Development of a High-Speed Electric Rotating Machine ^†

Abstract

High-speed electric machines enhance power density and eliminate the need for a gearbox in waste heat recovery microturbine systems. However, existing designs often suffer from high manufacturing costs and complex cooling requirements. This study presents the development, experimental validation, and comparative analysis of three high-speed machine designs. First, a lower-speed induction machine prototype, constructed using standardized components, was tested at an operating speed of 13,000 rpm. This prototype enabled experimental validation of the numerical model used for loss calculations. Experimental results showed total losses of 7.89 kW, closely matching the simulated value of 7.75 kW at an output power of 93.1 kW, i.e., an efficiency of 92.19%. Building on these findings, two smaller machine prototypes were developed: one featuring an induction squirrel-cage rotor and the other employing a surface-mounted permanent magnet rotor topology. Both machines were designed and evaluated using finite element analysis and conjugate heat transfer simulations. Their performance was analyzed under both sinusoidal and pulse-width-modulated voltage supply conditions. At an operating speed of 14,000 rpm, the permanent magnet machine outperformed the induction machine, achieving 63.2 kW of mechanical power and an efficiency of 96.21%, while operating at lower temperatures. In comparison, the induction machine delivered 52.4 kW of mechanical power with an efficiency of 94.64%. The primary novelty and contribution of this work lie in the implementation of a two-pole machine architecture capable of achieving an output power of 100 kW at operating speeds between 20,000 and 25,000 rpm. Compared with similar solutions reported in the literature, the proposed machines feature a simplified bearing arrangement and a more straightforward liquid-cooling system. These characteristics have the potential to reduce manufacturing costs and simplify maintenance during operation.

1. Introduction

Increasing machine speed from conventional values of approximately 3000 rpm to speeds exceeding 12,000 rpm significantly improves power density. This enables more compact designs and reduces material consumption and overall manufacturing costs. Furthermore, a high-speed machine can be directly coupled to the turbine without the need for a gearbox [1], making it particularly attractive for waste heat recovery applications. The research presented in this paper aims to address the challenge of developing high-speed machines that are both more affordable and easier to maintain.

Microturbine generator systems typically operate at speeds above 10,000 rpm and are connected to the electrical grid through power electronic converters. The requirement for continuous operation, often exceeding 8000 operating hours per year, frequently leads to machine designs that are complex and expensive to manufacture and maintain [2,3,4]. Common cooling solutions include water-jacket stator cooling combined with air-cooled rotors, as well as oil cooling of the entire active machine assembly. Similarly, complex bearing arrangements are often employed, including multiple rolling bearings (typically four or more per machine), magnetic bearings, or air bearings, depending on the target operating speed range and application requirements [5].

Several manufacturers currently offer microgenerators operating in the speed range between 10,000 and 40,000 rpm that are intended for integration into waste heat recovery installations [6]. Available designs are mostly based on the two-pole or the four-pole synchronous machines, using permanent magnets made from rare-earth materials. To withstand the high centripetal forces acting on the rotor at such rotational speeds, the rotor is typically reinforced by a retaining sleeve made of non-magnetic steel or carbon fiber [7]. In addition to permanent magnet machines, high-speed induction machines have also been widely investigated in the literature [8], including solid-rotor configurations [9,10,11,12,13,14] and machines with laminated rotors [15,16,17].

The underlying motivation for this research was to develop a high-speed machine with a simpler and more economical design. To achieve this, preference was given to standardized, commercially available components, including IEC-standard laminations, water-jacket cooling housings, conventional rolling-element bearings, and compatibility with existing industrial converter technology. Furthermore, the design was aimed at simplifying maintenance by minimizing the number of wear components that require periodic replacement.

To evaluate the feasibility of the high-speed induction machines, the first prototype was designed and tested at speeds above 10,000 rpm. Experiments were conducted at approximately 13,000 rpm to assess electromagnetic, mechanical, and thermal performance. The goal was to determine whether a structurally simpler and more cost-effective machine could reliably operate as a high-speed generator. Key design challenges and results were presented in [18].

Based on the results obtained from the initial prototype, further development focused on the design of a higher-speed microturbine generator. A two-pole machine architecture was selected to achieve operating speeds of up to 30,000 rpm. In contrast to the four-pole designs commonly reported in the literature [4,7,19,20,21,22,23], a two-pole configuration was intentionally adopted to avoid the use of power converters requiring fundamental operating frequencies above 600 Hz. This decision was motivated by both economic considerations and the desire to avoid classifications that may subject such equipment to export-control restrictions for dual-use technologies. Two machine topologies sharing a common stator design were considered: a surface-mounted permanent magnet (SPM) machine and an induction machine (IM).

The induction machine rotor was chosen as a standard IEC lamination cut, with aluminum cast bars and end rings. Due to mechanical criteria of the rotor, the rotational speed of 14,000 rpm was chosen as the operating limit, considering the power density of the machine, structural strength and resonant characteristics of the rotor.

The rotor with the surface-placed permanent magnets was sized to fit the same stator and casing as the squirrel-cage counterpart. Calculation analyses showed that this design fulfilled the required criteria for long-term operation at maximum continuous speed of 25,000 rpm, and the overspeed of 30,000 rpm.

Jung et al. [24] and Yu et al. [25] investigated the influence of pulse-width-modulated (PWM) excitation on losses and temperature distribution in permanent magnet synchronous machines. Their findings demonstrated that PWM excitation significantly increases losses in solid conductive materials, especially permanent magnets. Therefore, the effects of PWM excitation had to be considered in the simulation phase, to enable accurate prediction of permanent magnet temperatures during the machine design process.

The concept of solving the rotor cooling with internal air circulation was analyzed in detail. Although it proved insufficient, it is added in this paper as a reference point. Several alternative rotor-cooling approaches, including oil-jet cooling and rotating heat pipes [26,27], were evaluated during the development of the new machine prototypes. However, these solutions were considered excessively complex for the intended application. Wang et al. [28] proposed a recirculating hollow-shaft cooling system for machines operating at speeds of up to 5000 rpm. Although this operating range is well below the target speeds of the proposed microturbine generator, the cooling concept was assessed as technically feasible and was therefore chosen for further investigation and detailed analysis.

After the above design choices had been established, detailed electromagnetic, mechanical, and thermal analyses of the prototypes were carried out [29].

This paper starts with an overview of the materials and methods employed in the analysis and development of the machines investigated, first with the initial lower-speed prototype and followed by the more compact, higher-speed designs. The subsequent sections discuss the experimental measurements and comparative performance evaluation of the machine prototypes, supported by both simulation and measurement results. Finally, the results are discussed, and the principal conclusions of the study are presented.

2. Materials and Methods

2.1. Lower-Speed Prototype

The machine was designed and manufactured with an emphasis on the use of readily available, standardized components, as summarized in

Table 1. Standardized parts used to build the machine.

Component	Type
Casing	IEC 160 for water cooling
Lamination cut	IEC 160/2.135
Lamination steel	0.5 mm M270-50A
Squirrel cage	Cast aluminum
Wire	Enameled copper round size 0.85 mm
Bearing	6307 M/C4 Ball bearing

. A squirrel-cage induction machine topology based on a well-established IEC 160 [30] frame and a two-pole lamination design was selected. This configuration is known to exhibit low electromagnetic torque ripple, as well as low noise and vibration levels, under conventional operating conditions at speeds of up to 3600 rpm. An axial lamination length of 250 mm was chosen to meet the design requirements. The stator winding was configured with two parallel paths and comprised six conductors per slot, each consisting of 19 strands.

The main design challenges can be grouped into three categories: electromagnetic, mechanical, and thermal. From an electromagnetic perspective, it was necessary to mitigate the additional harmonic losses associated with low-inductance windings while retaining a standard stator lamination geometry and conventional machine topology. Mechanical considerations included ensuring that the natural resonant frequencies of the rotor–shaft system remained outside the intended operating speed range while preserving a conventional rolling-element bearing arrangement. From a thermal perspective, the design had to provide sufficient cooling capacity while avoiding, as far as possible, the use of additional external cooling equipment, such as auxiliary fans.

Several design modifications were introduced compared with conventional grid-connected machines to meet the previously defined objectives. The electrical design incorporates a random-wound stator winding rated at 530 V and 216.67 Hz (corresponding to a rotational speed of 13,000 rpm), with conductors of 0.85 mm diameter selected to reduce skin-effect losses. In addition, external inductance coils were installed between the machine and the power converter to mitigate current harmonics. Rated-load operation was achieved by applying a 20% flux increase through the voltage-boost functionality available in the converter control software [31]. This allowed the terminal voltage to reach the maximum permissible value of 530 V, thereby reducing the required current. Mechanical modifications were implemented to increase the rotor’s natural frequencies, while enhancements to the cooling system included air-intake channels near the bearings and exhaust openings integrated into the stator frame.

The initial machine dimensions were determined using analytical calculations, after which the design was refined through finite element method (FEM) and conjugate heat transfer (CHT) simulations. Electromagnetic analyses were performed in Ansys Maxwell to estimate machine losses under converter-fed operation. Mechanical analyses, including modal analysis and structural strength assessment, were conducted using Ansys Mechanical. Furthermore, fluid flow and thermal performance were investigated in Ansys Fluent to optimize the cooling system design.

2.1.1. Electromagnetic Simulations

Electromagnetic analyses were performed using a finite element method (FEM) model of the electrical machine coupled with an equivalent power converter model. Accurate representation of pulse-width modulation (PWM) effects requires small simulation time steps, as the PWM carrier frequency typically exceeds 10 kHz. In this study, the simulation time step was selected to provide 40 calculation points per PWM carrier period, representing a compromise between computational accuracy and simulation time. Figure 1 and Figure 2 illustrate the electrical machine model and the associated power converter model, respectively. To reduce computational effort, a half-machine model was employed, utilizing periodic boundary conditions and a zero magnetic vector potential boundary condition at the outer edge of the stator. The simulated magnetic flux density reached approximately 0.9 T in the rotor yoke and shaft, 1.3 T in the rotor teeth, 1.3 T in the stator yoke, and 1.6 T in the stator teeth.

The coupled machine–converter model enables the evaluation of PWM excitation effects on machine losses. However, standard material models do not account for minor hysteresis loops in the B–H characteristic, which can reduce the accuracy of iron-loss predictions. Furthermore, manufacturing processes such as lamination stamping or laser cutting may degrade the magnetic properties of the electrical steel. To account for these effects, a correction factor of 1.4 was applied to the calculated core losses, based on previous experimental experience.

Additional iron losses are generated in the air-gap region due to current ripple in the armature winding. In the FEM simulations, iron losses were calculated using the Steinmetz equation implemented within the software:

$$W_{Fe}\left[{\displaystyle \frac{\mathrm{W}}{\mathrm{k}\mathrm{g}}}\right]=k_{h}f{B}^b+k_c{f}^2{B}^2+k_e{f}^{1.5}{B}^{1.5},$$

(1)

where $f$ is the electrical frequency in Hz and $B$ is magnetic flux density in T. Coefficients $k_h$, $k_c$ and $k_e$ are hysteresis, eddy current and excess loss coefficients, respectively. Coefficient $b$ is dependent on the given material and is typically in a range between 1.5 and 2.5. All those coefficients are determined using curve fitting techniques. The eddy current loss in the permanent magnets can be calculated using [32]:

$$W_{mag}\left[\mathrm{W}\right]={\sum }_n\left\{{\int }_{magnet}{\displaystyle \frac{{\left|{\mathbf{J}}_n\right|}^2}{2\sigma }} dv \right\},$$

(2)

where ${\mathbf{J}}_n$ is the density of the induced current inside the permanent magnets and $\sigma$ is the electrical conductivity of the permanent magnet material.

The simulated PWM line voltage and the corresponding phase current are shown in Figure 3, while the resulting loss-density distribution within the machine is presented in Figure 4. The results indicate that the highest loss density occurs in the region adjacent to the air gap, exceeding 3.5 W/cm³. The loss density in the stator yoke and stator teeth reaches approximately 0.2 W/cm³ and 0.9 W/cm³, respectively. Rotor iron-loss density is significantly lower than that observed in other machine components, remaining at only a few hundred W/m³. In contrast, the rotor bars exhibit a loss density of approximately 1.5 W/cm³, except in the region closest to the air gap, where higher values are observed.

2.1.2. Thermal Simulations

Conjugate heat transfer (CHT) analyses were performed using the finite volume method (FVM) implemented in Ansys Fluent. The CHT approach simultaneously solves heat transfer in both solid and fluid domains while enforcing continuity of temperature and heat flux across all solid–fluid interfaces. Within each solid subdomain, the steady-state energy balance is governed by the heat conduction equation with a distributed volumetric heat source, obtained from the electromagnetic simulations in the form of loss-density distributions:

$$\nabla ·\left({\mathbf{k}}_s\nabla T\right)+S_V=0,$$

(3)

where ${\mathbf{k}}_s$ is the thermal conductivity tensor of the solid, $T$ is the temperature field and $S_V$ [W/m³] is the local loss density. To account for the non-uniform distribution of losses, the stator iron was divided into stator tooth and stator yoke regions, reflecting the higher loss density typically observed in the teeth. Similarly, the rotor iron domain was subdivided into two regions to represent the elevated losses occurring in the layer adjacent to the air gap. Heat transfer within the fluid domain was modeled using the coupled steady-state Reynolds-averaged Navier–Stokes (RANS) equations and the energy equation:

$$\nabla ·\left({\rho }_f\mathbf{u}\right)=0,$$

(4)

$${\rho }_f\left(\mathbf{u}·\nabla \right)\mathbf{u}=-\nabla p+\nabla ·({\mu }_{eff}\nabla \mathit{u}),$$

(5)

$${\rho }_f{c}_{p,f}\left(\mathit{u}·\nabla \right)T=\nabla ·(k_{eff}\nabla T),$$

(6)

where $\mathbf{u}$ is the fluid velocity vector field, $p$ is pressure and ${\rho }_f$, ${\mu }_f$, $c_{p,f}$, $k_f$ are the fluid density, effective dynamic viscosity, specific heat capacity and effective thermal conductivity, respectively. The effective dynamic viscosity and thermal conductivity consist of molecular and turbulent contributions and turbulence is modeled using the k-ω SST turbulence model. At the solid–fluid interfaces $\mathsf{\Gamma }$, the thermal balance equations are coupled into a single system:

$${\left.T_s\right|}_{\mathsf{\Gamma }}={\left.T_f\right|}_{\mathsf{\Gamma }},$$

(7)

$$-{\mathbf{k}}_s{\left.{\displaystyle \frac{\partial T_s}{\partial n}}\right|}_{\mathsf{\Gamma }}=-k_{eff}{\left.{\displaystyle \frac{\partial T_f}{\partial n}}\right|}_{\mathsf{\Gamma }},$$

(8)

where $T_s$ and $T_f$ are the temperatures of the solid and fluid sides of the interface, respectively, and $n$ is the interface normal vector. Equation (7) ensures continuity of the temperature field, while Equation (8) states that no heat is generated, lost, or stored on the interface. These equations enable direct calculation of local wall heat fluxes and near-wall temperature gradients.

The machine was primarily cooled by a liquid-cooled water-jacket housing incorporating a spiral coolant flow path, while secondary cooling was provided by internal air circulation generated by blades integrated into the rotor end rings, as shown in Figure 5. Particular attention was paid to the thermal behavior of the bearings, as their operating temperature constituted a critical design constraint. The heat generated in the bearings due to friction, $P_B$, was calculated as follows:

$$P_B=M\omega$$

(9)

where $\omega$ is the angular velocity and $M$ is the total friction torque found using the SKF model of bearing friction [33]:

$$M=M_{rr}+M_{sl}+M_{seal}+M_{drag},$$

(10)

where $M_{rr}$, $M_{sl}$, $M_{seal}$ and $M_{drag}$ are rolling friction, sliding friction, integrated seal friction and drag loss torque, respectively. The bearing temperature rise with respect to the coolant can be modeled as

$${∆T}_B=P_B{R}_{B,th},$$

(11)

where $R_{B,th}$ is the equivalent thermal resistance in the thermal network between the bearing and the coolant. Minimizing this term is essential for limiting the bearing temperature rise.

Therefore, particular attention was given to the heat-transfer path between the end shields and the water-jacket housing, as well as to maintaining the shaft temperature below that of the rotor body. This was considered essential for ensuring acceptable bearing operating temperatures.

To achieve the desired temperature gradient in the bearing region, four axial air-intake channels were machined into each shaft end. These channels enable ambient air to enter the machine and directly cool the shaft ends and inner bearing rings. As the air flows through the machine, it absorbs heat from the rotor end rings and rotor core, subsequently passing over the end-windings before being discharged through ventilation openings in the housing.

To reduce computational requirements, the machine’s axial symmetry was utilized in the CHT simulations. Figure 5 shows the temperature contours on one half of the rotor together with the corresponding airflow streamlines. Figure 6 shows the temperature contours on the axial cross-section of the machine. While the end shields, stator, and housing were included in the numerical model, they are disabled in the figure in order to emphasize the rotor temperature field and airflow trajectories.

2.1.3. Mechanical Simulations

The mechanical analysis was carried out in several sequential stages. First, a detailed CAD model of the machine, shown in Figure 7, was developed, and the residual unbalance of the prototype motor was experimentally determined following the balancing process. Electromagnetic forces acting on the stator teeth were then calculated numerically and converted into a format compatible with the mechanical simulation model using internally developed python code. Subsequently, the CAD geometry was adapted for mechanical analysis, and a modal analysis of the rotor–stator assembly was performed to determine its natural frequencies and mode shapes.

The modal analysis results in Figure 8 show that there are two eigenfrequencies of the rotor on bearings: an axial vibration mode at 57 Hz (blue) and the first bending vibration mode at 248 Hz (green). Since this bending frequency would be resonantly excited by the first-order electromagnetic excitation (inclined red) at a rotational speed of 14,880 rpm, the test had to be limited to an operating speed of 13,000 rpm.

2.2. Higher-Speed Prototypes

Table 2. Main geometry data of the simulated induction and permanent magnet machines.

	Parameter	Value
BOTH	Stator outer diameter	200 mm
	Stator inner diameter	110 mm
	Stator slots	36
	Air gap	1 mm
	Axial length	160 mm
	Shaft inner diameter	25 mm
IM	Rotor slots	30
	Shaft outer diameter	50 mm
PM	Rotor banding thickness	3 mm
	Magnet thickness	5.5 mm
	Magnet arc	150°
	Magnet grade	N30EH
	Shaft outer diameter	55 mm

presents the main geometric parameters of the simulated permanent magnet and induction machines. Both machine topologies employ the same stator design. The armature winding is arranged in two parallel paths, with six conductors per slot, each conductor comprising fourteen strands of 0.85 mm diameter copper wire.

The induction machine rotor is based on a standard IEC 132/2.110 [30] lamination stack featuring 30 double-cage rotor slots, similar to the rotor used in the initial induction machine prototype. The permanent magnet machine employs N30EH permanent magnets, which are suitable for high-temperature operation and can withstand temperatures of up to 200 °C.

Machines supplied by power converters typically exhibit higher losses than those operating under purely sinusoidal excitation due to the presence of harmonic components [24,25,34]. For well-characterized materials, conventional machine topologies, and standard operating frequencies, sufficiently accurate loss predictions can often be obtained using sinusoidal simulations supplemented by appropriate correction factors to account for converter-induced effects.

The calculations presented in this study incorporated the knowledge gained from testing the initial prototype. This included correction factors accounting for PWM-related losses and the degradation of magnetic properties caused by the lamination manufacturing process, as well as detailed consideration of armature end-winding length, copper slot fill factor, and other practical design parameters affecting machine performance and loss estimation.

2.2.1. Induction Machine

An initial induction machine design was developed using standard laminations for both the stator and rotor cores. The winding configuration and axial length were subsequently adjusted to achieve the desired performance requirements. Building upon this baseline design, the stator slot geometry was optimized for the intended application, resulting in slightly deeper slots and wider teeth. In addition, the stator core material was upgraded from 0.5 mm thick M270-50A electrical steel to 0.2 mm thick NO20 laminations (both materials acquired by Feintool, Lyss, Switzerland) significantly reducing high-frequency iron losses.

The simulations were initially performed under sinusoidal voltage excitation, with core losses adjusted using appropriate correction factors. Subsequently, detailed simulations incorporating PWM excitation were carried out. The resulting machine model is shown in Figure 9. The calculated magnetic flux density values in the main machine components were approximately 1.5 T in the rotor yoke and shaft, 1.3 T in the rotor teeth, 1.4 T in the stator yoke, and 1.2 T in the stator teeth.

Structural analyses included the determination of rolling-bearing stiffness, the design of the spring characteristics required to maintain bearing preload, the assessment of contact-pressure retention in interference-fitted assemblies during operation, and the strength evaluation of the main structural components. Figure 10 shows the contact-loss safety results and the strength safety factors of main structural components. The average contact pressure between the rotor laminations and the shaft, resulting from the interference fit, was approximately 45 MPa under cold conditions. At an operating speed of 15,000 rpm and under thermal loading, this pressure decreased to 4 MPa, which remained sufficient to ensure reliable mechanical contact. The lowest calculated safety factor was observed in the aluminum rotor cage, with a value of 1.18. Further increases in assembly interference to maintain adequate contact pressure at rotational speeds above 15,000 rpm were not feasible due to the limited mechanical strength of the aluminum cage.

2.2.2. Permanent Magnet Machine

A rapid initial electromagnetic analysis was performed using a 2D transient finite element method (FEM) model in Ansys Maxwell. Correction factors were applied to account for both core material degradation caused by the manufacturing process and the additional losses associated with PWM excitation. The overall correction factor applied to the simulated iron losses was 1.9, based on recommendations from Ansys Motor-CAD tutorial literature, engineering experience, and measurement data obtained from previously tested machines.

Permanent magnet losses were multiplied by a factor of five to provide a conservative estimate. This scaling factor was chosen to account for the higher eddy-current losses typically observed in surface-mounted permanent magnets compared with magnets embedded within the rotor lamination stack, as well as the additional losses introduced by PWM excitation. Even with this deliberately conservative correction, the calculated permanent magnet losses remained relatively low, below 30 W.

The simulation results indicated that rotor losses were sufficiently low to eliminate the need for rotor water cooling, suggesting that a simpler air-cooled solution would be adequate. Consequently, the rotor was designed with 14 circular axial cooling channels, each having a diameter approximately equal to one-third of the rotor yoke thickness.

The introduction of these channels disrupted the magnetic flux paths within the rotor yoke and the permanent magnets, resulting in local increases in loss density and a slight reduction in electromagnetic performance. To minimize these adverse effects, the cooling channels were positioned beneath the junctions between adjacent permanent magnets, where the loss density is naturally highest, as shown in Figure 11.

To obtain more accurate loss predictions, an additional set of transient simulations was conducted using a full three-dimensional (3D) FEM model of the two-pole generator. Unlike the previous two-dimensional analyses, the 3D model enabled the calculation of axial currents in the permanent magnets and the shaft, thereby capturing additional loss mechanisms that have a significant influence on the overall loss distribution and machine efficiency. An example of the 3D model used in these simulations is shown in Figure 12.

When the machine topology and operating conditions are substantially modified, accurate loss estimation requires simulation of the actual converter output applied to the machine armature. This was achieved through a coupled analysis involving the electromagnetic FEM model and a multiphysics electrical circuit simulator. Following the recommendations presented in [20], the permanent magnets were segmented in both the axial and tangential directions and electrically insulated to limit eddy-current paths. Figure 13 illustrates the coupled simulation model.

The FEM component was configured as described previously, while the electrical circuit model consisted of a three-phase voltage-source inverter (VSI) controlled using a field-oriented control (FOC) strategy. The FOC implementation included proportional–integral (PI) controllers for the d-axis and q-axis currents, a space vector pulse-width modulation (SVPWM) module, and the Clarke and Park transformations together with their inverse transformations [35].

Table 3. Main data of the coupled simulation.

Parameter	Value
DC link voltage	750 V
Switching frequency	12.5 kHz
Peak current (1st harmonic)	180 A
Phase advance angle	17°

summarizes the key parameters used in the coupled electromagnetic–circuit simulation to achieve the desired machine operating point. Figure 14 shows the measured line current waveform together with its fundamental-frequency component. The waveform exhibits a certain degree of distortion resulting from the combination of a relatively low inverter switching frequency and the low inductance of the machine winding, which limits the attenuation of higher-order current harmonics.

The geometry of the internal air-cooling circuit included several key elements, namely the channels within the stator housing, the rotor-mounted fan, and the axial cooling channels in the rotor core. Certain parts of the airflow path were partially predetermined, such as the region between the potted end-windings and the end brackets. These components were analyzed using 3D CHT simulations performed in Ansys Fluent.

A key challenge in this design stage was defining the geometry and placement of the rotor-mounted fan. Determining the fan configuration first required establishing the position of the axial cooling channels in the rotor core. The radial location of these channels was constrained by both electromagnetic performance and mechanical integrity. Numerical analyses indicated that the magnetic flux disturbance is minimized when the channels are positioned closer to the outer surface of the rotor core, which in turn imposed geometric constraints on the fan design. The final concept consists of a backward-bladed centrifugal fan combined with a locknut that also functions as an axial fan. The centrifugal fan geometry was designed following established guidelines from the literature [36].

The cooling channels within the stator housing were designed to maintain turbulent airflow while maximizing the wetted surface area to improve heat transfer. Initial thermal evaluation was carried out using steady-state three-dimensional conjugate heat transfer simulations assuming losses corresponding to sinusoidal supply conditions. Attention was given to thermal contact resistances along the main heat transfer paths, especially at the stator–housing interface [37,38]. In addition, anisotropic thermal properties of the stator windings were included in the model [39].

3. Results and Discussion

3.1. Lower–Speed Prototype

Two machines were manufactured to enable experimental testing in a back-to-back configuration. Each unit was initially tested under no-load conditions to verify the key electrical and mechanical parameters. During this stage, the power converter settings were also validated. The machines were gradually accelerated during these tests, reaching a maximum speed of 17,000 rpm, as shown in Figure 15.

Following the no-load tests, the machines were subjected to load testing. Experiments were performed at multiple load levels, with each operating point maintained until thermal and electrical steady-state conditions were established. Throughout the testing campaign, a comprehensive set of electrical, mechanical, and thermal quantities was monitored for both machines. The measured quantities included three-phase voltages and currents, rotor speed, and vibration amplitudes at the drive end (DE) and non-drive end (NDE).

Temperature measurements were acquired at several critical locations, including the stator end-windings, stator housing, cooling-water inlet and outlet, and the DE and NDE bearings. Figure 16 illustrates the back-to-back test setup used for validation of the first-generation prototypes. In this configuration, the water-jacket housings of both machines were connected in series. While functional, this arrangement provided less effective and less uniform cooling than a parallel connection. Consequently, a parallel cooling arrangement was adopted for the testing of the second-generation prototypes.

The results shown in Figure 17 and Figure 18 were obtained after 2.5 h of continuous operation at 13,000 rpm and a phase voltage of 306.5 V (equivalent to a line-to-line voltage of 530.9 V), once thermal steady-state conditions had been reached. The machine operating in motoring mode absorbed an apparent power of 123.8 kVA and an active power of 101.0 kW. At this operating point, the temperature of the stator end-windings reached approximately 122 °C.

The second machine, operating in generator mode, delivered 110.5 kVA of apparent power and 86.9 kW of active power, while the stator end-winding temperature stabilized at approximately 112 °C. For both machines, the stator housing temperature remained below 54 °C, bearing temperatures were approximately 90 °C, and the peak vibration velocity measured on the end shields remained below 1.5 mm/s.

The maximum permissible bearing temperature constituted the primary limitation to any further increase in machine power output. A secondary limitation resulted from the experimental cooling arrangement, in which both machines were connected in series within the water-cooling loop. As a consequence, the cooling-water temperatures differed significantly between the two machines, with one unit operating at water inlet and outlet temperatures of 17.5 °C and 26.9 °C, respectively, while the other was supplied with water at 27.2 °C and discharged it at 34.5 °C.

Despite the good agreement in total loss magnitude, notable differences were observed in the distribution of losses among individual machine components. The measured RMS armature current, including harmonic components, was approximately 9% lower than predicted, resulting in armature copper losses approximately 19% below the simulated values. In addition, the measured higher-harmonic iron losses were lower than expected. Conversely, the measured slip exceeded the calculated value by approximately 19%, which increased rotor losses and reduced the machine power factor relative to the simulation results.

A comparison of the measured and calculated results is provided in

Table 4. Comparison between measured and simulated data.

	Measured	Simulated
Phase voltage [V]	306.5	305.7
Phase current [A]	119.5	130.3
Power factor [-]	0.82	0.86
Slip [%]	0.7509	0.6112
Shaft power [kW]	93.11	94.60
Total loss [kW]	7.89	7.75

. Mechanical losses were estimated at approximately 250 W due to bearing friction and 600 W due to aerodynamic ventilation effects. Stray-load losses were assumed to be 1.5% of the machine output power, corresponding to approximately 1.4 kW. By combining the measured electromagnetic losses of 5.5 kW with the estimated mechanical and stray-load losses, the total machine losses were calculated to be approximately 7.75 kW.

3.2. Higher–Speed Prototypes

Experimental measurements were conducted using a back-to-back test configuration, as illustrated in Figure 19 and Figure 20. The machines were mounted on a common steel support structure, providing a semi-rigid connection between the machines and the foundation. Each machine incorporates a water-cooled housing, dedicated bearing-cooling channels, and a hollow shaft for active rotor cooling.

The coolant circulates from the water tank (1) through the radiator (2), after which it passes through a coolant manifold (3) that distributes the flow to the stator housing, the drive-end (DE) bearing, the non-drive-end (NDE) bearing, and the hollow shaft. The heated coolant is subsequently returned to the water tank, completing the cooling circuit.

The bearings are lubricated using a pressurized oil–air mist system (4), visible on the left-hand side of Figure 20, which provides a continuous and controlled supply of lubricant during operation.

During testing, temperatures were monitored at critical locations, including the end-windings, stator slots, stator outer surface, bearings, and several points along the coolant flow path. In addition, radial vibration levels were measured at both the DE and NDE using accelerometers mounted on the machine housing.

Figure 21 shows the data acquisition system used during the experimental campaign. The system consisted of Dewesoft SIRIUS UNI, Dewesoft KRYPTON-TH-HS, Dewesoft KRYPTON-RTD-HS, and Dewesoft SIRIUS XHS measurement modules. Sampling frequencies of 200 kHz and 10 kHz were used for electrical measurements and vibration measurements, respectively.

Temperature measurements were obtained using Class 1 Cu–Constantan thermocouples and Class B PT100 resistance temperature detectors (RTDs) in accordance with IEC 60751. The tolerance of the Class B PT100 sensors is given by:

$$\pm (0.3+0.005t),$$

(12)

where $t$ is the measured temperature in degrees Celsius. The tolerance value of thermocouples class 1 is calculated as:

$$\pm 0.004t \mathrm{or} 0.5 °\mathrm{C}$$

(13)

depending on which value is greater, where $t$ denotes the measured temperature in degrees Celsius. Vibration measurements were performed using Brüel & Kjær type 4507 and 4508 accelerometers.

3.2.1. Induction Machine

The induction machine was simulated at three operating points. Corresponding performance metrics are summarized in

Table 5. Simulation results for sine wave excitation.

Simulation Output	15 krpm	20 krpm	25 krpm
RMS current [A]	121	121	121
Torque [Nm]	38.7	39.5	38.6
Armature copper loss [W]	1182	1182	1182
Rotor cage loss [W]	592	605	618
Stator yoke loss [W]	287	420	568
Stator teeth loss [W]	164	260	380
Rotor iron loss [W]	167	290	445
Shaft loss [W]	0.1	0.1	0.1
Mechanical loss [W]	210	342	528
Stray loss [W]	602	801	997

.

Because the structural analysis indicated that operation at 25,000 rpm would generate excessive mechanical stresses in the rotor, 15,000 rpm was selected as the nominal operating speed of the prototype.

During experimental testing, increased vibration levels were observed at 15,000 rpm due to excitation of a natural frequency of the test bench by second-order electromagnetic force harmonics. This test bench vibration mode shape is shown in Figure 22. Although the measured vibration levels remained within the permissible limits specified by IEC 60034-14, testing was conducted at 14,000 rpm to ensure fully stable operation and to avoid resonance-related effects.

Experimental testing was performed with a DC-link voltage of 600 V and an inverter switching frequency of 12 kHz. Stray-load losses were assumed to be equal to 1.5% of the machine output power at the investigated operating point.

Table 6. Measurement and simulation results at 14,000 rpm for an induction machine prototype.

Simulation Output	Simulated	Measurement
Phase voltage (1st harm.) [V]	169.7	169.2
Phase current (1st harm.) [A]	112.8	120.0
Power factor (1st harm.) [-]	0.92	0.88
Slip [%]	0.8486	0.9859
Shaft power [kW]	53.3	52.4
Total loss [kW]	2.90	2.97

compares the measured and simulated machine performance parameters.

Overall, the simulation results are in good agreement with the experimental data. Compared with the calculated values, the measured current and slip were approximately 6% and 16% higher, respectively. The higher slip increased the rotor losses and reduced the machine power factor; however, the resulting total losses remained close to the predicted values.

It should be emphasized that PWM-related iron losses were neglected in the presented simulations. Applying a correction factor of 1.35 to the calculated iron losses increases the estimated total losses to approximately 3.1 kW. This factor was derived from previous experimental investigations and engineering experience. Furthermore, studies reported in the literature [40,41] indicate that PWM excitation can increase machine losses by approximately 25%. Consequently, the selected correction factor appears justified, especially given the relatively high operating frequency of the machine and the lower number of switching events per electrical cycle.

At an operating speed of 14,000 rpm and an output power of 53.3 kW, the induction machine exhibited a thermal hotspot of approximately 107 °C in the end-winding region. The measured temperatures of the stator slots, stator outer surface, and bearings were 79 °C, 39 °C, and 40–45 °C, respectively.

Under these operating conditions, the machine demonstrated stable mechanical performance with low vibration levels. The measured radial vibration velocity was 0.38 mm/s at the drive end (DE) and 0.48 mm/s at the non-drive end (NDE).

3.2.2. Permanent Magnet Machine

Simulations of machine operation under converter supply revealed that the loss distribution within the active machine components differs considerably from that obtained under sinusoidal excitation. As summarized in

Table 7. Simulation results for sine and PWM excitation at 25,000 rpm.

Simulation Output	Sine	PWM
RMS current [A]	140	143
Torque [Nm]	44.9	45.9
Copper loss [W]	1585	1650
Stator yoke loss [W]	445.9	454.3
Stator teeth loss [W]	143.3	182.7
Rotor yoke loss [W]	0.03	3.4
Magnet loss [W]	26.9	146.5
Shaft loss [W]	0.4	671.9

, the stator yoke losses remain nearly unchanged, with a deviation of less than 2%. In contrast, losses in the stator teeth, rotor yoke, permanent magnets, and shaft increase significantly.

Owing to their proximity to the air gap, the permanent magnets are more exposed to higher-order harmonic magnetic fields. These harmonics can penetrate the solid magnet material, inducing eddy currents and causing additional losses. The simulations performed under converter-fed operation showed that permanent magnet losses increased by nearly 450% compared with sinusoidal operation. Similar behavior has been reported for interior permanent magnet synchronous machines (IPMSMs), where eddy-current losses were found to increase substantially when the machine was supplied by PWM excitation rather than by a sinusoidal voltage source [24,25,32,40,41,42].

A significant increase in shaft losses was also observed, primarily due to the pronounced eddy-current effects that occur in solid conductive materials. The machine pole number may further influence this phenomenon. In a two-pole machine, the magnetic flux path traverses the shaft diametrically, resulting in higher induced eddy currents and, consequently, greater losses. By contrast, machines with multiple pole pairs exhibit shorter and more distributed magnetic flux paths, which may reduce the magnitude of these currents. Nevertheless, the substantial increase in shaft losses requires further investigation, as the possibility of numerical or modeling inaccuracies cannot be completely excluded.

A comparison of the total stator losses indicates that PWM excitation increases stator losses by approximately 5% relative to sinusoidal operation. The rotor, however, is affected much more strongly, with total rotor losses increasing by nearly a factor of 30 under PWM supply conditions.

Figure 23 illustrates the machine losses (iron losses and eddy-current losses) as a function of PWM switching frequency. The results show that reducing the switching frequency increases the losses, particularly in the permanent magnets, rotor shaft, and rotor core.

An initial structural modal analysis of rotor concept was performed using SKF SimPro Spindle software version 4.11.0.0, in which the rotor was simplified, and the coupled stiffness matrix of the SKF bearings from SKF database was used, see Figure 24.

Subsequently, a more detailed FEM-based modal analysis in Figure 25 of the complete generator mounted on a rigid test bench was performed. The model included the end shields, housing, rotor–shaft interference fit, permanent magnets, retaining bandage, orthotropic material properties, axial bearing preload, and the effects of thermal expansion. The modal analysis was carried out using a statically pre-stressed rotor condition and preloaded bearings, thereby ensuring a realistic representation of the machine’s operating state.

The modal analysis showed that there are two eigenfrequencies of the rotor on bearings: an axial vibration mode at 205 Hz (SKF SPS) and 197 Hz (FEM). The SKF SPS predicted the first bending vibration mode to 625 Hz at 25,000 rpm, while the FEM model was predicted to be significantly lower (464 Hz). In practice, FEM was shown to have predicted this natural frequency reasonably well, since an increase in vibrations was observed during the trial speed test at rotational speeds above 25,000 rpm.

Figure 26 shows the strength and operational safety were assessed by static structural FEM analysis of the rotor assembly. The analysis considers assembly condition (interference fits, bandage pretension, axial bearing force) and the operating condition (rotational speed and temperature-induced deformations). Three operating conditions were analyzed: assembly condition, operating speed of 25,000 rpm and the overspeed of 30,000 rpm. Special attention is given to the detailed modelling of contact surfaces, including possible separation and friction effects.

The main evaluation criteria are the potential loss of contact at the interference-fitted components, stress levels and the resulting safety factors. There is sufficient average contact pressure at 30,000 rpm at all contact surfaces: 5.1 MPa between lamination stack/shaft, 9.5 MPa at magnets/carbon bandage and non-magnetic insets/carbon bandage. Sufficient strength safety is achieved with minimal safety factors 1.32 in carbon bandage and 1.75 in magnets.

During the conceptual design phase, an enclosed internal air-cooling system was analyzed as a potential cooling solution. Figure 27 illustrates the temperature distribution across a cross-section of the microturbine generator for losses corresponding to operation under sinusoidal excitation. Under these operating conditions, the bearings represent the most thermally critical components, reaching temperatures of approximately 100 °C. The maximum end-winding temperature is approximately 150 °C, while the maximum temperature of the permanent magnets remains considerably lower, at approximately 92 °C.

A second thermal analysis was performed using loss values corresponding to converter-fed operation. The resulting temperature distribution, shown in Figure 28, differs significantly from that obtained under sinusoidal excitation. Most notably, the maximum temperature of the drive-end (DE) bearing increases to approximately 182 °C, substantially exceeding its permissible operating limit. Furthermore, the permanent magnets reach a peak temperature of approximately 191 °C, posing a significant risk of partial demagnetization. This risk becomes particularly critical under fault conditions, such as short-circuit events, given that the predicted magnet temperature approaches the maximum allowable operating temperature of the selected EH-grade magnet material.

At this power level, the proposed internal air-cooling system was unable to provide sufficient rotor cooling, indicating that an alternative cooling solution was required. Consequently, a water-cooled (WC) hollow-shaft concept was investigated, and the resulting temperature distribution is presented in Figure 29. A summary of the maximum temperatures of the main machine components under both sinusoidal and converter-fed operating conditions is provided in

Table 8. Component maximum temperature in case of sine wave and power converter operation.

Component	Tmax, sine [°C]	Tmax, PWM [°C]	Tmax, PWM, WC [°C]
End Windings	150	163	149
Slot Windings	119	137	131
Stator Yoke	84	98	89
Stator Teeth	99	133	109
Rotor Yoke	89	211	76
Magnets	93	191	83
Shaft	87	223	59
Bearings	100	182	60

. The results demonstrated satisfactory thermal performance, leading to the selection of the water-cooled hollow-shaft concept for the prototype machine.

The water-cooled hollow-shaft design demonstrated significantly improved thermal performance in the permanent magnet machine, resulting in lower temperatures throughout the entire assembly. Most importantly, rotor water cooling eliminated the risk of permanent magnet demagnetization, maintaining the maximum magnet temperature at approximately 83 °C. Similarly, the maximum bearing temperature decreased from 182 °C to 60 °C, bringing it well within the permissible operating range. All simulations were performed assuming an inlet cooling-water temperature of 40 °C.

Initial experimental measurements of the permanent magnet machine were conducted at 14,000 rpm to enable a direct comparison with the induction machine at the same operating point. During testing, the DC-link voltage was increased to 800 V, while the switching frequency was maintained at 12 kHz. Stray-load losses were assumed to be 0.5% of the machine output power at this operating point. The measured and simulated performance parameters at 14,000 rpm are summarized in

Table 9. Measurement and simulation results at 14,000 rpm for a PM machine prototype.

Simulation Output	Sine	PWM	Measurement
Phase voltage (1st harm.) [V]	203.2	213.1	202.8
Phase current (1st harm.) [A]	116.5	128.9	121.8
Power factor (1st harm.) [-]	0.90	0.80	0.86
Shaft power [kW]	63.3	62.9	63.2
Total loss [kW]	2.01	2.34	2.49

.

Compared with the experimental results, the measured current was approximately 4.5% higher than the value predicted by the sinusoidal-excitation simulation. Conversely, the current predicted by the PWM simulation was approximately 6% higher than the measured value. The power factor predicted by both simulation approaches deviated from the experimental results: the PWM model underestimated the power factor, whereas the sinusoidal model overestimated it.

Although both simulation approaches underestimated the total machine losses, the PWM-based model showed better agreement with the experimental measurements, exhibiting a discrepancy of approximately 6%. Applying the previously adopted PWM-related iron-loss correction factor to the sinusoidal simulation results increases the calculated total losses to 2.23 kW. However, this correction does not account for the elevated eddy-current losses induced in the permanent magnets by PWM harmonics, which explains the remaining difference between the measured and calculated values.

Throughout this operating condition, the machine demonstrated stable mechanical performance, with RMS radial vibration amplitudes of 1.65 mm/s at the drive end (DE) and 0.49 mm/s at the non-drive end (NDE).

When operating at 14,000 rpm and delivering 63.2 kW of output power, the permanent magnet machine exhibited a thermal hotspot of approximately 87 °C in the end-winding region. The measured temperatures of the stator slots, stator outer surface, and bearings were 72 °C, 39 °C, and 35–40 °C, respectively.

An additional operating point was evaluated using the permanent magnet machine, achieving output powers exceeding 100 kW at 20,500 rpm. The corresponding measured and simulated results are summarized in

Table 10. Measurement and simulation results at 20,500 rpm for a PM machine prototype.

Simulation Output	Simulated	Measurement
Phase voltage (1st harm.) [V]	326.6	290.6
Phase current (1st harm.) [A]	133.2	129.8
Power factor (1st harm.) [-]	0.97	0.89
Shaft power [kW]	101.8	100.2
Total loss [kW]	3.31	3.05

. Some discrepancies were observed between the measured and simulated data, indicating that further verification and model validation are required.

Figure 30 presents the measured operating data, including temperatures, vibration levels, and electrical quantities. Throughout the test, the machine maintained relatively low operating temperatures and acceptable vibration levels, demonstrating stable operation at this elevated power and speed.

3.3. Comparison of Prototypes

Table 11. Comparison of machine prototypes.

Parameter	P1	P2-IM	P2-SPM
Total active mass [kg]	76.1	32.7	32.1
Stator outer diameter [mm]	240	200	200
Rotor outer diameter [mm]	133.4	108	102
Axial length [mm]	250	160	160
Operating speed [rpm]	13,000	14,000	14,000	20,500
Operating frequency [Hz]	216	233.33	233.33	341.67
Mechanical power [kW]	93.1	52.4	63.2	100.0
Current [A]	119.5	120	121.8	129.4
Efficiency [%]	92.19	94.64	96.21	97.04
Water inlet temperature [°C]	17.5	31	31.5	34.5
End-winding temperature [°C]	122	107	87.5	101
Stator slot temperature [°C]	-	79	72	83
Outer stator area temperature [°C]	42	39	39	44
Bearing max. temperature [°C]	90	45	38	48
Radial vibration at DE [mm/s]	0.60	0.38	1.65	4.21
Radial vibration at NDE [mm/s]	1.45	0.48	0.49	2.36

presents a comparison between the initial lower-speed prototype and the newly developed high-speed prototypes. The initial prototype exhibits significantly greater mass and lower efficiency than the newer designs. However, owing to its substantially higher torque capability, it achieves a higher output power.

In contrast, the high-speed prototypes operate at lower temperatures, particularly in the bearings, which were identified as the most thermally critical components. The output power of the new prototypes was intentionally limited during testing to maintain current amplitudes comparable to those of the initial prototype. As the machines share an identical stator design, including the winding configuration, the operating point at 14,000 rpm provides a valid basis for direct performance comparison.

4. Conclusions

This study presented the development process and experimental validation of high-speed electrical machines, progressing from a larger, lower-speed machine to more compact designs capable of operating at higher rotational speeds. Load testing of the initial induction machine prototype at the speed of 13,000 rpm, with power level of 93.1 kW and efficiency of 92.19%, showed good agreement with the numerical predictions. These results provided validation of the core-loss and PWM correction factors required for further analysis.

The next generation of machines was evaluated at a common operating speed of 14,000 rpm. At this operating point, the surface-mounted permanent magnet machine outperformed the induction machine, delivering 63.2 kW at an efficiency of 96.21%, compared with 52.4 kW and an efficiency of 94.64% for the induction machine. The evolution of the design reduced the active mass by more than 50%, from 76.1 kg to approximately 32 kg. However, mechanical limitations restricted testing of the induction machine to 14,000 rpm due to rotor stresses and resonance-related constraints. At this operating point, both prototypes exhibited low vibration levels, ensuring smooth and stable operation.

Measurements performed on the induction machine confirmed that the cooling system provided effective heat dissipation during operation at 14,000 rpm. The absolute temperatures and corresponding temperature rises (TRs) are summarized below. Bearing temperatures remained below 45 °C (TR = 14 °C), while the stator slots and outer stator surface stabilized at approximately 79 °C (TR = 48 °C) and 39 °C (TR = 7 °C), respectively. The highest recorded temperature occurred in the end-winding region, reaching 107 °C (TR = 76 °C), thereby demonstrating the effectiveness of the proposed cooling arrangement.

Measurements performed on the permanent magnet machine at 14,000 rpm and an output power of 63.2 kW demonstrated excellent thermal performance. Bearing temperatures remained below 38 °C (TR = 6.5 °C), while the stator slots and outer stator surface reached approximately 72 °C (TR = 40.5 °C) and 39 °C (TR = 7.5 °C), respectively. The maximum recorded temperature was observed in the end-winding region, reaching 87.5 °C (TR = 56 °C).

Additional measurements were conducted on the permanent magnet synchronous machine at 20,500 rpm and 100 kW output power, achieving an efficiency of 97.04%. Bearing temperatures remained below 48 °C (TR = 13.5 °C), while the stator slots and outer stator surface measured approximately 83 °C (TR = 48.5 °C) and 44 °C (TR = 9.5 °C), respectively. The highest recorded temperature again occurred in the end-winding region, reaching 101 °C (TR = 66.5 °C).

In conclusion, high-speed electrical machines require particular attention to rotor mechanical design to ensure stable operation, low vibration levels, and long-term reliability. The carbon-fiber retaining band applied to the surface-mounted permanent magnet rotor provided excellent mechanical integrity at elevated rotational speeds. The cooling system is relatively complex, comprising cooling circuits for the stator housing, both bearings, and the hollow shaft. Nevertheless, the hollow-shaft water-cooling concept proved robust and capable of reliable operation at high rotational speeds while delivering excellent thermal performance.

Despite these positive results, several aspects of the design were identified as requiring further improvement. The hollow shaft implemented for rotor cooling represents a structural weakness that limits the maximum achievable operating speed. In addition, the magnetic properties of the shaft material contribute to increased electromagnetic losses. The shaft material may also raise long-term maintenance concerns due to its susceptibility to corrosion. Furthermore, the presence of the internal cooling channel necessitates the use of a more powerful water pump and a more complex piping system.

Additional challenges are associated with permanent magnet rotor design. Under severe fault conditions, such as a sudden armature winding short circuit caused by an IGBT module failure in the power converter, the surface-mounted magnets could be exposed to temperatures and demagnetizing fields sufficient to cause partial demagnetization. Furthermore, the procurement of EH-grade permanent magnets may become challenging due to supply chain constraints and export restrictions affecting their availability.

Future work will focus on increasing the operating speed toward 30,000 rpm, enabling direct coupling between the electrical machine and the turbine while simplifying the cooling system and reducing effects of the above-mentioned risk points. Further design improvements will be guided by the results of ongoing experimental investigations.