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17.1.11 Example of Bending Strength Calculation

Table 17-8A   Bending Strength Factors

No.

Item

 Symbol Unit Pinion Gear
1 Normal Module mn mm 2
2 Normal Pressure Angle an degree 20º
3 Helix Angle b 0º
4 Number of Teeth z   20 40
5 Center Distance ax mm 60
6 Coefficient of Profile Shift x   +0.15 -0.15
7 Pitch Circle Diameter d mm 40.000 80.000
8 Working Pitch Circle Diameter dw 40.000 80.000
9 Tooth Width b 20 20
10 Precision Grade     JIS 5 JIS 5
11 Manufacturing Method Hobbing
12 Surface Roughness 12.5 mm
13 Revolutions per Minute n rpm 1500 750
14 Linear Speed v m/s 3.142
15 Direction of Load     Unidictional
16 Duty Cycle   Cycles Over 107 cycles
17 Material     SCM 415
18 Heat Treatment Carburizing
19 Surface Hardness HV 600 ...640
20 Core Hardness HB 260 ... 280
21 Effective Carburized Depth mm 0.3 ... 0.5

Table 17-8B   Bending Strength Factors
No.

Item

 Symbol Unit Pinion Gear
1 Allowable Bending Stress at Root sFlim kgf/mm² 42.5
2 Normal Module mn mm 2
3 Tooth Width b 20
4 Tooth Profile Factor YF   2.568 2.535
5 Load Distribution Factor Ye   0.619
6 Helix Angle Factor Yb   1.0
7 Life Factor KL   1.0
8 Dimension Factor of Root Stress KFX   1.0
9 Dynamic Load Factor KV   1.4
10 Overload Factor KO   1.0
11 Safety Factor SF   1.2
12 Allowable Tangential Force on Working Pitch Circle Ftlim kgf 636.5 644.8
17.2 Surface Strength Of Spur And Helical Gears
   The following equations can be applied to both spur and helical gears, including double helical and internal gears, used in power transmission. The general range of application is:
Module:
Pitch Circle:
Linear Speed:
Rotating Speed:  		m
d
v
n		 1 .5 to 25 mm
25 to 3200 mm
less than 25 m/sec
less than 3600 rpm

17.2.1 Conversion Formulas
   To rate gears, the required transmitted power and torques must be converted to tooth forces. The same conversion formulas, Equations (17-1), (17-2) and (17-3), of SECTION 17 are applicable to surface strength calculations.

17.2.2 Surface Strength Equations
   As stated in SECTION 17.1. the tangential force. Ft, is not to exceed the allowable tangential force, Ftlim The same is true for

 the allowable Hertz surface stress, sHlim The Hertz stress sH is calculated from the tangential force, Ft For an acceptable design, it must be less than the allowable Hertz stress sHlim That is:
   sH £ sHlim                                               (17-12) 
   The tangential force, Ftlim, in kgf, at the standard pitch circle, can be calculated from Equation(17-13).
  
   The Hertz stress sH (kgf/mm²) is calculated from Equation (17-14). where u is the ratio of numbers of teeth in the gear pair.

    The "+" symbol in Equations (17-13) and (17-14) applies to two external gears in mesh, whereas the "-"  symbol is used for an internal gear and an external gear mesh. For the case of a rack and gear, the quantity u/(u±1) becomes 1.

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