Materials Processing Technology OPTIMIZATION OF SURFACE

Journal of

ELSEVIER

Journal of Materials Processing Technology 56 (1996) 54-65

Materials Processing Technology

OPTIMIZATION OF SURFACE FINISH IN END MILLING INCONEL 718

M. Alauddin, M.A. E1 Baradie and M.S.J. Hashmi Advanced Materials Processing Centre, Dublin City University, Ireland

ABSTRACT This paper presents an approach to optimize the surface finish in end milling Inconel 718 using uncoated carbide inserts under dry conditions. In view of this, the mathematical models for surface roughness have been developed in terms of speed and feed by response surface methodology. Response surface contours were constructed in speed feed planes by computer. From these contours it was possible to select a combination of cutting speed and feed that reduces machining time without increasing the surface roughness. These were obtained by superimposing the constant lines of metal removal rates on the surface roughness contours.

1.INTRODUCTION Inconel 718 is a nickel base superalloy containing a columbium(niobium) age-hardening addition that provides increased strength without a decrease in ductility. It is oxidation and corrosion resistant and can be used at temperatures in the range of - 217 ° to 700°C. Due to its good tensile, fatigue, creep and rupture strength, this material is used in the manufacture of components for liquid rockets, parts for aircraft turbine engines, cryogenic tankage etc. However, in general this alloy is difficult to machine [1,2] for the following reasons: -

-

----

High work hardening rates at machining, strain rates leading to high cutting forces Abrasiveness Tough, gummy and strong tendency to weld to the tool and to form built up edge Low thermal properties leading to high cutting temperatures

A high surface finish is required because of its use in the design of high strength and reliable components. This paper presents an approach to develop mathematical models for surface roughness in end milling Inconel 718 by response surface methodology (RSM) [3] in order to optimize the surface finish of the machined surface. RSM is a combination of mathematical and statistical techniques used in an empirical study of relationships and optimization, where several independent variables influence a dependent variable or response. In applying the RSM, the response or dependent variable is viewed as a surface to which a mathematical model is fitted. In this study, machining variables like speed and feed which are easily controllable are considered in building the model. The optimum cutting condition is obtained by constructing contours of constant surface roughness by computer and used for determining the optimum cutting conditions for a required surface roughness. 0924-0136/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSD10924-0136 (95) 01820-5

M. Alauddin et al. / Journal of Materials Processing Technology 56 (1996) 54-65

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2. WORKPIECE MATERIAL The Inconel 718 workpiece material used in the machining test was in hot forged and annealed condition. The chemical composition of the workpiece material conforms to the following specification(%): C

Mn

Si

Ti

A1

Co

Mo

Cb

Fe

Cr

Ni

0.08

0.35

0.35

0.60

0.80

1.00

3.00

5.00

17.00

19.00

52.82

The hardness of the workpiece material was measured and found to be 260 BHN.

3. SURFACE FINISH IN END MILLING OPERATIONS The basic geometry of the end milling process is shown in Fig. 1.

_9

a. 1

Ns

I

DI

ar

7 Fig.1 : End milling process

Where v = cutting speed (peripheral) of the cutter (m/rain) D = diameter of the cutter (mm) N s = rotational speed of the cutter (rev/min) fz = feed per tooth (ram/tooth) fm = feed per minute (mm/min) or table speed (= fz x z x N~) z = number of teeth in the cutter a. = axial depth of cut (mm) aT = radial depth (width) of cut (mm).

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M. Alauddin et al. / Journal of Materials Processing Technology 56 (1996) 54-65

In end milling operations, theoretical surface roughness is generally dependent on cutting conditions, workpiece material, cutting tools etc. as shown in Fig.2. However, the theoretical surface roughness value R~, for side milling operations by solid end mills is estimated by the following formula [4,5]:

R . --

32(R+

f, × z

)

(1)

Where Ra - surface roughness CLA Om), z - number of teeth in the cutter, R - radius of the cutter, + ve sign to up milling and - ve sign to down milling. The surface finish produced in face milling operations [6,7] by end mill inserts can be expressed as:

f~

(2)

R a - 32r Where r - nose radius of the end mill insert. The above formulae for surface roughness are a function of feed per tooth and tool geometry. The actual surface roughness is usually larger than the theoreti_cal surface roughness values obtained by these formulae, because, these formulae do not take into account built up edge formation, deflection and vibration which are usually a function of cutting conditions like speed and axial depth of cut.

4. DEVELOPMENT OF THE MATHEMATICAL MODEL BY RSM 4.1 Postulation of the mathematical model Factors which affect the surface finish in end milling are shown in Fig.2. However, for a particular work-tool geometry, the surface roughness in end milling is assumed to be a function of cutting conditions. Moreover, in a rigid work-tool system, a low value of axial depth of cut has a negligible effect on the surface roughness in end milling [8]. Therefore, in this study, the surface roughness in end milling is assumed-to be a function of cutting speed (v) and feed (f,). The multiplicative model [9] for the predictive surface roughness (response) in end milling in terms of the investigated independent variables can be expressed as: Ra = C vk fz I

(3)

Where I~, - predictive surface roughness CLA Oam), v - cutting speed (m/min), fz - feed per tooth (ram/tooth), and C, k, 1 - model parameters to be estimated. Taking natural logarithm converts the above intrinsically linear type nonlinear model into the first-order polynomial as: = boxo + b l X l + b2x2

(4)

The second-order model can be extended from the first-order model's equation as:

(5) Where ~, - predictive response (roughness) on natural logarithmic scale, while xo = 1 (a dummy variable) and x~, x 2 - the coded value ( logarithmic transformations) of v and fz respectively and b's - model parameters to be estimated using experimentally measured surface roughness (Ra) data.

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M. Alauddin et al. / Journal of Materials Processing Technology 56 (1996) 5 4 ~ 5

Input

~ Cutting process~ Output -I ¢DelJt'mlent

(Controllable indepcndent variahh.s)

m

var,ahle~; J

m

Speed Feed

Machine

Axial depth o f cut Cutting f l u i d Rigidity

Type of

Machina bility parameter

materia-i( Mierostruc#ure

Compnsition I

Workpiece

Properties t Ilard.css)

~[ End milling H

.__..~ operations S i d e milling

Tool geometry

Fare milling SI.I millinx

Surface] finish

Roughness

Wa¢iRes~ Eeeurs of form

Tool material -flies .Carbide ,~ialon, Tool geometry 'Rake,lleliz &clearance a n l i e , aase eadius.No. o~ Itelh & Diametee Cutter runout Tool wear - - Milling mode m --

I Tool

Fig.2: Factors influencing surface finish in end milling processes

4.2 Experimental Design A well designed series of experiments can substantially reduce the total number of experiments often carried out randomly. In order to determine the equation of the response surface, several experimental designs have been developed which attempt to approximate the equation using the smallest number of experiments possible. The most widely preferred classes of response surface design are the orthogonal fu'st-order and central composite second-order design. The orthogonal first-order design (with two factors) consisting of nine experiments has been used to develop the postulated f'Lrst-order model.These 9 tests consist of four points ( 22 ) located at the comers of the square and a centre point repeated five times as shown in Fig.3. As the first-order model is accepted only over a narrow range of variables, the experiments were extended to obtain a second order model. The central composite rotatable design for the second-order response surface consists of an additional 4 axial points called augments (Fig.3).

4.3 Coding of independent Variables The independent variables were coded taking into consideration the limitation and capacity of the milling machine. The coded values of the variables shown in Table i for use in equations (4) and (5) were obtained from the following transforming equations:

lnv - In18.37 xl = In24.10-In18.37 Inf

- In 0 . 0 7 5

-- m 0 . 0 9 8 - tn 0 . 0 7 5

(6)