Page 235 - Gear Technology Solutions

Figure 13: Normal distribution as a first level function

whereas:
j… argument of cosine function
zi… actual tooth
zm… number of teeth at the middle of the function = (n+2)/2
n… number of teeth of target gear
n+1… number of teeth at the end of the function

The amplitude of the cosine function in equation (1) changes from -1 to +1. In or-
der to receive an amplitude with the desired correction amount Corr normal to the
flank surface, in case of a modified A-axis rotation the cosine function has to be
multiplied with the following term:

•
)
Corr/(cosb cosa • RM • sing (2)

whereas:
Corr… correction amount perpendicular to flank surface (user input)
b… spiral angle of member
a… pressure angle of member
RM… mean cone distance
g… root angle of member

The maximum A-axis modification amount for a respective tooth becomes:

DAmax(zi) = Corr/( cosb • cosa • RM • sing) • cos[(n+2)/(-2) • (2p/n)+zi • (2p/n)] (3)
Whereas:
DAmax(zi)… maximal A-axis modification amplitude for tooth zi

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