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圆柱斜齿轮传动误差的补偿分析

发布时间:2018-10-31 14:30
【摘要】:渐开线圆柱斜齿轮具有传动平稳、啮合冲击和振动噪声小等特点,在高速重载和高性能需求的传动工业领域得到了广泛使用。但目前我国在高精度齿轮设计制造与国际先进水平存在差距,本文基于国家科技支撑计划课题,借鉴弧齿锥齿轮的主动设计研究理论,针对基于传动误差的高精密渐开线斜齿圆柱齿轮开展主动设计研究。本文基于共轭渐开线斜齿圆柱齿轮齿面啮合理论,分别建立了考虑滚刀安装误差以及轴线不平度引起的齿轮安装误差的齿面接触模型。基于TCA(Tooth Contact Analysis)技术,利用MATLAB软件实现了斜齿轮副的传动模拟分析,分析得到影响齿轮加工精度的滚刀安装误差和安装误差对斜齿轮的传动误差曲线和接触迹线的影响规律。基于误差补偿技术,依据加工误差补偿装配误差的理论,实现平行轴圆柱斜齿轮啮合质量的主动设计。论文内容主要有:1)基于滚刀加工原理的理论基础和螺旋齿面形成的方法论,推导了适合的啮合齿面方程和单位法矢量。运用微分几何和空间啮合原理中的矢量回转与坐标变换方法,建立了考虑滚刀安装误差的斜齿轮共轭齿面接触模型。基于齿轮副共轭运动理论,推导了两齿面在接触点处的TCA方程组和啮合表达式。基于MATLAB软件编制仿真分析程序,仿真结果表明:传动误差曲线对滚刀安装轴线交角偏差的敏感度较小,但随着该误差的增大,其敏感度升高;传动误差曲线对滚刀径向跳动量的敏感度较大,但随着该误差的增大,其敏感度在降低。2)根据平行轴渐开线斜齿轮副的齿廓啮合基本定理和渐开线的性质,推导结果表明,中心距误差对齿轮副的传动误差影响较小。将齿轮副装配过程中可能导致的各项安装偏差考虑在内,建立相关的接触数学模型,基于TCA技术,进行误差模拟分析。结果表明:轴线平面内和垂直平面内的平行度误差都会改变齿轮接触迹线位置,但随着轴线平面平行度误差的增加,接触迹线偏离无安装误差理论位置增加的幅度减小,其敏感性降低;随着垂直平面内的平行度误差的增加,接触迹线偏离无安装误差理论位置增加的幅度增大,其敏感性升高。3)基于误差补偿技术,通过改变滚刀安装误差值,实现被加工齿轮的齿面形状的改变,分析不同的加工误差来源对齿轮副安装误差所引起的接触迹线的补偿作用。通过接触迹线观察分析得出结论:通过改变滚刀安装轴线误差角,能实现齿面接触特性的可控制性。
[Abstract]:Involute cylindrical helical gears are widely used in the field of high speed heavy load and high performance drive industry because of their stable transmission, low meshing impact and low vibration noise. However, there is a gap between the design and manufacture of high-precision gears in China and the advanced level in the world. Based on the national science and technology support project, this paper draws lessons from the theory of active design of spiral bevel gears. The active design of high precision involute helical cylindrical gear based on transmission error is studied. In this paper, based on the meshing theory of conjugate involute helical cylindrical gears, a tooth surface contact model considering hob installation error and gear installation error caused by axis irregularity is established respectively. Based on TCA (Tooth Contact Analysis) technology, the transmission simulation analysis of helical gear pair is realized by using MATLAB software. The influence of hob installation error and installation error on helical gear transmission error curve and contact trace is analyzed. Based on error compensation technology and the theory of machining error compensating assembly error, the active design of meshing quality of parallel axis cylindrical helical gear is realized. The main contents of this paper are as follows: 1) based on the theoretical basis of hob machining principle and the methodology of helical tooth surface formation, the suitable meshing tooth surface equation and unit normal vector are derived. By using vector rotation and coordinate transformation in differential geometry and spatial meshing principle, a conjugate tooth contact model of helical gear considering hob installation error is established. Based on the theory of conjugate motion of gear pair, the TCA equations and meshing expressions of two tooth surfaces at contact point are derived. Based on the MATLAB software, the simulation results show that the sensitivity of the transmission error curve to the angle deviation of the hob mounting axis is small, but the sensitivity increases with the increase of the error. The sensitivity of transmission error curve to the radial runout of hob is great, but with the increase of the error, the sensitivity decreases. 2) according to the basic theorem of tooth profile meshing and the properties of involute helical gear pair of parallel axis, the derivation results show that, The center distance error has little effect on the transmission error of gear pair. Taking into account the possible installation deviations in the assembly process of gear pairs, the related contact mathematical model is established, and the error simulation analysis is carried out based on TCA technology. The results show that the parallelism error in the axis plane and the vertical plane will change the position of the gear contact trace, but with the increase of the parallelism error of the axis plane, the amplitude of the contact trace deviation from the theoretical position without installation error will decrease. Its sensitivity was decreased; With the increase of the parallelism error in the vertical plane, the range of contact trace deviation from the theoretical position without mounting error increases and its sensitivity increases. 3) based on error compensation technology, by changing the hob installation error value, The change of the tooth surface shape of the machined gear is realized, and the compensation effect of different machining error sources on the contact trace caused by the gear pair installation error is analyzed. Through the observation and analysis of contact trace, it is concluded that by changing the error angle of hob mounting axis, the controllability of tooth surface contact characteristics can be realized.
【学位授予单位】:太原理工大学
【学位级别】:硕士
【学位授予年份】:2016
【分类号】:TH132.41

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