THEORETICAL CONSIDERATION ON FORCE CALCULUS OF THE TOROIDAL AND TOROIDAL WITH CYLINDRICAL COLLAR COLD STRANGLING OF HOLLOW PARTS

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1 THEOETICAL CONSIDEATION ON FOCE CALCULUS OF THE TOOIDAL AND TOOIDAL WITH CYLINDICAL COLLA COLD STANGLING OF HOLLOW PATS Traian Lucian Severin, Lucian V. Severin, Stefan cel Mare University of Suceava, Faculty of Mechanical Enineerin, Mechatronics and Manaeent, oania, e-ail: Abstract. The paper presents the calculation of toroidal and toroidal with cylindrical collar stranlin force usin eneretically ethod by equalizin the echanical work of external deforation forces with that of internal strains of the blank defored zone. elationships obtained show that the total force of toroidal stranled is influenced by physical and echanical characteristics of the blank aterial, size of the toroidal surface, wall thickness of hollow or tubular parts and friction coefficient between the die and the workpiece. Also, to stranle toroidal with collar cylinder influences the connection radius between collar cylindrical and toroidal surface of the ould. Keywords: force neckin, toroidal neckin, neckin coefficient, cylindrical collar. Introduction Stranlin is a cold plastic deforation process cateory, which consists in decreasin cross-sectional diension of a hollow, tubular piece or circular bars. Decreasin cross-sectional diensions of the aterial of the blank takes place due by oveent in the radial direction fro the outside towards the centre of the section. Hollow tubular blanks or processed by ouldin the shape and size chanes durin processin on the basis of the chane wall thickness, althouh in practical ters it is believed that the wall thickness of the part is the sae as the wall thickness of the blank. Practical application processin is ettin various containers, war cartrides tubes, parts installation etc. Processin is done with oulds which have shape and diensions of the stranlin part. Shapes that can be obtained throuh the stranlin hollow or tubular parts are conical, conical with collar cylindrical, toroidal and toroidal with cylindrical collar []. Assessin the deree of deforation is throuh the stranlin coefficient that should always be hiher than the allowable aount for blank a used. This coefficient is defined as the ratio between d and D. Its value depends on the characteristics of plasticity of the aterial, the desin of the die, the relative thickness of the walls, etc. []. Stranlin dies can be desined to realize the neckin process free, or neckin to support the walls durin constriction []. Function shape and size part precision and stranlin pressin force, stranlin constructive ould is choosin. Free deforation constriction force ust be saller than the force that walls lose their stability. It is necessary to know the stranlin force and for choosin of pressin achine that is processed.. Calculation of toroidal stranlin force. A toroidal surface is obtained when stranlin is ade with a radius, and if is spherical neckin.

2 the work of internal tensions Li, that arise durin plastic deforation: (6) The eleentary work of internal tensions can be deterined fro the relationship []: L e L i Fiure.. Stranlin toroidal fors a- siple toroidal; b-toroidal with cylindrical collar Durin toroidal stranlin deforation theould acts upon workpiece by force (fiure ). Between toroidal surface of the ould and workpiece occurs durin deforation frictional force. By coposin the force resultant force projection of force N and N the is obtained. Vertical is the force required F to be applied to achieve constriction toroidal ould. So it can be written: F F F () were fv F it is the vertical coponent deforation force N and coponent of friction force F fv. is the vertical Correspondin to fiure can be written: F cos () fv F f F N sin () N (4) F f By substitutin equations (), () and (4) in (5) is obtained: F F c (5) Aount stranlin force value can be calculated usin the enery ethod to equal the external work of stranli force Le, with Fiure.. Toroidal stranlin force syste dli ci dv (7) in witch is the yield strenth of the aterial blank; i -deforations intensity in point M (fi. ); dv- eleentary volue that is defored by consuin dli eleentary echanical work. The intensity of deforations can be deterined by the relationship: c i z z ) (8) where, and z are the ain deforations direction and z (fi. ). The ain deforation in the circuferential direction, correspondin to fiure, is defined by the equation: () (9) in which cos () If you replace the expression () into (9) we obtain: cos () Eleentary volue dv correspondin fiure can be deterined by the relationship: dv da s () in which:,

3 da d d () Fiure Blank deforation schee at toroidal stranlin By replacin da in () and takin into account the relation () follows: dv cos s dd (4) If apply the law of volue constancy of cold plastic deforation at volue dv, can write: z (5) With soe approxiation, because the deforation is sall z-axis direction, can be considered z, and we can write: (6) Size specific deforation of walls in the radial direction ay be deterined by the equation: s s (7) s where: it is the initial thickness of the blank walls; s -defored thickness in point M of blank. Fro equation (7), takin into account the relations () and (6) ives the thickness s and thus: s s cos (8) With the value of s defined by (8) replaced in (4) follows: dv s cos d d (9) Deforations intensity value ay be located by substitutin equations (), (6) and (8) into equation (8) to ive: i cos () Usin relations (7), (9) and () ives the forula for calculatin the eleentary echanical work of internal tensions, as follows: dli cs cos cos d d () By interatin the relation () for the variable fro to and the variable fro to it obtain Li with the for: s cos d 4 L cs cos i () After the calculation results: 4 Li cs sin sin sin cos sin cos ) () The echanical work of the external stranlin force F can be deterinated by relationship: L F h (4) e in which, 5, because the deforation force increases fro to the axiu value F, and h is the displaceent in load. Correspondin to fiure, the displaceent in load h it can also be deterined by the relationship: h (5) Substitutin equation (5) to (4) was obtained: Le F (6)

4 Equallin relation () with (6) follows: 8 F cs sin sin sin cos ) sin (cos ) (7) For practical cases ay nelect soe of the ters that are low and safety ay be use relation (7) as siple: 8 sin F cs (8) This value of F be replaced in relationship (5) to ive the total stranlin toroidal force F shape: 8 sin F c s c (9). Calculation of toroidal with cylindrical collar neckin force Machinin of stranled part with cylindrical collar is a achinin of stranled toroidal part, where the old deforation continues after the stranled diaeter the value d r cos. Continued deforation blank after they reached this value it causes the aterial to bend and straihten the final on walls ould, forin a cylindrical collar with diaeter d (fiure 4). Fiure 4. Toroidal with cylindrical collar stranlin Thus, the total stranlin force Ft in this case would consist of two coponents: the total stranlin force F, and bendin and straihtenin force across r ould Fî, as: F F F () t î Bendin and straihtenin force of the blank across r is deterined fro the equalizin of echanical the work of the inner bendin oent on the anle with echanical the work of force Fî. The phenoenon is siilar to the conical and cylindrical collar stranlin, and calculation of expression Fî will be the followin for []: d,8 rs cos r F î () Substitutin relations (9) and () in () ives the forula for calculatin the total force of toroidal with cylindrical collar force Ft for: 8 sin F c s c d,8 rs cos r () 4. Conclusions Toroidal stranlin process analysis shows that in this case the total force of the stranlin is less than if conical stranlin at the sae deree of deforation. This is explained by the way in which the contact between tool and workpiece and inclusive in which takes place the deforation. For toroidal with cylindrical collar stranlin total deforation force at toroidal stranlin force add the necessary trainin collar force that has the sae shape as the conical with cylindrical collar stranlin. Toroidal stranlin force is influenced by physical and echanical characteristics of the aterial, the thickness of the blank, the radius of the enerator tor arc, the anle of the enerator arc tor and coefficient of friction. At toroidal with cylindrical collar stranlin, add the total force influencin the radius

5 continues of the ould between the cylindrical surface and tor, and the stranlin coefficient. ACKNOWLEDGEMENTS Financial support fro the POSCCE project Centru interat de cercetare, dezvoltare si inovare pentru ateriale Avansate, Nanotehnoloii si Sistee distribuite de fabricatie si control (MANSiD), Contract No. 67/9.4.5 is acknowleded. 6. eferences. [] Severin, L, V., Severin T.,L.,L., Cold stranlin hollow parts forces calculation of conical and conical with cylindrical collar. evista TEHNOMUS JOUNAL, nr., Editura Universității Suceava, Suceava 6; [] Teodorescu, M., Al., Tehnoloia presării la rece. Editura Didactică și Pedaoică, București, 98; [] Ponoariov, S., D., s.a., Calculul de rezistență în construcția de așini. Editura Tehnică, București 96; [4] oanovskii, V., P.,Ștanțarea și atrițarea la rece. Editura Tehnică, Bucurști 97. 4