Research and development of CNC machines dedicated to rotational metal forming processes have made it possible to form difficult non–circular geometries and even more difficult axially asymmetrical ones. New processes require not only the development of new methods for creating metal–forming trajectories but also the identification of their advantages and disadvantages. This article presents mathematical equations and algorithms for trajectory design in the rotational metal forming of axially asymmetrical parts. Simple algorithms using conditional while–loops were developed that are compatible with modern CNC machines. The algorithms were used to metal form parts with complex axially asymmetrical geometry. An analysis was conducted to evaluate the influence of selected technological parameters on the trajectory generation process. The impact of rotational symmetry was assessed by analysing the number of commands required to execute a single forming movement using mandrels with circular, elliptical, square, and asymmetrical cross–sections. The <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> angle was examined for values <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\alpha =90^{\circ }$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>90</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\alpha >90^{\circ }$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>></mo> <msup> <mn>90</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>, while differences in trajectory programming between absolute–G90 and incremental–G91 positioning systems were analysed. Results from FEM simulations and laboratory tests were presented, in which an axially asymmetrical mandrel was employed, and EN AW–1050A aluminium alloy was formed. Advantages and limitations of the proposed trajectory design method were discussed. A modern division for Rotational Metal Forming processes was proposed. RMF was divided into subcategories: axially symmetrical (Shear Forming—RMFSF and Metal Spinning—RMFMS) and asymmetrical processes (Rotationally Symmetrical—RMFRS and Axially Asymmetrical—RMFAA).

Simple programming algorithms in advanced rotational metal forming processes

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2026年3月14日

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Marcin Majewski,
Tomasz Gądek,
Marcin Lijewski,
Leszek Klimek

摘要

Research and development of CNC machines dedicated to rotational metal forming processes have made it possible to form difficult non–circular geometries and even more difficult axially asymmetrical ones. New processes require not only the development of new methods for creating metal–forming trajectories but also the identification of their advantages and disadvantages. This article presents mathematical equations and algorithms for trajectory design in the rotational metal forming of axially asymmetrical parts. Simple algorithms using conditional while–loops were developed that are compatible with modern CNC machines. The algorithms were used to metal form parts with complex axially asymmetrical geometry. An analysis was conducted to evaluate the influence of selected technological parameters on the trajectory generation process. The impact of rotational symmetry was assessed by analysing the number of commands required to execute a single forming movement using mandrels with circular, elliptical, square, and asymmetrical cross–sections. The $\alpha $ $α$ angle was examined for values $\alpha =90^{\circ }$ $α = 90^{\circ}$ and $\alpha >90^{\circ }$ $α > 90^{\circ}$ , while differences in trajectory programming between absolute–G90 and incremental–G91 positioning systems were analysed. Results from FEM simulations and laboratory tests were presented, in which an axially asymmetrical mandrel was employed, and EN AW–1050A aluminium alloy was formed. Advantages and limitations of the proposed trajectory design method were discussed. A modern division for Rotational Metal Forming processes was proposed. RMF was divided into subcategories: axially symmetrical (Shear Forming—RMF_SF and Metal Spinning—RMF_MS) and asymmetrical processes (Rotationally Symmetrical—RMF_RS and Axially Asymmetrical—RMF_AA).