Rigid Rotor System Research Articles

Identification in a Magnetically Levitated Rigid Rotor System Integrated with Misaligned Sensors and Active Magnetic Bearings

Identification in a Magnetically Levitated Rigid Rotor System Integrated with Misaligned Sensors and Active Magnetic Bearings

Fuzzy variable gain robust control of active magnetic bearings rigid rotor system

AbstractA high speed rigid rotor system supported by active magnetic bearings (AMBs) puts forward higher requirements on the performance of controllers. The fuzzy variable gain H‐infinity robust control (FVGRC) method is proposed to simplify controller design while suppressing system uncertainty. First, the T‐S fuzzy model of four‐degree‐of‐freedom (4‐DOF) AMBs was established based on the 4‐DOF AMBs rigid rotor equivalent coupling model optimised by the μ‐gap metric. Then, based on the fuzzy models of AMBs systems under different operating conditions, the relative optimal weight function value of H‐infinity robust controller was calculated when AMBs system was at value of the speed endpoint, and the fuzzy variable gain H‐infinity robust (FVGR) controller was designed on this basis. Finally, the simulation and experimental results showed that the FVGRC can simplify the model of controller and ensure the stable operation of AMBs rigid rotor system in the full speed range under high‐speed conditions.

Suppression of Gyroscopic Torque Disturbance in High Speed Magnetically Levitated Rigid Rotor Systems Based on Extended State Observer

The gyroscopic torque disturbances generated by base motion directly affects the stability of the high speed magnetically levitated centrifugal compressor (MLCC). This article explores a disturbance suppression method for the high-speed magnetically levitated rotor (MLR) system based on improved linear extended state observer (LESO). Firstly, the model of the high-speed MLR system with base motion is established, and the characteristics of the gyroscopic torque disturbance are analyzed. Then, a LESO with adaptive notch filter is designed for disturbance estimation and compensation of the magnetic bearing, and its convergence performance and disturbance tracking speed are deduced. Furthermore, due to the gain attenuation introduced by LESO, an innovative gain compensator is utilized to improve controller dynamic performance. Finally, simulation and experimental results demonstrate that the proposed method can effectively reject the gyroscopic torque disturbances in high speed MLCC.

Multi-Objective Optimal Design of μ–Controller for Active Magnetic Bearing in High-Speed Motor

In this paper, a control strategy based on the inverse system decoupling method and μ-synthesis is proposed to control vibration in a rigid rotor system with active magnetic bearings that are built into high-speed motors. First, the decoupling method is used to decouple the four-degrees-of-freedom state equation of the electromagnetic bearing rigid rotor system; the strongly coupled and nonlinear rotor system is thus decoupled into four independent subsystems, and the eigenvalues of the subsystems are then configured. The uncertain parametric perturbation method is used to model the subsystem, and the multi-objective ant colony algorithm is then used to optimize the sensitivity function and the pole positions to obtain the optimal μ-controller. The closed-loop system thus has the fastest possible response, the strongest internal stability, and the best disturbance rejection capability. Then, the unbalanced force compensation algorithm is used to compensate for the high-frequency eccentric vibration; this algorithm can attenuate the unbalanced eccentric vibration of the rotor to the greatest extent and improve the robust stability of the rotor system. Finally, simulations and experiments show that the proposed control strategy can allow the rotor to be suspended stably and suppress its low-frequency and high-frequency vibrations effectively, providing excellent internal and external stability.

Virtual prototype modeling and simulation of rigid rotor system supported by active magnetic bearings in Simscape

Virtual prototype modeling and simulation of rigid rotor system supported by active magnetic bearings in Simscape

Adaptive robust control of active magnetic bearings rigid rotor systems

Adaptive robust control of active magnetic bearings rigid rotor systems

Research on heat-elastic coupled vibration in a rotating rigid disk rotor system

Research on heat-elastic coupled vibration in a rotating rigid disk rotor system

A vibration model of a rotor system with the sinusoidal waviness by using the non-Hertzian solution

The nonlinear contact forces and deformations between the balls and raceways can cause very complex vibration behaviours of rotor systems with the waviness in the support bearings. However, almost all previous works that used sinusoidal waviness took the Hertzian solution as the calculation method, which is not an accurate method based on Johnson’s formulation since the changes in the curvature at the sinusoidal contact surfaces. To overcome this issue, a new dynamic model of a rigid rotor system with the waviness in the support bearings is proposed. To provide a more accurate nonlinear contact force formulation for the sinusoidal waviness profile, the model used the Johnson’s extended Hertzian contact model to replace Hertzian contact model. This model can consider the time-varying curvature between the mating sinusoidal surfaces. The lubricating condition in the support bearing is also considered. A comparative study on the effects of Hertzian contact model, simplified Hertzian contact model, and Johnson's extended Hertzian contact model on the nonlinear vibrations of the rotor system is developed. The effects of the waviness amplitude and orders on the vibrations of the rotor system are discussed. The comparative simulations show that the proposed model can provide a more reasonable approach for predicting the vibrations of the rigid rotor system. Moreover, the simulations give that the nonlinear contact forces in the support bearings can greatly affect the system vibrations.

A Method for Predicting the Influences of Bearing Support Stiffness and Position on the Vibrations of a Flexible Rotor System

The bearing support stiffness and position can greatly affect the vibrations of flexible rotor systems (FRSs). However, most previous works only focused on the effect of the bearing support stiffness on the critical speeds or modal characteristics including the natural frequencies and mode shapes of rigid rotor systems (RRSs). The previous studies missed the combined effects of the bearing support stiffness and position. To overcome this issue, an analytical method of a FRS based on the finite element (FE) method is proposed. Our model considers the bearing support stiffness and rotational inertia of FRS. The frequency equation of FRS is established for solving the critical speeds. The critical speeds and modal deformations of FRS from our model and the numerical model based on a commercial software are compared to verify the effectiveness of the presented method. The effects of the bearing support stiffness and position on the critical speeds of FRS are analyzed. The results show that the critical speeds are positively correlated with the bearing support stiffness. The critical speeds of FRS are also greatly affected by the bearing position. This study can provide some guidance for the optimization design method of bearing support stiffness and position in FRSs.

Wind Tunnel Studies on Hover and Forward Flight Performances of a Coaxial Rigid Rotor

The aerodynamic performance of a reduced-scale coaxial rigid rotor system in hover and steady forward flights was experimentally investigated to gain insights into the effect of interference between upper and lower rotors and the influences of the advance ratio, shaft tilt angle and lift offset. The rotor system featured by 2 m-diameter, four-bladed upper and lower hingeless rotors and was installed in a coaxial rotor test rig. Experiments were conducted in the Φ3.2 m wind tunnel at China Aerodynamics Research and Development Center (CARDC). The rotor system was tested in hover states at collective pitches ranging from 0° to 13° and it was also tested in forward flights at advance ratios up to 0.6, with specific focus on the shaft tilt angle and lift offset sweeps. To ensure that the coaxial rotor was operating in a similar manner to that of the real flight, the torque difference was trimmed to zero in hover flight, whilst the constant lift coefficient was maintained in forward flight. An isolated single-rotor configuration test was also conducted with the same pitch angle setting in the coaxial rotor. The hover test results demonstrate that the figure of merit (FM) value of the lower rotor is lower than that of the upper rotor, and both are lower than that of the isolated single rotor. Moreover, the coaxial rotor configuration can contribute to better hover efficiency under the same blade loading coefficient (CT/σ). In forward flight, the effective lift-to-drag (L/De) ratio of the coaxial rigid rotor does not monotonously change as the advance ratio increases. Increases in the required power and drag in the case with a high advance ratio of 0.6 leads to the decreasing L/De ratio of the rotor. Meanwhile, the L/De ratio of the rotor is relatively high when the rotor shaft is tilted backward. The increasing lift offset tends to result in reduced required rotor power and an increase in the rotor drag. When the effect of the reduced rotor power is greater than that of the increased rotor drag, the L/De ratio increases as the lift offset increases. The L/De ratio can benefit significantly from lift offset at a high advance ratio, but it is much less influenced by lift offset at a low advance ratio. The forward performance efficiency of the upper rotor is poorer than that of the lower rotor, which is significantly different from the case in the hover flight.

Dynamic Characteristics of a Misaligned Rigid Rotor System with Flexible Supports

A misaligned rigid rotor system with flexible supports differing from the traditional flexible rotor system, which refers to its practical rotating center line determined by supports offset from the theoretical one, often suffers support structure damage risk. In the present work, the dynamic characteristics of a misaligned rigid rotor system with flexible squirrel cage supports are focused, and the vibrations and the stress of its support structures under different misaligned offsets are investigated with experimental and simulated analysis. The finite element model for a rigid rotor system with flexible supports in a scaled test rig is established, and its strain energy distribution is analyzed to find that the first two modes of the system are referred to rigid-body modes and the strain energy is mainly distributed on the squirrel cage supports. Based on the analysis results, a rigid-flexible coupling dynamic model is proposed through a data exchange between ADAMS and ANSYS and validated by measurements. The misaligned conditions are focused on, and the influences of misalignment on the vibrations of the rigid rotor system and the reaction force and stress of its support structures are investigated analytically and experimentally. The results from simulation agree very well with the measurements and reveal that the static stress of squirrel cage increases just about proportionally with misalignment levels, but the vibration displacement amplitudes and stress amplitudes show very little change. The more serious the misaligned condition, the higher the static stress of the squirrel cage. Because misalignment will bring out the additional reaction forces in the misaligned direction, it will further result in higher stress and even more serious damage risk for the flexible supports than other parts in the rigid rotor system.

Dynamics of a rotor shaft driven by a non-ideal source through a universal joint

A rigid rotor system which is driven through a Universal joint (U-joint) and is mounted on weakly-damped flexible supports exhibits principal and combination type parametric instabilities at certain torque-speed combinations. In this article, the transient dynamics of such a non-linear system driven by a non-ideal source (a DC motor) is studied through numerical simulation of the bond graph model of the system. It is shown that the dynamic coupling between the DC motor and the whirling rotor in the non-ideal system can stabilize the system in the speed ranges where the corresponding ideal system is unstable. This stabilization depends upon the motor characteristic constant or the torque/speed constant; i.e. if two motors with different motor characteristic constants produce the same torque at the same operating speed (where the ideal system is unstable) then the motor with higher motor characteristic constant tends to better stabilize the system. This bounded-input bounded-output stabilization is shown to occur through repeated transitions between stable and unstable speed regions. Several simulation results for the system driven by ideal and non-ideal sources at different operating speeds are presented to derive motor sizing specifications.

Effect of ball bearing misalignment on dynamic characteristics of rotor system

A theoretical model with 5 degrees of freedom (DOF) is derived for a rigid rotor system supported by two ball bearings considering the changes of the bearing stiffness due to misalignment. And then radial and axial vibrations of the rotor system and its bearing reactions under different misaligned offsets are investigated with theoretical and numerical analysis. Then, the effects of misalignment on the vibrations of rotor and the bearing, the variation of stiffness and reaction characteristics of the misaligned ball bearing are predicted theoretically. It is concluded that angular misalignment may cause axial vibration and parallel misalignment can bring out extra moment loads for misaligned bearing.

Four-Factor Polarity Switching Control for Synchronous Vibration Suppression of Active Magnetic Bearings Rigid Rotors System in the Full Rotational Speed Range

In order to suppress the synchronous unbalance vibration of the active magnetic bearings (AMBs) rigid rotor system in the full rotational speed range, the polarity switching control (PSC) can effectively suppress the synchronous unbalance vibration of the AMBs-rigid rotor system before and after the rigid cylindrical mode frequency, and the impact of the switching polarity on the system was reduced by using a disturbance observer. However, considering the rigid conical mode, the PSC could not guarantee the synchronous unbalance vibration suppression of the AMBs-rigid rotor system in the full rotational speed range including the rigid cylindrical mode frequency and the rigid conical mode frequency, and the system stability also changes accordingly. This article proposes a synchronous unbalance vibration suppression method based on the four-factor PSC (4-FPSC), which adjusts four polarity factors to suppress the synchronous unbalance vibration before and after two rigid mode frequencies. Besides, the disturbance observer is also avoided. Finally, simulation and experiment results verify the 4-FPSC can effectively suppress the synchronous unbalance vibration of the AMBs-rigid rotor system in the full rotational speed range including the rigid cylindrical and conical mode frequencies.

Synchronous Vibration Control for Magnetically Suspended Rotor System Using a Variable Angle Compensation Algorithm

In active magnetic bearings (AMBs) supported rigid rotor systems, the unbalance compensation strategy based on a notch filter was often used to suppress the synchronous unbalance vibration when the rotor operates in the steady-state rotational speed. Whereas the rotor operates in a rotational-speed range including the critical rotational speeds, conventional notch filters should be improved to suppress the unbalance vibration. In most cases, improving the structure of the notch filter, such as a cross-feedback notch filter, phase-shift notch filter, adding the polarity switch or two-stage switch, was considered to make the notch filter work in the rotational-speed range. However, the improved notch filter may affect the stability of the AMBs rotor systems and result in large vibrations when the polarity switch or two-stage switch shifts. To avoid the shortcomings of these methods, a method using a variable angle compensation algorithm was proposed to suppress the synchronous unbalance vibration in finite iterative seeking processes, directly realizing unbalance compensation according to real-time rotor position. Finally, the effectiveness of the method proposed is verified by simulation and experiment results.

Thermal effect on stability and minimum oil film thickness of a deep/shallow pockets conical bearing

PurposeThis paper aims to study the influence of thermal effect on the performance for a high-speed conical hybrid bearing including stability and minimum oil film thickness.Design/methodology/approachA thermal hydrodynamic (THD) model and dynamic model of single mass rigid rotor system were established by taking conical hybrid bearing with shallow and deep pockets as the research object, dynamic coefficient and stability parameters of bearing-rotor system were obtained by using finite element method (FEM) and finite difference method (FDM) to solve computational models of Reynolds equation, energy equation and viscosity-temperature equation. Minimum oil film thickness was obtained based on bearing force balance. Dynamic coefficient was compared with previous findings.FindingsAfter considering thermal effect, the dimensionless critical mass decreases, a significant decrease in the instability speed, and the stability of the system decreases greatly; the minimum oil film thickness decreases because of thermal effect.Originality/valueThe thermal effect is combined with dynamic characteristics to analyze stability of the rotor system for a conical hybrid bearing. Influence of thermal effect on minimum oil film thickness is studied.Peer reviewThe peer review history for this article is available at:https://publons.com/publon/10.1108/ILT-12-2019-0542/

Development of a Novel Approach for Quantitative Estimation of Rotor Unbalance and Misalignment in a Rotor System Levitated by Active Magnetic Bearings

In the present paper, a novel model-based identification algorithm is developed to estimate the unbalance and AMB misalignment in a rigid rotor system levitated with active magnetic bearings (AMBs). For this, a mathematical model for an unbalanced and misaligned rigid rotor system consisting of a rigid rotor levitated by two active magnetic bearings has been developed. Two cases of the misalignment depending upon the amount of radial offset between the rigid rotor and active magnetic bearings have been examined for the investigation. In the first case, an unknown misalignment is considered that is to be estimated. In the second case, a trial misalignment is added in addition to the unknown misalignment. This is a novel concept proposed in line with the trial unbalance in rotor dynamic balancing. The equations of motion of the rigid rotor–misaligned AMB system are derived and numerically simulated to generate the time-domain rotor displacement and controlling current responses, which are further converted into frequency-domain signals assisted by the fast Fourier transform analysis. These responses have been utilized in the identification algorithm to estimate the unbalance and force–displacement and force–current stiffnesses of misaligned AMBs as well as the misalignment amount between the rotor and AMBs. Estimations of unbalance and AMB misalignment parameters have also been carried out at multiple speeds as well as against various levels of measurement signal noise and modelling errors. The developed identification algorithm is found to be effective and robust against these noise and modelling errors.

Vibration Suppression for Magnetically Levitated High-Speed Motors Based on Polarity Switching Tracking Filter and Disturbance Observer

For the unbalance vibration of the rigid rotor system on active magnetic bearings (AMBs) supported high-speed motors in the full rotational speed range, a method based on the polarity switching tracking filter (PSTF) and the disturbance observer (DO) is proposed to achieve vibration suppression. To identify the synchronous unbalance vibration, a positive polarity tracking filter and a negative one are adopted before and after the rigid critical rotational speed range, respectively. The rigid critical rotational speed is in this range whose lower/upper limit is the negative/positive polarity switching frequency. Although the PSTF can effectively reduce the rotor vibration when it rotates at subcritical rotational speed range and supercritical range, the vibration increases evidently and even destabilize the system within the rigid critical rotational speed range. It means that the PSTF cannot suppress the rotor unbalance vibration in the full rotational speed range. However, this vibration during the rigid critical rotational speed range can be considered as a kind of disturbance and the DO is adopted to observe it, then the vibration identified is compensated in the control current to reduce the rotor unbalance vibration in the rigid critical rotational speed range. Therefore, the method based on the PSTF and the DO can suppress the unbalance vibration in the full rotational speed range. Finally, simulation and experiment results demonstrate that the method proposed can effectively suppresses the synchronous unbalance vibration of the AMBs-rigid rotor system in the full rotational speed range.

Blade Passage Loads and Deformation of a Coaxial Rotor System in Hover

In a closely spaced, coaxial counter-rotating (CCR) rotor, the passage of upper and lower rotor blades over each other results in transient loads and blade deformation. This paper describes the measurement and numerical modeling of these transient loads and blade deformations in a single-bladed, 2-m-diam, rigid CCR rotor system in hover. Three-dimensional rotor blade deformation was measured using a time-resolved digital image correlation technique, simultaneously with the rotor thrust and pitch link loads. A numerical model of the rotor was developed using the comprehensive analysis CAMRAD II. This model was validated by measurements on an isolated single rotor and was used to explore the aerodynamic nature of the transient blade passage loads in the CCR rotor system. Rotating-frame natural frequencies were measured, and mode shapes of the first and second flap mode as well as the first lag mode of the rotor blade were extracted using the Complexity Pursuit algorithm. The 2-per-revolution tip displacement of the coaxial lower rotor due to the blade passages was found to be approximately 6% of the mean tip displacement. Vibratory thrust loads of the coaxial lower rotor were nearly 10% of the mean rotor thrust, whereas the vibratory pitch link loads were approximately 30% of the mean value. The numerical model predicted the vibratory hub and pitch link loads as well as out-of-plane deformations satisfactorily within the measurement uncertainties. With the validated analysis, additional numerical studies on the aerodynamic angles of attack, the inflow velocities from rotor–rotor interaction, and sectional lift distributions over the upper and lower coaxial rotor disks provided further insight into the sources of transient loads due to blade passage.

Investigation on Lubrication State of Sliding Bearings in Low-Speed Rotor System Subjected to Torque Load

In order to study the influence of torque load on the lubrication and wear of the sliding bearing of the rigid rotor system, the theoretical and experimental researches on the single-span rotor system with low speed were carried out. A special force sensor was used to measure the bearing load under different torque excitations, and the oil film pressure was calculated. The oil film pressure and thickness of sliding bearing under low speed (210r/min) were simulated by combining the lubrication theory. Based on the film thickness ratio theory, the corresponding relationship between the lubrication state and the torque load value was deduced. In addition, the wear rate and abrasive grain morphology of sliding bearing with different torque values were analyzed by means of oil sample preparation to verify this correspondence. The results show that the film thickness ratio has a logarithmic function relationship with the constant torque load, and the film thickness ratio curve can be used to determine the corresponding torque values under different lubrication states. The wear rate under mixed lubrication state increases exponentially with the torque load, and the main wear mechanism is adhesive wear and abrasive wear. The research results have certain guiding significance to the adjustment of the actual running condition of sliding bearing and its life prediction.