This research deals with a multi-stage deep-drawing operation. The research aim is to produce spline shapes using two methods (direct and indirect) for three-stages based on experimental work and FE model procedure. The direct method was performed to produce spline shapes from the blank for the first stage, while the second and third stages from shapes of the first and second stages, respectively. The indirect method was performed to produce spline shapes from the cylindrical shapes of three-stages. The multi-stage deep-drawing was completed to perform the experimental procedure required to produce a spline shape with inner dimensions of major axis D = 41.5,33.3,28.8, and miner axis d = 34,27.2,23.6 mm for the first, second, and third stages, respectively. Flat circular blanks (diameter Db = 80 mm and thickness t = 0.7mm) of low carbon steel (1 008 - AI S I) used in this research. FE analysis based on the ANSYS workbench program was used to model the multi-stage deep-drawing operation. The comparisons between results showed that the direct method was successful with the first stage, while it was failed with the second and third stages. For the three-stages, the maximum drawing force required to produce spline shape by the direct method is greater than the maximum drawing force required to produce spline shape by the indirect method. The maximum drawing force values equal to 41.650 kN, 33.175 kN, 33.11 kN for the first, second, and third stages, respectively, Also, for the three-stages, it was observed that it is possible to produce a complete spline shape without defects in the indirect method when comparing with the direct method.

In the current research, an analysis study was conducted to process of design of spline cup drawing. Deep-drawing tools (dies and punches) were designed and manufactured to implement the experimental work required to produce a spline cup with inner dimensions are height h=3 mm, width W=9.64 mm, and diameter d=34 mm, drawn from a circular blank of a di ameter D b = 8 0 mm, and thicknes s t = 0 . 7 mm made of low carbon steel (1008-AISI). To simulate the spline shape deep-drawing process, a commercial finite element program code ANSYS 19.0 Workbench was employed. The research aims to produce the spline shape and study the effect of the punch wall curvature radius on the drawing force, thickness distribution, and effective strains across the sidewall, major and minor axis curvature of a completely drawn spline cup using experimental testing and finite element modeling. From the comparisons between the experimental and finite element results, it was shown that the numerical results of a spline cup deep-drawing are good agreement with the results of the experiment and lie within an average of (4% - 8%). The drawing force and thinning for the small punch wall curvature radius is higher than the large punch wall curvature radius. The maximum drawing force and maximum thinning with the smallest punch wall curvature radius (0.5) at the minor axis curvature of a completely drawn spline cup. The maximum effective strain with the smallest punch wall curvature radius (0.5) at the minor axis curvature region at the completely drawn spline cup rim.

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