工学硕士学位论文 圆柱蜗杆测量及误差评定技术研究 RESEARCH ON THE TECHNOLOGY OF MEASUREMENT AND ERROR EVALUATION OF WORM 宣莉莉 哈尔滨工业大学 2009 年 6 月 国内图书分类号：TH113.2 学校代码：10213 国际图书分类号：621 密级：公开 工学硕士学位论文 圆柱蜗杆测量及误差评定技术研究 硕 士 研 究 生：宣莉莉 导 师：唐文彦教授 申请学位：工学硕士 学科：仪器科学与技术 所 在 单 位：自动化测试与控制系 答 辩 日 期：2009 年 6 月 授予学位单位：哈尔滨工业大学 Classified Index: TH113.2 U.D.C: 621 Thesis for the Degree of Master in Engineering RESEARCH ON THE TECHNOLOGY OF MEASUREMENT AND ERROR EVALUATION OF WORM Candidate： Xuan Lili Supervisor： Prof.Tang Wenyan Academic Degree Applied for： Master of Engineering Specialty： Instrumentation Science and Technology Affiliation： Automatic Testing and Control Dept Date of Defence： June, 2009 Degree-Conferring-Institution：Harbin Institute of Technology 哈尔滨工业大学工学硕士学位论文 - I - 摘 要 蜗杆传动装置在工业自动化发展中具有重要的地位， 广泛应用在机床、汽车、仪器、冶金机械等仪器设备中，为了确保在使用中的安全性、稳定性和可靠性，必须要求蜗杆传动正确，所以对蜗杆精度进行检测和分析是非常必要的。本文首先建立了蜗杆的理论模型，然后根据国标对各项误差定义推导出相应误差计算的函数表达式并设计出误差测量运动轨迹，使用VS.NET编程软件开发系统软件在CNC齿轮测量中心上实现蜗杆误差自动检测功能，最后对精度已知蜗杆进行了测量和误差评定实验，对系统的正确性进行验证。下面是本文完成的主要工作内容。 圆柱蜗杆造型包括 ZA、ZI、ZN、ZK 等多种。本文在查阅大量与蜗杆和 CNC 齿轮测量中心有关的国内外科技文献的基础上，利用微分几何和空间立体几何的相关知识建立了多种常用圆柱蜗杆的理论模型。根据圆柱蜗杆各项误差项的定义，结合蜗杆的理论模型，推导出蜗杆各项误差计算的方程，由此设计了相应的误差测量运动轨迹。采用测球半径的补偿方法对采集数据进行补偿处理，以保证误差计算前数据的准确性。 基于 VS.NET 开发系统测量软件和误差评定软件，能够实现在对蜗杆各项误差的自动测量和误差计算、评定、曲线显示、打印报表。把开发的系统软件在 CNC 齿轮测量中心进行系统联调实验，对已知精度等级的蜗杆进行测量来评价系统的性能，测量误差项包括：螺旋线误差、齿形误差、齿距误差、齿厚误差和啮合误差，并对测得结果进行了分析。 关键词： 蜗杆；测量；误差评定 哈尔滨工业大学工学硕士学位论文 - II - Abstract Worm-gearing device have an important position in the development of industrial automation, widely used in machine tools, automobiles, equipment, metallurgical machinery and other equipment. In order to ensure the safety, stability and reliability of use, the worm-gearing must carry out precisely, so to test and analyze the precision of the worm is very necessary . In this paper, firstly establish a theoretical model of the worm; and then according to the national standard of worm error definition, derive the formula for calculating the worm error and design the measuring trajectory, develop the system software based on the VS.NET programming software, which is used in CNC Gear Measurement Center to achieve automatic detection of worm; finally, measure each error of the worm that the precision rank is known to verify the system correctness. The type of cylindrical worm includes ZA, ZI, ZN and ZK and so on. In this paper, referring to great lot of scientific and technical literatures about worm and CNC, establish mathematical model of cylindrical worm on the basis of the differential geometry and three-dimensional geometry of space-related knowledge. Derive the formula of worm error items from the standard for worm error, and also design measuring trajectory based on the geometry model of worm. To ensuring data accuracy, use the compensation for the radius of probe to process the data from probe before being used to calculate the deviation. Develop the measurement and error assessment software based on VS.NET, which used in CNC Gear Measurement Center for worm, can achieve the automatic measurement of the error, error calculation, assessment, curve display band, print statements. On the CNC Gear Measurement Center, the measure system is evaluated by measuring the helix, profile, pitch, mesh error of the worm that the precision rank is known, and Analyze of measured results. Keywords: Worm, Measurement, Error evaluation 哈尔滨工业大学工学硕士学位论文 - III - 目 录 摘 要.I Abstract .II 第 1 章 绪论. 1 1.1 课题来源及研究意义 . 1 1.2 蜗杆测量及误差评定技术的研究现状和发展 . 2 1.2.1 国内外研究现状 . 2 1.2.2 未来发展趋势 . 4 1.3 主要研究内容 . 4 第 2 章 蜗杆理论模型的建立. 6 2.1 蜗杆及蜗杆传动工作原理. 6 2.1.1 蜗杆的分类 . 6 2.1.2 蜗杆的基本参数 . 6 2.1.3 蜗杆传动 . 8 2.2 蜗杆齿廓曲面的形成及齿面方程的建立 . 8 2.2.1 蜗杆齿廓曲