Prediction of Surface Roughness in End-milling Using Fuzzy Logic and its Comparison to Regression Analysis




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Prediction of Surface Roughness in End-milling Using Fuzzy Logic and its Comparison to Regression Analysis

Gala frēzēšanas virsmas raupjuma prognozēšana ar faziloģikas palīdzību, salīdzinot ar regresijas analīzi


A.Kromanis, J.Krizbergs.


Keywords: end milling, 3D surface roughness, fuzzy logic, regression analysis



Abstract: Nowadays, a use of highly automated machine tools in manufacturing requires reliable models and methods for prediction of surface roughness as output in machining process. This study focuses on developing empirical prediction models using regression analysis and fuzzy logic for surface roughness prediction in end-milling. The model considers the following cutting parameters: feed, cutting speed, depth of cut. Two competing data mining techniques, linear regression analysis and fuzzy logic, are used in developing empirical models. The values of surface roughness predicted by these models are then compared with those from measured – representing procedures for validation and comparison of models. In addition, as surface roughness parameters are used 3D surfaces roughness parameters, especially Sa, instead of 2D roughness parameters. This 3D approach gives more precise look at development of surface roughness in end-milling. Further research could be done in implementing these models in CNC adaptive control mechanisms.


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. 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 shown in Fig. 1. Every 10 mm wide cut 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.





Fig. 1. Sketch of machined workpiece showing cutted slot.


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.


3. Regression modeling


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

, (1)


where C – regression constant, Sa – 3D surface roughness (Sa –mean surface roughness) in μm, 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:

2)

The next step was evaluation of the model. Experiment data (technological parameters) were put into the model and surface roughness parameters (Sareg) 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).

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

Table1

Technological parameters (f; d; v), measured 3D surface roughness (Sameas), 3D surface roughness calculated from regression model (Sareg) and from fuzzy model (Safuzzy).


No

f

(mm/rev.)

d

(mm)

v

(m/min)

Sameas

(µm)

Sareg

Safuzzy

1

0.25

1.5

190

1.37

1.325

1.392

2

0.25

0.5

190

0.631

0.879

0.600

3

0.1

0.5

190

0.388

0.419

0.408

4

0.1

1.5

190

0.988

0.825

1.000

5

0.1

1.5

120

0.635

0.767

0.600

6

0.25

1.5

120

1.37

1.267

1.392

7

0.25

0.5

120

1.09

0.821

1.000

8

0.1

0.5

120

0.472

0.321

0.408

9

0.21

1

210

1.02

1.036

1.000

10

0.13

1

210

0.871

0.770

0.856

11

0.21

1

100

0.805

0.882

0.712

12

0.13

1

100

0.407

0.616

0.462






Fig. 2. 3D surface roughness visualization.





Fig. 3. Fuzzy model


relationships between technological parameters and surface roughness.

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 Sameasured is compared to Saregression and Safuzzy. It can be seen that Safuzzy values are closer to Sameasured than Saregression. It means that fuzzy prediction model is closer to the real values and more reliable in prediction surface roughness according to the technological parameters.

After graphical representation shown in Fig. 5 accuracy of each model was calculated. In paper (Lou et al., 1998) through experimentation,





Fig. 4. Membership functions for depth of cut (d), feed (f), cutting speed (v) and 3D surface roughness (Sa), respectively.





Fig. 5. Regression model and Fuzzy model validation diagram.


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%.


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 more complicated to develop than regression model (need of experience and knowledge), fuzzy model showed more reliable accuracy than regression model, respectively 85% and 95%.

Further research could be done in implementing prediction models, especially fuzzy models, into adaptive control systems of CNC.


11. References


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

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

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

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

5. FuzzyTECH 5.5 User’s Manual, INFORM GmbH, 2001.-102 p.


Artis Kromanis, M.Sc.ing.

Riga Technical University, Mechanical Engineering Institute

Address: Ezermalas Str. 6k, LV-1006, Riga, Latvia

Phone:+371 67089701, Fax: +371 67089739

e-mail: arai@latnet.lv


Juris Krizbergs, Dr.Sc.ing.

Riga Technical University, Mechanical Engineering Institute

Address: Ezermalas Str. 6k, LV-1006, Riga, Latvia

Phone:+371 67089701, Fax: +371 67089739

e-mail: juris.krizbergs@rtu.lv


A.Kromanis, J.Krizbergs. Gala frēzēšanas virsmas raupjuma prognozēšana ar faziloģikas palīdzību, salīdzinot ar regresijas analīzi.

Mūsdienās augsti automatizētu darbagaldu lietošana ražošanā prasa drošus virsmas raupjuma prognozēšanas modeļus un metodes. Šis pētījums ir veltīts empīrisku virsmas raupjuma prognozēšanas modeļu izveidei gala frēzēšanā, lietojot regresijas analīzes un faziloģikas metodes. Modeļi ietver sekojošus griešanas režīmus: padeve, griešanas ātrums, griešanas dziļums. Empīrisko modeļu izveidē ir lietotas divas konkurējošas datu apstrādes metodes – lineārā regresija un faziloģika. Ar šo modeļu palīdzību prognozētās virsmas raupjuma vērtības ir salīdzinātas ar izmērītajām, lai novērtētu un salīdzinātu modeļus. Kā virsmas raupjuma parametrs ir lietots 3D parametrs Sa 2D parametru vietā. Šī 3D pieeja dod precīzāku virsmas raupjuma veidošanās ainu. Tālākos pētījumos šie modeļi tiks pielietoti CNC adaptīvajā vadībā.


Кроманис A., Кризбергс Ю. Прогнозирование шероховатости поверхности после обработки концевой фрезой, используя фазилогику по сравнению с регрессионным анализом.

Применение в производстве высоко автоматизировнных станков требует надежных методов и моделей для прогнозирования шероховатости поверхности. Эти исследования фокусируются на разработке эмпирических моделей прогнозирования шероховатости поверхности в концевом фрезеровании, применяя ререссионный анализ и фазилогику. Модели используют следующие режими резания: подача,скорость и глубина резания. Два конкурирующих метода- линейная регрессия и фазилогика применяются для создания моделей. Прогнозированные значения сравнены с измеренными для оценки и сравнения моделей. Кроме того, вместо 2Д параметров шероховатости исследовался 3Д параметр Sa. Этот 3Д подход дает более точную оценку формирования шероховатости в концевом фрезеровании. Далее эти модели будут использованы для адаптивного управления CNC машин.


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