行星式輥軋機輥軋成型分析研究

Abstract

本研究針對行星式輥軋機輥軋的過程，運用有限元素分析以及上界限法來探討棒材和管件在輥軋過程中的成型變化，以期解決行星式輥軋機在生產時工件扭曲變形的情形。模擬採用三維彈塑性有限元素分析法，首先考慮輥輪的外型，及其置放時的壓下角、偏移角等參數，並對應生產時的狀況，加入適切的邊界條件、材料性質以建立適當的行星式輥軋的模組，同時參考齒輪創成的方法，運用嚙合方程式，找出輥輪與工件之間接觸關係。在進行更進一步的模擬分析前，先利用行星式三輥輪軋延試驗機與塑性黏土進行一系列的實驗，來驗證建置完成的模擬模組的合理性。接著運用此一完成驗證的模擬模組，針對不同的輥軋工作參數來觀察棒材成型時的變形及應力、應變的分佈情形。此外，亦整合了最佳化設計的方法，針對鋼棒前端凹陷之最小化，進行了雙設計變數的初步分析。 再針對行星式輥軋機生產無縫管的成型過程進行一系列的模擬分析，探討各輥軋參數對無縫管輥軋成型的影響。同時，藉由雙流線方程式可求得管件在輥軋時材料流動的三維速度場，進而運用上界限法，求出使塑性變形所消耗總功率為最小的動可容許速度場，從中求得管件在成型過程中各點的速度以及加工的能量，並與有限元素分析所求得的結果進行比較。

This dissertation adopts the finite element method and upper bound method to analyze the deformation of a rod and a seamless tube in the three-roll planetary rolling process. The three-dimensional elastic-plastic finite element simulation was employed to analyze both the deformation characteristics of this process and the distributions of stress and strain on the steel rod. The basic geometric model of the planetary rolling mill, that considers the roll profiles and the offset angle of the rolls, was first constructed. An algorithm called “Equation of Meshing” was proposed for application during simulation, from which the initial contact conditions between rolls and workpiece were derived. Before further analyses, the planetary three-roll experimental machine was used with plasticine in a series of experiments to confirm the correctness of the simulation model. Furthermore, an optimum design method was integrated into this analysis to obtain optimal design variables to reduce the cavity depth in the leading end of milled steel rods. The deformation of the hollow tube in the three-roll planetary rolling process was also analyzed systematically. The upper bound solution with kinematically admissible velocity fields derived from dual stream functions was applied to determine the velocity field and energy consumption of the rolling process. Results from analytical and numerical analysis were compared.