High-speed Rotor System Research Articles

Rotor dynamic experimental investigation of an ultra-high-speed permanent magnet synchronous motor supported on a three-pad bidirectional gas foil bearing

With a 10-kW, 120,000-r/min, ultra-high-speed permanent magnet synchronous motor taken as a prototype, experimental research is conducted on the rotor dynamic behaviours of a three-pad bidirectional gas foil bearing high-speed motor rotor system. Load-carrying properties of the three-pad bidirectional gas foil bearing are analysed, and natural frequencies of conical and parallel whirling modes of the elastically supported rotor are calculated based on an appropriate simplification to the stiffness and damping coefficients of the gas foil bearings. The prototype passes through a 90,000-r/min coast-down experiment. Experiments show that there are violent subsynchronous whirling motions that are evoked by the gas foil bearing–rotor system itself. The cause of shaft orbit drift is analysed, and the corresponding solution is put forward. The theoretical analysis and experimental results can offer a useful reference to the bearing–rotor system design of ultra-high-speed permanent magnet motors and its subsequent dynamic analysis.

Robust design method for dynamic properties of high-speed flexible rotor systems

Robust design method for dynamic properties of high-speed flexible rotor systems

Internal model control for the AMB high‐speed flywheel rotor system based on modal separation and inverse system method

To eliminate the influence of gyroscopic effect on system stability and to improve the control performances for the active magnetic bearing (AMB) high-speed flywheel rotor system, a novel control strategy based on the modal separation and inverse system method is proposed. The translational motions and rotational motions of the AMB flywheel rotor system are firstly decoupled by the modal separation, then the rotational motions are decoupled by the inverse system method, so that the AMB flywheel rotor system, which is a multivariable and strong coupled system, is decoupled into four subsystems. Finally, the subsystems are regulated by four two-degrees-of-freedom (2-DOF) internal model controllers, respectively. Furthermore, the stability, tracking and robustness of the novel control strategy are analysed theoretically, and its effectiveness on vibration control of the AMB high-speed flywheel rotor system is further investigated by simulations and experiments. The results show that the novel control strategy can achieve stable suspension and effectively suppress the vibration of the AMB high-speed flywheel rotor system from static state to 24,000 rpm, with the advantages of high stability, strong robustness, and good performances of tracking and disturbance rejection simultaneously.

Identification of Speed-Dependent Active Magnetic Bearing Parameters and Rotor Balancing in High-Speed Rotor Systems

Estimating residual unbalances of a flexible rotor that is fully levitated on active magnetic bearings (AMBs) are challenging tasks due to the modeling error of AMB rotordynamic parameters. In this work, an identification algorithm has been developed for the estimation of dynamic parameters of speed-dependent AMBs and residual unbalances in a high-speed flexible rotor-bearing system. Parameters are identified during an estimation process with the help of displacement and current information at AMB locations only. For reducing the finite element model to suit the measurement availability, an improved dynamic reduction scheme has been proposed, which considers the gyroscopic matrix also in the transformation matrix. For a numerical testing of the developed identification algorithm, a multidisk flexible-shaft rotor is considered, which is fully levitated on AMBs. Speed-dependent AMB parameters have been modeled by a cubic function. Proportional–integral–derivative (PID) controllers are used to control the supply current to AMBs. Displacements and currents are generated using the finite element method of the rotor-AMB numerical model. These responses have been used in the identification algorithm for the estimation of the AMB displacement and current stiffness as well as of residual unbalances, concurrently. The algorithm with the proposed reduction scheme has shown an excellent estimation agreement in the presence of noisy responses and bias errors in rotor model parameters.

Study on the Influence of Floating Ring Axial Length on Vibration Characteristics of High-speed and Light-load Turbocharger Rotor System

Study on the Influence of Floating Ring Axial Length on Vibration Characteristics of High-speed and Light-load Turbocharger Rotor System

Calculation and analysis of critical speed of high speed motor spindle rotor system

The traditional transfer matrix method used to calculate the critical speed of high-speed spindle motor rotor system will produce large errors. Taking the 170SD30 electrospindle as the analysis object, a high-speed electric spindle dynamics theoretical model was established based on the Riccati method, using Matlab to program and calculate the kinetic parameters of the first three critical speeds and natural frequencies of the high-speed spindle. Finally, the simulation data was compared with experimental data. The results show that the Riccati transfer matrix method is 2.3% more accurate than the traditional transfer matrix method, and it verifies the accuracy and feasibility of the Riccati transfer matrix method, and is of great significance to effectively guide the analysis and design of high-performance and high-speed motor spindle.

Nonlinear vibration response characteristics of high-speed flexible rotor system

Nonlinear vibration response characteristics of high-speed flexible rotor system

Semi-active vibration control of high-speed rotor system with electrorheological bearing fluid

Present work focuses on the use of electrorheological fluid (ERF) as a lubricant in the high speed turbocharger rotor supported on floating ring bearings. The rotor is analysed by finite element modelling with gyroscopic effects and bearing forces. The ERF contains one carrier fluid and active particles that react to external electric field, which induces a yield stress in the fluid increasing its viscosity. In order to control the rotor vibration amplitudes, the dynamic changes in the fluid viscosities at the inner and outer films of bearing are employed with external electric field. A case study of automotive turbocharger rotor is considered and the effect of semi-active control is illustrated on the dynamic response of the system.

The effect of changing disk parameters on whirling frequency of high speed rotor system

The requirement for efficiency improvement of machines has caused machine rotor to be designed to rotate at high speeds. It is known that whirling natural frequency of a shaft changes with the change of shaft speed and the design needs to avoid points of resonance where the whirling frequency equals the shaft speed. At high speeds, a shaft may have to carry a huge torque along and this torsional effect has been neglected in past shaft analyses. Whirling behaviour of high speed rotating shaft is investigated in this study with consideration of the torsional effect of the shaft. The shaft system under study consists of a shaft, discs and two bearings, and the focus is on the effect of the disc parameters. A finite element formulation is developed based on Nelson’s 5 degrees of freedom (DOF) per node element that includes the torsional degree of freedom. Bolotin’s method is applied to the derived Mathieu-Hill type of equation to get quadratic eigenvalues problem that gives the forward and backward frequencies of the shaft. Campbell’s diagrams are drawn in studying the effect of discs on the whirling behaviour of the shaft. It is found that the addition of disks on the shaft decreases the whirling frequency of the shaft and the frequency is lower for mass located at the centre of the shaft compared to the one located near to the end. The effect of torsional motion is found to be significant where the difference between critical speed of 4DOF and 5DOF models can be as high as 15%.

Gas–magnetic bearings in high-speed rotor systems

The cantilever overhang of a shaft on gas–magnetic bearings significantly affects the output characteristics of a high-speed rotor system. The rotational precision and rigidity of the rotor may be increased by adaptive control of the magnetic forces.

Optimization Design and Experimental Study of a Two-disk Rotor System Based on Multi-Island Genetic Algorithm

Abstract Based on rotor dynamics theory, a two-disk flexible rotor system representing an aero-engine with freely supported structure was established with commercial software ANSYS. The physical model of the two-disk rotor system was then integrated to the multidisciplinary design optimization software ISIGHT and the maximum vibration amplitudes experienced by the two disks when crossing the first critical speed were optimized using a multi-island genetic algorithm (MIGA). The optimization objective was to minimize the vibration amplitudes of the two disks when crossing the first critical speed. The position of disk 1 was selected as the optimization variable. The optimum position of disk 1 was obtained at the specified constraint that the variation of the first critical speed could not exceed the range of ±10 %. In order to validate the performance of the optimization design, the proof-of-transient experiments were conducted based on a high-speed flexible two-disk rotor system. Experimental results indicated that the maximum vibration amplitude of disk 1 when crossing the first critical speed declined by 60.9 % and the maximum vibration amplitude of disk 2 fell by 63.48 % after optimization. The optimization method found the optimum rotor positions of the flexible rotor system which resulted in minimum vibration amplitudes.

The Thermohydrodynamic Analysis of Sliding Bearing High-Speed Motorized Spindle by Rotor Dynamic

This is paper presents thermohydrodynamic characteristics of high speed motorized spindle sliding bearing rotor system. The dynamic characteristic of the oil film bearing is affected by temperature increment, thereby affecting the high-speed spindle rotor system dynamics. This study applied the hydrodynamic lubrication theory, the influence of temperature on the viscosity of lubricating oil, associated with the bearing stiffness, oil film damping and other performance parameters, is considered in generalized Reynolds equation of oil film bearing. The theoretical model of the sliding bearing rotor system is established by using the transfer matrix method to analyze the dynamic characteristic and verified by experiments. The results show the high temperature environment in the motorized spindle and the friction of the bearing lead to oil temperature rise and viscosity reduction, which influences the bearing capacity, stiffness and damping, hence impact on the critical speeds and modal shapes of the sliding bearing rotor system.

Dynamic characteristics analysis of a misaligned rotor-bearing system with squeeze film dampers

In this paper, a dynamic model is established for a two-stage rotor system connected by a gear coupling and supported on ball bearings with squeeze film dampers (SFDs). The nonlinear dynamic behavior of the rotor system is studied under misalignment fault condition. The meshing force of the gear coupling is calculated considering the deformation of the tooth caused by torque transmission and dynamic vibration. The contact force between the ball and race is computed based on the Hertzian elastic contact deformation theory and the elastohydrodynamic lubrication theory. The supported force of SFD is simulated by integrating the pressure distribution derived from Reynolds’s equation. The equations of motion are rewritten in non-dimensional differential form, and the fourth-order Runge-Kutta method is employed to solve the nonlinear dynamic equilibrium equations iteratively. To verify the validity of the dynamic model and the correctness of the numerical solution method, the experimental power spectra of the rotor system under various misalignment degrees are compared with the analytical results. The effects of several important parameters, such as the lubrication of the ball bearing, the centralizing spring stiffness, the radial clearance of SFD, and the misalignment of gear coupling, on the dynamic characteristics of the rotor system are investigated and discussed mainly focusing on the system stability. The response spectra, bifurcation diagrams, and Pointcare maps are analyzed accordingly. 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.

Simultaneous Temperature Compensation and Synchronous Error Elimination for Axial Displacement Sensors Using an Auxiliary Probe

The output stability of the displacement sensors is an important issue for safe operations in magnetic bearing supported high-speed rotor system. This paper proposes an effective postprocessing solution to the problems of temperature drift and synchronous measuring error for the axial displacement sensor in a 10-kW magnetically suspended motor. The proposed configuration of the axial displacement sensor consists of three probes: one pair is used to eliminate the synchronous measuring error, and the third probe is employed for the consideration of temperature drift. First, the generating mechanism of the synchronous measuring error caused by the improper assemble is presented, and an operational amplifier is proposed to obtain an accurate position of the axial center by adjusting the weights of sensing signals from one pair of probes. Then the scheme of temperature compensation using an auxiliary probe is presented. In order to obtain accurately the characteristics of temperature drift at the operating point, the detailed procedure is given to determine the temperature–drift ratio. Finally, the terms related to temperature drift and synchronous error in the final output of the displacement sensor are both eliminated. Experimental results on a magnetically suspended motor test rig show the effectiveness of the proposed solution.

Influence of the electromagnetic gap in gas–magnetic bearings on the output characteristics of high-speed rotor systems

The electromagnetic gap in gas–magnetic bearings has a considerable influence on the output load and rigidity characteristics of high-speed rotor systems, as shown by experiments and simulation.

A novel twin-shaft rotor layout with active magnetic couplings for vibration control

A novel rotor topology is proposed with the goal of reducing vibration in high speed rotor systems. Reduction in vibration at critical speeds is targeted. In essence, the novel topology consists of a hollow tube rotor coupled to a secondary non-rotating shaft located concentrically within the primary rotor. The two shafts are linked via a number of actively managed magnetic couplings. The topology is provided, along with an analysis comparing the out-of-balance vibration response of the proposed rotor to a comparable simple passive rotor. Designs for a test rig based on this topology are presented, together with an outline of anticipated testing and development of the idea. Special consideration is given to the design of the magnetic bearings, which form the system couplings. An internal-stator homopolar bearing design fabricated from soft magnetic composite is presented. The qualities of soft magnetic composite as a bearing core material are shown to be comparable with a standard laminated core with the added advantage of minimal eddy current losses within the primary rotor.

Characteristic Analysis and Simulated Test of Hybrid Bearing with the Introduction of Piezoelectric Controller

A novel hybrid bearing with the introduction of piezoelectric controller and tilting pads to control vibration actively is proposed in this paper, and the feasibility of this scheme is verified by theoretical calculation and experimental data. This scheme can control the vibration of bearing actively by using the electromechanical characteristics of piezoelectric ceramic transducer (PZT) components. The static internal character of PZT and static external characteristic of piezoelectric control component are analyzed, and the calculation equations of preload coefficient and driving force of the new bearing are given. The simulation setup of the new bearing is designed and developed. The data representing the relationship of displacement of pad pivot, driving force, voltage, and the simulation stiffness of liquid film are obtained in the test, and the feature parameters of piezoelectric control component are amended to analyze the relationship between preload coefficient of the bearing and driving voltage. The proposed new bearing has the function of controlling preload actively. The theoretical and experimental research results provide essential guidance for the detail design of this new bearing and also provide a new idea for the vibration control of high speed rotor systems.

Design, Modeling, Fabrication, and Test of a Large-Scale Single-Gimbal Magnetically Suspended Control Moment Gyro

A successful application of the single-gimbal magnetically suspended control moment gyro (SGMSCMG) requires careful attention not only to the electromagnetic design and feedback control design aspects of the magnetic bearing (MB) but also to the decoupling control aspects between the high-speed MB rotor system and the low-speed gimbal servo system. The key parts with low loss of a large-scale SGMSCMG for the large spacecraft application are proposed. The low-loss MBs that consist of the thrust and radial active MBs with PM bias are proposed for the magnetically suspended control moment gyro (MSCMG) when considering the gyro torque. Finally, test results show that the large-scale MSCMG meets the design requirements and can effectively output gyro torque of 209 Nm and angular momentum of 1200 Nms.

Study about the influence of cavitation on the dynamic characteristics for the sliding bearing

Sliding bearings are employed to support the rotor system and limit the vibration amplitude. In high speed rotor system, cavitation often occurs in the oil film and affects the dynamic characteristics of the sliding bearing greatly. In this paper, numerical method is adopted to simulate the cavitation in the oil film with homogeneous two-phase mixture flow using Singhal-et-al cavitation model in the commercial code FLUENT-solver. Cases without cavitation model were also calculated at the same time. Many computations with different frequency ratios were conducted. Then the rotor dynamic characteristics of the sliding bearing were retrieved. The results show that the cavitation has great influences on the pressure distribution in the oil film. As the rotational speed or whirling speed of the journal increases, the cavitation will become prominent. The dynamic coefficients of the bearing such as stiffness and damping with cavitation model considered are quite different from that without cavitation. So it is worth to pay attention to and do further study about the cavitation in the sliding bearing in the high speed rotor system.

Study on Fluid-Structure Interaction for the Multistage High Speed Centrifugal Pumps Rotors

In the designing process of high-speed multistage centrifugal pump, in addition to the hydraulic characteristics, the calculation problem of the axis of wet critical speed is the emphasis of concern. On the base of the finite element model of the "dry" state rotor dynamics, when the flow force play a individual role in physical separate discs and cylinder, resistance formula is derived. Establish the "wet" mode of motion equation of rotor disc and shaft section, then integrate the flow force into the motion equation of the whole system unit, we can find the fluid-solid coupling finite element model of the rotor dynamics. Write the calculation procedure with ANSYS APDL language, and the analysis and testing of fluidsolid coupling dynamics program to an actual high-speed multistage centrifugal pump rotor system is done.