(符纯中)外文翻译.doc

毕业论文（设计）外文译文题 目 同步带传动的误差分析 系 部 机械工程学院 专 业 机械设计制造及其自动化 年级 2010级 学生姓名 符纯中 学 号 101010129 指导教师 牟柳晨 同步带传动系统的误差分析 本文重点研究可行的位置估计方案的正时皮带传动的位置带传动（负载）是通过参考模型接收来自位置传感器连接到输入确定同步带的致动器。的传动误差的来源进行了详细的分析，并相应的数学模型是使用先验知识的过程开发。本文表明，这样的计划是非常有效的驱动系统不受外部载荷和操作条件不发生较大的变化，即环境温度，皮带张力。【摘要】 同步带 误差估计 间接测量 精度提高。1.简介：同步带传动是越来越多地利用旋转运动转换成高精度的运动控制系统中的翻译如喷墨打印机，绘图仪，专用数控机床，缠绕机，快速成型机，视觉系统，和一些生物医疗设备 1 。在这样的机器，车厢里面的专用设备，通常是由一个弹性的传输元件，例如定时皮带驱动。因此，该装置的直线运动必须精确控制，通过直接测量达到特定的目标任务在手。在这样的安排，弹性元件的主要缺点是，他们引进知名的非线性即摩擦，弹性，间隙，时间延迟，以伺服回路 2 。因此，为了实现所需的精度和定位精度，先进的控制方案1-6陪直接测量/反馈技术经常。需要注意的是，当特色旅游跨度/中风的关键通用机器很长（大于0.5米）；直接测量技术，包括传统的使用传感器即电位器，LVDT，线性表，激光干涉仪导致笨重，昂贵的解决方案。因此，本文的主要目的是提出切实可行的估计方案使用的信息来自对驱动轮的低成本传感器使车厢位置可估计所需的精度为“不那么苛刻的应用。需要注意的是，这种范式要求的传输错误的一个很好的模型的临界（TES）的同步带机构。尽管事实上，沿与相应的测量和评价技术的定义是众所周知的TE齿轮（动态）文献 7 ，只有少数的研究重点的正时皮带传动的TE特性。例如，kagotani等人。 8 目前在这一领域的文献综述。他们研究的螺旋同步带传动误差超过一个螺距滑轮的理论和实验研究。本文的其余部分安排如下。这一简短的介绍后，系统的数学模型，给出了仿真结果。其次，描述的实验设置。然后，一些实验研究了一个通用的同步带传动的传动特性的报告。收集的数据的基础上，本文对位置误差源的详细分析。在这些结果的运动学模型是在下面的章节中介绍。下一篇文章评价提出的模型的估计性能。最后，本文的结论与研究的关键点。2。数学建模与仿真图1的线性引导运输系统的数学模型。在该系统中，运动的电机通过同步带机构传递到带传动。必须有足够的间隙啮合齿确保运动平稳无联锁。这种反弹在磁滞现象的机理研究。有许多研究利用Preisach模型来描述各学科中遇到的滞后效应。一个基本迟滞算子是纯粹的定义的Preisach模型在和对应上下的滞环的交换价值。同样，表示每一个独特的滞后系统中的元素，（，）是一个任意的权重函数必须为每个系统 9 定义。请注意 Preisac模型是其他滞后模型中最著名的一部。然而，它不会在本研究由于Preisach模型具有非本地内存的考虑。那是，输出的电流值不依赖于输入的电流值只而且输入过去的极值。这是很可能的，两个输出重合在t0但结果完全不同的outputsv1（T）andv2（T）堡垒 t0因此他们暴露在相同的输入u（t）堡垒 t0 10 。另一个问题就是确定权重函数。实验必须在系统确定该函数。此外，方程（1）是一个双积分方程。其数值的实施必须使用他们的控制系统算法 11 。有两个动态情况下的数学模型：第一个模型的上部和下部的磁滞带作为系统朝着某一方向不中断和后者的模型时，车厢的运动方向变化的过渡区。同时，图1显示了军队在正时皮带发生。摩擦力正时皮带因此，对带传动的运动方程可写成 如果在连接到电动机小齿轮轴承摩擦忽略不计，带传动将通过对同步带产生的力差致动。带传动的自由体图是图2中描述的 （2）因此，对带传动的运动方程可写成其中在所述滑架的轴承代表库仑摩擦力。将会有一个弹性变形，由于正时皮带和小齿轮的齿之间的接触。其结果是，这会创建一个额外的张力差（F），在其上可写为正时皮带; (3)在（3），H（0） M 指的是同步带齿和齿轮之间/反弹的差距；kcorresponds牙齿的整体刚度。在这个模型中，军队是由弹性变形之间的同步带的齿和齿轮的齿。这种模式的一个可能的配置是牙齿脱落，带传动改变其运动方向，和同步带齿隙区域进入。力是通过只有摩擦力小齿轮和皮带之间传输的开发。这种现象持续下去即滑动直到反弹是封闭的小齿轮和齿同步带之间。在同步带的两侧的拉伸力变得 (4)在这里，F0指的是在皮带预紧力/张力。根据定义，摄动力（F1和F2）带上都是非负的数量少于预紧力F本身保证皮带承载能力。欧拉方程产生的拉力带力之间的关系 6。 (5)其中是在带的卷绕（接合）的角度（在这种情况下，的倍数）; （U）表示的“动能”摩擦系数依赖于小齿轮和皮带之间的相对圆周速度;并且是滑移速度。相容性条件要求在一侧皮带的长度变化（扩展名）必须在另一边（或反之亦然），在长度变化（收缩）匹配，因为应该有长度无（净额）变化带，即 (6) 其中AE（以牛顿为单位）是电缆的刚性。使用等式（4），（5）和（6）的动态力可以被计算为; (7) (8)然后，EQN。 （4）变 (9)因此，动力系统可能由方程描述： （10）请注意，在（10），带传动中心的平移（x）是输入（强制）这个常微分方程的功能。来计算（5）中，先进的摩擦模型，该模型考虑微滑移，以在一定程度上被使用。在这项研究中，LuGre模型的模型，这已经通过各种研究已成功地适应12-15，被选择用于此目的。在其最简单的形式的模型被表示为： (11)在这里，0，1，2模型系数；Z n的内部状态代表平均的接触表面上的鬃毛偏转；代表Streibeck速度；和表示静摩擦系数和动摩擦系数。当同步带的纵向振动是被忽略的，一个简单的运动学分析解释了小齿轮和皮带之间的相对速度 ( 12)其中，是指小齿轮的偏心量，并代表该小齿轮的初始角度。 基于这些方程数值解的追捧。图3和图4分别示出了该模型的输入和输出。在图4中，另一个模型输出表示对应于一种情况，不存在摩擦现象了小齿轮和皮带之间时，他们遇到了。因此，模型1对应于阻尼结构和模型2对应于一个无阻尼的结构。3.测试设置 为了研究一个通用的同步带传动的传动误差特性，坐标测量机的线性阶段已经适应了。图5描述了这种设置，其中一个直流电动机具有一个内置的齿轮箱经由同步带驱动滑架。这种设置的示意图在图6还给出而表1列出的安排使用的元素的重要技术数据。 高分辨率的线性度（LS）被集成到安装程序，以帮助建模和验证了该模型的估计性能。请注意，在这种设置中，最好是控制该托架准确的加速度/减速度;这样的自定义运动控制器用于在系统中。为了确定由传输系统中，位置引入的位移误差 主编码器（PE）的测量值与被直接耦合到所述线性段的滑架，该高分辨率线性标尺的相比较。然而，LS的测量轴和该PE的不会由于通过该级的物理布局所施加的限制相一致。因此，阿贝偏置误差将被列入间接观测到的位移误差;参见图7中的系统的元件具有几个缺点，还有与这些元件相关的多个硬和软的非线性;间隙（变速箱+同步带），时间延迟（正时皮带），摩擦（轴承），所述带的粘弹性行为，等等。因此，通过使用间接测量技术估计带传动的位置被证明是相当具有挑战性，并需要大量的建模工作。测量之间的差异采用下列形式通过传输系统： (13) 其中和是指位置测量的LS和PE分别。在这里，和表示阿贝偏移值。此外，和主轴和小角度旋转的位移误差由传输系统介绍。由于在（13）构成要素即抗摩擦轴承支持，相关的几何/运动学误差轴承轴；传动误差，以进行分离，通过相关的变换。图8描述了这样的位移误差和转角测量轴的主。 4.实验 在这项研究中，几个试验。首先，运动的重复性研究为前提，设计出可靠的参考模型。在这些测试中，电机的速度控制梯形路径准确地在图9中，所得到的位置跟踪误差在图10所示（基本上到零稳态）可以假定低，对于所有的实际目的。在这些条件下，定位误差模式（x = XLS -XPE）十二种不同的轨迹重叠印图11。它可以通过图12中的频率图进行验证，定位误差表现出滞后的特点，他们是非常可重复的。此属性表明先进的估计模型 16的发展。运输定位误差数据采集，然后通过一个低通滤波器被消除通过传动系统的介绍了高频谐波（变速箱+同步带）。事实上，在图11中的错误模式的仔细检查显示有关系统性能的关键点在调查： 正如前面提到的，阿贝偏移误差表现为上、下边界波形。因此，轴承零件的机械操作通常表现出不同的纹理在这些边界。 一个基本的谐波分量的大小与10微米的叠加到乐队和其频率等于齿通过频率的带，因此这些变化可以归因于形成的带误差 谐波是由电机的两级变速箱诱导似乎是完全可以忽略不计，而在间隙区的宽度为0.12毫米的过渡是非常快的带传动改变其运动方向。 未来的实验集中在速度上的传输误差的影响。图13显示了五个不同的位移误差沿跨度全行程的机制。正如从图中可以看出，在稳态速度急剧变化的非线性关系的性质只有轻微的影响。 最后，通过改变加速的电机，滑动的磁滞带内诱导的减速曲线研究了惯性力的影响。正如从图14可以看出，惯性力没有在截止距离相当大的影响。同样地，图15阐述关闭的距离时，运动的方向是在不同的中间位置颠倒。有趣的是，当运动的方向是相反的，动力传动齿脱离和微滑移的外部激励下的占主导地位的。作为这种现象的后果，带慢慢滑到齿对下一组从事传动。有一些努力开发动态模型，这种现象的解释满意，这种先进的模型的发展是一个活跃的研究领域在摩擦学中的 17 。 5。同步带机构的运动学模型 尽管他们在精密机械常用的传动元件，弹性的传输特性在文献中还没有得到充分的评估。因此，一个简单而有效的运动模型是本研究设计。不幸的是，轨迹被跟踪的频带内可以相当复杂，由于微滑移的过程成为占主导地位的地区并不能令人满意地描述。因此，而不是开发复杂的动态模型，用大量的自由参数；更务实的做法是在本文后面。事实上，轨迹呈现在图15显示三种不同的发展模式具有不同的物理意义和计算成本。这些模型的解释下。5.1模式1：线性过渡 首先，建立了滞环模型如图16所示。根据不同的行驶方向x和位置注册时的方向变化，线性路径遍历在乐队。 这里，A，B，米表示各行的值而H描述的滞后带。在这个表达式中，KIS时间指数;点x（k）是在t = KT whiley主编码器的位置（k）表示位置误差ATT = kT.Note即XD和码对应于主编码器的位置和误差，分别在运动方向上的变化被登记： (15)(16)5.2。模式2：指数化转变：作为第二替代方案中，该模型在图17中被考虑在内。在这个模型中，当运动方向发生变化，以指数路径遍历循环中作为.这里，A，B，A，B表示的指数曲线的参数而Xd和Yd是如（15）中所定义，（16）。 5.3。模式3：线性插值作为第三个和更全面的模型，线性插值模型代表的滞后带内跃迁被认为是：(18)其中F，R分别表示查找表的下部和上部带而ft和rt表示 使用印刷在图15中的瞬态数据创建多维查找表。 6结果与讨论。前两个模型的交叉检查，这些模型的第一个自由参数，通过最小二乘法使用相关的实验数据来确定。表2以表格形式列出这些参数。相对于所述第三（内插）模型，有关的参数是从那些线性模型的继承，而这已经得到了总共650个数据点的二维查找表，使用的是图15中的特性曲线而形成。一旦这些模型和查找表形成，所有的模型的估计性能通过一个复杂的方案，其中的滑架，如图18，通过它的路线突然改变其运动方向areassessed的估计位置误差结果在图19给出通过24.Similarly，表3归纳了所得到的数据的统计信息;模型是通过一个复杂的方案，其中的滑架，如图18，通过它的路线突然改变其运动方向上进行评估。估计位置误差结果在图19通过24.Similarly给出，表3归纳了所得到的数据的统计信息;请注意，在表3中，根均方误差被定义为 (19)模型1和2的性能非常接近彼此，由于这一事实，即拟合曲线十分相似。正如预期的那样，线性插值会产生最佳的性能，因为它是用于形成查找表中的数据基本上捕获过渡区域的本质。7结论本研究包括了一些经常使用在运动控制系统中的同步皮带机构的重要方面。本文的要点是：正时皮带驱动机构，它可以在运动控制系统的设计中使用的动态模型，推导出。仿真结果，这是基于发展模式，都与实验结果有很好的一致性。的实验研究，研究了这种机制的属性。在实验中，大量的数据在不同的工作条件下收集。所收集的数据被证明是在空间和时间中重复的字符。高重复性暗示的不同位置估计/观测技术的发展（和部署）。 一个巨大的错误减少（从365微米到30微米的水平达到先进水平）插值方法。所提出的技术，它依赖于间接测量，不会带来额外的（硬件）的整体系统成本。 本文阐明了先进的估计算法是非常有效的当传动系统不受外部荷载以及广泛变化的操作条件，如温度和皮带张力。Analysis and estimation of motion transmission errors of a timing belt drivehis paper focuses on viable position estimation schemes for timing belt drives where the position of the carriage (load) is to be determined via reference models receiving input from a position sensor attached to the actuator of the timing belt. A detailed analysis of the transmission error sources is presented, and a number of relevant mathematical models are developed using a priori knowledge of the process. This paper demonstrates that such schemes are very effective when the drive system is not subjected to external loads and operating conditions do not change considerably i.e. ambient temperature, belt tension.Key Words:Timing belts, error estimation, indirect measurement, accuracy enhancement.1. IntroductionTiming belt drives are increasingly utilized to convert rotary motion into translation in high-precision motioncontrol systems e.g. inkjet printers, plotters, specialized CNC machine tools, filament winding machines, rapid prototyping machines, vision systems, and some bio-medical equipment 1. In such machines, the carriage which houses a special apparatus is usually driven by an elastic transmission element e.g. timing belt. Thus,the linear motion of the apparatus must be controlled accurately via direct position measurements so as to attain the goals of the particular task at hand.The main disadvantage of elastic elements in such arrangements is that they introduce well-known nonlinearities i.e. friction, elasticity, backlash, time delay, to the servo loop 2. Therefore, in order to achieve the desired precision and positioning accuracy, advanced control schemes 1-6 accompany direct measurement/feedback techniques frequently. It is critical to note that when the characteristic travel-span/stroke of a generic machine is very long (0.5 m); the use of direct measurement techniques which includes traditional sensors i.e. potentiometers, LVDTs, linear scales, laser interferometers leads to both bulky and relatively expensive solutions. Hence, the main motivation of this paper is to propose feasible estimation schemes that use the information emanating from a low-cost sensor on the pulley of the drive so that the position of the carriagecan be estimated to the desired accuracy for “not-so-demanding” applications.It is critical to note that such a paradigm requires a good model for the transmission errors (TEs) of timing belt mechanisms. Despite the fact that the definition of TE along with the corresponding measurement and evaluation techniques is well-known in gear (dynamics) literature 7, there are only a handful of studies that focus on the TE characteristics of timing belt drives alone. For instance, Kagotani et al. 8 present a brief overview of the relevant literature in this field. Their study investigates the transmission errors of helical timing belts over a period of one pitch of the pulley both theoretically and experimentally.The rest of the paper is organized as follows. After this brief introduction, The system is modeled mathematically and simulation results are presented. Next, the experimental setup is described. Then, some experiments made to investigate the transmission characteristics of a generic timing belt drive is reported. Based on the data collected, this paper makes a detailed analysis of the source of position errors. Upon these results kinematic models are presented in the following section. The next article evaluates the estimation performance of the proposed models. Finally, the paper is concluded with the key points of the study.2. Mathematical modeling and simulationFigure1 illustrates the mathematical model of the linear guided carriage system. In that system, the motionof the motor is transmitted to the carriage via timing belt mechanism. There must be an enough clearancebetween the meshing teeth to ensure smooth motion without interlocking.This backlash in the mechanism results in hysteresis phenomenon. There are many studies utilizing the Preisach model to describe the hysteretic effects encountered in various disciplines. An elementary hysteresis operator is purely defined by the Preisach model asWhere and correspond to up- and down switching value of the hysteresis band. Similarly, indicates each unique hysteresis elements in the system where as (, ) is an arbitrary weight function which must be defined for each system 9. Note that the Preisach model is the most famous one among other hysteresis models. However, it will not be considered in this study owing to the fact that the Preisach model exhibits non-local memory. That is, the current value of the output does not depend on only the current value of the input but also the past extremum values of the input. It is quite possible that two outputs coincide at time t0but results in completely different outputsv1(t)andv2(t)fortt0 hence they exposure to the same input u(t)fortt0 10. Another problem of this model is to determine the weight function. Experiments must be done on the system to determine this function. Moreover, equation (1) is a double integral equation. Its numerical implementation must be realized to use them in control system algorithms 11.There are two dynamic cases in the mathematical model: first one model the upper and lower hysteresis band as the system moves in a certain direction without interrupt and the latter one models the transient region when the carriage changes its motion direction. Also, Figure 1 shows the forces occurred in the timing belt.If the friction on the bearings of the pinion attached to the motor is neglected, the carriage will beactuated by the difference of the forces created in the timing belt. The free body diagram of the carriage is described in Figure 2(1)Thus, the equation of the motion of the Carriage may be written(2)Where stands for the Coulomb friction in the bearings of the Carriage. There will be an elastic deformation due to the contact between the timing belt and the pinion teeth. As a result, this creates an additional tension force difference (f) on the timing belt which may be written as; (3)In (3), h(0) m refers to gap/backlash between teeth of the timing belt and the pinion;kcorresponds to overall rigidity of the teeth. In this model, forces are created by the elastic deformation between the timing belts teeth and the pinions teeth. A possible configuration of this model is that the teeth are disengaged, the carriage changes its motion direction, and the timing belt teeth enter backlash region. Force is transmitted through only frictional forces developed between the pinion and belt. This phenomenon continues i.e. slippage until the backlash is closed between the pinion and timing belt teeth. The tensile forces on both sides of the timing belt become; (4)Here,F0 refers to the preload/tension on the belt. By definition, the perturbation forces (F1 and F2)on the belt are all non-negative quantities and less than the preload F itself to ensure the load-carrying capability of the belt. The Euler equation yields the relation between the tensile belt forces as 6 (5)Where is the winding (engagement) angle of the belt (in this case, multiples of ); (u) stands for the“kinetic” friction coefficient which depends on the relative circumferential speed between the pinion and the belt; andis the slip velocity. The compatibility condition requires that the change in length (extension) of the belt on one side must match with the change in length (contraction) on the other side (or vice versa) because there should be no (net) change in the length of belt, that is (6)Where AE (in units of Newtons) is the rigidity of the cable. Using equations (4), (5) and (6) dynamic forces may be computed as; (7)(8)Then, eqn. ( 4) becomes (9)Thus, dynamic system may be described by the equation (10)Note that in (10), the translation of the carriage center (x) is the input (forcing) function of this ordinary differential equation. To compute in (5), an advanced friction model, which considers micro-slip to a certain extent, is used. In this study, LuGre model, which has been successfully adapted by various studies 12-15, is selected for this purpose. The model in its simplest form is expressed as(11)where a, 0 , 1, 2 are the model coefficients; z is n internal state representing average deflection of the bristles on the contacting surfaces; stands for the Streibeck velocity; and denote the kinetic and static friction coefficients respectively. When the longitudinal oscillation of the timing belt is neglected, a simple kinematic analysis explains the relative velocity between the pinion and the belt: (12)Where refers to the eccentricity of the pinion and represents the initial angle of the pinion.Based upon these equations a numerical solution is sought. Figure 3 and Figure 4 show the input and output of the model respectively. In Figure 4, another model output is represented corresponding to a situation that there is no friction phenomena anymore between the pinion and belt when they met. So, Model 1 corresponds to a damped structure and Model 2 corresponds to an undamped structure.3. Test setupTo study transmission error characteristics of a generic timing belt drive, the linear stage of a CMM has been adapted. Figure 5 describes this setup where a DC motor with a built-in gearbox drives the carriage via a timing belt. A schematic of this setup is also given in Figure 6 while Table 1 tabulates important technical data of elements used in the arrangement.A high resolution linear scale (LS) is integrated into the setup to help modeling and to verify the estimation performance of the proposed models. Notice that in this setup, it is desirable to control the acceleration /deceleration of the carriage accurately; so a custom motion controller is used in the system.In order to determine the displacement errors introduced by the transmission system, the positionmeasurements of the primary encoder (PE) is compared with those of the high-resolution linear scale that is directly coupled to the carriage of the linear stage. However, the measurement axes of the LS and that of the PE does not coincide due to the limitations imposed by the physical layout of the stage. Therefore the Abbe offset errors will be indirectly included to the observed displacement errors; see Figure 7. The elements of the system have several shortcomings, there are several hard- and soft-nonlinearities associated with these elements; backlash (gearbox + timing belt), time delay (timing belt), friction (bearings), visco-elastic behavior of the belt, and more. Thus, estimation of the position of the carriage by using indirect measurement techniques proves to be quite challenging and demands extensive modeling efforts.The difference between the measurements takes the following form by the transmission system:(13)Where and refer to the position measurements of the LS and PE respectively. Here, andindicates the value of Abbe offsets. Moreover,and are the small angular rotations about principal axes and is the displacement error introduced by the transmission system. Since in (13) constitutes the geometric/kinematics errors associated with support elements i.e. anti-friction bearings, bearing shafts; the transmission error, has to be isolated via relevant transformations. Figure 8 describes such displacement errors and angular rotations about principal axes of this CMM.4. ExperimentsThroughout this study, several tests are conducted. First, the repeatability of the motion is studied as a prerequisite to devise reliable reference models. In all these tests , the motors velocity which is controlled along a trapez