齿轮应力与变形精确分析中的有限元建模研究
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摘要
齿轮强度分析是轮齿承载能力、振动、噪声及修形等研究的基础。因此，建立比较精确的分析模型，准确求解受载轮齿的应力与变形具有重要意义。
本文首先比较研究了齿根应力与轮齿弹性变形的主要计算方法，指出了有限元法的广泛应用前景。进而对齿轮强度分析的有限元精确建模的一些主要技术环节进行了探讨：根据展成加工原理推导出比较精确的齿形曲线；采用基于纯文本数据文件的APDL与MATLAB的混合建模方法，创建具有复杂边界的轮齿几何模型；齿轮整体模型研究表明：“扩大”原始边界法在理论提法上存在一定的局限性；基于应力与形变等效原理，分析得到新的“有效边界”范围；推导出考虑齿轮等效误差与轮齿综合柔度时危险加载点判别式；考虑齿轮综合刚度，计算出接触轮齿在啮合周期内的载荷分配率；研究得出了齿轮强度有限元分析的两类平面问题判别的“齿宽条件”。
结合上述研究，对齿根应力与齿面变形的分布规律进行比较研究，结果表明了模型的可靠性。研究表明刀具齿项圆角对齿轮强度的影响比较显著，进而对Filiz经验式予以修正。考虑重合度和双齿啮合区相邻轮齿接触带来的应力叠加效应，对中间齿齿根应力与齿面弹性变形的载荷历程进行了比较研究。
基于轮齿变形的载荷历程数值解，推导出考虑齿轮等效误差与轮齿综合变形时线外啮入冲击点判别式，准确地计算出线外啮合阶段任意点的冲击力。建立粘弹斜冲击模型，推导出冲击摩擦系数的计算式；基于对其他学者的研究成果的整理，建议将包括线外啮合的啮合周期内摩擦类型分为三个阶段，并推荐了每个阶段摩擦系数比较适用的计算式。
On the basis of analysis of gear teeth strength, gear power capacity rating and profile correction, as well as vibration and noise of gearing, are studied. In view of accurate model, it is significant to investigate the deflection and stresses of engaging teeth precisely.
On root stresses and teeth compliance, the advances in different calculi commented comparatively, then applied prospect of Finite Element Method (FEM) in the field is emphasized. Some principal techniques of accurately modeling in FEM for gear failures are developed systematically. Chief studies are conducted as follows. According to fundamentals of engagement of tooth profiles, exact equations of meshing teeth profiles are derived. Geometrical model of gear teeth with complex boundary is posed, by which compound modeling with APDL and MATLAB , based on full-text data file. The studies in view of the whole gear show the theoretical limitations of "expanding" initial boundary. The new "effective boundary", determined by equivalent stresses and deflection , is proposed. Criterion of loading position, including effective machining error and integrated compliance of gear teeth, is presented. Taking into account comprehensive stiffness, load sharing ratio of the central tooth in a meshing cycle , is calculated. J
udgment of plane elasticity issues how to choose, in FEM analysis of spur gear strength, is put forward.
According to the above studies, the distributing rules of root stresses and teeth compliance are investigated comparatively, and the results testifying the reliability of the model. Notable influence of hob tip radii to root stresses and teeth compliance proved, empirical formula proposed by Filiz should be corrected. Then including the affection of "superimposed stress when two teeth gearing", load-history of root stresses and teeth compliance of central tooth is researched relatively.
Based on the numerical solution of teeth compliance by load -history analysis, and considering the error and distortion of gear teeth, the standard of the point situated at corner contact is probed and the impact forces, from the point situated at corner contact to theoretical line
HI
of action, are calculated accurately. After viscoelastic oblique impact model founded, the formula of lash friction coefficient is deduced. The studies of other researches interpreted and inducted, three friction models in factual mesh period, including corner contact, are proposed, then the calculi of friction coefficient corresponding each model.
本文首先比较研究了齿根应力与轮齿弹性变形的主要计算方法，指出了有限元法的广泛应用前景。进而对齿轮强度分析的有限元精确建模的一些主要技术环节进行了探讨：根据展成加工原理推导出比较精确的齿形曲线；采用基于纯文本数据文件的APDL与MATLAB的混合建模方法，创建具有复杂边界的轮齿几何模型；齿轮整体模型研究表明：“扩大”原始边界法在理论提法上存在一定的局限性；基于应力与形变等效原理，分析得到新的“有效边界”范围；推导出考虑齿轮等效误差与轮齿综合柔度时危险加载点判别式；考虑齿轮综合刚度，计算出接触轮齿在啮合周期内的载荷分配率；研究得出了齿轮强度有限元分析的两类平面问题判别的“齿宽条件”。
结合上述研究，对齿根应力与齿面变形的分布规律进行比较研究，结果表明了模型的可靠性。研究表明刀具齿项圆角对齿轮强度的影响比较显著，进而对Filiz经验式予以修正。考虑重合度和双齿啮合区相邻轮齿接触带来的应力叠加效应，对中间齿齿根应力与齿面弹性变形的载荷历程进行了比较研究。
基于轮齿变形的载荷历程数值解，推导出考虑齿轮等效误差与轮齿综合变形时线外啮入冲击点判别式，准确地计算出线外啮合阶段任意点的冲击力。建立粘弹斜冲击模型，推导出冲击摩擦系数的计算式；基于对其他学者的研究成果的整理，建议将包括线外啮合的啮合周期内摩擦类型分为三个阶段，并推荐了每个阶段摩擦系数比较适用的计算式。
On the basis of analysis of gear teeth strength, gear power capacity rating and profile correction, as well as vibration and noise of gearing, are studied. In view of accurate model, it is significant to investigate the deflection and stresses of engaging teeth precisely.
On root stresses and teeth compliance, the advances in different calculi commented comparatively, then applied prospect of Finite Element Method (FEM) in the field is emphasized. Some principal techniques of accurately modeling in FEM for gear failures are developed systematically. Chief studies are conducted as follows. According to fundamentals of engagement of tooth profiles, exact equations of meshing teeth profiles are derived. Geometrical model of gear teeth with complex boundary is posed, by which compound modeling with APDL and MATLAB , based on full-text data file. The studies in view of the whole gear show the theoretical limitations of "expanding" initial boundary. The new "effective boundary", determined by equivalent stresses and deflection , is proposed. Criterion of loading position, including effective machining error and integrated compliance of gear teeth, is presented. Taking into account comprehensive stiffness, load sharing ratio of the central tooth in a meshing cycle , is calculated. J
udgment of plane elasticity issues how to choose, in FEM analysis of spur gear strength, is put forward.
According to the above studies, the distributing rules of root stresses and teeth compliance are investigated comparatively, and the results testifying the reliability of the model. Notable influence of hob tip radii to root stresses and teeth compliance proved, empirical formula proposed by Filiz should be corrected. Then including the affection of "superimposed stress when two teeth gearing", load-history of root stresses and teeth compliance of central tooth is researched relatively.
Based on the numerical solution of teeth compliance by load -history analysis, and considering the error and distortion of gear teeth, the standard of the point situated at corner contact is probed and the impact forces, from the point situated at corner contact to theoretical line
HI
of action, are calculated accurately. After viscoelastic oblique impact model founded, the formula of lash friction coefficient is deduced. The studies of other researches interpreted and inducted, three friction models in factual mesh period, including corner contact, are proposed, then the calculi of friction coefficient corresponding each model.
引文
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