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Değişken Viskozite Altında Şaft Hızının Hidrodinamik Yatak-Şaft Sisteminin Rijitlik ve Sönüm Katsayıları Üzerindeki Etkileri

Yıl 2024, ERKEN GÖRÜNÜM, 1 - 1

Abdurrahim Dal

https://doi.org/10.2339/politeknik.1424395

Öz

Ağır yükler ver yüksek hızlarda çalışan hidrodinamik yatak-şaft sistemleri yatakların karakteristik özellikleri sebebiyle önemli rotor dinamiği kararsızlık problemlerine maruz kalırlar. Bu yatakların dinamik özellikleri ve kararlılıkları çalışma esnasında ortaya çıkan ısıdan doğrudan etkilenir. Bu .çalışmada, hidrodinamik yatak ile desteklenmiş yatak-şaft sisteminin dinamik karakteristikleri ve sistemin kararlılığı değşken viskozite altında araştırılmıştır. Yağlayıcının akışı değişken viskozite için Dowson denkleminden türetilmiş ve iki serbestlik dereceli bir yatak-şaft sistemi için pertürbasyon denklemleri elde edilmiştir. Yağ filmindeki ısı transferi 3-boyutlu enerji denklemi ile modellenmiş ve bu modele, yatak çapı yönünde meydana gelen ısı transferi de ısı iletim denklemi ile modellenerek dahil edilmiştir. Teorik modellerin eş zamanlı çözümü için, sonlu farklar metodunu esas alan bir çözüm algortiması geliştirilmiş ve şaft hızının farklı radial boşluğa sahip hidrodinamik yatakların dinamik katsayıları üzerindeki etkilerinin araştırılması için bir dizi benzetim gerçekleştirilmiştir. Yapılan benzetim sonuçları, şaft hızının artması ile yağ sıcaklığının arttığını ve yatağın statik ve dinamik özelliklerini azalttığı ve termal etkinin daha küçük boşluk değerleri için daha etkili olduğu tespit edilmiştir.

Anahtar Kelimeler

değişken viskozite dinamik karakteristikler rotor dinamiği

Etik Beyan

Bu makalenin yazar(lar)ı çalışmalarında kullandıkları materyal ve yöntemlerin etik kurul izni ve/veya yasal-özel bir izin gerektirmediğini beyan ederler.

Kaynakça

  • [1] Zhang Y., Wang W., Wei D., Wang G., Xu J., Liu K., “Coupling analysis of tribological and dynamical behavior for a thermal turbulent fluid lubricated floating ring bearing-rotor system at ultra-high speeds”, Tribology International, 165: 107325, (2022). https://doi.org/10.1016/j.triboint.2021.107325.
  • [2] Shi J., Zhao B., He T., Tu L., Lu X., Xu H., “Tribology and dynamic characteristics of textured journal-thrust coupled bearing considering thermal and pressure coupled effects”, Tribology International, 180: 108292, (2023). https://doi.org/10.1016/j.triboint.2023.108292
  • [3] Xu B, Guo H, Wu X, He Y, Wang X, Bai J., “Static and dynamic characteristics and stability analysis of high-speed water-lubricated hydrodynamic journal bearings”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 236(4): 701-720, (2022). https://doi.org/10.1177/13506501211027018.
  • [4] Sun X., Sepahvand K.K., Marburg S., “Stability Analysis of Rotor-Bearing Systems under the influence of misalignment and parameter uncertainty”, Applied Sciences, 11: 7918, (2021). https://doi.org/10.3390/app11177918
  • [5] Li Y., Liang F., Zhou Y., Ding S., Du F., Zhou M., Bi J., Cai Y., “Numerical and experimental investigation on thermohydrodynamic performance of turbocharger rotor-bearing system”, Applied Thermal Engineering, 121: 27-38, (2017). https://doi.org/10.1016/j.applthermaleng.2017.04.041.
  • [6] Tammineni N.M., Mutra R.R., “A review on recent advancements in an automotive turbocharger rotor system supported on the ball bearings, oil film and oil-free bearings”, Journal of Brazilian Society of Mechanical Science and Engineering. 45: 481, (2023). https://doi.org/10.1007/s40430-023-04383-8
  • [7] Feng H., Jiang S., Ji A., “Investigations of the static and dynamic characteristics of water-lubricated hydrodynamic journal bearing considering turbulent, thermohydrodynamic and misaligned effects”, Tribology International, 130: 245-260, (2019). https://doi.org/10.1016/j.triboint.2018.09.007
  • [8] Garg H.C., Kumar V., Sharda H.B., “Performance of slot-entry hybrid journal bearings considering combined influences of thermal effects and non-Newtonian behavior of lubricant”, Tribology International, 43(8): 1518-1531, (2010). https://doi.org/10.1016/j.triboint.2010.02.013
  • [9] Dowson D., Hudson J.D., Hunter B., March C.N., “An experimental investigation of the thermal equilibrium of steadily loaded journal bearings”, Proceedings of Instutation of Mechanical Engineering Conference Proceedings, 181: 70–80, (1966). https://doi.org/10.1243/pime_conf_1966_181_034_02
  • [10] Maneshian B., Nassab S.A.G., “Thermohydrodynamic analysis of turbulent flow in journal bearings running under different steady conditions”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 223(8): 1115-1127, (2009). https://doi:10.1243/13506501JET575
  • [11] Suganami T., Szeri A.Z., “A thermohydrodynamic analysis of journal bearings”, Trans. ASME, Journal of Lubrication Technology, 101: 7–21, (1979) .
  • [12] Pai R.S., Pai R., “Stability of four-axial and six-axial grooved water-lubricated journal bearings under dynamic load”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 222(5): 683-691, (2008). https://doi:10.1243/13506501JET356
  • [13] Shyu S., Fuli L., Yeau-Ren J., Wei-Ren L., Sheng-Jii H., “THD effects of static performance characteristics of ınfinitely wide turbulent journal bearings”, Tribology Transactions, 53(6): 948-956, (2010). https://doi:10.1080/10402004.2010.512116
  • [14] Shyu S.H., Lee W.R., Hsieh S.J., Liang S.M., “Static performance characteristics of finite-width turbulent journal bearings with THD effect”, Tribology Transactions, 55(3): 302-312, (2012). https://doi.org/10.1080/10402004.2011.654322
  • [15] Tala-Ighil N., Fillon M., “A numerical investigation of both thermal and texturing surface effects on the journal bearings static characteristics”, Tribology International, 90: 228-239, (2015). https://doi.org/10.1016/j.triboint.2015.02.032
  • [16] Li B., Sun J., Zhu S., Fu Y., Zhao X., Wang H., Qing T., Ren Y., Li Y., Zhu G., “Thermohydrodynamic lubrication analysis of misaligned journal bearing considering the axial movement of journal”, Tribology International, 135: 397-407, (2019). https://doi.org/10.1016/j.triboint.2019.03.031
  • [17] Zhu S., Sun J., Li B., Zhu G., “Thermal turbulent lubrication analysis of rough surface journal bearing with journal misalignment”, Tribology International, 144: 106109, (2020). https://doi.org/10.1016/j.triboint.2019.106109
  • [18] Xu B, Guo H, Wu X., He Y, Wang X, Bai J., “Static and dynamic characteristics and stability analysis of high-speed water-lubricated hydrodynamic journal bearings”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 236(4): 701-720, (2022). https://doi.org/10.1177/13506501211027018
  • [19] Klit P., Lund J.W., “Calculation of the dynamic coefficients of a journal bearing, using a variational approach”, ASME. Journal of Tribology, 108(3): 421–424, (1986). https://doi.org/10.1115/1.3261223
  • [20] Sawicki J.T., Rao T.V.V.L.N., “Nonlinear prediction of rotordynamic coefficients for a hydrodynamic journal bearing”, Tribology Transactions, 44(3): 367-374, (2001). https://doi.org/10.1080/10402000108982469
  • [21] Majumdar B.C., Pai R., Hargreaves D.J., “Analysis of water-lubricated journal bearings with multiple axial grooves”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 218(2): 135-146, (2004). https://doi:10.1177/135065010421800208
  • [22] Pai R., Rao D.S., Shenoy B.S., Pai R.S., “Stability characteristics of a Tri-taper journal bearing: A linearized perturbation approach”, Journal of Materials Research and Technology, 1(2): 84-90, (2012). https://doi.org/10.1016/S2238-7854(12)70016-9.
  • [23] Nagaraju Y., Joy M.L., Prabhakaran N.K., “Thermohydrodynamic analysis of a two-lobe journal bearing”, International Journal of Mechanical Science, 36(3): 209–217, (1994).
  • [24] Xu G., Zhou J., Geng H., Lu M., Yang L., Yu L., “Research on the static and dynamic characteristics of misaligned journal bearing considering the rurbulent and thermohydrodynamic efffects”, ASME. J. Tribol., 137 (2): 024504, (2015). https://doi.org/10.1115/1.4029333
  • [25] Shi J., Zhao B., He T., Tu L., Lu X., Xu H., “Tribology and dynamic characteristics of textured journal-thrust coupled bearing considering thermal and pressure coupled effects”, Tribology International, 180: 108292, (2023). https://doi.org/10.1016/j.triboint.2023.10829
  • [26] Dal A., Şahin M., Kilic M., “A thermohydrodynamic performance analysis of a fluid film bearing considering with geometrical parameters”, Journal of Thermal Engineering, 9(6): 1604-1617, (2023). https://doi:10.18186/thermal.1401279
  • [27] Dal A., Sahin M., Kilic, M., “Effects of geometrical parameters on thermohydrodynamic performance of a bearing operating with nanoparticle additive oil”, Industrial Lubrication and Tribology, 75(2): 255-262, (2023). https://doi.org/10.1108/ILT-12-2022-0369
  • [28] Ferron J., Frene J., Boncompain R., “A study of the thermohydrodynamic performance of a plain journal bearing comparison between theory and experiments”, ASME. J. of Lubrication Tech., 105(3): 422–428, (1983). https://doi.org/10.1115/1.3254632
  • [29] Dal, A., “İki Serbestlik Dereceli Rotor-Hidrodinamik Yatak Sisteminin Kararlılığının Termal Etki Altında İncelenmesi”, International Journal of Engineering Research and Development, 16(1): 304-319, (2024). https://doi.org/10.29137/umagd.1404559
  • [30] Saruhan, H., Kam, M., and Kara, F. “Dynamic Behavior Analysis of Rotor Supported by Damped Rolling Element Bearing Housing”, Journal Of Polytechnic, 20(1): 159-164, (2017).
  • [31] Şimşek, M., Salman, Nteziyaremye, Ö., Kaleli, H, Tunay, R., F., Durak, E., “Experimental Analysis of Effect to Friction of Commercial Oil Additive Used in Automobiles”. Journal Of Polytechnic, 1–1, (2024). https://doi.org/10.2339/politeknik.1204731.
  • [32] Gürkan, D., Okur, M., ve Korkut, İ. “Döngüsel Kompresörlerde Teknolojik Gelişmeler”, Journal Of Polytechnic, 26(1): 425-436, (2023). https://doi.org/10.2339/politeknik.1003699

Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity

Yıl 2024, ERKEN GÖRÜNÜM, 1 - 1

Abdurrahim Dal

https://doi.org/10.2339/politeknik.1424395

Öz

The rotating shaft-hydrodynamic bearings systems operated with high speed and/or heavy load conditions expose serious rotor-dynamics instability problems due to characteristics of the supporting bearings. The stability and the dynamics of these systems, directly relate to the lubricant properties that are directly affect by the heat generation. In this study, the dynamic characteristics of a shaft-hydrodynamic journal bearing and its stability were investigated under variable viscosity. The equations of lubricant flow were derived by Dowson’s equation under variable viscosity, and the perturbation equations were obtained for 2 degrees-of-freedom system. The heat transfers between oil and the journal surface was modelled in a 3-dimensional energy equation, and the heat transfer on the journal structure was also modelled with heat conduction equation. An algorithm based on finite difference scheme with successive over relaxation method was developed to solve the theoretical models, simultaneously, and a serial simulation was performed to investigate the variations of the dynamic coefficients of the bearing-shaft system concerning the rotating speed for different radial clearance values. It was determined that the high speed increases the lubricant temperature, and so the static and dynamic performance characteristics decrease, moreover, this effect is more dominant for the smaller radial clearance.

Anahtar Kelimeler

variable viscosity dynamic characteristics rotor dynamic hydrodynamic bearing

Etik Beyan

The author(s) of this article declare that the materials and methods used in this study do not require ethical committee permission and/or legal-special permission.

Kaynakça

  • [1] Zhang Y., Wang W., Wei D., Wang G., Xu J., Liu K., “Coupling analysis of tribological and dynamical behavior for a thermal turbulent fluid lubricated floating ring bearing-rotor system at ultra-high speeds”, Tribology International, 165: 107325, (2022). https://doi.org/10.1016/j.triboint.2021.107325.
  • [2] Shi J., Zhao B., He T., Tu L., Lu X., Xu H., “Tribology and dynamic characteristics of textured journal-thrust coupled bearing considering thermal and pressure coupled effects”, Tribology International, 180: 108292, (2023). https://doi.org/10.1016/j.triboint.2023.108292
  • [3] Xu B, Guo H, Wu X, He Y, Wang X, Bai J., “Static and dynamic characteristics and stability analysis of high-speed water-lubricated hydrodynamic journal bearings”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 236(4): 701-720, (2022). https://doi.org/10.1177/13506501211027018.
  • [4] Sun X., Sepahvand K.K., Marburg S., “Stability Analysis of Rotor-Bearing Systems under the influence of misalignment and parameter uncertainty”, Applied Sciences, 11: 7918, (2021). https://doi.org/10.3390/app11177918
  • [5] Li Y., Liang F., Zhou Y., Ding S., Du F., Zhou M., Bi J., Cai Y., “Numerical and experimental investigation on thermohydrodynamic performance of turbocharger rotor-bearing system”, Applied Thermal Engineering, 121: 27-38, (2017). https://doi.org/10.1016/j.applthermaleng.2017.04.041.
  • [6] Tammineni N.M., Mutra R.R., “A review on recent advancements in an automotive turbocharger rotor system supported on the ball bearings, oil film and oil-free bearings”, Journal of Brazilian Society of Mechanical Science and Engineering. 45: 481, (2023). https://doi.org/10.1007/s40430-023-04383-8
  • [7] Feng H., Jiang S., Ji A., “Investigations of the static and dynamic characteristics of water-lubricated hydrodynamic journal bearing considering turbulent, thermohydrodynamic and misaligned effects”, Tribology International, 130: 245-260, (2019). https://doi.org/10.1016/j.triboint.2018.09.007
  • [8] Garg H.C., Kumar V., Sharda H.B., “Performance of slot-entry hybrid journal bearings considering combined influences of thermal effects and non-Newtonian behavior of lubricant”, Tribology International, 43(8): 1518-1531, (2010). https://doi.org/10.1016/j.triboint.2010.02.013
  • [9] Dowson D., Hudson J.D., Hunter B., March C.N., “An experimental investigation of the thermal equilibrium of steadily loaded journal bearings”, Proceedings of Instutation of Mechanical Engineering Conference Proceedings, 181: 70–80, (1966). https://doi.org/10.1243/pime_conf_1966_181_034_02
  • [10] Maneshian B., Nassab S.A.G., “Thermohydrodynamic analysis of turbulent flow in journal bearings running under different steady conditions”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 223(8): 1115-1127, (2009). https://doi:10.1243/13506501JET575
  • [11] Suganami T., Szeri A.Z., “A thermohydrodynamic analysis of journal bearings”, Trans. ASME, Journal of Lubrication Technology, 101: 7–21, (1979) .
  • [12] Pai R.S., Pai R., “Stability of four-axial and six-axial grooved water-lubricated journal bearings under dynamic load”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 222(5): 683-691, (2008). https://doi:10.1243/13506501JET356
  • [13] Shyu S., Fuli L., Yeau-Ren J., Wei-Ren L., Sheng-Jii H., “THD effects of static performance characteristics of ınfinitely wide turbulent journal bearings”, Tribology Transactions, 53(6): 948-956, (2010). https://doi:10.1080/10402004.2010.512116
  • [14] Shyu S.H., Lee W.R., Hsieh S.J., Liang S.M., “Static performance characteristics of finite-width turbulent journal bearings with THD effect”, Tribology Transactions, 55(3): 302-312, (2012). https://doi.org/10.1080/10402004.2011.654322
  • [15] Tala-Ighil N., Fillon M., “A numerical investigation of both thermal and texturing surface effects on the journal bearings static characteristics”, Tribology International, 90: 228-239, (2015). https://doi.org/10.1016/j.triboint.2015.02.032
  • [16] Li B., Sun J., Zhu S., Fu Y., Zhao X., Wang H., Qing T., Ren Y., Li Y., Zhu G., “Thermohydrodynamic lubrication analysis of misaligned journal bearing considering the axial movement of journal”, Tribology International, 135: 397-407, (2019). https://doi.org/10.1016/j.triboint.2019.03.031
  • [17] Zhu S., Sun J., Li B., Zhu G., “Thermal turbulent lubrication analysis of rough surface journal bearing with journal misalignment”, Tribology International, 144: 106109, (2020). https://doi.org/10.1016/j.triboint.2019.106109
  • [18] Xu B, Guo H, Wu X., He Y, Wang X, Bai J., “Static and dynamic characteristics and stability analysis of high-speed water-lubricated hydrodynamic journal bearings”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 236(4): 701-720, (2022). https://doi.org/10.1177/13506501211027018
  • [19] Klit P., Lund J.W., “Calculation of the dynamic coefficients of a journal bearing, using a variational approach”, ASME. Journal of Tribology, 108(3): 421–424, (1986). https://doi.org/10.1115/1.3261223
  • [20] Sawicki J.T., Rao T.V.V.L.N., “Nonlinear prediction of rotordynamic coefficients for a hydrodynamic journal bearing”, Tribology Transactions, 44(3): 367-374, (2001). https://doi.org/10.1080/10402000108982469
  • [21] Majumdar B.C., Pai R., Hargreaves D.J., “Analysis of water-lubricated journal bearings with multiple axial grooves”, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology. 218(2): 135-146, (2004). https://doi:10.1177/135065010421800208
  • [22] Pai R., Rao D.S., Shenoy B.S., Pai R.S., “Stability characteristics of a Tri-taper journal bearing: A linearized perturbation approach”, Journal of Materials Research and Technology, 1(2): 84-90, (2012). https://doi.org/10.1016/S2238-7854(12)70016-9.
  • [23] Nagaraju Y., Joy M.L., Prabhakaran N.K., “Thermohydrodynamic analysis of a two-lobe journal bearing”, International Journal of Mechanical Science, 36(3): 209–217, (1994).
  • [24] Xu G., Zhou J., Geng H., Lu M., Yang L., Yu L., “Research on the static and dynamic characteristics of misaligned journal bearing considering the rurbulent and thermohydrodynamic efffects”, ASME. J. Tribol., 137 (2): 024504, (2015). https://doi.org/10.1115/1.4029333
  • [25] Shi J., Zhao B., He T., Tu L., Lu X., Xu H., “Tribology and dynamic characteristics of textured journal-thrust coupled bearing considering thermal and pressure coupled effects”, Tribology International, 180: 108292, (2023). https://doi.org/10.1016/j.triboint.2023.10829
  • [26] Dal A., Şahin M., Kilic M., “A thermohydrodynamic performance analysis of a fluid film bearing considering with geometrical parameters”, Journal of Thermal Engineering, 9(6): 1604-1617, (2023). https://doi:10.18186/thermal.1401279
  • [27] Dal A., Sahin M., Kilic, M., “Effects of geometrical parameters on thermohydrodynamic performance of a bearing operating with nanoparticle additive oil”, Industrial Lubrication and Tribology, 75(2): 255-262, (2023). https://doi.org/10.1108/ILT-12-2022-0369
  • [28] Ferron J., Frene J., Boncompain R., “A study of the thermohydrodynamic performance of a plain journal bearing comparison between theory and experiments”, ASME. J. of Lubrication Tech., 105(3): 422–428, (1983). https://doi.org/10.1115/1.3254632
  • [29] Dal, A., “İki Serbestlik Dereceli Rotor-Hidrodinamik Yatak Sisteminin Kararlılığının Termal Etki Altında İncelenmesi”, International Journal of Engineering Research and Development, 16(1): 304-319, (2024). https://doi.org/10.29137/umagd.1404559
  • [30] Saruhan, H., Kam, M., and Kara, F. “Dynamic Behavior Analysis of Rotor Supported by Damped Rolling Element Bearing Housing”, Journal Of Polytechnic, 20(1): 159-164, (2017).
  • [31] Şimşek, M., Salman, Nteziyaremye, Ö., Kaleli, H, Tunay, R., F., Durak, E., “Experimental Analysis of Effect to Friction of Commercial Oil Additive Used in Automobiles”. Journal Of Polytechnic, 1–1, (2024). https://doi.org/10.2339/politeknik.1204731.
  • [32] Gürkan, D., Okur, M., ve Korkut, İ. “Döngüsel Kompresörlerde Teknolojik Gelişmeler”, Journal Of Polytechnic, 26(1): 425-436, (2023). https://doi.org/10.2339/politeknik.1003699
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Dinamikler, Titreşim ve Titreşim Kontrolü, Makine Teorisi ve Dinamiği
Bölüm Araştırma Makalesi
Yazarlar

Abdurrahim Dal 0000-0002-7012-2148

Erken Görünüm Tarihi 28 Nisan 2024
Yayımlanma Tarihi
Gönderilme Tarihi 23 Ocak 2024
Kabul Tarihi 15 Nisan 2024
Yayımlandığı Sayı Yıl 2024 ERKEN GÖRÜNÜM

Kaynak Göster

APA Dal, A. (2024). Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity. Politeknik Dergisi1-1. https://doi.org/10.2339/politeknik.1424395
AMA Dal A. Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity. Politeknik Dergisi. Published online 01 Nisan 2024:1-1. doi:10.2339/politeknik.1424395
Chicago Dal, Abdurrahim. “Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity”. Politeknik Dergisi, Nisan (Nisan 2024), 1-1. https://doi.org/10.2339/politeknik.1424395.
EndNote Dal A (01 Nisan 2024) Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity. Politeknik Dergisi 1–1.
IEEE A. Dal, “Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity”, Politeknik Dergisi, ss. 1–1, Nisan 2024, doi: 10.2339/politeknik.1424395.
ISNAD Dal, Abdurrahim. “Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity”. Politeknik Dergisi. Nisan 2024. 1-1. https://doi.org/10.2339/politeknik.1424395.
JAMA Dal A. Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity. Politeknik Dergisi. 2024;:1–1.
MLA Dal, Abdurrahim. “Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity”. Politeknik Dergisi, 2024, ss. 1-1, doi:10.2339/politeknik.1424395.
Vancouver Dal A. Effects of the Shaft Speed on Stiffness and Damping Coefficients of Hydrodynamic Bearing-Shaft System under Variable Viscosity. Politeknik Dergisi. 2024:1-.
 
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