Table 8 Design of punch and die according to the best draw ratio (2.4) and inflow angle (9$$^\circ$$)

Stage Dimension of die Draw ratio and reduction ratio of cross-sectional area
1st stage Deep drawing $${D}_{0}$$ = 1,129 mm
$${\mathrm{d}p}_{1}$$ = 470.51 mm
$${\mathrm{d}i}_{1}$$ = 490.51 mm
$${D}_{0}/{\mathrm{d}p}_{1}=2.4$$
$${A}_{1}=\frac{\pi }{4}\left({{\mathrm{d}i}_{1}}^{2}-{{\mathrm{d}p}_{1}}^{2}\right)$$ = 15,095.7 mm2
2nd stage Redrawing $${\mathrm{d}p}_{2}$$ = 332.5 mm
$${\mathrm{d}i}_{2-1}$$ = 352.5 mm
$${\mathrm{d}}_{\mathrm{p}1}/{\mathrm{d}}_{\mathrm{p}2}=1.42$$
$${A}_{21}=\frac{\pi }{4}\left({{\mathrm{d}i}_{2-1}}^{2}-{{\mathrm{d}p}_{2}}^{2}\right)$$ = 10,760 mm2
Ironing 1 $${\mathrm{d}i}_{2-2}$$ = 346.7 mm $${A}_{22}=\frac{\pi }{4}\left({{\mathrm{d}i}_{2-2}}^{2}-{{\mathrm{d}p}_{2}}^{2}\right)$$ = 7,574.9 mm2
$${RA}_{Ironing,22}=1-\frac{{A}_{2-2}}{{A}_{2-1}}=29.6\%$$ (< 35%)
$${RA}_{total,2}=1-\frac{{A}_{2-2}}{{A}_{1}}=49.8\%$$ (< 50%)
3rd stage Ironing 2 $${\mathrm{d}p}_{3}$$ = 332.5 mm
$${\mathrm{d}i}_{3-1}$$ = 341.9 mm
$${A}_{31}=\frac{\pi }{4}\left({{\mathrm{d}i}_{3-1}}^{2}-{{\mathrm{d}p}_{3}}^{2}\right)$$ = 4,979 mm2
$${RA}_{Ironing,3-2}=1-\frac{{A}_{3-1}}{{A}_{2-2}}=34.3\%$$ (< 35%)
$${RA}_{total, 3}=1-\frac{{A}_{31}}{{A}_{22}}=34.3\%$$ (< 50%)