Dynamic Analysis of Rotor and Machine Structure in Ultra-High-Speed PMSM

In this paper, application examples of high-speed electrical machines are presented, and the machine structures are categorized. Key issues of design and control for the high-speed permanent magnet machines are reviewed, including bearings selection, rotor dynamics analysis and design, rotor stress analysis and protection, thermal analysis and design, electromagnetic losses analysis and reduction, sensorless control strategies, as well as comparison and selection of sine-wave and square-wave drive modes. Some challenges are also discussed, so that future studies could be focused.

A high-speed (HS) permanent magnet (PM) synchronous motor (HSPMSM) with a carbon fiber-reinforced plastic (CFRP) protective sleeve in the surface-mounted rotor was explored in this study. In view of retaining the PMs at HS operations, the high-strength CFRP sleeve was designed on the basis of a process that could be summarized as follows. First, a multi-physics analysis of the rotor was conducted. The requirements to the CFRP sleeve were obtained from electromagnetic analysis, loss analysis, heat flow coupling computational fluid dynamics analysis, structural analysis, and rotor dynamics analysis. Second, the CFRP sleeve was designed by theoretical analysis. From the results, the thickness values of the carbon fibers in the circumferential and helical directions were chosen to be 4 and 1 mm, respectively, while the helical angle of carbon fibers was chosen to be 70°. Then, a plate-shaped CFRP product and a cylindrical CFRP product were fabricated to verify the strength and stiffness of the CFRP sleeve. The performance test results show that the hoop strength and elastic modulus and the axial strength and elastic modulus of the plate-shaped CFRP products at 20 °C are 1963 MPa @ 156 GPa and 550 MPa @ 36 GPa, respectively. The hoop strain and axial strain of the cylindrical CFRP product under 35 MPa are about 3000 and 1900 μe, which meet the design requirements of the HSPMSM.

Parallel-vector design sensitivity analysis in structural dynamics

A rotordynamic analysis of two different high-speed permanent-magnet electrical machines has been performed. Their rotors are analysed separately and for each of them the analysis is performed for three different types of constructions depending on the type of the retaining sleeve. The first type of rotor construction has a carbon-fibre sleeve for retaining the magnets against the centrifugal forces and an aluminium shield for eddy currents. The retaining sleeve of the second construction is made from the titanium alloy Ti-6%Al-6%V-2%Sn and the sleeve of the third type of construction is made from the titanium alloy Ti-2.5%Cu. The last two constructions are examined without additional eddy-current shields. A numerical, finite-element, rotordynamic analysis for each type of rotor construction is performed. The numerical model is successfully compared with measured results for the natural frequencies. The analysis in this study shows that the rotor constructions retained with the titanium alloy Ti-6%Al-6%V-2%Sn sleeve provide better rotordynamic properties than the other types of rotor constructions.

International seismic building codes of practice specify a simplified method based on the first mode for the seismic analysis of regular structures and dynamic analysis for irregular structures. The number of modes to be used in the dynamic analysis of structures should be such that the sum total of the modal masses of all the modes considered is at least 90% of the total structural mass. Previous studies show that the 90% criterion for the number of modes considered may not result in correct responses in all the structural members of an irregular structure. The present study examines the rationale for using the codal provisions for the number of modes to be used for dynamic analysis of irregular building structures using the response spectrum method. Results of this study show that fundamental mode approach for regular structures and 90% modal mass criterion, given by the seismic building codes of practice for the number of modes to be considered for the dynamic analysis of irregular structures, are not adequate. It is observed that the present criterion results in the underestimation of shear forces in the top and bottom storeys according to the numerical examples considered. A simplified method is given for the elastic seismic analysis of irregular and complex structures using a “dynamic correction”, which can be extended to the nonlinear pushover analysis of structures.

Nonlinear static and dynamic analysis of framed structures

Nonlinear finite element for modeling reinforced concrete columns in three-dimensional dynamic analysis

Several procedures for non-linear static and dynamic analysis of structures have been developed in recent years. This paper discusses those procedures that have been implemented into the latest European and US seismic provisions: non-linear dynamic time-history analysis; N2 non-linear static method (Eurocode 8); non-linear static procedure NSP (FEMA 356) and improved capacity spectrum method CSM (FEMA 440). The presented methods differ in respect to accuracy, simplicity, transparency and clarity of theoretical background. Non-linear static procedures were developed with the aim of overcoming the insufficiency and limitations of linear methods, whilst at the same time maintaining a relatively simple application. All procedures incorporate performance-based concepts paying more attention to damage control. Application of the presented procedures is illustrated by means of an example of an eight-storey reinforced concrete frame building. The results obtained by non-linear dynamic time-history analysis and non-linear static procedures are compared. It is concluded that these non-linear static procedures are sustainable for application. Additionally, this paper discusses a recommendation in the Eurocode 8/1 that the capacity curve should be determined by pushover analysis for values of the control displacement ranging between zero and 150% of the target displacement. Maximum top displacement of the analyzed structure obtained by using dynamic method with real time-history records corresponds to 145% of the target displacement obtained using the non-linear static N2 procedure.

A preliminary analysis of the response of the BPX (Burning Plasma Experiment) machine structure to a seismic input was performed. MSC/NASTRAN, a general-purpose finite element computer code, was used. The purpose of this analysis was to assess the probable range of seismically induced stresses and deflections in the machine substructure which connects the machine to the test cell floor, with particular emphasis on the shear pins which will be used to attach the TF (toroidal field) coil modules to the machine substructure. The model consists of beams and plates which represent the mass and stiffness of the various components of the machine structure. These include the TF coils, PF (poloidal field) ring coils, PF solenoid, vacuum vessel, and machine substructure. The results of the current analysis indicate stresses in all load-bearing structural components fall well within the elastic limit (and below the machine design allowables) and the structure should not sustain any significant damage during a safe shutdown earthquake event. >

The intent of this paper is to illustrate how rotor dynamics analysis can be an effective tool to improve rotor dynamic characteristics. Analytical methods, such as undamped critical speeds, unbalance response and stability (damped eigenvalues) analysis are used to evaluate the vibration characteristics of rotating machinery. Advanced rotor dynamics software is capable of generating and analyzing rotor models. By removing undesirable sources of instability and ensuring reliable separation margin, rotor-stability improvement is validated. This study presents an overhung rotor with a proven stable operating history; however, higher power requirements and changes in components resulted in a potential resonant condition of concern. Based on the rotor dynamics analysis outputs, design changes were implemented to ensure the rotor will meet API’s vibration acceptance limits. After evaluating different design alternatives using computer modeling, a change in the inboard bearing diameter proved to be the best solution for attaining smooth operation. Although this paper focuses mainly on the analysis performed on an overhung rotor, the methodology used can be applied to any rotating equipment. It is clear that rotor dynamics analysis is a powerful instrument for predicting operating behavior, thus allowing for necessary changes in analytical modeling and ensuring more stable machines.

In sodium cooled fast breeder reactors (FBR), centrifugal sodium pumps are widely used to circulate the hot sodium in primary as well as in secondary loops. Performance of this critical component is very important in reactor circuits as it affects the load factor and availability of the plant. Operation of the centrifugal sodium pumps, limiting its vibration is a challenge in view of both safety and economy. Various experimental facilities have been set up at IGCAR for testing of FBR components. Vertical centrifugal sodium pumps are used to circulate hot sodium in these facilities. The pump shaft is supported by hydrostatic bearing (HSB) at the bottom and by tapper roller bearing at the top. As the HSB runs with the close tolerance, rotor dynamic analysis was carried out for ensuring its effectiveness and proper functioning of the pump. The results obtained from the analysis are also verified by conducting experiments. This paper discusses the rotor dynamic analysis carried out on a vertical sodium pump used to circulate sodium in steam generator test facility (SGTF) using the rotor dynamic analysis software. In this pump, shaft is supported at the top by tapper roller bearing and hydrostatic bearing at the bottom. Critical speeds and corresponding mode shapes were obtained in the operating range of the rotor speed. Stability analysis was performed for the rotor-bearing system to get the threshold speed of the rotor. Unbalance response of the pump was also carried out to estimate the amplitude of vibration at the bearing locations and compared with experimental results.

With the rapid development of science and technology as well as the comprehensive societal progress, the demand for electricity in all walks of life is also increasing. As is known to all, the mechanical structure and tension control of a transformer winding machine is the key to improving the quality of coil winding, due to coil winding being generally considered the core technology of transformer manufacturing. Aiming at the synchronous winding control problem of the conductor and insulating layer of the transformer winding machine, this paper presents a mechanical structure and tension control scheme of a new type of transformer winding machine. Based on the dynamic analysis and modeling of the mechanical structure of the winding machine, the speed control of the main speed roller by the fuzzy PID control rate is implemented initially. Combined with the actual demand of the project, the feasibility and effectiveness of the control target with different tension are verified by the simulation experiment and further compared with the traditional PID control method. The simulation results show that the proposed fuzzy PID control rate can realize the automatic and efficient winding of the transformer winding machine, showing that it is superior to the traditional PID control rate in overcoming the disturbance and controlling effect.

Improvement in the methods of analysis of structures, machines, aircrafts and ships is one of the most important problems in engineering today. The computational aspects of this problem are being tackled successfully due to developments in computer science. However, for an adequate description of the physical properties of structures, especially those made of newer, non- traditional materials, it is essential to further study their behaviour under different load and kinematic conditions and to develop appropriate physical models that provide a comprehensive and correct description of the actual state of deformation. The objective of this book is to adopt a unified approach for describing the large number of models of internal friction and to offer recommendations regarding the methods of taking it into account at the time of dynamic analysis. It is also intended to provide a comprehensive analysis of the various models, accompanied by detailed solutions of specific problems, which could serve as examples for dynamic analysis of real structures taking into account the effect of internal friction.

Dynamic response analysis of structure with hybrid random and interval uncertainties

Nonlinear dynamic journal bearing modeling within rotordynamic analyses requires the calculation of the nonlinear bearing forces particularly depending on shaft eccentricity and velocity. The bearing forces can be calculated properly using Reynolds differential equation and mass conserving cavitation algorithms, based for example on Elrod’s cavitation algorithm. This approach achieves high model accuracy and allows the consideration of additional effects like misalignment, variable viscosity and transient local oil distribution in the lubricant film. However, despite rising calculating capacity dynamic bearing analyses are still very CPU-time consuming and, consequently, approximation methods are commonly applied in multibody or rotordynamic analyses, especially in day-to-day business. While many approximation procedures are limited to special bearing geometries Glienicke et al. describe a method which is flexible to model different journal bearing geometries, as well as to consider many additional effects like oil supply pressure or starved lubrication conditions in a time averaged manner. It can be applied for both fixed-pad and tilting-pad journal bearings and its characteristic data is included in an a priori calculated map enabling a time-efficient call up of characteristic parameters of the bearing forces from a look-up table in dynamic simulations. Further, the data can be transferred to any other bearing if the requirements of the theory of similarity are supposed to be valid. In this investigation, the method is first successfully extended by the authors to consider misalignment. Secondly, the general idea of the procedure is transferred and applied to thrust bearings in order to enable a six degree of freedom rotordynamic modeling. In case of a simply lateral movement and rotation-symmetric bearing design the procedure is simple, though, in case of tilting movements it becomes more complicated. A misaligned thrust bearing provides tilting and cross-coupling moments. Cross coupling moments are smaller than the main moments, but have similar orders of magnitude and should therefore be considered. Strategies are investigated for a proper approximation of the nonlinear thrust bearing main and cross-coupling forces and moments. All steps are verified using a direct solution of Reynolds differential equation based on an extended mass conserving algorithm adapted from Elrod’s numerical implementation for the stationary case. Finally, the whole procedure and its application to rotordynamic analysis is verified by comparisons with results gained using direct online solution of Reynolds equation in rotordynamic simulation. While good simulation quality of this approximation approach is documented for selected rotor-bearing-systems in literature the range of validity is not clearly defined. Here, the influences of different parameters on the simulation error are investigated conducting different variation calculations for an overhung rotor with documented vibrational behavior from literature. It is shown that the simulation quality depends on the cavitation zone and decreases with rising vibrational velocity. The root cause for this upcoming error and a possible modification for the elimination of this limitation are presented.