具裂紋齒輪系統嚙合分析與動態模擬

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姓名

廖宜駿(I-chun Liao) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

具裂紋齒輪系統嚙合分析與動態模擬
(Meshing Analysis and Dynamic Simulation of a Cracked Spur Gear Pair)

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摘要(中)

本文主要探討目標為齒輪組之動態響應分析與齒輪故障時對系統動態特性的影響。研究方法為利用有限元素軟體ANSYS建立無裂紋齒輪組與有裂紋齒輪組的幾何模型，首先分析出齒輪接觸點的接觸力與變形量後計算出齒輪的嚙合剛度，接著討論當裂紋位置改變或齒輪被施予的負載改變時對於齒輪嚙合剛度的影響，並為了縮短分析齒輪嚙合剛度的時間，可將齒輪的嚙合剛度簡化成二個部分分別求取後再串聯，最後再以集中質量法，將以等效質量、等效彈簧、等效阻尼建立起齒輪動態系統模型，將齒輪的嚙合剛度代入齒輪的運動方程式，並以數值方法求解齒輪的動態響應，分析無裂紋齒輪組與有裂紋齒輪組在各種不同轉速下以頻譜分析找出有裂紋齒輪的故障特徵。

摘要(英)

The target of this research is to study the effects of a tooth crack to the dynamic characteristics of a spur gear pair. A finite element software, ANSYS, is used for the simulation. The meshing stiffness of the gear pair is calculated by analyzing the contact force and deformation. The stiffness is dependent of the crack position and the contact condition. For reducing the calculation time, each gear can also be divided into two smaller parts which is analogical to springs. Then, the gear dynamic model is developed by the lumped-parameter method for the vibration response, and the equations of motion are derived. The dynamic responses of the gear pair are solved by using the numerical method. The features of dynamic signals are found for spur gear pair with the tooth crack and compared with those for gears with no crack.

關鍵字(中)

★ 齒輪
★ 嚙合剛度
★ 裂紋
★ 齒輪系統

關鍵字(英)

論文目次

目錄 ……....…………………………………………………………….I
圖索引…………………………………………………………………...V
表索引…………………………………………………………………XV
第一章緒論……………………………………………………………..1
1-1 前言………………………………………………………………...1
1-2 文獻回顧…………………………………………………………...2
1-3 內容提要…………………………………………………………...5
第二章基本理論……………………………………………………......7
2-1 齒輪振動的原因…………………………………………………...7
2-1-1齒輪嚙合剛度…………………………………………………...7
2-1-2傳遞誤差………………………………………………………...8
2-2 統御方程式……………………………………………………….10
2-2-1平衡方程式…………………………………………………….11
2-2-2應變與位移之關係…………………………………………….11
2-2-3應力與應變之關係…………………………………………….12
2-3 有限元素法原理………………………………………………….13
2-3-1彈性常數矩陣與形狀函數…………………………………….13
2-3-2ANSYS分析原理………………………………………………14
2-4 龍格–庫塔法原理………………………………………………...14
2-5訊號加窗……………………………………………………………16
第三章 ANSYS分析與嚙合剛度計算原理…………………………...18
3-1 齒輪嚙合剛度計算………………………………………………...18
3-2 ANSYS分析流程………………………………………………...21
3-2-1材料性質設定………………………………………………….22
3-2-2建立齒輪模型………………………………………………….22
3-2-3網格劃分設定………………………………………………….24
3-2-4齒輪邊界條件設定…………………………………………….26
3-2-5齒輪接觸設定………………………………………………….28
3-2-6齒輪變形量之計算…………………………………………….29
第四章齒輪嚙合剛度比較……………………………………………31
4-1 無裂紋齒輪組及齒根有裂紋齒輪組嚙合剛度比較……………...31
4-1-1探討齒根裂紋齒輪組變形量………………………………….31
4-1-2齒根裂紋齒輪組接觸力……………………………………….33
4-1-3齒根齒輪組嚙合剛度………………………………………….33
4-1-4應力分布……………………………………………………….35
4-2 無裂紋齒輪組及齒間有裂紋齒組嚙合剛度比較………………...36
4-2-1探討齒間裂紋齒輪組變形量………………………………….37
4-2-2齒間裂紋齒輪組接觸力……………………………………….39
4-2-3齒間裂紋齒輪組嚙合剛度…………………………………….39
4-3逆時針力矩…………………………………………………………41
4-3-1逆時針力矩齒根裂紋齒輪組變形量………………………….41
4-3-2逆時針力矩齒根裂紋齒輪組接觸力………………………….42
4-3-3逆時針力矩齒根裂紋齒輪組嚙合剛度……………………….43
第五章齒輪嚙合剛度簡化分析……………………….……………...44
5-1簡化分析基本設定…………………………………………………44
5-1-1第一種簡化分析模型設定…………………………………….44
5-1-2第二種簡化分析模型設定…………………………………….45
5-2簡化分析嚙合剛度計算……………………………………………46
5-3齒輪接觸力設定……………………………………………………50
5-4齒輪組接觸力的簡化分析結果……………………………………51
5-4-1變形量………………………………………………………….52
5-4-2扭轉嚙合剛度………………………………………………….53
5-4-3結論…………………………………………………………….53
5-5內插接觸力下的簡化分析結果……………………………………54
第六章齒輪系統動態模擬……………………………………………56
6-1齒輪系統的數學模型………………………………………………56
6-1-1嚙合剛度內插曲線…………………………………………….58
6-2齒輪的振動特性分析………………………………………………58
6-2-1無裂紋齒輪組振動特性分析………………………………….59
6-2-2齒根裂紋齒輪組振動特性分析……………………………….60
6-3 簡化分析下的齒輪振動特性……………………………………...62
第七章結論與未來展望………………………………………………65
7-1結論…………………………………………………………………65
7-2未來展望……………………………………………………………67
參考文獻………………………………………………………………..68

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指導教授

黃以玫(Yi-mei Huang)

審核日期

2014-8-22

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