Search

The transmission based on precessional gear pairs, mostly used for rotation speed reduction, has some important advantages relative to the common gear drives, such as the capability to produce very low transmission ratios, or the high loading capacity/dimensions ratio (due to the fact that all the teeth of a precessional gear pair are simultaneously in contact during its functioning). One among the likeliest constructive solutions for the precessional gear pair uses a satellite built with conical rollers. However, its practical use is restricted by the difficulty to realize the central gear teeth machining without using special and relative complicated devices. This paper introduces a technological substitutive profile for the central gear tooth, which enables the use of a simpler and more productive method for working it, without bringing major negative consequences regarding the teeth contact correctness or the drive loading capacity. The profile was found by analyzing the contact surface and the pressure angle evolution during the contact between conjugate teeth. The paper also presents technological solutions to generate the new tooth profile by milling it with a disk-tool or an end-mill cutter, together with methods to profile the required tools. [ABSTRACT FROM AUTHOR]

The envelope theory provides a solid mathematical tool for accurate computations and design of milling tools that generate helical surfaces such as disk or end mill tools. Given an analytical description of the helical surface to be generated, and considering that the machined surface and milling tools are reciprocally enwrapping during the generation motions, one can deduce equations for the milling tool profile. However, this usually involves transcendent equations that require significant computational resources for their solution. More importantly, analytical representations of the surfaces to be generated are not always available, as in the case of measured discrete surfaces. To alleviate the issue, polynomial approximations of the entire helical surface or only of a spatial curve along the surface can be used as already published in previous works. The present study focuses on the methodology of finding the simplest polynomials when only a small number of points are known or measured from the surface to be generated. The numerical simulation and real examples show that third degree Bezier polynomials are suitable approximations for many practical situations. In such cases, not only computation complexity is highly reduced but also the measurement process is significantly simplified. The paper presents a methodology for the design of disk-cutting tools reciprocally enwrapping cylindrical helical surfaces of constant pitch when the helical surface generatrix is known in discrete form. The suggested method is using a small number of points belonging to the helical surface to be machined. Due to the use of a low-order Bezier polynomials representation of the helical surface generatrix, a small approximation error is introduced as shown in our numerical examples. Using as a reference the analytical representation of the generatrix, the exact axial section of the disk tool can be computed and compared to the axial section obtained using the methodology described in this paper. The approximation errors seem to be acceptable for many technical applications. Numerical simulations and examples were performed using a Java-based implementation of the suggested algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a simplified algorithm for the profiling of the rack gear tool to generate the active profile associated with rolling centrodes. The algorithm is based on the enveloping surfaces principles and reduces the computational problem by proposing an approximate representation of tool’s profile using only three or four points on the profile to be generated by using Bezier representations of the surfaces. The algorithm computes the coefficients of a Bezier substitution polynomial instead of computing hundreds of points on the active profile. This simplifies the solution methodology and requires only a limited number of points along the profile to be generated. The algorithm is computationally efficient and can also be used in the case when the active profile to be generated is physically measured at a few points. Examples include mill tools, splined shafts, and gears. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method based on the surfaces enveloping theory developed as a vertical application in the CATIA graphical design environment. This method is created for profiling tools intended to generate cylindrical helical surfaces with constant pitch. The devised method is applicable for the profiling of disc tools which are bounded by a primary peripheral surface of revolution. A few examples for the determination of the tool's 3D primary peripheral surface are presented such as helical flutes of cutting tools, worms with wide pitches, and gear involute flanks. The results are presented in both graphical and tabular form for completeness. Screen snapshots of the CATIA-based vertical application are also shown. [ABSTRACT FROM AUTHOR]

Generation of helical surfaces with cylinder-frontal tools (end mill tool or grinding wheels) as so as with cylindrical tools (planing tools) are proceedings used in the small lot productions manufacturing or for reparations. In many situations, the surfaces to be generated are known by measuring on three-dimensional measuring machines. In this way, is possible to define a generatrix expressed by sampled points, which impose specifically algorithms for the end mill tool's profiling. In this paper, specifically proposed are algorithms for end mill tool and planing tool profiling, designated to generate helical surfaces known in discrete form. More is assumed that the helical surface's generatrix may be expressed only by few points, three or four, so the helical surfaces generatrix may be expressed by inferior degree Bezier polynomials using topological geometry. One of the goals of this paper is to compare the numerical results obtained by the proposed algorithm with the results obtained from profiling theoretically methods, for the same surfaces types, in order to proof the new method quality. [ABSTRACT FROM AUTHOR]

The cutting processes with tools that generate “through-winding straight-involute teeth-gears”, tools associated with couples of centrodes-in-rolling (such as the rack-tool), are characterized by a fairly complicated cutting scheme, due to the specific shape of the tools and, at the same time, due to the rolling process of the axodes associated with the tool and the blank. The present solutions are not accorded well enough to the process and lead to significant variations in the detached chip area value regarding the machined wheel teeth number. It is accepted that the main cutting force size depends on the size of the area of the cutting layer (the geometrical area of the once detached chip by the assembly of operative edges of this kind of tools). The geometrical modeling of the generation process proves this and it could be considered a criterion for the reconfiguration of the cutting tool. In this work, there is defined a criterion so as to describe the cutting scheme, and based on this criterion we can compare the variation laws for the chip area size when generating the modeling of the cylindrical straight teethed gears. We propose a modeling of the cutting schemes in order to get new constructive forms of the cutting tools that will lead to cutting schemes adaptable to the number of teeth of the processed gear with the purpose of diminishing the teething cutting force. Also, there is presented a constructive solution for a rack-tool with reconfigurable structure with the purpose of according the teething process with the processed gear number of teeth. [ABSTRACT FROM AUTHOR]