摘要
本论文在国家自然科学基金和国家科技支撑计划的资助下,结合实际工程项目背景,开发了渐开线圆柱齿轮弹性啮合数值分析建模软件,为优化渐开线圆柱齿轮修形参数、精确齿轮强度校核以及行星传动均载特性研究提供有效方法。
随着工业对齿轮箱性能要求的大幅度提升和生产技术的快速发展,高精度硬齿面渐开线圆柱齿轮传动成为工业齿轮箱的主要发展趋势,为改善硬齿面齿轮的应力分布,提高齿轮寿命,降低齿轮箱的振动和噪声,齿轮修形设计已成为提升硬齿面齿轮传动性能不可或缺的核心技术。广泛应用的高效、高精度数控齿轮加工机床普遍具有齿轮修形加工能力,为经济可靠地生产高性能的修形齿轮提供了技术保障,目前迫切需要研究优化齿轮修形参数的设计方法,既显著提高硬齿面齿轮的传动性能又不额外增加成本,最大程度地发挥价格昂贵的齿轮精加工设备的优越性能。此外,齿轮应力精确计算和行星传动均载设计也成为挖掘齿轮极限承载能力提高齿轮传动性能的重要途径。
论文的主要研究内容如下：
提出渐开线圆柱齿轮三维有限元接触分析精细建模方法。编写Matlab程序以齿廓法线法求解齿轮廓线离散点坐标,在ANSYS中离散齿轮实体生成单元—节点拓扑结构,以正则表达式识别拓扑结构和节点坐标转存到SqlServer数据库模型,形成齿轮有限元节点模型。优化方法求解各条接触线方程,在此基础上编写齿轮有限元节点模型几何识别算法识别齿面节点集并规划接触带,导出节点规划的齿轮有限元节点模型,在ANSYS中重建齿轮有限元模型,应用APDL程序实现接触带单元分级剖分细化和多点约束边界单元细化。局部网格细化的齿轮有限元模型经齿面节点精确重建为实现齿轮高精度应力分析和齿轮修形参数优化奠定基础。
提出齿向、齿廓和综合修形的渐开线圆柱齿轮有限元接触分析快速精确建模方法。在局部网格细化的齿轮啮合有限元模型的基础上,按齿向修形函数和齿廓修形函数在齿面节点位置的修形量精确控制齿面节点的渐开线发生线长度,重新求解齿面上的节点坐标,实现直齿轮、斜齿轮、外齿轮和内齿轮的修形齿面节点快速精确重构,在ANSYS中重建齿面节点实现修形齿轮精确齿面快速建模,极大地提高了修形齿轮有限元接触分析建模效率。齿形优化以齿面上应力分布状况作为评价指标,按齿面应力分布趋势变更修形函数重建精确齿面修形的齿轮有限元模型,迭代求解修形齿轮接触问题,直至获得理想的齿面应力分布,完成齿轮修形参数优化。
提出行星传动均载特性有限元多柔体运动模拟评价方法。直齿行星传动可以用平面有限元建模,但是行星传动既存在行星轮自转又存在公转,各行星轮间载荷通过行星架和回转副传递。为了研究行星传动的均载行为,不仅建立了精确的齿轮有限元模型,还以刚度等效的梁单元模拟行星架、多点约束方程模拟回转副,实现行星传动系统的传动过程模拟。
A new approach was developed to optimize modification parameters of a pair of involute cylindrical gears, calculate gear stress accurately and research on characteristics of load sharing by floating components in a planetary gear system. This research was supported by the National Natural Science Foundation of China and the National Key Technology R&D Program.
Along with the improving quality demands for the performance of a gear box and rapidly developed technology, the high-precision hardened surface involute gear transmission has become a main trend in the gear transmission industry. The modification design for gear flanks has become one of the indispensable core technologies to improve the stress distribution on the teeth, lengthen gears service lives, and reduce the vibration and noise of a gear box. Widely used high-efficiency and high-precision Computer Number Control (CNC) gear machine tools generally have the capability of gear modification, which provide technical assurance to produce high-performance modification gears economically and reliably. There is an urgent need to research an approach to optimize the gear modification parameters. Using CNC gear machine tools to produce modified gears, not only notably improves the performance of the hardened surface gears transmission, but also does not increase additional costs, so we can make the best use of the predominant performance of the expensive gear finish machining tools. Moreover, accurate calculation of gear stress and load sharing design of a planetary transmission also become important ways to exploit gear ultimate bearing capacity and improve the performance of a gear transmission.
A method was put forward to build a refined3-D Finite Element Model (FEM) for a contact problem of involute cylindrical gears. The tooth profile normal method of the plane engagement theory was used to calculate a series of coordinates of a gear profile by programming the matlab code, and then topological structure of elements and nodes of the gear was generated in AN SYS software. The topological structure and the coordinates of the nodes were parsed with regular expression and transferred into a database model of Sqlserver, and then a gear node model was built. The functions of contact lines were solved by the optimization algorithm. Based on that, a node model geometric recognition algorithm was designed and used to identify the nodes on teeth flanks, and then to plan the nodes in the contact zone. After transferring the node model into ANSYS, the FEM of gears were reconstructed, and then APDL code was used to refine the elements in contact zones by grading division method and Multi-point constraints (MPC) equations method. The nodes on teeth flanks of the refined gear was precisely reconstructed, which is the base to accurately calculate the gear stress and optimize the modification parameters for a pair of involute gears.
A fast and accurate method was put forward to build an involute cylindrical gear FEM with lead modification, profile modification or comprehensive modification. Based on the refined gear meshing model, the magnitude of lead modification and profile modification at a node along the generating line of an involute was accurately calculated, and then the coordinates of the node was calculated and corrected including types of spur gears, helical gears, external gear pairs and internal gear pairs. The corrected nodes on the teeth flank were rebuilt in ANSYS software, then the gear FEM with modification was built, which dramatically improves the modeling efficiency for the contact analysis FEM of modified gears. Taking stress distribution on the teeth flanks as an evaluation index of gear modification, the gear modification parameters were corrected by modifying node coordinates on the tooth flank according to the trend of stress distribution on that. The contact problem of the modified gears was solved by iteration method until ideal stress distribution on the teeth flanks was achieved.
A method that flexible multi-body motion simulation evaluating the characteristics of a planetary gear system by finite element method was put forward. A planetary spur gear system can be modeled with2-D FEM; however, there are both rotation and revolution of planet gears, so the planet carrier and revolute pair have to be built for transferring loads to each planet gear. In order to study on the behaviors of load sharing among the planets, not only the gears FEM was built accurately, but also the planet carrier and the revolute pair were approximately simulated by beam element with equivalent stiffness and MPC to achieve motion simulation of the planetary gear system.
引文
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