非圆齿轮数字化齿面接触分析

发布时间：2018-04-12 19:42

本文选题：非圆齿轮 + 齿形接触分析　；参考：《哈尔滨工业大学》2013年硕士论文

【摘要】：随着计算机技术和数控加工的发展，非圆齿轮的设计和加工变得越来越容易。但是，根据齿轮副的实际齿廓精确计算其啮合过程，评价其传动性能的方法在非圆齿轮副传动中是一个空白。为了解决这一问题，本论文从非圆齿轮齿廓离散数据点入手，通过曲线拟合得到非圆齿轮齿廓的统一数学描述，基于齿廓啮合原理进行非圆齿轮传动数值模拟，构建了完整的非圆齿轮TCA(Tooth Contact Analysis，齿廓接触分析)方法。针对非圆齿轮齿廓不能像圆柱齿轮一样有精确的数学公式描述，论文中提出了将所有形式的非圆齿轮用其齿廓离散点为样条端点的分段三次样条函数统一表达，并且推导出了同一齿廓在旋转运动中的分段三次样条系数变换公式。 TCA过程的核心是主动齿轮齿廓与被动齿轮对应齿廓传动的数值计算。用两条光滑分段三次样条来描述主、被动轮齿廓，当主动齿转到一个角度，计算被动齿与其满足齿廓啮合定律时的角度，从而完成主动齿与被动齿传动的啮合计算过程。啮合计算的本质是迭代判断两条分段三次样条在平面中的位置关系，整个过程分为粗略判断(几何法)和精确判断(解非线性方程组)。为了提高粗略判断效率，提出了三次样条外接矩形的概念。同时，考虑到实际齿轮传动有可能有多对齿同时参与啮合，由误差控制准则，给出了考虑主动轮与被动轮所有齿廓的啮合传动计算方法。由TCA过程计算的啮合点、转角值、参与啮合齿对数、啮合齿序号等中间数据，可以精确得到瞬时重合度、滑动系数、传动比、反向间隙值等非圆齿轮齿廓传动的重要性能参数，为非圆齿轮副的设计校验提供了具体的量化数据。这样可以为非圆齿轮设计缩短时间，，提高设计的可靠性，有利于非圆齿轮的进一步推广应用。
[Abstract]:With the development of computer technology and NC machining, the design and machining of non-circular gears become more and more easy.However, according to the actual tooth profile of the gear pair, the meshing process is accurately calculated, and the method of evaluating its transmission performance is a blank in the non-circular gear pair transmission.In order to solve this problem, this paper starts with discrete data points of non-circular gear tooth profile, obtains unified mathematical description of non-circular gear tooth profile by curve fitting, and carries out numerical simulation of non-circular gear transmission based on tooth profile meshing principle.A complete method of TCA(Tooth Contact analysis (tooth profile contact analysis) for noncircular gears was constructed.In view of the fact that the tooth profile of a non-circular gear can not be described precisely as a cylindrical gear, a piecewise cubic spline function is proposed in this paper, in which all forms of non-circular gear are expressed as splines with discrete points of tooth profile as spline endpoints.The piecewise cubic spline coefficient transformation formula of the same tooth profile in rotating motion is derived.The core of the TCA process is the numerical calculation of the gear profile corresponding to the passive gear.Two smooth piecewise cubic splines are used to describe the tooth profiles of active and passive gears. When the active teeth turn to an angle, the angle between the passive teeth and the active teeth satisfying the tooth profile meshing law is calculated, thus the meshing calculation process between the active teeth and the passive gear drives is completed.The essence of meshing calculation is to iteratively judge the position relation of two piecewise cubic spline in the plane. The whole process is divided into rough judgment (geometric method) and accurate judgment (solving nonlinear equations).In order to improve the efficiency of rough judgment, the concept of cubic spline external rectangle is proposed.At the same time, considering that the actual gear transmission may have more than one pair of teeth in the meshing at the same time, according to the error control criterion, the calculation method of the meshing transmission considering all the tooth profiles of the active wheel and the passive gear is given.The important performance parameters of non-circular gear profile transmission, such as instantaneous coincidence degree, slip coefficient, transmission ratio, reverse clearance value and so on, can be accurately obtained from the meshing point, rotation angle value, the number of meshing teeth and the number of meshing teeth calculated by the TCA process.The quantitative data are provided for the design check of non-circular gear pair.This method can shorten the design time, improve the reliability of the design, and be beneficial to the further popularization and application of the non-circular gear.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TH132.41

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