The Computer-Assisted Design Method of Staggered-Tooth Milling Cutter for Manufacturing of the Complex Helical Surfaces Gheorghe Pleşu

Transcription

1 Advanced Materials Research Online: ISSN: , Vol. 1036, pp doi: / Trans Tech Publications, Switzerland The Computer-Assisted Design Method of Staggered-Tooth Milling Cutter for Manufacturing of the Complex Helical Surfaces Gheorghe Pleşu Gheorghe Asachi Technical University of Iasi-Romania, Department of Machine Tools, Blvd. Mangeron, No, 61-63, Iasi, Romania Keywords: the helical complex surface, staggered-tooth milling cutter, system of design, simulation. Abstract. The complex helical surfaces specific for the rotors of the helical compressors and of the screw pumps imply the production of a series of tools providing a high productivity. The staggeredtooth milling cutter achieve these conditions but their design gives rise to difficult problems. In order to optimize their parameters and to facilitate their design, a package of programs has been created to select the constructive parameters of the tool, to calculate the profiles of the blades, the angles of the surface of section, the dimensions of the elements of attachment. In order to include all these elements in an efficient system of design, a series of regular calculations were applied for various parameters that were then included through the CAD software for design and documentation AutoCAD; at the same time, several applications of verification, construction and simulation of the functioning of the tool and of the cutting process were designed. The method applied in this case reduced to a considerable extent the time of design and it also improved the constructive solutions of the staggered-tooth milling cutter. Introduction The staggered-tooth milling cutter is one of the most frequently used cutter-tools used to manufacture the complex helical surfaces. Taking into account the teeth arrangement, determining their profile and the one of the angles favorable for the cutting on the entire tooth supposes that in the computer-assisted system of design of the disk-tool we introduce modules specific for this solution that can be used in the case of much simpler solutions. The design of such a tool involves the solution of a series of problems related to the interconditioning from between the parameters in order to create functional characteristics in the conditions of the restrictions imposed by the characteristics of the machine tools meant for the generation of the tool and the ones for the manufacturing of the helical surfaces. At the same time, taking into account the complexity of the tool, a methodology of design was designed to: calculation of cutting edge profile; obtaining cutting angles at each point of the cutting edges; achieve continuous cutting; providing non- interference of the channels for disposal cutting teeth. Since in the technical literature staggered-tooth side milling cutter s issue, used in processing of complex helical surfaces, was approached in [1, 2], but not able to solve all the issues above, it was used in a more general approach of this type of tool which can be extracted as some particular cases the positive rank angle milling cutter and the plain milling cutter (slab mill). The advantage of staggered-tooth side milling cutter used at the processing of complex helical surfaces was previously pointed out [3] as well as the inexistence in the specialized literature of a design method of this type of cutters. Based on the analysis, there was made a picture of designing, proposed in Fig.1, and the realization of mathematical models to define numerical profile blades and to determine functional parameters for these milling cutters. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-11/05/16,21:57:44)

2 Advanced Materials Research Vol Making cutting angles at each point of the blade profile is a first issue of great importance for the construction of these milling cutters. Also, the condition of continuous non-interference in sharpening-cutting led to the establishment of formulas to determine the number of teeth of the tool. We find the formulae needed for the calculus of the static and functional angles in the specialized literature. This work presents only the modules of an original character used for establish the angle tilt of teeth and the profile of teeth. Fig. 1. Composition of the package for design of the staggered-tooth milling cutter Determining the angle of tilting ω 0 of the cutting blade of staggered-tooth milling cutter In order to provide the positive cutting angles in any point of the cutting, the tooth position in the body of the cutter needs to be settled according to the generating profile of the tool. The tooth position compared to the body is given by the following geometrical parameters: The angle ω 0 between the axial plan and the plan of the blade; The distance from the origin of the system of reference of the tool to the point of rotation of the blade -zω 0. The generating profile of the disk tool is given by the parameters R s, z s and σs. In order to form the appropriate cutting angles for the cutting process in any point of the blade, the point K around which the tool tooth is rotating must be placed after the last point of intersection between the normal to the generating profile and the rotation axis of the tool. According to the Fig. 2 the following condition must be preserved: L i /tgω 0 R si /tgφ i (1) where: R si the radius of general profile of the tool in any point; L i distance from the point considered on the edge of blade to the axis of rotation of the tool designed in O s y s z s plan; φ i - the angle between the tangent to the profile generator of the tool and axis of its rotation. Because at this stage of the milling cutter s design there is only known its general profile, the whole new parameters involved will be expressed on its coordinates. So, φ i angle and can be expressed in the following form:

3 390 Modern Technologies in Industrial Engineering II φ i π - σ si (2) Noting: zωi - distance from the point of tilting to current point on the profile generator. We see from Fig. 2 the following relation: Fig. 2. Determination of the tilt angle of the blade tgω 0 L i /z ωi (3) Expressing z ωi depending on other parameters as: z ωi z ω0 +z si (4) Using Eq. 1 in which replacements are made of 2, 3 and 4 may determine the relation of choosing the value of zω0 in the form: z ω0 R si. (5) ctg σ si The relation determines the point of rotation for two successive teeth of the milling cutter disk according to the profile generator of the tool s parameters. For each tooth will be chosen the points on the profile for ensuring an overlap of at least a few millimeters in the central area of the teeth and edge lengths as close in value. The analysis of the relation reveales the possibility of choosing points at different distances from the reference system for the two blades. However, the same angle is taken in most cases for the two blades. Based on the considerations presented above, a program has developed so as to allow automatic determination of their parameters for complying at the condition of obtaining favorable cutting angle for the whole profile of blades. The calculation of tool s profile in the plan of the cutting edge So as to achieve the milling cutter is necessary to know the profile of the blade in its plan. Problem to be solved is the profile generator input coordinates for each point of calculation, geometrical parameters describing the position of milling cutter blade against the tool body and the coordinates output data of the plan profile for each point. Solving the problem should be made

4 Advanced Materials Research Vol using a mathematical model that describes the transition from general profile of the tool, considered in its axial section which describes a rotating surface rotation, in the plan in which there is placed the tooth and also where the tool rotation describes the same surface rotation (Fig. 3). Fig. 3. The transition of axial section of the tool at the of the blade Considering Fig. 4 there are set generalized displacements connecting coordinate system attached to general profile of the tool O s x s y s z s to the coordinate systems attaches to the blade O p X p Y p Z p. There are introduced additional systems Kxyz, Kx'y'z' (K being the point to which the rotating blade are made), O p x p y p z p. Following plans were noted: T axial plan; T p the plan of the blade. Fig. 4. Coordinate systems of the tool and of the blade Switching O s x s y s z s system with Kxyz system is by translation along the O s z s axis. xp yp zp 1 A 3 (zω0 ) A 4 (-ω 0 ) A 3 (- zω0 ) cos ω 0 xs ys zs 1 (6)

5 392 Modern Technologies in Industrial Engineering II After the calculations are obtained the following relations: x p y p z p x s y s cos ω 0 + (z s + zω0 )sin (z s + zω0 )cos ω 0 - y s sin ω 0 zω 0 ω 0 - cosω 0 (7) Tooth plan equation in system O p x p y p z p is y p 0. Considering the circle related to the point Ci, in system O s x s y s z s, its equation is: x s y s z s R si R si z si sint cost (8) and in the system O p x p y p z p, taking into account the Eq. 7: x p R si sint y p ( z si + zω0 )sin z p ( z si + zω0 )cos ω 0 + R si costcos ω 0 - R si costsin ω 0 zω0 ω 0 - cos ω 0 With the intersection between tooth plan and the circle which corresponds to profile generator of the tool there are obtained point coordinates in the plan of the tooth: y p 0>(z si +z ωi )sinω 0 +R si costcosω 0 0 (10) The angle t that determines the position of point on the circle is given by: + ω t arccos[- (zsi zω0 )tg 0 ] (11) R si cos ω 0 Replaced in the formulas in equation (9) there are obtaining coordinates: xpi ± Rsi 2 - (zsi + zω0 )2 tg 2 ω0 zsi zpi cosω0 (12) The method of graphic calculus of the profile of the blade is based on one of the strong difficulties of the graphical environment resulted from the software product AutoCAD (Fig.5), that is to get high precision sections for revolution body of the disk tool which is obtained with command AutoCAD using the profile obtained, [4]. Using an AutoLISP program designed for the previously described body is made up of five sections which build the blades for two successive teeth (Fig.6). By this method we obtain the profile of the blade, graphically. In order to compare the resulted profiles, the ones resulted from the analytical method and the ones derived from the graphic method, we will apply the following procedure: we consider a sufficient number of points from the analytical profile where the minimal distance from the graphically calculated profile. The distance will be determined by the command AutoCAD dist. The following figure will present (9)

6 Advanced Materials Research Vol graphically the points in which these distances were measured, as well as their values. If we consider the maximal value, it is represented in the absolute error of the profile resulted from the graphic procedure applied for the blade. The maximal error occurred between the two curves is of mm (Fig.7). Fig. 5. AutoCAD based software package for the graphic method Fig. 6. The profiles of the blades and the body of the staggered-tooth milling cutter Fig. 7. Comparasion of the profiles of the both methods Conclusion The profile for the blades by the both methods was accurate. This gave us confirmation of the result of analytic method and offer possibility to reduce the time for design the tool. In the next applications we decided to use only graphical method for design of the tool. References [1] Kudeviţkii, Ia. V., Fasonnîe frezî (Shaped milling cutters). Leningrad, Maşinostroenie, (1978), pp [2] Csibi, V.I., Contribuţii la calculul numeric al angrenării, cu aplicaţii la generarea şi angrenarea suprafeţelor elicoidale cu profile speciale (Contributions to the numerical calculation of gearing, with applications to generation and meshing helical surfaces with special profiles), PhD Thesis, Politehnic Institute of Cluj-Napoca, (1990), pp [3] Pleşu, Gh., Contribuţii teoretice şi experimentale privind optimizarea utilajului tehnologic pentru prelucrarea suprafeţelor elicoidale complexe (Theoretical and experimental studies on optimization of technological equipment for processing complex helical surfaces), PhD Thesis, Technical University Gh. Asachi Iaşi, 256 pp., 1999 [4] Plesu, Gh., Grapho-analytical determination of the profile tool disc for manufacturing of complex helical surfaces Advanced Materials Research, Vol. 837, pp

7 Modern Technologies in Industrial Engineering II / The Computer-Assisted Design Method of Staggered-Tooth Milling Cutter for Manufacturing of the Complex Helical Surfaces /