以CNC內珩齒機進行螺旋齒輪齒面拓樸修整之研究

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姓名

蔡有淳(Yu-Chun Tsai) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

以CNC內珩齒機進行螺旋齒輪齒面拓樸修整之研究
(A Study on Topological tooth Modification of Helical Gears Using a CNC Internal Honing Machine)

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摘要(中)

珩齒(Gear honing)製程可進行螺旋齒輪之輪齒修整(Tooth modification)以降低振動噪音及改善接觸齒印(Contact pattern)，係於大批量生產齒輪時最具有經濟效益的精加工方法之一；而往往滾齒後齒面會有扭曲(Twist)現象，使得齒輪組在裝配誤差下會造成齒面邊緣接觸而產生應力集中及損壞。故本文建立了以CNC內珩齒機進行螺旋齒輪齒面拓樸修整之數學模型，於其中加入機台設計參數，利用敏感度矩陣法，在設定目標齒面法向偏差量後，計算出機台設計參數，並將設計參數代回齒面拓樸修整之數學模型，取得修整後齒面之法向偏差量。最後，將修整後齒面之法向偏差量匯入KISSsoft分析軟體，比較不同齒面修整下之齒面拓樸(Tooth flank topology)、齒面接觸及傳動誤差分析結果，以證實本文所提方法之可行性及優點。

摘要(英)

The internal gear honing process is one of the most economic ways to eliminate errors to localize and stabilize the bearing contact and reduce noise and vibration of the gear systems. In addition, the tooth surfaces of the gears are usually crowned with anti-twist tooth flanks. Gear with the anti-twist tooth flanks can make tooth contact concentrate by the center of tooth flank and avoid the tooth edge contact. Therefore, a mathematical model for the topological modification on gear tooth flanks by a CNC internal honing machine is proposed in this thesis. In the mathematical model, the additional parameters are added as the coefficients of machine settings and the singular value decomposition (SVD) is applied to solve these coefficient for the desired topological modification on tooth flanks. Moreover, the normal deviation at each point on the gear tooth is imported into KISSsoft to conduct the tooth contact analysis (TCA) and transmission error (TE) evaluation in the numerical examples. The results show the validity and practicability of the proposed model.

關鍵字(中)

★ CNC內珩齒機
★ 內珩齒
★ 齒面拓樸修整
★ 齒面接觸分析

關鍵字(英)

★ Internal gear honing
★ topological modification
★ TCA
★ TE

論文目次

摘要 I
Abstract II
謝誌 III
目錄 IV
圖目錄 VII
表目錄 X
符號對照表 XII
第1章緒論 1
1-1 研究背景 1
1-2 文獻回顧 3
1-3 研究動機及目的 4
1-4 論文架構 5
第2章內珩輪齒面數學模型之建立 6
2-1 齒條刀數學模型之建立 6
2-2 利用齒條刀創成標準螺旋齒輪之數學模型建立 7
2-3 利用螺旋齒輪創成內珩輪之數學模型建立 9
2-4 本章結論 11
第3章 CNC內珩齒機加工齒面之數學模型建立 12
3-1 內珩輪創成螺旋齒輪之泛用座標系統建立 12
3-2 利用CNC內珩齒工具機進行齒面修整之數學模型建立 18
3-2-1 CNC內珩齒工具機(Fässler HMX-400)介紹 18
3-2-2 CNC內珩齒工具機之座標系統建立 20
3-2-3 泛用座標系統與機台座標系統之比較 22
3-2-4 CNC內珩齒工具機進行齒面修整之數學模型建立 23
3-3 本章結論 28
第4章利用敏感度矩陣法進行齒面拓樸修整 29
4-1 敏感度矩陣法 29
4-2 敏感度矩陣建立 31
4-2-1 機台設計參數 31
4-2-2 敏感度矩陣 40
4-3 數值範例介紹 41
4-3-1 Case1：直線-圓弧線型 43
4-3-2 Case2：直線-二次曲線線型 44
4-3-3 Case3：對數函數線型 45
4-4 齒面拓樸修整 46
4-4-1 Case1：直線-圓弧線型之齒面修整結果 48
4-4-2 Case2：直線-二次曲線線型之齒面修整結果 50
4-4-3 Case3：對數函數線型之齒面修整結果 52
4-5 本章結論 54
第5章齒面接觸分析 55
5-1 KISSsoft分析軟體介紹 55
5-2 Case1：直線-圓弧線型 57
5-3 Case2：直線-二次曲線線型 58
5-4 Case3：對數函數線型 60
5-5 Case4：標準螺旋齒輪 61
5-6 在不同裝配誤差下各範例之比較 63
5-6-1 最大齒面接觸力 63
5-6-2 最大傳動誤差 64
5-6-3 最小傳動誤差 65
5-7 本章結論 65
第6章總結與未來展望 68
6-1 總結 68
6-2 未來展望 70
參考文獻 71
作者介紹 74

參考文獻

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指導教授

吳育仁(Yu-Ren Wu)

審核日期

2017-8-21

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