tool wear measurement

P.S.Sivasakthivel et. al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 1780-1789

PREDICTION OF TOOL WEAR FROM MACHINING PARAMETERS BY

RESPONSE SURFACE METHODOLOGY IN END MILLING

P.S. SIVASAKTHIVEL*

Department of Mechanical Engineering, Kumaraguru College of Technology

V. VEL MURUGAN

Department of Aeronautical Engineering, Kumaraguru College of Technology

R. SUDHAKARAN

Department of Mechanical Engineering, Kumaraguru College of Technology

E-Mail: - [email protected]

Abstract

Tool wear increases cutting force, vibration, temperature, etc in end milling and reduces surface finish of the machined work piece. Mathematical model has been developed to predict the tool wear in terms of machining parameters such as helix angle of cutting tool, spindle speed, feed rate, axial and radial depth of cut. Central composite rotatable second order response surface methodology was employed to create a mathematical model and the adequacy of the model was verified using analysis of variance. The experiments were conducted on aluminium Al 6063 by high speed steel end mill cutter and tool wear was measured using tool maker’s microscope. The direct and interaction effect of the machining parameter with tool wear were analyzed, which helped to select process parameter in order to reduce tool wear which ensures quality of milling. Key words: Response surface, analysis of variance, tool wear, mathematical model, end milling

1. Introduction

In manufacturing industries milling is fundamental metal cutting operation and end milling is the most frequent operation encountered, which was employed for making profiles, slots, engraves, contours, pockets in various components. During machining cutting tools are subjected to rubbing process, the friction between cutting tool and workpiece materials results in progressive loss of materials in cutting tool. Tool wear is a change of shape of tool from its original shape resulting from the gradual loss of tool material. Thus tool wear becomes an important parameter in the metal cutting process. The worm tool may cause significant degradation in the work piece quality [1]. The consequence of the tool wear are poor surface finish, increases in cutting force, increases in vibration of the machine tool, increases in tool-workpiece temperature during machining, decreases in dimension accuracy, increases in the cost and lowers the production efficiency and component quality. Tool wear can be categorized into several types as crater wear, notch wear, chipping, plastic deformation, ultimate failure and flank wear based on the tool wear phenomena. In practice flank wear is used to determine the tool life. Wear on the relief face is called flank wear and it occurs due to abrasive wear of the cutting tool against the machined surface. The propagation of the flank wear follows three stages, initial (or preliminary) wear, steady wear and severe (or ultimate or catastrophic) wear. When the flank wear reaches critical value (severe wear) the wear rate increases, cutting force and temperature increase rapidly and the surface roughness of the machined surface decreases [2]. Prediction of tool wear becomes

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important to increase the maximum utilization of tool and to minimize the machining cost [3]. An effective model is essential to predict the tool wear becomes necessary.

Mathematical modeling in terms of process parameters for tool wear has been carried out by many researchers. Kaye et al. [4] developed a mathematical model based on response surface methodology to predict tool flank wear using spindle speed change. The grey–Taguchi method was adopted to optimize the milling parameters of aluminum alloy with multiple performance characteristics and found flank wear are decreased from 0.177 mm to 0.067 mm [5]. Palanisamy et al. [3] developed a regression mathematical model to predict tool flank wear in terms of machining parameters such as cutting speed, feed and depth of cut. Predicted values of tool flank wear of the mathematical model compared with the experimental values. An abductive network was formulated for predicting tool life in milling operations using input parameters such as cutting speed, feed per tooth, and axial depth [6]. Oktem et al. [7] developed a mathematical model based on response surface methodology and optimized cutting condition for surface roughness using genetic algorithm. The first order and second order mathematical model, in terms of machining parameters tool geometry (radial rake angle and nose radius) and cutting conditions (cutting speed and feed rate) on machining performance was developed based on Taguchi’s experimental design method [8]. Ghosh et al. [9] proposed a neural network-based sensor fusion model to estimate average tool flank wear. A grey-fuzzy reasoning grade for tool life and material rate obtained from the grey-fuzzy logics analysis is used to determine the optimal cutting parameters such as spindle speed, feed per tooth, axial depth of cut and radial depth of cut [10]. Tamizharasan et al. [11] predicted the tool wear, tool life, quality of surface turned, and amount of material removed in hard turning by conducting experiments under different machining condition. Bouzid Sai [12] developed empirical model for tool life determination in connection with cutting speed and machining time. Tool wear are greatly influenced by the end milling process parameter. Selection of suitable combination of process parameter becomes important in reducing tool wear and thereby increasing tool life. In this present work the main objective is to develop a mathematical model to predict the tool wear in terms of machining parameters such as helix angle of cutting tool, spindle speed, feed rate, axial and radial depth of cut. After milling the tool wear was measured using Metzer tool maker’s microscope. The mathematical model helps us to study the direct and interaction effect of each parameter.

2. Response surface methodology

Response surface methodology is the most informative method of analysis of the result of a factorial experiment. In the present work, helix angle of cutting tool, spindle speed, feed rate, axial and radial depth of cut have been considered as the process parameters and the tool wear are taken as a response variable (table 1). The response tool wear ‘T’ can be expressed as a function of process parameters helix angle (α), spindle speed (N), feed rate (Z), axial (X) and radial depth of cut (Y).

Tool wear, T = ф (αiu, Niu, Ziu, Xiu, Yiu) + eu (1)

Where ф = response surface, eu = residual, u = no of observations in the factorial experiment and iu represents level of the ith factor in the uth observation.

When the mathematical form of ф is unknown, this function can be approximated satisfactorily within the experimental region by polynomials in terms of process parameter variable. Box and Hunter [13] proposed central composite rotatable design for fitting a second order response surface based on the criterion of rotatability. The selected design plan [13] chosen consists of 32 experiments (table 3). It is five factors - five levels central composite rotatable design consisting of 32 sets of coded conditions. The design for the above said experiment comprises of a ½ replication of 25 (=16) factorial design plus 6 center points and 10 star points. These correspond to first 16 rows, the last 6 rows and rows from 17 to 26 respectively in the design plan shown.

For ½ replicate the extra point included to form a central composite design, α becomes 2(k-1)/4 = 2. The upper limit of the parameter is coded as 2, lower limit as -2 and the coded values for intermediate values were calculated from the following relationship [14]:

minmax

minmax22

XX

XXXXi

(2)

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Where,

Xi – The required coded value of a variable X,

X – Is any value of the variable from X min to X max

Xmin – Is the lower limit of the variable.

Xmax – Is the upper limit of the variable.

The intermediate values coded as -1, 0 and1.

Table 1 Parameters and levels in milling

Parameter

Units Factor levels

-2 -1 0 1 2

Helix angle (α) Degree ( 0 ) 30 35 40 45 50

Spindle speed (N) Rpm 2000 2500 3000 3500 4000

Feed rate (Z) mm/rev 0.02 0.03 0.04 0.05 0.06

Axial depth of cut (X) mm 1.5 2 2.5 3 3.5

Radial depth of cut (Y) mm 1.5 2 2.5 3 3.5

3. Experimental setup

The experiments were conducted on a HASS vertical machining center: model tool room mill with high speed steel end mill cutter under dry condition. The work piece material was Aluminium alloy (Al 6063) commonly available machinable metal which finds application in automobile and valve industries. The dimension of the work piece specimen was 32mmX32mm in cross section and 40 mm in length. The tool wear was measured by using Metzer tool maker’s microscope on the flank surface of the end mill cutter specimen and the observations are tabulated to obtain the mathematical model (table 3)

4. Development of mathematical model

The general form of a quadratic polynomial which gives the relation between response surface ‘y’ and the process variable ‘x’ under investigation is given by

y = b0 + ixi + iixi2 + ijxi (3)

Where b0 = constant, bi = linear term coefficient, bii = quadratic term coefficient and bij = interaction term coefficient.

The values of the coefficients of the polynomials were calculated by multiple regression method. A statistical software QA Six Sigma DOEPC IV was used to calculate the values of these coefficients. The second order mathematical model was developed by neglecting the insignificant coefficients of the tool wear (T).

Tool wear (T) = 0.266 - 0.077α - 0.018 N - 0.023 X + 0.022 Y + 0.045 α 2 - 0.004 Z2 + 0.01 Y2 + 0.016 αN + 0.021 αZ + 0.044 αX – 0.014 αY + 0.022 NZ +0.014 NX - 0.021NY - 0.009ZX – 0.004ZY – 0.016 XY (4)

Where α = Helix angle in ( 0 ) N= cutting speed in RPM

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Z= Feed rate in mm/rev X= Axial depth of cut in mm

Y= Radial depth of cut in mm

Table 2 Adequacy of the model

Response Factors

df

Lack of

Fit -df

Pure

Error

F-ratio R- ratio Whether Model

is adequate model standard model standard

Tool Wear 17 8 6 3.584 6.37 70.185 4.56 Adequate

The adequacy of the model was tested using the analysis of variance (ANOVA) technique (table 2). The calculated F-ratio of the model does not exceed the standard value and the calculated R-ratio of the model is above the standard value for a desired 95% level of confidence. It is evident from the table 3 that the error between the experimental value and predicted value is less than 5%.

Table 3 Experimental design - Central composite design matrix

Specimen No

Control Factors Tool wear (mm)

α N Z X Y Observed

Value Predicted

Value %

Error 01 -1 -1 -1 -1 1 0.62 0.62 0.0 02 1 -1 -1 -1 -1 0.185 0.178 3.8 03 -1 1 -1 -1 -1 0.375 0.368 1.9 04 1 1 -1 -1 1 0.165 0.158 4.2 05 -1 -1 1 -1 -1 0.405 0.406 -0.2 06 1 -1 1 -1 1 0.285 0.284 0.4 07 -1 1 1 -1 1 0.45 0.45 0.0 08 1 1 1 -1 -1 0.265 0.256 3.4 09 -1 -1 -1 1 -1 0.35 0.354 -1.1 10 1 -1 -1 1 1 0.275 0.276 -0.4 11 -1 1 -1 1 1 0.315 0.318 -1.0 12 1 1 -1 1 -1 0.27 0.264 2.2 13 -1 -1 1 1 1 0.32 0.332 -3.8 14 1 -1 1 1 -1 0.23 0.23 0.0 15 -1 1 1 1 -1 0.305 0.304 0.3 16 1 1 1 1 1 0.275 0.274 0.4 17 -2 0 0 0 0 0.615 0.6 2.4 18 2 0 0 0 0 0.28 0.292 -4.3 19 0 -2 0 0 0 0.315 0.302 4.1 20 0 2 0 0 0 0.22 0.23 -4.5 21 0 0 -2 0 0 0.25 0.25 0.0 22 0 0 2 0 0 0.255 0.25 2.0 23 0 0 0 -2 0 0.3 0.312 -4.0 24 0 0 0 2 0 0.23 0.22 4.3 25 0 0 0 0 -2 0.255 0.262 -2.7 26 0 0 0 0 2 0.36 0.35 2.8 27 0 0 0 0 0 0.275 0.266 3.3 28 0 0 0 0 0 0.265 0.266 -0.4 29 0 0 0 0 0 0.275 0.266 3.3 30 0 0 0 0 0 0.265 0.266 -0.4 31 0 0 0 0 0 0.255 0.266 -4.3 32 0 0 0 0 0 0.265 0.266 -0.4

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5. Results and discussion

A mathematical model was developed to predict the tool wear by relating it with process parameters such as helix angle, spindle speed, feed rate, axial depth of cut and radial depth of cut. The direct and the interaction effects of these process parameters on tool wear were calculated plotted are shown in figs. 1-8 and the cause and effect were analyzed. The trends of the potted direct and the interaction effect of these process parameters help to determine which parameter and parameter interactions are statistically significant in decreasing the tool wear. For tool wear, most of the parameters are found to be apparently significant because the levels of significance of each parameter and interaction parameter factors are almost the same.

Direct effect of variables

In this work, the effects of helix angle, spindle speed, feed rate, axial depth of cut and radial depth of cut were experimentally investigated. From figs. 1-4 it is clear that the helix angle, spindle speed, axial depth of cut and radial depth of cut have a significant effect on tool wear.

Direct effect of helix angle

Fig. 1 shows the direct effect of helix angle on tool wear. From the figure it is understandable that the increase in helix angle resulted in reduced tool wear and it is minimal at the helix angle range of 400 – 450. The cutting action of the tooth formed by a straight flute is intermittent [15]. When the tooth enters the work piece, the whole length of the tooth takes the full load and the cutting forces increase rapidly. These cutting forces continue to increase which results in propagation of tool wear. It is evident the cutting tool with helix angle in between 400 – 450 were advantages to reduce tool wear.

Direct effect of spindle speed

From Fig 2 it is understandable that increase in spindle speed reduces the tool wear. Increase in spindle speed results in reduced cutting time [16], which in turn reduces the propagation of flank wear.

Direct effect of axial depth of cut

Fig 3 depicts the direct effect of axial depth of cut on tool wear. It is evident from the figure the tool wear decreases with the increase in axial depth of cut. Increase in axial depth of cut makes end mill cutter and work piece to be stable which resulted in reduced chatter vibration. These reductions in vibration in turn cause the propagation of flank wear within the steady region.

Direct effect of radial depth of cut

Fig 4 shows the direct effect of radial depth of cut on tool wear. From the figure it is understandable that the increase in radial depth of cut resulted in reduced tool wear. Increasing the width of the cut the adhering tendency of the aluminium Al 6063 gets increased which in turn propagates the too wear.

Fig 1. Direct effect of helix angle

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Fig 2. Direct effect of spindle speed

Fig 3. Direct effect of axial depth of cut

Fig 4. Direct effect of radial depth of cut

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Interaction effect of variables

Strong interaction was observed between various process parameters for tool wear. The most significant interaction effect was found between helix angle and axial depth of cut; spindle speed and feed rate; helix angle and feed rate; and spindle speed and radial depth of cut. The contour graph between these most significant process parameter interactions are shown in figs 5-8. The following conclusion can be made from these interaction plots.

Interaction effect of helix angle and axial depth of cut

The interaction effect of helix angle and axial depth of cut on tool wear is shown in the contour graph (fig. 5) reveals that as helix angle increases the tool wear decreases. The same trend continues for the change of level of axial depth of cut from 1.5 mm to 3 mm. The trend gets reversed for 3.5 mm axial depth of the cut, increase in helix angle increases the tool wear. For all the change of levels of axial depth of cut the tool wear is minimal in between 400 – 450 helix angles.

Interaction effect of spindle speed and feed rate

Fig 6 shows the interaction effect of spindle speed and feed rate on tool wear. From the figure it is clear that the tool wear decreases with increase in spindle feed for the feed rate in between 0.02 mm/rev – 0.04 mm/rev. The trend gets reversed for feed rate in between 0.5 mm/rev – 0.6 mm/rev, where tool wear increases with increases in spindle speed.

Interaction effect of helix angle and feed rate

Fig 7 shows the interaction effect of helix angle and feed rate on tool wear. From the figure it is understandable that the increase in helix angle resulted in reduced tool wear for all the levels of feed rate.

Interaction effect of spindle speed and radial depth of cut

Fig 8 shows the interaction effect of spindle speed and radial depth of cut on tool wear. From the figure it is clear that tool wear decreases with increase in spindle speed for the radial depth of cut in between 3.5 mm – 2mm. The trend gets reversed for radial depth of cut in between 2mm – 3mm, where tool wear increases with increase in spindle speed.

Fig 5. Contour graph of interaction effect of helix angle and axial depth of cut

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Fig 6. Contour graph of interaction effect of spindle speed and feed rate

Fig 7. Contour graph of interaction effect of helix angle and feed rate

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Fig 8. Contour graph of interaction effect of spindle speed and radial depth of cut

6. Conclusion

The following conclusions were arrived from the results of the present investigation.

The investigation presented a central composite rotatable second order response surface methodology to develop a mathematical model to predict tool wear in terms of helix angle, spindle speed, feed rate, axial and radial depth of cut.

The helix angle is the most significant parameter which reduces tool wear. The tool wear is minimal in between 400 – 450 helix angles.

The increase in spindle speed and axial depth of cut reduces the tool wear. The decrease in radial depth of cut reduces tool wear.

The interactions between the process parameters were analyzed and strong interactions were observed between helix angle and axial depth of cut; spindle speed and feed rate; helix angle and feed rate; and spindle speed and radial depth of cut.

Acknowledgment

The author would like to extend his gratitude for the financial support rendered by All India Council for Technical Education, New Delhi and Kumaraguru College of Technology, Coimbatore. The author also wishes to thank Mr. Sethupathy for technical assistance in machining.

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