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外 文 翻 译 毕业设计题目： 异形非圆锥齿轮行星轮系 水稻宽窄行分插机构设计 原文 1： Kinematic analysis of a rice transplanting mechanism with eccentric planetary gear trains 译文 1： 偏心齿轮行星轮系水稻插秧机的运动学分析 原文 2： Bevel gear of the latest developments in measurement technology 译文 2： 锥齿轮测量技术的最新进展 1 Kinematic analysis of a rice transplanting mechanism with eccentric planetary gear trains Abstract Although eccentric gear trains have been found useful in agricultural machinery such as rice transplanting machines, lack of a theoretic study on kinematics and dynamics of it has led to some difficulty to further improve the performances of the system. The main contribution of this paper is to develop the so-called kinematic parametric equation (kinematic model) for an eccentric planetary gear train without introducing the assumptions which are mainly related to the eccentricity of the system. A comparison of our kinematic model with the measured results achieved by Tatsuya Konishi et al. is also provided. Keywords: Eccentric planetary gear trains； Kinematics; Agricultural machine 1. Introduction Eccentric gears are similar to noncircular gears in the sense that kinematic behaviors of a pair of noncircular gears can be realized with a pair of eccentric gears. Their output behaviors, such as angular displacement and gear ratio, are a periodical function. The manufacturing of an eccentric gear is easier and the cost of manufacturing an eccentric gear is lower than that of manufacturing a noncircular gear. It is therefore worth to study the analysis and design method for eccentric gears with the objective to replace noncircular gears in some design practices. A few studies were presented on the analysis and design of a pair of eccentric gears. Mitome and Ishida 1 presented an analysis of kinematic behaviors and two typical design methods for a pair of eccentric gears. Hideo et al. 2 studied a simplified design method of pitch curves based on motion specifications for noncircular gears. Judd 3 optimized the timing mechanism using noncircular gearing. Takashi and Akira 4 studied a new steering mechanism using noncircular gears. Konishi et al. 5, Chen et al. 6, respectively, proposed kinematic analysis and parameter optimization of a rice transplanting mechanism containing eccentric planetary gear trains, but their analyses were all approximate in the sense that they assumed that the eccentricity of eccentric gears does not affect the meshing process of the teeth. There was no work reported on the kinematic and dynamic analysis of eccentric planetary gear trains. 2 The main contribution of the work to be reported in our paper is that we have developed the so- called parametric equation for the eccentric planetary gear train by using the result produced by Mitome and Ishida 1 on a pair of eccentric gears. The main difference of our work from others is that we consider the influence of eccentricity on the gear meshing process. A case will be studied to demonstrate the application of our equations in analysis of a rice transplanting mechanism. 2. Meshing transmission of a pair of eccentric gears 2.1. Displacement equations for eccentric gears The objective of displacement analysis for eccentric gears is to derive the relationship between two angular displacements of a pair of eccentric gears. Fig. 1 shows a pair of congruent eccentric gears with tooth number Z, module m, pressure angle in the initial position 0 and eccentricity . Gear 1 is a driving gear, and gear 2 a driven gear. The pitch curve equation of the driving gear in polar coordinate system can be written as: r1=(2 221) cos1 . （ 1） Fig. 1. Geometric characteristics of a pair of eccentric gears. Because 2R is the distance of centers of two gears, i.e., r1+ r2 = 2R, the pitch curve equation for the driven gear in polar coordinate system can be derived as: r2=2R (2 221) + cos1 . （ 2） Gear ratio is defined as: i21= 21= 12= 22211222 1+1. Let = e / R, the above equation can be rewritten as： i21 = 22(12 1)+1 1 （ 3） Angular displacement of the gear 2 can be obtained by integral of Eq. (3), i.e., 2 = 21110= 2 1212 sin1+cos110 1. (4) 3 Equations (3) and (4) show that the displacement of a pair of eccentric gears only depends on the eccentricity . 2 can only be solved by means of a numerical integral procedure, which is regarded difficult. In the following section, we will derive the so-called parametric equation for kinematic analysis without the need of numerical integral procedure. 2.2. Parametric equation of a pair of eccentric gears The parametric equation represents the relationships between input and output via a third parameter. When two teeth of mating gears have an involute form, the line of action is tangential to the two base circles. Since the base circles are also eccentric circles, the position of the tangent line will change its orientation during the gear meshing process. The moving coordinate system xoy is set up as shown in Fig. 2, in which the solid line shows an initial position of two gears, the dashed line shows relative position of the two gears after they rotate an angle. Because the two base circles are always tangential to the axis x, the position after a rotation can be considered such that the two base circles, respectively, make a pure rolling on the axis x through an angle. The following discussion is largely drawn from 1. In Fig. 2, O1, C1, O2, C2are, respectively, rotational and geometric centers of the two gears at the initial position; O1, C1, O2, C2 are, respectively, the corresponding position of the two gears after a rotation. 1and 2、 can be represented as: 1 = 1 + 0 ， 2 = 2 + 0， （ 5） where 1 and 2are rotational angles of the two gears relative to the line of the action, is the working pressure angle, and 0 is the initial pressure angle. Fig. 2. Motion of base circles of eccentric gears 4 3. Kinematic analysis for eccentric planetary gear trains 3.1. Basic equations Kinematic analysis for eccentric planetary gear train makes use the results obtained for eccentric fixed axis gear trains, combining the theory for planetary gear trains. We will first consider a standard scheme as shown in Fig. 5, and then consider a more complex situation. Fig.5. an eccentric planetary gear train with joint action gears: (a) initial position; (b) position after rotating an angular H. 3.2. Eccentric planetary gear trains Fig. 6. Angular displacement function of Fig.7. Gear ratio function of an eccentric an eccentric planetary gear train. planetary gear train Now, let us consider a more complex eccentric planetary gear train shown in Fig. 8. In Fig. 8, a mid-gear is presented. With the inversion approach, we obtain 1 where1 = ， 2= + ， = -， 3= + ， 1 2 are the working pressure angles between gear 1 and gear 2, gear 2 and gear 3; 1 2 are the rotational 5 angles of gear 1 and gear 2 relative to their line of action； 2 3 are, respectively, the rotational angles of gear 2 and gear 3 relative to their line of action. Hence, 2 = 2 + 2 1. Fig. 8. An eccentric planetary gear train with a mid-gear. 4 A case study The case study is carried out on a rice transplanting mechanism with eccentric planetary gear trains. Konishi et al. and Chen et al., respectively, studied the kinematics and parameters optimization of a rice transplanting mechanism containing eccentric planetary gear trains, but their studies were all based on the assumption that the eccentricity of eccentric gears does not affect their meshing transmission. Our objective is to calculate the trajectory of the planting finger. From the scheme as shown in Fig. 9, the first step is to find H . By means of the method described in Section 3.2, the kinematic behaviors of an eccentric planetary gear shown in Fig. 8 can be solved. 3 = 1 cos0+cos(0+1)cos0+cos(0+2)cos0cos(02)cos0cos(03)。 (25) Fig.9. A rice transplanting mechanism with eccentric planetary gear trains Figs. 10and 11 show angular displacement and gear ratio of an eccentric planetary 6 gear train when 0 = . Fig. 10. Angular displacements of an Fig. 11. Gear ration function of an eccentric planetary gear train with a mid-gear. eccentric planetary gear train with a mid-gear The trajectory of the planting finger can then be derived point O3 in the right coordinate system xoy are: 3 = s ( + 0), 3 = cos( + 0), (26) The equation of motion locus of planting finger can be written as: = 3 + cos ( 0 3)， = 3 + s ( 0 3)， （ 27） When L = 76 mm, H = 138 mm, 0 = 35, = 69, the motion loci of planting finger under various are shown in Fig. 12. Fig.12. Motion loci of planting finger Fig. 13. A measured motion locus of planting figure. Fig. 13 shows a measured motion locus of planting figure in a rice transplanting mechanism containing eccentric planetary gear trains, which was obtained by Konishi et al. Figs. 12 and 13 indicate that our computed results can be identical with the measured results only if the structural parameters, such as L， H， 0， ， are reasonably determined, because the curves shapes shown in them are in excellent agreement. But if according to 7 the results of theoretic analysis in the paper of Konishi et al., that is, kinematics of eccentric gear trains is identical with elliptic gear trains, the motion loci of planting figure relative to machine should be symmetric shape. 5 conclusion It is impossible to get an analytical solution for the relationship between the angular displacements of a pair of eccentric gears; the numerical solutions were thus studied. In this paper, a further simplification of the solving procedure was presented. Furthermore, the proposed solving procedure was used to solve for the eccentric planetary gear train. To verify our proposed solving procedure, a rice transplanting mechanism with eccentric planetary gear trains was studied. As a result, the results obtained using our approach are in excellent agreement with those directly measured. 8 偏心齿轮行星轮系水稻插秧机的运动学分析 摘要 虽然偏心轮系在农业机械例如水稻插秧机 中有很重要的作用，但是对它的运动学和动力学的原理分析的缺乏导致 进一步 提高 这个系统的功能存在 困难 。本文的主要目的 是 研究偏心齿轮行星轮系的运动参数方程（运动学模型）， 没有 介绍跟系统偏心 率 相关的主要假设。同时提供了我们的运动学模型和 Tatsuya Konishi等 做 的测量结果的对比。 关键词 ： 偏心齿轮行星轮系；运动学；农机 1. 前言 一对非圆齿轮的运转状态也可以理解成一对偏心齿轮的运转状态，在这个意义上， 偏心齿轮跟 非圆齿轮是相似的。它们输出的 转动特性 ， 如 角位移和 传动 比 ，是周期 函数 。加工一个偏心齿轮比加工一个非圆齿轮要简单，并且成本低。因此以在一些设计实践中 替代非圆齿轮为目的对偏心齿轮的分析 和 设计方法进行研究是 有价值 的。 关于一对偏心齿轮的分析和设计提出了一些课题。 Mitome 和 Ishida1提出了对一对偏心齿轮的运动特性的一种分析方法和两种典型的设计方法。 Hideo 等人研究了基于非圆齿轮节曲线运动 规律 的简化设计方法。 Judd 采用非圆齿轮传动装置优化了定时机构。 Takashi 和 Akira 研究了一种新的使用非圆齿轮的转向装置。 Konishi 等人 和 Chen 等人分别 提出了一种包含偏心齿轮行星轮系的水稻插秧机 的运动学分析和参数优化，但是他们的分析都是粗略的，在 他们假设 偏心齿轮的偏心 率不影响轮齿的啮合过程 的意义上。没有为记录偏心齿轮行星轮系的运动学和动力学分析 结果所做的 工作 。 本文中所报告的工作的主要贡献在于我们利用 Mitome 和 Ishida1对于一对偏心齿轮的研究结果对偏心齿轮行星轮系所谓的参数方程进行了优化。 我们的工作与别人的主要的区别是我们考虑到我们优化的方程在水稻插秧机的分析中的应用。 2.一对偏心齿轮的啮合传动 9 2.1 偏心齿轮的位移方程 对偏心齿轮的位移分析的目的是为了得到一对偏心齿轮的两个角位移之间的关系。图 1 中是 一对 齿数为 Z，模数为 m，初始位置压力角为 0 ，偏心率为 的相同的偏心齿轮。齿轮 1 是主动齿轮，齿轮 2 是从动齿轮。主动齿轮的节曲线方程在极坐标系下可以写成： r1=(2 221) cos1 . (1) 图 1. 偏心齿轮的几何特性 因为 2R 是两个齿轮的中心距，即 r1+r2=2R，从动齿轮的节曲线方程在极坐标系下可以 推导为： r2=2R (2 221) + cos1 . (2) 根据齿轮传动比的定义： i21= 21= 12= 22211222 1+1. 让 = e / R, 上式可以写成： i21 = 22(12 1)+1 1 (3) 齿轮 2 的角位移可以对方程（ 3）积分得到，即： 2 = 21110= 2 1212 sin1+cos110 1. (4) 方程（ 3）和（ 4）表明一对偏心齿轮的角位移仅与偏心率 有关。 2 只 可以通过 一些困难的数值积分法来求解。接下来我们将不使用数值积分法对运动学分析所谓的参数方程进行推导。 2.2 一对偏心齿轮的参数方程 10 参数方程通过第三个参数表示输入量和输出量之间的关系。当啮合齿轮的两个齿是渐开线的形状 ， 作用线与两个基圆相切。由于两个基圆也是偏心圆， 在齿轮的啮合过程中，切线的位置会改变方向。动坐标系的建立如图 2 所示，其中 实线 表 示两个齿轮的初始位置，虚线 表 示转动一个角度 后 两个齿轮的相对位置。因为这两个基圆 始终与 x 轴相切，转过一定角度后的位置可以看做是两个基圆分别在 x 轴上纯滚动过一个角度后的位置。 接下来的讨论主要 引自 1。在图 2 中， O1, C1, O2, C2 分别是两个齿轮在初始位置的转动中心和几何中心； O1, C1, O2, C2分别是两齿轮转过一定角度后的对应位置。 1、 2 可以表示为： 1 = 1 + 0 ， 2 = 2 + 0， （ 5） 其中， 1、 2是两个齿轮相对于作用线转动的角度， 是工作压力角， 0是初始压力角。 图 2. 偏心齿轮 基圆的运动 3.偏心齿轮行星轮系的运动学分析 3.1 基本方程 对偏心齿轮行星轮系的运动学分析利用从偏心固定轴齿轮系得到的结果，结合行星轮系的原理。我们首先考虑一个如图 5 所示的标准方案，然后再考虑更复杂的情况。 11 (a)初始位置； (b) 转过角度 H后的位置 图 5. 有同轴齿轮的偏心齿轮行星轮系 3.2 偏心齿轮行星轮系 图 6. 角位移函数 图 7. 传动比函数 现在，我们来考虑一种如图 8 所示的复杂的偏心齿轮行星轮系。在图 8 中，加入了一个中间齿轮。根据反演方法，我们得到： （ 24） 其中， 1 = ， 2= + ， = -， 3= + ， 1， 2分别是齿轮 1和 2 之间，齿轮 2 和 3 之间的工作压力角； 1， 2分别是齿轮 1 和齿轮 2 相对与它们的作用线转过的角度； 2， 3分别是齿轮 2 和齿轮 3 相对与它们的作用线转过的角度。因此， 2 = 2 + 2 1. 12 图 8. 有一个中间齿轮的偏心齿轮行星轮系 4. 案例研究 案例研究的是偏心齿轮行星轮系水稻分插机构。 Konishi 等人和 Chen 等人分别 研究 了一种包含偏心齿轮行星轮系的水稻插秧机的运动学分析和参数优化，但是他们的分析都是在偏心齿轮的偏心率不影响轮齿的啮合过程的假设 的基础 上 。 我们的目的是计算种植曲线的轨迹。从图 9 的方案 中第一步是找到 H。用3.2 部分介绍的方法可以求出图 8 中所示的偏心行星齿轮的运动特性。 3 = 1 cos0+cos(0+1)cos0+cos(0+2)cos0cos(02)cos0cos(03)。 图 9. 偏心齿轮行星轮系分插机构 图 10和 11分别表示的是当 0 = 时一对偏心行星齿轮的角位移和传动比。 种植曲线的轨迹可如下推导。点 O3在直角坐标系 xoy下的坐标 是： 3 = cos( + 0), 3 = s ( + 0), (26) 13 图 10. 偏心行星齿轮的角位移 图 11. 偏心行星齿轮的传动比 种植曲线的运动轨迹方程可以写成： = 3 + cos ( 0 3)， = 3 + s ( 0 3)， （ 27） 图 12 中表示了 当 L=76mm， H =138mm， 0=35 ， =69时， 种植曲线随 变化的运动轨迹。 图 13 表示了由 Konishi 等人实际测量得到的偏心齿轮行星轮系分插机构的种植曲线的运动轨迹。 图 12. 种植曲线的运动轨迹 图 13.测量的种植曲线运动轨迹 图 12 和 13 表明只要结构参数，如 L， H， 0， ， 合理地确定，我们的计算结果可以跟实测结果很好的吻合，因为曲线的形状很好的重合。但是如果根据Konishi 等人论文中的原理分析的结果，即， 偏心齿轮传动的运动 轨迹 与椭圆齿轮传动的运动轨迹相同， 机器 的种植曲线的运动轨迹是对称的。 5. 结论 一对 偏心齿轮的角位移之间的关系的解析解 是 不可能得到的 ，因此对 数值解进行了研究。在本文中， 提供了一种简化的 求解过程。此外， 还运用了 提出的解决方法来 求 解偏心 齿轮 行星轮系。为了验证我们提出的 解决方法 ， 对 偏心 齿轮 行14 星轮系 插秧机构进行了研究。 因此 ， 使用我们的方法 所获得的结果 跟那些实际测量结果很吻合。 15 Bevel gear of the latest developments in measurement technology 1 Overview Bevel gear drive mechanism in the car, helicopter, machine tools and electric tools manufacturing industry, has been widely used. The use of different performance of the bevel gears are also different quality requirements, can be summarized including: a good contact area, can be a reliable torque transmission power; good match geometry, a smooth transfer of the movement, in order to ensure uniform load , transmission smooth, vibration small, noise low. Factories are usually small devices and dual-spot detection of rolling contact tester to control the quality of bevel gear, but in reality it is very difficult to determine accurately the performance of the bevel gear. Bevel gear and the precision of measurement of cylindrical gears similar, can generally be classified into three types: Coordinate Geometry Analysis of measurement type. That is, the bevel gear as a geometric entity, its geometric elements, respectively, the geometric precision of individual measurements; Gear Measuring Center is the main measuring instruments. Comprehensive engagement measurement accuracy. That is, the bevel gear transmission as a component, the accuracy of their transmission, contact spots, a comprehensive measurement of the vibration noise. The measuring instruments are mainly one-sided meshing bevel gear tester, bevel gear meshing two-sided bevel gear measuring and inspection machine rolling. Bevel Gear the overall measurement error. It will bevel gear transmission as a function for the realization of the geometric entities, or by coordinate measuring method in accordance with the geometric precision of a single measurement to measure the overall error of bevel gears, bevel gears to achieve a single transmission error and the geometric precision of the intrinsic link between the quality of the analysis; or by mating single measurement, the use of mesh point scan measurement of bevel gears for the overall error of measurement, has been integrated bevel gear movement accuracy, contact spots, as well as the geometric 16 precision of the individual. Therefore, the overall error of measurement of bevel gear is a measurement of the first two methods of integration and development. With the coordinate measuring technology, computer control and measurement technology, in recent years, the overall error of measurement of bevel gear technology research development soon. Gear Measuring Center as a result of multi-cylinder coordinates, such as multi-function measurement instrument performance, data-processing capacity, bevel gear-type coordinates of analytic geometry measurement technology, has been the development of a single geometric error of measurement to the overall error of measurement of bevel gear, improved cone gear design, processing, quality testing to determine the accuracy and the use of the forecast performance of the bevel gear, such as the level of manufacturing technology. By Chinas own development, based on the control point movement - geometric measurement principle on one side of the bevel gear meshing point scanning technology and technology development based on the overall error of the bevel gear measuring instrument, it is more towards the production of the first line, so that China Bevel Gear measurement theory, the practical application of measurement technology has been further improved and developed. 2. The main bevel gear precision measurement method and apparatus 2.1 Coordinate-style geometric measurement and analysis equipment Machinery Exhibition into a straight bevel gear-type coordinate measuring instrument