航空弧齿锥齿轮的啮合特性分析及齿面设计研究

发布时间：2018-01-13 02:19

本文关键词：航空弧齿锥齿轮的啮合特性分析及齿面设计研究　出处：《西北工业大学》2015年博士论文　论文类型：学位论文

【摘要】：弧齿锥齿轮因具有传动平稳、承载能力强、结构紧凑等优点,被广泛应用于航空领域的传动中,作为航空发动机附件传动装置的关键部件,其啮合质量对系统的影响至关重要。齿面印痕和传动误差是评价啮合质量的关键指标,本文针对航空用弧齿锥齿轮,借助于轮齿几何接触分析(Tooth Contact Analysis,TCA)、承载接触分析(Loaded TCA,LTCA)等计算机仿真方法和试验测试手段,开展了高阶传动误差曲线的加工参数设计、啮合性能分析以及考虑齿面印痕偏移的小轮齿面再设计等一系列研究工作,形成软件系统并将其应用于航空产品的开发与试制。论文主要成果如下:(1)研究了弧齿锥齿轮小轮加工参数的逆向求解问题。已知小轮数值齿面,建立最小二乘法优化模型,采用基于置信域策略的L-M(Levenberg-Marquardt)迭代算法反求相应的小轮加工参数。该算法为高阶传动误差设计的小轮齿面主动修形技术提供了应用基础。(2)研究了弧齿锥齿轮传动误差的设计方法。一、在局部综合法的基础上,进行了二阶抛物线传动误差的优化设计;二、基于假想大轮加工小轮的概念,提出了小轮齿面的主动修形设计,预置高阶传动误差(四阶抛物线、七阶中凹型曲线)的设计参数,在与大轮完全共轭的小轮基准齿面上构建小轮修形齿面,采用上文所述的逆向求解算法反求小轮加工参数;三、在二阶抛物线传动误差的基础上,提出了高阶传动误差(七阶中凹型曲线)设计的变性系数修正法,直接控制高阶传动误差曲线上的设计啮合点,建立约束方程组,通过求解非线性方程组获得各阶变性系数,而其余加工参数仍与二阶抛物线传动误差设计相同。(3)研究了弧齿锥齿轮不同类型传动误差齿面的啮合性能。在设计重合度、传动误差曲线下端幅值大体相同的前提下,定量比较了二阶、四阶及七阶设计的齿轮副动态性能和强度性能。计算结果表明,轻载条件下四阶设计的振动较小,而工作载荷下七阶设计有更好的动态性能。相对于二阶设计,工作载荷下四阶、七阶设计均可以降低最大齿面接触应力和最大齿根弯曲应力的数值。(4)研究了基于齿面印痕偏移的弧齿锥齿轮当量安装错位反求和小轮齿面再设计。首先分析了可导致相同齿面印痕的不同安装错位组合之间的关系;然后提取齿面印痕的数字化特征,以逼近齿面接触迹线为目标,通过优化方法高精度地反求与齿面印痕匹配的当量安装错位;最后采用二阶抛物线传动误差的优化设计方法,在此错位下重新计算小轮加工参数。(5)对弧齿锥齿轮的啮合性能进行了试验验证。完成了二阶、四阶及七阶设计的齿轮副切齿、滚检、印痕发展及箱体振动加速度测试等试验内容。试验结果与理论分析基本一致,验证了齿面设计、切齿参数计算和啮合性能分析的正确性。
[Abstract]:Arc bevel gear is widely used in aeronautical transmission because of its advantages such as stable transmission, strong bearing capacity, compact structure, and so on, as the key component of the accessory transmission device of aero-engine. The tooth surface mark and transmission error are the key indexes to evaluate the meshing quality. This paper aims at the arc bevel gear used in aviation. With the aid of gear tooth geometric contact analysis, Tooth Contact Analysis (TCA) is used to carry the loaded TCA. The design of machining parameters of high-order transmission error curve has been carried out by means of computer simulation and test methods such as LTCA. Meshing performance analysis and a series of research work such as gear tooth surface redesign considering tooth surface imprint offset. The software system is formed and applied to the development and trial manufacture of aeronautical products. The main achievements in this paper are as follows: 1) the inverse solution of machining parameters of spiral bevel gear is studied. The numerical tooth surface of the small wheel is known. The optimization model of the least square method is established. L-MN Levenberg-Marquardt based on confidence region Strategy. The iterative algorithm is used to calculate the parameters of gear machining. The algorithm provides a basis for the active profile modification of gear surface in the design of high-order transmission error. The design method of the transmission error of spiral bevel gear is studied. Based on the local synthesis method, the optimal design of the second-order parabola transmission error is carried out. Secondly, based on the concept of hypothetical big wheel machining small wheel, this paper presents the design parameters of gear tooth surface active modification and preset high order transmission error (fourth order parabola, seventh order middle concave curve). The modified tooth surface of the small wheel is constructed on the base tooth surface of the small wheel which is completely conjugated with the big wheel, and the reverse solution algorithm mentioned above is used to reverse calculate the machining parameters of the small wheel. Thirdly, on the basis of the second order parabola transmission error, the variable coefficient correction method for the design of high order transmission error (seventh order middle concave curve) is proposed, which directly controls the design meshing point on the high order transmission error curve. The constraint equations are established and the variable coefficients of each order are obtained by solving the nonlinear equations. The other machining parameters are still the same as the second order parabola transmission error design. The meshing performance of the tooth surface of different types of transmission errors of arc bevel gear is studied. The dynamic and strength properties of the gear pairs designed in the second order, fourth order and seventh order are compared quantitatively on the premise that the amplitude of the bottom end of the transmission error curve is approximately the same. The calculated results show that the vibration of the fourth order design is smaller under the condition of light load. The seventh order design has better dynamic performance than the second order design, and the fourth order under the working load is better than the second order design. The seventh order design can reduce the maximum tooth surface contact stress and the maximum tooth root bending stress. Based on the offset of tooth surface impression, the reverse misalignment of spiral bevel gear and the re-design of gear surface are studied. Firstly, the relationship between different misalignment combinations that can lead to the same impression of tooth surface is analyzed. Then the digital feature of the tooth surface mark is extracted and the equivalent misalignment matching with the tooth surface mark is obtained by the optimization method aiming at approaching the contact line of the tooth surface. Finally, the meshing performance of spiral bevel gear is tested and verified by using the optimal design method of second-order parabola transmission error, and the machining parameters of small wheel are recalculated under this misalignment. The fourth and seventh order gear pair cutting, roll checking, mark development and vibration acceleration test of the box are tested. The experimental results are basically consistent with the theoretical analysis, and verify the tooth surface design. The correctness of tooth cutting parameter calculation and meshing performance analysis.
【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：V229

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