THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

376 14. Machinery Noise ControlFundamental tooth meshing frequencies are obtained fromf = nN60( ) 40= 3600 × = 2400 Hz for gear 160( ) 46= 1066 × = 1226.7 for gears 3 and 460If we compare the calculated results with the spectrum analysis, it seems thatthe 14- and 27-Hz discrete tones and vibration energy peaks correspond to thefundamental and the first harmonic of the tooth-error frequency for gear 4. Thiswould indicate that the shaft straightness and the teeth of gear 4 should be investigated.The discrete tones of 1227 and 2455 Hz correspond to the fundamentaland the first harmonic of the meshing frequencies of gears 3 and 4. Discrete tonesat 2400 and 4800 Hz correspond to the fundamental and the first harmonic of thetooth meshing frequency of gears 1 and 2.Contact Ratio (CR)The contact ratio CR for a pair of gears is defined as the average number of pairs ofteeth in contact. At least one pair must obviously be in contact at all times. Takinginto fact that tooth error, wear, shaft deflection, and machining tolerances affectthe way gears work, a contact ratio of 1.2 is selected as the practicable minimum.When the contact ratio is near minimum value, contact commences at the tips ofthe driven teeth, and impact loads due to teeth meshing are high. A contact ratioof 2 or more usually results in better tooth load distribution and quieter operation,since two or more teeth will be in contact at all times.In order to deal with contact ratio, we need to briefly review spur gear terminology:diametral pitch is defined by P d = N/d and d is the pitch (nominal) diameterof the gear, r is the pitch radius = d/2, φ is the pressure angle, and a is the addendumor extent of the tooth beyond the pitch radius, r a = r + a is the radius of theaddendum circle, and c = r 1 + r 2 (center distance for gears in mesh). It followsfrom Equation (14.19) for spur gears thatr 1= n 2r 2 n 1The pressure angle φ represents the angle of force transmission between gear teeth.Standard gears have pressure angles of 14.5 ◦ (a rather antiquated standard), 20 ◦ ,and 25 ◦ . The contact ratio between a pair of spur gears is given byCR =√r 2 a1 − r 2 1 cos2 φ +√r 2 a2 − r 2 2 cos2 φ − c sin φπ cos φP d(14.21)