Jussi Sopanen

Dynamic Torque Analysis of a Wind Turbine Drive Train Including a Direct-Driven Permanent-Magnet Generator

Mechanical interactions between a wind turbine and a direct-driven permanent-magnet synchronous generator (PMSG) are studied, and a model to analyze the system behavior is suggested. The proposed model can be applied to analyze the mechanical vibrations of direct-driven wind turbine installations both in steady state and in dynamic cases. The cogging torque and torque ripple of the PMSG are used as excitation sources in the mechanical model. Four different permanent-magnet rotor constructions are analyzed. It is shown that the maximum allowable value of the cogging torque of the direct-driven permanent-magnet wind generator in this case is 1.5%-2% of the rated torque even when the corresponding resonance frequency does not occur in the operational speed range of the wind turbine. Furthermore, it was noticed that the resonance caused by the excitation torque should occur at the lowest possible speed.

A Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation

In this paper, a new two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation is proposed. The nonlinear elastic forces of the beam element are obtained using a continuum mechanics approach, without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used in the longitudinal direction. The use of linear interpolation polynomials leads to the phenomenon known as shear locking. This defect is avoided through the adoption of selective integration within the numerical integration method. The proposed element is verified using several numerical examples. The results of the proposed element are compared to analytical solutions and the results for an existing shear deformable beam element. It is shown that by using the proposed element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior including the capturing of the centrifugal stiffening effect, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam elements.

Multidisciplinary Design Process of a 6-Slot 2-Pole High-Speed Permanent-Magnet Synchronous Machine

High-speed permanent-magnet synchronous machines (HS PMSMs) are a popular topology among modern electrical machines. Suitable applications for such machines are low-power vacuum pumps, compressors, and chillers. This paper describes a systematic design methodology for an HS PMSM using two case studies. The design process for such high-speed (HS) machines is multidisciplinary and highly iterative due to the complex interaction of the many design variables involved. Consequently, no single optimum solution exists, and multiple possible solutions can meet the customer requirements. Practical solutions should be within acceptable thermal limits, should be energy-efficient, and should be rigid enough to withstand the forces exerted during operation. The proposed design flow is divided into steps that are presented in this paper in the form of a flowchart with emphasis on mechanical aspects. Each step represents a task for a thermal, mechanical, or electrical engineer. The features of each step and the prerequisites for moving to the next step are discussed. The described methodology was implemented in the design of two HS PMSMs. The output performance results of the design flow are compared with measured results of the prototypes. The design process described in this paper provides a straightforward procedure for the multidisciplinary design of HS permanent magnet electrical machines.

Simple and Versatile Dynamic Model of Spherical Roller Bearing

Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB) is one variant witnessing increasing use because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This study introduces a computationally efficient, three-degree-of-freedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to the nonlinear Hertzian contact theory. The results reveal how some of the more important parameters, such as diametral clearance, the number of rollers, and osculation number, influence ultimate bearing performance. One pair of calculations looked at bearing displacement with respect to time for two separate arrangements of the caged side-by-side roller arrays, when they are aligned and when they are staggered. As theory suggests, significantly lower displacement variations were predicted for the staggered arrangement. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis.

Studies on the Stiffness Properties of the Absolute Nodal Coordinate Formulation for Three-Dimensional Beams

The objective of this study is to investigate the accuracy of elastic force models that can be used in the absolute nodal coordinate finite element formulation for the analysis of threedimensional beams. The elastic forces of the absolute nodal coordinate formulation can be derived using a continuum mechanics approach. This study investigates the accuracy and usability of such an approach for the three-dimensional absolute nodal coordinate beam element. This study also presents an improvement proposal for the use of a continuum mechanics approach in deriving the expression of the elastic forces of the beam element. The improvement proposal is verified using several numerical examples. Numerical examples show that the proposed elastic force model of the beam element agrees with analytical results as well as with solutions obtained using existing finite element formulation. The results also imply that the beam element does not suffer from the phenomenon called shear locking. In the beam element under investigation, global displacements and slopes are used as the nodal coordinates, which resulted in a large number of nodal degrees of freedom. This study provides a physical interpretation of the nodal coordinates used in the absolute nodal coordinate beam element. It is shown that the beam element based on the absolute nodal coordinate formulation relaxes the assumption of the rigid cross-section and is capable of representing a distortional deformation of the cross-section.© 2003 ASME

Multidisciplinary Design of a Permanent-Magnet Traction Motor for a Hybrid Bus Taking the Load Cycle into Account

An electrical and mechanical design process for a traction motor in a hybrid bus application is studied. Usually, the design process of an electric machine calls for close cooperation between various engineering disciplines. Compromises may be required to satisfy the boundary conditions of electrical, thermal, and mechanical performances. From the mechanical point of view, the stress values and the safety factors should be at a reasonable level and the construction lifetime predicted by a fatigue analysis. In a vehicle application, the motor has to be capable of generating high torque when accelerating, and in normal operation, the losses of the machine should be low to be able to cool the machine. Minimization of the no-load iron losses becomes a very important electrical design requirement if the traction motor and the generator are mechanically connected with an internal combustion engine when it is operating as the only source of torque. The manufacturing costs of the motor are also taken into account in this paper.

The design of rotor geometry in a permanent magnet traction motor for a hybrid bus

The paper addresses the electrical and mechanical design process of a traction motor for a hybrid bus application. In general, the design process of the electric motors requires intimate co-operation between different engineering disciplines. Often compromises are needed in order to satisfy both the electrical and mechanical performance specifications. From the mechanical point of view the stress values should be on reasonable level and safety factors should be taken into account. From the electrical point of view the torque level should be high while accelerating the traction motor and the losses of the machine should be small in order to be able to cool the machine and sustain high efficiency. In traction use the no-load iron losses will be loading the overall system all the time - also while driving direct with diesel engine. While selecting the best rotor design also the costs will be taken into account - one expensive part of the motor is the permanent magnet material. Therefore, the material price is estimated when selecting the rotor design.

Integrated hub-motor drive train for off-road vehicles

A new concept that integrates a permanent magnet (PM) synchronous motor (PMSM) and a 2-step planetary gearbox for heavy machinery electric traction is introduced. A clear need for this kind of a solution is recognized in the field of diesel-electric hybrid off-road vehicles as electrical machine cannot fulfill alone all the demands of the typical load cycles of working machines. The technology introduced also suits in some road vehicle use e.g. for buses or trucks. The benefits of the solution are pointed out and its functionality is proven by simulations. The dynamic performance of the driveline is analyzed using a co-simulation approach that accounts the mechanical system and the dynamics of the control system.

Transmission configuration effect on total efficiency of Electric Vehicle powertrain

This study investigates the impact of transmission topology on the combined mechanical and electrical efficiency of an Electric Vehicle (EV) by comparing two types of transmissions. In an EV, due to space restrictions, a relatively high-speed electric motor is used with a reduction gear to provide adequate torque production. Since the electric motors efficiency varies according to the amount of applied torque at different speeds, there is a question of whether a multi-step gearbox capable of increasing the electric efficiency by shifting operation points along constant power curves can also improve the powertrain overall efficiency. A mathematical model is developed for calculating the power losses due to movement of mechanical components. In this study, a geartrain is taken into closer analysis where a single reduction gear and a five-step gearbox are compared from an efficiency point of view.

Modeling and Dynamic Analysis of Spherical Roller Bearing with Localized Defects: Analytical Formulation to Calculate Defect Depth and Stiffness

Since spherical roller bearings can carry high load in both axial and radial direction, they are increasingly used in industrial machineries and it is becoming important to understand the dynamic behavior of SRBs, especially when they are affected by internal imperfections. This paper introduces a dynamic model for an SRB that includes an inner and outer race surface defect. The proposed model shows the behavior of the bearing as a function of defect location and size. The new dynamic model describes the contact forces between bearing rolling elements and race surfaces as nonlinear Hertzian contact deformations, taking radial clearance into account. Two defect cases were simulated: an elliptical surface on the inner and outer races. In elliptical surface concavity, it is assumed that roller-to-race-surface contact is continuous as each roller passes over the defect. Contact stiffness in the defect area varies as a function of the defect contact geometry. Compared to measurement data, the results obtained using the simulation are highly accurate.