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(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
齿轮传动时产生震动和噪音的主要原因是传输误差。有关影响噪音传输误差的两个主要函数已被查明：（1）一个是线性的对应误差；（2）一个是初步设计使用传输误差以减少噪音而引起的。它显示了传输误差的线性关系，在一个周期内形成了混合的循环啮合：（1）如点对点接触；（2）当从表面以曲线形式移动到起始点时就产生啮合。使用初步设计传输误差能够减少因为线性对应函数而引起的传输误差，减少噪音和避免移动接触。引起传输误差的负载函数已被研究。齿牙的损坏能够使在装载的齿轮传动中减少最大的传输误差。用计算机处理的模拟齿轮啮合，且齿轮传动装载和卸货技术已发展相当水平。