设计简介
摘要
双圆弧齿轮传动是近代发展起来的一种新型齿轮传动方式。对双圆弧齿轮的弯曲强度进行分析，在机械传动的数字化设计中起着垒关重要的作用。因此，建立比较实用的双圆弧齿轮弯曲应力数学模型，可以方便、快捷地求解双圆弧齿轮任一点的弯曲应力，具有一定的理论意义和工程实用价值。
论文首先评述了双圆弧齿轮国内外研发现状及其不足，分析比较了仅在凸齿处加载和在凸、凹齿处同时加载两种不同加载方式时弯曲应力的分布情况，得出结论:采取凸、凹齿同时加载的方式对双圆弧齿轮的弯曲应力进行研究，比仅在凸齿处加载的安全可靠性更高。然后，釆取凸、凹齿同时加载的方式，利用Pro/E软件强大的参数化建模功能和Pro/Mechanica模块的有限元分析功能，以及C语言及Excel的计算功能，基于折截面法和任意转角位置的双圆弧齿轮齿廓数学模型，构建了一个新的双圆弧齿轮弯曲应力数学模型。经过对新的弯曲应力数学模型的理论计算值和有限元仿真计算值进行分析比较，结果表明:用这两种方法得到的弯曲应力值非常接近。最后，应用该弯曲应力数学模型，详细分析了在不同刀具参数情况下双圆弧齿轮曲率半径对轮齿弯曲应力的影响规律。
应用本文新的双圆弧齿轮弯曲应力数学模型，可以直接得到双圆弧齿轮齿面上任一点的弯曲应力值，方便快捷，简单易行，为双圆弧齿轮的参数化设计提供了新的理论依据，同时对研究新型齿形和促进齿轮传动发展等都具有十分重要的意义。
关键词:双圆弧齿轮;有限元分析;弯曲应力数学模型;刀具参数
Abstract
Double circular-arc gear transmission is a new gear transmission mode which
developed in modern years。 It is crucial to analyze bending strength of the double
circular-arc gear in parametric design of the mechanical transmission。 Therefore， in order to solve the bending stress of the double circular-arc gear at any point quickly and easily， it has some theoretical and practical significance to establish its practicalmathematical model。
First of all， the domestic and foreign development situation and shortages of thedouble circular arc gear are briefly introduced， the differences of the bending stress areanalyzed and compared under two different loaded ways: one is loaded only at theconvex tooth profile and the another is loaded at both convex and concave toothprofiles。 It proves that the safety and reliability under the later way are much higherthan the first way。 Secondly， based on the broken-line section method and themathematical models of tooth profile of double-circulator-arc gear on any rotary angle position， with the powerful parameterized modeling capabilities of Pro/E software and the finite element analysis function of Pro/Mechanica software， as well as C language and calculation functions of the Excel spreadsheet， a new mathematical model of bending stress is obtained by adopting the method that the convex and concave tooth are loaded at the same time。 After comparing and analyzing the theoretical calculation values of the mathematical model of the bending stress with the values of finite element simulation， it comes to a conclusion that the two methods actually do not have much difference。 At last， in different cases， applying this new mathematical model of bending stress，the influence law that the cutting tool parameters such as the curvature radius impact on the bending stress of the double circular-arc gears，is analyzed。
Applying the new mathematical model of bending stress， the value of the bending stress on the tooth profile of the double circular-arc gears at any point can obtained comfortably， quickly and easily， it not only provides new theoretical basis for the mathematical design of the double circular-arc gears，but also has great significance for the research on the new tooth profile and the development of the gear transmission。
KeyWords: Double-circular-arce gear;Finite element analysis;Mathematical model of the bending stress; Tool parameters。
双圆弧齿轮传动是近代发展起来的一种新型齿轮传动方式。对双圆弧齿轮的弯曲强度进行分析，在机械传动的数字化设计中起着垒关重要的作用。因此，建立比较实用的双圆弧齿轮弯曲应力数学模型，可以方便、快捷地求解双圆弧齿轮任一点的弯曲应力，具有一定的理论意义和工程实用价值。
论文首先评述了双圆弧齿轮国内外研发现状及其不足，分析比较了仅在凸齿处加载和在凸、凹齿处同时加载两种不同加载方式时弯曲应力的分布情况，得出结论:采取凸、凹齿同时加载的方式对双圆弧齿轮的弯曲应力进行研究，比仅在凸齿处加载的安全可靠性更高。然后，釆取凸、凹齿同时加载的方式，利用Pro/E软件强大的参数化建模功能和Pro/Mechanica模块的有限元分析功能，以及C语言及Excel的计算功能，基于折截面法和任意转角位置的双圆弧齿轮齿廓数学模型，构建了一个新的双圆弧齿轮弯曲应力数学模型。经过对新的弯曲应力数学模型的理论计算值和有限元仿真计算值进行分析比较，结果表明:用这两种方法得到的弯曲应力值非常接近。最后，应用该弯曲应力数学模型，详细分析了在不同刀具参数情况下双圆弧齿轮曲率半径对轮齿弯曲应力的影响规律。
应用本文新的双圆弧齿轮弯曲应力数学模型，可以直接得到双圆弧齿轮齿面上任一点的弯曲应力值，方便快捷，简单易行，为双圆弧齿轮的参数化设计提供了新的理论依据，同时对研究新型齿形和促进齿轮传动发展等都具有十分重要的意义。
关键词:双圆弧齿轮;有限元分析;弯曲应力数学模型;刀具参数
Abstract
Double circular-arc gear transmission is a new gear transmission mode which
developed in modern years。 It is crucial to analyze bending strength of the double
circular-arc gear in parametric design of the mechanical transmission。 Therefore， in order to solve the bending stress of the double circular-arc gear at any point quickly and easily， it has some theoretical and practical significance to establish its practicalmathematical model。
First of all， the domestic and foreign development situation and shortages of thedouble circular arc gear are briefly introduced， the differences of the bending stress areanalyzed and compared under two different loaded ways: one is loaded only at theconvex tooth profile and the another is loaded at both convex and concave toothprofiles。 It proves that the safety and reliability under the later way are much higherthan the first way。 Secondly， based on the broken-line section method and themathematical models of tooth profile of double-circulator-arc gear on any rotary angle position， with the powerful parameterized modeling capabilities of Pro/E software and the finite element analysis function of Pro/Mechanica software， as well as C language and calculation functions of the Excel spreadsheet， a new mathematical model of bending stress is obtained by adopting the method that the convex and concave tooth are loaded at the same time。 After comparing and analyzing the theoretical calculation values of the mathematical model of the bending stress with the values of finite element simulation， it comes to a conclusion that the two methods actually do not have much difference。 At last， in different cases， applying this new mathematical model of bending stress，the influence law that the cutting tool parameters such as the curvature radius impact on the bending stress of the double circular-arc gears，is analyzed。
Applying the new mathematical model of bending stress， the value of the bending stress on the tooth profile of the double circular-arc gears at any point can obtained comfortably， quickly and easily， it not only provides new theoretical basis for the mathematical design of the double circular-arc gears，but also has great significance for the research on the new tooth profile and the development of the gear transmission。
KeyWords: Double-circular-arce gear;Finite element analysis;Mathematical model of the bending stress; Tool parameters。
