| 摘要: | 螺旋傘齒輪由於特殊的形狀與嚙合方式，其加工方式較圓柱形齒輪更為複雜；且除了使用模具鍛造鑄造的方式，現今工業上普遍使用專用機台加工螺旋傘齒輪來提升生產效率；其加工方式主要可分為由美國齒輪製造商Gleason公司引領的面銑式切製法，以及德國齒輪製造商Klingelnberg所研究的面滾式切製法。傳統上，傘齒輪的切製方式離不開專用的加工機台，機台上通常具有多種複雜的結構，特色是具有搖台機構的特殊設計；然而經過二十年來的發展，加工機台已具有極高的效率與精度；六軸CNC工具機已具有高自由度，可以完整的完成加工螺旋傘齒輪時的切削軌跡，突破以往傳統上因機械結構所造成限制。由於螺旋傘齒輪之外形與多種計算方式，使的初入門之學者難以理解容易混淆，因此本研究欲發展一套完整設計至創成加工螺旋傘齒輪之數學模型；於研究中基於逆運動學，從傳統加工螺旋傘齒輪之切削機的座標系統，建立面銑式加工螺旋傘齒輪的數學模型，使其應用於CNC切削機台上；然而由於Gleason切製螺旋齒輪之機械設定的不公開，尤其是雙面雙切削法，於文獻上揭露的更少，本研究基於已揭密的基礎機械設定原理為基礎，研究一套以雙面雙切削法創成螺旋傘齒輪之計算模型，並應用至立式五軸CNC加工機，並驗證所計算之齒面模型。最後為了可快速的護取齒面接觸結果來判斷齒面效能，以創成之螺旋傘齒輪模型，於齒輪模擬軟體KissSoft建立近似齒面模型，並進行齒面負載接觸模擬；此外使用有限元素之齒面接觸模擬，驗證KissSoft之近似齒面模型之接觸模擬結果為正確的。;The modelling of spiral bevel gears is more complex than the modelling of cylindrical gears due to the unique shape and engagement type. Except using mold forging and casting methods, dedicated machines are commonly employed to enhance the production efficiency of spiral bevel gears in industry. Traditionally, the cutting of bevel gears relies on specialized machining equipment, typically featuring various complex structures, with a distinctive design incorporating a cradle type mechanism. Nowadays six-axis CNC machine tools provide high freedom, high efficiency and high precision, enabling the complete execution of cutting path for manufacturing spiral bevel gears, overcoming previous limitations imposed by mechanical structures.
Because of the complex shape and various calculation methods associated with spiral bevel gears, beginners often find it challenging to comprehend. Therefore, this study aims to develop a comprehensive mathematical model for the design and manufacturing of spiral bevel gears. In the research, is based on inverse kinematics to establish a mathematical model for face-milling of spiral bevel gears and applied to CNC cutting machines, starting from the coordinate system of universal gear cutting machines. However, due to the mysterious mechanical settings for cutting of Spiral gears, particularly the duplex helical cutting method, which is less revealed in the literature, this study, based on disclosed fundamental mechanical principles, research for a duplex helical cutting method to create a mathematical model for spiral bevel gears. Subsequently, the model is implemented on a vertical five-axis CNC machine, and the accuracy of the calculated tooth surface model is confirmed through validation. To promptly evaluate tooth contact outcomes for assessing tooth surface performance, the generated spiral bevel gear model is employed to create an approximate tooth surface model within the gear simulation software KISSsoft. Following this, simulations for tooth surface load contact are conducted. Furthermore, finite element tooth contact simulations are utilized to validate the accuracy of the contact simulation results obtained from KISSsoft. |
