Near Net Shape Manufacturing of CuCr Vacuum Switching Contacts ...

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$Refractory metals in furnace construction and engineering$

WS 15/8 17th Plansee Seminar 2009, Vol. 3 Feist, Oberbreyer et al. (5) q (3) d (4) tan β 1 p a ferent level of triaxiality is used (e.g. a four-point bending test, Fig. 3a, (5)) determination of the strength parameters becomes over-determine which can help reducing potential errors by means of least-squareroot minimization. Alternatively, a higher order shear-failure surface could be determined from these test. ¥ p b (1) p (2) d d 2 d 3 d1 ¥0 ¥2 ¥3¥th (a) (b) Figure 3: Mechanical powder-characterization: (a) experimental determination of cap- and shear-failure surface parameters, (b) density dependence of cohesive strength d. The obtained shear-failure surface (in terms of d and β) is only valid for the given density-level ρ1 (Fig. 3). In order to determine the density-dependence of the strength parameters similar tests must be conducted at various other density levels ρ2, ρ3 . . . (Fig. 3b) relevant for PM production purposes. The obtained discrete values d1, d2 . . . and β1, β2 . . . for simulation purposes will be fitted using an appropriate regressionfunction (9b, c) (see Fig. 3b in case of cohesion d), which will be used to interpolate or extrapolate the strength parameters at any density ρ. Analytical assessment of PM-processed parts When designing the process-plan for a component to be produced on the PM manufacturing route the designer is mainly confronted with the question on how to arrive at the final nominal geometry. In particular he has to determine all relevant process-parameters like the geometry of the die, the fill-height of the powder-body, the required powder mass, the tools, their travel during compaction, the remaining axial force during ejection etc. This in most of the cases is done on a combined basis of experience and trialand-error approaches. In this respect, finite element analyses based on the described mathematical model can only help in accelerating the iterative trial-and-error procedure by virtually conducting the required experiments. However, also for the numerical simulations the process-parameters as given above have to be explicitly estimated or prescribed, respectively. This follows from the fact that the described mathematical model exactly represents the manufacturing process and follows the direction of its work-flow. In this context it is desirable to obtain appropriate initial estimates for the process-parameters serving as a valid initial guess for numerically simulated or experimentally conducted process-experiments. These initial estimates in principle should be obtained by starting from the nominal geometry of the component and stepping the entire process-chain right back to the fill-state. Through the irreversible character of the mathematical relationships employed for describing the constitutive state both in the compaction and sintering step, this however is only possible for very simple geometries based on analytical solutions under some assumptions:
Feist, Oberbreyer et al. 17th Plansee Seminar 2009, Vol. 3 WS 15/9 To this end, it is assumed that the density is homogeneous across the entire domain at any process-time. Since any friction taking place between the tools and the powder will preclude this assumption to hold, a frictionless state µ = 0 is assumed. Furthermore, it is assumed that the considered part will not change its topology during the entire process – however, it can change its size and its proportions (e.g. a cylindrical part will remain cylindrical, however, with changing diameter d and height h and changing ratio d/h). Under this assumption one can easily derive a step-back procedure as outlined below for geometric primitives as cubes, cones or cylinders. More complex geometries can be assembled from these primitives allowing the determination of initial guesses for process-parameters also for industrial components. For the sake of simplicity, the further outline is done by means of a single cylindrical part. The procedure starts by defining the nominal geometry of the part at the end of sintering given by its diameter ds and height hs, hence determining its volume Vs. In addition an approximate fill density ρf and a desired green density ρg have to be assumed – on the basis of the chosen green density the required axial compactionload Fz can be determined later and compared to the specifications of the press available for production. Hence, the chosen green density will become an adaptable parameter for the design. On basis of the selected green density the attainable sinter density ρs can be computed together with the radial and axial sinter strains εr and εz (cf. Fig. 2). Using the computed sinter density ρs and the given volume Vs one can determine the total mass m of the part. By reversely applying the sinter strains to the final geometry the geometrical parameters at the start of the sintering phase (i.e. the green state) dg and hg can be found. For the given green density ρg and the associated volumetric plastic strain εv (5) all constitutive parameters of the cap-plasticity model can be computed employing their evolution equations (8), (9) and (10). Hence, the constitutive state at the end of the compaction phase is fully given and the associated stress state in terms of the axial and radial stress σz and σr can be computed. Using the diameter of the green compact dg the maximum axial load Fz required for compaction can be found and compared to the load available with the press used within the later production. Using this stress state the radial and axial elastic deformations during the ejection-phase can be estimated in terms of the radial and axial elastic strains ε el r and ε el z using the density-dependent Young’s modulus (10). By reversely applying these strains on the green-compact geometry one arrives at the height hp and diameter dp of the powder-domain in the compacted state associated to the maximum compactionload. Diameter dp now must equal the diameter of the used die and consequently the diameter of the fillbody df . Postulating conservation of powder-mass m the fill volume Vf can be computed using fill-body diameter df and consequently its fill-height hf . Summarizing the outlined procedure it allows to determine appropriate initial estimates for the relevant process-parameters in the following principle given : ds, hs estimate : ρf, ρg determine : ρs, m, dg, hg, df, hf, Fz One of the most critical phases of the process-chain is certainly the ejection stage, where the compact radially constrained by the die is gradually turned to an unconstrained state. It is a common procedure to either keep a fixed residual axial load on the punches during ejection (load-control) or to keep the distance between the lower and upper punches fixed (displacement-control). Selecting an appropriate level of the associated process-parameters is a crucial feature for successful ejection: the application of a residual (16)
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Near Net Shape Manufacturing of CuCr Vacuum Switching Contacts ...

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