目前最廣泛流行的螺旋傘齒輪與戟齒輪的大量生產方式為面銑式與面滾式切製法，這兩種切削方式都需要在專用的切齒機上搭配特殊的切削刀具才能使用，國內現有的CNC傘齒輪切齒機皆仰賴國外進口，機台售價動輒一至兩千萬，對於小量或者中量生產的傘齒輪製造商來說，設備成本是一大負擔。近幾年國內五軸工具機蓬勃發展，機台的價格降低且對製造精度的要求提升，其具有足夠的自由度，能夠加工面銑式傘齒輪，相較於專用機，五軸工具機的售價便宜，且配備自動換刀的功能，使製造更佳地靈活。
本研究目的在發展五軸工具之螺旋傘齒輪加工技術，包含面銑式刀具與螺旋傘齒輪的設計與製造，藉此提高傘齒輪製造的靈活性以及降低齒輪專用機的設備成本。首先根據美國Gleason公司發展的SGDH (Generated Spiral Bevel Gears, Duplex–Helical Method)面銑式切製法，建立面銑式刀具與螺旋傘齒輪的數學模式，以及工作台傾斜式的五軸工具機座標系統；透過已建立的數學模式與逆向運動學，推導出面銑式刀具以及螺旋傘齒輪製造之五軸工具機的座標位置；再依據推導結果規劃刀具製造與齒輪製造的NC加工程式，並以VERICUT模擬軟體進行切削模擬，避免程式錯誤；最後再於五軸工具機上進行刀具與大小齒輪的切削實驗，驗證本論文數學模式推導的正確性。

The most widely popular mass production methods used in nowadays manufacturing of spiral bevel and hypoid gears are face-milling and face-hobbing methods. Both methods require special cutting tools and are implemented on the dedicated cutting machines. In domestic gear industry, CNC bevel gear cutting machines are all foreign products. The prices of imported machines range between 10 and 20 million NT dollars. Therefore, the cost of gear manufacture using above machines is too expensive for the small or moderate scale production. Five-axis CNC machines bloom in recent decades due to the reduced price and the soaring requirement of manufacturing accuracy. Five-axis machines have enough degrees of freedom to produce face-milled bevel gears. They are cheaper and offer more flexibility of automatic tool changing compared with those dedicated machine. Therefore, the five-axis machine is definitely a good alternative choice for bevel gear manufacturing.
This study aims to develop manufacturing technology for face-milled spiral bevel gear on a five-axis machine. The design and manufacture of face-milling cutter and spiral bevel gears are included. The developed technology largely increase flexibility and reduce equipment cost in bevel gear manufacturing. First, mathematical models of face-milling cutter and spiral bevel gear are established based on the SGDH method (Gleason, Generated Spiral Bevel Gears, Duplex–Helical Method). Coordinate systems of an AC Axis swing table five-axis machine are established. According to inverse kinematics, the five-axis coordinates for producing the face-milling cutter and the face-milled spiral bevel gear can be derived. The NC codes for cutting these two are further programmed according to derived five-axis coordinates. In order to avoid a collision during cutting process, the NC tool paths is examined using VERICUT NC simulation software. Finally, experiments for producing cutter and bevel gear are done to verify the correctness of the proposed mathematical models.

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