factor graph (No.5)
4.1

Reference pressure angle  n = 20°
Addendum ha0 = 1.000m

4.0

Dedendum hf 0 = 1.1188m
3.9

Cutter tip radius r = 0.12m
Spiral angle  m = 0°

3.8
- 0.3

3.7

- 0.4

x = - 0.5
3.7

- 0.2

3.6

3.6

- 0.1

3.5

3.5

x=0

3.4

3.4

3.3

3.3

3.2

3.2

0.1

Form factor YF0

3.1

3.1

3.0

3.0
0.2

2.9

2.9

2.8

2.8
0.3

2.7
2.6

2.7
2.6

0.4

2.5

2.5
x = 0.5

2.4

2.4

2.3

2.3

2.2

2.2

2.1

2.1

2.0

2.0

1.9

1.9

1.8

1.8

1.7
12

13

14

15

16

17 18 19 20

25

30

35

40 45 50 60

80 100200 400

1.7∞

Virtual number of teeth of spur gear Z

141

5.1.3 Load distribution factor Yε
Calculation of Load distribution factor is as follows.
Yε =

(b) R
 efer to Fig. 5 to calculate Transverse contact ratio

1εα . ................................................................................ (20)Herebyε α : Transverse contact ratio

ε a for Straight bevel gear with Reference pressure angle 20° or Spiral bevel gear with Normalpressure angle 20°. Use formula (16) to calculate
Virtual number of teeth of spur gear Zυ and thefollowing formula for u.

(a) Obtain Transverse contact ratio using following
formula (21-24). However use Straight bevel gear’s calculation formula for Zerol Bevel gear.

ha
Straight bevel gear : u = m . ........................................ (25)Straight bevel gear

Herebyha : Outer addendum (mm)m : Outer transverse module (mm)β m : Mean spiral angle (°)
From Fig. 5, calculate Transverse contact ratio ε α us-

Rra12 − Rrb 2 2 + Rra 2 2 − Rrb 2 2 − ( Rr1 + Rr 2)sinα..... (21)mπ cosαUse following summarized calculation formula (1) for
gear ratio u ≧ 2εα =Rra12 − Rrb12 + ha 2cosecα − Rr1sinα. ................. (22)mπ cosαSpiral bevel gearεα =Rra12 − Rrb12 + Rra 2 2 − Rrb 2 2 − ( Rr1 + Rr 2)sin α t . ..
(23)mπ cos α t
Use following summarized calculation formula (1) for
gear ratio υ ≧ 2εα =Rra12 − Rrb12 + ha 2cosecα t − Rr1sin α t............... (24)mπ cos α t
Note (1)	Formulas (21) and (23) becomes complicated for Gear section thus Gear is assumed
as Rack to show a summarized formula asfollows.
Hereby (refer to Fig. 4)εα =Rυ a : Tip diameter (mm) for Virtual spur gear on the
Back cone = Rυ + ha = γ secδ + haRυ b : Base radius (mm) for Virtual spur gear on the
Back cone
For Straight bevel gear = Rυ cosα =γ secδ cosα
For Spiral bevel gear = Rυ cosα t=γ secδ cosαt
Rυ : Back cone distance (mm) = γ secδγ : Radius of pitch circle (mm) = 0.5 zm
ha : Outer addendum (mm)α : Reference pressure angle (°)α t : Mean transverse pressure angle (°)
		= tan-1(tanα n / cosβ m)
α n : Normal reference pressure angle (°)β m : Mean spiral angle (°)δ : Pitch angle (°)
m : Outer transverse module (mm)z : Number of teeth
Subscript
1 : Pinion
2 : GearSpiral bevel gearha
: u = mcos β m ................................ (26)

ing following formulas.
Straight bevel gear : ε α = ε 1 + ε 2
Spiral bevel gear : ε α = Κε ’α
ε ’α = ε 1 + ε 2		Herebyεα: Transverse contact ratio for Straight bevelgear
ε ’α : Virtual spur gear transverse contact ratio for
Spiral bevel gear
ε 1, ε 2 : Obtain Virtual spur gear contact ratio from
Pitch point to Tooth tip for pinion and gearfrom Fig. 5: Use Table 2 conversion factor for Virtual spurkgear normal contact ratio to Transverse contact ratio for Spiral bevel gear.
		= cos2α n (cos2β m + tan2α n)αn: Normal reference pressure angle (°)β m : Mean spiral angle (°)
Fig. 4 Engagement of Virtual spur gear on the Back cone

For Spiral bevel gear,
use A and A t.

Table 2. Value of Conversion factor for Transverse contact ratio for Spiral bevel gear

142

Mean spiral angle β m
NormalReference pressure angle α n

15°

20°

25°

30°

35°

20°

0.940850.89671

0.842290.779240.70949

Fig. 5 Table to obtain Contact ratio

Reference pressure angle An = 20º
1.3

1.2

u =1.5
1.1
1.4
1.3

1.0

Contact ratio from Pitch point to tooth tip (E1 or E2)

1.2
0.9
1.1

1.0

0.8

0.9
0.7
0.8

0.7

0.6

0.6
0.5
0.5
0.4
0.4

0.3
0.3

12

15

20

30

Virtual number of teeth of Spur gear

Virtual number of teeth of Spur gear

(

zr =

zG z=

50

70

100

200

∞

z

)

cosD cos³ Bm3cos δ cos β m143

5.1.4 Spiral angle factor Yβ
Calculate Spiral angle factor using following formulas.
(Refer to Table 3 and Fig. 6)

5.1.6 Life factor KL
Refer to Table 2 of 5.1.5 under Spur gear.
5.1.7 Dimension factor for Tooth root factor KFXObtain Dimension factor for Tooth root factor fromtransverse module in Table 5.

βm

For 0° ≦ β m ≦ 30° : Yβ = 1 − 120 .................................... (27)
: Yβ = 0.75 ......................................... (27)'For β m ≧ 30°

Table 5. Dimension factor for Tooth root factor KFXTable 3. Spiral angle factor
βm

15°

20°

25°

Yβ

0.875

0.833

0.792

30°

35°
0.75

Fig. 6 Spiral angle factor

Spiral angle factor YB

1.00

0.90

0.80

Outer transverse modulem

Non surface
hardening gear

Surface hardeninggear

1.5 ＜ d ≦ 5

1.0

1.0

5 ＜d≦ 7

0.99

0.98

7 ＜d≦ 9

0.98

0.96

9 ＜ d ≦ 11

0.97

0.94

11 ＜ d ≦ 13

0.96

0.92

13 ＜ d ≦ 15

0.94

0.90

15 ＜ d ≦ 17

0.93

0.88

17 ＜ d ≦ 19

0.92

0.86

19 ＜ d ≦ 22

0.90

0.83

22 ＜ d ≦ 25

0.88

0.80

5.1.8 Tooth distributed factor for Tooth load KM
Calculate load distribution factor for Tooth trace from
Tables 6 and 7.

0.75
0

10

20

30

40

5.1.9 Dynamic load factor KV
Using Gear accuracy and Circumferential speed on
the Outer pitch circle from Table 8 to obtain Dynamic
factor.

Mean Spiral angle Bm (º)

5.1.5 Cutter diameter influence factor YC
Calculate Cutter diameter influence factor from Table
4 based on ratio cutter diameter for Length of tooth
trace. If cutter diameter is unknown, YC=1.0. Length oftooth trace to be b / cosβ m (mm).

5.1.10 Overload factor K0
Refer to formula (23) and Table 4 of 5.1.8 under Spurgear.

Table 4. Cutter diameter influence factor YC
Cutter diameter

Types

∞

6 times Length of tooth trace

5 times Length of tooth trace

4 times Length of tooth trace

Straight bevel gear

1.15

-

-

-

Spiral bevel gear
Zerol Bevel gear

-

1.00

0.95

0.90

Table 6. Tooth trace load distribution factor KM for Spiral bevel, Zerol bevel and Straight bevel gears (Crowning)

Stiffness of axis and gearbox

Full support to both gears

Support to one side of gear

Support to both gears on one side

Especially strong

1.2

1.35

1.5

Normal

1.4

1.6

1.8

Weak

1.55

1.75

2.0

Table 7. Tooth trace load distributed factor KM for Straight bevel gear without Crowning

Stiffness of axis and gearbox

144

Full support to both gears

Support to one side of gear

Support to both gears on one side

Especially strong

1.05

1.15

1.35

Normal

1.6

1.8

2.1

Weak

2.2

2.5

2.8

Table 8. Dynamic factor KV
Circumferential velocity (m/s)

System of accuracy
from JIS B1704

Below 1

1 ＜υ ≦ 3

3 ＜υ ≦ 5

5 ＜υ ≦ 8

8 ＜ υ ≦ 12

12 ＜ υ ≦ 18

18 ＜ υ ≦ 25

1

1.0

1.1

1.15

1.2

1.3

1.5

1.7

2

1.0

1.2

1.3

1.4

1.5

1.7

-

3

1.0

1.3

1.4

1.5

1.7

-

-

4

1.1

1.4

1.5

1.7

-

-

-

5

1.2

1.5

1.7

-

-

-

-

6

1.4

1.7

-

-

-

-

-

5.1.11 Reliability factor KR
Reliability factor is as follows(1) General cases KR = 1.2(2) Special cases
If clearly understood the usage conditions of impact
from prime mover, driver side, stiffness of gearbox
and axis for calculating Tooth bending strength.
When determining numerical values of KM, KL, K0 using. ..................................................................................... KR =1.0.
In situations opposite from above where numericalvalues of K0 and KM are uncertain (use KL as 1.0 in thiscase)................................................................................... KR = 1.4

5.2.4 Contact ratio factor ZεObtain Contact ratio factor using following formula.
Refer to Fig. 4 of 5.2.4 under Spur gear.
Straight bevel gear : Zε =1.0. ............................................ (29)
Spiral bevel gear :In case of ε β ≦ 1,
In case of ε β ＞ 1,

5.2 H
 ow to calculate factors from calculation formulafor Surface durability.
The following stipulates types of factor from calculation formula of Surface durability in previous paragraph.

2.3

ZH =

2cos β b. ............................................................ (28)sin α t cos α t

Herebyβ b : tan-1(tanβ m cosα t)
α t : Mean transverse pressure angle (°)α n : Normal reference pressure angle (°)β m : Mean spiral angle (°)
Obtain domain factor from Fig. 7 with Normal reference pressure angle 20°, 22.5°and 25°.
5.2.3 Elasticity factor ZM
Refer to Table 6 of 5.2.3 under Spur gear

1

ε α ............................................ (31)

2.6
2.5

5.2.2 Domain zone ZH
Calculation of Domain zone is as follows.

Zε =

εβ
ε α ............................. (30)

Fig. 7 Zone factor

5.1.12 Allowable tooth root bending stress σ Flim
Refer to Tables 9, 10 and 13 of 5.1.10 under Spur gear.

5.2.1 Facewidth b (mm)Facewidth b is stipulated to the Facewidth on Pitch
cone. For different Facewidth between Pinion andGear, select the narrower Effective facewidth.

Zε = 1 − ε β +An =20°Zone factor ZH

2.4

22.5°
25°

2.2
2.1
2.0
1.9
1.8
1.7

0°

Hereby5° 10° 15° 20° 25° 30° 35° 40° 45°
Mean spiral angle Bmε α : Transverse contact ratio
ε β : Overlap ratio
Calculate Transverse contact ratio from 5.1.3 (a) underBevel gear.
Overlap ratio is defined below
btan β mReεβ =..................................................... (32)Re − 0.5b π m
HerebyRe : Cone distance (mm)b : Facewidth (mm)β m : Mean spiral angle (°)
m : Outer transverse module (mm)5.2.5 Spiral angle factor for Surface durability Zβ
Spiral angle factor for Surface durability is difficult to
stipulate accurately due to insufficient data. Calculation formula is Zβ ＝ 1.0...................................................... (33)145

Lubricating oil factor ZL

5.2.6 Life factor for Surface durability KHL
Refer to Table 7 of 5.2.6 under Spur gear.

Lubricating oil factor ZL

5.2.7 Lubricating oil factor ZL
For the 2 types of gear stated below, obtain Lubricating oil factor from Fig.8 based on Kinematic viscosity(cSt) at 50°C.
Fig. 8 Lubricating oil factor
1.2
1.0

Surface hardened gear0

1.0

Surface hardened gear

0.9
0.8
0.5

1
2
4
6 8 1020 25 (40) (60)
Circumferential velocity U(m/s) on the Outer pitch circle

Nitriding
steel

100
200
Kinematic viscosity (cSt) at 50ºC

300

SACM 645
and others

5.2.8 Roughness factor ZR

Material

Carbon steel and Alloysteel for structural use

1.1

0.7

Surface hardened gear

Thermal reﬁned gear

1

5

15
20
10
Average roughness Rmax m (Mm)25

5.2.9 Lubricating speed factor ZV
For the 2 types of gear stated below, obtain Lubricating velocity factor from Fig. 10 based on Circumferential velocity υ (m/s) on the Outer pitch circle.
(1) Thermal refined gear (1): Use solid line in Fig. 10.
(2) Surface hardened gear: Use broken line in Fig. 10.
Refer to 5.2.7 for Note (1) and Remark

146

130 - 140

Nitriding
period (h)σ Hlim kgf/mm2
Relative curvature radius (mm) (2)Below 10

10 - 20

Above 20

2

100

90

80

4

110

100

90

6

120

110

100

Fig. 11 Relative curvature radius
Relative curvature radius (mm)Roughness factor ZR

Herebya = Rm (sinδ 1 + cosδ 1)
Rm : Mean cone distance (mm)
δ 1 : Pitch angle (°) of Pinion(1) Thermal refined gear (1): Use solid line in Fig. 9.
(2) Surface hardened gear: Use broken line in Fig. 9.
Refer to 5.2.7 for Note (1) and Remark
Fig. 9 Roughness factor

0.8

120

Note (1)	Applicable to Salt bath and Gas Nitro-carburizing gears.
(2)	Use Fig. 11 to obtain Relative curvature radius
Remark. Use properly adjusted material for core.

R max1 + R max 2 3 100( µ m) ................................... (34)
2
a

0.9

NormalSustained period of
Nitriding treatment

Table 12. Nitrocarburizing gear (1)For 2 types of gear stated below, obtain average ofmaximum height of profile factor from Fig. 9 basedon mean roughness of flank Rmaxm(μ m). Use the following formula to obtain the average of maximum
height of profile roughness of flank Rmaxm from Rmax1,
Rmax2. (Meaning of Rmax1, Rmax2 is Maximum height if
profile roughness of flank inclusive of the effects ofwarm up and test run.)

1.0

Above HV 650

σ Hlim kgf/mm2

Note (1)	Applicable to Gear with proper Nitriding
depth and hardened surface to improve
Surface durability. When Surface hardness isremarkably lower than above table. Starting
point of maximum shear-stress force at innergear tooth is remarkably deeper than depthof Nitriding, take note of providing a larger
safety factor than usual.

(1) Thermal refined gear (1): Use solid line in Fig. 8.
(2) Surface hardened gear: Use broken line in Fig. 8.
Note (1)	Thermal refined gear includes gear with
quenching, tempering and normalizing.
Remark: Casting steel gear is equivalent to thermal
refined gear.

R max m =Flank hardness(reference)

Material

0.9
0.8

Thermal reﬁned gear

1.1

Table 11. Nitriding gear (1)Thermal reﬁned gear

1.1

Fig. 10 Lubricating speed factor

1.2

20
20

10

0

Gear ratio
1

60

2
3
4

50
40

5
6

30

20
15

10

10
8
7
6
5

80 100

150

400
200
300
Centre distance A (mm)500 600 700 800

5.2.10 Hardness ratio factor ZW
Refer to formula (35) and Table 8 from 5.2.10 under
Spur gear.
5.2.11 Diameter factor KHX for Surface durability
If Tooth profile and gear size increases, Surface durability also increases but has a tendency to increase
disproportionately. Due to insufficient data at the
moment, Dimension factor KHX = 1.0 .......................... (35)5.2.12 T ooth trace load distribution factor KHβ for Surface durability
Obtain Tooth trace load distribution factor for Surface
durability from Tables 9 and 10. If both gears are without surface hardening, use 90% of values from Tables
9 and 10.
Table 9. T ooth trace load distribution factor KHβ for
Spiral Bevel, Zerol Bevel and Straight bevel
gears (including Crowning)
Condition for gear support
Stiffness of axis andFull support to Support to one Support to both
gearboxboth gears
side of gear
gears on one side
Especially strong

1.3

1.5

1.7

Normal

1.6

1.85

2.1

Weak

1.75

2.1

2.5

Table 10. T ooth trace load distribution factor KHβ for
Straight bevel gear without Crowning.
Condition for gear support
Stiffness of axis andFullsupportto Support to one Support to both
gearboxboth gears
side of gear
gears on one side
Especially strong

1.3

1.5

1.7

Normal

1.85

2.1

2.6

Weak

2.8

3.3

3.8

5.2.13 Dynamic factor KV
Refer to Table 8 from 5.1.9 under Bevel gear.
5.2.14 Overload factor Ko
Refer to formula (23) and Table 4 of 5.1.8 under Spurgear.
5.2.15 Reliability factor CR
Reliability factor for Surface durability is above 1.15.
5.2.16 Allowable hertz stress σ Hlim
Refer to Tables 9 ~ 12 for Allowable hertz stress. For
values not listed, use interpolation. Meaning of flank’s hardness is hardness near Pitch circle.

147