Preliminary Study on Fixture Layout Optimization Using Element Strain Energy
The objective of positioning the fixture elements in
the fixture is to make the workpiece stiff, so that geometric errors in
the manufacturing process can be reduced. Most of the work for
optimal fixture layout used the minimization of the sum of the nodal
deflection normal to the surface as objective function. All deflections
in other direction have been neglected. We propose a new method for
fixture layout optimization in this paper, which uses the element
strain energy. The deformations in all the directions have been
considered in this way. The objective function in this method is to
minimize the sum of square of element strain energy. Strain energy
and stiffness are inversely proportional to each other. The
optimization problem is solved by the sequential quadratic
programming method. Three different kinds of case studies are
presented, and results are compared with the method using nodal
deflections as objective function 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:51966", author = "Zeshan Ahmad and Matteo Zoppi and Rezia Molfino", title = "Preliminary Study on Fixture Layout Optimization Using Element Strain Energy", abstract = "The objective of positioning the fixture elements in
the fixture is to make the workpiece stiff, so that geometric errors in
the manufacturing process can be reduced. Most of the work for
optimal fixture layout used the minimization of the sum of the nodal
deflection normal to the surface as objective function. All deflections
in other direction have been neglected. We propose a new method for
fixture layout optimization in this paper, which uses the element
strain energy. The deformations in all the directions have been
considered in this way. The objective function in this method is to
minimize the sum of square of element strain energy. Strain energy
and stiffness are inversely proportional to each other. The
optimization problem is solved by the sequential quadratic
programming method. Three different kinds of case studies are
presented, and results are compared with the method using nodal
deflections as objective function to verify the propose method.", keywords = "Fixture layout, optimization, strain energy, quadratic
programming.", volume = "7", number = "4", pages = "558-7", }
