植牙手機為執行植牙手術切除病變的牙齦組織的牙科手術器械之一，牙科手機有低轉速和高轉速兩種類型，前者為高扭矩是導致齒輪破壞的原因。為了達到20：1的減速比，植牙手機需要三個齒輪對，包括一組行星齒輪系和兩個直傘齒輪對。由於空間大小的限制，直傘齒輪的齒面為非標準齒型，無法使用現有齒輪強度標準(如AGMA 908-B89 and ASNI/AGMA ISO 2003-B97)進行齒輪強度的計算。
本研究目的為建立直傘齒輪強度分析之數學模型，首先將商用產品以2.5D及3D進行量測，並以此為基礎進行兩個齒輪對的齒輪幾何重建。由於直傘齒輪的製造是以成形法製作，故根據直傘齒輪齒面建立齒面拓樸點數學模式。為了趨近於共軛齒面已達更好的接觸性能，故使用齒面相對修形決定小齒輪的齒面。在這裡採用ANSYS參數化設計語言(ANSYS Parameter Design Language, APDL)進行植牙手機齒輪對的靜態應力分析，根據數學模型且透過Mathematica軟件來自動產生APDL腳本檔，包括前處理、求解以及後處理，因此多位置應力分析可以快速得到齒輪對在不同的旋轉角度接觸位置的腳本檔，最後應力分析結果可以改善植牙手機齒輪強度的基礎。

The implant dental handpiece is one of dental surgical instruments for performing root implant surgery to remove diseased gum tissue. There are two types of the implant dental handpieces: low speed and high speed. The former is induced high torque and that causes gear failure. In order to reduce the speed by the ratio 1/20, the implant dental handpiece needs three gear pairs, including the planetary gear train and two straight bevel gear pairs. Due to the limitation of space size, the design of straight bevel gear tooth surface is not standard. The exist gear strength standard (for example AGMA 908-B89 and ASNI/AGMA ISO 2003-B97) cannot be applied for calculation.
This research aims to establish a mathematical model of strength analysis of straight bevel gear pair. First, the 2.5D and 3D measurements are done from the commercial product and are the basis to rebuild the gear geometries of both gear pairs. Considering gear manufacture, a formate cutting method is adopted to produce the tooth surface of straight bevel gear. Its mathematical model is then established for further calculation of flank topographic points. In order to approach the conjugated tooth surfaces for better contact performance, the ease-off is adopted for determining the pinion tooth surfaces while the gear is a target. ANSYS Parametric Design Language (APDL) is here adopted for static stress analysis of implants dental handpiece gear pairs. According to the mathematical model, the APDL script file is automatically generated through software Wolfram Mathematica, in which the preprocessor, solution and postprocessor are included. Therefore, multi-position stress analyses can be quickly obtained through script files with the positions of contact gear pair in different gear rotation angles. Finally, the stress analysis result can be as a foundation to improve the gear strength of the implant dental handpiece.

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