3d Surface Roughness Prediction Technique In End Milling

6th International DAAAM Baltic Conference INDUSTRIAL ENGINEERING 24-26 April 2008, Tallinn, Estonia

3D SURFACE ROUGHNESS PREDICTION TECHNIQUE IN ENDMILLING USING REGRESSION ANALYSIS Kromanis, A.; Krizbergs, J.

Abstract: Purpose of the study is to develop a technique to predict a surface roughness of part to be machined according to technological parameters. Such technique could be achieved by making mathematical model of machining. In this study as machining process a milling process is chosen, especially endmilling. Additionally to the study, one of the key factors, which differ from similar studies, is that as surface parameters the 3D surface parameters are used. In this study all the surface parameters are expressed as 3D parameters. 3D surface parameters give more precise picture of the surface; therefore it is possible more precisely to evaluate the surface parameters according to technological parameters. In result of the study, the mathematical model of end-milling is achieved and qualitative analysis is maintained. Achieved model could help technologists to understand more completely the process of forming surface roughness. Key words: 3D surface roughness; prediction; milling; regression.

are not so accurate for surface roughness prediction because they do not count many other very important technological parameters. One of the means to build a more precise prediction model is to use regression analysis. In this study regression analysis is used to predict the surface roughness according to technological parameters in end milling. Experiment is conducted to acquire necessary data and regression analysis is used to reach the credible surface roughness prediction model. According to this model manufacturing engineers could set cutting machines without any long-term adjusting. Material and time economy could be reached and also quality maintained. Further to describe the machined surface 3D parameters are introduced. In this paper a 3D surface roughness parameter like Sa (average absolute deviation of the surface) is used. 3D surface roughness parameters give more precise picture of the surface, because it shows the real environment of the surface.

1. INTRODUCTION

2. MATERIAL PROCESSING USING END MILL – SEQUENCE OF EXPERIMENT

The quality of surface plays a very important role in functionality of produced part. Therefore, it is necessary to develop methods, which can be used for the prediction of the surface roughness according to technological parameters. There is known some surface roughness models, mainly based on tools geometrical properties and basic technological parameters, mainly feed (f). Theses models

Aim of the experiment is to find relationships between surface roughness (Average absolute deviation of the surface – Sa) of machined workpiece and used technological parameters (cutting speed – v; feed – f; cutting depth – a). Workpiece was machined by using end mill in predetermined cutting conditions. After machining a workpiece surface is measured and 3D surface roughness values are

obtained. The next step is to process mathematical statistic analysis, after which it is possible to evaluate the influence of technological parameters on forming surface roughness. 2.1 Initial data of the experiment Machined workpiece material is stainless steel (Stainless steel EN 1.4301 – X5CrNi18-10). 12 end-milling cuts are made on workpiece. Every cut is made with different technological parameters (See table 2). Machining was made by using carbide end mill, which diameter is 10 mm and it has 4 teeth.

Fig. 1. Drawing of machined workpiece Simultaneously with choosing material of workpiece, a table (See table 1) with technological parameters was made. As technological parameters the following parameters were chosen: v – cutting speed (m/min); s – feed (mm/rev.) and a – cutting depth (mm). Table 1. Listing of technological parameters No. f a v (mm) (mm) (m/min) 1. 0,25 1,5 190 2. 0,25 0,5 190 3. 0,1 0,5 190 4. 0,1 1,5 190 5. 0,1 1,5 120 6. 0,25 1,5 120 7. 0,25 0,5 120 8. 0,1 0,5 120 9. 0,21 1 210 10. 0,13 1 210 11. 0,21 1 100 12. 0,13 1 100

There is known some publications where to existing parameters, some additional parameters are put, like material of machined workpiece and geometry of endmill [1]. Machined workpiece material and tool geometry is counted so far as correct technological parameters to be chosen. In real life material to be machined is chosen by designer neither by technologists nor CNC operator. It means that this parameter is hard to control in process. Tool geometry could be better controlled as a material of workpiece to be machined. Nevertheless, tool geometry can not be changed during the cutting process. The only really changeable parameters in process are cutting speed (v), cutting depth (a) and feed (f). These parameters were chosen to control the cutting process and to make evaluation of the machined workpiece’s 3D surface roughness according to technological parameters. Referring to the Table 2, limits for the technological parameters are chosen accordingly: - cutting speed (v): 120≤v≤190 m/min; - feed (f): 0.1≤s≤0.25 mm/rev.; - cutting depth (a): 0.5≤t≤1.5 mm. Designation of parameter limits is essential, because choosing parameters outside designated range can result in appropriate results of experiment. Out of this range it is almost impossible to get satisfied results to analyze the influences of technological parameters to 3D surface roughness parameters. Parameters in positions from 9 to 12 are control parameters. 2.2 Mathematical formulation or regression analysis The main task for regression analysis is to show relationship between result (3D surface roughness) and factors (v, f, a) and to evaluate a function of this relationship:

Sa = f (v, f , a ) + ε

(1)

In the equation (1) Sa is average absolute deviation of the 3D surface roughness, f is

response function and v, f, a are variables of milling, and E is error, which is distributed on Sa average value. Concerning previous equation (1), relationship between the surface roughness (Sa) and technological parameters (v, f, a) can be written into following style: Sa = C ⋅ f a1 ⋅ a a 2 ⋅ v a3 , (2)

where C is constant and a1, a2, a3 are exponents. To maintain defining of constant and exponents, a mathematical model has to be linearized, using following logarithmic transformation: ln Sa = ln C + a1 ln f + a2 ln a + a3 ln v (3) Further this equation (3) is simplified (4), for using it in statistical analysis program called MiniTab. lnSa is replaced by y, lnC by b0, a1lnf by b1x1, a2lna by b2x2 and a3lnv by b3x3: y = b0 + b1 x1 + b2 x2 + b3 x3

(4)

2.3 3D surface roughness measurements When the machining of workpiece is finished a surface roughness measurement is performed. For measurements Taylor Hobson Form Talysurf Intra 50 profilometer – profilograph was used. On every machined groove a 3x3 mm measurement field was chosen. Every field was scanned by 15 strokes and every stroke included 100 measurement points. Obtained results were processed in TalySurf Intra program. Further the measured examples were levelled (Fig. 2) to eliminate form defects. Only surface roughness data were processed for 3D surface roughness measurement.

Fig. 2. Representation of 3D surface roughness of machined workpiece: on the left side –surface roughness before levelling; on the right side –surface roughness after levelling When results of 3D surface roughness (Sa) was obtained, then they were written in MiniTab program for processing. Table 4 shows the data, which were used for processing in MiniTab. 2.4 Results of experiment The final data for processing are shown in table 2. Showed Sa values are average from 3 measurement samples.

Table 2. Chosen technological parameters and obtained Sa (average absolute deviation of the surface) No.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10 11. 12.

f (mm)

0.25 0.25 0.1 0.1 0.1 0.25 0.25 0.1 0.21 0.13 0.21 0.13

a (mm)

1.5 0.5 0.5 1.5 1.5 1.5 0.5 0.5 1 1 1 1

v (m/min)

190 190 190 190 120 120 120 120 210 210 100 100

Sa (µm)

1.37 0.631 0.388 0.988 0.635 1.37 1.09 0.472 1.02 0.871 0.805 0.47

As seen form Table 2, measurements in positions 9 to 12 are control measurements (marked in grey). Technological parameters in these positions were taken with offset. All these data were put into MiniTab program and following regression equation was reached:

Sa = −0,403 + 3,33 s + 0,446 t + 0,00140 v (5)

Also regression analysis showed that cutting speed (v) had little influence on formation of surface roughness. Therefore, to simplify further calculations the cutting speed (v) is omitted. Sa = −0,403 + 3,33 f + 0,446a

(6)

Such optimized equation (6) ease further calculations. There is no further need to calculate values, which do not influence overall result. It is quite important that we consider that the time is one of the most important indicators of productivity. 3. ANALYSIS OF TECHNOLOGIGAL PARAMETERS INFLUENCE ON SURFACE ROUGHNESS

Considering above mentioned workpiece machining and data processing, using regression analysis, and quality analysis of table 2, we can conclude that surface roughness is more influenced by cutting depth (a) and feed (f). In this case cutting speed (v) has minimal influence. There raises a question, why cutting depth (a) and feed (f) have such a big influence on surface roughness, but cutting speed (v) does not? From practice it is known that in most cases the biggest influence come from cutting speed (v). One of possible explanations could be the range of parameter’s change. For example, cutting depth (a) range is from 0.5 mm to 1.5 mm. It means that change from 0.5 mm to 1.5 mm in relative percents is 200 %. For feed (f) it is 150 %, but for cutting speed (v) it is 58 %. Remarkably less than for cutting depth (a) and feed (f). For example, if cutting depth (a) changed from 8 to 9 mm, the actual range of change in percents would be 12.5 %. Considering previous conclusion, it could result that in this case cutting depth (a) would have considerable less influence on surface roughness (Sa). To confirm correctives of such approach, more experiments should be done. Taking

account such a feature of analysis could improve existing prediction models and improve algorithms for choosing effective technological parameters. This approach still needs some more experimental data to improve its credentials. From further analyzing of experimental data we can obtain two extreme values (the smallest and the biggest 3D surface roughness): The smallest Sa = 0.338 micrometers: f = 0.1 mm.; t = 0.5 mm; v = 190 m/min. The biggest Sa = 1.37 micrometers: f = 0.1 mm/rev.; t = 0.5 mm; v = 190 m/min. From these data we can conclude that the smallest surface roughness (Sa) is reached by using the smallest feed (f) and cutting depth (a) and the biggest cutting speed (v). But once again analyzing technological parameters, which were used to reach the biggest possible surface roughness (Sa), we conclude that it is necessary to use opposite technological parameter values: the biggest feed (f) and cutting depth (a); but cutting speed (v) played small influence and stayed on the top of its value. Once again it is possible to confirm that the biggest influence on surface roughness was made by such technological parameters like cutting depth (a) and feed (f), but cutting speed (v) has considerable small influence. 4. OTHER PREDICTION METHODS

Here are described other methods, which could be useful for making surface roughness prediction models. 4.1 Fuzzy logic The most recent method for analyzing cutting factors influence on surface roughness is the Fuzzy logic or Fuzzy system. Fuzzy logic is concerned with the continuous transition from truth to false states, as opposed to the discrete true/false transition in binary logic. Fuzzy logic is

particularly attractive due too its ability to solve problems in the absence of accurate mathematical models. Computational neural networks give a number of attractive properties for modeling complex manufacturing process or systems: universal function approximation capability, resistance to noisy or missing data. Instead of operating with numeric values of variables and using mathematical functions to describe relationships, fuzzy logic uses common everyday language to describe variables and uses fuzzy linguistic rules to define relationships. The fuzzy logic is quite a new method for building mathematical models and its still needs development.

surface, were used, which give more realistic view of surface roughness. The study showed that technological parameter range also plays a very important role on forming surface roughness. Study results can be used by technologists and other manufacturing specialists to set up cutting parameters in end-milling. Further research could be concentrate on development of knowledge data base. This data base could contain information about surface roughness values according to used technological parameters. Further research should be done to confirm, that the range of variation of technological parameters influences its performance on forming surface roughness. 11. REFERENCES

4.2 Other methods The next type of analysis, which can be used is Analysis of Variance also known as ANOVA. Some steps in this analysis are similar to Regression analysis. Another method is Response Surface Methodology, which is also known from some publications. The next method, which can be used, is Taguchi Method Analysis. The Taguchi method is used to identify impact of various parameters on an output and figure out how to control them to reduce the variability in that output. These types of methods can be combined to compare the effectiveness of each other. 5. CONCLUSION

From this experiment we can conclude that regression analysis can be used trusty to find relationships between surface roughness parameters (Sa) and technological parameters (v, a, f). This study has a different approach on evaluation of machined surface roughness. 3D surface roughness parameters, mainly Sa - average absolute deviation of the

1. N. Suresh Kumar Reddy, P. Venkateswara Rao. Selection of optimal tool geometry and cutting conditions using a surface roughness prediction model for end milling. – International Journal of Advanced manufacturing Technologies, 2005, 1202 – 1210. 6. ACKNOWLEDGMENT

This work has been partly supported by the European Social Fund within National Program “Support for carrying out doctoral study program’s and post-doctoral researches” project “Support for development of doctoral studies in Riga Technical University”. 7. CORRESPONDING ADDRESS

MSc. Artis Kromanis Riga Technical University, Department of Mechanical Engineering Ezermalas St. 6, LV-1006 Riga, Latvia Phone: +37126779672, E-mail: [email protected]