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ScienceDirect

Procedía Technology 12 (2014) 420 - 426

The 7th International Conference Interdisciplinarity in Engineering (INTER-ENG 2013)

Influence of radial finishing trajectories to the roughness obtained

by milling of spherical surfaces

Paul Chetan*, Vasile Bolos, Alexandru Pozdirca, Andrea Peterlicean

Petru Maior University ofTirgu Mures, Nicolae Iorga Street, No. 1, Targu Mures 540088, Romania

Abstract

The paper aims at studying the influence of the radial trajectory in finishing a spherical surface on the roughness obtained using a toroidal milling cutter. A mathematical model is proposed with entry values represented by the technological parameters (cutting speed, pitch speed), the tool's geometrical parameters (tool diameter, corner radius) and the half-finished product (radius of the sphere) to determine the theoretical height of the irregularities left after milling. To check the results an experimental model is proposed with results analyzed on four samples.

©2013TheAuthors.PublishedbyElsevierLtd.

Selectionandpeer-reviewunderresponsibilityofthePetru Maior University of Tirgu Mures.

Keywords. Roughness; milling; toric end-mill; radial trajectories; surface

1. Introduction

Milling is a processing procedure of cutting that eliminates the excess material from the half-finished product under the form of small elements, called chips. These chips appear from the intermittent interference of the cutting tool, the mill and the half-finished product. This cyclic interference is generated by the tool's rotation with the blades positioned at space intervals and by the relative feed of the tool and half-finished product. As such, the processed surface is made of a series of geometrical elements (small surfaces) generated individually by each cutting

* Corresponding author. Tel.: +40-744-917-188; fax: +40-265-262-275. E-mail address: paul.chetan@ing.upm.ro

2212-0173 © 2013 The Authors. Published by Elsevier Ltd.

Selection and peer-review under responsibility of the Petru Maior University of Tirgu Mures. doi:10.1016/j.protcy.2013.12.508

edge of the tool. Roughness is defined as an assembly of surface irregularities whose pitch is relatively small and which generally comprises irregularities generated after the manufacturing process employed and/or determined by other factors [24]. The roughness of surfaces processed by milling is determined by the micro-irregularities that appear following the technological process and represents the marks left by the tool blade on the surface of the processed part. They are characterized by the periodicity of occurrence, the period being influenced by the size of the directing or generator pitch. As such, mathematical models can be developed that express the dependence of the size of the generated micro-irregularities and the geometrical elements of the tool, the technological elements of the cutting process. At the same time, the shape of the half-finished product influences these analytical relations.

Unwanted results in the cutting processes are generated by various aspects, such as vibrations, the wear of the tool, built-up blade, thermal effects. These phenomena have been studied by [18], [18], [26], [16], [17]. The influence of the milling force over the processing errors and the effects of the cutting tool - support system deformation on the processed surface are presented in various papers by [9], [10], [11], [12], [13], [14], [15]. The optimization of cutting processes in view of increasing yield and quality, two apparently opposite technical parameters, is based on the study of the influence of each of the parameters. This is made by the variation of one of these parameters while the others are maintained constant. The optimization criterion considered in this paper is the quality of the surface, the purpose being the determination of technological conditions for obtaining the best roughness.

The height of the irregularities generated by milling a sculptural surface with spherical mills is a subject that was intensively debated at the beginning of the '90's, together with the strong development of the CAD&CAM applications and numerical command machine tools. Various papers focus on the kinematics of the milling process using spherical tools on processing centers with 3 axes, research published by [1], [2], [3], [4], [5], [6], [7], [8], [20], [21], [22], [23].

2. The mathematical model

A reference system X0Y0Z0 is considered, attached to the core of the die and a reference system X1Y1Z1 attached to the toroidal mill that rotates around its own axis with a rev speed n and it moves on the trajectories on curves obtained by the intersection of the spherical area with vertical planes that contain the central axis of the part, sweeping the entire formation area (Figure 1). The movement of the mill can be upwards or downwards.

Both axes Z (of the part and of the tool) are thus established so as to have the direction of the axis Z of the numerical command machine tool and its positive sense. As the part is circular the direction and the sense of the axes X and Y are not important, they are chosen arbitrarily.

Fig. 1. The case of radial trajectories

As initial data we shall consider: • Cutting velocity Vc

• Pitch feed fz

• Diameterof thetool D1

• Corner radius of the tool R2

• The number of teeth Z

• The radius of the half-finished product Rs

Figure 2 presents the geometrical elements that influence the value of the theoretical roughness of the surface

thus generated.

Fig. 2. Geometrical element

Pitch feed velocity of the tool on the directing trajectory is defined with the relation: 1000 -V„

vf = A •z •

2 • 60 • (R1 + R2)-k

[mm/sec]

The space s between two moments (noted with t ) where successive tool blades touch on the surface of the part shall be :

s = /-Vf = Rs-AO

The angular velocity is determined with the relation: 1000 -K,

m = 2 • k ■ n = -

[rad/secl

60 ■ (R1 ■ R2) Time, as a value is deduced from the relation:

x 60-x-(R, + R,) r 7

t = — =-^-^ [sec]

m 1000 -V„

To determine the size of the theoretical roughness h, the geometrical construction in figure 2 is used. The height of the roughness h is determined with the relation:

h = O0 A - Rs

Using the sine theorem in the triangle OOOIA (Figure 2) we obtain:

Ol A _ OxO0 _ O0A ■ sin B sin v

Cin --' '

From this relation we determine: (R1 + R2) ■ sin/

O0 ^ = -

Angles p and y are obtained as follows. From 6 we extract:

sin P = -

(Rs + Ri) ■sm-

From 2 we obtain: Ad _ t-Vf

From triangle OOOIA the angle y is determined :

r = 180-p-*fL 2

Introducing into 7 relations 8, 9 and 10 we obtain:

(Rs + R2) ■ sin

O0 A =-

180 - arcsinl +

/ -Vj- >1 / -Vj- ^

2 • R, I 2 ■ R,

(R. + R2) . Ad

-. sin-

From 5 we obtain the height of the theoretical irregularities h. (Rs + R2) ■ sin

180 - arcsinf +

'-vf 1 '-vf"

2 • R, I 2 ■ R,

(R. + R2) . Ad

-. sin-

It is noted that roughness is not influenced by theposition of the tool given by parameter 0.

Considering the following entry data:

• Cutting velocity Vc = 180 [m/min]

• Pitch feed fz = 0.05 [mm/rot]

• Number of teeth Z = 2

• Diameter of the mill D = 6 [mm]

• Corner radius of the rool R2 = 2 [mm]

• Radius of the half-finished product Rs = 50 [mm]

For the case with the described values we obtain Ra = 0.162507 [pm].

3. Experimental activity

The experiment was made on the 3 axes processing centre Mori Seiki Duravertical 5080 found in the machine tool lab of Petru Maior University. The material used, a stainless steel, is coded DIN X40Crl4 (commercial name STAVAX, code Werkstoff 1.2083) with the chemical composition C0,36-0,42 %, Si max. 1%, Mn max. 1%, P max. 0,03 %, S max. 0,03%, Cr 12,5-14,5 %. The half-finished product having a spherical shape was obtained grinding operations, with a processing addition of 0.3 mm, followed by heat treatment, thus reaching the hardness of 48 HRC. The half-finishing phase follows the heat treatment, keeping an addition for the finishing of 0.1 mm and it is made by the same positioning as the one in the finishing phase. A technological process thus constructed maintains the processing addition constant for the finishing phase, a fundamental aspect for the correct evaluation of the experimental data. For finishing a toroidal mill Pokolm Voha was using with a diameter of 6 mm, with 2 teeth and a corner radius of 2 mm. The material of the tool is tungsten carbide covered with a layer of Ti. Using a toroidal mill has the advantage of a smaller variation of the cutting velocity as compared to tools with a spherical head. Securing the tools is made with a clamp system so that the assembly of tool and support has a radial outlet under 20 ^m. The cooling of the tool is made using an air jet (Figure 3).__

Fig. 3. Experimental study

Considering the same technological and geometrical values 4 samples were manufactured (figure 4). The quality of the processed surfaces was appreciated by two methods: a quantitative one, by measuring the roughness and an evaluative one by examining the topography of the enhanced surface over the microscope. The study of the surface quality was made using a roughness gauge made by Taylor-Hobson, England. The measurements on each surface were made in two directions, according to figure 5 and the data is presented in table 1.

Table 1. Determined 'values for the experimental roughness

MI Mil Mill MIV Media

Horizontal 0.241 0.245 0.285 0.203 0.2435

Vertical 0.271 0.344 0.288 0.321 0.306

The case study highlighted a grouping of the core formation area after the milling phase around the value Ra = 0.25-0,30 |im. The fact that the data is grouped in this way, without big variations, denotes a stable cutting process with parameters optimized for such a stainless steel.

4. Conclusions

• In the case of radial trajectories roughness is not influenced by the position of the tool given by the parameter 0 (parameter which positions the tool on the spherical area);

• In the case of using radial trajectories the value of the surface roughness is constant on the entire surface;

• The establishment of the finishing strategy has an important impact over the surface quality and processing time.

Fig. 4. Processed sample an measurement

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