Читать книгу Bearing Dynamic Coefficients in Rotordynamics - Lukasz Brenkacz - Страница 13
ОглавлениеSymbols 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 , rad, angles defining position of outlet and inlet edges of lubricating pockets ω frequency, rad/s, rotational speed, rpmΩjournal angular velocity, rad/s
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), disturbing parametersZ matrix of dynamic coefficients of bearings
