Page 224 - Gear Technology Solutions

tooth mesh motion error which is parabolic in Figure 3 instead of sinusoidal.
Due to the parabolic motion error not only fz, but also the multiples of fz are
present in the Fourier analysis result. Each of those harmonic frequency bars
is surrounded by side bands caused by the gear and pinion runout. Instead of
ignoring the differences between parabolic and sinusoidal function, the Fourier
analysis expresses the residuals between parabolic motion graph and sine
function in additional sine functions of higher orders [6].

16.4 Noise Reduction Solutions in Other Fields

The idea of purposely introducing spacing errors between the teeth was literal-
ly taken from the pitch variation of automotive cooling fan blades and the irreg-
ular spacing of the pattern on vehicle tires [7]. The unequal spacing of the
cooling fan was calculated with Bessel functions. It achieves the conversion of
the single frequency (red dashed line in Figure 4) into side bands, shown as
solid black lines. The side bands convert a harsh sounding fan noise into
smooth buzzing. The tire with its differently spaced treads in Figure 4 accom-
plishes a similar effect as the unequally spaced fan.

Figure 4: Separation of parabolic and harmonic motion transmission elements

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