(2) The misalignment of gear drive is caused by an error of the shaft angle, Δγ ≠ 0.
(3) A predesigned parabolic function for absorption of transmission errors caused by Δγ ≠ 0 is provided. （Such a function for a double-crowned pinion tooth surface is obtained by plunging of the generating disk, or by modified roll of the grinding worm.）
(4) TCA (tooth contact analysis) for unloaded and loaded gear drives are applied for determination of transmission errors caused by Δγ. This enables to investigate the influence of the load on the magnitude and shape of the function of transmission errors.
(5) Application of a computer program for finite element analysis [3] enables to determine the stresses of a loaded gear drive.
(6) Formation of bearing contact is investigated.
 Table 1.
Design parameters
Number of teeth of the pinion, N1    21
Number of teeth of the gear, N2    77
Normal module, mn    5.08 mm
Normal pressure angle, αn    25°
Hand of helix of the pinion    Left-hand
Helix angle, β    30°
Face width, b    70 mm
Parabolic coefficient of pinion rack-cutter, aca
0.002 mm−1
Radius of the worm pitch cylinder, rwa
98 mm
Parabolic coefficient of pinion modified roll, amrb
0.00008 rad/mm2
Applied torque to the pinionc
250 N m
(i) Example 1: An aligned gear drive (Δγ = 0) is considered. The gear drive is unloaded. A parabolic function with the maximal value of transmission errors Δ 2( 1) = 8″ is provided (Fig. 6(a)). The cycle of meshing is  . The bearing contact on the pinion and gear tooth surfaces is oriented almost longitudinally (Fig. 6(b) and (c)).
 
 (24K)
Fig. 6. Results of computation for an unloaded gear drive without misalignment: (a) function of transmission errors; (b) and (c) paths of contact on pinion and gear tooth surfaces.
 6. Comparison of the power of noise for two functions of transmission errors
6.1. Conceptual consideration of applied approach
Determination of the power of the signal of noise is based on the assumption that the velocity of oscillation of the generated acoustic waves is proportional to the fluctuation of the instantaneous value of the velocity of the gears. This assumption (even if not accurate in general) is good as the first guess, since it allows to avoid application of a complex dynamic model of the gear drive.
We emphasize that the proposed approach is applied for the following conditions:
(a) The goal is the determination of difference of power of signals, but not the determination of absolute values of signals.
(b) The difference of power of signals is the result mainly of the difference of first derivatives of two smooth functions of transmission errors.
The proposed approach is based on the comparison of the root mean square of the signals (in rms) caused by two functions of transmission errors [9]. Such comparison yields the simulation of the intensity (the power) of the signal defined as
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