High-speed Rotor System Research Articles

A comprehensive review on crack detection schemes and modelling techniques in high-speed rotor systems

ABSTRACT The combination of a rotor and bearings plays a pivotal role in various industrial applications, including gas turbines, compressors, turbochargers, aircraft engines, and wind generators. Ensuring the structural integrity of the rotor-bearing assembly during static and dynamic conditions is most important, as any failure could lead to unpredictable losses. Due to their continuous operation, high-speed rotors are more susceptible to faults such as misalignment, bow, eccentricity, and cracks. Among these faults, cracks are the most predominant fault that affects the system’s reliability. Despite significant advancements in rotor dynamics, cracks still threaten the integrity and performance of the rotor-bearing assembly. This review paper aims to thoroughly review the challenges and issues associated with crack formation in high-speed rotor systems. Various crack detection methods are also explored using vibration signals obtained from the rotor-bearing unit and their associated processing techniques. This study also gives an extensive overview of different crack modelling and analysis techniques. Furthermore, a novel rotor-bearing model is modelled using the finite element method, and the numerical results obtained from this model are validated with the existing literature model. This review paper will serve as a valuable resource for researchers that offers insights into the latest advancements and emphasises the importance of crack detection for ensuring the reliability of high-speed rotor systems.

Dynamic and stability comparison analysis of the high-speed turbocharger rotor system with and without thrust bearing via machine learning schemes

Dynamic and stability comparison analysis of the high-speed turbocharger rotor system with and without thrust bearing via machine learning schemes

Dynamic characteristics of a magnetic bearing based on high-temperature superconductors in the event of rotor and stator misalignment

Aim: This study aims to analyze the influence of harmonic excitations during bearing misalignment on the power and mechanical characteristics of a high-speed magnetic bearing based on tape high-temperature superconducting composites.
 Methods. Numerical multiphysics analysis of a superconducting magnetic bearing was performed using the finite element method in Comsol Multiphysics.
 Results. When there is a deviation from coaxiality in the arrangement of the magnetic elements of the HTS bearing, harmonic excitations, vibrations, and beats appear, leading to a deterioration in the load characteristics of the device and a decrease in the dynamic permeability of the magnetic system.
 Conclusion. The developed numerical model makes it possible to predict the dynamic and mechanical characteristics of high-speed HTS bearings and can be used to develop high-speed rotor systems.

Gyroscopic effect evaluation and resonance speed prediction of complex high-speed rotor system based on energy

Making full use of gyro effect to adjust resonance speed distribution is of great significance for avoiding resonance design of high-speed rotor system. Existing rotor dynamics research often regards gyro effect term as an implicit quantity to be solved in dynamic equation of complex rotors, but does not carry out quantitative evaluation on its gyroscopic effect. Therefore, this paper decomposes kinetic energy components of the rotor, deduces equilibrium relationship between modal kinetic energy and potential energy of the rotor system at a specific speed, defines the ratios of gyro kinetic energy to lateral vibration energy/elastic potential energy in modal vibration as parameters to evaluate the degree to which the gyro effect affects resonance characteristics. Based on this, the gyro effect of a typical complex high-speed rotor system is evaluated. The derivation process also shows that, modal shape directly determines the gyro energy ratios, ultimately determines the change amplitude of resonance speed. Then a method to predict resonance speed under gyro effect based on modal shape is proposed, and experimental verification is carried out. The results show that, it is feasible and concrete to understand gyroscopic effect from the perspective of system energy equilibrium and transformation.

Pivot Stiffness Effect on Transient Dynamic Characteristic of Tilting Pad Journal Bearing-Rotor System Passing through Critical Speed

Tilting pad journal bearings (TPJBs) are widely applied in the high-speed rotor system whose working speed is higher than its critical speed due to excellent hydrodynamic lubrication and stability. Pivot stiffness is one of the key design parameters of TPJBs compared to other journal bearings and has become particularly important for optimizing the performance of TPJB-rotor systems. In order to improve the vibration and critical characteristics of rotor systems, the transient dynamic characteristic of a TPJB-rotor system passing through the critical speed is investigated considering different pivot stiffness ratios. A time-varying dynamics model of a symmetrical single-disc rotor supported by four-pad TPJBs is established considering constant acceleration conditions and nonlinear hydrodynamic bearing force. The disc vibration characteristic, journal vibration characteristic, pad vibration characteristic, and hydrodynamic bearing force are analyzed by using Bode plot, shaft center orbit, pad phase orbit, waterfall plot, and time history. The results show that the pivot stiffness plays a major role in the suppression of resonance amplitude and working amplitude of a TPJB-rotor system, without changing the frequency characteristic of the system. This study provides a theoretical basis for the pivot stiffness design of TPJBs and the vibration suppression of rotor systems.

Structural design optimization of a high-speed rotor system for mechanical vibration mitigation

This work proposes a design optimization approach for a high-speed rotor system, commonly used in a wide range of industrial applications, in order to address the issue with the flexural flexibility of a rotor system which can cause significant vibration and noise problems due to shaft whirl. For this purpose, the numerical modeling of a flexible rotor system was used to carry out the optimization process considering the effects of the mass and transverse natural frequency to the optimized design. Torque and geometrical sizing were also incorporated as the constraints in the optimization. The rotor system was modeled as a multi-disc Jeffcott rotor system that allows a rapid design optimization process. A case study on a high-speed rotor was carried out to demonstrate the effectiveness of the developed optimization approach, yielding the reduction of the rotor mass by at least 45.6%, while the fundamental transverse natural frequency has been increased by 2.91% as the result.

Numerical investigations on high-speed turbo-compressor rotor systems with air ring bearings: Nonlinear vibration behavior and optimization

Regarding aerodynamic bearings, mainly two basic types can be distinguished: air bearings with a rigid housing and air foil bearings with an elastic supporting structure. Here, a modified bearing concept -- called air ring bearing -- is investigated, which may be considered as a further development of rigid air bearings or as a combination of the two basic bearing types. The idea of air ring bearings is to insert a ring-shaped bearing bushing between the shaft and the foil structure. Alternatively, a visco-elastic supporting structure (e.g., an elastomer) can be applied to connect the bushing ring with the housing. In the first case, external dissipation is mainly generated by dry friction. In the latter case, viscous damping is used to provide external dissipation. Due to the external friction/damping generated by the ring mounting structure, rotor systems with air ring bearings can be operated above the linear threshold speed of instability so that stable self-excited vibrations with moderate amplitudes can be achieved in the complete speed range. Here, a detailed transient co-simulation model for rotor systems with air ring bearings is presented. The rotor is represented by a multibody model. The air films of the two bearings are represented by two nonlinear time-dependent finite element systems. The multibody model and the two finite element subsystems are solved simultaneously by means of an explicit sequential co-simulation technique. Due to the strong nonlinearities, the system shows interesting vibration and bifurcation effects, which are investigated in detail with the help of run-up simulations.

Dynamic Property Design of High-speed Rotor System Based on Strain Energy Distribution

Dynamic Property Design of High-speed Rotor System Based on Strain Energy Distribution

Analytical and experimental investigation on stability of rotor system with spline coupling considering torque, friction coefficient and external damping

The spline coupling is widely used in high-speed rotor systems. As the lack of good understanding of the instability and influence behaviors, the spline induced instability is still not well controlled. From the view of dynamics, torque, friction coefficient and external damping are key factors that influence the stability directly. In this paper, the mechanism and influence law of spline induced instability are investigated. A new model to predict the threshold speed of instability of spline coupled rotor accurately is proposed. A criterion to determine the stability of rotor through judging the relative displacement between splines is derived. Then the effects of torque, friction coefficient and external damping on stability are investigated. Corresponding experiments are carried out to validate the model. The characteristics of instability caused by spline are observed successfully through repeated experiments. Results demonstrate that the mechanism of instability caused by spline is the relative effect of the internal damping from spline coupling and the external damping. This investigation can help with the prediction of instability caused by the spline and the regulation of rotor stability.

Vibratory loads behavior of a high-speed lift-offset coaxial rotor system

Vibratory loads behavior of a high-speed lift-offset coaxial rotor system

Optimizing energy dissipation in gas foil bearings to eliminate bifurcations of limit cycles in unbalanced rotor systems

High-speed rotor systems mounted on gas foil bearings present bifurcations which change the quality of stability, and may compromise the operability of rotating systems, or increase noise level when amplitude of specific harmonics drastically increases. The paper identifies the dissipating work in the gas film to be the source of self-excited motions driving the rotor whirling close to bearing’s surface. The energy flow among the components of a rotor gas foil bearing system with unbalance is evaluated for various design sets of bump foil properties, rotor stiffness and unbalance magnitude. The paper presents a methodology to retain the dissipating work at positive values during the periodic limit cycle motions caused by unbalance. An optimization technique is embedded in the pseudo-arc length continuation of limit cycles, those evaluated (when exist) utilizing an orthogonal collocation method. The optimization scheme considers the bump foil stiffness and damping as the variables for which bifurcations do not appear in a certain speed range. It is found that secondary Hopf (Neimark–Sacker) bifurcations, which trigger large limit cycle motions, do not exist in the unbalanced rotors when bump foil properties follow the optimization pattern. Period-doubling (flip) bifurcations are possible to occur, without driving the rotor in high response amplitude. Different design sets of rotor stiffness and unbalance magnitude are investigated for the efficiency of the method to eliminate bifurcations. The quality of the optimization pattern allows optimization in real time, and gas foil bearing properties shift values during operation, eliminating bifurcations and allowing operation at higher speed margins. Compliant bump foil is found to enhance the stability of the system.

Analytical Modeling of Air Gap Magnetic Fields and Bearing Force of a Novel Hybrid Magnetic Thrust Bearing

In this article, an analytical method is presented for modeling the complex air gap field distribution and the magnetic force of a novel permanent magnet (PM) bias hybrid magnetic thrust bearing (HMTB). This bearing has a very compact structure and is proposed to replace the traditional magnetic thrust bearings (MTBs) for high-speed rotor systems. The proposed method introduces the notion of the complicated air gap field, calculated from the Schwarz–Christoffel transformation of the air gap geometry, to take into account the effect of slot fringing and leakage. As a result, accurate solutions of the flux distribution and the bearing force can be obtained, which shows good agreement with the results of the finite-element method (FEM). The prototype of the HMTB is designed, analyzed, and tested. The results of the analytical model are compared with experimental data.

Turbocharger rotor vibration reduction methodology with an active control scheme

The turbocharger rotors are often supported on the dual film floating ring bearings that are meant for high-speed applications. The damping ability of these bearings is relatively high. However, due to highly nonlinear bearing forces, often system instability occurs. The present work focuses on the dynamic analysis and active vibration control studies of a practical turbocharger rotor system with the use electromagnetic actuator (EMA) system. Initially, the system is analyzed using the finite element approach. The inner and outer film forces are considered along with rotor imbalance forces. The dynamic responses at the critical operating speeds are obtained numerically. To minimize the vibration amplitudes, a tiny EMA system is installed at one of the nodes along the shaft. The effect of the EMA parameters such as the number of turns of winding coil around a pole ( N c) and pole-face area ( A a) on the response of the system is studied. Further, an open-loop control configuration is practically studied by using a vibration shaker at the bearing node under different operating speeds, and the percentage reduction in critical vibration amplitudes is recorded. The EMA system is effectively controlling the high-speed rotor system vibrations. The EMA parameters N c and A a are influencing the system vibration response. Further, an experimental result has given considerable vibration reduction with the present approach.

Nonlinear behaviors analysis of high-speed rotor system supported by aerostatic bearings

In the paper, the dynamic model of aerostatic bearing-rotor system combining rotor motion equation and transient Reynolds equation is established to study influences of rotational speed, unbalance, rotor mass and supply pressure on the nonlinear behaviors of rotor system. The results reveal abundant nonlinear phenomenon consisting of 3 T-periodic, 5 T-periodic and quasi-periodic motions. Furthermore, chosen proper unbalance, smaller rotor mass and larger supple pressure can control the nonlinear vibration and improve the system stability. The results provide a theoretical basis for a simple and feasible method to control the nonlinear vibration of rotor system by adjusting supply pressure.

A modified damping model of vector form intrinsic finite element method for high-speed spiral bevel gear dynamic characteristics analysis

The vector form intrinsic finite element (VFIFE) method is springing up as a new numerical method in strong non-linear structural analysis for its good convergence, but has been constricted in static or transient analysis. To overwhelm its disadvantages, a new damping model was proposed: the value of damping force is proportional to relative velocity instead of absolute velocity, which could avoid inaccuracy in high-speed dynamic analysis. The accuracy and efficiency of the proposed method proved under low speed; dynamic characteristics and vibration rules have been verified under high speed. Simulation results showed that the modified VFIFE method could obtain numerical solutions with good efficiency and accuracy. Based on this modified method, high-speed vibration rules of spiral bevel gear pair under different loads have been concluded. The proposed method also provides a new way to solve high-speed rotor system dynamic problems.

Effect of the inlet oil temperature on vibration characteristics of the high-speed turbocharger rotor system

The inlet oil temperature of the rotor system with high-speed and light-load turbocharger will change during operation, which will change the vibration characteristics of the rotor system and even cause vibration accidents. Taking a certain type of high-speed and light-load turbocharger rotor system as the research object, the changes in oil film viscosity, friction power consumption, oil film temperature rise, and ring speed ratio with the inlet oil temperature of floating ring bearings are analyzed. A dynamic finite-element model of the turbocharger rotor–floating-ring-bearing system is constructed, and the finite-element model is verified through the critical speed and colormap spectrogram. The Newmark integral method is used to analyze the nonlinear transient response of the rotor system, and the influence of the inlet oil temperature on the vibration response characteristics of the rotor system is studied. The results show that an increase in the inlet oil temperature leads to a decrease in the internal and external oil film viscosities, frictional power consumption, temperature rise, and an increase in the ring speed ratio. When the inlet oil temperature increases from 50 °C to 130 °C, the amplitude of the inner oil film oscillation will gradually decrease, but the amplitude of the outer oil film vortex will gradually increase, and the journal speed point where the inner oil film oscillation and the outer oil film vortex will appear about 30% in advance. In summary, the rotor vibration is better when the inlet oil temperature is about 90 °C. The conclusion of this paper can provide a theoretical reference for selecting the operating parameters of the rotor system with the least vibration for high-speed light-load turbochargers.

Effects of Transmission Ratio on the Nonlinear Vibration Characteristics of a Gear-Driven High-Speed Centrifugal Pump

The gear transmission system is widely used in high-speed centrifugal pump to improve the operating speed and hydraulic performances of the whole pump. Vibration characteristics and the stability of these high-speed rotor systems with gear transmission have great impacts on the stability of the whole fluid transmission system of the plant. Based on the lumped-mass method and the principle of displacement equilibrium of the rotor system, a coupled lateral-torsional dynamic model describing the gear-rotor-seal-bearing (GRSB) system of high-speed centrifugal pumps which has considered the nonlinear factors within the gear pair, nonlinear forces of bearings, and those of the seals is proposed. Then, the stability and nonlinear vibration responses of a model GRSB system under different gear transmission ratios (i) have been studied. The following conclusions are drawn from the results: (1) The components with frequencies like fp, f g , fm, and 2fm have great impacts on the vibration responses of the gear pair, especially the fm component; moreover, the amplitude of fm first increases and then decreases with the ratio increase and reaches the maximum value under the ratio of 3. (2) A jump motion state will occur when the ratio i is 1.25 and the stability of the system is obviously worse than the bifurcation state. Quite different from those under the other states, under this jump motion state, the 0.2 f g component and 0.5fp component will appear in the vibration responses of both gears and become the most contributed two factors to the responses of the driven gear. (3) In the design process, the transmission ratio of a high-speed centrifugal pump with a simplified GRSB system should be specially designed to avoid the jump-point state and the maximum-amplitude-of-fm state to ensure the stability of the system as well as reduce the mechanical impacts and noises.

Radial position control for magnetically suspended high‐speed flywheel energy storage system with inverse system method and extended 2‐DOF PID controller

To achieve high-precision position control for the active magnetic bearing high-speed flywheel rotor system (AMB-HFRS), a novel control strategy based on inverse system method and extended two-degree-of-freedom (2-DOF) proportional–integral–derivative (PID) controller is proposed in this study. First, the inverse system method is employed to decouple the AMB flywheel rotor system with strong non-linear and coupling, into four independent subsystems. Subsequently, extended 2-DOF PID controllers are used to regulate the decoupled subsystems, to obtain good performances of disturbance rejection and tracking simultaneously. In the extended 2-DOF PID controller, a differential signal is produced by a velocity observer to improve the ability of against noise. Finally, the characteristics of stability, tracking, disturbance rejection and robustness of the control strategy proposed are analysed in theory, and its ability and effectiveness to control the radial position of the AMB-HFRS are further studied by simulations and experiments. It is shown that the control strategy proposed can keep the AMB-HFRS suspending stably from static state to the speed of 24,000 rpm, has the advantages of good tracking, high disturbance rejection, strong robustness and good ability of against noise.

Suppression of Synchronous Current Using Double Input Improved Adaptive Notch Filter Algorithm

In order to suppress the influence of the synchronous vibration generated by the unbalance of magnetically suspended control moment gyro on the attitude control accuracy and stability of the satellite platform, this article first introduces the working principle of the magnetically suspended high-speed rotor system, and also establishes the dynamic model of the magnetically suspended rotor with unbalance mass. At the same time, the main sources of unbalance vibration are also analyzed. Finally, an improved adaptive notch filter based on double input is designed. The filter takes the rotor radial X, Y two-channel displacement sensor signals as inputs, and uses the characteristics orthogonal to each other to simultaneously enter the system. The rotor can be automatically balanced by adjusting the convergence factor and the compensation angle to adaptively suppress the synchronous current in a widely operating speed range. Simulation and experimental results show that the method can effectively eliminate the synchronous current in a widely operating speed range and improve the stability of the system. This research on the microvibration of the rotor is of great significance and application value.

The Dynamic Characteristic of a Faulted Rotor System with Multi-Objective Optimization Designed SFD

As an important part of the turbomachinery, the rotor–bearing system has been upgraded to provide a high rotating speed in order to meet the demand of high power production. With increasing demand for stability, the squeeze film damper (SFD) has been widely used in industrial machinery because it can reduce the vibration amplitude and suppress the external force. Usually, it shows inadaptability under the different working conditions where the SFD parameters didn’t change appropriately. Therefore, the reasonable choice of operational parameters of SFD is the key solution that can provide viscous damping effectively and restrain the nonlinear vibration generated by faults. In this paper, the mathematical model of a rotor-ball bearing-SFD system considering the misalignment fault and misalignment-rubbing coupling fault is built first. Then the dynamic characteristics under typical working conditions (ω = 1000 rad/s) of the faulted rotor are discussed. The vibration attenuation effects of the SFD parameters selected by using the multi-objective optimization method on the dynamic responses are analyzed. The results show that when the rotor system operates under different states, the value and the sensitivity of optimization parameters are altered. With no fault, the amplitude of fundamental frequency decrease 23%. With the misalignment fault, the amplitude of the fundamental frequency decreases by 43.4%, the amplitude of 2× fundamental frequency decreases by 27.5%, and the amplitude of 3× fundamental frequency decreases by 66.7%. With the misalignment-rubbing coupling fault, the amplitude of fundamental frequency reduces by 7.4%, the amplitude of 2× fundamental frequency drops by 51.5%, and the amplitude of 3× fundamental frequency drops by 16.8%. Overall, the feasibility of the optimization method of the variable-structured SFD operational parameters for the faulted rotor system is verified. These parametric analyses are very helpful in the development of a high-speed rotor system and provide a theoretical reference for the vibration control and optimal design of rotating machinery.