Rotor Mass Research Articles

Design optimization of vehicle asynchronous motors based on fractional harmonic response analysis

Abstract. To make vehicles more reliable and efficient, many researchers have tried to improve the rotor performance. Although certain achievements have been made, the previous finite element model did not reflect the historical process of the motor rotor well, and the rigidity and mass in rotor optimization are less discussed together. This paper firstly introduces fractional order into a finite element model to conduct the harmonic response analysis. Then, we propose an optimal design framework of a rotor. In the framework, objective functions of rigidity and mass are defined, and the relationship between high rigidity and the first-order frequency is discussed. In order to find the optimal values, an accelerated optimization method based on response surface (ARSO) is proposed to find the suitable design parameters of rigidity and mass. Because the higher rigidity can be transformed into the first-order natural frequency by objective function, this paper analyzes the first-order frequency and mass of a motor rotor in the experiment. The results proved that not only is the fractional model effective, but also the ARSO can optimize the rotor structure. The first-order natural frequency of asynchronous motor rotor is increased by 11.2 %, and the mass is reduced by 13.8 %, which can realize high stiffness and light mass of asynchronous motor rotors.

Research on Vibration Suppression Method Based on Coaxial Stacking Measurement

A dynamic analysis model of the unbalanced vibration response of a single-rotor system is established to study the corresponding mechanism of the unbalanced excitation force and vibration response caused by the deviation of the rotor mass centroid in this paper, and finally to achieve the combined rotor vibration suppression. First, the installation of multi-stage rotors during vibration was studied, and the rotor mass centroid transfer model in the rotating coordinate system was established to obtain the unbalanced excitation force vectors of the rotors at all levels based on the traditional stacking assembly method and axiality measurement. Second, the rotor unbalance excitation force vectors were substituted at all levels to establish the finite element analysis model of the single-rotor system. Finally, a simulation analysis was carried out for the stacking assembly of the three-stage rotor, and the rotor test piece was used for the vibration experiment. The results show that the optimal assembly phase of the multi-stage rotor obtained by the dynamic analysis model of the unbalanced vibration response of the single-rotor system can effectively suppress the vibration of the combined rotor.

Overview of Canada's energy storage related research activities: A perspective

Overview of Canada's energy storage related research activities: A perspective

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.

Regional rotor blade waste quantification in Germany until 2040

Worldwide, wind turbine stocks are ageing and questions of reuse and recycling particularly of rotor blades become urgent. Especially, rising rotor blade wastes face lacking good recycling options and exact quantification is difficult due to information gaps on the rotor blade size, mass and exact material composition. In a combined approach, the expected rotor blade waste is quantified and localized on a national level for Germany until 2040. Fibre-reinforced plastics (FRP) from rotor blades are in focus and differentiated into two material classes: glass-fibre reinforced plastics (GFRP) and glass- and carbon-fibre reinforced plastics (GFRP/CFRP). The quantification approach is based on a national power plant stock database (Marktstammdatenregister) and regression models, combined with a power class-based estimation for missing datasets. As a result, between 325,726 and 429,525 t of waste from the GFRP material class and between 76,927 t and 211,721 t of waste from the GFRP/CFRP material class arise from obsolete rotor blades in Germany until 2040. This corresponds to a share of between 11% and 32% of wind turbines with GFRP/CFRP rotor blade material in Germany. For GFRP, waste peaks in 2021, 2035 and 2037 are expected with around 40,000 t of waste per year. For GFRP/CFRP, waste peaks in 2036 and 2037 will induce more than 20,000 t/a. Mostly affected federal states are Lower Saxony, Brandenburg, North Rhine-Westphalia and Schleswig-Holstein. The methods are applicable and transferable to other countries, particularly with ageing wind turbines fleets.

Implementation of Variable Blade Inertia in OpenFAST to Integrate a Flywheel System in the Rotor of a Wind Turbine

In this paper, the integration of the dynamic behavior of the flywheel system into the load simulation tool OpenFAST is presented. The flywheel system enables a wind turbine to vary the inertia of its rotor blades to control the power production and, most importantly, to affect the vibratory behavior of wind turbine components. Consequently, in order to simulate the behavior of a wind turbine with a flywheel system in its rotor, the variable blade characteristics need to be considered in the load simulation tool. Currently, computer-aided engineering tools for simulating the mechanical loads of wind turbines are not designed to simulate variable blade inertia. Hence, the goal of this paper is to explain how variable inertias of rotor blades are implanted in such load simulation tools as OpenFAST. OpenFAST is used because of it is free, publicly available, and well documentation. Moreover, OpenFAST is open source, which allows modifications in its source code. This add-on in the load simulation is applied to correct rotor mass imbalance. It can also be applied in many cases related to the change in the inertia of wind turbine rotor blades during its operation as, for example, atmospheric ice accretion on the blades, smart blades, etc.

A tribo-dynamic model of coupled journal-thrust water-lubricated bearings under propeller disturbance

The main purpose of this study is to develop a tribo-dynamic numerical model for coupled journal-thrust water-lubricated bearings (also referred as coupled bearings) used in rim driven thruster under propeller disturbance, in which the four degree of freedom (4-DOF) dynamic model of the propeller rotor is bridged with the transient mixed friction model of the coupled bearing. A validating experiment for the coupled water-lubricated bearing is performed to support the correctness of the developed tribo-dynamic model. In the model, the disturbing forces and moment caused by the propeller are calculated by the quasi-steady method. Based on the numerical study, the transient coupling effects between the dynamic characteristic of the propeller rotor and the mixed friction of the coupled bearing are revealed. Furthermore, parametric studies are carried out to identify the effects of the structural and working condition parameters on the tribo-dynamic responses of the coupled bearing. Numerical results indicate that disturbing moment leads to the increase in the transient contact force of the coupled bearing, and the coupling hydrodynamic pressure at the common boundary significantly affects the tribo-dynamic behaviors of the coupled bearing. Parametric studies demonstrate that there exists the optimal radial clearance and tilting angle to minimize the transient contact force of the coupled bearing during operation. In addition, numerical studies reveal that the propeller rotor mass is an important parameter affecting the tribo-dynamic responses of the thrust bearing.

Dynamic modeling of rotor-bearing-housing system with local defect on ball bearing using mass distribution and energy methods

The rotor-bearing-housing system is widely used in rotating machines, which influences the performance of the whole machine. Considering the distribution of rotor mass, the rotor-bearing-housing system with local defect in the outer ring is modeled based on the energy method. In order to make the model agree well with the experimental results, a new rotor mass distribution method was introduced in the modeling process. The simulated vibration signal was obtained by solving the dynamic equations with the Runge-Kutta method. The vibration responses of rotor-bearing-housing system under different distributed disks at both drive end and fan end are simulated. In the simulation results, the outer ring fault signal at the drive end and the vibration signal at the fan end are compared with the experimental signals to discuss the influence of rotor mass distribution on the vibration response of the bearing at both ends of the system. The results show that the simulation signal generated by the dynamic model of the rotor-bearing-housing system with a more uniform rotor mass distribution is more consistent with the experimental signal. The vibration response of the faulty bearing at drive end is compared at different defect sizes, and the variation trend of the amplitude of their characteristic frequency is obtained. This method is helpful for structural optimization and fault diagnosis of the rotor-bearing-housing system.

Compensation control of rotor mass eccentric vibration for bearingless induction motors

Aiming at the rotor mass eccentric vibration caused by the mechanical unbalance of a bearingless induction motor (BL-IM), an unbalance mass radius product (UMRP) strategy is proposed to compensate for rotor displacement. By analyzing the principle and influence of the unbalanced vibration of BL-IM’s, a rotating coordinate system is established according to the rotor centroid, the size and orientation of the UMRP is sought by the search algorithm. Then the control signal for the unbalanced vibration compensation is calculated by the compensator, the centrifugal force caused by the mass unbalance is offset by the control signal, and the vibration amplitude of the rotor is weakened. Finally, the compensation effect is verified by the proposed strategy in the MATLAB/Simulink platform and an experimental prototype. Simulation and experimental results show that the rotor displacement peak-to-peak value about 10 µm. In addition, the radial displacement of the rotor is significantly reduced by the proposed compensation control strategy, and the anti-disturbance capability of the system is improved. The correctness and effectiveness of the proposed method are verified.

Inerter-enhanced tuned mass damper for vibration damping of floating offshore wind turbines

This paper investigates the use of an inerter-enhanced vibration absorber, the rotational inertia double tuned mass damper (RIDTMD), for damping in-plane vibrations of a floating offshore wind turbine (FOWT). First, a 17-degree-of-freedom (17-DOF) aero-hydro-servo-elastic model for the FOWT is developed and verified, based on which the damper performance can be evaluated in the time domain (TD) with realisitc load conditions. Next, a reduced-order 6-DOF model is established for the RIDTMD-controlled FOWT in-plane vibrations including rotor mass moment of inertia, hydrodynamic added mass, as well as stiffness contributions from mooring lines and buoyancy. This model enables revealing the dynamics of the coupled spar-tower-RIDTMD system, and provides an efficient yet robust procedure for optimal tuning of the FOWT-mounted RIDTMD in the frequency domain (FD). Comparison of the optimal RIDTMD and the optimal TMD is performed in both FD and TD. It is seen that both TMD and RIDTMD effectively suppress tower side-side vibrations when mounted at the tower top. RIDTMD consistently outperforms TMD due to the extra DOF (extra resonance) introduced into the device, at the cost of slightly larger damper stroke. Both dampers positively influence spar roll motion and blade edgewise vibration as well.

Detection of mass imbalance in the rotor of wind turbines using Support Vector Machine

Condition monitoring systems (CMS) are essential to reduce costs in the wind energy sector. This paper proposes a method based on Support Vector Machine (SVM) to detect rotor mass imbalance for a multi-class imbalance problem, using the estimated speed as an input variable, obtained through a combination of electrical quantities (currents and voltages). Moreover, it is sought to obtain the magnitude of the rotor mass imbalance. With the aid of statistical tools, intermediate classes can be estimated, other than the ones proposed for the SVM. Besides, if the azimuth position is provided, the angular position of the mass imbalance can be also obtained. A 1.5 MW three-bladed wind turbine model with a permanent magnet synchronous generator, was considered, and a database was built numerically using the software Turbsim, FAST, and Simulink. From the database, the Power Spectral Density (PSD) technique was used to transform the input data from the time to the frequency domain. Then, the SVM algorithm and statistical analysis were used to classify the magnitude and the angular position of the imbalance. Different scenarios of mass imbalance were tested under different wind speeds and turbulence intensities. The results demonstrate the satisfactory performance of the proposed method.

Structural design and optimization of a series of 13.2 MW downwind rotors

The quest for reduced LCOE has driven significant growth in wind turbine size. A key question to enable larger rotor designs is how to configure and optimize structural designs to constrain blade mass and cost while satisfying a growing set of challenging structural design requirements. In this paper, we investigate the performance of a series of three two-bladed downwind rotors with different blade lengths (104.3-m, 122.9-m, and 143.4-m) all rated at 13.2 MW. The primary goals are to achieve 25% rotor mass and 25% LCOE reduction. A comparative analysis of the structural performance and economics of this family rotors is presented. To further explore optimization opportunities for large rotors, we present new results in a root and spar cap design optimization. In summary, we present structural design solutions that achieve 25% rotor mass reduction in a SUMR13i design (104.3-m) and 25% LCOE reduction in a SUMR13C design (143.4-m).

Nonlinear Analysis of Stability and Rotational Accuracy of an Unbalanced Rotor Supported by Aerostatic Journal Bearings

This paper presents the nonlinear analysis of stability and dynamic rotational accuracy of an unbalanced rotor supported by aerostatic journal bearings. A finite element method is utilized with the Runge-Kutta fourth order method to solve the transient Reynolds equation and the rotor dynamics equations simultaneously for the dynamic response analysis of the rotor. The dynamic behavior of the rotor center is analyzed under different rotor masses. It is shown that the dynamic responses of the rotor strongly depend on the rotor mass. The periodic, multi-periodic or quasi-periodic motions are observed as the rotor mass changes. Under a given operating speed, the mass at which the resonance occurs is studied and its relationship with the mass of the rotor at the threshold of instability is found for the first time. The influences of supply pressure, bearing clearance, orifice diameter and eccentric distance on the rotational accuracy, the resonance and instability threshold are also investigated. The result of this study can provide guidance for designing aerostatic bearing rotor systems with required running accuracy and stability.

Coupling effect of unbalanced magnetic pull and ball bearing on nonlinear vibration of motor rotor system

In this article, the coupling effects of the unbalanced magnetic pull and ball bearing on nonlinear vibration of the three-phase asynchronous motor are investigated with the experimental and numerical methods. A test rig of a motor whose rotor supported by ball bearings is used and a 2 degrees of freedom magnetic solid coupling dynamic model of the motor rotor system is presented. The nonlinear dynamic response and spectrum are obtained from experiments and numerical analysis. The numerical results are in good agreement with test data, thus validating the presented model. It is found that the unbalanced magnetic pull and ball bearing forces possess the significantly interactional and nonlinear influences on the rotor dynamic characteristics. Small magnetic pull could impact the nonlinear bearing-rotor system, resulting in remarkable changes in the dynamic characteristics of the system. The effects of rotational speed and the rotor mass eccentricity on dynamic behaviors of the motor are discussed, and the results show that the magnetic pull gradually increases the amplitude of the ball bearing-rotor system, and its effect decreases with the increment of the rotational speed and mass eccentricity.

Modeling the Operation of a Centrifugal Pump with a Rotor Imbalance

A mathematical model of nonstationary rotation modes of the rotor of a centrifugal pump is built with allowance for the displacement of the rotor mass center relative to the rotation axis that causes vibrations in cooling systems of spacecraft. The process of acceleration and ascent of the rotor with subsequently reaching the mode of quasi-stationary oscillations is considered.

A new three-node element for bending, free vibration and buckling analysis of composite laminated beams based on FSDT theory

In this paper, a new three-node element with three degrees of freedom per node is proposed for bending, free vibration and buckling analysis of laminated beams. The element’s formulation is based on the first-order shear deformation theory (FSDT). For this aim, transverse displacement and rotation field of the element are selected from fifth and fourth order, respectively. Moreover, the shear strain is varied as quadratic function throughout the element. It is worth noting that the quadratic function can be used for axial displacement field. By employing equilibrium equation, curvature and shear strain relations of laminated beam with FSDT theory, the exact and explicit shape functions of the displacement fields are obtained. By utilizing the obtained shape functions, the explicit form of the stiffness matrix is calculated for the element. On the other hand, by using the governing equation of the free vibration and buckling of the beam, the explicit form of the translation and rotary mass matrices, and geometric stiffness matrix of the element are obtained. It should be mentioned, the proposed element is free of shear locking. Finally, several numerical tests fulfill to assess the robustness of the developed element. For this purpose, bending, free vibration and buckling analysis of laminated beams with different boundary conditions and aspect ratios are performed. The results of the numerical tests demonstrate high accuracy and efficiency of the proposed element for free vibration and buckling analysis of laminated beams.

Bifurcation and Nonlinear Behavior Analysis of Dual-Directional Coupled Aerodynamic Bearing Systems

Dual-directional coupled aerodynamic bearing (DCAB) systems have received considerable attention over the past few years. These systems are primarily used to solve air lubrication problems in high-precision mechanisms and equipment that run at a high rotational speed and require high rigidity and precision. DCABs have the advantages of axial and radial thrust and provide high rigidity, dual-directional support, and high load-carrying capacity. In DCAB systems, the nonlinearity of the air film pressure and dynamic problems, such as critical speed, unbalanced air supply, or poor design, can cause the instability of the rotor-bearing system and phenomena such as nonperiodic or chaotic motion under certain parameters or conditions. Therefore, to investigate what conditions lead to nonperiodic phenomena and to avoid irregular vibration, the properties and performance of the DCAB system were explored in detail by using three numerical methods for verifying the accuracy of the numerical results. The rotor behavior was also studied by analyzing the spectral response, the bifurcation phenomenon, Poincaré maps, and the maximum Lyapunov exponent. The numerical results indicate that chaos occurs in the DCAB system for specific ranges of the rotor mass and bearing number. For example, when the rotor mass (mr) is 5.7 kg, chaotic regions where the maximum Lyapunov exponents are greater than 0 occur at bearing number ranges of 3.96–3.98 and 4.63–5.02. The coupling effect of the rotor mass and bearing number was also determined. This effect can provide an important guideline for avoiding an unstable state.

Active Aerodynamic Load Control for Improved Wind Turbine Design

Historically, cost reduction in wind energy has been accomplished by increasing hub heights and rotor diameters to capture more energy per turbine. However, larger wind turbines cannot be expected to lead to lower LCOE without the addition of new technologies. Capital costs grow rapidly with rotor diameter, faster than the rated power, because as rotor diameter increases, the blades get heavier and more costly. The growth in blade mass with blade length is accelerated by the additional structure that must be added to withstand unsteady aerodynamic loads caused by turbulence, gusts, wind shear, misaligned yaw, upwind wakes, and the tower shadow. This paper presents a holistic design solution to integrate active load control via dielectric barrier discharge (DBD) plasma actuators into wind turbine rotors along with initial findings on load reduction, actuator development, and rotor mass reduction.

Reduction of the High-Speed Magnetically Suspended Centrifugal Compressor Harmonic Vibration Using Cascaded Phase-Shifted Notch Filters

In the active magnetic bearing (AMB)-rotor control system, rotor mass unbalance and displacement sensors runout will bring about harmonic current, which would further result in vibration force transmitted to machine housing. The undesired machine vibration would pose a potential threat to system stability and performance degradation. In order to attenuate harmonic current, this work has proposed a scheme of control system with cascaded mode phase-shift notch filters, and the system stability has been analysed. The harmonic current reduction performances of the system with cascaded mode notch filters are compared with that with parallel mode notch filters. Theoretical analysis has demonstrated that the proposed cascaded mode control system could achieve the same suppression performance as the commonly used parallel mode control system, which is also verified by simulation results. Experiments carried out on a high-speed magnetically suspended centrifugal compressor have validated that the proposed method is effective for harmonic current reduction.

Mathematical simulation of vibration signature of ball bearing defects in a rotor bearing system

This paper presents the analytical model of a ball bearing with localized defect in the outer race. The outer raceway defect is modelled based on the reduction in the contact force due to localised increase in the clearance. The contact forces are modelled based on Hertzian contact deformation theory. The geometry of the defect is considered as a half sinusoidal wave. The contact between the ball and the outer raceway is modelled using non-linear springs, acted upon rotor mass. The system governing equations of motion are obtained and represented in state space form. Numerical simulations are carried out using MATLAB environment to study the effect of outer race defect on vibration responses. Time and Frequency domain characteristics of the simulated vibration signals are obtained.