The ®nite element analysis on planetary rolling process Chih-Kang Shih, Chinghua Hung * , Ray-Quen Hsu Department of Mechanical Engineering, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, Taiwan, ROC Abstract This paper is focused on using the ®nite element method to simulate and analyze the planetary rolling process. First, a basic geometric model of the planetary rolling mill that considers roll pro®les and offset angle of the rolls was constructed. Then, a three-dimensional elastic±plastic ®nite element simulation was used to analyze both the deformation characteristics of this process and the distributions of stress and strain in the workpieces. During simulations, an algorithm called Equation of Meshing was proposed by which the initial contact conditions between the rollers and the workpiece were successfully derived. Finally, an optimum design method was integrated into this analysis for seeking the best design variables in order to reduce the cavity conditions in the leading end of milled steel rods. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Finite element analysis; Planetary rolling process; Equation of Meshing 1. Introduction Traditionally, most stainless steel rods are manufactured in the roughing rolling process with large reduction ratio by several 2-high rolling mills. Six to eight conventional mills can be replaced when using one planetary rolling mill Planetenshra Ègwalzwerk, PSW as shown in Fig. 1 [1]) in the roughing rolling process. The PSW mainly contains three conical rollers and an external ring. As shown in Fig.2,therollersareinclinedandarelocatedequallyaround the axis of the workpiece and their axes intersect that of the workpiece by an offset angle. This offset angle makes the workpiecemoveforwardastherollersrotate.Therollersare positioned by the ring. The ring encloses the rollers and rotatesinthedirectionoppositetothatoftherollers.Besides ®xing the rollers, the main purpose of the ring is to counter- act the twisting deformation of the workpiece during rolling process and help to keep the rods round after rolling. The usage of PSW decreases the cost of operation and main- tenance and reduces the required plant space. Furthermore, the advantages of PSW include ¯exibility of ingot size, low rolling load, low lateral spread of material [2,3] and a low temperature drop between the leading and trailing end of the rolled bar [4]. These characteristics help to raise the preci- sion, to homogenize the quality and to increase the competi- tiveness of the products. Therearesomereportsabouttheplanetaryrollingprocess in the literature. In analytical research, Hwang et al. [5] used the upper bound method and elementary mechanics analysis to analyze the force and torque of the rollers. A dual stream function has been proposed for investigating the plastic deformation behavior of the rod during the planetary rolling process [6]. Most experimental researches conducted the rolling experiments with plasticine, the material properties of which can be adjusted to meet that of stainless steel at elevatedtemperature.AoyagiandOhta[7]observedthe¯ow of the material, the load and torque on the rollers, and the pressure distribution on rollers during rolling process with different cross-section reduction rates. In addition, they studied the in¯uence of the offset angle on the exit velocity of the rods. Nishio et al. [8] discussed the quality character- istics of rolled products with different offset angles and roller pro®les. On numerical analysis, Li [9] used the elasto- plastic ®nite element method to analyze the elementary deformation behavior of the planetary rolling process. How- ever, few researches have been done on completely simulat- ing the planetary rolling process with three-dimensional ®nite element deformation analysis. The purpose of this studywasthustofurtheranalyzetheplanetaryrollingprocess with ®nite element simulations and systematically obtain the effects of the rolling parameters. Because the simulation of the planetary rolling process is three-dimensional with the characteristics of non-linearity and large deformation, the numerical calculation demands ef®cient and powerful soft- ware. The vectorized explicit ®nite element code LS- DYNA3D [10] has thus been selected as the simulation tool. Journal of Materials Processing Technology 113 2001) 115±123 * Corresponding author. Fax: 886-35-720-634. E-mail address: chhung@cc.nctu.edu.tw C. Hung). 0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII:S0924-013601)00643-4