DOI: https://doi.org/10.20535/2521-1943.2020.0.219256

Improving the performance of human hip implants by improving the processing quality and geometric accuracy of their spherical surfaces

Raul Turmanidze, G. Popkhadze, К. Inasharidze

Abstract


In view of the fact that the endo-prosthesis heads of human hip-joint are operated in extreme conditions, in respect of load, the selection of corresponding material and also increase of precision and quality of machining of spherical surfaces is rather topical task.

In the submitted work are reviewed the problems connected with definition of the influence degree of orientation of the sapphire crystal on its workability during diamond grinding with a butt of the ring and elaboration of the perspective, original scheme of formation of the incomplete spherical surface, particularly, of the sapphire head of endo-prosthesis of the human hip-joint.


Keywords


single crystal sapphire, anisotropy, grindability, endoprosthesis, precision grinding, forming, spherical surface.

References


K.-J. Bathe, Finite Element Procedures, 2nd ed., Watertown, MA, 2016.

N.G. Afendikova, “Istoriya metoda Galerkina i ego rol' v tvorchestve M.V. Keldysha”, Preprinty IPM im. M.V. Keldysha, no. 77, pp. 3–17, 2014. http://library.keldysh.ru/preprint.asp?id=2014-77

S.P. Demidov, Teoriya uprugosti [Theory of elasticity], Moscow, Russia: Vyssha shkola, 1979.

C.A.J. Fletcher, Computational Galerkin methods, New-York, USA: Springer–Verlag, 1984.

S.P. Timoshenko and S. Woinowsky-Krieger, Theory of plates and shells, 2nd ed., New–York, USA: McGraw-Hill Inc., 1959.

I. Elishakoff et al., “Rigorous versus naïve implementation of the Galerkin method for stepped beam”, Acta Mechanica, vol. 230, pp. 3861–3873, 2019, doi:https://doi.org/10.1007/s00707-019-02393-z

G.B. Warburton, “The vibration of rectangular plates”, Proc. Inst. Mech. Engrs., vol. 168, pp. 371–384, 1954, doi:https://doi:10.1243/PIME_PROC_1954_168_040_02

P. Moreno-García, J.V. Araújo dos Santos, and H. Lopes, “A review and study on Ritz method admissible functions with emphasis on buckling and free vibration of isotropic and anisotropic beams and plates”, Archives of Computational Methods in Engineering, vol. 25, pp. 785–815, 2018. https://doi.org/10.1007/s11831-017-9214-7

U. Lee, Spectral element method in structural dynamics, John Wiley and Sons (Asia), Singapore, 2009 https://doi.org/10.1002/9780470823767

J.T.-S. Wangand C.-C. Lin, “Dynamic analysis of generally supported beams using Fourier series”, Journal of Sound and Vibration, vol. 196, no. 3, pp. 285–293, 1996. https://doi.org/10.1006/jsvi.1996.0484

S. Zhang, L. Xu, and R. Li, “New exact series solutions for transverse vibration of rotationally-restrained orthotropic plates”, Applied Mathematical Modeling, vol. 65, pp. 348–360, 2019. https://doi.org/10.1016/j.apm.2018.08.033


GOST Style Citations


[1] K.-J. Bathe, Finite Element Procedures, 2nd ed., Watertown, MA, 2016.

[2] N.G. Afendikova, “Istoriya metoda Galerkina i ego rol' v tvorchestve M.V. Keldysha”, Preprinty IPM im. M.V. Keldysha, no. 77, pp. 3–17, 2014 http://library.keldysh.ru/preprint.asp?id=2014-77

[3] S.P. Demidov, Teoriya uprugosti [Theory of elasticity], Moscow, Russia: Vyssha shkola, 1979.

[4] C.A.J. Fletcher, Computational Galerkin methods, New-York, USA: Springer–Verlag, 1984.

[5] S.P. Timoshenko and S. Woinowsky-Krieger, Theory of plates and shells, 2nd ed., New–York, USA: McGraw-Hill Inc., 1959.

[6] I. Elishakoff et al., “Rigorous versus naïve implementation of the Galerkin method for stepped beam”, Acta Mechanica, vol. 230, pp. 3861–3873, 2019, doi:https://doi.org/10.1007/s00707-019-02393-z

[7] G.B. Warburton, “The vibration of rectangular plates”, Proc. Inst. Mech. Engrs., vol. 168, pp. 371–384, 1954, doi:https://doi:10.1243/PIME_PROC_1954_168_040_02

[8] P. Moreno-García, J.V. Araújo dos Santos, and H. Lopes, “A review and study on Ritz method admissible functions with emphasis on buckling and free vibration of isotropic and anisotropic beams and plates”, Archives of Computational Methods in Engineering, vol. 25, pp. 785–815, 2018. https://doi.org/10.1007/s11831-017-9214-7

[9] U. Lee, Spectral element method in structural dynamics, John Wiley and Sons (Asia), Singapore, 2009 https://doi.org/10.1002/9780470823767

[10] J.T.-S. Wangand C.-C. Lin, “Dynamic analysis of generally supported beams using Fourier series”, Journal of Sound and Vibration, vol. 196, no. 3, pp. 285–293, 1996. https://doi.org/10.1006/jsvi.1996.0484

[11] S. Zhang, L. Xu, and R. Li, “New exact series solutions for transverse vibration of rotationally-restrained orthotropic plates”, Applied Mathematical Modeling, vol. 65, pp. 348–360, 2019. https://doi.org/10.1016/j.apm.2018.08.033





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