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Table 4 Optimum friction \( {\mu}_d \) and exponent gradient m obtained through MDO for FGT inversion tube

From: Multi-objective optimization of functionally graded thickness tubes under external inversion over circular dies

Number of cycle

Design parameter interval

Optimal exponent gradient \( m \)

Optimal friction \( {\mu}_{\mathrm{d}} \)

SEA (kJ/kg)

P max (kN)

1

3 < m < 4

0.01 < μ d < 0.02

4

0.02

44.16

49.51

2

4 < m < 5

0.02 < μ d < 0.03

5

0.029

48.2

43.29

3

5 < m < 6

0.03 < μ d < 0.04

5.8

0.031

51.3

39.43

4

6 < m < 8

0.03 < μ d < 0.035

7.3

0.03

54.6

35.18

5

7 < m < 8

0.03 < μ d < 0.033

7.3

0.031

57.9

33.2