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研究生:翁武燕
研究生(外文):Wu-Yan Wong
論文名稱:含裂紋損傷的直齒圓柱齒輪振動特性研究
指導教授:張俊 教授吳育仁 副教授
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2019
畢業學年度:107
語文別:中文
論文頁數:91
中文關鍵詞:直齒圓柱齒輪非線性動力學裂紋損傷故障診斷嚙合剛度
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直齒圓柱齒輪作為應用最為廣泛的一類齒輪傳動,在使役過程中容易產生裂紋損傷。
已有研究表明,裂紋損傷對直齒輪傳動的振動特性具有顯著影響。為保障齒輪傳動系統的運行安全,有必要分析裂紋損傷與傳動系統動力學行為之間的關聯,明晰損傷程度和傳動系統動態特性之間的定量關係。有鑑於此,本文以直齒圓柱齒輪為研究物件,開展含裂紋損傷的傳動系統振動特性研究,總結全文,主要研究內容如下:首先,計入時變嚙合剛度、齒側間隙、轉子彎扭效應和箱體支承柔性,並綜合考慮齒輪、轉子、軸承和箱體之間的耦合關係,建立了 12 自由度的 直齒圓柱齒輪傳動系統剛柔耦合非線性動力學模型。採用 Runge Kutta 法求解了該類傳動系統的動力學方程,獲得了系統的穩態回應。分析表明, 齒輪對 沿嚙合線方向的相對動態位移在一階 嚙 頻處的振幅最大,而齒輪和軸承的振動位移則在三階 嚙 頻處振幅最大。相關結果為齒輪傳動
系統的振動抑制提供了力學依據。其次,基於勢能法,推導了含齒根裂紋與分度圓處裂紋損傷的直齒輪對 時變嚙合剛度,並提出了裂紋深度百分比這一表徵裂紋損傷程度的指標。在此基礎上,進一步比較了齒根裂紋和分度圓處裂紋損傷對齒輪時變嚙合剛度的影響,並分析二者的不同。通過將含齒輪裂紋損傷的嚙合剛度模型與所建立的齒輪非線性動力學模型相結合,建立了含裂紋損傷的直齒輪傳動系統 非線性動力學模型,並據此研究了裂紋損傷對傳動系統動態特性的影響 。此外,進一步分析了裂紋損傷的故障機理,引入了峭度、裕度因數、峰值
因數和脈衝因數等無 因次 指 標,作為故障程度的判別依據,為齒輪系統的故障預警提供了參考依據 。
本文的研究可為齒輪傳動系統的線上監測和故障診斷提供理論基礎,具有一定的工程運用價值。
As the most widely used type of gear transmission system, cylindrical spur gears areprone to generate crack failure during service. Previous studies have shown that crack failurehas a significant impact on the vibration characteristics of spur gears. It is necessary to
analyze the relationship between crack failure and dynamic behavior of transmission system,and to clarify the quantitative relationship between degree of failure and dynamic characteristics of transmission system in order to ensure the operation safety of the gear
transmission system. In view of this, this paper takes cylindrical spur gear as the research object to study the vibration characteristics of transmission syst em with crack failure.
Firstly, taking the time varying meshing stiffness, backlash, bending and torsion effect of the rotor and the flexibility of the box support into account, and comprehensively considering the coupling relationship among the gears, the rotor, the bearing and the box, a rigid flexible coupling non linear dynamic model of a 12 degree of freedom cylindrical spur gear transmission system is established. The dynamic equation of this kind of transmission system is solved by Runge Kutta method to obtain the steady state response of the system. The
analysis shows that the relative dynamic displacement of gear pair along the meshing line has the largest amplitude at the first order meshing frequency, while the vibration displacement of gear and b earing has the largest amplitude at the third order meshing frequency. The relevant results provide a mechanical basis for vibration suppression of gear transmission system.
Secondly, based on the potential energy method, the time
varying meshing stiffness of spur gear pairs with root crack and reference circle crack failure is deduced, and the percentage of crack depth is proposed as an index to characterize the degree of crack failure.
On the basis of this,the effects of root crack and reference circle cr ack failure on the time varying meshing stiffness of gears are further compared, and the differences between them are analyzed. The non linear dynamic model of spur gear transmission system with
crack failure is established by combining the meshing stiffne ss model with gear crack failure
with the established non linear dynamic model of gears, and the influence of crack failure on
the dynamic characteristics of transmission system is investigated. In addition, the failure
mechanism of crack failure is furthe r analyzed. Dimensionless indexes such as kurtosis,
margin factor, peak factor and pulse factor are introduced as criteria for judging the degree of
failure, which provides a reference for early warning of failure of gear system.
This research can provide theoretical basis for on line monitoring and failure diagnosis of gear transmission system, and has certain engineering application value.
III
Keywords: spur gear
Keywords: spur gear,, nonlinear dynamicsnonlinear dynamics,, crack failurecrack failure,, fault diagnosisfault diagnosis,, meshing stiffnessmeshing stiffness
摘要
I
Abstract
II
致謝
IV
目錄
V
圖目錄
VII
表目錄
X

1 章 緒論 1
1.1
前言 1
1.2
文獻回顧 2
1.2.1
齒輪系統非線性動力學研究 2
1.2.2
齒輪裂紋故障機理研究 6
1.3
論文框架 9

2 章 齒輪 轉子 軸承 箱體系統動力學建模與分析 11
2.1
引言 11
2.2
齒輪 轉子 軸承 箱體系統動力學模型 11
2.3
齒輪傳動系統動態激勵研究 15
2.3.1
嚙合剛度激勵 15
2.3.2
轉子剛度計算 23
2.3.3
滾動軸承支承剛度計算 24
2.3.4
箱體支承剛度計算 24
2.4
齒輪動力學求解 28
2.5
齒輪振動特性分析 29
2.5
小結 31

3 章含齒根裂紋故障的齒輪傳動系統機理研究 33
3.1
引言 33
3.2
含齒根裂紋故障的輪齒嚙合剛度計算 33
3.2.1
齒根裂紋沿深度變化對輪齒嚙合剛度的影響 33
3.2.2
齒根裂紋沿齒寬方向對輪齒嚙合剛度的影響 40
3.
3 含裂紋故障的齒輪系統動力學響應 42
3.
3 .1 齒根裂紋沿裂紋深度對齒輪 系統動力學回應的影響 43
3.
3 .2 齒根裂紋沿齒寬方向對齒輪系統動力學回應的影響 48
3.
4 小結 52

4 章 含分度圓處裂紋故障的齒輪傳動系統機理研究 54
4
.1 引言 54
4
2 含分度圓處裂紋故障的輪齒嚙合剛度計算 54
4
2 .1 分度圓處裂紋沿裂紋深度對輪齒嚙合剛度的影響 54
4
2 .2 分度圓處裂紋沿齒寬方向對輪齒嚙合剛度的影響 58
4
3 含裂紋故障的齒輪系統動力學響應 61
4
3 1 分度圓處裂紋沿裂紋深度對齒輪系統動力學回應的影響 61
4
3 2 分度 圓處裂紋沿齒寬方向對齒輪系統動力學回應的影響 66
4
4 小結 70

5 章 結論 72
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