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Metal cutting of tooth gears by a method of a nonlinear generating process of a profile

In this article, the perspective methods of milling of tooth gears by disk cutters with the nonlinear coordination between feeding movements are presented. Besides, the algorithm of the contour calculation of sophisticated reconciled movements of a tool and a gear blank is described.


Introduction
Metal cutting of gear wheels of a various profile including an involute one is carried out by special pitch tools: hobbing cutters, gear shape cutters, chasers and other pitch tools. Such surfaces are shaped by two coordinated movements of shaping at a constant ratio of a feeding rotation of a work piece and gear shape cutters, chasers tools, the rotational main movement of a cutter and a feeding rotation of a work piece for hobbing cutters. Thus the shape of a tool generating flat varies at the profile form change of a gear wheel tooth contour, a module, an angle of involute profile. It demands the application of a big spectrum of complicated, expensive and special tools [1,2]. Therefore, these methods are low efficient in small-batch and unit productions, and the application of tools running based on a method of copying, does not ensure high accuracy and quality of a surface [3][4][5].
For the purpose of the efficiency increase of the cutter life use, it is necessary to develop a system of control and cutter recovery taking into account the mentioned factors of dispersion. For this, the development of a simulator for the process of adequate cutter life use, taking into consideration the factors emphasized, is necessary [8,9].

Materials and methods
During the development of the simulator of cutter life use, taking into account the dispersion factors mentioned, the following models of tool wear were used: a fan model, an accumulation model, a complex model and a breakout pattern. To solve the problem identified, we used the methods of probability theory and those of mathematical statistics.

Metal cutting of gear wheels with three nonlinear movements of forming
Shaping of working surfaces of teeth is carried out by a disk cutter of a trapezoidal (conical) profile, herewith, each working side of a gear tooth profile is executed by the rectilinear corresponding side of a tool profile, and a combined, slot profile of the gear wheel coupling with working sites of a work piece profile is carried out by its cylindrical surface. Profile processing of each slot is made by three simultaneous forming movements which are coordinated nonlinearly and lie in one plain of shaping and the principal rotation of cutter zo ω ( Figure  1). One of them, a uniform rotation of gear wheel 1 X ω , and the other two, Z S and Y S , will agree with rotational 1 X ω so that during processing of profiles sites, rectilinear generators roll along a work surface. In this manner, the rectilinear generator of a flared section of a cutter should be sequentially tangent to each point of a processed profile. Ratios between separate movements constantly vary depending on the position of the top of the cutting edge and the magnitude of its slippage regarding the cutting surface. The designed method of processing of difficult surfaces allows increasing precision owing to profiles generating process of a work piece by rectilinear generators of a tool; besides, it is multipurpose since involute wheels processing of a various module and wheels with non-standard profile angles can be manufactured by cutters of one standard size.

Sophisticated trajectory installation and coordinated feedings movements during processing of gear wheels of a non-evolvent profile
The method of a nonlinear rolling is applicable for wheels of a non-evolvent profile, for example, for Novikov's meshing wheels or a cycloidal profile [10].
The main task for the implementation of the described method by any function is establishment of the functional correlation between separate movements of shaping that is reduced to the establishment of tool top migrations on the shaft, 1 Z Z S ∆ , and 1 Y Y S ∆ in step-by-step increments depending on a rotation angle of a work piece ϕ in the direction of angle feeding 1 X ω . For this purpose, the cutter should sequentially touch the working surface of the tooth at each point of the profile [9]. That is, the processing side of the tool profile at each point should be tangent to the processed side of the profile of a work piece ( Figure 2).
The following designations were used: 1, ' 1 -consecutive positions of the side of a tool profile; 2, (1) The cutter profile should be tangent to all consecutive positions of the surface profile described by function ( ) z f y = in the same coordinate system. During the turning movement of the tooth profile to angle ϕ , the cutter profile will be displaced from point ( ) ; (11)