Abstract: A method of multi-objective optimization is proposed to improve the quality of crushed materials and vibration performance of the rotor。 This method is driven by the first order natural frequency and the radius of the rotor。 The Central Composite Design (CCD) experiment method is used to guide the selection of appropriate structure finite element analysis samples in design space。 The quadratic polynomials are employed to construct response surface (RS) model based on the response outputs of these samples obtained by analyzing the first order natural frequency, the harmonic and mass with the software ANSYS。 Well-distributed samples are generated in the design space by shifted Hamersley sampling method。 The prominent points are selected by the weighing method as initial samples。 The multi-objective genetic algorithm is used to obtain the Pareto optimal solution set。 Through the optimization, the first order natural frequency is increased by 5。5%; the radius of the rotor is enlarged by 2。5% and the amplitude of the vibration is decreased by 11% at the position of bearing。 At the same time, the rotor mass does not change much。 The results show the strong engineering practicability of the proposed method。76180

Keywords: Finite-element analysis, multi-objective optimization, optimization design, response surface methodology。

1。 INTRODUCTION

Impact crusher is a new style, high efficiency crushing equipment and widely used in mining, metallurgy, building industry, and so on。 Because of rapidly rotating rotor this kind of crushers have the problems of vibrations and loud noise in crushing operations。 Structure parameters of the rotor influence not only the vibration of the machine, but also impact crusher structure size and the crushing product quality。 In recent years, optimization design of the crusher rotor has been paid more and more attention。 The literature [1] discussed the finite element modal analysis of the rotor, the natural frequency and the mode shapes are calculated through modal analysis。 But the study was limited to a preliminary analysis of the vibration characteristics of a rotor body。 The literature [2] analyzed stress on the rotor, and optimized to reduce the stress concentration by changing the rotor size。 This research had achieved some results, but it is only a simple optimization based on finite element analysis, limited to the single design goal, and did not consider the effect of rotor structure on crushing performance in optimization process。 

In this work, the domestic CF250 impact crusher is considered as the research object。 A multi-objective optimization method is presented。 In order to improve the vibration characteristics and the crushing product quality, the central composite design(CCD) experiment method, the response surface(RS) model, shifted Hamersley sampling method and genetic algorithm are all adopted to carry out multi-objective optimization for the rotor。 This method avoids premature phenomenon and low local searching ability of the Multi - objective evolutionary algorithm (MOEA), provide a reference for the optimization design of other mechanical structure。

2。 OPTIMIZATION MODEL

The rotor component of CF250 impact crusher is shown in Fig。 (1)。 The parametric model is established with ANSYS code as shown in Fig。 (2)。 Tetrahedron elements were used in the finite analysis of the rotor base and shaft。 The physical parameter type of the mesh was set to Mechancal。

2。1。 Determination of the Objective Function

One of the optimization goals is to improve the dynamic characteristics of the rotor and to reduce the vibration of the rotor system by optimizing the structure parameters of the rotor and shaft。 To improve the unit mass stiffness of the rotor can reduce the vibration of the rotor and the crusher under working condition and make the rotor vibration be suitable for the intended purpose。 So one of the optimization objective functions is the first natural frequency, which is closely related with the vibration of the rotor system。