NDLI: Tool profiling for generation of discrete helical surfaces

Content Provider	Springer Nature Link
Author	Oancea, Nicolae Popa, Ionut Teodor, Virgil Gabriel Oancea, Victor G.
Copyright Year	2010
Abstract	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.
Starting Page	37
Ending Page	46
Page Count	10
File Format	PDF
ISSN	02683768
Journal	The International Journal of Advanced Manufacturing Technology
Volume Number	50
Issue Number	1-4
e-ISSN	14333015
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-01-21
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Discrete surfaces Bezier polynomials Approximate profiling Computer-Aided Engineering (CAD, CAE) and Design Mechanical Engineering Production/Logistics Industrial and Production Engineering
Content Type	Text
Resource Type	Article
Subject	Industrial and Manufacturing Engineering Control and Systems Engineering Mechanical Engineering Computer Science Applications Software

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