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Table 15-7 Allowable Values of Running Errors, mm

Grade Tooth-to-Tooth Composite Error Total Composite Error
0 1.12m + 3.55 (1.4W + 4.0) + 0.5(1.12m + 3.55)
1 1.6m + 5.0 (2.0W + 5.6) + 0.5(1.6m + 5.0)
2 2.24m + 7.1 (2.8W + 8.0) + 0.5(2.24m + 7.1)
3 3.15m + 10.0 (4.0W + 11.2) + 0.5(3.15m + 10.0)
4 4.5m + 14.0 (5.6W + 16.0) + 0.5(4.5m + 14.0)
5 6.3m + 20.0 (8.0W + 22.4) + 0.5(6.3m + 20.0)
6 9.0m + 28.0 (11.2W + 31.5) + 0.5(9.0m + 28.0)
7 12.5m + 40.0 (22.4W + 63.0) + 0.5(12.5m + 40.0)
8 18.0m + 56.0 (45.0W + 125.0) + 0.5(18.0m + 56.0)

        where: W = Tolerance unit =
                   d  = Pitch diameter (mm)
                  m  = Module

SECTION 16 GEAR FORCES
    In designing a gear, it is important to analyze the magnitude and direction of the forces acting upon the gear teeth, shaft, bearings, etc. In analyzing these forces, an idealized assumption is made that the tooth forces are acting upon the central part of the tooth flank.
16.1 Forces In A Spur Gear Mesh
The spur gear's transmission force Fn, which is normal to the tooth surface, as in Figure 16-1, can be resolved into a tangential component, Fu, and a radial component, Fr Refer to Equation (16-1).

The direction of the forces acting on the gears are shown in Figure 16-2. The tangential component of the drive gear, Fu1, is equal to the driven gear's tangential component, Fu2, but the directions are opposite. Similarly, the same is true of the radial components.

16.2 Forces In A Helical Gear Mesh
    The helical gear's transmission force, Fn, which is normal to the tooth surfaces, can be resolved into a tangential component, F1, and a radial component, Fr, as shown in Figure 16-3.

Table 16-1 Forces Acting Upon a Gear
Types of Gears Tangential Force, Fu Axial Force, Fa Radial Force, fr
Spur Gear Fu =  2000 T
            d  

----

 Fu tan a
Helical Gear Fu tan b Fu tan an
     cos b 
Straight Bevel Gear   When convex surface is working:
Spiral Bevel Gear Fu = 2000 T
          dm 
dm is the central
pitch diameter
dm = d - bsind		   Fu  (tanansind-sinbmcosd)
cosbm		   Fu  (tanancosd-sinbmsind)
cosbm
When concave surface is working:
  Fu  (tanansind-sinbmcosd)
cosbm		   Fu  (tanancosd-sinbmsind)
cosbm
Worm drive Worm (Driver) Fu = 2000 T1
          d1  		Fu  cosancosg-msing
     cosansing+mcosg 		Fu          sinan       
     cosansing+mcosg
Wheel (Driven) Fu  cosancosg-msing
     cosansing+mcosg 		Fu
Screw
Gear
( S = 90º )
b=45º		 Driver
gear		 Fu = 2000 T1
          d1  		Fu  cosansinb-mcosb
     cosancosb+msinb 		Fu          sinan       
     cosancosb+msinb
Driven Gear Fu  cosansinb-mcosb
     cosancosb+msinb 		Fu

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