Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Measurement Science Review

The Journal of Institute of Measurement Science of Slovak Academy of Sciences

6 Issues per year

IMPACT FACTOR 2016: 1.344

CiteScore 2016: 1.88

SCImago Journal Rank (SJR) 2016: 0.495
Source Normalized Impact per Paper (SNIP) 2016: 1.419

Open Access
See all formats and pricing
More options …
Volume 18, Issue 3


Dimensional and Geometrical Errors in Vacuum Thermoforming Products: An Approach to Modeling and Optimization by Multiple Response Optimization

W. O. Leite
  • Corresponding author
  • Campus Betim, Departamento de Mecânica, Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerias, Rua Itaguaçu, No. 595 - São Caetano, 32677-780, Betim, Brasil
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ J. C. Campos Rubio
  • Escola de Engenharia, Departamento de Engenharia Mecânica,Universidade Federal de Minas Gerais, Av. Pres. Antônio Carlos, No.6627 - Pampulha, 31270-901, Belo Horizonte, Brasil
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ F. Mata
  • Escuela de Ingeniería Minera e Industrial de Almadén, Departamento Mecánica Aplicada e Ingeniería de Proyectos, Universidad de Castilla-La Mancha, Plaza Manuel Meca No.1,13400, Almadén, España
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ I. Hanafi
  • Ecole National des Sciences Appliquées d' Al Hoceima (ENSAH), Department of Civil and Environmental Engineering, BP. 03, Ajdir, Al Hoceima, Morocco
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ A. Carrasco
  • Escuela de Ingeniería Minera e Industrial de Almadén, Departamento de Filología Moderna, Universidad de Castilla-La Mancha, Plaza Manuel Meca No.1,13400, Almadén, España
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-06-12 | DOI: https://doi.org/10.1515/msr-2018-0017


In the vacuum thermoforming process, the product deviations depend on several parameters of the system, which make the analysis, the computational modeling, and the optimization of errors a multi-variable process with conflicting objectives. In this sense, the aim of this work was to study the dimensional and geometrical errors as well as the optimization (minimization) of these errors in one typical vacuum thermoforming product made of polystyrene (PS). In particular, it was intended to predict and minimize errors in a range of ideal tolerances using Multiple Response Optimization (MRO) Models. Thus, through the fractional factorial design (2k-p), initial experimental tests were performed using proposed measurement procedures, and Analysis of Variance being the data analysis is discussed. Following that, the MRO models were implemented which were also validated to represent the sample data. Through this analysis of the results, it can be concluded that the regression models of errors are not linear functions, hence, the developed models are valid for the studied process, and finally that the validation results proved the efficiency of MOR models developed, but these models will not be able to generalize to new situations in a range far from the values studied.

Keywords: Dimensional and geometrical errors; vacuum thermoforming process; multiple response optimization; plastics processing


  • [1] Throne, J.L. (2008). Understanding Thermoforming (2th ed.). Hanser, 279.Google Scholar

  • [2] Sala, G., Landro, L.D., Cassago, D. (2002). A numerical and experimental approach to optimise sheet stamping technologies: Polymers thermoforming. Journal of Materials and Design, 23, 21-39.Google Scholar

  • [3] Throne, J.L. (1996). Technology of Thermoforming. Hanser, 882.Google Scholar

  • [4] Kuttner, R., Karjust, K., Ponlak, M. (2007). The design and production technology of large composite plastic products. Proceedings of the Estonian Academy of Sciences: Engineering, 13 (2), 117-128.Google Scholar

  • [5] Muralisrinivasan, N.S. (2010). Update on Troubleshooting in Thermoforming. Smithers Rapra Technology.Google Scholar

  • [6] Ghobadnam, M., Mosaddegh, P., Rejani, M.R., Amirabadi, H., Ghaei, A. (2015). Numerical and experimental analysis of HIPS sheets in thermoforming process. International Journal of Advanced Manufacturing Technology, 76, 1079-1089.Google Scholar

  • [7] Yang, C., Hung, S.W. (2004). Modeling and optimization of a plastic thermoforming process. Journal of Reinforced Plastics and Composites, 23 (1), 109-121.Google Scholar

  • [8] Yang, C., Hung, S.W. (2004). Optimising the thermoforming process of polymeric foams: An approach by using the Taguchi method and the utility concept. The International Journal of Advanced Manufacturing Technology, 24, 353-360.Google Scholar

  • [9] Klein, P. (2009). Fundamentals of Plastics Thermoforming (11th ed.). Morgan & Claypool Publishers.Google Scholar

  • [10] Engelmann, S. (2012). Optimizing a thermoforming process for packaging. In Advanced Thermoforming: Methods, Machines and Materials, Applications and Automation. John Wiley & Sons, 125-136.Google Scholar

  • [11] Leite, W.O., Campos Rubio, J.C., Mata Cabrera, F., Carrasco, A., Hanafi, I. (2018). Vacuum thermoforming process: An approach to modeling and optimization using artificial neural networks. Polymers, 10 (143), 1-17.Google Scholar

  • [12] Pasandideh, S.H, Niakti, S.T.A., Atyabi, S.M. (2014). A new approach to solve multi-response statistical optimization problems using neural network, genetic algorithm, and goal attainment methods. International Journal of Advanced Manufacturing Technology, 75, 1149-1162.Google Scholar

  • [13] Warby, M.K., Whitemana, J.R., Jiang, W.G., Warwick, P., Wright, T. (2003). Finite element simulation of thermoforming processes for polymer sheets. Mathematics and Computers in Simulation, 61, 209-218.Google Scholar

  • [14] Yhan, Z., Zhang, H. (2000). Wall thickness distribution in thermoformed food containers produced by a Benco aseptic. Polymer Engineering & Science, 40 (1), 1-10.Google Scholar

  • [15] Erdogan, E.S., Eksi, O. (2014). Prediction of wall thickness distribution in simple thermoforming moulds. Journal of Mechanical Engineering, 60 (3), 195-202.Google Scholar

  • [16] Kumar, A., Kumar, V., Kumar, J. (2013). Multiresponse optimization of process parameters based on response surface methodology for pure titanium using WEDM process. International Journal of Advanced Manufacturing Technology, 68, 2645-2668.Google Scholar

  • [17] Kommoji, S., Banerjee, R., Bhatnaga, N., Ghosh, K.G. (2015). Studies on the stretching behaviour of medium gauge high impact polystyrene sheets during positive thermoforming. Journal of Plastic Film & Sheeting, 31 (1), 96-112.Google Scholar

  • [18] Velsker, M., Eerme, M., Majak, J., Pohlak, M., Karjust, K. (2011). Artificial neural networks and evolutionary algorithms in engineering design. Journal of Achievements in Materials and Manufacturing Engineering, 44 (1), 88-95.Google Scholar

  • [19] Martin, P.J., Keaney, T., McCool, R. (2014). Development of a multivariable online monitoring system for the thermoforming process. Polymer Engineering & Science, 54 (12), 2815-2823.Google Scholar

  • [20] Chy, M.M.I., Boulet, B., Haidar, A. (2011). A model predictive controller of plastic sheet temperature for a thermoforming process. In American Control Conference (ACC), San Francisco, CA, USA, 4410-4415.Google Scholar

  • [21] Boutaous, M., Bourgin, P., Heng, D., Garcia, D. (2005). Optimization of radiant heating using the ray tracing method: Application to thermoforming. Journal of Advanced Science, 17 (1-2), 139-145.Google Scholar

  • [22] Zhen-Zhe, L., Cheng, T.H., Shen, Y., Xuan, D.J. (2015). Optimal heater control with technology of fault tolerance for compensating thermoforming preheating system. Advances in Materials Science and Engineering, 2015 (12), 1-5.Google Scholar

  • [23] Meziane, F., Vadera, S., Kobbacy, K., Proudlove, N. (1990). Intelligent systems in manufacturing: Current developments and future prospects. Integrated Manufacturing Systems, 11 (4), 218-238.Google Scholar

  • [24] Tadeusiewicz, R. (2011). Introduction to intelligent systems. In Intelligent Systems: The Industrial Electronic Handbook (2nd ed.). CRC Press, 1.1-1.12.Google Scholar

  • [25] Pham, D.T., Pham, P.T.N. (2001). Computational intelligence for manufacturing. In Computational Intelligence in Manufacturing Handbook. CRC Press, 1.1-1.8.Google Scholar

  • [26] Costa, N., Garcia, J. (2016). Using a multiple response optimization approach to optimize the coefficient of performance. Applied Thermal Engineering, 96, 137-143.Google Scholar

  • [27] Fogliatto, F. (2008). Multiresponse optimization of products with functional quality characteristics. Quality and Reliability Engineering International, 24, 927-939.Google Scholar

  • [28] Jeyapaul, R., Shahabudeen, P., Krishnaiah, K. (2005). Quality management research by considering multiresponse problems in the Taguchi method - a review. International Journal of Advanced Manufacturing Technology, 26, 1331-1337.Google Scholar

  • [29] Pal, S., Gauri, S.K. (2010). Assessing effectiveness of the various performance metrics for multi-response optimization using multiple regression. Computers & Industrial Engineering, 59, 976-985.Google Scholar

  • [30] Khanlou, H.M., Ang, B.C., Talebian, S., Barzani, M.M., Silakhori, M., Fauzi, H. (2015). Multi-response analysis in the processing of poly (methyl methacrylate) nano-fibres membrane by electrospinning based on response surface methodology: Fibre diameter and bead formation. Measurement, 65, 193-206.Google Scholar

  • [31] EL-Taweel, T.A. (2009). Multi-response optimization of EDM with Al-Cu-Si-TiC P/M composite electrode. International Journal of Advanced Manufacturing Technology, 44, 100-113.Google Scholar

  • [32] Montgomery, D.C. (2013). Design and Analysis of Experiments (8th ed.). John Wiley, 10.1-10.9.Google Scholar

  • [33] Wan, W., Birch, J.B. (2011). A semiparametric technique for the multi-response optimization problem. Quality and Reliability Engineering International, 27, 47-59.Google Scholar

  • [34] Rosen, S.R. (2002). Thermoforming: Improving Process Performance. Society of Manufacturing Engineers.Google Scholar

  • [35] Montgomery, D.C. (2013). Design and Analysis of Experiments (8th ed.). John Wiley, 9.1-9.7.Google Scholar

  • [36] Kumar, P.S., Kumar, G.K., Kommoji, S., Banerjee, R., Ghosh, A.K. (2014). The effect of material characteristics and mould parameters on the thermoforming of thick polypropylene sheets. Journal of Plastic Film & Sheeting, 30 (2), 162-180.Google Scholar

About the article

Received: 2017-12-12

Accepted: 2018-05-14

Published Online: 2018-06-12

Published in Print: 2018-06-01

Citation Information: Measurement Science Review, Volume 18, Issue 3, Pages 113–122, ISSN (Online) 1335-8871, DOI: https://doi.org/10.1515/msr-2018-0017.

Export Citation

© 2018 W. O. Leite, published by Sciendo. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Comments (0)

Please log in or register to comment.
Log in