Fixture Layout Optimization Using Element Strain Energy and Genetic Algorithm
The stiffness of the workpiece is very important to reduce the errors in manufacturing process. The high stiffness of the workpiece can be achieved by optimal positioning of fixture elements in the fixture. The minimization of the sum of the nodal deflection normal to the surface is used as objective function in previous research. The deflection in other direction has been neglected. The 3-2-1 fixturing principle is not valid for metal sheets due to its flexible nature. We propose a new fixture layout optimization method N-3-2-1 for metal sheets that uses the strain energy of the finite elements. This method combines the genetic algorithm and finite element analysis. The objective function in this method is to minimize the sum of all the element strain energy. By using the concept of element strain energy, the deformations in all the directions have been considered. Strain energy and stiffness are inversely proportional to each other. So, lower the value of strain energy, higher will be the stiffness. Two different kinds of case studies are presented. The case studies are solved for both objective functions; element strain energy and nodal deflection. The result are compared to verify the propose method.
[1] G. Prabhaharan, K. P. Padmanaban, R. Krishnakumar, “Machining
fixture layout optimization using FEM and evolutionary techniques,”
International Journal of Advanced Manufacturing Technology, vol. 32,
pp. 1090-1103, 2007.
[2] R. J. Menassa, W.R. DeVries, “Optimization methods applied to
selecting support positions in fixture design,” ASME Journal of
Engineering for Industry, vol. 113, pp. 412-418, 1991.
[3] R. T. Meyer, F.W. Liou, “Fixture analysis under dynamic machining,”
International Journal of Production Research, vol. 35, no. 5, pp. 1471-
1489, 1997.
[4] U. Roy, J. Liao, “Geometric reasoning for re-allocation of supporting
and clamping positions in the automated fixture design system,” IEEE
Transactions, vol. 31, pp. 313-322, 1999.
[5] Z. J. Tao, A. S. Kumar, A. Y. C. Nee, “A computational geometry
approach to optimum clamping synthesis of machining fixtures,”
International Journal of Production Research, vol. 37, no. 15, pp.
3495-3517, 1999.
[6] B. Li, S. N. Melkote, “Improved workpiece location accuracy through
fixture layout optimization,” International Journal of Machine Tools
and Manufacture, vol. 39, pp. 871-883, 1999.
[7] Y. J. Liao, S. J. Hu, “Flexible multibody dynamics based fixture–
workpiece analysis model for fixturing stability,” International Journal
of Machine Tools and Manufacture, vol. 40, pp. 343-362, 2000.
[8] B. Li, S. N. Melkote, “Optimal fixture design accounting for the effect
of workpiece dynamics,” International Journal of Advanced
Manufacturing Technology, vol. 18, pp. 701-707, 2001.
[9] E. Y. T. Tan, A. S. Kumar, J. Y. H. Fuh, A. Y. C. Nee, “Modeling,
analysis and verification of optimal fixturing design,” IEEE
Transactions on Automation Science and Engineering, vol. 1, no. 2,
pp. 121-132, 2004.
[10] N. Amaral, J. J. Rencis, Y. Rong, “Development of a finite element
analysis tool for fixture design integrity verification and optimization,”
International Journal of Advanced Manufacturing Technology, vol. 21,
pp. 411-419, 2004.
[11] W. Cai, S. J. Hu, and J. X. Yuan, “Deformable sheet metal fixturing:
principles, algorithms, and simulations,” Journal of Manufacturing
Science and Engineering, vol.118, issue 3, pp. 318-324, 1996.
[12] B. Li and B. W. Shiu, “Principle and simulation of fixture configuration
design for sheet metal assembly with laser welding. Part 2: optimal
configuration design with the genetic algorithm,” International Journal
of Advanced Manufacturing Technology, vol. 18, pp. 276-284, 2001
[13] B. Li, B. W. Shiu and K. J. Lau, “Fixture configuration design for sheet
metal assembly with laser welding: A case study,” The International
Journal of Advanced Manufacturing Technology, vol. 19, pp. 501-509.
[14] W Cai, “Fixture optimization for sheet panel assembly considering
welding gun variations,” Journal of Mechanical Engineering Science,
vol. 222, pp. 235-246, 2008
[15] J. Ma, M. Y. Wang, “Compliant fixture layout design using topology
optimization method,” 2011 IEEE International Conference on
Robotics and Automation, Shanghai, China, May 9-13, 2011.
[16] H. Cheng, Y. Li, K.F. Zhang, C. Luan, Y.W. Xu, M. H. Li,
“Optimization method of fixture layout for aeronautical thin-walled
structures with automated riveting,” Assembly Automation, vol. 32, pp.
323- 332, 2012.
[17] L. Xiong, R. Molfino, M. Zoppi, “Fixture layout optimization for
flexible aerospace parts based on self-reconfigurable swarm intelligent
fixture system,” The International Journal of Advanced Manufacturing
Technology, pp. 1-9, 2012.
[1] G. Prabhaharan, K. P. Padmanaban, R. Krishnakumar, “Machining
fixture layout optimization using FEM and evolutionary techniques,”
International Journal of Advanced Manufacturing Technology, vol. 32,
pp. 1090-1103, 2007.
[2] R. J. Menassa, W.R. DeVries, “Optimization methods applied to
selecting support positions in fixture design,” ASME Journal of
Engineering for Industry, vol. 113, pp. 412-418, 1991.
[3] R. T. Meyer, F.W. Liou, “Fixture analysis under dynamic machining,”
International Journal of Production Research, vol. 35, no. 5, pp. 1471-
1489, 1997.
[4] U. Roy, J. Liao, “Geometric reasoning for re-allocation of supporting
and clamping positions in the automated fixture design system,” IEEE
Transactions, vol. 31, pp. 313-322, 1999.
[5] Z. J. Tao, A. S. Kumar, A. Y. C. Nee, “A computational geometry
approach to optimum clamping synthesis of machining fixtures,”
International Journal of Production Research, vol. 37, no. 15, pp.
3495-3517, 1999.
[6] B. Li, S. N. Melkote, “Improved workpiece location accuracy through
fixture layout optimization,” International Journal of Machine Tools
and Manufacture, vol. 39, pp. 871-883, 1999.
[7] Y. J. Liao, S. J. Hu, “Flexible multibody dynamics based fixture–
workpiece analysis model for fixturing stability,” International Journal
of Machine Tools and Manufacture, vol. 40, pp. 343-362, 2000.
[8] B. Li, S. N. Melkote, “Optimal fixture design accounting for the effect
of workpiece dynamics,” International Journal of Advanced
Manufacturing Technology, vol. 18, pp. 701-707, 2001.
[9] E. Y. T. Tan, A. S. Kumar, J. Y. H. Fuh, A. Y. C. Nee, “Modeling,
analysis and verification of optimal fixturing design,” IEEE
Transactions on Automation Science and Engineering, vol. 1, no. 2,
pp. 121-132, 2004.
[10] N. Amaral, J. J. Rencis, Y. Rong, “Development of a finite element
analysis tool for fixture design integrity verification and optimization,”
International Journal of Advanced Manufacturing Technology, vol. 21,
pp. 411-419, 2004.
[11] W. Cai, S. J. Hu, and J. X. Yuan, “Deformable sheet metal fixturing:
principles, algorithms, and simulations,” Journal of Manufacturing
Science and Engineering, vol.118, issue 3, pp. 318-324, 1996.
[12] B. Li and B. W. Shiu, “Principle and simulation of fixture configuration
design for sheet metal assembly with laser welding. Part 2: optimal
configuration design with the genetic algorithm,” International Journal
of Advanced Manufacturing Technology, vol. 18, pp. 276-284, 2001
[13] B. Li, B. W. Shiu and K. J. Lau, “Fixture configuration design for sheet
metal assembly with laser welding: A case study,” The International
Journal of Advanced Manufacturing Technology, vol. 19, pp. 501-509.
[14] W Cai, “Fixture optimization for sheet panel assembly considering
welding gun variations,” Journal of Mechanical Engineering Science,
vol. 222, pp. 235-246, 2008
[15] J. Ma, M. Y. Wang, “Compliant fixture layout design using topology
optimization method,” 2011 IEEE International Conference on
Robotics and Automation, Shanghai, China, May 9-13, 2011.
[16] H. Cheng, Y. Li, K.F. Zhang, C. Luan, Y.W. Xu, M. H. Li,
“Optimization method of fixture layout for aeronautical thin-walled
structures with automated riveting,” Assembly Automation, vol. 32, pp.
323- 332, 2012.
[17] L. Xiong, R. Molfino, M. Zoppi, “Fixture layout optimization for
flexible aerospace parts based on self-reconfigurable swarm intelligent
fixture system,” The International Journal of Advanced Manufacturing
Technology, pp. 1-9, 2012.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:65262", author = "Zeshan Ahmad and Matteo Zoppi and Rezia Molfino", title = "Fixture Layout Optimization Using Element Strain Energy and Genetic Algorithm", abstract = "The stiffness of the workpiece is very important to reduce the errors in manufacturing process. The high stiffness of the workpiece can be achieved by optimal positioning of fixture elements in the fixture. The minimization of the sum of the nodal deflection normal to the surface is used as objective function in previous research. The deflection in other direction has been neglected. The 3-2-1 fixturing principle is not valid for metal sheets due to its flexible nature. We propose a new fixture layout optimization method N-3-2-1 for metal sheets that uses the strain energy of the finite elements. This method combines the genetic algorithm and finite element analysis. The objective function in this method is to minimize the sum of all the element strain energy. By using the concept of element strain energy, the deformations in all the directions have been considered. Strain energy and stiffness are inversely proportional to each other. So, lower the value of strain energy, higher will be the stiffness. Two different kinds of case studies are presented. The case studies are solved for both objective functions; element strain energy and nodal deflection. The result are compared to verify the propose method.
", keywords = "Fixture layout, optimization, fixturing element, genetic algorithm.", volume = "7", number = "10", pages = "1937-7", }
