the blank material, so as to avoid the defects of fracture, wrinkle and serious thinning。
2。3Finite element modeling
In this work, we use DYNAFORM to simulate the deep drawing process of the head, and establish finite element modeling based on the actual die structure, as shown in Fig。 3。 Numerical simulation parameters are set as follows: the material of head is BTC 330R; the elastic modulus is 289 GPa; the Poisson ratio is 0。28; the hardening coefficient is 568。9 MPa; the hardenability
value is 0。34; and the anisotropic parameter is 1。488;
Fig。 4 Schematic diagram of objective functions definition
diameter of punch (Dp) is 343。6 mm, and diameter of die (Dd) is 350 mm。 Meanwhile, punch, die and blank holder default as being rigid。 The friction coefficient of sheet metal contacting with rigid die is 0。12。
The objective function Dt is defined as
where k represents the number of units which is tested; t0 represents the initial sheet thickness; ti represents the final sheet thickness。
Fig。 3 Finite element model of drawing: 1−Die; 2−Blank; 3−Binder; 4−Punch
3Multi-objective optimization based on response surface method
The best combination of process or geometry design variables can be got using RSM, which will lead to a desired sheet metal part without any defects, such as fracture, wrinkles and thickness varying, etc。
3。1Objective function
The forming defects can be quantified by objective function, which can judge the formability of sheet metal parts as criteria。 In this work, the fracture, wrinkle and thickness varying are considered the optimization targets。 According to the definition of wrinkle and fracture forming limit curves raised in Ref。 [6], the fracture Df, wrinkling Dw, and thickness varying Dt corresponding objective function are constructed as follows, based on the constraints of forming limit curve, as shown in Fig。 4。
The fracture function Df can be formulated as
3。2
Experimental design
In most cases, the relationship between the response variables and the independent variables are unknown。 In the present experimental investigation, response surface methodology is applied to establishing polynomial equation so as to get the optimal combination of parameters, in terms of the efficiency and accuracy of optimization。 Finding a suitable approximation to the true relationship is the first step in RSM。 Meanwhile, determining reasonable variables and levels is significant。
Thus, we adopt the same idea as ZHOU et al [2]—central
composite design and steepest ascent design were adopted to arrange variables and experiments。 There are four variables, i。e。 the fillet radius, the position of draw-bead, the blank size and the blank-holding force。 The four variables were respectively represented by x1, x2, x3, x4, and the fracture function, the wrinkling function and the thickness function are respectively represented by Df, Dw and Dt for brevity。
The steepest ascent design is introduced in the present investigation for its efficiency。 With this technique, the region for each variable is correctly defined。 The results of steepest ascent design are listed in Table1。
It shows that the minimum values of the three
objective values appear when the experiment is tested at
the parameter combination of No。3。 It can be concluded
The wrinkling function Dw can be formulated as
that the optimum parameter combination will exist near
the parameter combination of No。3。 Thus, the center point of response surface experiments is set at (3, 385, 遗传算法的热水器水箱盖的冲压成形过程英文文献和中文翻译(3):http://www.youerw.com/fanyi/lunwen_92717.html