拓樸最佳化應用於戟齒輪加工機結構設計與開發;Structural Design and Development of bevel gear cutting machine using the Topology optimization method

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Title:	拓樸最佳化應用於戟齒輪加工機結構設計與開發;Structural Design and Development of bevel gear cutting machine using the Topology optimization method
Authors:	陳宣彤;Chen, Xuan-Tong
Contributors:	機械工程系研究所
Keywords:	參數化分析;工具機;拓樸最佳化;有限元素法;最佳配重之等效剛性曲線擬合;Parametric analysis;Machine tool;Topology optimization;Finite element method;The technique of the curve-fitting between the equivalent stiffness and the optimal weight ratio
Date:	2018
Issue Date:	2019-05-23 12:52:38 (UTC+8)
Publisher:	機械工程系研究所
Abstract:	機台進行輕量化拓樸設計時，往往需要不斷的嘗試及修正才能決定該鑄件所需之重量，此為相當耗時之過程。本研究將發展最佳配重之等校剛性曲線擬合技術，基於拓樸最佳化之密度函數法概念，鑄件結構拓樸設計區域之材料係數為設計變量，在機台結構細部設計前先進行最佳配重比分析，以預估結構靜剛性與自然模態頻率；各鑄件配重結果為拓樸最佳化分析之拘束條件，以此流程進行機台設計，各鑄件只需進行一次拓樸最佳化分析，將有效提升開發設計效率。首先對各鑄件進行不同質量分佈之拓樸最佳化分析，評估鑄件體積與剛性變化趨勢，對此趨勢進行曲線擬合定義出關係式後，將此關係式代入整機有限元素模型進行參數最佳化分析，該鑄件結構為實心，以各鑄件之體積定義為變數，整機模態頻率閃避機台加工頻率且同時達到靜剛性之需求為目標，透過此分析可以得到機台之最佳配重比，根據此配重比再進行拓樸最佳化分析，得到機台之最佳結構設計。研究結果將可直接嘉惠於國內工具機設計。 The required mass of casting for machine tool was determined by a lot of attempts and corrections under the lightweight topology optimization design. The above iterative analysis is a time-consuming process. This study will develop the technique of the curve-fitting between the equivalent stiffness and the optimal weight ratio. The design variables are the material property of the topological design area based on the density function method of topology optimization, i.e. density and young’s modulus. The analysis for the optimal weight ratio between each casting component is utilized to predict the static stiffness and the natural frequency before the detailed rib design of each casting. The results of weight arrangement between each component are the constraints of the topology optimization analysis. Following this process only needs one topology optimization analysis for each casting component. The design efficiency will be improved effectively.First, the topology optimization analyses under different weight arrangement for each casting are utilized to evaluate the variant trend between different volume and corresponding equivalent stiffness. The function between the volume and equivalent stiffness was defined by curve fitting. The function was put into the finite element modeling in order to execute the parametric optimization analysis. The internal structure of casting is solid. The variable is the volume of casting. The objective is to let the natural frequency of the machine tool against the processing frequency and achieve the required static stiffness. The optimal weight ratio of each casting was acquired to proceed topology optimization analysis of rib structure. The research result will directly benefit the domestic machine tool design.
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