Mathematical Rotordynamic Model Regarding Excitation Due to Elliptical Shaft Journals in Electrical Motors Considering the Gyroscopic Effect

The paper presents a mathematical rotordynamic model regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors also considering the gyroscopic effect. For this kind of excitation, a mathematical rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness in the air gap of the electrical motor and the mass moment of inertia of the rotor and therefore also considering the gyroscopic effect. The solution of the linear differential equation system leads to the mathematical description of the absolute orbits of the shaft centre, the shaft journals and the bearing housings and to the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be derived with this mathematical rotordynamic model.

A COMPUTATIONAL APPROACH FOR PRESSURE DISTRIBUTION AND ROTORDYNAMIC COEFFICIENTS OF JOURNAL BEARINGS WITH COMBINED RADIAL AND MISALIGNMENT MOTIONS

A computational approach is presented to handle an enlarged linear rotordynamic model whichsimultaneously includes both radial and misalignment motions.The interactive force and momentbetween the rotating and non-rotating members are modeled using an adaptation of the classicalReynolds lubrication equation for incompressible laminar isoviscous films.First,the governingequation is derived and the method of solution is introduced based on a 2-dimension,9-point cen-tral difference.Second,force and moment components are computed by numerical integration ofthe film pressure distribution.Finally,the rotordynamic coefficients are yielded according to thegeneralized force gradients.

Effects of tooth bending damage on the leakage performance and rotordynamic coefficients of labyrinth seals

Tooth bending damage resulting from an intense impact by the rotor sometimes occurs in the transient operation.To investigate the influence of after-damage clearance and tooth bending length on the leakage performance and rotordynamic coefficients of labyrinth seals,three tooth bending damages were taken into consideration,including the unbent tooth damage(abbreviated as Unbent),the partial tooth bending damage(abbreviated as Pbent)and the complete tooth bending damage(abbreviated as Cbent).The transient CFD solution was utilized to calculate the leakage flow rates and rotordynamic coefficients of labyrinth seals with clearances of 0.3,0.4,0.5,0.6 mm for three tooth bending damages.The obtained result shows that the Unbent tooth damage leaks least while the Pbent tooth bending damage leaks most,and an increase of 6.1%for Cbent tooth bending damage and an increase of 19.4%for Pbent tooth bending damage are discovered at the tooth clearance of 0.6 mm in comparison with the Unbent tooth damage.Compared to the Unbent tooth damage,the effective damping for Pbent tooth bending damage and Cbent tooth bending damage is lower and drops by 9.7%–33.6%and 8.5%–22.6%respectively at the tooth clearance of 0.6 mm,suggesting that Pbent tooth bending damage or Cbent tooth bending damage tends to weaken the seal stability when compared to the Unbent tooth damage.

A transient bulk flow model with circular whirl motion for rotordynamic coefficients of annular seals

Bulk flow model with perturbation simplification has been used to calculate rotordynamic coefficients in annular seals which have significant influences on the dynamic behavior of rotors in turbomachinery. In this work, a transient bulk flow model with arbitrary rotor motion is developed, and the boundary conditions and friction factor in the model are calibrated with steady Computational Fluid Dynamics（CFD） analysis. The numerical solution scheme is developed based on the finite element method to obtain the transient reaction force in the seal clearance. With a periodic circular rotor orbit, the transient forces at multiple whirling frequencies are used to evaluate the rotordynamic coefficients. The leakage flowrate of CFD analysis has good agreement with experimental results and the calibrated parameters in bulk flow model are dependent on operating conditions. Although CFD calibration improves the accuracy of the perturbed bulk flow model, the direct damping is overestimated and the cross-coupled damping is underestimated. Compared with the perturbed model, the predictions of the transient bulk flow model are more agreeable with the experiment.

Effect of bristle pack position on the rotordynamic characteristics of brush-labyrinth seals at various operating conditions

Over the last few decades,the research on the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals is not sufficient.To this end,two kinds of brush-labyrinth seals for the bristle pack element installed upstream of the labyrinth teeth named BSU and installed downstream of the labyrinth teeth called BSD were used to investigate the effect of bristle pack position on the rotordynamic characteristics of the brush-labyrinth seals.Using the numerical model combining the porous medium model and the whirling rotor method,the rotordynamic characteristics of the BSU and BSD at various operating conditions including four kinds of pressure ratios,five kinds of inlet preswirl speeds and four kinds of rotor spinning speeds were conducted.The obtained results show that the effects of operating conditions on rotordynamic coefficients for the different seal configurations are different.The direct stiffness,cross-coupled stiffness and direct damping of the BSU are lower than those of the BSD.The rotordynamic coefficients of the BSU are more insensitive to the operating conditions variation.From the perspective of the seal stability,the BSU is a better brush-labyrinth seal configuration at high pressure ratio,high positive preswirl or high rotor spinning speed conditions.While in the case of low pressure ratio,low positive preswirl or low rotor spinning speed conditions,the BSD is a better choice.

Numerical investigation on leakage and rotordynamic performance of the honeycomb seal with swirl-reverse rings

Honeycomb seals are a crucial component to restrict the leakage flow and improve system stability for the turbomachines and aero-engines.In this work,the leakage and rotordynamic performance of honeycomb seals with the Swirl-Reverse Ring(SRR)is predicted by employing the approach of Computational Fluid Dynamics(CFD)and the multifrequency whirling model theory.Numerical results show that the positive preswirl flow and circumferential velocity can be effectively weakened for the honeycomb seal as SRR is introduced.The obtained results also suggest that the direct stiffness,direct damping,and effective stiffness will not reduce,for the honeycomb seal is introduced to SRR.However,the honeycomb seal with SRR can significantly reduce the crosscoupled stiffness and remarkably enhance the effective damping.Meanwhile,the absolute value of negative tangential force acting on the rotor surface significantly increased for the honeycomb seal introduced SRR.Therefore,the whirling velocity of the rotor would be weakened.This phenomenon would be conducive to improve the stability of the rotor.Besides,the performance of SRR can be further enhanced when SRR possesses a smaller bending angle,and a higher arrangement density and height.

Effect of hole arrangement patterns on the leakage and rotordynamic characteristics of the honeycomb seal

The honeycomb seal is a vital component to reduce the leakage flow and improvethe system stability for the turbomachines. In this work, a three-dimensional model is established for the interlaced hole honeycomb seal (IHHCS) and the non-interlaced hole honeycombseal (NIHHCS) to investigate its leakage and rotordynamic characteristics by adopting computational fluid dynamics (CFD). Results show that the hole arrangement patterns have littleimpact on the pressure drop and turbulence kinetic energy distribution for the seals, and theIHHCS possesses a slightly lower leakage flow rate than the NIHHCS. Moreover, the numericalresults also show that the NIHHCS possesses a better rotordynamic performance than theIHHCS at all investigated conditions. Both seals show a larger k and a lower Ceff with the increase of the positive preswirl ratios and rotational speeds, while the negative preswirl ratioswould reduce the k and improve the Ceff. The NIHHCS possesses a higher absolute value ofFt for all operating conditions, this could explain the distinction of Ceff for both seals atdifferent working conditions.

Rotordynamic characteristics prediction for scallop damper seals using computational fluid dynamics

Enhancing damping characteristic is one of the effective methods to solve the instability problem of the rotor system.The three-dimensional numerical analysis model of scallop damper seal was established,and the effects of inlet pressures,preswirl ratios,rotational speeds,interlaced angles and seal cavity depths on the rotordynamic characteristics of scallop damper seal were studied based on dynamic mesh method and multi-frequencies elliptic whirling model.Results show that the direct stiffness of the scallop damper seal increases with decreasing inlet pressure and increasing rotational speed and cavity depth.When the seal cavity is interlaced by a certain angle,which shows positive direct stiffness.The effective damping of the scallop damper seal increases with the increasing inlet pressure,the decreasing preswirl ratio and the rotational speed and cavity depth.There exists an optimal interlaced angle to maximize the effective damping and the system stability.The leakage of the scallop damper seal is significantly reduced with decreasing inlet pressure.The preswirl will reduce the leakage flowrate,and the rotational speed has a slight effect on the leakage performance.The leakage of the scallop damper seal decreases with increasing seal cavity depth.

Effects of Semi-floating Ring Bearing Outer Clearance on the Subsynchronous Oscillation of Turbocharger Rotor

Semi-floating ring bearing（SFRB） is developed to control the vibration of turbocharger rotor. The outer clearance of SFRB affects the magnitude and frequency of nonlinear whirl motion, which is significant for the design of turbocharger. In order to explore the effects of outer clearance, a transient finite element analysis program for rotor and oil film bearing is built and validated by a published experimental case. The nonlinear dynamic behaviors ofrotor-SFRB system are simulated. According to the simulation results, two representative subsynchronous oscillations excited by the two hearings respectively are discovered. As the outer clearance of SFRB increases from 24 ~tm to 60 pro, the low-frequency subsynchronous oscillation experiences three steps, including a strong start, a gradual recession and a combination with the other one. At the same time, the high-frequency subsynchronous oscillation starts to appear gradually, then strengthens, and finally combines. If gravity and unbalance are neglected, the combination will start starts from high rotor speed and extents to low rotor speed, just like a ＂zipper＂. It is found from the quantitative analysis that when the outer clearance increases, the vibration amplitude experiences large value firstly, then reduction, and suddenly increasing after combination. A useful design principle of SFRB outer clearance for minimum vibration amplitude is proposed： the outer clearance value should be chosen to keep the frequency of two subsynchronous oscillations clearly separated and their amplitudes close.

Mathematical Multibody Model of a Soft Mounted Induction Motor Regarding Forced Vibrations Due to Dynamic Rotor Eccentricities Considering Electromagnetic Field Damping

The paper presents a mathematical multibody model of a soft mounted induction motor with sleeve bearings regarding forced vibrations caused by dynamic rotor eccentricities considering electromagnetic field damping. The multibody model contains the mass of the stator, rotor, shaft journals and bearing housings, the electromagnetic forces with respect of electromagnetic field damping, stiffness and internal (rotating) damping of the rotor, different kinds of dynamic rotor eccentricity, stiffness and damping of the bearing housings and end shields, stiffness and damping of the oil film of the sleeve bearings and stiffness and damping of the foundation. With this multibody model, the bearing housing vibrations and the relative shaft vibrations in the sleeve bearings can be derived.

Dynamic Stability Analysis of Periodically Time-Varying Rotor System with a Transverse Crack

Fatigue cracks may appear in horizontal rotating machinery due to periodic stresses imposed to its shaft. The investigation of stability behavior of cracked rotors can lead to proper diagnosis of machinery and to prevent possible accidents caused by the rotor failure. In this study, the dynamic stability of a rotor with a transverse crack is investigated. Models of both open and breathing cracks are developed and then used in the model of a cracked Jeffcot (de Laval) rotor. The stability of rotor motion equations represented by differential equations with periodic coefficients is investigated using Floquet theory. While both crack models show instability regions around the first un-damped frequency, sub-harmonic regions are predicted by the breathing crack models. Compared to perturbation methods frequently used to determine the stability regions, the transition matrix approach used in this study can be applied to complex models of rotors and consequently may help in the identification of cracks in rotating machinery.

压缩机可倾瓦轴承先进模型预测与测试数据的对比

The paper details fundamental progress on the analysis of tilting pad journal bearings that includes both pivot flexibility and pad surface deformation due to pressure and pad crowning due to thermal effects.The work introduces a novel model for the mixing of flow and thermal energy at a lubricant feed port that sets the temperature of the lubricant entering a pad leading edge. Precise estimation of this temperature, the inlet oil viscosity, and the flow rate entering a pad largely determines the temperature rise along the pad lubricated surface as well as the drag power loss, and ultimately the bearing load capacity. The model predictions are validated against bearing test data applicable to a compressor. The paper delivers recommendations for a novel feed port efficiency parameter that represents various types of oil supply configurations. Importantly enough, and as is done in actual practice, the model allows the specification of the delivery flow date into the bearing rather than a supply pressure.

Influence of the Foundation on the Threshold of Stability for Rotating Machines with Roller Bearings—A Theoretical Analysis

The paper presents a mathematical model for analyzing the threshold of stability for rotating machines, where the rotor is linked to the stator by roller bearings, bearing housings and end-shields and where the stator feet are mounted on a soft foundation. The internal (rotating) damping of the rotor is the only source of instability, which is considered in the paper. After the mathematical coherences of the multibody model are described, a procedure is presented for deriving the threshold of stability. Additionally, a numerical example is shown, where the threshold of stability is calculated for different boundary conditions. It could be demonstrated, that the stiffness of the foundation—even if the foundation stiffness is isotropic—can help stabilizing this kind of vibration system in the same way as orthotropic bearing stiffness or orthotropic bearing housing and end-shield stiffness for a rigid foundation.

空气箔片轴承技术在高速单级燃料电池空压机上的应用

The motivation to use air foil bearings in fuel cell compressors is driven by the demand for oil-free and high-power density system to reduce system volume and weight.The characteristics of air foil bearings that realize this demand are its independency on auxiliary system and no scheduled maintenance as well as their superb performance at high speeds.However,integration of the foil bearings to the compressor needs rigorous developmental tests for the bearing to withstand high g-load during vehicle maneuver and to remain stable in rotordynamics under external destabilizing forces.This paper presents multi-pads foil bearing technology applicable to single stage high speed fuel cell air compressors.Two different multi-pad air foil bearing designs(two-pad vs three-pad)were tested using a high-speed spin test rig to identify the differences in rotordynamics responses.The two-pad bearing is superior in rotordynamics without any sub-synchronous vibration while three-pad bearing provides more uniform load capacity in all directions with less rotordynamics stability.Frequency-domain modal analyses verify the experimental observations.Axial foil bearings with 38mmouter diameter was designed and tested up to 140krpm with load capacity of 90N(1.4bar specific load capacity).Finally,a platform design of single stage 15kWfuel cell compressor with rated speed of 130krpm is proposed using the multi-pad foil bearings and axial foil bearings developed through this paper.