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Contribution to the development of supplementary guidelines of embodiment design for roller conveyors D. 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. INTRODUCTION In 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 SYSTEMS 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 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 PROJECT The 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. 2010 Management and Control of Production Logistics University of Coimbra, Portugal September 8-10, 2010 978-3-902661-81-4/10/$20.00 2010 IFAC 47 10.3182/20100908-3-PT-3007.00012 Fig. 1. Roller conveyor 4. MEASUREMENT SYSTEM USED An 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 speed Furthermore, 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 container Fig. 4. Measuring conveying roller 5. GOAL OF RESEARCH With 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 two MCPL 2010 Coimbra, Portugal, Sept 8-10, 2010 48 response 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 EXPERIMENTATION A 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 level combination factor B factor C factor A = cube points = axial points = center point factor level combination factor B factor C factor A = cube points = axial points = center pointFig. 5. Central composite design Therefore 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 levels Level Factor - -1 0 + 1 + Conveyor speed m/s 0.29 0.42 0.66 0.90 1.02 Weight conveyed kg 15 20 30 40 45 Roller pitch mm 75 100 150 200 200 7. EVALUATION OF THE TEST RESULTS The 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 0.8 conveyor speed m/s 15 weight conveyed kg 20 25 30 35 40 45 0.9 1.0 0.7 0.6 0.5 0.4 0.3 0.9512 0.9507 0.9502 0.9502 0.9497 0.9492 0.9492 0.9497 0.9497Fig. 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 conveyor MCPL 2010 Coimbra, Portugal, Sept 8-10, 2010 49 speed 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/s 0.8 conveyor speed m/s 15 weight conveyed kg 20 25 30 35 40 45 23.99 16.99 0.9 1.0 0.7 0.6 0.5 0.4 0.3 25.74 22.24 20.49 18.74 15.99Fig. 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. 0.8 conveyor speed m/s 15 weight conveyed kg 20 25 30 35 40 45 16.99 0.9 1.0 0.7 0.6 0.5 0.4 0.3 0.9512 0.9507 15.99 Average vibration of the container m/s Quotient of the container speed and the conveyor speedFig. 8. Optimal parameter ranges of both response variables The 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. The 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 the MCPL 2010 Coimbra, Portugal, Sept 8-10, 2010 50 allover 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. 15 20 25 30 Formula Vibration m/s 15,873 0,947 0,948 0,949 0,95 0,951 0,952 Formula Slip 0,951151 0 0,25 0,5 0,75 1 Desirability 0,831709 50 100 150 200 101 10 15 20 25 30 35 40 45 50 19,92352 10 20 30 40 50 60 70 80 28,97342 0 0,25 0,5 0,75 1 Roller Pitch Weight Conveyed Frequency 100 20 29 Vibration Slip DesirabilityFig. 9. Desirability Profile Plot 8. CONCLUSION This analysis provides for the first time an opportunity to adapt the embodiment design of roller conveyors to customer requirements. For that purpose two requirements have been chosen and for them respectively one statistical model has been developed. The methodology of DoE (Design of Experiments) was used during the performance of the research project. In a pre-research those factors among the potential were determined which influence the conveying and the mechanical load on the components. These basic factors have been regarded in the further research. With the two models the response variables have been optimised. The factor levels of the predictor variables which affect the response variables have been identi