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An axisymmetric PFEM formulation for bottle forming simulation

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Abstract

A numerical model for bottle forming simulation is proposed. It is based upon the Particle Finite Element Method (PFEM) and is developed for the simulation of bottles characterized by rotational symmetry. The PFEM strategy is adapted to suit the problem of interest. Axisymmetric version of the formulation is developed and a modified contact algorithm is applied. This results in a method characterized by excellent computational efficiency and volume conservation characteristics. The model is validated. An example modelling the final blow process is solved. Bottle wall thickness is estimated and the mass conservation of the method is analysed.

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Notes

  1. Note that \( \bar{\mathbf{v }} = \bar{\mathbf{v }} _a=[ \bar{\mathbf{v }} _r (r,z)\,\,\,\, \bar{\mathbf{v }} (r,z)]^T\) and \( \bar{\mathbf{p }} = \bar{\mathbf{p }} _a= \bar{\mathbf{p }} _a(r,z)\) are the discrete counterparts \( \mathbf v _a\) and \(p_a\) respectively. We shall omit the a index in what follows.

  2. The maximum velocity can be also estimated by noticing that the volume of the paraboloid defined by the velocity profile must be equal to the area of the inlet multiplied by the inlet velocity. Taking into account the no-slip condition applied at the area where the constant non-zero flux is applied is \(A_\mathrm{flux}=\pi (R-h)^2\), where h is the mesh size. Thus: \(V_\mathrm{paraboloiod}=v_{\max }\frac{1}{2}\pi R^2=\pi (R-h)^2 v_i\). Thus (taking \(R=0.1\), \(h=0.0025\)) we obtain: \(v_{\max }\approx 0.19\) m/s.

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Acknowledgments

The author expresses his gratitude to the Spanish Ministerio de Economia y Competitividad for the FPDI-2013-18471 grant that allowed to perform this work.

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  1. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Gran Capitán s/n, 08034, Barcelona, Spain

    Pavel B. Ryzhakov

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Correspondence to Pavel B. Ryzhakov.

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Ryzhakov, P.B. An axisymmetric PFEM formulation for bottle forming simulation. Comp. Part. Mech. 4, 3–12 (2017). https://doi.org/10.1007/s40571-016-0114-7

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