Improvement of the design of radial lobe bearing on gas lubrication and development of the corresponding calculation software system

Abstract

BACKGROUND: With the increase in rotation speeds of turbomachinery shafts, particularly for aviation and space applications due to the requirements for compactness and mass reduction, the issue of bearing life becomes relevant. For such devices, it is promising to use gas lubricated petal bearings (GLPB), which do not require additional systems and operate on the gas of the turbomachine working flow with excellent damping characteristics. Despite the attractiveness of GLPB designs, they are difficult to calculate because the direct work is performed by a thin layer of gas instead of balls, as in classical bearings. The efficiency of a GLPB depends directly on its design, especially the shape of the lobes and the amount of clearance between the shaft and the lobe.

AIM: To develop a mathematical model of the operation of a gas lubricated lobe bearing to determine the pressure distribution across the lobe surface and the corresponding computer program for calculations.

METHODS: Computational modeling of radial GLPB operation is accomplished with the determination of pressure in the lubrication layer. Moreover, its corresponding integral characteristics within the Reynolds model and the equation for the height of the lubrication layer under several assumptions are determined.

RESULTS: In this research, a computer program has been developed that allows for automated calculation of the space of change of variables and functions, the layout of a single table and output, construction of a volumetric model for its subsequent use in CAD systems, and generation of pressure graphs. Herein, the calculation of each variant is faster than similar calculations in the MathCAD environment. The same convenience consists of the block structure of the program, the visual setting of interrelations between blocks, and various and understandable outputs, suitable for both the report (construction of graphs) and drawings and visualization.

CONCLUSION: A specialized software package for parametric optimization of gas dynamic characteristics of GLPB has been developed. The developed tool permits the calculation of several cases and facilitates the selection of the optimal gap shape based on numerous proposed criteria. Among other things, the calculation allows us to see the variations in a different operating mode of the plant, use of a different substance with different dimensions, and choose the optimum that will suit a particular plant. Moreover, it is possible to expand the limits of applicability of petal bearings, such as at low speeds or large diameters.

Keywords

gas lubricated petal bearings / gas lubrication / gas dynamic characteristics / calculation of petal bearings

References

[1] Bardagi T, Dravet A, Doussinault M. inventor; Safran Aircraft Engines SAS, assignee. Turbomachine nozzle with noise reduction. United States patent US 6935098. 2005 Aug 30. Accessed: 10.07.2023. Available from: https://patentimages.storage.googleapis.com/92/ff/21/d8dc058507f902/US6935098.pdf

[2] Bardagi T., Dravet A., Doussinault M. inventor; Safran Aircraft Engines SAS, assignee. Turbomachine nozzle with noise reduction. United States patent US 6935098. 2005 Aug 30. Дата обращения: 10.07.2023. Доступ по ссылке: https://patentimages.storage.googleapis.com/92/ff/21/d8dc058507f902/US6935098.pdf

[3] Lieblein J, Zelen M. Statistical investigation of the fatigue life of deep-groove ball bearings. Journal of research of the national bureau of standards. 1956;57(5):273–316. Accessed: 10.07.2023. Available from: https://nvlpubs.nist.gov/nistpubs/jres/057/5/V57.N05.A04.pdf

[4] Lieblein J., Zelen M. Statistical investigation of the fatigue life of deep-groove ball bearings // Journal of research of the national bureau of standards. Vol. 57, N 5. P. 273-316. Дата обращения: 10.07.2023. Доступ по ссылке: https://nvlpubs.nist.gov/nistpubs/jres/057/5/V57.N05.A04.pdf

[5] Jones AB. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions. J. Basic Eng. 1960;82(2):309-320. doi: 10.1115/1.3662587

[6] Jones A.B. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions // J. Basic Eng. 1960. Vol. 82, N 2. P. 309–320. doi: 10.1115/1.3662587

[7] Bornstein KR. Dynamic load capabilities of active electromagnetic bearings. J. Tribol. 1991;113(3):598–603. doi: 10.1115/1.2920665

[8] Bornstein K.R. Dynamic load capabilities of active electromagnetic bearings // J. Tribol. 1991. Vol. 113, N 3. P. 598–603. doi: 10.1115/1.2920665

[9] Grob D, Pradetto JC, Dessibourg D. inventor; MAN Energy Solutions SE, assignee. Cooling system for electromagnetic bearings of a turbocompressor. United States patent US 6464469. Patent and Trademark Office. Accessed: 10.07.2023. Available from: https://patentimages.storage.googleapis.com/c3/e2/75/2e118a4cd1aa63/US6464469.pdf

[10] Grob D., Pradetto J.C., Dessibourg D. inventor; MAN Energy Solutions SE, assignee . Cooling system for electromagnetic bearings of a turbocompressor. United States patent US 6464469. Patent and Trademark Office. Дата обращения: 10.07.2023. Доступ по ссылке: https://patentimages.storage.googleapis.com/c3/e2/75/2e118a4cd1aa63/US6464469.pdf

[11] Gribinichenko MV, Kurenskii AV, Kutsenko NV. Hybrid foil bearing with gas lubrication. Russian Engineering Research. 2016;36(3):198–200.

[12] Gribinichenko M.V., Kurenskii A.V., Kutsenko N.V. Hybrid foil bearing with gas lubrication // Russian Engineering Research. Vol.36, N 3. P. 198–200.

[13] Beschastnykh VN, Ravikovich YuA. Gas bearing of a heavy rotor of gas turbine engines. Development experience and implementation prospects. Vestnik MAI. 2010;17(3):91–98. (In Russ).

[14] Бесчастных В.Н., Равикович Ю.А. Газовый подшипник тяжелого ротора газотурбинных двигателей. Опыт разработки и перспективы внедрения // Вестник МАИ. 2010. Т. 17, № 3. С. 91–98.

[15] Beschastnykh VN, Ravikovich YuA, Sokolov AN. Determination of the static load rating of a segmental gas-static bearing. Vestnik MAI. 2009;16(1):84–94. (In Russ).

[16] Бесчастных В.Н., Равикович Ю.А., Соколов А.Н. Определение статической грузоподъемности сегментного газостатического подшипника // Вестник МАИ. 2009. Т. 16, № 1. С. 84-94.

[17] Bulat PV, Uskov VN. On the study of the oscillatory motion of the gas-suspended rotor of turbo-refrigeration machines and expanders. Part I. Problem statement. Vestnik Mezhdunarodnoy akademii kholoda. 2012;3:3–7. (In Russ).

[18] Булат П.В., Усков В.Н. Об исследовании колебательного движения газоподвесного ротора турбохолодильных машин и детандеров. Часть I. Постановка задачи // Вестник Международной академии холода. 2012. № 3. С. 3–7.

[19] Bulat PV, Uskov VN. On the study of the oscillatory motion of the gas-suspended rotor of turbo-refrigeration machines and expanders. Part II. Pressure fluctuations in the system of supply nozzles in supercritical mode. Vestnik Mezhdunarodnoy akademii kholoda. 2012;1:57–60. (In Russ).

[20] Булат П.В., Усков В.Н. Об исследовании колебательного движения газоподвесного ротора турбохолодильных машин и детандеров. Часть II. Колебания давления в системе питающих форсунок при сверхкритическом режиме // Вестник Международной академии холода. 2012. № 1. С. 57–60.

[21] Bulat PV, Zasukhin ON, Prodan NV. Peculiarities of application of turbulence models in the calculation of flows in supersonic paths of advanced jet engines. Dvigatel. 2012;1(79):20–23. (In Russ).

[22] Булат П.В., Засухин О.Н., Продан Н.В. Особенности применения моделей турбулентности при расчете течений в сверхзвуковых трактах перспективных реактивных двигателей // Двигатель. 2012. № 1(79). С. 20–23.

[23] Bulat PV, Smirnova OS, Prodan NV. Application of controlled gas- and hydrostatic bearings in turbopump units of combined rocket engines. Fundamentalnye issledovaniya. 2013;4(2):335–339. (In Russ).

[24] Булат П.В., Смирнова О.С., Продан Н.В. Применение управляемых газо- и гидростатических подшипников в турбонасосных агрегатах комбинированных ЖРД // Фундаментальные исследования. 2013. № 4(2). С. 335–339.

[25] Dellacorte C, Lukaszewicz V, Valco MJ, et al. Performance and Durability of High Temperature Foil Air Bearings for Oil-Free Turbomachinery. Tribol. Trans. 2000;43(4):774–780. doi: 10.1080/10402000008982407

[26] Dellacorte C., Lukaszewicz V., Valco M.J., et al. Performance and Durability of High Temperature Foil Air Bearings for Oil-Free Turbomachinery // Tribology Transactions. 2000. Vol. 43, N 4. P. 774–780. doi: 10.1080/10402000008982407

[27] Grassam NS, Powell JW. Micro Turbine Developments Ltd. London: Butterworths; 1964.

[28] Grassam N.S., Powell J.W. Micro Turbine Developments Ltd. London: Butterworths, 1964.

[29] Listopadov IV, Shershnev BB. Modeling a segmented gas bearing. ANSYS Solutions. Russkaya redaktsiya. Zima. 2006:43–45. (In Russ).

[30] Листопадов И. В., Шершнев Б. Б. Моделирование сегментного газового подшипника //ANSYS Solutions. Русская редакция. Зима. 2006. С. 43–45.

[31] Hisabe Y, Osada N, Ohtani T, et al. inventor; Ebara Corp, assignee. Gas dynamic bearing for spindle motor. United States patent US 4998033. 1991 Mar. 5. Accessed: 10.07.2023. Available from: https://patentimages.storage.googleapis.com/7e/7d/20/a266d602466c6a/US4998033.pdf

[32] Hisabe Y., Osada N., Ohtani T., et al. inventor; Ebara Corp, assignee. Gas dynamic bearing for spindle motor. United States patent US 1991 Mar. 5.

[33] Lund JW. Calculation of stiffness and damping properties of gas bearings. J. Lubr. Tech. 1968;90(4):793-803. Accessed: 10.07.2023. Available from: https://patentimages.storage.googleapis.com/7e/7d/20/a266d602466c6a/US4998033.pdf

[34] Lund J.W. Calculation of stiffness and damping properties of gas bearings // Journal of Lubrication Technology. 1968. Vol. 90, N 4. P. 793–803. Дата обращения: 10.07.2023. Доступ по ссылке: https://patentimages.storage.googleapis.com/7e/7d/20/a266d602466c6a/US4998033.pdf

[35] Pan CHT, Sternlicht B. On the translatory whirl motion of a vertical rotor in plain cylindrical gas-dynamic journal bearings. J. Basic Eng. 1962;84(1):152–158. doi: 10.1115/1.3657237

[36] Pan C.H.T., Sternlicht B. On the translatory whirl motion of a vertical rotor in plain cylindrical gas-dynamic journal bearings // J. Basic Eng. 1962. Vol. 84, N 1. P. 152–158. doi: 10.1115/1.3657237

[37] Yamazaki M, inventor; Toshiba Corp, assignee. Dynamic pressure air bearing. United States patent US 4797009. Accessed: 10.07.2023. Available from: https://patentimages.storage.googleapis.com/a6/9c/02/640df9efbf5884/US4797009.pdf

[38] Yamazaki M. inventor; Toshiba Corp, assignee. Dynamic pressure air bearing. United States patent US 4797009. Дата обращения: 10.07.2023. Доступ по ссылке: https://patentimages.storage.googleapis.com/a6/9c/02/640df9efbf5884/US4797009.pdf

[39] Bruckner RJ, DellaCorte C, Prahl JM. Analytic modeling of the hydrodynamic, thermal, and structural behavior of foil thrust bearings. NTRS - NASA Technical Reports Server; 2005. Accessed: 10.07.2023. Available from: https://ntrs.nasa.gov/api/citations/20050203843/downloads/20050203843.pdf

[40] Bruckner R.J., DellaCorte C., Prahl J.M. Analytic modeling of the hydrodynamic, thermal, and structural behavior of foil thrust bearings. NTRS – NASA Technical Reports Server, 2005. Дата обращения: 10.07.2023. Доступ по ссылке: https://ntrs.nasa.gov/api/citations/20050203843/downloads/20050203843.pdf

[41] Zvonarev PN. Razrabotka metoda rascheta radialnykh uprugogazodinamicheskikh podshipnikov s predvaritelno napryazhennymi lepestkami dlya malykh turbomashin nizkotemperaturnykh ustanovok [dissertation] Moscow; 2005. (In Russ).

[42] Звонарев П.Н. Разработка метода расчета радиальных упругогазодинамических подшипников с предварительно напряженными лепестками для малых турбомашин низкотемпературных установок: дис. д-ра. техн. наук. М., 2005.

RIGHTS & PERMISSIONS

Eco-Vector