【作者】 张华中；

【导师】 杨平；

【作者基本信息】 江苏大学 ， 机械电子工程， 2006， 硕士

【摘要】 微齿轮是微机械中极为重要的传动零件，其应用遍及各个领域。目前人们已经对微齿轮做了大量的研究，但基本上集中于解决微齿轮的制造问题，而对微齿轮的设计基础研究几乎为空白，例如微齿轮传动啮合接触中啮合齿面的摩擦。论文从以下几个方面对微齿轮进行研究。微齿轮在啮合接触过程中由于传递动力必然发生应力应变。在分析微齿轮应力应变时，由于尺寸效应必须考虑微观力（在此仅考虑范德华力）影响。本文推导了处于二维空间任意位置的渐开线数学模型，在此基础上利用泰勒公式建立渐开线简化数学模型，根据Hamaker假设和Morse势函数，引入分子动力学的截断半径，提出了一种计算微齿轮啮合接触中两啮合齿廓间范德华力的连续介质方法。使用Matlab编写程序分析了一系列微齿轮啮合接触过程中啮合齿廓间的范德华力。结合宏观齿轮理论中的齿根弯曲静强度校核公式引入微观力得到修正公式。运用修正公式和ANSYS对微齿轮系进行弯曲静强度分析，对比理论和数值分析结果接近。人们对微摩擦已经做了许多研究，但对于微齿轮啮合接触过程中摩擦特性的研究几乎没有。本文利用分子动力学对纳米齿轮啮合接触过程中单齿啮合区域的摩擦特性进行模拟。结果表明：在单齿啮合区域，摩擦力出现了类似于宏观齿轮摩擦的特性，但0摩擦力并不出现在节点处；当增加z方向原子层数时，摩擦力最大值增大，而最小值减小，因而摩擦力曲线变得陡峭；当增加主动轮的角速度w₁时，摩擦力最大值和最小值没有变化，只是摩擦力曲线变得更陡峭；当改变阻力转矩时，摩擦力曲线没有变化。最后推导了处于二维空间任意位置的齿根过渡曲线数学模型，介绍了行星齿轮系的安装理论和运动学数学模型，绘制了微行星齿轮系运动学程序流程图。基于以上理论采用Java编写了微行星齿轮系的运动学仿真程序。此程序不仅能手动或自动实现微行星齿轮系设计，而且可根据需要扩展。更多还原

【Abstract】 Micro-gear is a very important part which is used to transmit torque , rotary motion and power in micro-machine and its application covers many fields. Currently, a lot of researches on micro-gear are done and mainly focus on the fabrication of micro-gear, but the researches on the basic design theories of micro-gear hardly exist, for example, the friction between two micro-gears. The following is researched.The stress and strain of micro-gears are induced when they mesh and transmit power. Because of size effect the effect of micro-forces on the stress and strain is taken into account. In this paper, the mathematic model of an optional involute in two dimensions is reasoned and simplified based on Taylor Expression and the simplified mathematic model of an involute is got. Based on the simplified mathematic model, Hamaker Assumption, Morse potential and the cutting-off radius in molecular dynamics, a continuous computational method of van der waals force between the just contacting gear profiles is presented. A program is programmed using Matlab and a series of van der waals forces are computed using this program. Micro-forces are taken into account in the equation used to check the static bending strength of a gear tooth and the corrected equation is obtained. The difference between the results which are got individually using the corrected equation and ANSYS is small.A lot of researches on micro-tribology are done, but the researches on the friction between micro-gears hardly exsit. In this paper, molecular dynamics is utilized to simulate the frictional properties when a pair of nano-teeth only meshed. The results are follows. When a pair of nano-teeth only meshes, the change of the frictional force is similar to one between macro-gears, the fictional force in node isn’t 0．When the number of the atomic layer in z direction increases, the maximum of the frictional force is larger and the minimum of the frictional force is smaller, so the curve of the frictional force becomes steeper. When the angular velocity of the powered gear increases, the maximum and the minimum of the frictional force are invariable, but the curve of the frictional force becomes steeper. When the resisting torque increases, the curve of the frictional force doesn’t alter.In the end, a mathematic model of a fillet in two dimensions is reasoned, the installation and the kinetic model of planetary micro-gear system are introduced and the kinetic program flow diagram of planetary micro-gear system is drawn. Based on the foregoing, the kinetic program of planetary micro-gear system is programmed by Java. The program can not only manually or automatically design a planetary micro-gear system also be expanded.更多还原