Page 220 - Gear Technology Solutions

16 Psychoacoustic Flank Form Modulations with MicroForm

16.1 Background

The science of psychoacoustics is the study of sound perception. Sound pattern
optimization has become very popular in the resent years. Brecher et al. [1, 2, 3, 4]
show in their research papers how they apply psychoacoustics to the noise emit-
ted by gears. Brecher applies from tooth to tooth individually different flank form
changes to reduce the tonality. Tonality is used as a psychoacoustic measure, in
order to judge how gear noise is received by the human ear and evaluated by the
brain. Gear noise might be perceived as non-disturbing or not noticeable; even if a
sound pressure measurement or a single flank test indicates that the gearset is
loud and disturbing according to traditional rules.

Topography scattering, as proposed by Brecher, addresses spiral angle and pres-
sure angle changes on the flank surfaces of the gears to be optimized. The spiral
angle and pressure angle changes have different amounts from tooth to tooth. In
the examples [1, 2, 3 and 4], random distributions as well as normal distributions
have been applied in order to quantify the changing spiral angle and pressure an-
gle amounts from tooth to tooth.

16.2 The Function of the Ear

The physics of sound transmission is based on the compression and expan-
sion of solid materials as well as fluids. The mathematical function of the com-
pression and expansion of elastic materials is most likely always a sinusoidal
function. The assumption that all sounds which are transmitted and emitted
consist solely of sinusoidal elements seems reasonable.

The concert pitch A of 440 Hz from a tuning fork, sounds to the human ear dif-
ferent than from a violin or from a piano. The reasons are overtones which
consist of higher harmonics, side bands and/or other elements in the sound
waves which might not be captured by the FFT. However, the fact that the 440
Hz can be recognized precisely by a listener is explained with the higher har-
monics accompanying the fundamental frequency [5].

The assumption that the ear tends to recognize only harmonic signals is par-
tially correct. The outer ear acts as an equalizer and compressor which boosts
the sound pressure by 15 to 20 dB. The airwaves actuate the eardrum which in
turn actuates the ossicles which act as equalizer, compressor and impedance

205