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with these boundary conditions the second level third order function (Figure 3) be-
comes:
3
3
DA(zi,qj) = DAmax(zi) • [8• (qj-q0) /(qs-qe) ] (9)
Whereas:
qs… start roll position
q0… center roll position
qe… end roll position
16.13 Amplitude and Frequency Change
In order to provide second level tooth bound functions which can be optimized and
adjusted regarding their amplitude and their wave-length, the following equation
(10) was developed. This equation only applies to the sinusoidal flank form modifi-
cation:
qm = (qs+qe)/2
qs ≤ qj < qm => f = fToe (user input) ; Amp = AToe (user input)
qm ≤ qj < qe => f = fHeel (user input) ; Amp = AHeel (user input)
DA(zi,qj) = DAmax(zi) • Amp • sin[2pf• (qj-qm)/(qs-qe)] (10)
Whereas:
qm.. mean roll position
tToe… frequency toe section
fHeel… frequency heel section
f… actual frequency
AToe… amplitude in toe section
AHeel… Amplitude in heel section
Amp… actual amplitude
Figure 14: Two section sine function with different frequencies
and amplitudes in the two sections
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