Effect of the multiaxis milling kinematics on the chip formation and cutting forces and herewith on the surface roughness K. D. Bouzakis, P. Aichouh, K. Efstathiou Laboratory for Machine Tools and Manufacturing Engineering, Mechanical Engineering Department, Aristoteles University of Thessaloniki, 54006, Greece Tel. 0030 31 996079, 0030 31 996021, Fax. 0030 31 996059, [email protected] ABSTRACT. CAD/CAM systems offer various possibilities for milling of free form surfaces, but most of them without taking into account the expected surface topomorphy which depends on the milling kinematic and on the cutting conditions.In order to determine the expected roughness and the surface topomorphy considering the cutting parameters, a computer supported simulation algorithm ”BALLMILL”, is developed, which enables the calculation of the surface topomorphy and roughness in multy axis milling with ball end tools. The various tendencies in the occurring surface integrity can be explained with the aid of chip formation and cutting force calculations which are also described.With the aid of a mathematical simulation the individual movements of the workpiece and the cutting tool are determined as well as, the penetration of the cutting tool edge into the workpiece. Thus the final surface topomorphy is formed and the roughness as well as the chip geometry and cutting force components can be calculated for different milling kinematics and cutting conditions. A series of experimental tests and measurements have been carried out in order to validate the compliance of the experimental results to the corresponding ones obtained by means of the developed algorithm. Using the introduced method the expected roughness for various milling kinematics can be estimated and used to predict appropriate cutting conditions to fulfil surface topomorphy requirements. KEY WORDS: Milling, Chip, Cutting force, Roughness

1. Introduction In end milling operations of free form surfaces with ball end tools, depending on the workpiece geometry and on the cutting kinematics, individual milling processes can be distinguished. In 4-axis milling of free form surfaces eight different milling kinematics (see figure 1) can be identified, depending on the tool inclination angle with respect to the final workpiece elementary surfaces (see detail A in the upper part of figure 1). The occurring workpiece surface roughness is influenced by the milling kinematics as well as by the cutting conditions [EVE 89], [WER 93], [BIE 91], [BOU 96].

Figure 1. Potential milling kinematics with ball end tools In order to determine the expected roughness considering the cutting kinematics, the computer program “BALLMILL” is developed. In this simulation the initial part geometry, the NC code and the tool geometry are taken into account. By means of

the developed milling simulation, parameters like the undeformed chip geometry and the cutting force components are determined [BOU 99b]. The chip geometry is required for the determination of the cutting forces. Furthermore it can be used to explain differences in the experimentally derived roughness in various milling kinematics. 2. Simulation of the multiaxis milling In multiaxis milling the ‘chain’, tool.-workpiece.- machine tool, is analysed by means of five individual coordinate systems (see figure 2). The various tool and workpiece motions are described through distinguished displacements or rotations, in the corresponding coordinate systems and these motions are overlaid by means of coordinate transformations. To describe the cutting tool shape, the cutting edge is considered to be divided into elementary edges. On the other hand the workpiece geometry is calculated on parallel reference section levels. Each elementary cutting edge path, intersects the reference levels Li, by which the workpiece geometry is described (see figure 3). The trace of the cutting edge path on the reference planes, in relation to the instantaneous workpiece shape before cutting, is taken as a base for the calculation of the penetrations between tool and workpiece and for the determination of the instantaneous workpiece geometry and surface topomorphy , [BOU 96].

3. Determination of the undeformed chip geometry With the aid of the milling simulation described above, the intersections of the cutting edge with the workpiece reference levels, can be calculated in successive tool revolving positions. Such intersections for a particular position are shown in the upper left part of figure 4. These intersections describe the chip cross section as illustrated in the right part of figure 4 for a particular revolving position.

Figure 2. Mathematical description of multi axis milling

Figure 3. Determination of the workpiece surface topomorphy

Figure 4. Determination of the undeformed chip geometry

In the lower part of figure 4 the chip cross section over the development of the cutting edge is shown. The synthesis of the cross sections of the undeformed chip geometry, in successive tool revolving positions provides the whole undeformed chip geometry (see lower left part of figure 4) [BOU 98]. 4. Determination of the cutting force components In multiaxis milling of free form surfaces with ball end tools the cutting force varies along the tool path due to the variation of the chip cross section geometry in successive tool penetration positions. The cutting force components can be calculated with the aid of equation [KIE 52]: Fi = b ki,11 h1-mi, i=c,t,n where: b h ki, 1-mi

-chip width, -chip thickness, -cutting coefficients

The chip geometry (width b, thickness h) is calculated using the program “BALLMILL”. The cutting force components on the cutting edge coordinate system Fc, Ft and Fn can be determined through coordinate transformation of the measured one. The coefficients ki,11 and 1-mi, corresponds to the combination of tool and workpiece material, can be estimated with the aid of an analytical-experimental procedure (see figure 5) [AIC 00].

Figure 5. Determination of the cutting force coefficients ki,11 and 1-mi

With the aid of the calculated chip geometry and having experimentallyanalytically determined the cutting force coefficients for the combination of tool and workpiece material, it is possible to calculate the cutting force components Fc, Ft and Fn for various cutting conditions and kinematics without the need of conducting the corresponding experiments (see figure 6).

Figure 6. Determination of the cutting force components 5. Chip geometry in multi axis milling at various cutting conditions Typical results of the chip geometry determination are shown in figure 7. In this figure is demonstrated the chip geometry and its formation area on the tool for the case of down milling (tool contact angle f =0) with ball end tool accompanied by two cutting edges. The chip is formatted in the area of the tool nose and this area forms the end workpiece surface. That means low cutting speeds at the tool nose equal to 0) due to the small effective tool diameter and plastic material deformation instead of material cutting [SCH 95]. In this milling case cuts only one of the two cutting edges alternately. The calculated underformed chip geometry is validated by the shape of the real chip (see lower right part of figure 7). The modification of the produced chip is owing to the deformation mechanisms that occur during cutting. By means of the developed simulation algorithm, the influence of the cutting conditions (feedrate fy, radial cutting depth axy) and tool axis inclination on the undeformed chip geometry for various milling kinematics can be determined. Figure 8 illustrates the undeformed chip geometry as well as its formation region along the cutting tool edge in the case of push down milling. Increasing the tool inclination angle f nf, the distance between the tool nose and the region of the cutting edge where the chip is formed becomes bigger. The calculated chip geometry for the case of oblique plunge milling is shown in figure 9. In this case of milling for small

tool axis inclination angle, the chip is formatted by both cutting edges simultaneously in contrary to the other milling kinematics [AIC 00].

Figure 7. Chip geometry and its formation area on the tool cutting edge

Figure 8. Chip geometry in push down milling

Figure 9. Chip geometry in oblique plunge down milling 6. Cutting force components and tool deflection in multi axis milling at various cutting conditios In figure 10 are illustrated the measured and calculated cutting force components Fc, Ft and Fn, for different feedrates, in the oblique reverse down milling using the known ceofficients,. The tool inclination angle is 30o and the workpiece material is GS45. As its expected, increasing the feedrate leads to higher cutting force components values. This result can be detected from the calculated as well as the measured cutting force components. From figure 10 can be deduced that there is a good agreement between the measured and the calculated cutting force components. A comparison between calculated and measured cutting force components for various milling kinematics is illustrated in figure 11. The convergence of the calculated and measured cutting force components signals is very satisfaction. These results show that different cutting kinematics lead to different cutting force values, due to the different way at which the chip is formed and removed. The calculation of the surface topomorphy and roughness as mentioned in paragraph 2, takes into consideration the kinematic of the milling process. The cutting forces lead to a deflection of the cutting tool. These deflections should be considered in the calculation of the surface roughness [TON 89a].

Figure 10. Cutting force components for different feedrates

Figure 11. Cutting force components for different milling kinematics

Figure 12. Calculated cutting tool deflections Using the calculated cutting force components, the deflection of the cutting tool is calculated for every successive revolving position by analytical means. Hereupon, the tool was modeled as circular cross section beam. In figure 12 are illustrated the cutting force components, and the corresponding deflections of the cutting tool for the push up milling 7. Workpiece surface integrity in multi axis milling at various cutting conditions Further significant parameters, which can be determined using the developed computer supported simulation of the milling process are the resulting surface topomorphy and roughness. In figure 13 the resulting surface topomorphy and chip geometry in down milling is illustrated. Hereby considering 2 successive tool penetrations (i, i+1) in 2 successive tool passes (n, n+1), it is possible to determine the part of the chip where the final surface cutting takes place (area B). The cutting force and the occurring tool deflections at the revolving positions, when the workpiece material in area B is removed, and where a part of the final workpiece surface is formed affect the resulting roughness of the workpiece surface. Therefore it was taken into consideration in predicting the expected roughness of the workpiece surface.

Figure 13. Chip formation, Surface topomorphy and roughness in down milling

Figure 14. Calculated cutting force components and its corresponding cutting tool

Figure 14 shows the manner in which the chip is removed from the final surface for the oblique plunge up and push up milling. The corresponding maximum cutting force and tool deflection normal to the workpiece surface component, occurring during the phase of forming the final surface are also calculated. Considering these data the occurring various values of roughness in multi axis milling with different cutting kinematics can be elucidated. In the case of oblique plunge up milling, the cutting edge at the beginning of the cutting process forms a part of the final workpiece surface. Thus the cutting edge is free of build up edges and due to the small chip cross sections, the cutting force and the corresponding tool deflection are low. Herewith reduced roughness values are measured in comparison to push up milling, where parts of the final workpiece surface are manufactured at the end of the tool penetration into the workpiece material. Simultaneously build up edges are existing on the cutting edge and a higher cutting force acts, leading to an increased tool deflection. Owing to the aforementioned considerations comparisons of the potential multi axis milling kinematics concerning the expected workpiece surface roughness can be conducted. Figure 15 shows a classification of the main multi axis milling kinematics regarding the occurring workpiece surface integrity. The criteria of this systematic approach were the cutting force magnitude, their fluctuation and the existance of build up edges during manufacturing of the final workpiece surface elementary areas. The best results regarding the surface roughness were achieved in oblique plunge up and oblique reverse down milling, whereas in the case of push up milling the highest roughness values were expected and also measured. Moreover the influence of some manufacturing parameter as for example of the feed rate, of the radial cutting depth and of the tool axis inclination angle on the surface topomorphy is investigated by means of the developed mathematical procedure. The inclination angle of the tool axis relative to the final workpiece surface, significantly influences the occurring surface roughness [BOU 99a], [SCH 95], [TON 89b]. This effect is shown in figure 16, in the case of pull down milling. Increasing this angle from 0 up to 5o, the roughness values initially sinks. Subsequently the roughness increases progressively with the tool angle. These trends are occurring from the corresponding calculated surface topomorphies, inserted in the lower part of the figure [AIC 00]. To check the validity of the previous introduced computational results, appropriate investigations were carried out. In figure 17 the influence of the tool axis inclination on the surface roughness for different cutting kinematics is shown. The calculated values take into account the calculated kinematic roughness and the corresponding cutting tool deflection for different tool inclination angles. These values have the same behavior with the measured one, although a deviation of the experimental results from the corresponding calculated ones, depending on the material properties and on other parameters like the chip formation and the chip flow exists. Especially the chip formation and the chip flow differ in each of the investigated milling cases.

Figure 15. Influence of the chip formation, cutting force and kinematic on the surface integrity in multi axis milling According to the obtained milling results with further workpiece materials, the measured roughness mean values lie higher, at a distance of dm, concerning the corresponding computed values and within a scatter region of a width d (see figure 18). The parameters dm and d vary, depending on the workpiece material and on the cutting kinematics as it can be seen in the related diagrams for some materials in this figure. The investigated materials are widely used by the Greek company “Metallic Constructions” (METKA S.A).

Figure 16. Calculated roughness and surface topomorphy for different tool inclination angles

Figure 17. Calculated and measured roughness in various milling kinematics

Figure 18. Calculated and measured roughness by various milling kinematics for different workpiece material 8. Optimisation of the multiaxis milling kinematics considering the surface roughness Based on the above mentioned analytical experimental results, a computer supported algorithm is developed. Hereby, by means of an interactive procedure for various machining parameters, the expected roughness values are predicted. Considering as optimisation criteria the achievement of the following targets: a) the resulting surface roughness must be less than the prescribed one, b) the machining time have to be kept as low as possible, the optimum cutting conditions, to obtain the prescribed roughness at the lowest milling time can be determined [BOU 99a]. With the aid of “Help” menu, of the developed computational procudure, the user has the possibility to see the influence of various cutting parameters (cutting depth, feedrate, tool inclination angle, milling kinematic etc.) on the surface roughness. Using “Input menu” (see figure 19), machine type, cutting kinematic, tool inclination angle, geometry of the tool and the workpiece, cutting speed, axial cutting depth, and the prescribed roughness are selected. In order to calculate combinations of radial cutting depth and feedrate, which satisfy the permitted workpiece surface roughness, the minimum values of the feedrate and radial cutting depth and the corresponding increments have to be defined.

Figure 19. Data input menu

Figure 20. Calculated combination for feedrate and radial cutting depth

With the aid of the previous selected and registered parameters, pairs of values for radial cutting depth and feedrate are calculated, as shown in “Optimisation results” (see figure 20). For each combination, the expected roughness value and the normalised cutting time are also calculated and graphically presented. Based on this information the user selects the most appropriate combination for the machining of the part. Finally in menu “Output” of the developed program shown in the figure 21, are listed all the selected and calculated parameters for the machining of the workpiece illustrated in the same figure.

Figure 21. Optimum cutting parameters for the machining of the part 9. Conclusions The various milling possibilities to finish free form surfaces with ball end tools lead to different chip geometry and cutting forces. In order to achieve low roughness values, besides an optimisation of the cutting conditions and kinematics, it is necessary to know the part of the chip geometry and the cutting force, at the revolving positions of the cutting tool, in which the final surface of the workpiece formed. The knowledge of these parameters is required for the determination of the corresponding cutting tool deflections. Furthermore it is necessary to modify the tool inclination angle and the milling kinematic. Using the presented programme “BALMILL” the occurring roughness in mutiaxis milling can be estimated, and optimum cutting conditions can be suggested in order to achieve prescribed roughness values. Herewith the optimum milling strategy is determined.

10. References [AIC 00] AICHOUH, P., Determination of the chip geometry, cutting force and the expected roughness in free form surfaces milling, with ball end tools, Thessaloniki, 2000 [BOU 99a] BOUZAKIS, K.-D., AICHOUH P., EFSTATHIOU K., KOUTOUPAS, G., ANTONIADIS, A., ”A Computer Supported Simulation of Multiaxis Milling to determine optimum cutting kinematics concerning the occurring surface roughness”, 2nd International German and French Conference on High Speed Machining, Darmstadt, Germany, p.203-209, 1999. [BOU 99b] BOUZAKIS, K., AICHOUH, P., EFSTATHIOU K., “Analytical–Experimental determination of the chip geometry and the cutting force in multiaxis milling of free form surfaces with ball end tools”, 5th Conference “Machine Tools–Manufacturing processes”, p. 147-157, 2-3 December, Thessaloniki, 1999. [BOU 98c] BOUZAKIS K., AICHOUH P., EFSTATHIOU K., “A computer supported simulation of multy axis milling to determine the chip geometry and the surface topomorphy”, 9th DAAM International Symposium, Cluj-Napoca, Romania, p.57-58, 1998. [BOU 96d] BOUZAKIS, K.-D., EFSTATHIOU, K., ANTONIADIS, A., CHARACHALIOU, C., AICHOUH, P., “Analytical experimental determination of surface roughness in milling”, Balkantrib’96, International Conference on Tribology, Thessaloniki, p.131-140, 1996. [SCH 95] SCHULZ, H., HOCK, ST. “High-Speed Milling of Dies and Moulds-Cutting Conditions and Technology”, anals of CIRP, p.35-38, Vol. 44/1/1995. [KRU 94] KRUTH, J-P., KLEWAIS, P. “Optimization and Dynamic Adaptation of the Cutter Inclination during Five_Axis Milling of Sculptured Surfaces”. anals of CIRP, p.443-448, Vol. 43/1/1994. [WER 93] WERNER, A., Prozessauslegung und Prozesssicherheit beim Einstazt von schlanken Schaftfraesern, TH Aachen, 1993 [BIE 91] BIEKER, R., CAM-gerechte Technologie fuer die NC-Fraesbearbeitung von Stahlhohlformen, Diss. TH Aachen, 1991 [TON 89a] TONSHOFF, H.K., Hohlformbearbeitung durch Drei- und Funfachsenfrasen, VDI-Z 131(9), p.77-81, 1989 [TON 89b] TONSHOFF H.K., HERMANDEZ – CAMACHO, J., “Die Manufacturing by 5 – and 3–axes Milling”, Mech. Working Tech., Vol 20, p.105-119, 1989 [EVE 89] EVERSHEIM, W., KOENIG, W., BIEKER, R., COBANOGLOU, M. T., NC– Fraesbeareitung von vergueteten Schmiedegesenken, VDI – Z 131, Nr. 4, p.99-103, 1989 [BOU 85] BOUZAKIS, K.-D., METHENITIS, G., “Determination of the values of the technological parameters, which are used to describe the time course of cutting force components in milling”. anals of CIRP, p.141-144, Vol. 34/1/1985. [KIE 52] KIENZLE, O., Prediction of Forces and Power in Machine Tools for Metal-cutting, VDI-Z 94, Duesseldorf , p.299-305. 1952

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