傘齒輪是一種用於傳遞旋轉運動和扭力的機械零件，因齒輪的齒面是斜面的可允許非平行軸之間的動力傳輸，並可承受高負載運轉時接觸上比起其他齒輪更平滑，故傳動性能高及噪音低。而傘齒輪中之螺旋傘齒輪由於特殊的形狀與其嚙合方式在製造上容易產生誤差，而大齒數比之螺旋傘齒輪又因其構造，即使誤差極小也會產生嚴重後果，會導致齒輪在傳動時會因接觸狀態不良導致傳動效率降低；而通常發現齒面接觸不良時會針對齒面進行修形加工，而在修形前須了解目前齒面接觸狀態再決定修形方式及量值，故求得接觸不良之狀態在進行修形時是重要之一環。本研究利用逆向工程方式將螺旋傘齒輪齒面之點資料進行處理並透過曲面擬合方式建構出齒面之數學模型；再將齒輪裝配至運動位置後利用最小轉角法搭配自身設計之干涉檢查模型，確定齒面間正確嚙合點之轉角，進而得出齒輪組之接觸線及傳動誤差；再將嚙合轉角代入到齒輪組運動位置即可利用變形四元樹法及常用之紅丹顆粒大小6 求得齒印範圍，建立出齒面接觸數學模型；最後透過模擬軟體KISSsoft利用其拓樸功能建立出真實齒面近似模型並且作接觸分析；針對齒面接觸數學模型及KISSsoft之接觸分析結果相互探討螺旋傘齒輪組齒面接觸之性能狀態，並針對齒面作修形且提高齒面接觸性能。;Spiral bevel gears are mechanical components used for transmitting rotational motion and torque. Due to the inclined tooth surfaces of these gears, they allow for power transmission between non-parallel axes, and they can withstand high loads while providing smoother contact compared to other gears. Therefore, they exhibit high transmission performance and low noise levels. However, spiral bevel gears, especially spiral bevel gears with a large tooth-to-tooth ratio, are prone to manufacturing errors due to their unique shape and meshing method. Even minor errors in manufacturing can have serious consequences, leading to decreased transmission efficiency due to poor contact conditions during operation. Typically, when poor tooth surface contact is detected, corrective shaping processes are applied to the tooth surface. However, it is crucial to understand the current tooth surface contact state before determining the method and amount of shaping. This study utilizes reverse engineering methods to process point data of spiral bevel gear tooth surfaces and construct mathematical models of the tooth surfaces through surface fitting techniques. After assembling the gears into their operational positions, the correct meshing angles between tooth surfaces are determined using the minimal rotation angle method combined with a self-designed interference checking model. This process allows for the determination of contact lines and transmission errors of the gear assembly. By incorporating the meshing angles into the gear assembly′s motion positions, the range of tooth imprints is calculated using deformation quaternion methods and commonly used red dan particle sizes. This establishes mathematical models of tooth surface contact. Finally, simulation software KISSsoft is employed to establish approximate models of real tooth surfaces and conduct contact analyses. The performance state of the spiral bevel gear assembly′s tooth surface contact is discussed based on the mathematical models of tooth surface contact and the results of KISSsoft′s contact analysis. Furthermore, corrective shaping processes are proposed to improve the tooth surface contact performance.
