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For an indirectextrusion, the stamp often features a tip with a slightangle, which can be neglected in the followingconsiderations.It is necessary to determine all geometric dimensionsof the product from the data mentioned. These dimensionsare shown in Figure 1.For an axisymmetric cup with given outer diameter d0and length l, the volume (3) and the surface (4) render asystem of two equations with the two unknowndimensions d1 and l1:Vdldl =−ΠΠ44 02121 (3)A d dl dl =⋅++Π ΠΠ 42 02001 (4)This results in()dVdlddlA 1022 0204=−+−ΠΠ Π(5)lVdld102124=−−ΠΠ(6)Wall and bottom thickness are calculated using d0 andl. The elementary theory of plasticity can now be applied.Therefore, the flow curve of the respective material mustbe available in the system.The procedure for the shaft with two differentdiameters is similar. With given outer diameter d0, lengthl and angle α, the volume, the surface and the lengthconstitute a system of three equations with the unknowndimensions d1, l1 and l2. The angle α must be chosen inorder to obtain a solvable set of equations. This set ofequations is nonlinear and must be solved numerically.5 Zinc-phosphate coatingCold extrusion is a process requiring high standards ontooling. Special attention must be given to the lubricationduring the actual forming.The semi-finished product is subjected to a complexsurface treatment consisting of – among others – severalsteps of pickling and rinsing. Finally, a zinc-phosphatecoating is applied. This coating in combination with oil isalmost exclusively used as a lubricating system [4] forcold extrusions. Although there is currently researchbeing conducted on replacing or drastically reducing thecoating, no alternative has been found yet which canguarantee cost-effectiveness [5].The zinc-phosphate coating, which almost always hasto be washed off after the forming process, causes twomajor problems to the manufacturer:• soiling of the press• difficult and expensive disposalThe last aspect in particular makes the phosphatecoating the ecologically most critical part of the coldextrusion process.5.1 Surface enlargementThe amount of coating necessary depends on thetribological conditions during the forming process. Theseare determined largely by the surface enlargement of theworkpiece. The surface enlargement is defined as thequotient between the surfaces of the formed part and thesemi-finished product used to make the part: SA formed partA semi finished product=−()()(7)Typical values for S are 1.5…3 for direct extrusion and4…11 for cup extrusion [2]. Furthermore, the amount ofcoating usually lies between 8…20 g/ m² of the semi-finished product surface [2, 6].5.2 Calculation from the CAD-dataThese data are linked together for calculating the zinc-phosphate coating necessary for a given part. In theproduct design environment, the final part is designed.The surface enlargement, however, is a function of theshape differences between semi-finished product and finalpart.The overall maximum outer diameter of the workpiecedoes not change during simple, one-stage extrusionprocesses. Part volume, surface and maximum outerdiameter are available from the CAD-system.Using one of the metal forming fundamentals, volumeconstancy, the geometry of the semi-finished product usedcan be calculated.With volume V and maximum diameter d0 given, andthe fact that a cylinder is used as the semi-finishedproduct, the dimensions of the cylinder can be calculated.SolvingV dl = Π 0220(8)for l0 yieldslVd0 24=Π 0(9)The surface of the semi-finished product is nowdetermined asA ddl = + 220ΠΠ200(10)for both direct and indirect extrusion.After retrieving the surface of the formed part from theCAD-system, the surface enlargement can be calculatedusing equation (7).
The calculation of the surface of theformed part, which exists virtually within the productdesign environment, is a function implemented in anymajor CAD-system. Therefore, no additional formulashave to be applied.Assuming a linear relationship between surfaceenlargement and amount of coating, the specific mass ofzinc-phosphate coating for the production of a part usingdirect or indirect extrusion is now derived asmSgmgm sp =+ 133 666 22.. (11)Multiplied by the surface of the semi-finished productthe total amount of zinc-phosphate coating results inA m m sp total⋅ = (12)Two aspects must be emphasized: The above methodcan only be applied to simple, one-stage formingprocesses. More complex processes do not necessarilyfeature an unchanged maximum diameter of theworkpiece, which is used here to calculate the surfaceenlargement.Also, the fact that direct extrusion can be conductedeither with rods coated on the lateral area as well as theend faces or with sections cut from a pre-coated wire andtherefore not having coating on their end faces iscurrently neglected. One way to deal with this would be afurther consideration of the maximum outer diameter.Since there is practically no wire in use with a diameterover 45 mm, a distinction could be drawn there. This,however, still leaves a diameter area which is not definite,as not all parts with a maximum diameter under 45 mmare produced from pre-coated wire.6 Interface to evaluation system and CAD-systemAs mentioned in chapter 3, the LCI data is required bythe evaluation system. An evaluation of the product isimpossible without this data. The object-oriented CoOMmodel, which includes the core model and all partialmodels including the forming partial model, is compiledinto a database scheme. Also, an interface is createdwhich enables the database and the CAD-system tocommunicate with each other, e. g. to exchange geometryinformation.The evaluation system and the CAD-system areintegrated in the product design environment on basis ofthe object-oriented information model. Since the databaseis linked to the CAD-system and has been created basedon the CoOM model, the evaluation system can assess theLCI data provided by the process models including thecold extrusion model. After processing the LCI data andconducting the LCA, the results are displayed to theproduct developer.