Simulation testing of cutting force in the process of barrel milling machining

The paper presents simulation tests of cutting force in the process of barrel milling. The analyzes were carried out on concave and convex surfaces with different radii of curvature.

In industrial practice, an increase in the use of five-axis milling is observed, especially during the production of components with complex shapes, such as rotors, blades and dies.The machining of such parts is most often carried out in a spherical milling strategy (fig.1a).It allows you to make any shape, but it is characterized by very low efficiency.That is why new milling designs are being sought, which will enable the increase of the surface machining efficiency.
One of such constructions is a barrel mill with a repeatedly increased radius of the cutting edge shape rn (fig. 1b).This solution contributes to increasing the axial infeed of br (machining path width), and thus -repeatedly increasing the surface machining efficiency.However, the change in the axial infeed results in a significant increase in the crosssection area of the cutting layer and the effective cutting edge length [1,5,6,8,10].
In addition, in the case of a barrel milling cutter, the curvature radius of the machined surface influences the area of the cutting layer (fig.2).Depending on the sign of curvature ("+" convex, "-" concave) and values, the conditions of contact between the tool and the workpiece change [9].* Dr hab.inż.Jan Burek prof.PRz (jburek@prz.edu.pl),mgr inż.Karol Żurawski (zurawski@prz.edu.pl),mgr inż.Piotr Żurek (p_zurek@prz.edu.pl)-Katedra Technik Wytwarzania i Automatyzacji Politechniki Rzeszowskiej Fig. 2. Radius of curvature of concave and convex surface [4] The change of these parameters directly affects the values and course of the cutting force components.The cutting force causes elastic deformations of the machine tooltoolworkpiece system and affects the shape errors of the workpiece surface.Therefore, its analysis is extremely important in the process of five-axis machining with the use of a barrel milling cutter, especially considering the radius of curvature of the machined surface [9].
The mechanistic model (1) was adopted for the tests, while the simulation analysis was used to determine the length of the cutting edge S and the cross-sectional area of the machined layer A. The distribution of the cutting forces for the barrel milling cutter is shown in fig. 3 [1,7].{  t =  te  +  tc   r =  re  +  rc   a =  ae  +  ac  (1) where: Ft -tangential component of the cutting force, Fr -radial component of the cutting force, Fa -axial component of the cutting force, S -active length of the cutting edge, A -cross-sectional area of the cutting layer, Kte, Kre, Kae -edge proportionality factors affecting the cutting edge, determined experimentally, Ktc, Krc, Kac -proportionality factors related to shear, determined experimentally.
The aim of the research was to determine the courses and values of the components of the cutting force in the machining of concave and convex surfaces with different values of the radius of curvature.

Research methodology
The values of the cutting force components were determined using Boolean operations carried out between the test model and the tool model.The model assumes a barrel milling cutter with a radius of cutting edge rn = 85 mm.The feed per tooth was fz = 0.2 mm.The test models were surfaces with different radii of curvature (tab.I).
First, test models of the workpiece were prepared in the NX 11 system.Next, the test bodies were imported into the hyperMill system, where they were used to develop machining paths for each model and an intermediate code was generated.
The next step was to model the tool, which was copied in a pattern created based on the previously imported intermediate code.80 copies per one revolution of the tool were made.Then, the tool models were subtracted from the object model.As a result of this operation, the cross-sectional area of the cutting layer and the length of the active cutting edge were obtained (fig.4).These parameters (tab.II) were applied in mechanistic formulas allowing to determine the components of the cutting forces occurring in the process [2,4,11].

Analysis of results
Figs. 5-11 present graphs of dependences of the cutting force Ft, Fr, Fa for different values of curvature radius rk1, rk2 as a function of the angle of rotation of the tool φ.
To compare the effect of the radii of curvatures rk1, rk2, the values of the cutting force components obtained by simulating the flat surface machining were first examined (fig.5).Subsequently, tests were carried out for a concave surface with a radius of curvature rk1 = -25 mm (fig.6).On the basis of the presented courses of the cutting force components, it can be stated that the maximum value of the Ft component is 500 N.In relation to the results obtained during the flat surface machining, an increase of approx.60% took place.In the case of the Fr component, the maximum value reached 290 N, which is also an increase compared to the results obtained for the flat surface machining by approx.60%.However, the value of the Fa component was a maximum of 45 N, which indicates an increase of approx.50% in the flat surface machining.
The test results for the concave surface with the radius of curvature rk1 = -50 mm are shown in fig. 7. The tangential component was Ft = 426 N, which is a value greater by approx.38% in relation to the results obtained for the flat surface.Also, the radial component was greater than the value for a flat surface by approx.38% and was Fr = 180 N.The increase of the axial force was about 22%.
In the case of a convex surface with a radius of r1 = + 25 mm, the tangent component was Ft = 292 N, which is a value about 16% lower compared to a flat surface (fig.8).The difference in radial components was 5%, while the axial component reached the value Fr = 26 N -about 13% less than the results obtained for a flat surface.With the increase of the radius of curvature rk1 to +50 mm, the components of the forces increase and approach the results obtained for the flat surface (fig.9).When machining a convex surface with radius rk2 = 300 mm, the components of the cutting forces Ft, Fr, Fa do not change significantly (fig.11).In addition, it can be deduced from the graphs of the course of the individual components of the cutting force that always two blades simultaneously have contact with the machined surface.

Fig. 4 .
Fig. 4. Analysis of the cross-section area of the cutting layer determined by Boolean operations

Fig. 5 .
Fig. 5. Course of the components of the cutting force of a flat surface From the presented waveforms, the tangential component Ft obtained the highest value -about 310N.The value of the radial component Fr reached approx.210 N and the axial component Fa -approximately 30N.Subsequently, tests were carried out for a concave surface with a radius of curvature rk1 = -25 mm (fig.6).

Fig. 6 .
Fig. 6.Course of the cutting force components for the concave surface with curvature rk1 = -25 mm

Fig. 7 .
Fig. 7. Course of the cutting force components for the concave surface with curvature rk1 = -50 mm

Fig. 8 .
Fig. 8. Course of the cutting force components for a convex surface with curvature rk1 = +25 mm

Fig. 9 .
Fig. 9. Course of the cutting force components for the convex surface with curvature rk1 = +50 mm In the case of surfaces with curvature rk2 = -300 mm (fig.10), the tangent component Ft = 350 N, i.e. by about 10% more compared to the flat surface.The radial component, on the other hand, reached the value Fr = 227 N -about 5% more with regard to the machining of a flat surface.On the other hand, the value of the Fa axial component was 32 N.It is important that in the case of machining concave surfaces the values of the minimum values of the courses of the cutting forces are increased.

Fig. 10 .
Fig. 10.Course of the cutting force components for the concave surface with curvature rk2 = -300 mm