Advanced Technologies for Developing Countries
June 28-30, 2006
Rijeka, Croatia /
MATHEMATICALMODELINGOFSURFACE ROUGHNESS IN TURNING PROCESS
D. Bajić, I.Špar and I.Veža
Keywords: longitudinal turning, surface roughness, cutting parameters
1. Introduction
Production of technical surfaces of the machine components is realized either by the method of chips forming machining or the one without metal removal. During the machining and the usage of machine parts the given surfaces are exposed to the effect of the various kinds of burdening. The most important ones are mechanical and chemical burdening that result with dilapidation of parts and corrosion. Microscopically observed, technical surfaces are not geometrical level surfaces with the ideal smoothness but rather rough level surfaces characterized by series of uneven spots of different forms and disposition.
The dimension of the surface roughness can affect the following elements:
- the decrease of dynamic endurance,
- intensified friction and dilapidation of the tribo-burdened surfaces,
- the decrease of overlap of a contraction link which effects the decrease of its carrying capacity,
- speeding up the corrosion.
2. Aim of analysis
We can differ the roughness proceeded from direction of the main motion (measurements are made in direction of machining) and the roughness came out of the direction of feed motion (measurements are made vertically the traces of machining).
The first type of the roughness is characterized by the important activity of separation of scraps whereas, beside the layer on the front surface, material and the geometry of tools, the cutting speed plays the important role as well. However, the roughness dimension depends on elastic deformation of tools, machine tool and the geometry of tools.
The second type of roughness is rather important for the surface quality and can be approximately measured on the basis of geometry of the cutting part of tools and machining kinematics.The main elements that determine the cutting parameters of chip forming machining or rather the turning work are speed of metal removal (cutting speed) vc,depth of cut ap,andfeed f.
Technological and manufacturing processes demand appliance of modern and complex mathematical and other methods so they can achieve the best possible results. Therefore experimentation and analysis and off course the best possible mathematical approximation of the process and its by-effects are necessary in order to select the best working parameters i.e. achieving required surface roughness.
Optimal surface roughness is necessary because of improvement of corrosion resistace, tribology attributes and estetic apearance. Exceedingly low surface roughness requires additional expenses of production. Therefore selection of optimal cutting parameters is necessary in order to achieve optimal values of surface roughness.
Knowledge of the principles of chips forming machining and influence of the impact factors are the necessary postulates in:
- designing machines that will fulfill the production optimum,
- achieving high quality products concerning precision and quality of machined surfaces (surface roughness),
- designing manufacturing processes that require not only fulfillment of productivity requirements but also necessary economical needs.
This paper shows correlation of input parameters: cutting speed, the depth of cut and a feed to roughness of machined surface. Aim of analysis is to retrieve mathematical model that shows dependence of roughness on input parameters and there for can be used in machining.
3. Factors that influence surface roughness
The roughness of the machined surface is seen through micro-geometrical irregularities of the surface. The evaluation of the quality of machined surface is based on the judgment of its roughness. Theoretical roughness depends exclusively on tools geometry and applied process of machining whereas a real roughness appears as the result of theoretical roughness though with bigger or lesser occasional roughness provoked by the many factors. The surface roughness is influenced by the most important factors such as:
- cutting parameters,
- tool geometry,
- build-up edge,
- process time,
- work piece and tool material,
- tool wear,
- dynamical behavior of cutting system,
- appliance of coolants and lubricants.
Cutting speed influence is associated to generation of build-up edge i.e. build-up edge’s influence on surface roughness of processed surface. At lower cutting speed (0.16-0.6[m/s]), generation of build-up edge results with grater surface roughness.
Increment of cutting speed results causes decrement of build-up edge influence that induces as reduction of surface roughness. With further increment of cutting speed, nature of particles separation changes, what results as decrement of plastic deformation causing surface roughness reduction. Unlimited increment of cutting speed doesn’t influence roughness because it causes greater tool wear that keeps surface roughness approximately on the same level.
Feed influences surface roughness directly proportional. Feed increment results as increment of surface roughness. However feed influence is related to cutting tool nose radius influence. Unlimited reduction of feed does not result with reduction of surface roughness. At some level, value of cutting tool nose radius prevents further reduction of surface roughness causing it to stay at minimum possible level.
Cutting tool nose radius influences surface roughness inversely proportional. Increment of cutting tool nose radius value causes reduction of surface roughness. Reduction of surface roughness is limited with some minimal value. Further increment of cutting tool nose radius value causes vibrations that have negative influence in surface roughness.
From geometrical perspective, the depth of cut doesn’t influence surface roughness because it has no influence on size and form of bumps. However, influence of depth of cut is indirect trough generation of build-up edge, deformation of separated particles, cutting temperature, cutting forces, vibrations etc.
Figure 1 shows influential factors on surface roughness regarding chip-forming machining.
4. Conditions of experiment
Experiments are performed on lathe machine “PRVOMAJSKA” D420/1500. Work piece material is steel 34CrNiMo6 (DIN). The experiments are carried out by the tool for external machining (SANDVIK Coromant), which consist of tool holder mark PTGNR 2020 K 16 and insert mark TNMG 16 04 08 – PF 4015.
The “SURTRONIC 3+” instrument, produced by Rank Taylor Hobson, has done the measurements of surface roughness. Also post processing module was used. Module connects to “SURTRONIC 3+”, directly trough the R232 cable. Module possessed integral thermal printer which prints appearance of profile and measured values. All experiments were done without appliance of coolants and lubricants.
Figure 1. Influential factors on surface roughness
5. Planning and realization of experiment
Experiment planning connotes prediction of processes and results based on knowledge and experience that will end up giving new cognitions if using rational research methods. In experiment planning, multifactor design of second degree was used. Since turning is characterized by lot of factor that directly or indirectly due to their value, influence on progress and outcome of experiment, and also because of statistic nature of process, it is necessary that process is analyzed using multifactor design.
The multifactor design of the second degree has been used to carry out this experiment. Actually, in order to learn more about the maximum or minimum of the process or its function it is necessary to approximate it by the polynomial of the second rather than the polynomial of the first degree.Due to limited number of parameters that can be analyzed, the following parameters have been selected:
- cutting speed, vc
- feed, f
- depth of cut, ap
Whilst applying central composite design the empiric polynomial model of the second degree is taken as the first step:
(1)
b0, bi, bij, bii– regression coefficients
Xi – coded values of input parameters
The needed experimental point number is calculated using following equation:
(2)
2k – the design number within basic points
nα – the design number on the central axes,
no – the repeated design number of the average level.
According to equation (2), it is necessary to perform 8 tests (3 factors on 2 levels), 6 repetitions on middle level and 6 tests on center axis (summed: 20 tests) so multifactor design would be accurate.
The selected values of cutting parameters are the following:
- cutting speed:vc,max = 250 [m/min]
vc,min = 150 [m/min]
- depth of cut:ap,max = 1,2 [mm]
ap,min = 0,6 [mm]
- feed:fmax = 0,28 [mm/r]
fmin= 0,16 [mm/r].
Adding the points to the central axes where xi = ± αα, and α=1.682, the 3-factorial design can be presented in table 1.
Table 1. Physic values and coded indexes of input factors
Input parameters / Coded values of input parametersx-i / x-i,min / x-i0 / xi,max / x+i
-1,682 / -1 / 0 / +1 / +1,682
x1 =vc (m/min) / 115.9 / 150 / 200 / 250 / 284.1
x2 =ap (mm) / 0,4 / 0,6 / 0,9 / 1,2 / 1,4
x3 =f (mm/r) / 0,125 / 0,16 / 0,22 / 0,28 / 0,315
Measuring of surface roughness was carried out five times for each test, and table 2 shows their average value.
Table 2. Results of the surface roughness measurements
Test number / INPUT / OUTPUTvcm/min / a pmm / fmm/r / Ra [μm]
1. / 150 / 0.6 / 0.16 / 1.44
2. / 250 / 0.6 / 0.16 / 1.04
3. / 150 / 1.2 / 0.16 / 1.87
4. / 250 / 1.2 / 0.16 / 1.47
5. / 150 / 0.6 / 0.28 / 3.37
6. / 250 / 0.6 / 0.28 / 3.47
7. / 150 / 1.2 / 0.28 / 3.24
8. / 250 / 1.2 / 0.28 / 3.26
9. / 200 / 0.9 / 0.224 / 2.25
10. / 200 / 0.9 / 0.224 / 2.26
11. / 200 / 0.9 / 0.224 / 2.26
12. / 200 / 0.9 / 0.224 / 2.67
13. / 200 / 0.9 / 0.224 / 2.67
14. / 200 / 0.9 / 0.224 / 2.65
15. / 115.9 / 0.9 / 0.224 / 2.29
16. / 284.1 / 0.9 / 0.224 / 1.99
17. / 200 / 0.4 / 0.224 / 2.22
18. / 200 / 1.4 / 0.224 / 2.35
19. / 200 / 0.9 / 0.125 / 1.61
20. / 200 / 0.9 / 0.315 / 4.63
6. The results given by statistics analysis
Measured results were analyzed using software package DESIGN EXPERT 6.0. Regression analysis gave following results as displayed in table 2.
Table 2. Overview of regression coefficients and evaluation of significance
VALUE / STANDARD ERROR / LEVEL OF SIGNIFICANCEconst. / 2.46 / 0.071 / 0.0001
vc / -0.087 / 0.047 / 0.0968
f / 0.92 / 0.047 / 0.0001
vc2 / -0.14 / 0.046 / 0.0129
ap2 / -0.088 / 0.046 / 0.0856
f 2 / 0.21 / 0.046 / 0.0011
/ 0.11 / 0.062 / 0.0926
/ -0.15 / 0.062 / 0.0357
Functional correlation of surface roughness to cutting speed vc, depth of cut ap and feed f is given with equation 3:
(3)
Following figures (2, 3, 4, 5) show correlation of surface roughness to cutting speed vc, depth of cut ap and feed f.
Figure 2. Depth of cut and cutting speed impact on the surface roughness f=const.=0.16[mm/okr.] / Figure 3. Depth of cut and cutting speed impact on the surface roughness f=const.=0.22[mm/okr.]Figure 4. Depth of cut and cutting speed impact on the surface roughness f=const.=0.28[mm/okr.] / Figure 5. Feed and cutting speed impact on the surface roughness ap=const.=0.6[mm]
7. Conclusion
The main goal of this paper is to retrieve a mathematical model that associates input parameters: cutting speed vc, depth of cut ap and feed f, with surface roughness of processed surface Ra.
Results of conducted experiments were analyzed using regression methods. Mathematical model presents quite well the performance of the average arithmetic roughness and it can be used for the evaluation of the surface roughness value in longitudinal turning work, whilst applying specific cutting parameters. Also it can be used to select cutting parameters in order to achieve specific demanding roughness.
Relating to given equation (3) and diagrams (Figures 2, 3, 4 and 5) it is worth to point out the following conclusions:
- Cutting speed has no substantial influence on surface roughness in analyzed area and that influence depends on feed and depth of cut.At small feed values of feed, figure 2., increment of cutting speed results with decrement of surface roughness. At middle feed values, figure 3., increment of cutting speed (vc≤200[m/min]) results with increment of surface roughness. Further increment of cutting speed reduces surface roughness.At greatest feed values, cutting speed (vc200[m/min]) is proportional to surface roughness. Further increase of cutting speed (vc≤250[m/min]) slightly decrements surface roughness.
- As expected, feed has the greatest impact on the surface roughness. The more it decreases the more it improves surface roughness.
- As expected, at small feed values increment of cutting depth results with increment of surface roughness.
- Surprisingly, at great feed values, increment of cutting depth results with decrement of surface roughness. What happens with microstructure of material, geometrical accuracy and dimensional precision is questionable. Further increment of cutting depth is limited with strength of tool material, beginning of vibrations and power of turning machine.
References
[1]Bilić, B.,Bajić, D.,Veža, I., “Optimization of cutting parameters regarding surface roughness during longitudinal turning”, 15th DAAAM International symposium: Intelligent Manufacturing & Automation: Globalisation – Technology – Men - Nature, Vienna, 2004., pp. 039-040.
[2]Bajic, D., “Ispitivanje ovisnosti hrapavosti obradjene površine o utjecajnim cimbenicima pri obradi kratkohodnim honovanjem”, Strojarstvo, Vol. 44, No. 3-6, (July, 2002) pp. 101-116, ISSN 0562-1887.
[3]Cebalo, R., Bajic, D., Bilic, B., “ Optimization of the super-finishing process”, Proceedings of the 3rd DAAAM International Conference ATDC’04, pp. 101-107, ISBN 953-6114-68-2, Split, July, 2004.
[4]Farago, F. T., Curtis, M. A., “Handbook of Dimensional Measurement (3rd ed.)”, Industrial Press Inc., 1994, ISBN 0-8311-3053-9, New York.
[5]Montgomery, D., C., Design and Analysis of Experiments, John Wiley & Sons, Inc., 1997, ISBN 0-471-31649-0, New York
[6]
Dražen Bajić, Associate Professor
FESB/University of Split, R. Boškovića bb, Split, Croatia, +385 (0)21-305 777, +385 (0)21-463 877,
Ivan Špar, Student
FESB/University of Split, R. Boškovića bb, Split, Croatia, +385 (0)21-305 777, +385 (0)21-463 877,
Ivica Veža, Professor
FESB/University of Split, R. Boškovića bb, Split, Croatia, +385 (0)21-305 777, +385 (0)21-463 877,
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