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2. MATERIALS AND METHODS
At the next step, the synthesis of layouts is conducted based on the consideration of the MS (A ), matrix, which is included in the basic equation of MS formation
¯
r0=A e¯4 (1)
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Table I. Variations of matrix modificationAmandAt.
Option number Am At
1. A4A2−HyA3−HzA4− A4A2HyA3HzA4−At
2. A5A1−HxA3−HzA5− A5A1HxA3HzA5−At
3. A6A1−HxA2−HyA6− A6A1HxA2HyA6−At
4. A4A2HyA3HzA3p A4−A2−HyA3−HzA3−pAt
5. A4A2HyA3HzA2p A4−A2−HyA3−HzA2−pAt
6. A5A1HxA3HzA3p A5−A1−HxA3−HzA3−pAt
7. A5A1HxA3HzA1p A5−A1−HxA3−HzA1−pAt
8. A6A1HxA2HyA1p A6−A1−HxA2−HzA1−pAt
9. A6A1HxA2HyA2p A6−A1−HxA2−HzA2−pAt
where e¯4—radius vector of origin e¯4 = 0 0 0 1T MC and changes in the struc- ture of MS, by modifying the decomposition of the matrix A as
A =Aa1AmAa2At (2) where Aa1, Aa2—fixture coordinate transformation matri- ces; Am—machine coordinate transformation matrix;
At—tool coordinate transformation matrix.
Example.Let be
A =A6A3zA1x (3) whereA6—matrix, taking into account the rotation of the workpiece around theZaxis at an angle
A6=
⎡
⎢⎢
⎣
cos −sin 0 0
sin cos 0 0
0 0 0 0
0 0 0 1
⎤
⎥⎥
⎦ (4)
Fig. 1. Functional model of the synthesis process for machining parts with double curvature surfaces.
A3z—Z-axis transition matrix
A3z=
⎡
⎢⎢
⎢⎢
⎢⎣
1 0 0 0
0 1 0 0
0 0 1 z
0 0 0 1
⎤
⎥⎥
⎥⎥
⎥⎦
(5)
A1x—X-axis transition matrix
A1x=
⎡
⎢⎢
⎢⎢
⎢⎣
1 0 0 x
0 1 0 0
0 0 1 0
0 0 0 1
⎤
⎥⎥
⎥⎥
⎥⎦
(6)
(1) at the firs step, the matrixA results in the form A =AmAt (7) whereAm=E;
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(2) modify the matricesAmandAt using the approaches, given in Table I.
In Table I adopted the following designation:
A4,A5,A6—around the axesX,Y,Z;
A1Hx, A2Hy,A3Hz—along the axesX,Y, Z;
Fig. 2. Formation of the system of machined surfaces.
—rotation parameter of the workpiece or tool;
Hx, Hy, Hz—parameters of the initial displacement of the tool relative to the workpiece, respectively, along the axesX,Y,Z;
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P—the rate of the linear movement of the tool to the parameter of the workpiece rotation [11].
3. RESULTS AND DISCUSSION
On the basis of the proposed concept of the methodol- ogy for the synthesis of processing circuits for parts with double curvature surfaces, it is advisable to consider the synthesis process as a system of interrelated functional transformations (Fig. 1): description of the processed sur- face; synthesis of initial structures of SS; modification of initial structures of SS; synthesis of tool-making surfaces;
the formation of the space design parameters of tools.
The implementation of the transformation “Description of the machined surface” is connected with the need for a mathematical representation of this surface as a function and its parameters in homogeneous coordinates based on the vector of structural parameters of the machined surface and parameters determining its position relative to the part.
In work [12], the question of the mathematical represen- tation of the description of various surfaces was consid- ered in detail; therefore, we consider only a few points. We will consider surfaces that allow four ways of presentation (Fig. 2).
Issues related to the implementation of the transforma- tion “Synthesis of the initial structures of CC” were dis- cussed in detail in works [1–8], where the structure of the shaping system was described as a model consisting of the coordinate code of the shaping system and the corre- sponding transformation (Fig. 3). Thus, the synthesis of CC structures should include three main stages: the forma- tion of coordinate and velocity CC codes; distribution of formative movements between the machine, devices and tools; formation of layout codes CC. At this stage, the main dimensional chains are identified that correspond to the processing of specified surfaces.
As a result of such modeling, each element of the tech- nical maintenance (machine, tool and tool) will have its
Fig. 3. Synthesis of variants of the structure-forming system.
own set of shaping movements. To implement the transfor- mation “modification of the initial structures of the CC”
in the framework of the developed concept, it is proposed to obtain additional variants of high-performance process- ing schemes that correspond to milling with a mill with a constructive radial feed and pull, perform additional trans- formations discussed earlier. To implement the transforma- tion “Synthesis of producing surfaces of tools,” it is vital to evaluate the nodes of the producing faces of the tool in its own coordinate system, under which all the shaping statuses will be fulfilled (which will be discussed later).
4. CONCLUSION
In order to form the space of design factors, within the framework of the transformation “Forming the space of design parameters of tools,” it is advisable to build a com- plex of mathematical models, which will allow creating the space of the initial design parameters essential for a given project level in the early design stages and establish analyt- ical dependencies (dimensional relationships and material properties) between the design parameters and the main indicators of quality.
Acknowledgments: The work was supported by a scholarship of the President of the Russian Federation to young scientists and graduate students. Project number CII-2950.2019.1.
References
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pp.282–286.
2. Reshetov, D.N.,1986. Accuracy of machine tools.Mechanical Engi- neering, edited by D. N. Reshetov and V. T. Portman, Moscow, Russia, Science Technology in North, pp.335–339.
3. Kuts, V., Ivakhnenko, A. and Khandozhko, A.,(2015). Cutting force research influence on the formation of double curvature surfaces in technological systems with parallel structure mechanisms.2015 International Conference on Mechanical Engineering, Automation and Control Systems(MEACS), Tomsk, pp.1–4.
4. Ivakhnenko, A.G.,2010.Structural-Parametric Synthesis of Techno- logical Systems, edited by A. G. Ivakhnenko and V. V. Kuts, Kursk, State Tech. Un-t. Kursk. pp.150–160.
5. Ivakhnenko, A.G.,2013.Pre-Design Studies of Metal-Cutting Sys- tems, edited by A. G. Ivakhnenko and V. V. Kuts, Kursk, Southwest State University, pp.180–189.
6. Ivakhnenko, A.G.,2015. Methodology of structural-parametric syn- thesis of metal-cutting systems. Monograph, edited by A. G.
Ivakhnenko, V. V. Kuts, O. Yu. Erenkov, A. V. Oleinik and M. Yu.
Sarilov, KnaSTU. pp.282–286.
7. Ivakhnenko, A.G., 2010. Identification of Geometrical Errors of Metal-Cutting Machine Tools That Affect the Accuracy of Process- ing, edited by A. G. Ivakhnenko, V. V. Kuts and S. B. Dolzhenkova, Moscow, Russia, News of Kursk State Technical University, Vol. 2, pp.60–65.
8. Anikeeva, O.V.,2013. Prediction of parametric reliability of pre- cision process equipment. Fundamental and Applied Problems of Engineering and Technology, edited by O. V. Anikeeva, A. G.
Ivakhnenko and V. V. Kuts, Liptsek, Russia, Vol. 2, pp.159–164.
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9. Kuts, V.V., 2012. Ensuring the accuracy of a specialized metal- cutting system for processing RC-profile shafts at an early design stage.Series Technique and Technology, edited by V. V. Kuts and Yu. A. Maksimenko, Moscow, Russia, News of South-West State University, Vol. 2, pp.65–69.
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Publishing House of the Khabarovsk State Technical University.
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Received: 1 January 2019. Accepted: 11 March 2019.
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Printed in the United States of America
Computational and Theoretical Nanoscience Vol. 16, 5282–5286, 2019
A Targeted Study on Simulation and Optimization of Shipping Systems
Masoud Gorgich
Department of Industrial Engineering, Faculty of Engineering, University of Velayat, Iranshahr, 9911131311, Iran
Over the last four decades, containers have found their special place as suitable and necessary tool for packaging in maritime transportation. With growing increase in container manufacturing, num- bers of container terminals and their competition become significant. This study aims to simulate the container terminal operation and its improvement. Simulation is carried out by Arena software.
For this purpose, first base model with primary assumptions is simulated and results are obtained.
At the end of first stage several scenarios are defined and using the software, the required results are obtained. Then, we seek a way to improve the existing model to obtain better results. There are several methods for this. Since in this system there are several main factors that affect performance of the entire system, decision making management, simulation and optimization methods in ship- ping systems based on design of experiment are used. Then the effect of the factors on evaluation function, intended by a decision maker, are determined. After simulation, the obtained results are examined by the Taguchi method to determine which level in each factor is the best state and which factor is more effective in the entire process. Results demonstrated that number of berths are the most important factor in the process improvement and it should receive more attention.
Keywords: Simulation and Optimization, International Transportation, Shipping Systems, Arena.
1. INTRODUCTION
Nowadays, without efficient use of information technol- ogy and optimization methods, it cannot be thought about shipping operation. Recently, in order to improve contain- ers relocation, ports have encountered major challenges.
Based on the charts presented by UNCTAD, trade through container transportation between 2003 to 2025 will have 5.32% average growth [1]. Today, most international ship- ments in maritime ports are located and displaced in con- tainers. Recently, the intense competition between ports, especially in Asia and Europe, has led ports to move towards providing more facilities, improving operations and reducing costs [2]. Therefore, how to improve ser- vice efficiency and reduce costs is a fundamental issue in such ports. In general, there are two approaches to this: The first is the increase in the number of loading and unloading equipment, the second is to adopt the most effective operational program. It is very difficult to model complex systems such as manufacturing systems, supply chain and container terminals using algebraic equations.
Discrete event simulation is a useful tool for evaluating the performance of these systems. Even though simula- tion only evaluates a given plan, it does not provide any optimization function. So it is necessary to integrate sim- ulation and optimization. Optimization of simulation is
the process of finding the best value of system decision variables whose performance is evaluated by simulation outputs [3]. Recently, most papers have used scheduling models to model the operation. But in such complex prob- lems, the optimal answer cannot be obtained using math- ematical models alone. Hence, the use of simulation and optimization has been increasing, Recently. In this study, a mathematical model and simulation was first developed for the problem, and then, simulation model was imple- mented using the software, and an initial answer would be used for the mathematical model. Then, using this solu- tion and innovative techniques, the mathematical model is solved. At each step, the results are compared with those of previous steps, and if the answers were better the algo- rithm would stop, otherwise it would re-simulate the model this time with more recent solutions obtained from solving the mathematical model.