基于精确齿面建模的弧齿锥齿轮有限元分析

发布时间：2018-02-22 22:51

  本文关键词： 弧齿锥齿轮 建模 有限元 接触分析 ANSYS 扭转角　出处：《浙江大学》2011年硕士论文　论文类型：学位论文

【摘要】：弧齿锥齿轮由于承载能力大,重合度大,平稳传递载荷,在高速传动时明显地减少噪声和振动,可以获得很大的传动比,对安装误差敏感性小,因而得到非常广泛的应用。本文以某发射装置末级传动系统中的弧齿锥齿轮为研究对象,运用MATLAB、VB、SolidWorks和ANSYS等工具,对其接触问题进行了研究。本文主要研究内容如下： 1.基于齿轮啮合原理和局部共轭原理,按照平顶产形轮加工原理及加工过程中之间的相对位置关系,建立了刀具坐标系、机床坐标系、工件坐标系等坐标系,详细地推导了各坐标系之间的矩阵转换,通过产形面和齿面啮合方程分别确定了大轮和小轮的齿面方程。分析比较了曲面不同参数的选择,确定了合适的参数来表示齿面方程,以方便其在MATLAB中实现,为后续建立弧齿锥齿轮模型奠定了基础。 2.根据推导的齿面方程,运用MATLAB编程计算出齿面上的数据点,导入SolidWorks,基于SolidWorks API技术,利用VB编程创建轮齿曲面,运用曲面裁剪、缝合等操作,创建一个轮齿,最后阵列切除形成完整齿轮,建立了大小轮的精确三维模型,按啮合关系装配,为后面有限元分析提供基础。利用VB编程检验插值曲面,以保证齿面误差符合有限元分析的要求。 3.结合建立的弧齿锥齿轮精确模型,在ANSYS软件中建立了弧齿锥齿轮的有限元模型,试划分网格得到理想的网格密度,试验验证取得合理的FKN值,分析了弧齿锥齿轮在同一啮合位置下不同载荷下的接触情况,得出了不同载荷作用下的接触区变化关系曲线,分析了大小轮的齿根应力,得到了接触应力和主应力沿齿向分布曲线。特别是首次得到了输入力矩与小弧齿锥齿轮扭转角之间的函数关系,这一结论可用于精确控制某发射装置。分析了一个啮合周期内的弧齿锥齿轮的啮合状况。 4.针对弧齿锥齿轮在加工和安装过程中存在的三种误差,分别分析了齿圈轴向位移偏差ΔfAM、轴间距偏差ΔfA、轴交角偏差ΔE∑三种安装误差对弧齿锥齿轮传动过程中的接触状态、应力应变的变化情况的影响。
[Abstract]:Because of its large bearing capacity, high coincidence and steady load transfer, the spiral bevel gear can obviously reduce the noise and vibration in high speed transmission, so it can obtain a very large transmission ratio and is less sensitive to the installation error. Therefore, it has been widely used. In this paper, the contact problem of spiral bevel gear in the last stage transmission system of a launcher is studied by means of MATLAB, VB, SolidWorks and ANSYS. The main contents of this paper are as follows:. 1. Based on the gear meshing principle and the local conjugate principle, according to the machining principle of flat-top production wheel and the relative position relation between the machining process, the coordinate system of tool, machine tool, workpiece and so on are established. The matrix transformation between the coordinate systems is derived in detail. The tooth surface equations of the large and small wheels are determined by the meshing equations of the generating surfaces and the tooth surfaces, respectively. The selection of different parameters of the surfaces is analyzed and compared, and the appropriate parameters are determined to represent the tooth surface equations. In order to facilitate its implementation in MATLAB, it lays a foundation for the subsequent establishment of arc bevel gear model. 2.According to the derived tooth surface equation, the data points on the tooth surface are calculated by MATLAB programming, and imported into SolidWorks.Based on SolidWorks API technology, the tooth surface is created by VB programming, and a gear tooth is created by cutting and suturing the tooth surface, etc. Finally, the complete gear is obtained by array excision, and the accurate three-dimensional model of the wheel is established, which is assembled according to the meshing relation, which provides the foundation for the finite element analysis behind. The interpolation surface is tested by VB programming. In order to ensure that the tooth surface error meets the requirements of finite element analysis. 3. The finite element model of spiral bevel gear is established in ANSYS software. The ideal mesh density is obtained by mesh division, and the reasonable FKN value is verified by experiments. The contact condition of arc bevel gear under different loads at the same meshing position is analyzed. The curve of contact zone variation under different loads is obtained, and the tooth root stress of large and small wheel is analyzed. The distribution curves of contact stress and principal stress along the tooth direction are obtained, especially the functional relationship between the input moment and the torsional angle of the bevel gear with small arc teeth is obtained for the first time. This conclusion can be used to control an emitter accurately. The meshing condition of a spiral bevel gear in a meshing period is analyzed. 4. Aiming at the three kinds of errors existing in the process of machining and installation of spiral bevel gears, the contact state of three kinds of installation errors in the transmission process of spiral bevel gears are analyzed respectively, such as axial displacement deviation 螖 f AM, axial spacing deviation 螖 f A, axis intersection angle deviation 螖 E 鈭，

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