Introduction To Pump Rotordynamics
Introduction to Pump RotordynamicsLuis San AndrésMast-Childs Tribology ProfessorTurbomachinery LaboratoryTexas A&M UniversityCollege Station, TX 77843-3123USALsanandres@mengr.tamu.eduABSTRACTThe lecture introduces the basic problems in the rotordynamics of turbomachinery, excessive vibrationand instability. The acceptable performance of a turbomachine depends on the adequate design andoperation of the bearing and seal elements supporting a rotor. Descriptions of the basic principles oflubrication follow with details on the operation of hydrodynamic and hydrostatic lubricated bearings andseals. The differences among these elements are highlighted with a brief account on their effects onrotordynamics. The basic equations for the modeling of linear rotor-bearing systems are given along withan example for the rotordynamics of a multiple stage compressor. Pump rotordynamics is introducednoting the major difference with other rotating systems, i.e. hydraulic side loads, static and dynamic, dueto pressure changes in the volute and flow conditions in an impeller, dynamic forces from seals – neckring and interstage and balance pistons, and impeller-rotor interaction forces. Accounting for the actionof these elements is of importance to adequately predict the performance and troubleshoot therotordynamics of high performance pumps. An example of rotordynamic analysis of a multiple-stageliquid pump stresses the differences between “wet’ and “dry” predictions, i.e. operation with and withoutthe pumping liquid.1.0 INTRODUCTIONA turbomachinery is a rotating structure where the load or the driver handles a process fluid from whichpower is extracted or delivered to. Examples of turbomachines include pumps and compressors, gas andsteam turbines, turbo generators and turbo expanders, turbochargers, APU (auxiliary power units), etc.Most turbomachinery is supported on oil lubricated fluid film bearings, although modern advances andenvironmental restrictions are pushing towards the implementation of process fluid bearings and even gasbearing applications. Fluid film bearings are used due to their adequate load support, good dampingcharacteristics and absence of wear if properly designed and operated.Turbomachines also include a number of other mechanical elements which provide stiffness and dampingcharacteristics and affect the dynamics of the rotor-bearing system. Impeller seals, floating ring seals,thrust collars and balance pistons are a few of these elements.The adequate operation of a turbomachine is defined by its ability to tolerate normal (and even abnormal)vibrations levels without affecting significantly its overall performance (reliability and efficiency).The rotordynamics of turbomachinery encompasses the structural analysis of rotors (shafts and disks) andthe design of fluid film bearings and seals that determine the best dynamic performance given the requiredSan Andrés, L. (2006) Introduction to Pump Rotordynamics. In Design and Analysis of High Speed Pumps (pp. 9-1 – 9-26). Educational NotesRTO-EN-AVT-143, Paper 9. Neuilly-sur-Seine, France: RTO. Available from: 439-1
Introduction to Pump Rotordynamicsoperating conditions. This best performance is denoted by well-characterized natural frequencies (andcritical speeds) with amplitudes of synchronous dynamic response within required standards anddemonstrated absence of subsynchronous vibration instabilities.A rotordynamic analysis considers the interaction between the elastic and inertia properties of the rotorand the mechanical impedances from the fluid film bearing supports, oil seal rings, seals, etc.The most commonly recurring problems in rotordynamics are [1]1.2.Excessive steady state synchronous vibration levels.Sub harmonic rotor instabilities.Steady state vibration levels may be reduced by:a) Improving balancing.b) Modifying rotor-bearing systems: tune system critical speeds out of RPM operating range.c) Introducing damping to limit peak amplitudes at critical speeds that must be traversed.Sub harmonic rotor instabilities may be avoided by:a) Raising the natural frequency of rotor system as much as possible.b) Eliminating the instability mechanism, i.e. change bearing design if oil whip is present.c) Introducing damping to raise onset speed above the operating speed range.Rotordynamic instabilities have become more common as the speed and power of turbomachineryincreased. These instabilities can sometimes be erratic, seemingly increasing vibration amplitudes for noapparent reason. A common denominator among many stability problems is that they tend to grow withtime as the affected component(s) begins to wear or fatigue.For example, two typical destabilizing forces well documented in the technical literature are due to theaerodynamic effects of labyrinth seals and the hydrodynamic effects of lubricated cylindrical bearings andfloating oil ring seals in centrifugal compressors. Load, gas molecular weight, and oil pressure andtemperature are factors to generate severe problems in problematic turbomachinery.The detailed study of rotordynamics demands accurate knowledge of the particular mechanical elementssupporting the rotor, i.e. fluid film bearings and seals.2.0 DESCRIPTIONS OF FLUID FILM BEARINGSFluid film bearings are machine elements designed to produce smooth (low friction) motion between solidsurfaces in relative motion and to generate a load support for mechanical components. The lubricant orfluid between the surfaces may be a liquid, a gas or even a solid (coating).Fluid film bearings, if well designed, are able to support static and dynamic loads, and consequently, theireffects on the performance of rotating machinery are of great importance.These notes focus on the analysis of bearings with a full film separating the mechanical surfaces. Theword film implies that the fluid thickness (gap or clearance) separating the surfaces is several orders ofmagnitude smaller than the other dimensions of the bearing, i.e. width and length. Yet the film thickness islarger than the micro asperities in the surfaces thus warranting operation without contact of surfaces.The basic operational principles of fluid film bearings are hydrodynamic, hydrostatic or hybrid (acombination of the former two).9-2RTO-EN-AVT-143
Introduction to Pump Rotordynamics2.1Hydrodynamic or Self-Acting Fluid Film BearingsIn hydrodynamic bearings there is relative motion between two mechanical surfaces with a particular“wedge like” shape, See Figure 1. The fluid dragged into the film generates a hydrodynamic pressure fieldable to support an externally applied load, static and/or dynamic. In general [2]:AdvantagesDisadvantagesDo not require external source of pressure. Thermal effects affect performance if film thickness isFluid flow is dragged into the convergent too small or available flow rate is too low.gap in the direction of the surface relativeRequire of surface relative motion to generate loadmotion.support.Support heavy loads. The load support is afunction of the lubricant viscosity, surface Induce large drag torque (power losses) and potentialspeed, surface area, film thickness and surface damage at start-up (before lift-off) and touchdown.geometry of the bearing.Long life (infinite in theory) without wear of Potential to induce hydrodynamic instability, i.e. lossof effective damping for operation well above criticalsurfaces.speed of rotor-bearing system.Provide stiffness and damping coefficients oflarge magnitude.2.2Hydrostatic or Externally-Pressurized Fluid Film BearingsIn hydrostatic bearings, an external source of pressurized fluid forces the lubricant to flow between thesurfaces, thus enabling their separation and the ability to support a load without surface contact, and mostimportantly, without relative motion. See Figure 2 for a typical geometry. In general [2]:AdvantagesDisadvantagesSupport very large loads. The load support is Require ancillary equipment. Larger installation anda function of the pressure drop across the maintenance costs.bearing and the area of fluid pressure action.Need of fluid filtration equipment. Loss of performanceLoad does not depend on film thickness or with fluid contamination.lubricant viscosity.High power consumption because of pumping losses.Long life (infinite in theory) without wear ofPotential to induce hydrodynamic instability in hybridsurfacesmode operation.Provide stiffness and damping coefficients ofvery large magnitude. Excellent for exact Potential to show pneumatic hammer instability forhighly compressible fluids, i.e. loss of damping at lowpositioning and control.and high frequencies of operation due to complianceand time lag of trapped fluid volumes.RTO-EN-AVT-1439-3
Introduction to Pump RotordynamicsJournal rotationPressureRelative motionPressureHydrodynamicwedgeFluidPlain journal bearingSlider bearingFigure 1: Schematic Views of Hydrodynamic (Self-Acting) Fluid Film Bearing.PressurePsPrrestrictorFluid at PsrecessfilmHydrostatic journal bearingFigure 2: Schematic Views of Hydrostatic (Pressurized) Fluid Film Bearing.Figure 3 depicts schematic views of hydrodynamic journal bearings, single and multiple lobes, andmultiple pads. The cylindrical bearings feature feed ports for lubricant inlet as well as pad or lobesmachined with a preload to generate a film wedge upon shaft rotation.9-4RTO-EN-AVT-143
Introduction to Pump RotordynamicsPLAIN JOURNALBEARINGPARTIAL ARCJOURNAL BEARINGFLOATING RINGJOURNAL BEARINGDamTop halfBottom halfPRESSURE DAM JOURNAL BEARINGReliefGrooveTILTING PAD JOURNALBEARINGFigure 3: Schematic Views of Typical Cylindrical Journal Bearings.2.3Squeeze Film DampersNormal motions can also generate hydrodynamic pressures in the thin film separating two surfaces. Thissqueeze film action mechanism works effectively only for compressive loads, i.e. those forcing theapproach of one surface to the other. Squeeze film dampers are routinely implemented to reduceRTO-EN-AVT-1439-5
Introduction to Pump Rotordynamicsvibration amplitudes and isolate structural components in gas jet engines, high performance compressors,and occasionally in water pumps.A squeeze film damper consists of an inner non rotating journal and a stationary outer bearing, both ofnearly identical diameters. Figure 4 shows an idealized schematic of this type of fluid film bearing. Ajournal is mounted on the external race of a rolling element bearing and prevented from spinning withloose pins or a squirrel cage that provides a centering elastic mechanism. The annular thin film, typicallyless than 0.250 mm, between the journal and housing is filled with a lubricant provided as a splash fromthe rolling bearing elements lubrication system or by a dedicated pressurized delivery. In operation, as thejournal moves due to dynamic forces acting on the system, the fluid is displaced to accommodate thesemotions. As a result, hydrodynamic squeeze film pressures exert reaction forces on the journal and providefor a mechanism to attenuate transmitted forces and to reduce the rotor amplitude of motion ntfilmhousingFigure 4: Typical Squeeze Film Damper Configuration.2.4Annular Pressure SealsRadial seals (annular, labyrinth or honeycomb) separate regions of high pressure and low pressure inrotating machinery and their function is to minimize the leakage and improve the overall efficiency of arotating machine extracting or delivering power to a fluid. Typical applications include neck ring seals onimpeller eyes and inter stage seals as well as balance pistons in pump and compressor applications, asdepicted in Figure 5. Seals have larger clearances than load carrying bearings. Yet their impact on therotordynamics of turbomachinery is of importance since seals are located at rotor positions where largevibrations occur [4].Interstage SealImpeller Eye SealBalance Piston SealFigure 5: Seals in a Multistage Centrifugal Pump or Compressor.9-6RTO-EN-AVT-143
Introduction to Pump RotordynamicsExtensive testing has shown that seals with macroscopic roughness; i.e. textured stator surfaces, offermajor improvements in reducing leakage as well as cross-coupled stiffness coefficients [5]. Figure 6depicts two textured seals and a conventional labyrinth seal (teeth on stator). A textured surface like around-hole pattern or a honeycomb increases the friction thus reducing leakage, and aids to retard thedevelopment of the circumferential flow velocity -the physical condition generating the cross-coupledstiffness coefficients. In the past 10 years, compressor and pump manufacturers, as well as users, areimplementing textured seals with great commercial success [6].Hole-Pattern SealUnwrapHoneycomb SealUnwrapLabyrinth SealFigure 6: Hole-Pattern, Honeycomb and Labyrinth Seal Configurations.3.0 BASICS OF A ROTORDYNAMIC ANALYSISThe objectives of a rotordynamic analysis are:a) To model the rotor (shaft and disks) and to determine its free-free natural frequencies.b) To model the fluid film bearing and seal elements and to calculate the mechanical impedances(stiffness, damping and inertia force coefficients connecting the rotor to its casing).c)To perform an eigenvalue analysis, i.e. to predict the damped natural frequencies and dampingratios for the different modes (rigid and elastic) of vibration of the rotor as the rotor speedincreases to values well above its design operating conditions. Positive damping ratios evidencethe absence of rotordynamic instability.d) To perform a synchronous response analysis to calibrated imbalances in order to predict themaximum amplitudes of vibration, the safe passage through critical speeds and to estimate theloads transmitted through the bearing supports.e) To certify the reliable performance of the rotor-bearing system satisfying established engineeringcriteria (API qualification) and to emit recommendations to improve the system performance(response and stability).RTO-EN-AVT-1439-7
Introduction to Pump RotordynamicsIt is important to stress that the tasks (objectives) above need of extensive experimental and field supportverification. Analysis without adequate field or shop measurements is usually not very useful inrotordynamics.3.1Equations of Motion for Rotor-Bearing SystemThe general equations for lateral motions of a rotor are [4]:([M ] [N ])R {u } Ω [G ]R {u } [K ]R {u} {F (u, u , t )}(1)where [M] and [N] are global translational and rotary mass matrices, [G] and [K] are gyroscopic andstiffness matrices, Ω is the rotor speed, {u}represent the rotor displacements (translations and rotations),and {F (u , u , t )} denote bearing and seal reaction forces and the distributed imbalance vector, for example,The in-house finite element rotordynamics code[7] is based on Timoshenko beam theory [8] andimplements component-mode synthesis [9] to model multiple shaft rotors. The program interfaces with anumber of bearing and seal codes also developed in-house.3.2Representations of Bearing and Seal ForcesIn a linear lateral rotordynamics model, bearing and seal reaction forces are linear functions of the rotormotion. Bearing dynamic forces along directions (X, Y) perpendicular to the rotor spin axis (Z) arerepresented in terms of force coefficients (See Figure 7), i.e. FX K XX F K Y YXK XY X C XX K YY B Y CYXC XY X CYY B Y (2)where [K]B and [C]B denote matrices of stiffness and damping force coefficients. The force coefficients arestrictly valid for small amplitude motions or perturbations about an equilibrium condition. The static loadacting on each bearing and shaft speed determine the equilibrium state. Force coefficients for oillubricated bearings are frequency independent parameters, though changing with the operating shaft speedand load condition. Fluid film bearings handling compressible liquids and gases generate frequencydependent force coefficients.YδYZδXXFigure 7: DOF Lateral Displacements (X,Y) and Angulations (δX, δY).The representation of liquid seal forces for lateral motions (X, Y) is given as [4] FX K XX F K Y YX9-8K XY X C XX K YY S Y CYXC XY CYY S X M XX Y M YXM XY M YY S X Y (3)RTO-EN-AVT-143
Introduction to Pump Rotordynamicswhere [K]S, [C]S and [M]S represent matrices of stiffness, damping and inertia force coefficients. Addedmass coefficients are of importance in liquid seals due to the large density of the fluid pumped.Dynamic reaction forces in gas seals are nowadays represented as FX K XX (ω ) K XY (ω ) X C XX (ω ) C XY (ω ) F K (ω ) K (ω ) Y C (ω ) C (ω ) YYYY Y YX S YX S X Y (4)with force coefficients showing a complicated dependency on frequency [5].Balance pistons are represented as long seals, and thus these elements can also generate bending moments(MX,Y) due to lateral displacements, as well as reaction forces due to dynamic angulations (φX, φY) aroundthe (X, Y) axes, i.e. [4] FX FY MX MY K XX K YX - K δXX - K δXYK XYK XδXK XXK XδYK δXYK δXδXK δXXK δXδYK XδY X C XX C XY K XδX Y C YX C XX - K δXδY φ X C δXX C δXY φK δXδX Y C δXY C δXXC XδXC XδYC δXδXC δXδYC XδY X M XX C XδX Y M YX - C δXδY φ X M δXX C δXδX φY M δXYM XYM XδXM XXM XδYM δXYM δXδXM δXXM δXδYM XδY X M XδX Y M δXδY φ X M δXδX φY (5)Incidentally, aerodynamic (or hydraulic) forces from impeller interactions in centrifugal compressors (orpumps) and axial flow turbines are also represented in a similar form.Forces and moments from support bearings and seal force coefficients are integrated into the equations ofmotion (1) renderingwhere[ M ] {u } [[C ] Ω [G ]R ]{u } [K ]{u} {Fext (u, u , t )}(6)[M ] ([ M ] [ N ])R [ M ] S ;[K ] [K ]R [ K ] B [ K ] S ;[C ] [C ] B [C ] S ;(7)are the system inertia, stiffness and damping matrices. Above sub-indices B and S represent thecontributions of bearing and seals.To determine the damped natural frequencies of the rotor-bearing system, the homogeneous form of Eqn.(6) is solved. The general solution is of the form, {u} {v} est which renders the following eigenvalueproblem.[[K ] s [C ] Ω s [G ]R] s 2 [M ] {v} {0}(8)Solution of the characteristic equation (8), a polynomial in s, leads to the set of eigenvalues s λ i ω andeigenvectors {v}, also known as natural damped mode shapes. Note that the system eigenvalues are rotorspeed dependent (Ω). For stability, the real part of all eigenvalues must be negative, i.e. λ 0.For synchronous response to imbalance, the vector forcing function is periodic and proportional to rotorspeed, Ω2. Letting {Fext} {m x u eiφ } Ω2 eiΩt , the system response, {u} {w} eiΩt is obtained by solutionof the complex algebraic equation[[K ] i Ω [C ] i Ω [G ]2RRTO-EN-AVT-143]{ Ω 2 [M ] {w} m x u e i φ}(9)9-9
Introduction to Pump RotordynamicsA nonlinear rotordynamics analysis does not rely on linearized bearing and seal force coefficients. Forexample, bearing reaction forces are expressed as general impedance formulas,Fα f α X , Y , X , Y ; α X ,Y that are evaluated at each time step in a transient response analysis to specific()events such as machinery start-up, blade loss simulations, etc. Current (personal) computer technologywith extremely fast processors has enabled the routine implementation of nonlinear models in an efficientmanner. Refer to [10] for details on the development of a virtual tool for turbocharger nonlinearrotordynamics that has reduced by 70% cycle time in the development of new rotor-bearing systems.4.0 EXAMPLE OF A ROTORDYNAMIC ANALYSISThe brief description below details the steps and results of a rotordynamic analysis performed on a sevenstage compressor handling a light hydrocarbon mixture, see Figure 8.Figur
The rotordynamics of turbomachinery encompasses the structural analysis of rotors (shafts and disks) and the design of fluid film bearings and seals that determine the best dynamic performance given the required San Andrés, L. (2006) Introduction to Pump Rotordynamics. In Design and Analysis
3042f012 dpa pump 3042f022 dpa pump 3042f050 dpa pump 3042f052 dpa pump 3042f062 dpa pump 3042f080 dpa pump 3042f101 dpa pump 3042f102 dpa pump 12 volt 3042f110 dpa pump 3042f150 dpa pump 3042f152 dpa pump 3042f152-r dpa pump 3042f170 dpa pump 3042f171 dpa pump 3042f172 dpa pump 3042f210 dpa pump 3042f212 dpa pump 3042f213 dpa pump 3042f213-r .
9w9310 776c, 776d, 777b, 777d 9t6577 pump g gear 9t6813 pump g 9t7414 pump gr 9t7465 pump g 9t7468 pump g 9t8919 pump gp 9t9839 pump g 9t9909 pump g 9w1723 pump g 9w1724 pump g 9w4704 pump g 9w9310 pump g part no. application 07430-72203 d65a, d65e, d65p, d65s, d75a 07436-72202 d135a, d80a, d80e, d80p, d85a, d85c, d85e, d85p, d95s
HANDBOOK OF ROTORDYNAMICS Fredric R Ehrich Editor-in-Chief lnv.-Nr. . Systems with Planar Asymmetry / 1.113 1.7.5. Nonlinear Transmission Distortion / 7.777 1.8. Torsional and Longitudinal Vibration / 1.118 . Types of Balancing / 3.5 3.1.4. Instrumentation and Vibration Me
4) Alarm Valve System 38 5) Butterfly Valve 38 L) Fire Fighting Pump 1) Portable Pump 39 I) Low Discharge Pump 39 II) High Discharge Pump 39 2) Aqua Float, The Floating Pump 40 3) Turbo Pump 40 4) Dewatering Pump 41 I) Ejector Pump 41 II) Adjustable Ejector Pump 41 5) Portable Water Mist System 41 M) Miscellaneous
Drum Cvr, Follower, Air Cplr./Nipple, Grease Hose, Cntrl Vlv., Caster Base 5:1 Bare Pump 5:1 Stub/Universal Pump 5:1 55 Gal Pump 5:1 16 Gal Pump 5:1 275 Gal Pump 5:1 Wall Mount Pump 5:1 55 Gal Lube Truck Pump 50:1 Pump, 3", 120 Lb Bare 50:1 Pump ,3", 400 Lb Bare 50:1 3" 120 Lb Stationary Pkg 50:1 3" 400 Lb Stationary Pkg 50:1 3" 120 Lb Hoist .
piston pump diaphragm pump screw pump gear pump Hydraulic pump . A positive displacement pump must not be operated against a closed valve on the discharge side of the pump because . A hydraulic ra
Byron Jackson Pump Div. Borg-Warner Cascade Pump Co. Johnston Pump Co. Kubota, Ltd. Patterson Pump Div., Dubie-Clark Co. Peerless Pump U.S. Pumps Worthington Pump Inc. PUMPS, SCREW Lakeside Pump Co. Link-Belt, Div. of FMC Passevant Mfg. PUMPS, SUBMERSIBLE A/C Pipe Inc. Aurora Pump, Unit General Signal Corp.
On Getting What You Want: Our Method of Manifestation This point cannot be overemphasized. You need to see that the way it is now is the way you have chosen it to be on some level.
