Jonathan Z. Bird

Portland State University | PSU · Department of Electrical and Computer Engineering

This paper re-examines the basis for each eddy current stiffness term computed from prior published steady-state eddy current models. The paper corrects prior analysis work by confirming, through the use of 2-D and 3-D dynamic finite element analysis modelling, that when a magnetic source is moving over an infinite-wide and infinite-long conductive...

This paper used an analytic based 3-D second order vector potential model to study the vertical dynamic force ripple and dynamic airgap height change when using a one pole-pair electrodynamic wheel (EDW) maglev vehicle. A one-pole pair EDW creates the lowest lift specific power; however transient finite element analysis (FEA) also shows that the on...

Complex conjugate impedance matching is a key concept for wave energy converter design. Matching the impedance of the power take-off (PTO) system to the complex conjugate of the wave energy converter's (WEC) impedance ensures efficient transfer of energy from the WEC body motion to electrical power. In low frequency waves, impedance matching often...

This paper presents the magnetic, thermal and mechanical design details as well as testing result for a high mass torque density coaxial magnetic gear (MG). The MG was designed for use in an electric aircraft application and has a 12.4:1 gear ratio. The MG was designed to be competitive with a mechanical equivalent aircraft gear and had a calculate...

This article presents the electromagnetic and mechanical design and analyses of a 7.67:1 gear ratio magnetic gear (MG) for a wave energy converter demonstrator. A 2-D and 3-D magnetostatic finite-element analysis (FEA) was conducted to maximize the mass torque density. To increase torque without increasing the diameter, a unique dual-stack rotor to...

This paper studies the influence of cogging torque and unbalanced radial magnetic forces on vibrations and acoustic noise properties in concentric magnetic gears. The study involves three physical demonstrators, each with unique properties that make them interesting study cases. The first magnetic gear have pronounced cogging torque due to the pole...

This article presents the electromagnetic and mechanical design as well as experimental testing results for a 9.5:1 gear ratio, series connected, coaxial magnetic gear (MG) for use in a marine hydrokinetic generator. A two- and three-dimensional magnetostatic finite-element analysis (FEA) sizing analysis was also conducted and a torque density comp...

This paper presents the construction and testing results for a 63.3:1 dual-stage coaxial magnetic gear for use in a marine hydrokinetic generator demonstrator application. The dual-stage magnetic gear is composed of series-connected coaxial magnetic gear. The stage-2 magnetic gear utilizes Halbach magnet arrays on both rotors and has a 9.5:1 gear r...

This paper presents the practical design, analysis, and experimental testing results and encountered issues for a 5.67:1 Halbach rotor magnetic gear with a ferromagnetic back support. Testing results for both a Halbach rotor magnetic gear with rectangular modulation supports and a bridgeless circular modulation support rod design is evaluated. The...

This paper reviews the power density and torque density of permanent magnet motor technology that is currently commercially developed for use in electric aircraft. The review shows that in order to meet the ambitious electrical motor power density goals recently set forth the power density of a motor needs to more than double. The requirements impo...

This paper presents the analysis and mechanical design of a 15.9kW magnetic gear (MG) with a 12.4:1 gear ratio and a computed 53 N•m/kg mass torque density. When the MG is connected in series with a high-speed motor it forms an aircraft MG drivetrain. The target specifications are based on the quad-electric aircraft propulsion system needed for hov...

Laminated structures are commonly employed in magnetic gears based on their ability to direct magnetic flux, while inhibiting eddy currents. Unfortunately, the stiffness of the laminated structure is much lower than a solid part, which can lead to unacceptable deflections, given the large magnetic forces and small air gaps in magnetic gears. Finite...

This study analyzes and verifies the electromagnetic performance and thrust characteristics of linear magnetic gears using subdomain-based analytical methods. By simplifying the analytical model, the governing equations of each domain are calculated based on the Maxwell equation. In addition, the undetermined coefficients of the governing equations...

This paper investigates a new type of axial cycloidal magnetic gear (CMG) that can minimize the unbalanced radial force within the CMG structure. The unbalanced radial force was decomposed into an eccentric coupling force and an eccentric quadrature force. These two force components were studied separately for both the radial and axial CMG typologi...

Magnetic machine designers must consider a variety of mechanical and thermal aspects, particularly as the size increases and the air-gaps between rotors and stators decrease. In these instances, increased losses due to eddy currents can create elevated temperatures, which in turn create significant thermal deformation of components that compromises...

An axial-flux magnetic gear (MG) is integrated into a radial field stator to construct a unique magnetically geared generator for low input speed applications. The high-speed rotor of the axial-flux MG uses a flux-focusing typology. This paper presents the stator design and experimental testing of this unique proof-of-principle axial-flux focusing...

The torque density characteristics for an axial flux magnetic gear using a flux‐focusing topology is experimentally studied when using neodymium iron boron (NdFeB) rare‐earth magnets. A geometric parameter sweep analysis was utilised in order to maximise both the calculated volumetric and mass torque density. The calculated torque and torque densit...

This paper investigates the volumetric torquedensity performance of a radial and an axial cycloidal magneticgear when using a Halbach magnet rotor typology. The analysisis conducted in order to determine the geometric design rulesthat yield the highest volumetric torque density. Theperformance is studied with respect to pole-pair number, orbitlengt...

The design of the second stage of a 59:1 multi-stage magnetic gearbox for a wind turbine demonstrator is presented. The multi-stage series-connected magnetic gearbox is composed of a 6.45 first stage and 9.14 second stage. A flux-focusing spoke-type rotor typology is used with a unique segmented fully laminated design. The impact of structural desi...

The electromagnetic design of the second stage of a 59:1 multistage magnetic gearbox for a wind turbine demonstrator is presented. The multistage series connected magnetic gearbox is composed of a 6.45:1 first stage and 9.14:1 second stage magnetic gear. The magnetic gears utilize a flux focusing spoke type rotor typology with a unique segmented fu...

The design of the first stage of a 59:1 multistage magnetic gearbox for a wind turbine demonstrator is presented. The multistage magnetic gearbox (MSMG) is composed of a two stage magnetic gearbox (MG). The first stage of the MSMG has a gear ratio of 6.45. A spoke type MG rotor typology is used with a unique segmented fully laminated rotor structur...

A magnetically geared lead screw is able to convert high-speed rotation to low-speed translation via magnetic gearing. In this paper a new type of magnetically geared lead screw is presented that uses translator rings without any skewing. The magnetic gearing is accomplished by utilizing an inner rotor with helically skewed magnets and an outer cyl...

This paper presents the performance comparison between a flux concentration (FC) and triple-permanent magnet (PM) consequent pole (CP) magnetic gear (MG) rotor typology with the same 7.5:1 gear ratio. The triple PM CP MG is unique in that it can create torque change through two field heterodyning pole combinations. The performance with respect to v...

A realistically sized magnetically geared lead screw is designed, analyzed and experimentally tested in this paper. By using mag-netic gearing this device is able to convert low speed linear mo-tion into high speed rotary motion. The advantage of the pro-posed design over alternative linear magnetic gear and magnetic lead screw devices is that the...

This paper describes an analytical model of a single stage of a series- connected multi- stage coaxial magnetic gear (MSMG). This model is a system of spring-mass-dampers which is then used to investigate the vibrational modes and natural frequencies of the system at the rotational speeds observed during operation. This approach includes the bendin...

In this paper a 1:4.25 ratio ferrite magnet and NdFeB magnet flux-focusing magnetic gearbox with a high pole count is analyzed. A simple parameter sweep analysis is used to show that higher than previously published torque density values are achievable. Experimental results are then presented for the NdFeB design that confirm the calculations and a...

In this paper an axial flux magnetic gear (AFMG) is proposed that has an integrated outer stator. This axial flux magnetically geared motor (AFMGM) is unique in that the stator shares the high-speed rotor with the AFMG, so there is no need for a separate rotor. The high speed and low speed rotors use a flux-focusing typology. The stator is mounted...

The design of the first stage of a 59:1 multistage magnetic gearbox for a wind turbine demonstrator is presented. The multistage magnetic gearbox (MSMG) is composed of a two stage magnetic gearbox (MG). The first stage of the MSMG has a gear ratio of 6:45. A spoke type MG rotor typology is used with a unique segmented fully laminated rotor structur...

Halbach array magnetic gearboxes have been discussed as being able to create high torque density. However, Halbach arrays are difficult to mechanically assembly and often the effective air-gap must be made larger in order to provide space for a retaining sleeve. This paper investigates the benefits of using an additional ferromagnetic retaining pol...

In this paper the concept of magnetic rolling resistance (MRR) is introduced. The MRR is particularly useful when trying to characterize maglev devices that operate with a slip. Approaches to minimize the MRR for an electrodynamic wheel magnetic suspension device are discussed. MRR is calculated from the power losses and it is shown that by using M...

This paper derives the closed form 3-D analytical torque equations for an ideal radial Halbach rotor magnetic coupling. The performance of the radial Halbach coupling is then compared with an ideal axial Halbach rotor coupling. The closed form equations and comparison gives insight into the upper torque density limits of Nd-Fe-B based magnetic devi...

This paper presents the design investigation and experimental testing of a flux-focusing magnetic gearbox with a three piece laminated rotor structure. Each rotor is made of a single lamination stack held together via thin lamination bridges. It is calculated that mechanical bridges reduces the torque density from 156Nm/L to 139Nm/L (a reduction of...

This digests presents the closed form 3-D analytical equations for an axial and radial Halbach rotor magnetic coupling. The closed form equations give insight into the upper torque density limits of NdFeB based magnetic devices. The performance of the axial and radial coupling is compared.

The eddy current induction in a conductive medium with finite width and thickness due to a moving magnetic rotor is studied. The presented formulation is based on the second order vector potential and the magnetic scalar potential and takes into account the magnetic field interaction through the edges of the conductive medium. The eddy current fiel...

A 3-D analytical model is presented for a Halbach axial magnetic coupling. The field and torque are determined by first solving a 2-D field problem at the radial location in which the radial flux density is assumed zero. The solution to the 2-D problem is then incorporated into a 3-D magnetic charge sheet model so as to enable the complete 3-D fiel...

This paper investigates the performance capabilities of a continuously variable magnetic gearbox that utilizes a flux focusing rotor structure. A fractional slot stator winding is designed to couple to the outer rotor of an existing magnetic gearbox in order to enable the magnetic gearbox to operate with a variable gear ratio.

The purpose of this paper is to present the derivation of a 3-D analytical solution of a null-flux electrodynamic suspension device for a conductive plate. The device consists of a linear Halbach magnet array placed above and below a conductive plate. The eddy current forces are derived using the second order vector potential. When the conductive p...

A magnetic gearbox (MG) offer the ability to operate with low noise and vibration. It's non-contact operation means that no gear lubrication is required and MGs have inherent overload protection [1-4]. A MG also has the potential for high efficiency [5]. Coaxial MG's have been shown to be capable of achieving active region torque densities above 20...

By translationally moving a magnetic source above a conductive plate guideway both levitation and drag forces are created. Unfortunately, the electrodynamic drag force can be quite high [1]. Kratz studied a double Halbach array topology, such as shown in Fig 1 [1], and used a simple curve fitting approximation to model the forces. Kratz experimenta...

Experimental results are presented for three different low-speed flux-focusing magnetic gearboxes. The performance of the magnetic gearbox is compared when utilizing ferrite and NdFeB and also a hybrid design, in which ferrite magnets are used in the inner rotor and NdFeB magnets are used in the outer rotor. The peak torque and efficiency are measu...

In this paper, the 3-D forces created by induced eddy currents in a conductive plate of finite thickness are derived using the concept of magnetic charge and energy. Using this approach the exact steady state based eddy-current damping and stiffness matrices for an arbitrary magnetic source moving above a conductive plate are derived. The damping a...

Purpose – The purpose of this paper is to validate dynamic analytic force modeling techniques with experimental results. The performance of previously presented 2-D and 3-D eddy current models will be assessed when the steady-state models are coupled to a dynamic mechanical model. Design/methodology/approach – The previously presented 2-D analytic...

In this paper a 1:4.25 ratio ferrite magnet and NdFeB magnet flux-focusing magnetic gearbox with a high pole count is analyzed. A simple parameter sweep analysis is used to show that higher than previously published torque density values are achievable. Experimental results are then presented for the NdFeB design that confirm the calculations and a...

In this paper the mechanical deflection of steel bars, of different length, in a flux focusing magnetic gear is studied. The mechanical deflection is caused by the magnetic attraction between the steel bars and the inner and outer rotor magnets of the magnetic gear. An iterative magnetomechanical approach using commercial finite element analysis so...

Purpose – A 3-D analytic modeling technique for calculating the eddy current distribution, force and power loss in a conductive plate of finite width and thickness is presented. The derived equations are expressed in a general form so that any magnetic source can be utilized. The model assumes the length of the conductive plate is large and the thi...

This paper investigates the mechanical deflection within steel bars in a flux focusing magnetic gear. The deflection is caused by the magnetic attraction between the steel bars and the inner and outer rotor magnets. The non-linearity within the steel is considered. Experimental results are presented.

This paper presents an analytic based eddy current torque analysis procedure. The equations are derived using the second-order vector potential and the magnetic rotor is modeled using the magnetic charge sheet concept. The formulation enables the damping and stiffness equations to be derived. The equations are numerically computed and the accuracy...

This paper investigates a novel transverse flux magnetic gear using ferrite and NdFeB magnets. The transverse flux magnetic gear topology offers the advantage of a simpler mechanical construction. In order to increase the air-gap flux density the magnets are arranged in flux focusing configuration. The performance when using soft magnetic composite...

In this paper the torque density characteristics for an axial magnetic gear using a flux focusing topology is studied when using (NdFeB) rare-earth magnets. The torque density is improved by conducting a basic geometric sweep analysis of the most important variable parameters. It is calculated that an extremely high torque density can be achieved w...

The experimental results are presented for a low speed flux focusing magnetic gear utilizing ferrite magnets. The performance of this ferrite magnetic gear is compared with a hybrid magnet magnetic gear with NdFeB magnets on the inner rotor and ferrite magnets on the outer rotor. The peak torque and efficiency is measured.

This paper investigates a novel axial magnetic gear using ferrite magnets. In order to increase the air-gap flux density the ferrite magnets are arranged in flux focusing configuration. The simulation results presented in this paper indicate that a relatively high torque density can be achieved when using only ferrite magnets.

A magnetic gear is presented that is capable of continuously varying the gear ratio in order to enable constant magnified output speed to be generated from variable input speed. A flux focusing (spoke type) inner rotor is utilized and the performance of the device is assessed when using three different stator winding configurations. In order to stu...

A 2-D analytic based eddy-current transient model for a conducting plate is derived that is capable of accounting for continuous changes in the input conditions. Only the source field on the surface of the conducting plate needs to be known. In addition, a 2-D steady-state analytic based eddy-current model that is capable of accounting for frequenc...

A modeling approach is presented that enables the 3-D field external to a complicated magnetic source to be reproduced using an equivalent fictitious magnetic charge sheet. It is shown that the value of the equivalent magnetic charge sheet can be determined from the normal component of the magnetic source. The field distribution due to a cylindrica...

When a magnetic source is moved and/or oscillating above a conductive linear plate a traveling time varying magnetic field is created in the airgap. This field induces eddy currents in the plate that can simultaneously create normal and tangential forces. The transient fields and the forces created by the magnetic source are modeled using a novel 2...

A magnetic gear offers many advantages over its mechanical counterpart such as contact free torque production, no gear lubrication and inherent overload protection. However, current magnetic gear designs use large quantities of rare-earth magnet material and unfortunately the high cost of rare-earth material makes the magnetic gear uncompetitive wi...

This paper presents an ocean energy power take-off system using paddle like wave energy converter (WEC), magnetic gear and efficient power converter architecture. As the WEC oscillates at a low speed of about 5-25 rpm, the direct drive generator is not an efficient design. To increase the generator speed a cost effective flux focusing magnetic gear...

Two-dimensional (2-D) force and power loss equations are derived for the case when an arbitrary magnetic source is moving and/or rotating above a conductive plate composed of linear material. The problem is formulated using both the magnetic vector and scalar potential. In order to compute the forces and power loss due to the induced eddy currents,...

A magnetic gear offers many advantages over its mechanical counterpart such as contact free torque production, no gear lubrication and inherent overload protection. However, current magnetic gear designs use large quantities of rare-earth magnet material and unfortunately the high cost of rare-earth material makes the magnetic gear uncompetitive wi...

When a magnetic rotor is simultaneously rotated and translationally moved above an aluminum guideway a traveling time-varying magnetic field is created in the air-gap. This field induces eddy currents in the guideway that can simultaneously create suspension and propulsion or braking forces. The transient fields and the forces created by this movin...

When a rotor is simultaneously rotated and translationally moved above an aluminum guideway a traveling time-varying magnetic field is created in the air-gap. This field induces eddy currents in the guideway that can simultaneously create suspension and propulsion or breaking forces. The field and forces created by this moving rotor are modeled usi...

An efficient three-dimensional transient finite element method for calculating the lift, thrust and lateral forces created when a magnetic rotor is both translationally moved and rotated above an aluminum sheet guideway is presented. The rotor field is calculated from an equivalent fictitious magnetic charge sheet formula. The rotor field's effect...

When a Halbach rotor is simultaneously rotated and translationally moved above a split-sheet aluminum guideway a traveling time-varying magnetic field is created in the air gap. This field induces eddy currents in the guideway that can simultaneously create suspension and propulsion forces. If the rotor is offset from the center then a re-centering...

We present a two-dimensional complex steady-state finite-element method for calculating the lift and thrust or breaking forces created when a magnetic rotor is translationally moved and rotated over a conducting sheet. The method replaces the magnetic rotor with an equivalent current sheet by equating the current sheet's and magnet rotor's magnetic...

When a magnetic rotor is both rotated and translationally moved above a conductive, nonmagnetic, guideway eddy currents are induced that can simultaneously create lift, thrust, and lateral forces. In order to model these forces, a 3D finite-element model with a magnetic charge boundary has been created. The modeling of the rotational motion of magn...

The mechanical rotation of a radially positioned permanent-magnet Halbach array above a conducting, nonmagnetic track induces eddy currents in the track that can inductively create suspension and propulsion forces simultaneously. The parameters that affect the performance of this electrodynamic wheel are studied using a 2-D steady-state finite-elem...

The goal of this thesis has been to investigate whether a very low cost and efficient form of high-speed maglev (magnetic levitation) ground transportation is feasible. The thesis has focused on studying an integrated method of creating the maglev forces using a Halbach magnet rotor, termed an electrodynamic wheel. When magnets are electromechanica...