Page 234 - Gear Technology Solutions

Figure 12: Modified material removal along path of contact section

In Figure 12 a section is made perpendicular to the flank surface and along the
path of contact. In this section drawing the first order change of the A-axis is
shown as a blue graph. In addition to first order changes, other, more complex
functions can also be realized. For example, third order functions as well as sinus-
oidal functions have been successfully applied.

16.11 First Level Modification

First, the maximal modification amounts for each individual tooth are calculated in
the first level of calculations. The maximal modification amount for one particular
tooth is calculated as cosine function or as normal distribution. Figure 13 shows
symbolically how the tooth form changes from tooth to tooth, defined by the nor-
mal distribution. In Figure 13 only the maximal change of each tooth is shown.

Cosine First Level Function type: cos [j]:
The function should start at j = –p at the first tooth and end at j = +p at the last
tooth plus 1. At the mean number of teeth (n+2)/2 (does not have to be integer)
the argument j should be zero.

From these boundary conditions:
j = -p if zi = 1
j = +p if zi = n+1
j = 0 if zi = zm

The cosine function becomes:
cos[j] = cos[(n+2)/(-2) • (2p/n)+zi • (2p/n)] (1)

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