28基于UG二次开发技术的麻花钻、扩孔钻、铰刀设计系统研究
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Journal of Materials Processing Technology 77 (1998) 153159Cutting forces in the end milling of Inconel 718M. Alauddina, M.A. Mazida, M.A. El Baradib,*, M.S.J. HashmibaDepartment of Mechanical Engineering, BIT Dhaka, Gazipur, BangladeshbSchool of Mechanical and Manufacturing Engineering, Dublin City Uni6ersity, Glasne6in, Dublin 9, IrelandAbstractInconel 718 is a nickel-base alloy that is difficult to machine, a high cutting force being generated in the machining of thisadvanced material. This paper presents a study of the influence of the machining conditions on the average cutting forces forhalf-immersion end milling in the up- and down-milling modes. The cutting tests were carried out under dry conditions usingcarbide inserts. 1998 Elsevier Science S.A. All rights reserved.Keywords: Cutting forces; Milling modes; Nickel-base alloy1. IntroductionInconel 718 is a nickel-base alloy containing a nio-bium (columbium) age-hardening addition that pro-vides increased strength without decrease in ductility.This alloy is non-magnetic, oxidation- and corrosion-resistant and can be used at temperatures in the rangeof 217 to 700C 1. In the case of nickel-base alloys,the critical phase in the microstructure is the highvolume fraction, micron-sized, coherent particles of Ni3(Al, X)(g%) embedded within a solid-solution strength-ened nickel (g) matrix. In the case of Inconel 718, the g%phase X corresponds to the presence of columbium,titanium or tantalum, whereas the g matrix containvarying amounts of chromium, molybdenum or cobalt.The increased difficulty of dislocation motion throughthe g%:g microstructure is responsible for the retentionof its high strength at elevated temperature. Due to itsgood tensile, fatigue, creep and rupture strength, thisadvanced material is used in the manufacture of com-ponents for liquid rockets, parts for aircraft turbineengines, cryogenic tankage, etc. Hence, nowadays theability to machine Inconel 718 is increasingly de-manded. Metal machining has a long history and goodcutting tools have been developed, but still advancedmaterials such as Inconel 718 are difficult to machine.The basic reasons for the difficulty in machining thisalloy are as follows 24: (i) high work-hardening atmachining strain rates; (ii) abrasiveness; (iii) toughness,gumminess and a strong tendency to weld to the tooland to form a built-up edge; (iv) low thermal propertiesleading to high cutting temperatures; and (v) a tendencyfor the maximum tool-face temperature to be close tothe tool tip.This paper presents an approach to study the influ-ence of the machining conditions (speed, feed and axialdepth of cut) on the average cutting forces for half-im-mersion end milling in the up- and down-millingmodes. The cutting tests were carried out under dryconditions using carbide inserts.2. Workpiece material and machine toolThe Inconel 718 workpiece material used in the ma-chining test was in the hot forged and annealed condi-tion. The chemical composition of the workpiecematerial confirms to the following specification (wt.%):0.08 C; 0.35 Mn; 0.35 Si; 0.60 Ti; 0.80 Al; 1.00 Co; 3.00Mo; 5.00 Nb; 17.00 Fe; 19.00 Cr; 52.82 Ni. The hard-ness of the workpiece material was measured and foundto be 260 BHN.The tool material (insert) was uncoated tungstencarbide:ISO K20 or AISI M15 (Sandvik grade H13A)5 with an approximate composition of 94% WC and6% Co. The end mill with carbide inserts (SandvikU-Max R215.44 5 used in this work was 25 mm* Corresponding author. Tel.: 353 1 704551; fax: 353 17045345; e-mail: baradiemdcu.ie0924-0136:98:$19.00 1998 Elsevier Science S.A. All rights reserved.PII S0924-0136(97)00412-3M. Alauddin et al. : Journal of Materials Processing Technology 77 (1998) 153159154diameter and right-hand helix (left-hand cut). The toolholder (end mill body) was similar to En 46:En 47 steelwith a hardness range of 42 to 46 Rc. The number ofindexable carbide inserts of the cutter was 2, the incli-nation angle was 5 and nose radius was 0.8 mm.The milling operations (up- and down-cutting) werecarried out on a Cincinnati Universal Machine (8 kW).3. Cutting-force components in end millingThe cutting-force components acting on one tooth ofthe end mill cutter are shown in Fig. 1, where the tablesystem of cutting forces 6 is: Fxinstantaneous feedcomponent (the projection of resultant cutting force inthe X direction); Fyinstantaneous normal component(the projection of resultant cutting force in the Y direc-tion); Fzinstantaneous vertical component (the pro-jection of resultant force in the Z direction); andFRinstantaneous resultant cutting force (table sys-tem) acting on the workpiece.The table system of cutting forces does not dependon the kinematics of the cutting and is, therefore,stationary.The cutter system of cutting forces is: Ftinstanta-neous tangential component (force passing through thetangent to the circle circumscribed on the contour ofthe cutter cross-section); Frinstantaneous radial com-ponent (perpendicular to the cutter axis and actingalong the radius of the cutter or tip of the tooth;Fainstantaneous axial component of the cutting force(passing through the axis of the cutter); FR% instanta-neous resultant cutting force (cutter system) acting onthe cutter.3.1. A6erage cutting force in multi-tooth end millingAlthough the average cutting forces are not the max-imum cutting forces encountered in an end-milling op-eration, it is still useful for engineers to have aknowledge of their levels in designing machine toolsand setting up the cutting system. In multi-tooth endmilling, if several teeth are cutting simultaneously thenthe total average cutting forces acting on the teeth ofthe cutter (table system) per cut are:FXT%zci 1d(i ) Fxi(ci) (1)FYT%zci 1d(i ) Fyi(ci) (2)FZT%zci 1d(i ) Fzi(ci) (3)where:d(i )10if c15c2otherwiseand where FXT, FTYand FZTare the total averagecutting forces acting on the teeth of the cutter per cut inX, Y and Z directions respectively, Fx, Fyand Fzare theinstantaneous cutting forces on an individual tooth percut in the X, Y and Z directions respectively, ciis theinstantaneous (cutting) angle of the cutter, c1is theentry angle of the cutter, c2is the exit angle of thecutter and zcis the number of teeth cutting simulta-neously. Note that zcis not rounded off to the nearestwhole number and can be determined as:zcz cs360(4)Thus, for a multi-tooth milling cutter of uniform toothpitch the average cutting forces (table system) per toothare:FxaFXTzc(5)FyaFYTzc(6)FzaFZTzc(7)Where z is the number of teeth (inserts) in the cutter,and csis the swept angle ( c2c1) which can bedetermined in terms of the cutting parameters 6.In multi-tooth milling, the average tangential force,Ftaper tooth and the average radial force per tooth, Fraare:FtaFtzc(8)FraFrzc(9)where Ftand Frare the instantaneous tangential andradial cutting forces acting per tooth of the cutter percut, respectively.Fig. 1. Cutting-force components acting on one tooth of an end mill.M. Alauddin et al. : Journal of Materials Processing Technology 77 (1998) 153159 1553.2. Relationship between the table and the cuttersystem of cutting forcesFrom Fig. 1, the averge resultant cutting force (tablesystem), FRaacting on the workpiece can be shown to be:FRap10(F2xaF2yaF2za) (10)whilst the average resultant cutting force (cutting sys-tem), FRa% , acting on the cutter can be shown to be:FRa% p10(F2taF2raF2aa) (11)For static equilibrium it is assumed that FRFR% (orFRaFRa% ) and that when the cutter is correctly mounted,the cutter axis and spindle axis coincide, so that thenFzFa(or FzaFaa) is usually assumed.The relationship of the cutting forces in end millingwith a cutter having a straight tooth (neglecting the helixangle for a small axial depth of cut) is assumed as a planesystem in which the axial forces are equal to zero in boththe up- and down-milling mode, so that Fig. 1 is possibleto relate the forces on the milling table to those on thecutter for both modes of milling:FxaFtacos(ci) Frasin(ci)FyaFtasin(ci) Fracos(ci)up milling (12)FxaFtacos(ci) Frasin(ci)FyaFtasin(ci) Fracos(ci)down milling (13)4. Experimental set-upThe milling machine was equipped with a table-type3-component piezoelectric transducer. Data acquisitionof the average cutting force (table system) was performedby a computer via an A:D converter. The cutting-forcesignals were also recorded on a UV recorder to confirmthe results obtained by the computer. The tangentialcutting force was obtained using Eqs. (12) and (13) whilethe resultant cutting force was obtained using Eq. (10).5. Analysis of results5.1. Influence of the cutting speed on the cutting forcesin the end milling of Inconel 718 in the up- anddown-modeThe measured (experimental) cutting forces (Fxa, Fyaand Fza) and the calculated tangential and resultantcutting forces (Ftaand FRa) are plotted against cuttingspeed for an axial depth of cut of 1.2 mm in the up- anddown-milling modes in Fig. 2. From this figure, it isobserved that all of the cutting forces decreases as thecutting speed increases, which may be attributed to thefollowing: (i) it is usually observed that as the cuttingspeed decreases, the shear angle also decreases, a smallshear angle giving a long shear plane, for a fixed shearstrength, an increase in shear-plane area increasing theshear forces required to produce the stress required fordeformation; (ii) at low cutting speed the friction coeffi-cient increases, hence increasing cutting forces.From Fig. 2, it is seen in the case of up milling thatthe Fxacomponent is the highest in the table system ofcutting force. The reason may be analyzed from Eq. (12),in which Fxais the sum of two resolved components ofthe cutter system of cutting forces, whilst Fyais thesubtraction of two resolved components of the cuttersystem of cutting forces. However, from Fig. 2, it is seenthat in the case of down milling, the Fyacomponent isthe largest amongst the table system of cutting forces.The reason may be analysed from Eq. (13) in which Fyacomponent is the sum of two resolved components of thecutter system of cutting forces whilst Fxacomponent isthe subtraction of two resolved components of the cuttersystem of cutting forces. There is no significant differenceobserved in the case of other components of cuttingforces at up and down milling.5.2. The influence of feed on the cutting forces in theend milling Inonel 718 in the up- and down-millingmodeThe measured (experimental) cutting forces (Fxa, Fyaand Fza) and the calculated tangential and resultantcutting forces (Ftaand FRaare plotted against feed foran axial depth of cut of 1.2 mm in the up- anddown-milling mode in Fig. 3, from which figure it isobserved that all of the cutting forces increase as the feedrate increases. The reason for this increase of cuttingforce with the increase of feed is due to an increase ofchi load per tooth as the feed rate increases. From Fig.3, it is observed that in the case of up-milling, the Fxacomponent of cutting forces is the highest in the tablesystem of cutting forces, whilst in the case of downmilling, the Fyacomponent is the largest in the tablesystem of cutting forces (the reason is mentioned inSection 5.1). There are no significant differences observedin the case of other components of cutting forces for up-and down-milling.5.3. The influence of the axial depth of cut on thecutting forces in the end milling of Inconel 718 in theup- and down-milling modeThe measured (experimental) cutting forces (Fxa, Fyaand Fza) and the calculated tangential and resultantcutting forces (Ftaand FRa) are plotted against axialdepth of cut for cutting speed of 16.17 m min1in theup- and down-milling mode in Fig. 4, from which figureit is observed that all of the cutting forces increasealmost linearly with the increase of axial depth of cut.This is due to the size of cut per tooth increasing as theaxial depth of cut increase. From Fig. 4, it is observedM. Alauddin et al. : Journal of Materials Processing Technology 77 (1998) 153159156Fig. 2. Influence of the cutting speed in up- and down-milling.M. Alauddin et al. : Journal of Materials Processing Technology 77 (1998) 153159 157Fig. 3. Influence of the feed rate in up- and down-milling.M. Alauddin et al. : Journal of Materials Processing Technology 77 (1998) 153159158Fig. 4. Influence of the axial depth of cut in up- and down-milling.M. Alauddin et al. : Journal of Materials Processing Technology 77 (1998) 153159 159that in the case of up-milling the Fxacomponent of thatin the case of up-milling the Fxacomponent of that inthe case of up-milling the Fxacomponent of that in thecase of up-milling the Fxacomponent of cutting forcesis the highest in the table system of cutting forces,whilst in the case of down-milling, the Fyacomponent isthe largest in the table system of cutting forces (thereason is mentioned in Section 5.1). There are nosignificant differences observed in the case of othercomponents of cutting forces for up- and down-milling.6. Conclusions1. The cutting forces decrease as the cutting speedincreases (1125 m min1) for up- and down-endmilling.2. The cutting forces increase as the feed rate increasesfor up- and down-end milling.3. The cutting forces increase as the axial depth of cutincreases for up- and down-end milling.4. The Fxacomponent is the highest in the up-millingmode, whilst in the down-milling mode the Fyacomponent is the highest in the table system ofcutting forces.References1 D. Smithbert, Inconel Machining Manual, Report No. 6M59-559, Manufacturing Research and Development, Boeing Com-mercial Airplane Company, 1987.2 M.C. Shaw, N. Nakayama, Machining high strength materials,Anal. CIRP 15 (1967) 4555.3 J.M. Galimberti, Improved metal removal rates for difficult tomachine alloys, Creative Manufacturing Seminar, ASTME,196263, pp. SP 63194.4 Machining the Huntington Alloys, Technical Bulletin T-12,Huntington Alloy Product Division, The Int. Nickel Co. Inc.,Hun
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