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Comparsion of prediction of cutting forces with real quantities--part two: comparsion of calculated, and measured forces.

Abstract: Continuation of previous research works (Grzesiak & Krolikowski 2005 and 2006) concerning inaccuracy of curvilinear profiles milling with a flexible cutting tool is presented in paper. Above-mentioned works used calculated values of forces acting between tool and machined part. Presented research was made to measure these forces, and compare their values with the values calculated earlier and check if the method of calculation of forces would provide adequate results.

Key words: milling, cutting forces, cutting tool deformation, milling inaccuracy.


Many milling operations requires application of long and slim cutting tools. Especially when machined object has a curvilinear concave surfaces with small radius of curvature. It is obvious that long and slim tool enables machining of hardly accessible areas, but as the side effect, a risk of deflection under the influence of cutting forces occurs. Such deformation will directly influence on precision and geometrical accuracy of manufactured object. Therefore to improve the milling accuracy one should predict a possible direction and dimension of cutting tool deformation and modify / adapt machining and/or operation parameters to compensate mentioned deviations in order to keep required tolerances of shape and dimensions. Presented in paper, and former research concern examination of methods of prediction cutting forces and deflections of cutting tool, caused by the cutting process, during operations of profile milling of curvilinear shapes. This part of research is concentrated on measuring of cutting forces during process, in order to compare results of measurements and verify if assumed methods of calculating forces gives proper values of forces acting on working tool.


2.1 Correlation with former research

As a comparative analysis it was obviously assumed to use the same shape of samples as applied to perform a prior research works. Model consist of five different second level surfaces polynomial connected tangent: two parabolic, two elliptic, and sinusoidal contours applied (fig. 1).


For the calculations of values of cutting forces, curvilinear contour of the model was divided regularly by points on the profile due to correlate measured deviations with forces occurring in the same points of surface. It was necessary because the cutting forces change in relation to profile curvature. While measuring forces it was impossible to determine points of measurements on the profile.

Measuring system bases on bit rate reading so it reads given number of values per second. It is then impossible to determine exact points of profile where measurements was done, because it would be necessary to start measuring anytime precisely in the same position of tool against work piece. In this case forces was calculated for 138 points on profile, to create a diagram of course of force values in dependence on orientation of cutting tool according to profile. For all these points was measured angle of contact of tool with machined material (Grzesiak & Krolikowski, 2005, 2006). Calculated values was used to create diagram which shows approximate dependence of calculated forces values on profile curvature at all length of the profile (Fig. 2)



Experimenal examination were carried out at Mikron VCE-500 milling center, which is placed in technological department of Szczecin University of Technology. Tools used for research were end HSS mills dia. 10mm. with four blades. Work parameters was taken as maximum recommended by tool producer, so values of cutting forces was predicted to be high. Measurements was done using six--axial Kistler dynamometer mounted on the milling machine table. Examinated work piece was fixed directly to dynamometer using simple fixing clamps with steel plates beneath, only for secure dynamometer from damage, as shown on the Fig. 3.

Rough milling was performed to prepare work piece with exactly 1mm allowance for final process. It was made in the same fixing as experiment, to prevent eventual deviations, which could occur while unfixing and fixing work piece.


Results of the measuring was sent directly to computer with sampling 64/s during all the milling progress. Such sampling with feed ratio 80mm/min makes reading value of force in every 0.021mm of profile. For every sample was made a diagram similar as for calculated forces to compare values of forces and shape of the diagram, along the profile. Sample diagram is shown on fig. 4. As one can easily imagine values read by dynamometer was highly spread, so the diagrams had to be smoothed.



After comparing diagrams of forces measured during experiments, and calculated forces values its easy to see, that shapes of diagrams are very similar. That means, that assumed method of calculating forces provides good results as a matter of changes of values in dependence on curvature. Also direction of milling doesn't seem to have significant influence on forces values, as it was noticed while forces calculation.

It proves, that methods of predicting cutting forces are at least partly proper. Values of calculated forces, however are higher than real forces measured during research. Two problems were concluded: firstly, despite optimistic results shape of deviation diagrams of cutting forces, analytical calculation does not provide satisfactory results, by proper forces values; secondly, deviations of machined part, which was measured as higher than calculated (Grzesiak & Krolikowski 2005), despite that measured forces values was lower than calculated. That can indicate, that assumptions about stiffness of machine tool was incorrect. Probably examination of static stiffness of machine would give an answer if flexibility of it is negligible small. Results of measurement of deviations of profile accuracy, although, carried out according to the same methodology as in prior research, provided abnormally high deviations. This is caused probably due to Kistler dynamometer which lowered the stiffness of machine-tool system.

One very interesting conclusion could be driven after comparing the measured forces (fig. 4) and results of comparison of theoretical analysis of cutting forces using classical and FEM methods (Fig. 5). It could be easily observed that shape of deviations between classical and FEM methods of analysis and real measured forces after FFT are comparable, so the conclusion could be driven: classical methods of calculating the cutting forces by single equation with semi experimental coefficients are unusable at processes with more than one variable of cutting direction (i.e. X&Y). We do not need to say what would happen at multiaxial machining. The analysis of multiaxial milling is to be the subject of further research in our team.



Collective work(1990) Poradnik inzyniera--Obrobka skrawaniem, (Engineer's handbook -Machining),vol. II. WNT, Warszawa

Dylag, Z. Jakubowicz, A. Orlos, Z. (1996) Wytrzymalosac materialow. (Strength of materials). Vol I WNT, Warszawa.

Gorski, E. (1999) Poradnik frezera. (Miller's handbook). WNT, Warszawa.

Grzesiak, D. D. & Krolikowski, M. A. (2006) Comparsion of Prediction of cutting forces with real quantities--part one: Method of research and results of analysis. Proceedings of the 17th international DAAAM symposium "Intelligent Manufacturing & Automation: Focus on Mechatronics and Robotics", Katalinic, B. (Ed.), pp. 147-148, ISSN 1726-9679, Vienna, november 2006, DAAAM, Vienna

Grzesik, W. (1998) Podstawy skrawania materialow metalowych. (Basics of milling of metallic materials). WNT, Warszawa.

Olszak, W. (2001) Obrobka skrawaniem i narzedzia, Rozdzial 5--Proces skrawania (Machining and tools, Part 5-Machining process). Wydawnictwo Politechniki Szczecinskiej, Szczecin.

Olszak, W. (2005) Obrobka skrawaniem, Rozdzial 11-Frezowanie. (Machining, Part 11-Milling). Wydawnictwo Politechniki Szczecinskiej, Szczecin.
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Author:Filipowicz, Krzysztof; Grzesiak, Dariusz; Krolikowski, Marcin
Publication:Annals of DAAAM & Proceedings
Article Type:Technical report
Geographic Code:4EUAU
Date:Jan 1, 2007
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