In order to make the hammer obtain larger kinetic energy before it collides with materials and get better crushing effect, the rotor radius want to be increased appropriately。 The bigger the rotor radius is, the larger is its average kinetic energy per unit mass。 Make the rotor radius bigger, crushing product should be finer and the crushing product quality should be improved [3-5]。 So rotor radius is considered as another optimization objective function。

2。2。 Selection of Design Variables

Generally, parameters of the rotor such as diameter, span and mass distribution may be changed to attain the goal of the optimization。 However, in some cases, rotor structure parameters are not simply determined by dynamics requirements of the rotor。 The diameter of the rotor axis d and axis length l are restricted by performance and design requirements of the rotor and can not be arbitrarily changed。

The two rotor bearings are bought-in components and their size cannot be changed。 So d2 and l3 are restricted by rotor bearings and can not be arbitrarily changed too。 Therefore, four shaft diameters and six axis length in Fig。 (3)。 Are selected as design variables。 Considering the rotor structure should be symmetrical, the two bilaterally symmetrical axes have a uniform size。 So l1, l2, l4 and d1, d3 are selected as design parameters。 Total 7 design parameters are selected。

2。3。 Multi-Objective Optimal Model

According to the above analysis, the optimization problem has two objectives; one is increasing the first-order natural frequency of the rotor to reduce the rotor vibration in the procession of work; two is increasing the rotor radius based on the constraints are fulfilled in order to increasing the rotor impact energy the kinetic and improving crushing effect。 Seven dimension parameters of the rotor are evaluated as design variables。 The maximum unbalance response of rotor bearing and the rotor mass are constraint conditions in this optimization。 The multi-objective optimization mathematical model of the rotor is as follows。

where X is design variables; f1 (X) denotes the first-order natural frequency; R (X) is the rotor radius; m (X) is the rotor body mass; M0 is the rotor body mass before optimizing;  is design domain; di denotes the lower limit of a design variable; di denotes the upper limit of a design variable; n is the number of design variables, n=7; , respectively denotes the upper and lower limit of the hammer thickness, H , H respectively denotes the upper and lower limit of the hammer height。

3。 PROCEDURES OF OPTIMIZATION DESIGN

The optimization Procedures of the rotor is shown in Fig。 (4)。 First, establish the mathematical model of design parameters and target parameters; the design parameters range are determined refer to the original size; select test points using central composite experimental design method; get the response set of the test points on sample by ANSYS

finite element analysis; then, use ANSYS Workbench Design Exploration (AWB DX) optimization module built the response surface model; uniformly sample in the n-dimensional feasible solution region by Shifted Hamersley sampling method; sort sample points through weighing function and obtain initial population of genetic algorithm; multi- objective genetic algorithm is employed to obtain the optimized results of the response surface; judge whether the optimized result can meet the design requirement, if it is the optimal solution then output the result; otherwise, update the optimization objective function model, return to genetic algorithm to obtain optimal results。

3。1。 Central Composite Experimental Design

Test points selection affects response surface accuracy。 The response surface even can not be constructed if the test point is not ideal, therefore test points should be selected bythe experimental design theory [6-8]。 Central composite design (CCD) method can provide much information and the test error by numerical experiments in the center and its extension points with minimal work cycle。 When solving RS problem, the center point estimate equal to the structure finite element analysis result and other design points unbiased estimate by least squares method。 The central composite face (CCF) method is the most simple and quick, each test variable only has three level。 CCF method is also not easy to fail for the effect of error sources [9, 10]。 CCF method is used to choose test points in this work。