Advertisement

Prediction of 3D grinding temperature field based on meshless method considering infinite element

  • Zixuan Wang
  • Yan Li
  • Tianbiao Yu
  • Ji Zhao
  • P. H. Wen
ORIGINAL ARTICLE
  • 41 Downloads

Abstract

A three-dimensional numerical model to calculate the grinding temperature field distribution is presented. The finite block method, which is developed from meshless method, is used to deal with the stationary and the transient heat conduction problems in this paper. The influences of workpiece feed velocity, cooling coefficient, and the depth of cut on temperature distribution are considered. The model with temperature-dependent thermal conductivity and specific heat is presented. The Lagrange partial differential matrix from the heat transfer governing equation is obtained by using Lagrange series and mapping technique. The grinding wheel-workpiece contact area is assumed as a moving distributed square heat source. The Laplace transformation method and Durbin’s inverse technique are employed in the transient heat conduction analysis. The results of the developed model are compared with others’ finite element method solutions and analytical solutions where a good agreement is demonstrated. And the finite block method was proved a better convergence and accuracy than finite element method by comparing the ABAQUS results. In addition, the three-dimensional infinite element is introduced to perform the thermal analysis, and there is a great of advantages in the simulation of large boundary problems.

Keywords

Meshless finite block method Infinite element Mapping technique Differential matrix Grinding processes Heat transfer 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Funding information

The work was funded by China Scholarship Council, the Fundamental Research Funds for the Central Universities (N160306006), National Natural Science Foundation of China (51275084), and Science and technology project of Shenyang (18006001).

References

  1. 1.
    Li HN, Axinte D (2017) On a stochastically grain-discretised model for 2D/3D temperature mapping prediction in grinding. Int J Mach Tool Manu 116:60–76CrossRefGoogle Scholar
  2. 2.
    Malkin S, Guo C (2007) Thermal analysis of grinding. CIRP Ann Manuf Technol 56(2):760–782CrossRefGoogle Scholar
  3. 3.
    Jaeger J Moving sources of heat and the temperature at sliding contacts. In J. Proc. Roy. Soc. NSW 1942:203–224Google Scholar
  4. 4.
    Malkin S (1984) Inclined moving heat source model for calculating metal cutting temperatures. J Eng Ind 106:179CrossRefGoogle Scholar
  5. 5.
    Moulik P, Yang H, Chandrasekar S (2001) Simulation of thermal stresses due to grinding. Int J Mech Sci 43(3):831–851CrossRefGoogle Scholar
  6. 6.
    Gu RJ, Shillor M, Barber GC, Jen T (2004) Thermal analysis of the grinding process. Math Comput Model 39(9):991–1003.  https://doi.org/10.1016/S0895-7177(04)90530-4 MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Lavine AS (2000) An exact solution for surface temperature in down grinding. Int J Heat Mass Transf 43(24):4447–4456.  https://doi.org/10.1016/S0017-9310(00)00024-7 CrossRefzbMATHGoogle Scholar
  8. 8.
    Mamalis A, Manolakos D, Markopoulos A, Kunádrk J, Gyáni K (2003) Thermal modelling of surface grinding using implicit finite element techniques. Int J Adv Manuf Tech 21(12):929–934CrossRefGoogle Scholar
  9. 9.
    Parente MPL, Jorge RMN, Vieira AA, Baptista AM (2012) Experimental and numerical study of the temperature field during creep feed grinding. Int J Adv Manuf Tech 61(1–4):127–134CrossRefGoogle Scholar
  10. 10.
    Malkin S (1974) Thermal aspects of grinding: part 2—surface temperatures and workpiece burn. J Eng Ind 96(4):1184–1191.  https://doi.org/10.1115/1.3438493 CrossRefGoogle Scholar
  11. 11.
    Des Ruisseaux NR, Zerkle RD (1970) Thermal analysis of the grinding process. J Eng Ind 92(2):428–433.  https://doi.org/10.1115/1.3427768 CrossRefGoogle Scholar
  12. 12.
    Kuo WL, Lin JF (2006) General temperature rise solution for a moving plane heat source problem in surface grinding. Int J Adv Manuf Tech 31(3–4):268–277CrossRefGoogle Scholar
  13. 13.
    Foeckerer T, Zaeh M, Zhang OB (2013) A three-dimensional analytical model to predict the thermo-metallurgical effects within the surface layer during grinding and grind-hardening. Int J Heat Mass Transf 56(1):223–237CrossRefGoogle Scholar
  14. 14.
    Lavisse B, Lefebvre A, Sinot O, Henrion E, Lemarié S, Tidu A (2017) Grinding heat flux distribution by an inverse heat transfer method with a foil/workpiece thermocouple under oil lubrication. Int J Adv Manuf Tech 1–3:1–14Google Scholar
  15. 15.
    Wang D, Ge P, Sun S, Jiang J, Liu X (2017) Investigation on the heat source profile on the finished surface in grinding based on the inverse heat transfer analysis. Int J Adv Manuf Tech 92(2):1–16Google Scholar
  16. 16.
    Li J, Li J (2005) Temperature distribution in workpiece during scratching and grinding. Mater Sci Eng A 409(1):108–119CrossRefGoogle Scholar
  17. 17.
    Mao C, Zhou Z, Guo K, Li X (2010) Numerical simulation and experimental validation of the temperature field in surface grinding. Mach Sci Technol 14(3):344–364CrossRefGoogle Scholar
  18. 18.
    Ding Z, Jiang X, Guo M, Liang SY (2018) Investigation of the grinding temperature and energy partition during cylindrical grinding. Int J Adv Manuf Tech:1–12Google Scholar
  19. 19.
    Wang X, Yu T, Sun X, Shi Y, Wang W (2016) Study of 3D grinding temperature field based on finite difference method: considering machining parameters and energy partition. Int J Adv Manuf Tech 84(5):1–13Google Scholar
  20. 20.
    Guo C, Malkin S (1995) Analysis of transient temperatures in grinding. J Eng Ind 117(4):571–577.  https://doi.org/10.1115/1.2803535 CrossRefGoogle Scholar
  21. 21.
    Zhang J, Li C, Zhang Y, Yang M, Jia D, Hou Y, Li R (2018) Temperature field model and experimental verification on cryogenic air nanofluid minimum quantity lubrication grinding. Int J Adv Manuf Tech 97(1–4):209–228CrossRefGoogle Scholar
  22. 22.
    Hou ZB, Komanduri R (2004) On the mechanics of the grinding process, part III—thermal analysis of the abrasive cut-off operation. Int J Mach Tool Manu 44(44):271–289CrossRefGoogle Scholar
  23. 23.
    DesRuisseaux NR, Zerkle R (1970) Temperature in semi-infinite and cylindrical bodies subjected to moving heat sources and surface cooling. J Heat Transf 92(3):456–464CrossRefGoogle Scholar
  24. 24.
    Biermann D, Schneider M (1997) Modeling and simulation of workpiece temperature in grinding by finite element analysis. Mach Sci Technol 1(2):173–183CrossRefGoogle Scholar
  25. 25.
    Rowe WB (2001) Thermal analysis of high efficiency deep grinding. Int J Mach Tool Manu 41(1):1–19.  https://doi.org/10.1016/S0890-6955(00)00074-2 CrossRefGoogle Scholar
  26. 26.
    Rowe WB, Jin T (2001) Temperatures in high efficiency deep grinding (HEDG). CIRP Ann Manuf Technol 50(1):205–208CrossRefGoogle Scholar
  27. 27.
    Mahdi M, Zhang L (1995) The finite element thermal analysis of grinding processes by ADINA. Comput Struct 56(2):313–320.  https://doi.org/10.1016/0045-7949(95)00024-B CrossRefGoogle Scholar
  28. 28.
    Guo C, Malkin S (1995) Analysis of energy partition in grinding. J Eng Ind 117(1):55–61.  https://doi.org/10.1115/1.2803278 CrossRefGoogle Scholar
  29. 29.
    Kim H-J, Kim N-K, Kwak J-S (2006) Heat flux distribution model by sequential algorithm of inverse heat transfer for determining workpiece temperature in creep feed grinding. Int J Mach Tool Manu 46(15):2086–2093.  https://doi.org/10.1016/j.ijmachtools.2005.12.007 CrossRefGoogle Scholar
  30. 30.
    Mohamed A-MO, Warkentin A, Bauer R (2012) Variable heat flux in numerical simulation of grinding temperatures. Int J Adv Manuf Tech 63(5):549–554CrossRefGoogle Scholar
  31. 31.
    Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Method Appl M 139(1):3–47.  https://doi.org/10.1016/S0045-7825(96)01078-X CrossRefzbMATHGoogle Scholar
  32. 32.
    Sladek J, Sladek V, Zhang C (2003) Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method. Comput Mater Sci 28(3):494–504.  https://doi.org/10.1016/j.commatsci.2003.08.006 CrossRefGoogle Scholar
  33. 33.
    Sladek V, Sladek J, Zhang C (2005) Local integro-differential equations with domain elements for the numerical solution of partial differential equations with variable coefficients. J Eng Math 51(3):261–282.  https://doi.org/10.1007/s10665-004-3692-y MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Li M, Wen P (2014) Finite block method for transient heat conduction analysis in functionally graded media. Int J Numer Meth Eng 99(5):372–390MathSciNetCrossRefGoogle Scholar
  35. 35.
    Lei M, Li M, Wen PH, Bailey CG (2018) Moving boundary analysis in heat conduction with multilayer composites by finite block method. Eng Anal Bound Elem 89:36–44.  https://doi.org/10.1016/j.enganabound.2018.01.009 MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Li J, Liu JZ, Korakianitis T, Wen PH (2017) Finite block method in fracture analysis with functionally graded materials. Eng Anal Bound Elem 82:57–67MathSciNetCrossRefGoogle Scholar
  37. 37.
    Wen PH, Cao P, Korakianitis T (2014) Finite block method in elasticity. Eng Anal Bound Elem 46 (Supplement C) 46:116–125.  https://doi.org/10.1016/j.enganabound.2014.05.006 MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Li M, Lei M, Munjiza A, Wen P (2015) Frictional contact analysis of functionally graded materials with Lagrange finite block method. Int J Numer Meth Eng 103(6):391–412MathSciNetCrossRefGoogle Scholar
  39. 39.
    Li M, Meng L, Hinneh P, Wen P (2016) Finite block method for interface cracks. Eng Fract Mech 156:25–40CrossRefGoogle Scholar
  40. 40.
    Zhang J, Ge P, Jen TC, Zhang L (2009) Experimental and numerical studies of AISI1020 steel in grind-hardening. Int J Heat Mass Transf 52(3–4):787–795CrossRefGoogle Scholar
  41. 41.
    Durbin F (1974) Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate's method. Comput J 17(4):371–376.  https://doi.org/10.1093/comjnl/17.4.371 MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Pearce TRA, Fricker DC, Harrison AJL (2004) Predicting the occurrence of grind hardening in cubic boron nitride grinding of crankshaft steel. Proc. Inst. Mech. Eng. Part B-J. Eng. Manuf. 218(10):1339–1356CrossRefGoogle Scholar
  43. 43.
    Wood WL (1976) On the finite element solution of an exterior boundary value problem. Int J Numer Meth Eng 10(4):885–891CrossRefGoogle Scholar
  44. 44.
    Bettess P, Zienkiewicz O (1977) Diffraction and refraction of surface waves using finite and infinite elements. Int J Numer Meth Eng 11(8):1271–1290MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangPeople’s Republic of China
  2. 2.School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduPeople’s Republic of China
  3. 3.Department of MathematicsCity University of Hong KongKowloon TongHong Kong
  4. 4.School of Engineering and Materials ScienceQueen Mary University of LondonLondonUK

Personalised recommendations