齒輪系統是常見的機械零組件之一（如機械沖床中），齒的耐磨性和抗疲勞性是影響齒輪壽命的關鍵因素，其可利用熱處理製程加以改善。為了提高齒輪的耐磨性，硬化能是主要的追求目標。如鋼鐵硬化處理中的淬火製程就扮演著重要的角色。然而，傳統以物理測試獲取的熱處理最佳化技術常須耗費龐大的勞力及物力(成本)。故數值模擬技術就是種有效降低成本的替代方式，該技術結合物理模型與數值計算方法，可應用於多數的熱處理製程。
本文建立正齒輪熱處理製程的數值模擬，研究齒輪的溫度變化、相變化和殘餘應力分佈。同時進行了相關的實驗驗證(數值)模擬的正確性。結果證實(數值)模擬具有相當的準確性。淬火時，冷卻時間對於麻田散鐵組織的分佈和硬化深度有很大的影響，而高熱傳係數的製程介質，不會影響(工件)最大硬度值，但會縮短達到最高硬度值的製程時間。齒根中較大的壓縮殘餘應力僅只出現在齒輪齒面的周圍，而朝齒根方向時則會逐漸減小。

Gear system is one of most common mechanical parts for machinery, such as mechanical press machine. Wear resistance and fatigue resistance of the teeth are the most critical factors influencing gear life and can be improved using heat treatment process. To improve wear resistance, the achievement of desired hardenability is the main goal. Therefore, the steel hardening technique such as induction hardening (commonly used in gear) and quenching process takes an important role for this treatment. However, traditional physical testing for optimizing heat treatment techniques must be obtained at the expense of large amounts of labor and materials. Numerical simulation, an economic alternative technique which is based on some physical models and by combining with some numerical calculation methods can become breakthrough solution for those numerous heat treatment tests.
A numerical method is built to simulate the induction hardening-heat treatment process of the spur gear. The evolution of temperature, phase transformation, and residual stress distribution of gear tooth have been studied according to the simulation results. The hardness experimental validation is also conducted to analyze the accuracy of the numerical method. As the results, the numerical method is not too accurate in predicting the real hardness distribution due to some issues such as measurement error, parameter data mismatch between simulation and real case, and skin depth phenomenon in induction hardening which is difficult to be implemented in numerical method. Cooling time during quenching takes a big role on the distribution of martensite evolution and the hardening depth, the higher heat transfer coefficient of quenchant does not increase the maximum hardness value, but shorten the quenching time to reach it, quenching process leaves massive compressive residual stresses in the root of gear teeth and tensile residual stresses in the tip of gear teeth, design of gear influence the distortion in the gear geometry.

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