【作者】 李太福；

【导师】 黄茂林；

【作者基本信息】 重庆大学 ， 机械设计及理论， 2004， 博士

【摘要】 平面连杆机构、齿轮机构与行星齿轮传动机构等平面闭链机构是工程实际中应用非常广泛的机构类型，它是以“平面约束结构”为基础，以保证其能够实现平面运动。这种人为的强制平面约束，使平面闭链机械系统成为超静定的过约束机构，并造成机械系统工作品质对误差的敏感。根据广义约束的观点，由于机械的工作受到各种内部和外部约束(包括几何约束、运动约束、动力约束及工作环境条件的约束等)的综合作用，实际上要保证这些约束精确的平面性是不可能的。制造误差(特别是形位误差)、安装误差、构件动力学参数(质量分布、惯性力等)的非平面性、构件的变形、外部环境(如温度、重力场等)及工作条件的变化等，都会造成对平面约束的干扰，使其具有不确定性。平面约束不确定性导致理论上不影响机械顺畅运动的过约束形成障碍，并对机械系统的工作性能、特别是动力学性能造成一系列严重影响，这些影响主要表现在以下几个方面：1) 过约束系统的障碍和超静定性质，导致构件及运动副元素在运转过程中的强制变形，使运动副中的作用力急剧增大，机械效率降低；还使运动副的磨损加快，降低了机械工作的可靠性、精度和使用寿命。2) 由于上述弹性变形和附加载荷一般是周期性或随机性的，加上运动副间隙的增大，这是引起系统振动、冲击和噪声的重要根源，因此影响了机械工作的平稳性，并造成了对环境的噪声污染。3) 过约束障碍还会造成安装拆卸的困难，影响产品的顺应性要求，不利于产品的自动、快捷的装配。4) 为了降低平面约束不确定性、消除或减小过约束的影响，保证平面运动约束，需要有较高的制造精度和结构刚度等，从而提高了制造的难度和成本。5) 平面约束不确定性将导致机械中力的不均衡性及实现自动调节和补偿的困难，影响机械工作的静定性和动态稳定性以及对外部环境变化的适应性。 因此，为满足现代科学技术发展和市场竞争的需要，针对以上问题，本文以各种不确定性系统理论为基础，以研究高品质、低成本、强稳健的机械产品为目标，探索面向不确定性的机械系统稳健性设计方法和基础理论，其主要的研究内容及创新点如下： ① 从认知科学的“概念”、数学的“集合”与面向对象思想的“类”和“对象”等角度提出不确定性，讨论了各种不确定性分类、产生原因等知识。应用不确定性系统理论分析了目前各机构学著述中所提到的几何约束、运动约束、动力约束等的不确定性。 ② 指出经典著述中关于“约束”与“自由度”仅仅从质上区分，而没有量的区别，把“约束”与“自由度”看作绝对对立概念的不足，并从不确定性思想根源重庆大学博士学位论文出发，提出了“约束”与“自由度”概念(集合或类)的不确定性。引入了基于集对分析思想的不确定性系统模型，并探讨了如何把该模型应用于“约束”与“自由度”的不确定性分析，建立了相应的“约束”与“自由度”不确定性系统模型。实例分析表明，该模型不仅从质上区分了“约束”与“自由度”，而且从量上给予了刻画。反映了“约束”与“自由度”的质量互变、对立统一的辨证思想。 ③讨论了运动副约束、重复运动副和平面闭链机构中的过约束。作者讨论现有的自调性机构设计方法，这些方法通过过约束分析，消除机构中的过约束，使其成为静定机构，能够实现无障碍装配，没有讨论机构运动过程中新生的约束。然而，在实际运行过程中，由于惯性力、运动摩擦力等，机构又可能新生约束，又可能出现过约束。这时，机构能否自动调整位置和姿态，时时处于静定状态，还要进行自调性分析。作者以曲柄摇块机构为例，提出了自调性机构设计的一般方法，该方法也适合其它连杆机构，具有一定的普遍意义。 ④对具有一个中间自调齿轮的齿轮机构无过约束设计方案，深入的进行了其自调机理的分析。详细分析了具有中间自调齿轮的齿轮机构在水平面和垂直面内，输入、输出轴的不平行度对齿轮机构径向间隙的要求，提出其能实现自调的条件。以本论文的实验研究装置为例，引入了中心距不确定状况下的重迭系数、压力角等计算公式，以两齿轮啮合时的分度圆不能相割为最小中心距，以两齿轮啮合的重迭系数不小于1为最大中心距，从而得到相应的中心距范围。并得出了两齿轮传动轴在各种不平行度下的径向间隙和法向间隙的计算公式。 ⑤应用不确定性系统理论，详细分析了机械零件误差和公差的不确定性，引入信息型灰数和层次型灰数等概念及其计算公式，提出应用这些灰数描述机械零件尺寸公差，并举实例证明了这种描述是正确的。进一步提出应用灰数来描述形位公差，探讨了灰数计算公式在形位公差综合和累积中的应用，并应用本课题的实验装置为例，用灰数表示其中心距允差，以及水平面和垂直面内，输入、输出轴的不平行度允差。在此基础上，设齿轮传动机构的某几个形位公差为未知数(灰色数值)，通过形位公差的综合与累积的计算关系，以最终形位公差不小于无过约束自调齿轮机构的最大允差为约束条件，在质量一成本模型基础之上，以成本最低为优化目标，建立了基于质量一成本模型的稳健性设计方程。这种方程求解的直接结果就是一个具体的更多还原

【Abstract】 The planar closed-chain mechanism is a kind of type which has been applied in practical engineering widely, such as the planar linkage mechanism, the gear mechanism, the planet gear mechanism and so on. These mechanisms are based on the structure of planar constraint so that it can realize planar movements. The man-made planar constraint will result that the constraints of a planar closed-chain becomes indeterminate-statically, so the performance of mechanical system is very sensitive to error. According to a viewpoint of generalized constraints, since the run of a mechanical system is subjected to all kinds of action from internal and external constraints, such as geometry constraints, kinematic constraints, dynamic constraints, constraints from working environments and so on, in fact, it is hardly impossible to ensure accurate planar characteristics of these constraints. For example, manufacturing errors, especially errors of profile and position, assembly errors, nonplanar characteristics of dynamic parameters of components (such as the distribution of mass, inertia forces, etc.), deformation of components, external environments (such as the temperature, the field of the gravity), varying of the condition and so on, all that will disturb the planar constraints, and make it uncertain. For uncertainties of planar constraints, it will result that over-constraints becomes obstacle and influence smooth movement of a mechanical system, and bring about a series of seriously influences on the performance of the machines, especially on their dynamic behavior and the quality. The shortcoming mainly show as following aspects: 1) The obstacle and the characteristic of indeterminate resulted from over-constraints, will lead to compelled deformation of links and kinematic pairs in process of running, and make action forces in kinematic pairs increase sharply, so the mechanical efficiency decrease obviously. Meanwhile, the abrasion of kinematic pairs is rapidly, so it is low in the reliability, poor in precision, short in life. 2) Because the above-mentioned elastic deformation and additional load is periodicity or randomicity generally, in addition, the clearance of kinematic pairs is increasing, all that will be primarily reason resulted into vibration, shock and noise. Therefore, it will influence the stability of machine running, and cause the pollution to environments. 3) The obstacle of over-constraints also will lead to difficulty of assembly and disassembly, and is unfavorable to assemble and disassemble automatically. 4) In order to decrease uncertainties of planar constraints, eliminate andreduce effects of over-constraints, ensure planar movement constraints, it is necessary to promote manufacturing precision and rigidity of structure, so manufacturing difficulty and cost will increase greatly. 5) Uncertainties of planar constraint will resulted that forces in machine is unbalance, it is difficult to realize self-adjustability and compensability, all that influences machine in determinate-statically, dynamic stability, adaptability to external environment.Therefore, in order to meet requirements of developments of modern science and technology and competitions of market, aimed at above-mentioned problems, this paper on the basis of all kinds of uncertain system theory, takes machine products of high quality, low cost and strong robustness as targets, explores methods and basic theory for robustness design of mechanical system oriented from uncertainties. Its mainly research contents and innovations show as following:(1) The viewpoint of uncertainty is presented from "concept "in cognizing science, "set" in mathematic, "class" and "object" in object-oriented idea, and author makes some discuss on classification of all kinds of uncertainties, reasons and emergences. Uncertainties in geometry constraints, kinematic constraints and dynamic constraints, which are mentioned in today several mechanism books, are analyzed by uncertain system theory.(2) In this paper, author points out a shortcoming that traditi更多还原