Optimal Tolerance Allocation for Multi-body Mechanical Systems

工業用機械臂公差優化設計

賴新一(Hsin-Yi Lai) ； 賴明潔(Ming-Chieh Lai) ； 陳朝光(Chao-Kuang Chen)

《中國機械工程學刊》 38卷3期 (2017/06) Pp. 221-230

摘要

Tolerance allocation is a key process for multi-body mechanical system design and assembly. It plays a significant role in linking design features together including design requirements, product quality, manufacturing costs and system performance. An innovative CPT (cost-precision-time) approach along with a comprehensive computer program is presented in this paper to meet the aforementioned multi-objective design needs. The CPT is a systematic design procedure comprising a Monte Carlo method for tolerance allocation, and genetic algorithms / factorial design for comprehensive cost consideration. Two different production models including a Fortini’s clutch and a SCARA robot, are employed to verify the overall quality and reliability of the CPT method. The design results show that the CPT method is capable of 3D tolerance design for static structures, dynamic systems and robotic models. The tolerance models thus obtained by using CPT approach are sufficiently accurate and more economic as compared to those obtained by using other methods that are presented in literature. The CPT method and associated design procedure presented here is thus proved to be systematic, economic and accurate for comprehensive tolerance design of given industrial production systems.

關鍵字

Tolerance allocation ； Multibody systems ； Genetic algorithms ； Monte Carlo ； Factorial design

並列摘要

公差設計為機械設計與製造中之重要指標，常被用來作為生產品質和成本間之取捨。近年來，機械臂已在各項產業中被廣泛使用，尤其在機械製造領域，機械臂常被用於置物、取物、焊接、噴漆、銑床、鑽床、組裝等製程，其精度已成為產品加工時必須考量的重要因素。當本文以並聯式機械臂作為設計例時，所得結果為，終端定位精度每提升0.01mm，平均總成本約增加28%，故準確訂定公差精度是適當調控生產成本與產品品質所不可或缺。有鑒於此，本研究乃針對機械臂之長度與節點公差進行設計，並考量精度與成本之最佳化綜合指標。在給定產品精度下，模擬零件生產製造及機械臂之運作，利用所撰寫之基因演算程式求得最佳公差設定，並運用蒙地卡羅法模擬機械臂零件製造的真實情況，將機械臂視為一個多體系統進行分析，代入機械臂的運動方程以模擬機械臂之真實運動，得到運動範圍內各作用點之精度誤差。當符合精度要求，則將公差代入經濟成本方程(economic costfunction)和質量損失方程(quality loss function)，將兩者相加以得出綜合成本(comprehensive cost)。滿足演算終止條件後，最低成本者即為最佳公差設計。為印證所提理論與程序流程，本文使用了Fortini’s 離合器和SCARA機械臂兩種模型作為範例，實際採用本文所提方法進行分析與模擬，得出分析結果後與文獻及常用傳統公差設計結果進行比對。最後從基因演算模擬實例所得結論包括: 本文所提基因演算法於公差設計可滿足產品生產與品質服務之設計要求，也同時滿足製程精度與品質服務之最低成本要求。本方法還可套用到不同型態的機械系統上，程式應用範圍廣泛，可用於靜態離合器系統乃至三維動態機械臂，提供業界自動化設計流程使用，且其結果優於傳統WCM(worst-casemodel)和RSS(root sum squared)之模擬結果。