【作者】 梁栋；

【导师】 陈兵奎；

【作者基本信息】 重庆大学 ， 机械工程， 2015， 博士

【摘要】 齿轮是制造装备业和国防工业中极其重要的关键基础件。高端重大装备对高性能齿轮传动的需求迫切且逐年增长,齿轮产品尽管在技术手段和性能方面有了长足的发展,但是与国际先进水平相比仍然存在较大差距。以直升机等为代表的航空航天飞行器,以风力发电等为代表的新能源装备,以坦克等为代表的武器装备以及高铁、舰船等重大装备都对齿轮传动提出了更高性能的要求,可概括为:长寿命、高承载能力、高可靠、高功重比(轻量化)、低噪声等。高性能的齿轮传动的研发已成为我国相关工业领域发展中的一个关键科学技术问题,也是机械工程领域传动机械学科研究的重要前沿。啮合齿面是运动和动力变换的直接作用面,也是齿轮创新发展的关键要素。本文充分考虑曲线接触的多样性,以曲线为啮合几何元素开展齿轮传动啮合新理论、新技术研究。相关内容对阐释现有齿轮传动的啮合原理及创立新型高性能齿轮传动提供了理论基础,对于满足重大装备对高性能齿轮传动的需求将产生重要作用,具有十分重要的理论意义和广泛的工程应用前景。论文的主要工作可概括如下:①在定义曲线连续相切接触的基础上,提出共轭曲线的概念,给出曲线共轭接触的基本条件;建立共轭曲线齿轮基本啮合原理,开展共轭曲线啮合数学描述,基于微分几何学分析并论证共轭曲线沿给定接触角方向的法向矢量,求解啮合函数关系,推导共轭曲线方程等,并开展实例应用。②从几何及接触特性分析入手,揭示共轭曲线啮合的一般规律及性质。提出共轭曲线密切面建模方法,基于弧长参数概念推导共轭曲线曲率及挠率,论证单参数曲线族包络的基本条件及特征点;探寻不同接触位置条件下的啮合函数变化规律,讨论共轭曲线接触的唯一性和同一性,描述共轭曲线的啮合运动基本特性。③基于共轭曲线原理构建具有优良曲线接触特性的啮合管齿面,提出以适当半径的球面沿共轭曲线的指定等距线包络运动成型啮合管的等距包络方法,建立共轭曲线齿轮啮合管齿面的构建理论,推导共轭曲线的等距线方程、啮合齿面方程等,构建多种接触齿面模型。在共轭曲线啮合理论的研究基础上,提出新型共轭曲线齿轮传动。④分析共轭曲线齿轮啮合管齿面几何及接触特性,提出齿轮满足传动比恒定和连续转动的一般条件;定义啮合管齿面压力角,描述齿面特征曲线及脊线,讨论啮合管齿面根切问题,建立诱导法曲率及挠率一般计算方法;开展啮合管齿面啮合及曲率干涉分析,基于共轭曲线原理建立齿面滑动计算理论与方法,论证齿面共轭继承特性,揭示共轭曲线齿轮轮齿齿面的啮合实质。⑤介绍传统圆弧齿轮传动及特点,提出基于共轭曲线啮合理论的圆弧齿轮传动啮合新原理,论述其成型原理与方法、几何及运动特性、啮合特性等,揭示与一般圆弧齿轮传动的内在联系,阐释圆弧齿轮传动的一般原理和啮合本质,实现共轭曲线啮合理论的重要理论应用。更多还原

【Abstract】 Gear drive plays an important role in the manufacturing equipments and national defence industry. The demands on gear transmission with high performance for major mechanism are gradually increased. The performance and technology of gears have been developed effectively in China. However, there is still a gap between current domestic and international levels. Not only the aerial, spacecraft and new energy fields, but also the weapon, high-speed rail and ship aspects all raise higher requirements for properties characterized by long lifetime, high load capacity, high reliability, low weight and low noise, etc. The innovation and development of gear drive with high performance have become a key scientific and technical issue in relative industrial fields and is also the scientific research frontier of mechanical engineering field.Tooth surfaces are the direct surfaces of action for motion and power transmission and they are also the important innovation points for gear development. Considering the diversity of curve contact, the new theory and technology of gear transmission are investigated in this article based on curve meshing element. It lays the theoretical foundation for explaining the meshing principles of existing gear drive and proposing the new types of gearing. This research will play an important part in improving the whole gear performance and it has a significant theoretical meaning and a broad application prospect. The prime content of the paper may summarize as follows:① Conjugate curves are put forward based on the definition of continuous and tangency contact between curves. The contact conditions of conjugate curves are given. Meshing principle of conjugate-curve gears is proposed and mathematical descriptions of contact are carried out. Based on differential geometry, the normal vector to contact point in arbitrary direction of contact angle is discussed. The meshing relationship along given contact position between conjugate curves is derived and the equation of conjugated curve is also deduced. The application examples of planar and spatial curves are obtained.② The meshing rule and property of conjugate curves are revealed through the discussions of geometric and contact characteristics. The modeling method of osculating plane is put forward. The calculations of curvature and torsion of conjugate curves based on arc length parameter are provided. Enveloping conditions of the family of curves with single parameter are demonstrated and the characteristic point is analyzed. The varietal law of meshing equation under different contact positions is discussed. Meshing unique and identity of conjugate curves are reflected, respectively. General motion property of conjugate curves is also described.③ The tubular tooth surfaces which have the characteristics of conjugate curves are generated according to the principle of conjugate curves. The equidistance-enveloping approach is provided to generate the tooth surfaces. It means that a spherical body with given radius performs the continuous enveloping motion along the designated equidistant curves of conjugate curves. The equations of equidistant curves and tubular tooth surfaces are derived, respectively. Different contact patterns of tooth surfaces are generated based on the various equidistance and direction. The new types of conjugate-curve gear transmission are proposed on the basis of meshing theory of conjugate curves.④ The geometric and contact characteristics of tubular meshing tooth surfaces are analyzed. The general conditions of tooth surfaces for keeping the fixed gear ratio and continuous transmission are proposed. Pressure angle of tubular meshing tooth surfaces is defined in terms of a space curve trihedron model. The characteristic line and ridge line are described, respectively. According to gear geometry, the non-undercutting conditions of tooth surfaces are discussed and the calculation methods of induced normal curvature and torsion are provided. The meshing and curvature interferences of tubular tooth surfaces are analyzed. A new approach to the calculation of sliding ratio of conjugate-curve gear pair based on conjugate curves is put forward. The conjugate successive property of tubular tooth surfaces is demonstrated. The nature and meshing rule of tooth surfaces are revealed.⑤ General principle and characteristics of conventional circular arc gear drive are introduced. The meshing principle of circular arc gears based on conjugate curves is put forward. The meshing theory of traditional circular arc gearing is newly explained and meshing essence of tooth surfaces is also revealed through the analysis of generation principle, geometric and motion characteristics, meshing property, etc. The relationship between two kinds of theories is demonstrated and the important application of conjugate curves theory can be realized.更多还原