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【中文 4000 字】对辊式输送机实施设计补充指南发展的贡献摘要：目前，内部逻辑系统的规划和设计重点在于最大限度地满足机械要求的技术质量等级。这种顺应性通常是通过机械部件过大来实现的。由于大量的电驱动部件，因此在设计这种系统时重新定位尤为必要。针对内部逻辑系统的实施方案设计的当前指导方针不足以优化这些工厂关于其服务条件。这就是为什么改进的统计模型是在 DoE 的基础上开发出来的。这些模型有助于为这些工厂的实例设计产生新的指导方针。1.简介在过去五年里，内部物流业增长了大约 50（哈恩 - 沃尔纳）。德国知名的物流研究机构预测，未来内部医学系统的大量使用将继续增加。输送机系统的可靠性是最重要的要求之一，因为在内部逻辑系统发生故障的情况下，高成本的成本。对于内部语言学植物，声称超过 98的可用性。为了确保这一说法，制造商应对强大的模块和系统。此外，使用的标准组件已获得服务并在现场得到证实。对于内部统计系统的规划和安装，只需要很短的实现时间。这就是为什么常常使用标准组件的原因。另一方面，从所提到的这些问题，导致这些植物及其组分的尺寸过大。迄今为止，缺少能够适应要求的内部逻辑系统设计的实施方案设计准则。在智能维护概念（Kuhn 等人）的配合下，内部逻辑系统的规划和服务范围内存在优化需求。2.内在系统的实际设计目前，内部逻辑系统的规划和设计重点在于最大限度地满足机械要求的技术质量评级。考虑到高度的结构安全系数，通常通过加大机械部件来实现这种兼容性。输送过程中单个部件受到影响的程度（部件上的机械负载）被忽略。到目前为止，在粗略的参考值和经验值的帮助下进行了内部统计系统的实施设计。因此，如传送容器和传送的内容一样，边界条件未被充分考虑。由于电动部件众多，因此在输送机系统设计中的重新定位尤为必要。针对内部逻辑系统的实施方案设计的当前指导方针不足以优化这些工厂关于其服务条件。3.实现项目子项目 B1 的目标是为内部逻辑系统的实施方案设计生成适用的指导方针。该子项目是 DFG（德国研究基金会）资助的多特蒙德大学合作研究中心696“物流随需应变”项目的十二个子项目之一。首要任务之一是评估内部逻辑系统的当前发展状况。辊式输送机已被选为示例性工厂（图 1）。正是在这个工厂里，研究了工厂的参数及其处理对输送行为和部件的影响。关于内部逻辑系统的设计，传送容器和传送的内容都没有充分考虑。但是，这些会影响部件上的输送行为和机械负载。检测输送容器和部件上的机械负载的前提是收集 mesurands。为此，使用电子测量设备制备了输送容器和输送辊。根据被测量，统计模型已经在DoE（实验设计）的帮助下开发出来。这些模型有助于为内部逻辑系统的实例设计产生新的指导方针。图 1.滚筒输送机4.使用测量系统为实验分析开发了适用的测量系统。该系统由三部分组成。在测量部分安装了光纤光导传感器，以检测传送带速度。光源的红外光将被固定在输送辊包层上的反射器反射（图 2）。通过这个信号可以计算输送辊的圆周速度。图 2.确定传送带速度的测量系统此外，通常的输送容器已经准备好具有挡光板的接收器。容器的有效速度可以与安装在测量部分上的两个挡光板发射器结合使用进行诊断。在输送容器的底部安装一个加速度传感器，可以测量三个轴的加速度。因此在运输过程中可以测量作用在容器上的振动（图 3）。第三个测量部件是测量输送辊。为此，轴的每一端都配有两个力传感器。这样就可以测量重力加速度和输送方向的力（图 4）。因此输送辊上的机械负载是可诊断的。图 3.测量输送容器图 4.测量输送辊5.研究成果在 DoE（实验设计）的帮助下，必须针对选定的客户需求开发统计模型。通过这个回归分析被使用。回归分析是一种统计学方法，利用两个或更多定量变量之间的关系，以便可以从其他变量或其他变量中预测一个变量。在这个过程中，变量之间的函数关系用数学公式表示。因此描述了预测变量对响应变量的影响（Kutner 等人）。设备的特定参数及其处理对输送过程有影响。这种影响将在未来由这些模型预测。输送容器由工厂中串联布置的输送辊承载和驱动。当输送辊上升时，输送容器受到振动。正如一些预研究所显示的那样，这些碎石的强度和频率取决于输送辊的距离（输送辊间距），输送机速度和输送的重量。此外，在输送辊的包层和输送容器的底部之间存在相对速度。这个滑移的数量也取决于前面提到的三个参数。在第一步中，分析了两个响应变量。这些一方面是输送容器达到的有效速度与输送器速度的商，另一方面是影响容器的振动的平均值。输送辊间距，输送机速度和输送重量被选为预测变量。在进一步分析中，输送辊上的机械负载将被确定为第三响应变量。6.设计和试验已经创建了一个中央复合设计来进行实验。这样的设计对于将曲面二次曲面建模为连续因子很有用。如果两者中的任何一个在因子区域内，则中央复合模型可以精确定位最小或最大响应。每种情况下的因素都设定为五个等级。这个设计可以绘制三个因素（图 5）。它将全因子设计（立方体点（-1 / + 1）与另外两个部分（轴向点（-/ +）和中心点（ 0）组合在一起。一个完整的因子设计由所有因素水平的组合组成（Kleppmann）。图 5.中央复合设计因此必须确定这些因素的可接受共域。传送带速度通过变频器无级变化。目前安装的设备的传送带速度范围为 v = 0.3 m / s 至 v = 1.0 m / s。所使用的容器对输送重量的限制为 m = 50kg。由于安装了测量设备和传输技术，测量输送容器的净重平均为 m = 15kg。属于输送容器的组件的面积是 A = 600400mm 2。输送辊之间的最大可接受距离为 t = 200 mm，因为容器应始终由三个输送辊承载以防止倾斜。辊的直径是 d = 50mm。所以最小距离是 t = 75 毫米（25 毫米可用空间）。根据这些共域选择特定的因子水平（表 1）。表 1.因子水平等级因素- -1 0 + 1 + 带速m/s0.29 0.42 0.66 0.90 1.02传送物重量 kg 15 20 30 40 45滚子周节 mm 75 100 150 200 2007.测试结果的评估测试结果的评估涉及两种模型，其中四次多项式形成基础。这些模型用于确定滚筒和容器之间的滑动以及容器在重力加速度方向上的平均振动。根据工厂的某些参数和处理情况，这些模型可以诊断由输送造成的对容器的影响。这些模型可以在等值线图中进行说明。等值线图是二元函数的二维描述。轮廓线中描述了特定点的功能值。图 6.响应变量“容器达到的速度与传送带速度的商”的等值线图在这个分析中，已经分析了三个预测变量。要在等值线图中绘制模型，必须保持一个预测变量不变。在这种情况下，轮廓图是针对 t = 100 毫米的恒定输送辊间距进行绘制的。根据传送带速度和传送的重量绘制响应变量（图 6 和7）。在图 6 中，绘制了容器达到的速度与输送机速度的商。由于输送辊的距离也影响输送机速度，因此选择最小输送辊间距处的输送机速度作为参考值。 1的响应表示辊和容器之间不存在滑动。通过图表可以清楚地看出，在 v = 0.38 - 0.48 m / s 和 m = 15 - 18 kg 的范围内可以达到最高响应变量。确定容器平均振动的模型如图 7 所示。很明显，如果传送的重量和设备的速度保持在一定限度内，由输送引起的振动将会减少。 v = 0.44 m / s 和 m = 24.5 kg 或 v = 0.40 m / s 和 m = 37 kg 时振动最小。图 7.响应变量“容器在重力加速度方向上的平均振动”的等值线图通过将图的最佳范围放在彼此之上，参数的范围变得清晰，其中两个响应变量可以被优化（图 8）。为了减少这两者，应该选择输送容器的平均振动以及输送辊和输送容器之间的相对速度：在 m = 18-20kg 和 v = 4.35m / s 的输送机速度之间输送的重量。但是这些参数仅在 t = 100 mm 的输送辊间距时有效。图 8.两个响应变量的最佳参数范围考虑到所有三个预测变量，将比较每个输送辊间距的轮廓图以优化两个分析的响应变量。这种优化方式非常耗时。优化响应变量的另一种方法是使用统计软件 JMP 的合意性分析器。如果在分析中已经测量了多个响应变量并且结果的可取性涉及多个或全部这些响应，则该功能是必需的。例如，一个响应变量必须最大化，另一个最小化，第三个必须保持接近目标值。通过 JMP 的合意性分析器，可以为每个响应变量指定一个合意函数。整体合意性可以定义为每个响应变量的合意性的几何平均数（SAS Institute Inc.）。为了获得无振动的输送过程，响应可变振动应该被最小化。输送辊上的输送容器的滑动也应该最小化。响应变量是输送容器达到的速度与输送速度的商。1 的回答表示不存在任何单据。这就是为什么响应变量必须最大化以最小化滑差。使用 JMP 进行优化的结果在图 9 中给出。图的最后一列显示了每个响应变量的可调整的合意性函数。响应变量振动必须最小化并且响应变量滑移必须最大化。图 9 中曲线的最后一行显示了每个响应的合意迹线。最后一行纵坐标图中“合意”字旁边的数值是合意度量的几何平均值。预测变量旁边的数值是预测变量的因子水平，可以优化整体满意度。通过理想的轮廓仪必须选择 t = 100mm 的辊距和 m = 20kg 的重量，并且必须将输送带速度可调节的变频器设置在频率 f = 29Hz 至达到最好的整体愿望。 f = 29 Hz 的频率相当于 v = 0.42 m / s 的传送带速度。这些值与图形优化的值几乎相同。图 9.合意性剖面图8.结论这种分析首次提供了一个机会，使辊式输送机的实施方案设计符合客户的要求。为此目的，已经选择了两个要求，并分别为它们制定了一个统计模型。在研究项目的执行过程中使用了 DoE（实验设计）的方法。在预研究中，确定潜在因素中影响部件输送和机械负载的因素。在进一步的研究中已经考虑到了这些基本因素。通过这两个模型，响应变量得到了优化。已经确定影响响应变量的预测变量的因子水平以达到这种优化。在该分析中已经考虑了两个响应变量：输送容器的振动和输送辊与输送容器之间的滑动。在进一步的实验中将考虑另一个要求。这将是内部学工厂的机械负载，这将通过已经设计的测量辊来确定。通过测量，将开发另一种统计模型来预测输送辊上的机械载荷。这个模型将被用于与另外两个模型结合起来，为辊式输送机的实施设计设定新的指导方针。如果提供了多个预测变量或响应变量，我们将能够从图中查看自由参数或通过模型公式计算它们。基于此，可以确定输送辊上的机械负载。借助于这些特性，可以根据机械载荷来设计标准部件，或者可以从模块化结构系统中选择它们。2010 Management and Control of Production Logistics University of Coimbra, PortugalSeptember 8-10, 2010Contribution to the development of supplementary guidelines of embodiment design for roller conveyorsD. Wieczorek*. B. Knne*TU Dortmund University, Dortmund, Germany(Tel.: 49-231-7552751; e-mail: dorothee.wieczorektu-dortmund.de)* TU Dortmund University, Dortmund, Germany(Tel.: 49-231-7552602; e-mail: bernd.kuennetu-dortmund.de)Abstract: Currently the focus of planning and designing intralogistic systems lies on the technical quality rating in the form of maximum fulfilment of the mechanical requirements. This compliancy is often achieved by oversizing the mechanical components. A re-orientation in designing such systems is especially necessary because of the multitude of electrically-driven components. The current guidelines for embodiment design for intralogistic systems are not sufficient to optimise such plants regarding their service conditions. That is why adapted statistical models have been developed with the help of DoE based on measurands. These models conduce to generate new guidelines for embodiment design for such plants.1. INTRODUCTIONIn the last five years the intralogistic industry has grown by approximately 50% (Hahn-Woernle). Leading German institutes for logistics prognosticate that the large employment of intralogistic systems will continue to increase in the future. The reliability of conveyor systems ranks among the most important requirements because of the high consequential costs in case of malfunction of intralogistic systems. For intralogistic plants availabilities of more than 98% are claimed. In order to ensure this claim manufacturers react with robust modules and systems. Furthermore, standard components are used which have been approved in service and proved themselves in the field. For the planning and the installation of intralogistic systems only a short realisation time is available. That is why standard components often are used. From these problems mentioned, on the other hand, results an oversizing of such plants and their components. Heretofore, guidelines for embodiment design which enable a design of intralogistic systems adapted to requirements have been missing. There exists demand on optimisation in the range of planning and service of intralogistic systems in conjunction with an intelligent maintenance concept (Kuhn et al.).2. ACTUAL EMBODIMENT DESIGN OF INTRALOGISTIC SYSTEMSCurrently the focus of planning and designing intralogistic systems lies on the technical quality rating in the form of maximum fulfilment of the mechanical requirements. This compliancy is often achieved by oversizing the mechanical components considering a high constructional safety factor. The degree to which individual components are affected (the mechanical load on the components) during the conveying process is disregarded. Up to now the embodiment design of intralogistic systems has been carried out with the help of rough reference values and empirical values. Thereby,boundary conditions, like the conveying container and the content conveyed, are not adequately considered. A re- orientation in designing conveyor systems is especially necessary because of the multitude of electrically-driven components. The current guidelines for embodiment design for intralogistic systems are not sufficient to optimise such plants regarding their service conditions.3. RESEARCH PROJECTThe goal of the subprojekt B1 is to generate applicable guidelines for embodiment design of intralogistic systems. This subproject is one of twelve subprojects of the Collaborative Research Center 696 Logistics on Demand“ at TU Dortmund University funded by the DFG (German Research Foundation). One of the first tasks was to evaluate the current development status of intralogistic systems. The roller conveyor has been chosen as an example plant (Fig. 1). It is this very plant at which the influence has been researched which the parameters of the plant and its handling have on the conveying behavior and the components. Both the conveying container and the content conveyed are not adequately considered as regards the design of intralogistic systems. These, however, do have influence on the conveying behavior and the mechanical load on the components.The detection of the mechanical load on the conveying container and the components presupposes the collection of mesurands. For that purpose a conveying container and a conveying roller have been prepared with electronic measuring equipment. Based on the measurands statistical models have been developed with the help of DoE (Design of Experiments). These models conduce to generate new guidelines for embodiment design of intralogistic systems.978-3-902661-81-4/10/$20.00 2010 IFAC 47 10.3182/20100908-3-PT-3007.00012MCPL 2010Coimbra, Portugal, Sept 8-10, 201048Fig. 1. Roller conveyor4. MEASUREMENT SYSTEM USEDAn applicable measurement system has been developed for the experimental analysis. This system comprises three components. A fiber-optic light guide sensor has been installed on the measured section to detect the conveyor speed. The infrared light of the light source will be reflected by the reflector affixed to the cladding of a conveying roller (Fig. 2). By this signal the peripheral speed of the conveying roller can be calculated.Fig. 2. Measuring system to determine the conveyor speedFurthermore, a usual conveying container has been prepared with a receiver of a light barrier. The effective speed of the container is diagnosable in combination with two transmitters of a light barrier installed on the measured section. At the bottom of the conveying container an acceleration sensor is affixed which is able to measure the acceleration in three axes. So the vibration acting on the container can be measured during the conveyance (Fig. 3).The third measuring component is a measuring conveying roller. For that purpose each end of the axis is fitted with two force sensors. In this way the forces in the direction of the gravitational acceleration and in the conveying direction can be measured (Fig. 4). Thereby the mechanical load on the conveying roller is diagnosable.Fig. 3. Measuring conveying containerFig. 4. Measuring conveying roller5. GOAL OF RESEARCHWith the help of DoE (Design of Experiments) statistical models have to be developed for selected customer requirements. By this Regression Analysis was used. Regression Analysis is a statistical methodology that utilises the relation between two or more quantitative variables so that one variable can be predicted from the other, or others. In that process a functional relation between variables is expressed by a mathematical formula. Thereby the effects of the predictor variables on the response variable are described (Kutner et al.).The particular parameters of the plant and its handling have an influence on the conveying process. This influence is to be predicted by these models in the future. The conveying container is carried and driven by conveying rollers arranged in series in the plant. While ascending a conveying roller the conveying container is exposed to vibration. The intensity and the frequency of these crushes depend on the distance of the conveying rollers (conveying roller pitch), the conveyor speed and the weight conveyed, as shown by some pre- research. Furthermore, there exists a relative speed between the cladding of the conveying rollers and the bottom of the conveying container. The quantity of this slip also depends on the three parameters mentioned before. In a first step twoMCPL 2010Coimbra, Portugal, Sept 8-10, 2010490.94920.94970.94920.94970.95020.9512 0.9507 0.95020.9497response variables have been analysed. These are on the one hand the quotient of the effective speed reached by the conveying container and the conveyor speed, and on the other hand the average of the vibration which influences the container. The conveying roller pitch, the conveyor speed and the weight conveyed were chosen as predictor variables. In a further analysis the mechanical load on the conveying rollers will be determined as a third response variable.6. DESIGN AND EXPERIMENTATIONA central composite design has been created to carry out the experiments. Such a design is useful for modeling a curved quadratic surface to continuous factors. A central composite model can pinpoint a minimum or maximum response, if either of the two is inside the factor region. The factors are set at five levels in each case. This design can be graphed for three factors (Fig. 5). It combines a full factorial design (cube points (-1/+1) with two further parts, the axial points (-/+) and a center point (0). A full factorial design consists of all combinations of the levels of the factors (Kleppmann).factor Cfactor Bfactor Afactor level combination = cube points= axial points= center pointFig. 5. Central composite designTherefore the acceptable co-domains of the factors have to be identified. The conveyor speed is steplessly variable by a frequency converter. The conveyor speed of plants currently installed ranges from v = 0.3 m/s to v = 1.0 m/s. The allowance for the weight conveyed is limited to m = 50 kg by the container which is used. The net weight of the measuring conveying container averages m = 15 kg because of the measuring equipment and transmission technology installed. The area of assembly belonging to the conveying container is A = 600 x 400 mm. The maximum acceptable distance between the conveying rollers is t = 200 mm because the container should always be carried by three conveying rollers to prevent tilting. The diameter of the rollers is d = 50 mm. So the minimum distance is t = 75 mm (25 mm free space). The particular factor levels have been chosen according to these co-domains (Table 1).Table 1. Factor levelsLevelFactor - -1 0 + 1 + Conveyor speed m/s 0.29 0.42 0.66 0.90 1.02Weight conveyed kg 15 20 30 40 45Roller pitch mm 75 100 150 200 2007. EVALUATION OF THE TEST RESULTSThe evaluation of the test results involves two models, of which a polynomial with the degree four forms the basis. These models are to determine the slip between the rollers and the container and the average vibration of the container in the direction of the gravitational acceleration. The effect on the container caused by the conveying can be diagnosed with these models depending on certain parameters of the plant and the handling. The models can be clarified in contour diagrams. A contour diagram is a two-dimensional description of a bivariate function. The function value at a specific point is described in a contour line.Quotient of the container speed and the conveyor speed 1.00.315 20 25 30 35 40 45weight conveyed kgFig. 6. Contour diagram of the response variable “quotient of the speed reached by the container and the conveyor speed”In this analysis three predictor variables have been analysed. To plot the models in a contour diagram one predictor variable has to be kept constant. In this case the contour diagrams are drafted for a constant conveying roller pitch of t = 100 mm. The response variables are plotted against the conveyor speed and the weight conveyed (Fig. 6 and 7). In the diagram in Fig. 6 the quotient of the speed reached by the container and the conveyor speed is drawn. The conveyorconveyor speedm/sMCPL 2010Coimbra, Portugal, Sept 8-10, 20105025.7423.9922.2420.4918.7416.9915.9916.9915.990.9512 0.9507speed at the minimum conveying roller pitch has been chosen as the reference value because the distance of the conveying rollers also influences the conveyor speed. The response of 1 represents that no slip is existing between the rollers and the container. It becomes clear by means of the diagram that the highest response variable will be reached in the range of v = 0.38 - 0.48 m/s and m = 15 - 18 kg.The model to determine the average vibration of the container is shown in Fig. 7. It becomes clear that the vibration caused by the conveying will be reduced if the weight conveyed and the velocity of the plant remain within a certain limit. The least vibration will be reached by v = 0.44 m/s and m = 24.5 kg or v = 0.40 m/s and m = 37 kg.Average vibration of the container m/s1.00.91.00.315 20 25 30 35 40 45weight conveyed kg15 20 25 30 35 40 45weight conveyed kgQuotient of the container speed and the conveyor speedAverage vibration of the container m/sFig. 8. Optimal parameter ranges of both response variablesThe contour diagrams of every conveying roller pitch are to be compared to optimise the two analysed response variables considering all three predictor variables. This way of optimisation is very time-consuming.An alternative way to optimise the response variables is to use the desirability profiler of the statistical software JMP. This function is necessary if in an analysis multiple response variables have been measured and the desirability of the outcome involves several or all of these responses. For example, one response variable has to be maximised, another minimised and a third one has to be kept close to a target value. With the desirability profiler of JMP it is possible to specify a desirability function for each response variable. TheFig. 7. Contour diagram of the response variable “average vibration of the container in the direction of the gravitational acceleration”By putting the optimal ranges of the diagrams on top of each other the range of the parameters becomes clear in which both response variables can be optimised (Fig. 8). To reduce both, the average vibration of the conveying container and the relative speed between the conveying rollers and the conveying container a weight conveyed between m = 18 - 20 kg and a conveyor speed of v = 4.35 m/s should be chosen. But these parameters are valid only at a conveying roller pitch of t = 100 mm.overall desirability can be defined as the geometric mean of the desirability for each response variable (SAS Institute Inc.).To get a vibration-free conveying process the response variable vibration should be minimised. The slip of the conveying container on the conveying rollers should be minimised, too. The response variable is the quotient of the speed reached by the conveying container and the conveying speed. A response of 1 represents that no slip is existing. That is why the response variable has to be maximised to minimise the slip.The result of the optimisation with JMP is given in Fig. 9. The last column of the plot shows the adjustable desirability function for each response variable. The response variable vibration has to be minimise and the response variable slip has to be maximise. The last row of the plot in Fig. 9 shows the desirability trace for each response. The numerical value beside the word “desirability” in the plot on the vertical axis of the last row is the geometric mean of the desirability measures. The numerical value beside the predictor variables is the factor level of the predictor variables with which theconveyor speedm/sconveyorspeedm/sMCPL 2010Coimbra, Portugal, Sept 8-10, 201051101 19,92352 28,97342 s/mno i tabr iVSlip150200allover desirability can be optimised. By means of the desirability profiler a roller pitch of t = 100 mm and a weight conveyed of m = 20 kg have to be chosen and the frequency converter with which the conveyor speed is adjustable has to be set on the frequency f = 29 Hz to reach the best allover desirability. The frequency of f = 29 Hz is equivalent to a conveyor speed of v = 0.42 m/s. These values are nearly the same like the values of the graphical optimization.302520150,9520,9510,950,9490,9480,947In this analysis two response variables have been considered: the vibration of the conveying container and the slip between the conveying rollers and the conveying container. In further experiments another requirement will be considered. This will be the mechanical load on the intralogistic plant which will be determined with the measuring roller already engineered. By means of the measurands a further statistical model will be developed to predict the mechanical load on the conveying rollers. This model will