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Title:
Application of Mathematical Modelling to Virtual
Manufacturing
By:
Mohsen Soori
Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic),
Tehran, Iran
Date:
10 November 2018
Abstract: To analyze and modify manufacturing process in virtual environments,
mathematical modelling can be used. Effects and behavior of the system are simulated by
mathematical concepts in order to be analyzed and modified. So, different parameters of the
process can be analyzed in order to be optimized. Thus, efficiency of part production can be
increased by applying optimization methods to the simulated manufacturing process in virtual
environments. Modification can also be presented to the simulated system in virtual
environments by analyzing and decreasing errors of manufacturing process. Therefore,
accuracy of produced parts can be increased in order to improve efficiency of part production.
Overall, mathematical modelling can develop manufacturing process by providing analysis
abilities in virtual environments.
Keywords: Mathematical modelling, Virtual manufacturing, Production optimization,
Efficiency of part production, Accuracy of produced parts
References
[1] Soori, M., Arezoo, B. and Habibi, M., 2013. Dimensional and geometrical errors of three-axis
CNC milling machines in a virtual machining system. Computer-Aided Design, 45(11), pp.1306-
1313.
[2] Soori, M., Arezoo, B. and Habibi, M., 2014. Virtual machining considering dimensional,
geometrical and tool deflection errors in three-axis CNC milling machines. Journal of
Manufacturing Systems, 33(4), pp.498-507.
[3] Nourazar, S.S., Soori, M. and Nazari-Golshan, A., 2015. On the exact solution of Newell-
Whitehead-Segel equation using the homotopy perturbation method. Australian Journal of
Basic and Applied Sciences 5 (8), pp.1400-1411.
[4] Soori, M., Arezoo, B. and Habibi, M., 2016. Tool Deflection Error of Three-Axis Computer
Numerical Control Milling Machines, Monitoring and Minimizing by a Virtual Machining System.
Journal of Manufacturing Science and Engineering, 138(8), pp. 081005.
[5] Soori, M., Arezoo, B. and Habibi, M., 2017. Accuracy analysis of tool deflection error
modeling in prediction of milled surfaces by a virtual machining system. International Journal of
Computer Applications in Technology, 55(4), pp. 308-321.
[6] Soori, M., Nourazar, S.S. and Nazari-Golshan, A., 2015. Application of the Variational
Iteration Method and the Homotopy Perturbation Method to the Fisher Type Equation. Int. J.
Math. Computation, 27(3), pp.1-9.
[7] Nourazar, S.S., Soori, M. and Nazari-Golshan, A., 2015. On the Homotopy Perturbation
Method for the Exact Solution of Fitzhugh–Nagumo Equation. International Journal of
Mathematics & Computation™, 27(1), pp.32-43.
[8] M. Abramovici, D. Gerhard, A Flexible Web-based PDM Approach to Support Virtual
Engineering Cooperation, Proceedings of the 33rd Annual Hawaii International Conference on
System Sciences HICSS, DOI: 10.1109/HICSS.2000.926882, 2000.
[9] Nourazar, S.S., Soori, M. and Nazari-Golshan, A., 2015. On the Exact Solution of Burgers-
Huxley Equation Using the Homotopy Perturbation Method. Journal of Applied Mathematics
and Physics, 3(03), p.28.

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Application of Mathematical Modelling to Virtual Manufacturing

  • 1. Title: Application of Mathematical Modelling to Virtual Manufacturing By: Mohsen Soori Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran Date: 10 November 2018 Abstract: To analyze and modify manufacturing process in virtual environments, mathematical modelling can be used. Effects and behavior of the system are simulated by mathematical concepts in order to be analyzed and modified. So, different parameters of the process can be analyzed in order to be optimized. Thus, efficiency of part production can be increased by applying optimization methods to the simulated manufacturing process in virtual environments. Modification can also be presented to the simulated system in virtual environments by analyzing and decreasing errors of manufacturing process. Therefore, accuracy of produced parts can be increased in order to improve efficiency of part production. Overall, mathematical modelling can develop manufacturing process by providing analysis abilities in virtual environments. Keywords: Mathematical modelling, Virtual manufacturing, Production optimization, Efficiency of part production, Accuracy of produced parts References [1] Soori, M., Arezoo, B. and Habibi, M., 2013. Dimensional and geometrical errors of three-axis CNC milling machines in a virtual machining system. Computer-Aided Design, 45(11), pp.1306- 1313. [2] Soori, M., Arezoo, B. and Habibi, M., 2014. Virtual machining considering dimensional, geometrical and tool deflection errors in three-axis CNC milling machines. Journal of Manufacturing Systems, 33(4), pp.498-507. [3] Nourazar, S.S., Soori, M. and Nazari-Golshan, A., 2015. On the exact solution of Newell- Whitehead-Segel equation using the homotopy perturbation method. Australian Journal of Basic and Applied Sciences 5 (8), pp.1400-1411. [4] Soori, M., Arezoo, B. and Habibi, M., 2016. Tool Deflection Error of Three-Axis Computer Numerical Control Milling Machines, Monitoring and Minimizing by a Virtual Machining System. Journal of Manufacturing Science and Engineering, 138(8), pp. 081005.
  • 2. [5] Soori, M., Arezoo, B. and Habibi, M., 2017. Accuracy analysis of tool deflection error modeling in prediction of milled surfaces by a virtual machining system. International Journal of Computer Applications in Technology, 55(4), pp. 308-321. [6] Soori, M., Nourazar, S.S. and Nazari-Golshan, A., 2015. Application of the Variational Iteration Method and the Homotopy Perturbation Method to the Fisher Type Equation. Int. J. Math. Computation, 27(3), pp.1-9. [7] Nourazar, S.S., Soori, M. and Nazari-Golshan, A., 2015. On the Homotopy Perturbation Method for the Exact Solution of Fitzhugh–Nagumo Equation. International Journal of Mathematics & Computation™, 27(1), pp.32-43. [8] M. Abramovici, D. Gerhard, A Flexible Web-based PDM Approach to Support Virtual Engineering Cooperation, Proceedings of the 33rd Annual Hawaii International Conference on System Sciences HICSS, DOI: 10.1109/HICSS.2000.926882, 2000. [9] Nourazar, S.S., Soori, M. and Nazari-Golshan, A., 2015. On the Exact Solution of Burgers- Huxley Equation Using the Homotopy Perturbation Method. Journal of Applied Mathematics and Physics, 3(03), p.28.