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Table 6 Optimum die radius r 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 die radius \( r\;\left(\mathrm{mm}\right) \)

DAF

P max (kN)

1

3 < m < 4

0.01 < μ d < 0.02

4

0.02

1.2

59.66

2

4 < m < 5

0.02 < μ d < 0.03

4.8

0.028

1.3

57.34

3

5 < m < 6

0.03 < μ d < 0.04

5.7

0.031

1.4

52.23

4

6 < m < 8

0.03 < μ d < 0.035

6.3

0.031

1.5

50.42

5

6 < m < 7

0.03 < μ d < 0.033

6.1

0.033

1.5

50.01