• Jelena Stanojkovic Faculty of Technical Sciences
  • Milos Madic Faculty of Mechanical Engineering
Keywords: Dimensional analysis, Buckingham's π theorem, production process


Dimensional analysis is a tool used to understand and analyze various problems in engineering. This analysis is useful for calculating dimensionless parameters and gives an answer as to which group of parameters affects the problem. Dimensional analysis can be represented using Buckingham's π-theorem. This paper provides an overview of the literature on the application of dimensional analysis and Buckingham's π theorem for various processing processes. The review period is observed in the period from 2007 until today. The main focus remains of the production process, performance and parameters of process, dimension and years of publication. Review work in this area aims to provide ready-made information in one place that can be very useful to future researchers in this direction of research.


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9. Szirtes, T., Rozsa, P, Applied dimensional analysis and modelling, 2nd edition, Butterworth-Heinemann, (2007).
10. Santiago, J. G., A first course in dimensional analysis, Massachusetts Institute of Technology, (2019).
11. Langhaar, H. L., Dimensional analysis and theory of models, John Wiley & Sons Ltd, (1951).
12. Singh, D., Shukla, R. S., Integration of quality characteristics models as a software-based graphical interface for machining of AA6351 aluminum alloy using abrasive water jet process, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 42, No. 6, (2020).
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14. Poros, D., Zaborski, S., Wisniewska, M., Experimental model on the wire wear for WEDM of hard to machine materials, Journal of Machine Engineering, Vol. 19, No. 4, pp. 110-121, (2019).
15. Ueda, T., Suzuki, K., Shamoto, E., Fundamental study on cutting temperature in high speed cutting of difficult-to-cut materials, 20th Machining Innovations Conference for Aerospace Industry 2020, pp. 86-92, Hannover, Germany, (2020).
16. Zakryewski, T., Kozak, J., Witt, M, Debowska-Wasak, M., Dimensional analysis of the effect of SLM parameters on surface roughness and material density, 20th CIRP Conference on electro physical and chemical machining, Vol. 95, pp. 115-220, Zurich, Switzerland, (2020).
17. Kumar, S., Singh, R., Batish, A., Singh, T.P., Modeling the tool wear rate in powder mixed electro-discharge machining of titanium alloys using dimensional analysis of cryogenically treated electrodes and workpiece, Journal of Process Mechanical Engineering, Vol. 231, pp. 271–282, (2015).
18. Chalisgaonkar, R., Kumar, J., Multi-response optimization and modeling of trim cut WEDM operation of commercially pure titanium (CPTi) considering multiple user's preferences, Engineering Science and Technology, an International Journal, Vol. 28, No. 2, pp. 1-10, (2014).
19. Phate, M. R., Toney, S. B., Modeling and prediction of WEDM performance parameters for Al/SiCp MMC using dimensional analysis and artificial neural network, Engineering Science and Technology, an International Journal, Vol. 22, No. 2, pp. 468–476, (2019).
20. Bobbili, R., Madhu, V., Gogia, A. K., Modelling and analysis of material removal rate and surface roughness in wire-cut EDM of armour materials, Engineering Science and Technology, an International Journal, Vol. 18, No. 4, pp. 664-668, (2015).
21. Talla, G., Sahoo, K. S., Gangopadhyay, S., Biswas, C. K., Modeling and multi-objective optimization of powder mixed electric discharge machining process of aluminum/alumina metal matrix composite, Engineering Science and Technology, an International Journal, Vol. 18, No. 3, pp. 369-373, (2015).
22. Estrada-Díaz, J. A, Elías-Zúñiga, A., Martínez-Romero, O., Rodríguez-Salinas J., Olvera-Trejo, D., A mathematical dimensional model for predicting bulk density of inconel 718 parts produced by selective laser melting, Materials, Vol. 14, No. 3, pp. 512-532, (2021).
23. Mandal, N. K., Singh, N. K., Kumar, U. C., Kumar, V., Semi-empirical modelling of surface roughness in CNC end milling, International Journal of Mechatronics, Electrical and Computer Technology (IJMEC), Vol. 6. No. 22, pp. 3099-3109, (2016).
24. Kushwah, S. S., Kasdekar, K. D., Agrawal, S., Mathematical and prediction modeling of material removal rate for evaluating the effects of process parameters, Advances in Intelligent Systems and Computing, Vol. 696, pp. 509-523, (2018).
25. Kivade, S. B., Murthy, S. N., Vardhan, H., The use of dimensional analysis and optimization of pneumatic drilling operations and operating parameters, Journal of The Institution of Engineers (India): Series D, Vol. 93, No. 1, pp. 31-36, (2012).
26. Katikamand, S., Diwakar Redd, V., Dimensional analysis of form drilling parameters by using matrix method of Buckingham pi-theoremy, Journal of Emerging Technologies and Innovative Research, Vol. 5, No. 2, pp. 291-295, (2018).
27. Hemavathy, S., Anil Kumar T., Das, B., Modelling studies on surface roughness of laminated glass cut by abrasive water jet, International Journal of Mechanical Engineering and Technology, Vol. 11, No. 1, pp. 1-8, (2020).
28. Dave, H. K., Desai, K. P., Raval, H. K., Development of semi empirical model for predicting material removal rate during orbital electro discharge machining of Inconel 718, International Journal of Machining and Machinability of Materials, Vol. 13, No. 2, pp. 215-229, (2013).
29. Kadua, R. S., Awarib, G. K., Sakhalec, C. N., Modakd, J. P., Formulation of mathematical model for the investigation of tool wears in boring machining operation on cast iron using carbide and CBN tools, Procedia Materials Science, Vol. 6, pp. 1710-1724, (2014).
30. Alauddin, M., Zhang, L. C., Grinding force modelling: combining dimensional analysis with response surface methodology, International Journal of. Manufacturing Technology and Management, Vol. 12, No. 1, pp. (2007).
31. Chen, T., Wang, C., Investigation into roughness of surface polished by abrasive water jet with Taguchi method and dimensional analysis, Materials Science Forum, Vol. 723, pp. 188-195, (2013).
32. Mahajan, K. C. Mote, M. L., Patil, B. V, Patil, H. G., Phate, M. R., Formulation and simulation of a field data based model for the turning process by using response surface method, International Journal of Advanced Scientific and Technical Research, Vol. 2, pp. 355-370, (2013).
33. Mate, D. M., Awari, G. K., Sakhale, C. N., Formulation of experimental data based model for aluminum alloy HE15 operation with burnishing tool on lathe machine using dimensional analysis, International Journal of Research in Mechanical Engineering, Vol. 1, No. 2, pp. 80-90, (2013).
34. Phate1, M., Tatwawadi, V., Modak, J., Formulation of a generalized field data based model for the surface roughness of aluminium 6063 in dry turning operation, Science Journal, Vol. 5, No. 7, pp. 38-46, (2012).
35. Phate, M., Toney, S., Phate,V., Optimization of performance parameters for OHNS die steel using dimensional analysis integrated with desirability function, International Journal of Industrial Engineering & Production Research, Vol. 30, No. 1, pp. 11-23, (2019).
36. Kumar, J., Khamba, J. S., Mohapatra, S. K., Investigating and modeling tool-wear rate in the ultrasonic machining of titanium, International Journal of Advanced Manufacturing Technology, Vol. 41, pp. 1107–1117, (2009).
37. Kumar, J., Khamba, J. S., Modeling the material removal rate in ultrasonic machining of titanium using dimensional analysis, International Journal of Advanced Manufacturing Technology, Vol. 48, pp. 103–119, (2010).
38. Mangesh, R. P., Tatwawad, V. H., Mathematical models of material removal rate & power consumption for dry turning of ferrous material using dimensional analysis in Indian prospective, Jordan Journal of Mechanical and Industrial Engineering, Vol. 9, No. 1, pp. 27-38, (2015).
39. Patel S., Prajapti, J. M., Patel, D., Patel, M., Patel, K., Evaluation of different approach for WEDM process optimization, Materials Today, Vol. 66, No. 4, pp. 1988-1993, (2022).
40. Abudu S., Cui C., King J. P., Abudukadeer K., Comparison of performance of statistical models in
forecasting monthly streamflow of Kizil River, China, Water Science and Engineering, Vol. 3, No. 3, pp. 269-281, (2010).
41. Mani, M. R., Investigating the effect of process parameters on dimensional accuracy and ultimate tensile strength of micro injection moulded micro parts, The University of Nottingham, (2015).
42. Reddy, G. M., Reddy V. D., Kumar, B. S., Shyamsunder, J., Experimental investigation on radial ball bearing parameters using Taguchi method, Journal of Applied and Computational Mehanices, Vol. 4, No. 1, pp. 69-74. (2018).
43. Pontes, F. J., Ferreira J. R., Silva, M. B., Paiva A. P., Balestrassi, P. P., Artificial neural networks for machining processes surface roughness modeling, The International Journal of Advanced Manufacturing Technology, Vol. 49, pp. 879–902 (2010).
44. Ahmad S. A., Saad A., S. Shahnawaz A., Dimensional analysis for contamination severity assessment on high voltage insulators, 2007 International Conference on Intelligent and Advanced Systems, (2007).
45. Gilberto P., Influence and residuals inrestricte generalized linear models, Journal of Statistical Computation and Simulation, Vol. 51, No. 2-4, pp. 315-331, (1995).
How to Cite
Stanojkovic, J., & Madic, M. (2023). APPLICATION OF DIMENSIONAL ANALYSIS FOR MODELING MANUFACTURING PROCESSES: A REVIEW. Nonconventional Technologies Review, 27(2). Retrieved from