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2.2. Spiral bevel gears
Localization of contact of generated spiral bevel gears is provided by application of two mismatched head-cutters Σp and Σg used for generation of the pinion and the gear, respectively [7]. Two head-cutters Σp and Σg have a common line C of generating tooth surfaces (in the case when profile crowning is provided). In the case of double-crowning, the mismatched generating surfaces Σp and Σg of the head-cutters have only a common single point of tangency, but not a line of tangency. Double-crowning of a generated gear may be achieved by tilting of one of the pair of generating head-cutters, or by proper installment of one of the head-cutters. It is very popular for the modern technology that during the generation of one of the mating gears, usually of the pinion, modified roll is provided [7].
2.3. Worm gear drives with cylindrical worm
Very often the technology of manufacturing of a worm-gear is based on the following approach. The generation of the worm-gear is performed by a hob that is identical to the worm of the gear drive. The applied machine-tool settings simulate the meshing of the worm and worm-gear of the drive. However, manufacture with observation of these conditions causes an unfavorable bearing contact, and high level of transmission errors. Minimization of such disadvantages may be achieved by various ways:
(i) by long-time lapping of the produced gear drive in the box of the drive;
(ii) by running of the gear drive under gradually increased load, up to the maximal load;
(iii) by shaving of the worm-gear in the box of the drive by using a shaver with minimized deviations of the worm-member, etc.
The authors’ approach is based on localization of bearing contact by application of: (a) an oversized hob, and (b) modification of geometry (see below).
There are various types of geometry of worm gear drives [7], but the preferable one is the drive with Klingelnberg’s type of worm. Such a worm is generated by a disk with profiles of a circular cone [7]. The relative motion of the worm with respect to the generating disk is a screw one (in the process of generation).
Very often localization of bearing contact in a worm gear drive is achieved by application of a hob that is oversized in comparison with the worm of the drive.
3. Types of meshing and basic functions of transmission errors
It is assumed that the tooth surfaces are at any instant in point tangency due to the localization of contact. Henceforth, we will consider two types of meshing: (i) surface-to-surface, and (ii) surface-to-curve. Surface-to-surface tangency is provided by the observation of equality of position vectors and surface unit normals [7]. Surface-to-curve meshing is the result of existence of edge contact [7].
The algorithm of TCA for surface-to-surface tangency is based on the following vector equations [7]:
that represent in fixed coordinate system Sf position vectors and surface unit normals . Here, (ui, θi) are the surface parameters and ( 1, 2) determine the angular positions of surfaces.
The algorithm for surface-to-curve tangency is represented in Sf by equations [7]
Here, represents the surface that is in mesh with curve is the tangent to the curve of the edge.
Application of TCA allows to discover both types of meshing, surface-to-surface and surface-to-curve. Computerized simulation of meshing is an iterative process based on numerical solution of nonlinear equations [8].
By applying double-crowning to one of the mating surfaces, it becomes possible to: (i) avoid edge contact, and (ii) obtain a predesigned parabolic function [7] (Fig. 1). Application of a predesigned parabolic function is the precondition of reduction of noise.
(17K)
Fig. 1. Illustration of: (a) transmission functions 1 of a misaligned gear drive and linear function 2 of an ideal gear drive without misalignment; (b) periodic functions Δ 2( 1) of transmission errors formed by parabolas.