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Mathematical Model for Built-in Dishwasher to Study Door Open and Close Forces and Sealing with Monte Carlo Simulations

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Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)

Abstract

The objective of the study is to demonstrate the development of a mathematical model for a built-in dishwasher to study door open and close forces and sealing. A mathematical model is used to compute several characteristics associated with the closing and latching of the door of built-in dishwasher. The input file to the mathematical model consists of rows and columns of numerical data. Most of the columns represent relevant drawing dimensions that influence the door close and latch event. Each row represents a unique value of drawing dimension and the variance that is determined using the tolerance of the dimension. The outputs of the mathematical model are door open and close forces, gasket compressions (minimum and maximum), force gradient and door angle at the final position. This mathematical model is further used in Monte Carlo simulation to optimize door opening/closing forces and robust sealing design. To carry out Monte Carlo simulations, a mathematical model is embedded and the input file is modified in such a way that each unique value is statistically determined. Each row represents a scenario of values corresponding to the drawing dimensions. The output of this study needs data analysis of different outcomes and their chances of occurrence.

Keywords

  • Door forces
  • Sealing
  • Latch
  • Tub seal
  • Mathcad
  • Monte Carlo

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Abbreviations

\(f\left( x \right)\) :

Seal force (N)

\(h\left( x \right)\) :

Height of the compressed area (mm)

\(L(x)\) :

Latch force (N)

\({\text{LL}}\) :

Lower limit (dimensionless)

\(M1\) :

Seal moment (N-mm)

\(M2\) :

Latch moment (N-mm)

\({\text{TL}}\) :

Threshold limit (dimensionless)

\({\text{UL}}\) :

Upper limit (dimensionless)

References

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Correspondence to Krishna Chaitanya Kusupudi .

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Kusupudi, K.C., Mandal, A., Barik, D. (2020). Mathematical Model for Built-in Dishwasher to Study Door Open and Close Forces and Sealing with Monte Carlo Simulations. In: Li, C., Chandrasekhar, U., Onwubolu, G. (eds) Advances in Engineering Design and Simulation. Lecture Notes on Multidisciplinary Industrial Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-8468-4_4

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  • DOI: https://doi.org/10.1007/978-981-13-8468-4_4

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-8467-7

  • Online ISBN: 978-981-13-8468-4

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