【作者】 李婷；

【导师】 潘存云；

【作者基本信息】 国防科学技术大学 ， 机械工程， 2009， 博士

【摘要】 随着现代齿轮传动技术的发展,在一些新兴的需要多自由度传动的领域,比如机器人领域、仿生技术领域、矢量推进技术领域等,采用传统的单自由度齿轮传动机构给研究工作带来了一定难度,因而,当Trallfa球齿轮——世界上第一种双自由度齿轮传动机构问世时,立即引起了工程界的广泛关注。但是由于Trallfa球齿轮的离散锥形轮齿存在加工难度大、齿廓承载能力低等缺陷,因此,并没有得到推广应用。此后一些学者对Trallfa球齿轮的齿形设计作了一些改进,出现了离散圆弧齿、离散渐开线环形齿、离散锥形齿等双自由度球齿轮传动机构,但由于都没能突破离散齿的齿形设计局限,因此在降低加工难度和提高承载能力方面的效果不佳。本文研究的渐开线环形齿球齿轮轮齿在球面上连续分布,克服了离散齿的局限,具有易于加工和承载能力较高的特点。目前,在传动的基本原理和运动学分析等方面进行了初步研究,但是作为双自由度齿轮传动机构,其传动特性比传统齿轮复杂,必须经过更加深入的传动理论研究才能为其传动技术的进一步发展奠定良好的理论基础。本论文研究工作的主要任务就是深入研究渐开线环形齿球齿轮传动的若干理论问题,建立一个相对完整的球齿轮传动理论体系,也期望能对双自由度齿轮传动技术的发展起到一定的推动作用。论文的研究工作包括以下几个部分:1.研究了球齿轮副的双自由度共轭齿面啮合问题。建立了球齿轮副的双参数运动学模型,对球齿轮副的两种基本机构——理想机构与万向节式机构进行了运动学原理分析。在此基础上,分析了球齿轮相啮合齿面在接触点处的相对运动情况,建立了球齿轮副的双参数啮合方程,据此得到了相应的啮合面方程及共轭齿面方程。采用计算机仿真方法对两种球齿轮机构的双自由度共轭齿面啮合原理进行了分析与验证,结果表明,理想机构与万向节式机构的相啮合齿面都是共轭齿面。2.采用滑动系数作为衡量球齿轮齿面滑动磨损程度的重要指标。结合球齿轮副的双自由度啮合原理及滑动系数的基本定义,对球齿轮齿面的滑动系数计算方法进行了研究,并给出了具体的计算公式,其齿面的滑动系数是关于运动参数——偏摆角φ_y1和方位角φ_z1的二元函数,并与球齿轮沿空间两个分方向运动的角速度比ε有关。据此,对球齿轮理想机构与万向节式机构的齿面滑动系数进行了分析计算,由两种球齿轮机构滑动系数分布规律分析可知:球齿轮齿廓中部的滑动磨损最轻,齿顶次之,齿根磨损最为严重。而且,在万向节式机构中,安装轴对齿面滑动磨损的影响是良性的。3.进行了球齿轮齿面接触特性分析与应力分析。通过理论证明,球齿轮是马鞍面与凸面之间的接触:除极轴重合位置为线接触外,其余位置都为点接触。建立了用于计算机仿真计算的球齿轮齿面啮合模型,通过求解5个方程组成的非线性方程组,可以得到齿面上瞬时接触点的位置,据此对球齿轮副接触点轨迹进行了研究。采用曲率分析法与齿面分离拓扑法相结合对球齿轮的接触椭圆进行了理论与仿真计算,得到了接触椭圆在球齿轮齿面上的分布规律。采用有限元法,对球齿轮齿廓强度最弱的中凸齿进行了接触应力与弯曲应力的有限元计算。结果表明:接触应力在齿面上呈椭圆状分布;在不计重合度时,接触应力在齿中部较小,在齿根部与齿顶部较大;在考虑重合度时,齿根部与齿顶部的接触应力明显减小;弯曲应力较小,最大值出现在轮齿中部。4.分析研究了安装误差对球齿轮机构传动误差的影响。分别建立了球齿轮副的两种最常用机构——万向节式机构与指向机构的传动误差模型与指向误差模型。分别建立了两种机构在存在安装误差——定轴与动轴的轴向偏差(包括竖直与水平轴向偏差)及中心距误差时的运动学模型。在此基础上,对万向节式机构的传动误差进行了计算与分析;分别采用两种指向误差的评价方法,对指向机构的指向误差进行了计算与分析。结果对球齿轮机构的装配及其传动误差的测量具有重要的参考价值。5.采用磨削加工方法解决球齿轮精加工问题。根据球齿轮的齿形特点,分别采用成形法与范成法两种方法对球齿轮磨削加工方法进行了研究。针对成形法磨削,根据磨削加工所需的自由度要求,设计了磨削机床及指状砂轮,分析了机床运动链之间的运动关系及指状砂轮的磨削原理。针对范成法磨削加工,同样设计了磨削机床及盘形砂轮,建立了球齿轮与盘形砂轮之间的共轭啮合运动方程式,详细分析了由盘形砂轮加工球齿轮渐开线齿面及齿根过渡曲面的生成原理。最后,在建立盘形砂轮数学模型的基础上,得到了采用盘形砂轮加工球齿轮齿廓曲面的数学模型,据此可进行机床加工参数的设置与调整。更多还原

【Abstract】 With the development of modern gear transmission technology, in some rising fields which need multi-degree-of-freedom transmission, such as the fields of robotics, bionics, and vector propulsion, and so on, the traditional single-degree-of-freedom gear mechanisms increase the difficulty about the research work. So, Trallfa spherical gear, the first 2-DOF gear mechanism, is focused on in engineering immediately. However, since Trallfa spherical gear with discrete cone-shaped concave teeth has two disadvantages: difficulty to manufacture and low load capacity, it hasn’t been used widly. Afterword, some researchers redesigned the tooth of Trallfa spherical gear, and some 2-DOF gear mechanisms appeared, such as spherical gear with discrete circular arc teeth, spherical gear with discrete ring-involute teeth, spherical gear with discrete cone teeth and so on. These teeth designs haven’t broken through the limitation of discrete teeth; therefore the difficulties in manufacture and low load capacity haven’t been improved evidently. A spherical gear with continuous ring-involute tooth studied in this paper overcomes the defects of discrete teeth and has the advantages of easy manufacture and good load capacity. Some basic researches about its transmission theory and kinematic analysis have been made. However, as a 2-DOF gear driven mechanism, the transmission characteristics of the spherical gear with continuous ring-involute tooth are more complex than the traditional gears, and therefore it is very necessary to make in-depth research in theory for the progress of its transmission technology. This thesis is dedicated to solving some problems in theory about the spherical gear transmission, in order to set up a relatively whole system of transmission theory of the spherical gear, and promote the development of 2-DOF gear transmission technology. The major research efforts include the following aspects.1. The 2-DOF meshing theory of conjugate surfaces of the spherical gear pair is studied. The two-parameter kinematic model of the spherical gear pair is established, and the kinematic analysis of two basic mechanisms, the ideal mechanism and the gimbal mechanism, is performed. And then, the relative movement between two teeth surfaces in mesh is analyzed and based on the two-parameter meshing model, the equations of the meshing cone surface and conjugate surface are established. The simulation of the conjugate meshing principle of the ideal mechanism and the gimbal mechanism indicates that the teeth surfaces in mesh are the conjugate surfaces.2. Sliding ratio is an important index which can evaluate the wear of spherical gear tooth surface. According to the 2-DOF meshing theory of the spherical gear and the basic definition of sliding ratio, the calculating method of the sliding ratio of the spherical gear is studied, and the specific equation is received, which is a dual function with the swaying angleφ_y1 and the azimuth angleφ_z1 and relates to the angle velocity ratioεalong with two respective motion directions. Then, the sliding ratios of the teeth surfaces in mesh in the ideal mechanism and the gimbal mechanism are computed and analyzed and according to the distribution of sliding ratio, the following rules can be gotten: wear on tooth middle part is slight; wear on tooth tip is relatively severer; wear on tooth base is the severest. In addition, in the gimbal mechanism, the installed axes have a good effect on sliding wear of tooth surface of the spherical gear.3. The tooth contact characteristics analysis and stress analysis for the spherical gear are investigated. Theoretical derivation validates that tooth contact form of the meshing spherical gears is a point contact between a convexity and a saddle surface except the position in which the polar axes of two spherical gears are collinear to each other. Then, the meshing model of the spherical gear pair for computer simulation is set up, and the position of instantaneous contact point of two spherical gears can be gotten using the nonlinear solver composed of five equations. Furthermore, the contact point paths of the spherical gear in mesh are studied. Combined the curvature analysis method with the tooth surface separation topology method, the contact ellipse of the spherical gear pair is calculated and simulated, and the distributing rule is gained. Finite element analysis is applied to perform contact stress analysis and bending stress analysis of the convex tooth, the weakest tooth. The result indicates that: the distributing form of contact stress is an ellipse; regardless of contact ratio, contact stress is large on tooth base and tooth tip, and contact stress is little on tooth middle part; considering contact ratio, contact stress is evidently decreased on tooth base and tooth tip; bending stress is little, and the maximum of bending stress occurs on tooth middle part.4. The effect of assemble errors on the transmission error of the spherical gear mechanism is analyzed and simulated. The transmission error model and pointing error models of two mechanisms of the spherical gear sets in common use, the gimbal mechanism and the pointing mechanism, are set up, respectively. After that, the kinematic models of two mechanisms with assemble errors are built, and the assemble errors comprise the vertical and horizontial axial misalignment of the fixed axis and rotating axis, and the center distance error of two spherical gears, respectively. With these models above, the transmission errors of the gimbal mechanism are simulated and analyzed, and using two computation methods, the pointing errors of the pointing mechanism are simulated and analyzed. The results are useful for the installation and measurement of the spherical gear pairs in practice.5. Grinding method is the key for solving the finishing machining problem of the spherical gear. According to tooth surface characteristics of the spherical gear, with forming method and generating method, respectively, the grinding manufacture of the spherical gear are researched. To grinding with the forming method, according to the required degrees of freedom, a grinding machine and a fingerlike grinding wheel are designed, then the relationship of motions of the machine is analyzed and the grinding principle of the fingerlike grinding wheel is studied. To grinding with the generating method, similarly, a grinding mchine and plate grinding wheels are designed, and then the conjugate meshing kinematic equations are set up. The generating process of the involute tooth surface and the tooth base surface with the plate grinding wheels are introduced in detail. In the end, based on the mathematical models of the plate grinding wheels, the mathematical models of the spherical gear pair are received and the machining parameters can be set and adjusted.更多还原