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A gradient-based optimal control problem in creep-feed grinding

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Abstract

The research presented in this study deals with the analysis, modeling, and optimization of thermal effects in the creep-feed grinding process. Advanced grinding technology is investigated, which is defined as an extreme production process accompanied by large amounts of interface thermal energy, which results in a heat-affected zone of the workpiece. An optimal control problem based on the conjugate gradient method was used. The optimal control approach simulated heat flux distribution in grinding for selected machining conditions based on the measured temperature inside the workpiece. A further goal of the control problem is to optimize the objective function to find the control variables for the desired process state. The optimization algorithm to minimize the objective function was conducted based on the critical heat flux parameters. Namely, by optimizing the relationship between the heating power and duration, the optimum grinding conditions are determined to achieve high productivity and quality. The solution of the gradient-based optimal control problem was obtained by the iterative numerical optimization technique. The results of the optimal heat control problem showed a good agreement with the experimental data.

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References

  1. Malkin S, Guo C (2008) Grinding technology: theory and application of machining with abrasives. Industrial Press Inc, New York

    Google Scholar 

  2. Rowe W (2013) Principles of modern grinding technology. William Andrew Publishing, New York

    Google Scholar 

  3. Ozturk S (2018) Grinding of flat glass with Fe- and Cu-based diamond tools. Proc Inst Mech Eng Part B J Eng Manuf 227:102–108. https://doi.org/10.1177/0954405416673113

    Article  Google Scholar 

  4. Kopac J, Krajni P (2006) High-performance grinding – a review. J Mater Process Technol 175:278–284. https://doi.org/10.1016/j.jmatprotec.2005.04.010

    Article  Google Scholar 

  5. Tawakoli T (1993) High efficiency deep grinding. VDI-Verlag and Mechanical Engineering Publications, London

    Google Scholar 

  6. Wasif M, Iqbal SA, Ahmed A et al (2019) Optimization of simplified grinding wheel geometry for the accurate generation of end-mill cutters using the five-axis CNC grinding process. Int J Adv Manuf Technol 105:4325–4344. https://doi.org/10.1007/s00170-019-04547-8

    Article  Google Scholar 

  7. Gu Y, Li H, Du B, Ding W (2019) Towards the understanding of creep-feed deep grinding of DD6 nickel-based single-crystal superalloy. Int J Adv Manuf Technol 100:445–455. https://doi.org/10.1007/s00170-018-2686-2

    Article  Google Scholar 

  8. Guo C, Malkin S (1994) Analytical and experimental investigation of burnout in creep-feed grinding. CIRP Ann 43:283–286. https://doi.org/10.1016/S0007-8506(07)62214-8

    Article  Google Scholar 

  9. Gostimirovic M, Sekulic M, Kopac J, Kovac P (2011) Optimal control of workpiece thermal state in creep-feed grinding using inverse heat conduction analysis. Stroj vestn - J Mech Eng 57:730–738. https://doi.org/10.5545/sv-jme.2010.075

    Article  Google Scholar 

  10. Zhu X, Wang W, Jiang R, Liu X, Lin K (2020) Performances of Ni3Al-based intermetallic IC10 in creep-feed grinding. Int J Adv Manuf Technol 108:809–820. https://doi.org/10.1007/s00170-020-05408-5

    Article  Google Scholar 

  11. Salmon SC (1979) Creep-feed surface grinding. University of Bristol, England

    Google Scholar 

  12. Albert M (1982) Taking the creep out of creep-feed grinding. Modern Machine Shop 80–87

  13. Webster J, Brinksmeier E, Heinzel C, Wittman M, Thoens K (2002) Assessment of grinding fluid effectiveness in continuous-dress creep feed grinding. CIRP Ann 48:581–598. https://doi.org/10.1016/S0007-8506(07)61507-8

    Article  Google Scholar 

  14. Heinzel C, Antsupov G (2012) Prevention of wheel clogging in creep-feed grinding by efficient tool cleaning. CIRP Ann 61:323–326. https://doi.org/10.1016/j.cirp.2012.03.056

    Article  Google Scholar 

  15. Rouly E, Bauer RJ, Warkentin A (2017) An investigation into the effect of nozzle shape and jet pressure in profile creep-feed grinding. Proc Inst Mech Eng Part B J Eng Manuf 231:1116–1130. https://doi.org/10.1177/0954405415584960

    Article  Google Scholar 

  16. Kim HJ, Kim NK, Kwak JS (2006) Heat flux distribution model by sequential algorithm of inverse heat transfer determining workpiece temperature in creep feed grinding. Int J Mach Tools Manuf 46:2086–2093. https://doi.org/10.1016/j.ijmachtools.2005.12.007

    Article  Google Scholar 

  17. Vidal G, Ortega N, Bravo H, Dubar M, González H (2018) An analysis of electroplated cBN grinding wheel wear and conditioning during creep feed grinding of aeronautical alloys. Metals 8:350. https://doi.org/10.3390/met8050350

    Article  Google Scholar 

  18. Li BK, Miao Q, Li M et al (2020) An investigation on machined surface quality and tool wear during creep feed grinding of powder metallurgy nickel-based superalloy FGH96 with alumina abrasive wheels. Adv Manuf 8:160–176. https://doi.org/10.1007/s40436-020-00305-2

    Article  MathSciNet  Google Scholar 

  19. Miao Q, Ding W, Xu J et al (2021) Creep feed grinding induced gradient microstructures in the superficial layer of turbine blade root of single crystal nickel-based superalloy. Int J Extrem Manuf 3:045102. https://doi.org/10.1088/2631-7990/ac1e05

    Article  Google Scholar 

  20. Taylor FW (1907) On the art of cutting metals. Trans ASME 29:231–248

    Google Scholar 

  21. Alden GI (1914) Operation of grinding wheels in machine grinding. Trans ASME 36:451–460

    Google Scholar 

  22. Guest JJ (1915) Theory of grinding with reference to the selection of speeds in plain and internal work. Proc Inst Mech Eng 89:543–590

    Article  Google Scholar 

  23. Chapman WH (1920) Cylindrical grinding in 1920. Trans Am Soc Mech Engrs 42:595–620

    Google Scholar 

  24. Dall AH (1946) Rounding effect in centerless grinding. Mech Eng 4:325–329

    Google Scholar 

  25. Marshall ER, Shaw MC (1952) Forces in dry surface grinding. Trans ASME 74:51–59

    Google Scholar 

  26. Outwater JO, Shaw MC (1952) Surface temperatures in grinding Trans ASME 74:73–81

    Google Scholar 

  27. Peklenik J (1964) Contribution to the theory of surface characterization. CIRP Ann 12:173–176

    Google Scholar 

  28. Malkin S (1981) Grinding cycle optimization. CIRP Ann 30:223–226. https://doi.org/10.1016/S0007-8506(07)60930-5

    Article  Google Scholar 

  29. Tönshoff HK, Peters J, Inasaki I, Paul T (1992) Modelling and simulation of grinding processes. CIRP Ann 41:677–688. https://doi.org/10.1016/S0007-8506(07)63254-5

    Article  Google Scholar 

  30. Brinksmeier E, Tönshoff HK, Czenkusch C, Heinzel C (1998) Modelling and optimization of grinding processes. J Intell Manuf 9:303–314. https://doi.org/10.1023/A:1008908724050

    Article  Google Scholar 

  31. Sedighi M, Afshari D (2010) Creep feed grinding optimization by an integrated GA-NN system. J Intell Manuf 21:657–663. https://doi.org/10.1007/s10845-009-0243-4

    Article  Google Scholar 

  32. Zhang ZY, Shang W, Ding HH, Guo J, Wang HY et al (2016) Thermal model and temperature field in rail grinding process based on a moving heat source. Appl Therm Eng 106:855–864. https://doi.org/10.1016/j.applthermaleng.2016.06.071

    Article  Google Scholar 

  33. Agarwal S, Dandge SS, Chakraborty S (2020) Parametric analysis of a grinding process using the rough sets theory. FU Mech Eng 18:91–106. https://doi.org/10.22190/FUME191118007A

    Article  Google Scholar 

  34. Khalilpourazari S, Khalilpourazary S (2020) Optimization of time, cost and surface roughness in grinding process using a robust multi-objective dragonfly algorithm. Neural Comput Appl 32:3987–3998. https://doi.org/10.1007/s00521-018-3872-8

    Article  Google Scholar 

  35. Madic M, Gostimirovic M, Rodic D, Radovanovic M, Coteata M (2022) Mathematical modelling of the CO2 laser cutting process using genetic programming. FU Mech Eng. https://doi.org/10.22190/FUME210810003M

  36. Ozturk S, Kahraman MF (2019) Modeling and optimization of machining parameters during grinding of flat glass using response surface methodology and probabilistic uncertainty analysis based on Monte Carlo simulation. Measurement 145:274–291. https://doi.org/10.1016/j.measurement.2019.05.098

    Article  Google Scholar 

  37. Kahraman MF, Ozturk S (2019) Experimental study of newly structural design grinding wheel considering response surface optimization and Monte Carlo simulation. Measurement 147:106825. https://doi.org/10.1016/j.measurement.2019.07.053

    Article  Google Scholar 

  38. Kahraman MF, Ozturk S (2019) Uncertainty analysis of cutting parameters during grinding based on RSM optimization and Monte Carlo simulation. Mater Test 61:1215–1219. https://doi.org/10.3139/120.111443

    Article  Google Scholar 

  39. Wang Z, Zhang T, Yu T, Zhao J (2020) Assessment and optimization of grinding process on AISI 1045 steel in terms of green manufacturing using orthogonal experimental design and grey relational analysis. J Clean Prod 253:119896. https://doi.org/10.1016/j.jclepro.2019.119896

    Article  Google Scholar 

  40. Pontryagin LS, Boltayanskii VG, Gamkrelidze RV, Mishchenko EF (1962) The mathematical theory of optimal processes. John Wiley & Sons, New York

    Google Scholar 

  41. Guinn T (1976) Reduction of delayed optimal control problems to nondelayed problems. J Optim Theory Appl 18:371–377. https://doi.org/10.1007/BF00933135

    Article  MathSciNet  MATH  Google Scholar 

  42. Jajarmi A, Pariz N, Effati S, Vahidian Kamyad A (2012) Infinite horizon optimal control for nonlinear interconnected large-scale dynamical systems with an application to optimal attitude control. Asian J Control 14:1239–1250. https://doi.org/10.1002/asjc.452

    Article  MathSciNet  MATH  Google Scholar 

  43. Betts JT (1998) Survey of numerical methods for trajectory optimization. J Guid Control Dyn 21:193–207. https://doi.org/10.2514/2.4231

    Article  MATH  Google Scholar 

  44. Hestenes MR, Stiefel E (1952) Method of conjugate gradient for solving linear systems. J Res Natl Bur Stand 5:409–436. https://doi.org/10.6028/jres.049.044

    Article  MathSciNet  MATH  Google Scholar 

  45. Fletcher R, Reeves C (1964) Function minimization by conjugate gradients. Comput J 7:149–154. https://doi.org/10.1093/comjnl/7.2.149

    Article  MathSciNet  MATH  Google Scholar 

  46. Lasdon LS, Mitter SK, Waren AD (1967) The conjugate gradient method for optimal control problems. IEEE Trans Autom Control 12:132–138. https://doi.org/10.1109/TAC.1967.1098538

    Article  MathSciNet  Google Scholar 

  47. Quintana VH, Davison EJ (1974) Clipping-offgradient algorithms to compute optimal controls 461 with constrained magnitude. Int J Control 20:243–255

    Article  Google Scholar 

  48. Koivo HN, Mayorga RV (1978) A robust conjugate-gradient algorithm for optimal control problems. Preprints of 7th Congress of IFAC:1093–1100, Pergamon Press, Oxford

  49. Koren Y, Ben-Uri J (1973) Flank-wear model and optimization of machining process and its control in turning. Proc Inst Mech Eng 187:301–307. https://doi.org/10.1243/PIME_PROC_1973_187_112_02

    Article  Google Scholar 

  50. Butt R (1993) Optimum design with finite elements: design of electrochemical machining. J Comput Appl Math 47:151–165. https://doi.org/10.1016/0377-0427(93)90002-S

    Article  MathSciNet  MATH  Google Scholar 

  51. Yan MT (2010) An adaptive control system with self-organizing fuzzy sliding mode control strategy for micro wire-EDM machines. Int J Adv Manuf Technol 50:315–328. https://doi.org/10.1007/s00170-009-2481-1

    Article  Google Scholar 

  52. Gostimirovic M, Sekulic M, Trifunovic M, Madic M, Rodic D (2021) Stability analysis of the inverse heat transfer problem in the optimization of the machining process. Appl Therm Eng 195:117174. https://doi.org/10.1016/j.applthermaleng.2021.117174

    Article  Google Scholar 

  53. Tikhonov AN, Arsenin VY (1977) Solution of ill-posed problems. Winston & Sons, Washington

    MATH  Google Scholar 

  54. Alifanov OM (1994) Inverse heat transfer problems. Springer, Berlin

    Book  Google Scholar 

  55. Colaco MJ, Orlande HRB, Dulikravich GS (2006) Inverse and optimization problems in heat transfer. J Braz Soc Mech Sci Eng 28:1–24. https://doi.org/10.1590/S1678-58782006000100001

    Article  Google Scholar 

  56. Polak E, Ribière G (1969) Note Sur la Convergence de Méthodes de Directions Conjuguées. Revue Francaise d’Informatique et de Recherche Opérationnelle 16:35–43

    MATH  Google Scholar 

  57. Jaeger JC (1942) Moving sources of heat and temperature at sliding contacts. Proc R Soc NSW 76:203–224

    Google Scholar 

  58. Gostimirovic M, Kovac P, Sekulic M (2011) An inverse heat transfer problem for optimization of the thermal process in machining. Sadhana - Acad P Eng S 36:489–504. https://doi.org/10.1007/s12046-011-0034-4

    Article  Google Scholar 

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Funding

This paper presents a part of researching at the Project No. 451–03-68/2020–14/200156 financed by Ministry of Education, Science and Technological Development of the Republic of Serbia.

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Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21000, Novi Sad, Serbia

    Marin Gostimirovic, Milenko Sekulic, Dragan Rodic & Andjelko Aleksic

  2. Faculty of Mechanical Engineering, University of Nis, A. Medvedeva 14, 18000, Nis, Serbia

    Milos Madic

Authors
  1. Marin Gostimirovic
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  2. Milos Madic
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  3. Milenko Sekulic
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  4. Dragan Rodic
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  5. Andjelko Aleksic
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Contributions

M. Gostimirovic conceived of the presented idea, developed the theory, methodology, software, and wrote original draft. M. Madic verified the mathematical model and helped shape the research, analysis, and design. M. Sekulic supervised the findings of this work and provided critical feedback. D. Rodic and A. Aleksic conceived and planned the experiments and performed the necessary measurements.

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Correspondence to Marin Gostimirovic.

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Gostimirovic, M., Madic, M., Sekulic, M. et al. A gradient-based optimal control problem in creep-feed grinding. Int J Adv Manuf Technol 121, 4777–4791 (2022). https://doi.org/10.1007/s00170-022-09609-y

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