Prediction of surface roughness in end-milling using fuzzy logic and its comparison to regression analysis.

Kromanis, Artis ; Krizbergs, Juris

1. INTRODUCTION

Quality of surface roughness plays a very important role in manufacturing. It is essential to maintain desired surface roughness during cutting process. It is necessary to establish models which can be used to predict surface roughness according to used technological parameters. Cutting parameters are variables which are non-linear, interdependent or hard to quantify with satisfactory precision. Such models would increase understanding about surface roughness forming process according to various technological parameters. There were attempts to develop empirical models with such a data mining techniques like regression analysis and computational neural networks (Feng & Wang, 2002). Regression analysis is a technique for modeling the relationship between two or more variables and is well known from previous studies (Lou et al., 1998). In this study empirical models were developed by using two methods: regression analysis and fuzzy logic. Exact novelty is a use of fuzzy logic to develop a more precise prediction model. In most recent years Fuzzy logic has invade in industry. Fuzzy logic is derived from fuzzy set theory (Zadeh, 1965) dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic (Boolean Logic). Fuzzy logic is the same as "imprecise logic" or a new way of expressing probability. Despite the advantages of classical Boolean Logic accuracy it has major drawback: it cannot reproduce human thought patterns (Inform, 2001). That's where Fuzzy logic does its work. It allows represent a human thought (experience and knowledge) in mathematical manner, which allows incorporate the ambiguous, approximate nature of human logic into computers. This human thought could be thought of CNC operator who manages cutting regimes to maintain desired surface roughness (Tomomitsu, 1997). Using this method a fuzzy model was developed and compared with quite common regression model.

2. DESIGN OF EXPERIMENT

Machined workpiece material was stainless steel (Stainless steel EN 1.4301--X5CrNi18-10). 12 end-milling cuts were made as part of it is shown in Fig. 1. Every cut (10mm wide) was made with different technological parameters as shown in table 1. Machining was made by using carbide end-mill with diameter 10 mm, and having 4 teeth.

[FIGURE 1 OMITTED]

As technological parameters the following data were chosen: f--feed (mm/rev.); d--depth of cut (mm) and v--cutting speed (m/min) (see Table 1). After conducting cutting process a surface roughness (Sa--mean surface roughness) was measured. It was performed on Taylor Hobson Form Talysurf Intra 50 profilograph. Obtained results were processed in TalySurf Intra software. Fig. 2 shows a visualization of measured 3D surface roughness.

[FIGURE 2 OMITTED]

3. REGRESSION MODELING

A functional relationship between surface roughness and the independent variables under investigation is defined by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

where C--regression constant, Sa--3D surface roughness (Sa mean surface roughness) in [micro]m, f--feed in mm/rev., d--depth of cut in mm, and v--cutting speed in m/min.

After logarithmic transformation the nonlinear form of Equation 1 was converted into a linear form, which then was used to develop regression model. To establish the prediction model, a software package MiniTab was used to perform the regression analysis using data of the table 1.

After conducting regression analysis in MiniTab a following regression model was developed:

Sa = -0,403 + 3,33f + 0,446d + 0,00140v. (2)

The next step was evaluation of the model. Experiment data (technological parameters) were put into the model and surface roughness parameters ([Sa.sub.reg]) were calculated (see Table 1).

4. FUZZY MODELING

Fuzzy modelling was performed in fuzzyTECH software. First of all, a fuzzy model must be designed, which shows relationships among input data, operator and output data (see Fig. 3).

[FIGURE 3 OMITTED]

The next step is to define membership functions for all input and output parameters (see Fig. 4) and to draw a rule book, which defines relationships between technological parameters and surface roughness

[FIGURE 4 OMITTED]

In some extent fuzzy modelling requires quite sufficient knowledge about the cutting process. Experience is necessary factor to draw correct membership functions and reliable rule block, which describes relationships between surface roughness and technological parameters.

5. MODEL VALIDATION

The final step in the study was validation of models. Cutting parameters were put into both regression model and fuzzy model. Graphical representation of data is shown in Fig. 5 where [Sa.sub.measured] is compared to [Sa.sub.regression] and [Sa.sub.fuzzy.] It can be seen that [Sa.sub.fuzzy] values are closer to [Sa.sub.measured] than [Sa.sub.regression]. It means that fuzzy prediction model is closer to the real values and more reliable in prediction surface roughness according to the technological parameters.

Accuracy of each model was calculated. Regression model proved capable of predicting the profile roughness (Ra) with about 90% accuracy. After calculations accuracy of regression model was about 85%, but accuracy of Fuzzy model was about 95%.

[FIGURE 5 OMITTED]

6. CONCLUSION

Study showed that it is possible to predict surface roughness according to technological parameters. Both regression and fuzzy models were built.

Although fuzzy model is a bit complicated to develop than regression model (need of experience and knowledge), it showed more reliable accuracy than regression model regression model 85% and fuzzy model 95%.

Further research could be done in implementing prediction models, especially fuzzy models, into adaptive control systems of CNC. Additionally, Fuzzy model learning capability could be improved by implementing neural networks.

7. REFERENCES

Feng C. X. & Wang X. F. (2002). Surface Roughness Predictive Modeling: Neural Networks versus Regression. IIETransactions on Design and Manufacturing. 42 p.

Lou M. S.; Chen J. C. & Li C. M. (1998). Surface Roughness Prediction technique For CNC End-Milling. Journal of Industrial Technology. Vol. 15, No. 1 (November 1998), 1-6.

Tomomitsu N. (1997). Device and corresponding method for determining a fuzzy logic conclusion based on a plurality of machining rules, USPTO, US 5598512, USA

Zadeh L. A. (1965). Fuzzy Sets. Information And Control. Vol. 8, 338-353.

*** (2001) fuzzyTECH 5.5 User's Manual, INFORM GmbH, pg.102

Tab. 1. Technological parameters (f; d; v), measured 3D surface
roughness ([Sa.sub.meas]), 3D surface roughness calculated from
regression model ([Sa.sub.reg]) and from fuzzy model ([Sa.sub.fuzzy])

No f d v [Sa.sub.meas]
 (mm/rev.) (mm) (m/min) [[micro]m]

1 0.25 1.5 190 1.37
2 0.25 0.5 190 0.631
3 0.1 0.5 190 0.388
4 0.1 1.5 190 0.988
5 0.1 1.5 120 0.635
6 0.25 1.5 120 1.37
7 0.25 0.5 120 1.09
8 0.1 0.5 120 0.472
9 0.21 1 210 1.02
10 0.13 1 210 0.871
11 0.21 1 100 0.805
12 0.13 1 100 0.407

No [Sa.sub.reg] [Sa.sub.fuzzy]

1 1.325 1.392
2 0.879 0.600
3 0.419 0.408
4 0.825 1.000
5 0.767 0.600
6 1.267 1.392
7 0.821 1.000
8 0.321 0.408
9 1.036 1.000
10 0.770 0.856
11 0.882 0.712
12 0.616 0.462