【作者】 魏巍；

【导师】 张连洪；

【作者基本信息】 天津大学 ， 机械制造及其自动化， 2011， 博士

【摘要】 螺旋锥齿轮铣齿机是加工螺旋锥齿轮的关键制造装备,铣齿机精度直接影响螺旋锥齿轮的齿面加工精度,进而影响齿轮传动的准确性、平稳性及载荷均匀性等性能。由于螺旋锥齿轮铣齿机的结构和加工原理复杂,机床精度与齿面加工精度的映射关系难以确定,使得机床的精度设计仍停留在以经验设计为主的阶段。这可能导致机床精度不足,所加工的齿轮达不到传动性能要求;或机床精度过度冗余,增加机床制造成本。针对上述问题,本文对螺旋锥齿轮铣齿机精度设计进行了研究,提出了面向齿轮传动性能的螺旋锥齿轮铣齿机精度设计方法,以期在保证齿轮传动性能的同时合理控制机床的制造成本。论文的主要研究内容和成果如下:(1)针对螺旋锥齿轮副展成法大轮和变性法小轮,分别建立了共轭齿面和过渡曲面的数学模型,通过将齿面离散点计算值与理论值进行对比分析,验证了齿面数学模型的正确性。(2)明确了齿面根切和未根切时齿面形状的两种拓扑形式,通过引入齿高方向的比例变量,提出了一种判别根切的数值算法。通过在轴截面上对离散点进行规划,提出了一种基于离散点求解的螺旋锥齿轮建模方法,该方法具有较好的通用性,无论是否发生根切都能准确描述齿面形状。(3)针对齿面接触分析中接触点求解不稳定和接触轨迹边界难以确定的问题,提出了一种基于自适应步长的齿面接触轨迹边界求解算法,同时设计了一套接触点求解初始值设定规则;针对接触区求解,提出了一种基于真实齿面的接触区数值算法,避免了传统的接触区计算中将齿面法截线用二阶抛物线代替导致的误差。(4)根据多体系统运动学理论,全面考虑机床各部件的几何误差,建立了包含几何误差的机床各部件相邻体变换矩阵,进而得到了误差齿面方程;以齿形偏差和齿距偏差来表征机床各部件的几何误差对齿轮副传动性能的影响,建立了几何误差综合作用下齿形偏差及齿距偏差的多阶回归近似模型。(5)根据齿面加工精度要求,采用蒙特卡罗方法进行铣齿机精度分析,获得了机床各项几何精度的初始值和上、下限。以铣齿机制造成本为优化目标,以齿面加工精度要求为约束条件,建立了铣齿机精度设计综合优化模型,采用直接启发搜索算法对其求解,得到了机床各项几何精度的优化值,并通过样机测试,验证了精度设计方法及结果的合理性。(6)基于上述成果,提炼了面向齿轮传动性能的螺旋锥齿轮铣齿机精度设计的技术流程;应用CAD二次开发及数据库技术,开发了螺旋锥齿轮铣齿机精度设计软件系统。本文研究的具体对象是螺旋锥齿轮铣齿机,但就其理念和原理而言,也适用其它基于复杂加工原理的制造装备精度设计,具有一般性意义。更多还原

【Abstract】 Spiral bevel gear milling machine is a key equipment of spiral bevel gear manufacturing. The precision of the machine directly influences the machining precision of the gears, and further influences the transmission performances as the accuracy, the stability and the load uniformity of the gear transmission. Due to the complexity of the structure and the working principle of the machine, and thus the difficulty to set up the mapping relationship between the precision of the machine and the machining precision of the gear, the up-to-date conventional precision design of the spiral bevel gear milling machine is still experience based. Such precision design may lead to a poor design with insufficient precision, or over precision unnecessarily increasing manufacturing cost and difficulty. Aimed to improve such a shortage of the precision design and to give an appropriate estimation of the cost-effective precision of the machine, the gear transmission performance oriented design methodology for the precision of the spiral bevel gear milling machine is proposed and studied in this thesis. The methodology is expected to help engineers to design cost-effective machine tool. The contens and contributions of the thesis are as follows:(1) Mathematical models for the tooth meshing surface and the transition surface are established of the gear by hobbing with uniform rolling ratio and the pinion by hobbing with modified rolling ratio. The models are validated to be correct via the comparative analysis between the theoretical and model-calculated discrete points of the tooth surface.(2) Two types of topology are clarified for normal and undercutting tooth profiles of the spiral bevel gears. A numerical algorithm for judging undercutting is set up via introducing a variable of tooth height ratio. A 3-D modeling method is proposed for the spiral bevel gear by planning and calculating the discrete points on the axial cross section of the gear. This method is applicable to both normal and undercutting tooth profiles.(3) Algorithms for solving the boundary of contact trajectory with adaptive iterative step and for setting initial coordinates of the contact points on the tooth surfaces are proposed, which resolved the unstability in solving the contact points and the difficulty in determining the boundary of contact trajectory. An algorithm is developed based on the real tooth surface for solving the contact region in spiral bevel gear pair, which can eliminate the error in the conventional tooth contact analysis (TCA) of parabolic tooth surface approximation.(4) Adjacent body transformation matrixes for the spiral bevel gear milling machine are established, which comprehensively contain geometrical errors of the machine with multi-body kinematics. Then the tooth surface models with geometrical errors are obtained. Choosing tooth profile error and circular pitch error as items of tooth surface error evaluation, approximate models of tooth profile error and circular pitch error are established by regression analysis.(5) According to the requirements of tooth surface precision, precision analysis of the machine is carried out by Monte Carlo method. The initial values and bounds of accuracy specifications are determined from the precision analysis. A comprehensive optimal model is established,by taking the minimization of the manufacturing cost of the machine as the objective and the requirements of tooth surface precision as the constraints. The optimal precision specifications of the machine are obtained by solving the optimal model with Directed Heuristic Search algorithm. The optimal precision specifications are in better accordance with the mockup test results, which shows that the proposed design methodology for the precision of the machine in this thesis is reasonable.(6) A technical flowchart for the precision design of the spiral bevel gear milling machine is summarized based on the achievements of this thesis. And a software system for the precision design is developed with using re-development of CAD and database technique.Although the object of this thesis is the spiral bevel gear milling machine, the idea and the principle of the methodology are also applicable to other manufacturing equipments of complicated structure and working principle.更多还原