Authors :
Amal P R; Anjumol K S; Unnikrishnan S; Dilip V; George Oommen
Volume/Issue :
Volume 9 - 2024, Issue 8 - August
Google Scholar :
https://tinyurl.com/bdetzzsy
Scribd :
https://tinyurl.com/2nn8dvfs
DOI :
https://doi.org/10.38124/ijisrt/IJISRT24AUG1039
Abstract :
Assembly of discrete parts guided by
hardware design specification constitutes the final phase
in product manufacturing. In the course of mass
production of components, mating parts with geometric
or dimensional deviation from their intended design can
be made acceptable by the identification of suitable pairs
after analysing design fit and tolerance limits. By
transforming this application-specific problem into a
unified mathematical model, an optimal solution can be
achieved that minimizes the rejection of non-conforming
fabricated parts. Regardless of the type and range of a
design fit, the problem can be mapped into a matrix
using a ranking function defined by the user. The
ranking function is modifiable as per the user
requirements and may vary based on the selection
criteria for an assembly. Based on the type of ranking
function used, the tabulated matrix is solved using the
Hungarian minimization/maximization algorithm, which
is a powerful combinatorial optimization algorithm that
solves the classical assignment problem in mathematics.
This approach ensures maximum number of suiting
pairs as well as nominal suiting of parts with each other
resulting in high-quality products and maximum
utilization of fabricated resources.
Keywords :
Optimisation, Part Suiting, Hungarian Algorithm, Fit, Tolerance, Assembly.
References :
- Mansoor, E.M. (1961) “Selective assembly – its analysis and applications“, International Journal of Production Research, Vol. 1, No. 1, pp.13–24, doi:10.1080/00207546108943070.
- Fang, X.D. and Zhang, Y. (1995) “A new algorithm for minimising the surplus parts in selective assembly“, Computers and Industrial Engineering, Vol. 28, No. 2, pp.341–50.
- Bondy, Jhon Adrian; Murty, U.S.R (1976 ), “Graph Theory with Applications”, ISBN 0-444-19451-7, page 5.
- Zhang, Y. and Fang, X.D. (1999) “Predict and assure the matchable degree in selective assembly via PCI-based tolerance“, Journal of Manufacturing Science and Engineering, Vol. 121, No. 3, pp.494–500.
- Kannan, S., Jayabalan, V. and Jeevanantham, K. (2003) “Genetic algorithm for minimizing
assembly variation in selective assembly“, International Journal of Production Research,Vol. 41, No. 14, pp.3301–13, doi:10.1080/ 0020754031000109143.
- Kannan, S.M., Jeevanantham, A.K. and Jayabalan, V. (2008) “Modelling and analysis of selective assembly using Taguchi’s loss function“, International Journal of Production Research,Vol. 46, No. 15, pp.4309–30, doi: 10.1080/00207540701241891.
- Tan, M.H.Y. and Wu, C.F.J. (2012) “Generalized selective assembly“, IIE Transactions, Vol. 44, No. 1, pp.27–42, doi:10.1080/0740817X.2010.551649.
- Dantan, J-Y., Gayton, N., Dumas, A., Etienne, A. and Qureshi, A.J. (2012) “Mathematical issues in mechanical tolerance analysis“, Proceedings of 13th National AIP Primeca Conference, No. 1, pp.1–12.
- Babu, J.R. and Asha, A. (2015) “Minimising assembly loss for a complex assembly using
Taguchi’s concept in selective assembly“, International Journal of Productivity and Quality Management, Vol. 15, No. 3, pp.335–56.
- Diestel, Reinhard (2005), “Graph Theory” (3rd ed.), ISBN 3-540-26182-6. Electronic edition, page 17.
- H. W. Kuhn. “The Hungarian Method for the Assignment Problem”.
- James Munkres. “Algorithms for the Assignment and Transportation Problems”.
Assembly of discrete parts guided by
hardware design specification constitutes the final phase
in product manufacturing. In the course of mass
production of components, mating parts with geometric
or dimensional deviation from their intended design can
be made acceptable by the identification of suitable pairs
after analysing design fit and tolerance limits. By
transforming this application-specific problem into a
unified mathematical model, an optimal solution can be
achieved that minimizes the rejection of non-conforming
fabricated parts. Regardless of the type and range of a
design fit, the problem can be mapped into a matrix
using a ranking function defined by the user. The
ranking function is modifiable as per the user
requirements and may vary based on the selection
criteria for an assembly. Based on the type of ranking
function used, the tabulated matrix is solved using the
Hungarian minimization/maximization algorithm, which
is a powerful combinatorial optimization algorithm that
solves the classical assignment problem in mathematics.
This approach ensures maximum number of suiting
pairs as well as nominal suiting of parts with each other
resulting in high-quality products and maximum
utilization of fabricated resources.
Keywords :
Optimisation, Part Suiting, Hungarian Algorithm, Fit, Tolerance, Assembly.