Material Choice for spindle of machine tools

Transcription

1 IOP Confeence Seies: Mateials Science and Engineeing Mateial Choice fo spindle of machine tools To cite this aticle: S Gouasmi et al 202 IOP Conf. Se.: Mate. Sci. Eng Related content - Kelvin pobing method Wen Li and D Y Li - Ductile Mateials unde Combined Stess Walte A Scoble - A new one-dimensional two-node layeed composite beam element Xiaoshan Lin and Y X Zhang View the aticle online fo updates and enhancements. This content was downloaded fom IP addess on 06/02/208 at 03:08

2 MATERIAUX 200 IOP Conf. Seies: Mateials Science and Engineeing 28 ( doi:0.088/ x/28//0205 Mateial Choice fo spindle of machine tools S. Gouasmi a, B. Mezoug a, G. Abba b, L. Kheedine a a Laboatoie de echeche en mécanique des matéiaux et maintenance industielle, Dépatement Génie Mécanique, Faculté des Sciences de l Ingénieu, Univesité Badji Mokhta, B.P 2, Annaba Algéie b Laboatoie de Génie Industiel et de Poduction mécanique, ENIM, Metz, Fance sassigouasmi@yahoo.com Abstact. The equiements of contempoay industy and the flashing development of moden sciences impose estictions on the majoity of the elements of machines; the esulting financial constaints can be satisfied by a bette output of the poduction equipment. As fo those concening the design, the esistance and the coect opeation of the poduct, these equie the development of inceasingly pecise pats, theefoe the use of inceasingly poweful tools [5]. The pecision of machining and the output of the machine tools ae geneally detemined by the pecision of otation of the spindle, indeed, moe this one is lage moe the dimensions to obtain ae in the zone of toleance and the defects of shape ae minimized. Duing the development of the machine tool, the spindle which by definition is a otating shaft eceiving and tansmitting to the wok piece o the cutting tool the otational movement, must be designed accoding to cetain optimal paametes to be able to ensue the pecision equied. This study will be devoted to the choice of the mateial of the spindle fulfilling the imposed equiements of pecision.. Intoduction Usually, the mateial choice is made accoding to economical, technological, functional, and availability consideations, etc. Woking stess being known, one then dimensions the pat in such way that this one esists to the imposed loads. Figue. Compaison between Tidimensional and simple state of stess To whom any coespondence should be addessed. Published unde licence by Ltd

3 MATERIAUX 200 IOP Conf. Seies: Mateials Science and Engineeing 28 ( doi:0.088/ x/28//0205 In ou case the poblem aises diffeently: dimensions ae imposed by the calculation of pecision and equied igidity but without taking into account the matte implemented. The loads to which the spindle is subjected not being able to modify dimensions, it is nevetheless necessay to guaantee esistance as well volumetic as supeficial of the spindle. Fo that it is necessay to detemine the maximum equivalent stess the spindle undegoes as shown in Fig.. Ou goal will be eached thanks be to the choice of a facto named citeion of esistance [2], [] Once this one calculated, it will not emain any moe that to choose a mateial whose esistance is highe than that evaluated peviously 2. Detemination of the stesses We ae in the geneal case of loading, since in the coss-section unde consideation (beaing C Fig. 2, thee is a simultaneous action of simple bending, tosion and compession in addition to the adial and tangential stesses due to otation. 2.. Bending and compession Figue 2. Shea and moment diagams espectively. Mz y 4F f I D d z a 2 2 ( σ f = stess at a citical point in tension o compession due to a combination of bending and axial load, N/mm 2 M z = bending moment, Nmm y = distance fom neutal axis to oute suface, mm I z = axial moment of inetia of coss section, mm 4 F a = axial load, N D, d = oute and ine diamete of coss section espectively, mm TyQz f I b τ f = tansvese shea, N/mm 2 T y = tansvese shea load on the coss section, N b y = with of the section containing the citical point, mm Q z = moment of the coss-sectional aea unde consideation, mm 3 z y 2

4 MATERIAUX 200 IOP Conf. Seies: Mateials Science and Engineeing 28 ( doi:0.088/ x/28//0205 Tosion: M t t I M t = tosional moment, N-mm ρ = distance fom neutal axis to point of inteest, mm I p = pola moment of inetia of coss section, mm Stesses due to intefeence and otation We detemine the value of these stesses at the location of beaing C by consideing the fitted pats as thick-walled cylindes [4], as shown in Fig. 5 and supeposing [], [3] the stesses due to the pessue with those due to otation. p Stesses due to pessue Figue 3. Intefeence fits. 2 2 p R ( p ( R σ = adial stess, N/mm 2 R = oute adius of the spindle at C, mm = inne adius of the spindle at C, mm = distance fom neutal axis to point of inteest, mm p R ( p ( R σ θ = tangential stesses, N/mm 2 p = pessue at the contact suface, N/mm 2 The pessue at the contact suface may be calculated by the following equation[4]: δ = the total intefeence, mm d c = oute diamete of of the spindle, mm d i = inne diamete of of the spindle, mm p d d d d dc[ ] E d d E d d E E c i c i i o i( c i o( o i i o 3

5 MATERIAUX 200 IOP Conf. Seies: Mateials Science and Engineeing 28 ( doi:0.088/ x/28//0205 d o = outside diamete of oute membe, mm E i = modulus of elasticity of inne membe, N/mm 2 E o = modulus of elasticity of oute membe, N/mm 2 ν i = Poisson s atio fo inne membe ν o = Poisson s atio fo oute membe stesses due to otation ( R R [( ( ( ] 8 R R ν = Poisson s atio fo inne membe μ = masse density, Kg/mm 3 ω = speed of otation fo spindle, ad/s ( R R [( ( ( ( ] 8 R 3 R σ θ = tangential stess 3. Discussion Accoding to the Maximum pincipal stess theoy [7] (Von Misès citeion, the mateial fails by yielding when the maximum pincipal stess exceeds the tensile yield stength, o the minimum pincipal stess exceeds the compessive yield stength. Although it used in many softwaes, this theoy has some limitations. Futhemoe, failue in ductile mateials is fundamentally a sheaing phenomenon, and one would theefoe assume the failue citeia fo such mateials to ely upon sheaing athe than tensile stesses. The maximum shea stess theoy [6] (Tesca o Guest citeion in ecognition of thei contibution to its application, is an outgowth of the expeimental obsevation that a ductile mateial yields as a esult of slip o shea along cystalline planes. This theoy pedicts that yielding will stat when the maximum shea stess in the mateial equals the maximum shea stess at yielding in a simple tension test (fo ductile mateial. If the point M (σ, σ 2, σ 3 is out of the envelope of the theshold of Tesca shown in Fig. 4, yielding will occu. The stesses σ, σ 2 and σ 3 ae called pincipal stesses and ae shown in Fig.. Good ageement with expeiment has been ealized fo ductile mateials. Numeical example: Lets take σ = 208 N/mm 2, σ 2 = -08 N/mm 2, σ 3 = 200 N/mm 2 and y p = 270 N/mm 2. The citeion of tesca pedicts that this state of stess will poduce the flow in the mateial. Figue 4. gaphical epesentation of Tesca citeion. 4

6 MATERIAUX 200 IOP Conf. Seies: Mateials Science and Engineeing 28 ( doi:0.088/ x/28// Conclusion: Fom the viewpoint of mechanical design, it is impeative that some pactical guides be available to pedict yielding unde the conditions of stess as they ae likely to exist in sevice. To meet this need and to undestand the basis of mateial failue, the maximum pincipal theoy (Von Mises citeion and the maximum shea stess theoy (Tesca citeion have been used. The latte seems to be moe advantageous. Refeences: [] Bazegui A, Bui-Quoc T, Bion A, Mcintye G, Labege C 985 Resistance des matéiaux, Edition de l Ecole polytechnique de Monteal. [2] Anissimov A 993 Calcul des baes dans le cas de sollicitation composée (Patie -de RDM2, U.S.T.H.B. [3] Fanchon J. L 200 Guide de Mécanique Sciences et technologies industielles, Nathan. [4] Hall A. S, Holowenko A. R, Laughlin H. G 96 Machine Design, McGaw-Hill. [5] Selivanov S 984 Calcul et élaboation des ensembles boches-palies, Univesité de Annaba. [6] Ugual A. C, Fenste S. K 975 Advanced Stength and Applied Elasticity, Teaneck, New Jesey. [7] Bathod Ch Module SPM2A, Résistance des Matéiaux, IUT Annecy. 5