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Influence of machining by finishing milling on surface characteristics
International Journal of Machine Tools & Manufacture 41 (2001) 443–450
Influence of machining by finishing milling on surface characteristics W. Bouzid Saı¨ b
a,*
, N. Ben Salah a, J.L. Lebrun
b
a Laboratory of Metallurgy and Materials, LMM, ENIT, Bp 37 Le Belvedere, Tunis 1002, Tunisia Laboratory of Mechanical and Material Microstructure, LM3, ENSAM, 151 Bd de l’Hoˆpital 75013, Paris, France
Received 24 November 1999; received in revised form 4 July 2000; accepted 13 July 2000
Abstract The aim of this study is to analyse the evolution of residual stresses, microstructure, microhardness and roughness in relation to the different parameters of milling. For finishing milling, parameters are cutting speed and feed. The hole drilling strain gage technique was used to determine the residual stresses. These are measured from the surface to the bottom of the treated workpiece. Two different materials were used in this study: a carbon steel (CS) and a duplex stainless steel (DSS). The latter belongs to a high strength stainless steel family with high corrosion resistance properties. In this study, we have used the experimental system method to analyse the evolution of different surface characteristics in connection with cutting phenomena which are cutting forces, chip geometry and cutting temperature. We have noted that a high value of cutting speed used with a small value of feed improves the quality of the machined surface. 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction Cutting includes all the processes which can be used to obtain mechanical workpieces with all the imposed dimensional and geometrical specifications. Using milling as the finishing operation of pieces after heat treatment of injection casting or pumps working in sea water has begun to replace grinding. This process has many advantages such as flexibility, low price and a simple machining range. Hence, the aim of such a machining method is not only to obtain the required dimensional accuracy and surface finish but more importantly the microstructure in the material surface. The finishing operation has the biggest influence on the surface quality defined through rough* Corresponding author. E-mail address: [email protected] (W. Bouzid Saı¨).
0890-6955/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 0 ) 0 0 0 6 9 - 9
444
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
ness, microhardness and residual stresses [1,2]. Cutting parameters have an important influence on machined surface characteristics [3,4]. Thus, to optimise parameters, some tests defined through an experimental design system must be done for milling to change feed and cutting speed (Fig. 1). Cutting depth has a small influence on the surface characteristics [5,6]. To evaluate residual stresses in variation with depth from machined surface, the hole drilling method has been used [7–9]. This destructive method consists of drilling an incremental hole and in measuring the surface strains at each increment. Optimal use of tool characteristics is available only if the machine has a high dynamic rigidity and thermal stability. This process should not decrease the fatigue life of the workpiece. Hence we have studied the influence of milling on surface quality and on affected depth from machined surface.
2. Experimental techniques 2.1. Workpiece materials Two different materials were chosen for this study: duplex stainless steel (DSS) (Table 1) used for sea water circulation pumps in a thermal power plant. Duplex stainless steels offer excellent corrosion resistance together with high mechanical properties, good weldability and castability which make them suitable for marine applications [10]. Samples have been solutionized at 1100°C/1 h, followed by water quenching then aged at 800°C/1 h. The hardness of this material is equal to 300 for a load of 200 g. Microstructural observations of homogenized duplex stainless steel have shown classical (δ+γ microstructure. After aging at 800°C, almost δ-phase transformed into eutectoid like constituent [11,12] (Fig. 2). The second material has been used to understand milling phenomena. Its composition is shown
Fig. 1. Geometric and kinematic parameters of milling.
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
445
Table 1 DSS composition, wt% C
Si
Mn
Cr
Mo
Ni
N
Cu
0.02
0.62
0.49
24.66
2.81
7.43
0.16
2.52
Table 2 Carbon steel composition, wt% C
Mn
Si
S
P
0.35
0.5
0.15
0.035
0.03
in Table 2. Samples were annealed at 800°C/30 min for stress relieving. Initial hardness of this material is 160 Hv. 2.2. Cutting parameters Only cutting speed Vc (m/min) and feed f (mm/rev) are variables. The edge number (z) of the cutting carbide tool is set to eight for all tests, cutting depth to 0.5 mm and the tool diameter to 100 mm. The parameters used are placed between 160 and 440 m/min for the cutting speed (Vc) and beween 0.05 and 0.2 mm/rev for the feed (f=fz·z). fz is the feed per tooth. The experimental plane method consists of a small number of tests to determine empirical models of phenomena variation with different cutting parameters. Orthogonal Taguchi tables were
Fig. 2.
Microstructure of samples aged at 800°C/1 h, optical micrograph.
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W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
used (L16) which correspond to 42 tests. The number of variables is 2 and the number of levels for any variable is 4 (Table 3). 2.3. Hole drilling strain gage technique To determine residual stress components, the hole drilling strain gage rosette method was used. The strain gage rosette CEA-06-062um-120 is adhered directly on the machined surface. One of the three gages is positioned in the feed direction. For drilling, a 2 mm diameter carbide tool is used with a rotation speed of 1200 rev/min. A cylindrical hole is drilled incrementally in the center of the strain gage rosette. Strains due to residual stresses vary and depend on the drilled hole depth increment. Residual stresses are then calculated with linear relationships based on the principle of strain superposition at each increment of drilling of the isotropic material and on the elasticity behaviour during relaxation of stresses [9]. The first holes have been drilled incrementally in steps of 50 µm depth.
3. Results and discussions 3.1. Roughness Ra (mm) Roughness has been analysed through the Ra factor. Fig. 3 shows its evolution with feed. For milling of the CS samples, an increase in roughness can be observed, together with the increase of the feed. Thus Ra was seen to vary from 5.9 µm to 9.6 µm when f increases from 0.05 to 0.2 mm/rev. Cutting speed remains constant and equal to 160 m/min. For the two materials, we have noted that an increase in cutting speed improves the roughness of the machined surface (Fig. 3). Values of Ra for the DSS material are bigger than the Ra for the CS samples. This is due to the differences in microstructure and hardness between materials. The decrease of Ra when cutting speed increases can be explained by the diminution of tool chip contact length [13,14], the decrease of cutting forces and therefore the diminution of deformations [15,16].
Table 3 Taguchi orthogonal arrays f (mm/rev)
0.05 0.10 0.15 0.20
Vc (m/min) 160
220
315
440
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
Fig. 3.
447
Roughness evolution with feed and cutting speed.
3.2. Microhardness The Vickers hardness number has been measured with a load equal to 200 g. Microhardness is greatest near the surface layer and decreases rapidly as the depth increases (Figs. 4–6). This is due to the fact that the region confined to the surface is subjected to maximum work hardening. The depth of this work hardened layer will vary depending on the type of mechanical and thermal interaction. For carbon steel samples with increasing feed, the maximum value of microhardness is higher and penetrates deeper into the surface layer. This is due to an increase in both chip thickness and tool chip contact length. Hence, cutting temperature and cutting forces change in the same direction as the feed (Figs. 4 and 6). In addition, it can be seen that, at high speeds, microhardness is high which confirms that temperatures reach higher levels. No major changes of surface layer depth are noted (Fig. 5).
Fig. 4. DSS Vickers microhardness evolution with depth from machined surface (load=200 g, f=0.1 mm/rev, Vc=355 m/min).
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W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
Fig. 5. CS Vickers microhardness evolution with depth from machined surface for different values of cutting speed (load=200 g, f=0.2 mm/rev).
Fig. 6. CS Vickers microhardness evolution with depth from machined surface for different values of feed (Vc=160 m/min).
3.3. Residual stresses Fig. 7 shows the evolution of feed direction residual stress with the depth from machined surface. As the feed and cutting speed increase, the residual stress reaches a higher level (from 450 to 1300 N/mm2), and penetrates deeper into the surface layer (from 200 to 500 µm). In addition, it can be noted that the feed perpendicular direction residual stresses in the surface layer have been displaced in negative direction (⫺500 N/mm2) relative to the stress level of about 1300 N/mm2 produced in parallel feed direction (Fig. 8). Affected thicknesses are similar.
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
449
Fig. 7. Parallel residual stress evolution for the CS material.
Fig. 8. Perpendicular residual stress evolution for the CS material.
4. Summary In this paper, we intended to show that by selecting specific milling conditions, very good results can be obtained. For any chip forming cutting process, the main objective is to obtain the best quality of machined surface which depends on roughness, microhardness, residual stresses and material microstructure. Roughness results have shown that small values of cutting speed give poor surface quality. This is due to a formation of a built up edge. Optimal value of cutting speed exists between 220 and 440 m/min for small values of feed. Microhardness increases with feed and cutting speed, hence to improve wear and fatigue material resistance, the cutting speed must be high. High values of speed give significant surface tensile residual stress and a small affected thickness (100–150 microns).
450
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
Acknowledgements Thanks are due to M. Sidhom, responsible to the Laboratory of Mechanics and Materials “Ecole Supe´rieure des Sciences et Techniques de Tunis” for his assistance in residual stress measuring. References [1] D.W. Wu, Y. Matsumoto, The effect of hardness on residual stresses in orthogonal machining of AISI 4340 steel, Journal of Engineering for Industry 112 (1990) 245–253. [2] S. Katayama, T. Imai, Effect of tool materials on surface machined roughness and cutting force of low-carbon resulfurized free machining steels, ISIJ International 30 (4) (1990) 331–337. [3] C.R. Liu, M.M. Barash, Variables governing patterns of mechanical residual stress in a machined surface, Journal of Engineering for Industry 104 (1982) 257. [4] B. Scholtes, Residual stresses introduced by machining, Advances in Surface Treatments 4 (1987) 59–71. [5] G.M. Zhang, S.G. Kappor, Dynamic generation of machined surfaces, Part 2: construction of surface topography, Journal of Engineering for Industry 113 (1991) 145–153. [6] E. Macherauch, V. Hauk, Residual stresses in science and technology, International Conference on Residual Stresses, Garnisch, Partenkirchen, 1986. [7] Z. Wu, J. Lu, B. Han, Study of residual stress distribution by a combined method of Moire´ interferometry and incremental hole drilling, Part I: Theory, J. Applied Mechanics 65 (1998) 837. [8] Z. Wu, J. Lu, B. Han, Study of residual stress distribution by a combined method of Moire´ interferometry and incremental hole drilling, Part II: Theory, J. Applied Mechanics 65 (1998) 845. [9] A. Niku Lari, J. Lu, J.F. Flavenot, Measurement of residual stress distribution by the incremental hole drilling method, J. Mechanical Working Technology 11 (2) (1985). [10] F. Dupoiron, J.P. Audouard, Duplex stainless steels: a high mechanical properties stainless steels family, Scandinavion Journal of Metallurgy 25 (1996) 95. [11] N. Ben Salah, W. Bouzid, Modification by mechanical treatments of a duplex stainless steel and its influence on localized corrosion in sea water, Microstructural Science 25 (1997) 107–112. [12] N. Ben Salah, M.A. Chaouachi, A. Chellouf, Role of surface finishing on pitting corrosion in sea water of a duplex stainless steel, Journal of Materials Engineering and Performance 5 (2) (1996) 220. [13] P.L.B. Oxley, Development and application of predictive machining theory, CIRP, International Workshop on Modeling of Machining Operations. Manufacturing Research Center. Atlanta. USA, 1998. [14] M.E. Merchant, Mechanics of the metal cutting process: I. Orthogonal cutting and a type 2 chip, J. of Applied Physics 16 (5) (1945) 267. [15] F. Klocke, M. Rehse, On line force modeling in milling, CIRP, International Workshop on Modeling of Machining Operations. Manufacturing Research Center, Atlanta, USA, 1998. [16] S.Y. Liang, Closed form analytical modeling of milling forces and its applications, CIRP, International Workshop on Modeling of Machining Operations. Manufacturing Research Center, Atlanta, USA, 1998.
Influence of machining by finishing milling on surface characteristics W. Bouzid Saı¨ b
a,*
, N. Ben Salah a, J.L. Lebrun
b
a Laboratory of Metallurgy and Materials, LMM, ENIT, Bp 37 Le Belvedere, Tunis 1002, Tunisia Laboratory of Mechanical and Material Microstructure, LM3, ENSAM, 151 Bd de l’Hoˆpital 75013, Paris, France
Received 24 November 1999; received in revised form 4 July 2000; accepted 13 July 2000
Abstract The aim of this study is to analyse the evolution of residual stresses, microstructure, microhardness and roughness in relation to the different parameters of milling. For finishing milling, parameters are cutting speed and feed. The hole drilling strain gage technique was used to determine the residual stresses. These are measured from the surface to the bottom of the treated workpiece. Two different materials were used in this study: a carbon steel (CS) and a duplex stainless steel (DSS). The latter belongs to a high strength stainless steel family with high corrosion resistance properties. In this study, we have used the experimental system method to analyse the evolution of different surface characteristics in connection with cutting phenomena which are cutting forces, chip geometry and cutting temperature. We have noted that a high value of cutting speed used with a small value of feed improves the quality of the machined surface. 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction Cutting includes all the processes which can be used to obtain mechanical workpieces with all the imposed dimensional and geometrical specifications. Using milling as the finishing operation of pieces after heat treatment of injection casting or pumps working in sea water has begun to replace grinding. This process has many advantages such as flexibility, low price and a simple machining range. Hence, the aim of such a machining method is not only to obtain the required dimensional accuracy and surface finish but more importantly the microstructure in the material surface. The finishing operation has the biggest influence on the surface quality defined through rough* Corresponding author. E-mail address: [email protected] (W. Bouzid Saı¨).
0890-6955/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 0 ) 0 0 0 6 9 - 9
444
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
ness, microhardness and residual stresses [1,2]. Cutting parameters have an important influence on machined surface characteristics [3,4]. Thus, to optimise parameters, some tests defined through an experimental design system must be done for milling to change feed and cutting speed (Fig. 1). Cutting depth has a small influence on the surface characteristics [5,6]. To evaluate residual stresses in variation with depth from machined surface, the hole drilling method has been used [7–9]. This destructive method consists of drilling an incremental hole and in measuring the surface strains at each increment. Optimal use of tool characteristics is available only if the machine has a high dynamic rigidity and thermal stability. This process should not decrease the fatigue life of the workpiece. Hence we have studied the influence of milling on surface quality and on affected depth from machined surface.
2. Experimental techniques 2.1. Workpiece materials Two different materials were chosen for this study: duplex stainless steel (DSS) (Table 1) used for sea water circulation pumps in a thermal power plant. Duplex stainless steels offer excellent corrosion resistance together with high mechanical properties, good weldability and castability which make them suitable for marine applications [10]. Samples have been solutionized at 1100°C/1 h, followed by water quenching then aged at 800°C/1 h. The hardness of this material is equal to 300 for a load of 200 g. Microstructural observations of homogenized duplex stainless steel have shown classical (δ+γ microstructure. After aging at 800°C, almost δ-phase transformed into eutectoid like constituent [11,12] (Fig. 2). The second material has been used to understand milling phenomena. Its composition is shown
Fig. 1. Geometric and kinematic parameters of milling.
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
445
Table 1 DSS composition, wt% C
Si
Mn
Cr
Mo
Ni
N
Cu
0.02
0.62
0.49
24.66
2.81
7.43
0.16
2.52
Table 2 Carbon steel composition, wt% C
Mn
Si
S
P
0.35
0.5
0.15
0.035
0.03
in Table 2. Samples were annealed at 800°C/30 min for stress relieving. Initial hardness of this material is 160 Hv. 2.2. Cutting parameters Only cutting speed Vc (m/min) and feed f (mm/rev) are variables. The edge number (z) of the cutting carbide tool is set to eight for all tests, cutting depth to 0.5 mm and the tool diameter to 100 mm. The parameters used are placed between 160 and 440 m/min for the cutting speed (Vc) and beween 0.05 and 0.2 mm/rev for the feed (f=fz·z). fz is the feed per tooth. The experimental plane method consists of a small number of tests to determine empirical models of phenomena variation with different cutting parameters. Orthogonal Taguchi tables were
Fig. 2.
Microstructure of samples aged at 800°C/1 h, optical micrograph.
446
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
used (L16) which correspond to 42 tests. The number of variables is 2 and the number of levels for any variable is 4 (Table 3). 2.3. Hole drilling strain gage technique To determine residual stress components, the hole drilling strain gage rosette method was used. The strain gage rosette CEA-06-062um-120 is adhered directly on the machined surface. One of the three gages is positioned in the feed direction. For drilling, a 2 mm diameter carbide tool is used with a rotation speed of 1200 rev/min. A cylindrical hole is drilled incrementally in the center of the strain gage rosette. Strains due to residual stresses vary and depend on the drilled hole depth increment. Residual stresses are then calculated with linear relationships based on the principle of strain superposition at each increment of drilling of the isotropic material and on the elasticity behaviour during relaxation of stresses [9]. The first holes have been drilled incrementally in steps of 50 µm depth.
3. Results and discussions 3.1. Roughness Ra (mm) Roughness has been analysed through the Ra factor. Fig. 3 shows its evolution with feed. For milling of the CS samples, an increase in roughness can be observed, together with the increase of the feed. Thus Ra was seen to vary from 5.9 µm to 9.6 µm when f increases from 0.05 to 0.2 mm/rev. Cutting speed remains constant and equal to 160 m/min. For the two materials, we have noted that an increase in cutting speed improves the roughness of the machined surface (Fig. 3). Values of Ra for the DSS material are bigger than the Ra for the CS samples. This is due to the differences in microstructure and hardness between materials. The decrease of Ra when cutting speed increases can be explained by the diminution of tool chip contact length [13,14], the decrease of cutting forces and therefore the diminution of deformations [15,16].
Table 3 Taguchi orthogonal arrays f (mm/rev)
0.05 0.10 0.15 0.20
Vc (m/min) 160
220
315
440
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
Fig. 3.
447
Roughness evolution with feed and cutting speed.
3.2. Microhardness The Vickers hardness number has been measured with a load equal to 200 g. Microhardness is greatest near the surface layer and decreases rapidly as the depth increases (Figs. 4–6). This is due to the fact that the region confined to the surface is subjected to maximum work hardening. The depth of this work hardened layer will vary depending on the type of mechanical and thermal interaction. For carbon steel samples with increasing feed, the maximum value of microhardness is higher and penetrates deeper into the surface layer. This is due to an increase in both chip thickness and tool chip contact length. Hence, cutting temperature and cutting forces change in the same direction as the feed (Figs. 4 and 6). In addition, it can be seen that, at high speeds, microhardness is high which confirms that temperatures reach higher levels. No major changes of surface layer depth are noted (Fig. 5).
Fig. 4. DSS Vickers microhardness evolution with depth from machined surface (load=200 g, f=0.1 mm/rev, Vc=355 m/min).
448
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
Fig. 5. CS Vickers microhardness evolution with depth from machined surface for different values of cutting speed (load=200 g, f=0.2 mm/rev).
Fig. 6. CS Vickers microhardness evolution with depth from machined surface for different values of feed (Vc=160 m/min).
3.3. Residual stresses Fig. 7 shows the evolution of feed direction residual stress with the depth from machined surface. As the feed and cutting speed increase, the residual stress reaches a higher level (from 450 to 1300 N/mm2), and penetrates deeper into the surface layer (from 200 to 500 µm). In addition, it can be noted that the feed perpendicular direction residual stresses in the surface layer have been displaced in negative direction (⫺500 N/mm2) relative to the stress level of about 1300 N/mm2 produced in parallel feed direction (Fig. 8). Affected thicknesses are similar.
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
449
Fig. 7. Parallel residual stress evolution for the CS material.
Fig. 8. Perpendicular residual stress evolution for the CS material.
4. Summary In this paper, we intended to show that by selecting specific milling conditions, very good results can be obtained. For any chip forming cutting process, the main objective is to obtain the best quality of machined surface which depends on roughness, microhardness, residual stresses and material microstructure. Roughness results have shown that small values of cutting speed give poor surface quality. This is due to a formation of a built up edge. Optimal value of cutting speed exists between 220 and 440 m/min for small values of feed. Microhardness increases with feed and cutting speed, hence to improve wear and fatigue material resistance, the cutting speed must be high. High values of speed give significant surface tensile residual stress and a small affected thickness (100–150 microns).
450
W. Bouzid Saı¨ et al. / International Journal of Machine Tools & Manufacture 41 (2001) 443–450
Acknowledgements Thanks are due to M. Sidhom, responsible to the Laboratory of Mechanics and Materials “Ecole Supe´rieure des Sciences et Techniques de Tunis” for his assistance in residual stress measuring. References [1] D.W. Wu, Y. Matsumoto, The effect of hardness on residual stresses in orthogonal machining of AISI 4340 steel, Journal of Engineering for Industry 112 (1990) 245–253. [2] S. Katayama, T. Imai, Effect of tool materials on surface machined roughness and cutting force of low-carbon resulfurized free machining steels, ISIJ International 30 (4) (1990) 331–337. [3] C.R. Liu, M.M. Barash, Variables governing patterns of mechanical residual stress in a machined surface, Journal of Engineering for Industry 104 (1982) 257. [4] B. Scholtes, Residual stresses introduced by machining, Advances in Surface Treatments 4 (1987) 59–71. [5] G.M. Zhang, S.G. Kappor, Dynamic generation of machined surfaces, Part 2: construction of surface topography, Journal of Engineering for Industry 113 (1991) 145–153. [6] E. Macherauch, V. Hauk, Residual stresses in science and technology, International Conference on Residual Stresses, Garnisch, Partenkirchen, 1986. [7] Z. Wu, J. Lu, B. Han, Study of residual stress distribution by a combined method of Moire´ interferometry and incremental hole drilling, Part I: Theory, J. Applied Mechanics 65 (1998) 837. [8] Z. Wu, J. Lu, B. Han, Study of residual stress distribution by a combined method of Moire´ interferometry and incremental hole drilling, Part II: Theory, J. Applied Mechanics 65 (1998) 845. [9] A. Niku Lari, J. Lu, J.F. Flavenot, Measurement of residual stress distribution by the incremental hole drilling method, J. Mechanical Working Technology 11 (2) (1985). [10] F. Dupoiron, J.P. Audouard, Duplex stainless steels: a high mechanical properties stainless steels family, Scandinavion Journal of Metallurgy 25 (1996) 95. [11] N. Ben Salah, W. Bouzid, Modification by mechanical treatments of a duplex stainless steel and its influence on localized corrosion in sea water, Microstructural Science 25 (1997) 107–112. [12] N. Ben Salah, M.A. Chaouachi, A. Chellouf, Role of surface finishing on pitting corrosion in sea water of a duplex stainless steel, Journal of Materials Engineering and Performance 5 (2) (1996) 220. [13] P.L.B. Oxley, Development and application of predictive machining theory, CIRP, International Workshop on Modeling of Machining Operations. Manufacturing Research Center. Atlanta. USA, 1998. [14] M.E. Merchant, Mechanics of the metal cutting process: I. Orthogonal cutting and a type 2 chip, J. of Applied Physics 16 (5) (1945) 267. [15] F. Klocke, M. Rehse, On line force modeling in milling, CIRP, International Workshop on Modeling of Machining Operations. Manufacturing Research Center, Atlanta, USA, 1998. [16] S.Y. Liang, Closed form analytical modeling of milling forces and its applications, CIRP, International Workshop on Modeling of Machining Operations. Manufacturing Research Center, Atlanta, USA, 1998.