非圆齿轮马达的动态分析
发布时间：2019-04-13 17:09
【摘要】：非圆齿轮具有传动平稳、结构紧凑、易实现动平衡以及能实现周期性的变速运动的特点,将非圆齿轮应用于液压马达,可以使马达兼备体积小、排量大、耐油污等特点。但是由于非圆齿轮的压力角、啮合力方向、中心矩等时刻变化,其动力学研究具有一定的难度,以往的研究只局限于两个外啮合的非圆齿轮,本文基于增大马达排量、平衡系统的径向力提出了高阶椭圆齿轮马达,并对椭圆行星齿轮系统的振动特性进行了研究。首先,对椭圆行星齿轮系统的结构、齿轮的啮合原理以及轮系的运动关系进行了研究,运用数值分析方法得出了太阳轮及内齿圈的节曲线方程。推导了利用三次样条插值已知轮系中一个椭圆齿轮的节曲线,绘制出其他齿轮的节曲线以及齿廓的方法,开发了参数化设计椭圆行星齿轮结构的交互界面,实现了通过输入相关参数就能得到不同椭圆轮系节曲线的功能。其次,从椭圆齿轮系统的动态性能及使用寿命理论出发,建立了系统的扭转振动力学模型。对模型中的激振因素如:齿轮本身的形状结构,太阳轮轴上的输出转速、时变啮和刚度、综合误差及齿轮副间隙等进行了研究。再次,用啮合线上的位移作为自变量推导了椭圆齿轮特殊的振动微分方程,用高精度的Runge-kutta方法对该方程进行了求解。以6-8阶椭圆行星齿轮系统作为算例,采用逐段线性近似的方法分析其时域响应、相图、频谱图等,研究了系统的动态响应,分析了阻尼和转速对动态响应的影响。最后,针对非圆齿轮的特性,完成了通过利用线切割仿真软件对非圆齿轮进行加工仿真、代码生成及传输,最终进行了加工实施。本文利用插值法和节曲线参数化的GUI界面简化了椭圆齿轮的设计流程,所建立的动力学模型和微分方程适用于所有变中心矩的行星齿轮系统,利用线切割仿真软件简化了非圆齿轮的加工过程。本文的动力学分析结果对非圆齿轮的振动、非圆齿轮马达的噪声检测及减振措施提供了理论依据。
[Abstract]:Non-circular gear has the characteristics of stable transmission, compact structure, easy to realize dynamic balance and periodic variable-speed motion. The application of non-circular gear to hydraulic motor can make the motor have the characteristics of small volume, large displacement, oil resistance and so on. However, it is difficult to study the dynamics of non-circular gear due to the pressure angle, the direction of engagement force and the center moment. The previous research is limited to two non-circular gears with external meshing. This paper is based on increasing the displacement of motor. The radial force of the balancing system is presented, and the vibration characteristics of the elliptical planetary gear system are studied. Firstly, the structure of the elliptical planetary gear system, the meshing principle of the gear and the motion relation of the gear train are studied. The nodal curve equations of the solar wheel and the inner gear ring are obtained by using the numerical analysis method. This paper deduces the method of using cubic spline interpolation to know the nodal curve of one elliptical gear in gear train, draws the pitch curve and tooth profile of other gears, and develops the interactive interface of parametric design of elliptical planetary gear structure. The function of different elliptic gear system nodal curves can be obtained by inputting relevant parameters. Secondly, based on the dynamic performance and service life theory of elliptical gear system, the torsional vibration dynamic model of the system is established. The excitation factors in the model, such as the shape and structure of the gear itself, the output speed on the shaft of the solar wheel, the time-varying meshing stiffness, the comprehensive error and the clearance of the gear pair, are studied. Thirdly, the special vibration differential equation of elliptical gear is derived by using the displacement on the meshing line as the independent variable, and the equation is solved by high precision Runge-kutta method. Taking the elliptical planetary gear system of order 6-8 as an example, the time-domain response, phase diagram and frequency spectrum of the system are analyzed by means of piecewise linear approximation. The dynamic response of the system is studied, and the influence of damping and rotational speed on the dynamic response is analyzed. Finally, according to the characteristics of non-circular gear, the machining simulation, code generation and transmission of non-circular gear by wire cutting simulation software are completed, and finally the machining implementation is carried out. In this paper, the design flow of elliptical gear is simplified by interpolation method and GUI interface of nodal curve parameterization. The dynamic model and differential equation are suitable for all planetary gear systems with variable center moment. The machining process of non-circular gear is simplified by wire cutting simulation software. The results of dynamic analysis in this paper provide a theoretical basis for the vibration of non-circular gears, the noise detection of non-circular gear motors and the measures to reduce vibration.
【学位授予单位】：沈阳工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH132.41
本文编号：2457776
[Abstract]:Non-circular gear has the characteristics of stable transmission, compact structure, easy to realize dynamic balance and periodic variable-speed motion. The application of non-circular gear to hydraulic motor can make the motor have the characteristics of small volume, large displacement, oil resistance and so on. However, it is difficult to study the dynamics of non-circular gear due to the pressure angle, the direction of engagement force and the center moment. The previous research is limited to two non-circular gears with external meshing. This paper is based on increasing the displacement of motor. The radial force of the balancing system is presented, and the vibration characteristics of the elliptical planetary gear system are studied. Firstly, the structure of the elliptical planetary gear system, the meshing principle of the gear and the motion relation of the gear train are studied. The nodal curve equations of the solar wheel and the inner gear ring are obtained by using the numerical analysis method. This paper deduces the method of using cubic spline interpolation to know the nodal curve of one elliptical gear in gear train, draws the pitch curve and tooth profile of other gears, and develops the interactive interface of parametric design of elliptical planetary gear structure. The function of different elliptic gear system nodal curves can be obtained by inputting relevant parameters. Secondly, based on the dynamic performance and service life theory of elliptical gear system, the torsional vibration dynamic model of the system is established. The excitation factors in the model, such as the shape and structure of the gear itself, the output speed on the shaft of the solar wheel, the time-varying meshing stiffness, the comprehensive error and the clearance of the gear pair, are studied. Thirdly, the special vibration differential equation of elliptical gear is derived by using the displacement on the meshing line as the independent variable, and the equation is solved by high precision Runge-kutta method. Taking the elliptical planetary gear system of order 6-8 as an example, the time-domain response, phase diagram and frequency spectrum of the system are analyzed by means of piecewise linear approximation. The dynamic response of the system is studied, and the influence of damping and rotational speed on the dynamic response is analyzed. Finally, according to the characteristics of non-circular gear, the machining simulation, code generation and transmission of non-circular gear by wire cutting simulation software are completed, and finally the machining implementation is carried out. In this paper, the design flow of elliptical gear is simplified by interpolation method and GUI interface of nodal curve parameterization. The dynamic model and differential equation are suitable for all planetary gear systems with variable center moment. The machining process of non-circular gear is simplified by wire cutting simulation software. The results of dynamic analysis in this paper provide a theoretical basis for the vibration of non-circular gears, the noise detection of non-circular gear motors and the measures to reduce vibration.
【学位授予单位】：沈阳工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH132.41
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