Bearing Dynamic Coefficients in Rotordynamics. Lukasz Brenkacz
coefficients of hydrodynamic bearings (linear and non‐linear). The range of applicability of various calculation methods was determined based on measurements made for a rotating machine equipped with hydrodynamic bearings with clearly non‐linear operating characteristics.
Experimental research was carried out with the use of the impulse method, on the basis of which dynamic parameters of hydrodynamic bearings were determined. The applied method with a linear calculation algorithm allows the determination of stiffness and damping coefficients and the determination of mass coefficients in one algorithm. The stiffness and damping coefficients cannot be determined directly, thus indirect calculation methods are used. The mass of the rotor is a directly measurable parameter. Indirectly calculated mass coefficients can be compared with the known mass of the rotor. On this basis, it is possible to make preliminary estimations of the correctness of the results obtained.
As part of the study, the sensitivity analysis of the aforementioned experimental method was carried out with the use of a model created in Samcef Rotors software. The influence of unbalance, displacement of measuring sensors, and various variants of driving force were analyzed. Based on experimental research, dynamic coefficients of hydrodynamic bearings in a wide range of rotational speeds, taking into account resonance speeds and higher speeds, were determined. They were verified using Abaqus software.
Numerical calculations of stiffness and damping coefficients of hydrodynamic bearings with the use of linear and non‐linear calculation models developed by IMP PAN in Gdańsk were also carried out. The obtained results were verified. The stiffness and damping parameters of hydrodynamic bearings determined using numerical models (linear and non‐linear) were compared with the results of experimental research. From this comparison it was possible to evaluate the differences in the values of dynamic coefficients of bearings calculated on the basis of linear and non‐linear numerical methods and the experimental method.
I would like to thank all employees of the Turbine Dynamics and Diagnostics Department of the Polish Academy of Sciences for their kindness, for the atmosphere of friendship that they surrounded me with throughout the entire period of work, and for the fact that I could always count on their support and research experience. In particular, I would like to express my gratitude to Professor Grzegorz Żywica and Professor Jan Kiciński.
Łukasz Breńkacz
Gdańsk, November 2020
Symbols and Abbreviations
Symbols
β i,kdimensionless damping coefficients of lubricating film, i,k = x,y γ i,kdimensionless stiffness coefficients of lubricating film, i,k = x,y μ dynamic viscosity of oil, N·s/m2 = Pa·s μ o oil viscosity at temperature T, N·s/m2 = Pa·sΠdimensionless hydrodynamic pressure, Π = p(ΔR/R)2/μΩΠ*pressure at static equilibrium point σ standard deviation τ dimensionless time τ = ωt ψ angular coordinate
Abbreviations
A integral values according to Eq. (9.2)B integral values according to Eq. (9.2)c dampingc s ijdamping coefficients of bearing no. s, N·s/m, s = 1,2; i,j = x,yd shaft and bearing journal diameter, mD disk diameter, mDz bearing housing diameter, mD s ijdisplacement of bearing no. s in the frequency domain, m, s = 1,2; i,j = x,yFNiforce in the N direction, N = x,yF s i,jflexibility vector of bearing no. s, m/N, s = 1,2; i,j = x,yF 1, F2functions describing dynamic coefficients of bearingsH s i,jstiffness vector of bearing no. s, N/m, s = 1,2; i,j = x,yh lubrication gap thickness, mH dimensionless thickness of lubrication gap, H = h/ΔRk stiffnessk s ijstiffness coefficients of bearing no. s, N/m, s = 1,2; i,j = x,yL bearing housing width, mm massm s ijmass coefficients of bearing no. s, kg, s = 1,2; i,j = x,yOccenter of bearing journalOpcenter of the coordinate system associated with the bearing housing P force acting on the bearingp hydrodynamic pressure in the lubricating film, PaR journal radius, mΔRradial bearing backlash, mS Sommerfeld number (dimensionless load‐bearing capacity of bearings), S = Pst(ΔR/R)2/LDμΩt time, su, v, wspeed components of the liquid element in the coordinate system x, y, z, m/sU 1, V1, W1components of lower sliding surface speed, m/sU 2, V2, W2components of upper sliding surface speed, m/sWx , Wydynamic components of the reaction of lubricating film, NΔWx, ΔWychanges in the dynamic components of the reactions of lubricating film, NW static components (at equilibrium point) of the reactions of lubricating film, Nx&c.ovline; mean valuex,y,z coordinatesXc,Yc,Zcrectangular coordinate system related to the position of the journal center (Oc)st at the static equilibrium point, mXp,Yp,Zprectangular coordinate system related to the bearing housing center Op, mXc,Yc,Zcdimensionless rectangular coordinate system related to the position of the journal center (Oc)st at the static equilibrium point (Xc = xc/ΔR)
About the Companion Website
The book is accompanied by a companion website:
www.wiley.com/go/brenkacz/bearingdynamiccoefficients
The website includes:
Computational codes
Recordings
Конец ознакомительного фрагмента.
Текст предоставлен ООО «ЛитРес».
Прочитайте эту книгу целиком, купив полную легальную версию на ЛитРес.
Безопасно оплатить книгу можно банковской картой Visa, MasterCard, Maestro, со счета мобильного телефона, с платежного терминала, в салоне МТС или Связной, через PayPal, WebMoney, Яндекс.Деньги, QIWI Кошелек, бонусными картами или другим удобным Вам способом.