Materials Applicable to an Axially-Laminated Synchronous Reluctance Machine Considering Mechanical and Electromagnetic Aspects

High-speed electric machines aim for compact, direct-driven elevated speed applications and highly efficient operation, especially when a gearbox can be avoided. The design of these types of machines is highly iterative, combining multiphysics optimization and leading to custom types of machines that fulfill the application-specific requirements. The Axially Laminated Synchronous Reluctance Machine (ALASynRM) with a solid rotor is one of the motor types that can be considered for high-speed applications. An axially laminated solid rotor structure combines magnetic and nonmagnetic layers rigidly bonded to each other by vacuum brazing, hot isostatic pressing, soldering, explosion welding, or even additive manufacturing. In this study, six nonmagnetic materials and nine magnetic materials are cross-compared. The results show clear differences in performance, efficiency, and physical properties of the rotor when made of different material combinations and can thereby suggest the best pairs when the application-specific performance criteria are known. The study is carried out on a 12 kW machine with a maximum speed of 24000 rpm.


I. INTRODUCTION
H IGH-SPEED electric machines are used in several ap- plications with various topologies, such as the Axially Laminated Synchronous Reluctance Motor (ALASynRM) [1], where a high rotation speed brings added value, e.g., in compressor, blower, or turbine applications in which a high efficiency is desired [2].High-speed electric machines can be implemented with various techniques.The surface velocity, i.e., the peripheral velocity of the rotor, can be used as an indicative parameter when considering feasible motor technologies.High-speed machines with a moderate surface velocity (i.e., below 150 m/s) can be implemented using Permanent Magnet (PM) topologies, such as Interior Permanent Magnet (IPM), or rotor Surface Permanent Magnet (SPM) versions.These can be realized with the traditional laminated rotor construction [3].For higher surface speeds, Induction Machines (IMs) with a solid rotor structure can be more feasible in practice [4].A high-speed IM can also be equipped with a slitted solid rotor to improve the electromagnetic performance in cases where magnetic steel is employed alone, without a cage winding, in the rotor construction, [5].A squirrel cage can be added to a solid-steel core to further improve the electromagnetic characteristics of the motor [6].However, the structure and material strength of the squirrel cage reduce the rotor strength and maximum speed of the rotor compared with the slitted solid rotor.Therefore, this study investigates whether the solid rotor could be replaced by an axially laminated synchronous reluctance rotor.
In high-speed machines, especially high-power machines, the rigidity and length of the rotor limit the speed and maximum achievable power, as the maximum diameter is limited by the stresses experienced, and the length of the electric machine is restricted by its dynamic response (rotor and stator dynamics) [7].An increased length reduces the rotor critical speeds and easily leads to mechanical resonance problems [8].Depending on the applied topology, the machine can be designed for subcritical operation, i.e., operating below the first bending frequency of the rotor, or supercritical operation, where the first bending frequency is passed.In supercritical applications, passing of the bending frequency without increasing the overall vibrations requires careful design, rotor balancing, and effective damping by means of, e.g., an active magnetic bearing system [9].
A promising alternative approach to achieving a high surface velocity and a high efficiency is the axially laminated anisotropic rotor shown, e.g., in [10].The axially laminated synchronous reluctance rotor can be implemented with various materials [1].Fundamentally, a pair of compatible magnetic and nonmagnetic steels is needed.This study evaluates different magnetic and nonmagnetic materials and their performance in a high-speed electric machine.The performance is a compromise of mechanical, electrical, thermal, and manufacturability properties of the materials and their availability.In the case of an ALASynRM rotor, from the mechanical perspective, a low material density, a high yield strength, an equal thermal expansion coefficient, and good manufacturability are desired material properties while the costs and availability should be acceptable.From the electromagnetic perspective, both the magnetic and nonmagnetic steels should have a high resistivity to reduce eddy current losses (or a very high conductivity to reduce the penetration depth of the eddy currents and thereby also losses), and the magnetic steel should have a high magnetic permeability and a high saturation flux density to increase the magnetic anisotropy of the rotor.
In an ALASynRM rotor, the losses are concentrated on the rotor surface, because a significant part of the losses are highfrequency harmonic losses.From a thermal viewpoint, high thermal conductivity is desired for both materials to maintain a balanced temperature in the rotor.A high thermal conductivity enables having a low-temperature gradient within the rotor.It thereby reduces the risk of shaft bending as a result of thermal stresses in the nonhomogeneous rotor.
From the viewpoint of manufacturability, it is desired that both materials are well available, easily machinable to required tolerances, and feasible to form a metallic contact between the material layers to ensure a rigid and homogeneous structure.
The main research target presented in this article, extending the authors' research in [1], is to investigate different materials (currently applied in different high-speed electric machines) and their combinations in an ALASynRM rotor and to highlight the most promising design variants.Compared to the previous study, the investigation is extended with a simulated and experimental mechanical analysis of a vacuum-brazed manufactured Inconel 600 -S355MC rotor, i.e., a stress and experimental modal analysis to verify the connection between the steel parts and the difference in the thermal expansion coefficient.In addition, measurements of the phase inductance, torque, and torque ripple are carried out in order to verify the simulation results.Further, because the materials presented in the article are often applied in other high-speed electrical machines, this article can be a source of detailed characteristics of these materials needed for reliable machine simulation.In the study, the performance of a highspeed, solid-rotor, synchronous reluctance motor is investigated and compared when using possible materials in the magnetic and nonmagnetic layers.The motor used in the comparison has a rated power of 12 kW at a rated speed of 24000 rpm.A 2D transient electromagnetic Finite Element (FE) analysis is used in the computation of the electromagnetic performance.The following aspects are taken into account: torque, torque ripple, efficiency, power factor, stator core losses, and rotor eddy current losses.
The article is organized as follows: materials typically used in different high-speed motor typologies are presented in Section II with the focus on the physical properties of the materials.Further, the applicability of these materials to the ALASynRM is discussed.Section III discusses the mechanical durability of the solution comparing FE analyses and experimental results.The method for the comparison of the machine variants using different materials in rotor nonmagnetic and magnetic layers is evaluated and shown in Section IV; for the model verification, additional experimental tests are carried out on the manufactured motor.Then, the results and a comparison of the simulations are shown in Section V. Finally, conclusions are summarized in Section VI.

II. MATERIALS FOR A HIGH-SPEED ELECTRICAL MOTOR
Selection of suitable materials for a high-speed electrical motor strongly depends on the topology of the motor; a considerable amount of literature has been published on the design of high-speed IMs [7], [10], [11], [12], PM motors [13], [14], [15], [16], [17], [18], and Synchronous Reluctance Motors (SynRMs) [10], [19], [20], [21], [22], [23], [24], presenting different combinations of the materials applied.Tables I and II show the mechanical, thermal, and electrical properties of the studied magnetic and nonmagnetic materials, respectively.Terzic et al. [11] compared several materials for a dual-stator high-speed drag cup induction motor.The stators were made from standard electrical steel, the windings used copper Litz wire in order to reduce the skin effect, and for the rotor cup, three different materials were proposed: Cu 3 -Mg (brass), Al 7075 T6 (aluminum alloy), and Be-Cu (beryllium copper).Abramenko et al. [10] analyzed a solid-rotor induction motor composed of the commercial magnetic steel S355MC core equipped with copper end rings to reduce the rotor equivalent resistance and to increase the overall performance.Barta et al. [12] compared different materials both for a solid rotor and a laminated one, but it was concluded that to reach a very high peripheral speed it is not possible to use a laminated rotor.For the solid rotor, they also proposed to use the Glidcop or beryllium-copper alloys, which have a higher mechanical strength compared with pure copper.For the magnetic materials, the commonly available grades of 41CrAlMo7, 41CrMo4, and S355MC steels were compared, and for more demanding applications the AerMet and maraging steels can be employed.These steels were originally developed for military aircraft applications.
In high-speed Permanent-Magnet (PM) motors, the trend shown in [13], [14], [15], [16], [17], [18] is to use a 2-pole rotor with a sleeve to maintain the magnet in place at high speeds.The typical magnet type used for high-speed motors is Sm 2 Co 17 because of its capability to operate at elevated temperatures (above 150 • C), while for the sleeve, four different materials are proposed: Inconel 718, carbon fiber, austenitic steel, and a titanium alloy.
On the other hand, in the literature, several topologies for the SynRMs have been presented: starting from the use of a laminated rotor core (in which the peripheral speed is below 150 m/s) optimized solution for minimizing the impact of the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE I MAGNETIC MATERIALS FOCUSED IN THE STUDY TABLE II NONMAGNETIC MATERIALS FOCUSED IN THE STUDY
inner ribs [19] or resin-aided ribless solutions [20] (peripheral speed of 50 m/s), [21] (peripheral speed of 125 m/s) to guarantee the mechanical integrity without affecting the electromagnetic performance.Another possible solution to obtain a ribless structure is adopting a dual phase material by using magnetic and nonmagnetic layers in the rotor [22] (peripheral speed of 100 m/s); with all these solutions, it is not possible to reach ultrahigh speeds (higher than 150 m/s).In order to reach higher peripheral speeds, solid-rotor solutions have to be used.Ikäheimo et al. [23] proposed a new concept for the solid rotor motor.Their design is composed of a round iron rod array held together with a casting of Cu-Al alloy similar to Hidruax 1.This material was chosen because of its availability and structural properties.Another innovative concept for the solid-rotor synchronous reluctance machine is shown in [10] and [24] and consists of metallic bonds between the nonmagnetic and ferromagnetic layers.The structure is similar to the axially laminated machine but uses thicker layers.In this way, it is possible to obtain a very high value of saliency ratio (higher than 10) but with a lower efficiency, because this solution presents higher rotor losses as a result of air-gap space harmonics and the low electrical resistance of the rotor.It, however, presents good values for the power factor.
This work focuses on possible combinations of materials that can be used for a high-speed solid-rotor axially-laminated synchronous reluctance motor (and other motor types) that would be suitable for their mechanical (concerning a high-speed application), electrical, and magnetic properties.For the nonmagnetic layer, the following materials were chosen and compared: AISI 304, AISI 316, Creusabro, Inconel 600, Inconel 718, and titanium grade 5; while for the magnetic layers, AISI 1010, AISI 1018, AISI 1020, AISI 430, 4CrMn16-4 8302 (Imacro M), 34CrNiMo6, S355MC, X20Cr13 and 40CrMoV5-1 were

III. MODELLING AND SIMULATION OF ALASYNRM
Fig. 3 depicts the geometry used to analyze the behavior of the ALASynRM rotor with the material combination S355MC (material number 1.0976) for the magnetic material and Inconel 600 (2.4816) for the nonmagnetic material.The manufactured prototype was used to verify the mechanical and electrical simulations.The analytical and finite element (FE) analyses were performed with the material parameters given in Tables I and II.The laminate layer thicknesses for the rotor were selected based Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.on the availability of the materials.For ease of manufacturing, a thicker S355MC (1.0976) (6.00 mm) magnetic layer was chosen for the middle layer of the rotor.All other laminate layers had a thickness of 3.00 mm.The laminated structure was manufactured by joining the laminates by vacuum brazing.The rotor mass was measured with a platform scale (Kern & Sohn GmbH ITB35KIP, Germany), and the mass of the manufactured rotor was 7.998 kg.The 3D model of the rotor had a mass of 7.896 kg with the given material parameters and geometry.

A. Mechanical Analysis
The FE models for the mechanical and modal analyses were constructed in ANSYS Workbench 2021 R2 based on the geometry shown in Fig. 3.The FE analyses were performed to study the mechanical behavior of the structure, i.e., stresses and deformations of the rotor in the nominal operating conditions; a modal analysis was also performed to study the natural frequencies of the rotor.The mesh density of the FE models was optimized to have at least two quadratic element layers in each laminate layer.Table III gives the mesh details for both analyses.In the mechanical analyses, the rotor was subject to a rotational velocity of 24 000 rpm and an even temperature of 150 • C, while the zero strain temperature was set to 22 • C. The mechanical analysis was completed with two load cases: Load case I with an elevated temperature and a rotational load and Load case II with only an elevated temperature.A free-free modal analysis was conducted, i.e., no loads and boundary conditions were applied.All laminated layers were assumed to have a homogeneous bonding between the laminates, and therefore, a fixed constraint was applied between the layers.

B. Electromagnetic Analysis
To carry out the simulations, a commercial finite element software, Maxwell2D within Ansys Electronic Desktop, was used as presented and discussed in [1].
The stator windings of the machine have short-pitching to reduce the harmonic fields in the air gap and, thereby, losses in the rotor.More detailed information about the machine geometry can be found in [10].The rotor has one central layer made of magnetic material with 6.0 mm thickness and 16 nonmagnetic and 14 magnetic layers of 3 mm thickness, bonded by vacuum brazing with a copper layer of 0.1 mm.The nominal speed of the motor is 24 000 rpm.The diameter of the rotor active part is 98.5 mm (peripheral velocity 124 m/s), and the nominal power is 12 kW.The simulations consider the stator winding delta connection with a sinusoidal line current supply.
The delta connection leads to a third harmonic component and its multiples in the winding current even though the line current is sinusoidal.This phenomenon can slightly increase the machine losses.This connection is necessary in order to avoid an increase in the supply voltage.The simulation step size was selected as 6.25 µs, 1/400 of the value of the fundamental period, which is 2.5 ms, considering a base speed of 24000 rpm.The selected time step allows to analyze the effects of the high harmonic losses in the stator and the rotor.The analyses show that the rotor magnetic layers are not saturated, and they operate with a level of flux density close to the knee of the B-H curve in order to maximize the torque/current ratio guaranteeing a very high saliency ratio [1].The simulations are carried out with the adjusted phase current value to reach the same output torque of 4.77 Nm with a current angle control of 45 • for every combination.This simulation is repeated for all combinations of the material in order to verify the impact of the modification of the material on the performance and to find out which are the most suitable materials for the ALASynRM rotor.
Several combinations of magnetic and nonmagnetic materials in an AlASynRM and the corresponding motor performance were evaluated by transient electromagnetic analysis (shown in the next Section).It also evaluates the rotor losses that are produced by the spatial harmonics in the machine.To obtain more reliable results and take into account the end effect, 3D Finite Element Analysis (FEA) should be used, but the high computational time required by these kinds of simulations makes it nonfeasible for the comparison of several material combinations.With 2D FE calculations, the fundamental differences can be assessed.To obtain reliable results in a reasonable time for a conceptual design selection, it is possible to use 2D finite element analysis and assume that all the rotor layers are connected to each other with a null resistance.This consideration might lead to slightly higher computed losses while keeping a safety margin in the efficiency results [10].This approach is suitable for the scope of this work because only varying the material is investigated, and possible errors caused by neglecting the end effect will be present in all the simulated cases, thus allowing a fair comparative study.The eddy current losses are concentrated on the rotor surface because they are mostly generated by the higher-order air-gap flux harmonics.These losses have been considered in the following efficiency computation, and their distribution is presented in Fig. 4.

IV. EXPERIMENTAL RESULTS
Experimental tests are carried out to verify the mechanical and electromagnetic models.The ALaSynRM high-speed machine rotor manufacturing process induces changes in materials' microstructure due to the high temperature joining method.Therefore, experimental verification is needed to understand if degradation of material properties compromises the analyses and results.For this reason, both mechanical and electromagnetic test setups are realized for model verification.From a mechanical point of view, the rotor dimension under different thermal conditions (temperature increase up to 150 • C) is evaluated to verify the equivalent thermal expansion in both directions (according to the d-and q-axis).Moreover, an experimental modal analysis is carried out; the rotor is suspended by flexible ropes to have a free-free boundary condition to investigate also the rotor's equivalent stiffness in both directions.By this, the structure integrity can be verified before full-speed operation.Because it was not possible to run the motor with commercial converters, the experimental verification of the electromagnetic model is made with the inductance profile, torque ripple, and average torque measurements at static conditions.All these parameters allow to verify the flux harmonics in the rotor (associated with the eddy current losses) and the main variables such as axes inductances and output torque.

A. Mechanical Results
The temperature of the S355MC (1.0976)-Inconel 600 (2.4816) rotor was increased with a heating rate of 32.5 • C/h up to a temperature of 150 • C. Additionally, as the rotor reached the target temperature, the rotor was kept in the heat treatment oven for one hour to ensure thorough heating of the rotor and to avoid a decrease in the rotor temperature during the diameter measuring.The increase in diameters was measured perpendicular (⊥) to the laminate thickness direction and parallel (||) to the laminates (see Fig. 3) with a digital micrometer (Mitutoyo 293-524-30, Japan) in three different locations of the rotor active section.Each diameter was measured three times to minimize measurement errors.The rotor temperature was observed with thermocouples during the whole experiment.The thermal expansion of the S355MC (1.0976)-Inconel 600 (2.4816) rotor active section with a nominal diameter of 98.5 mm can be analytically analyzed as follows.Because the rotor construction has an almost equal distribution of magnetic and nonmagnetic layers, the average thermal expansion for both materials represents the total thermal expansion of the rotor diameter.A theoretical calculation suggests that if the rotor temperature is increased by 128 • C, the rotor expands 0.141 mm when calculating the average thermal expansion.
In the Experimental Modal Analysis (EMA) [25], the rotor is suspended by flexible ropes corresponding to free-free boundary conditions.The rotor is excited by an automatic hammer (Alpha Solution AS-1220), and the vibration response is measured with a scanning laser doppler vibrometer (Polytec PSV-500).Table IV provides the FE analysis results for both the mechanical analysis and the modal analysis of the S355MC (1.0976)-Inconel 600 (2.4816) rotor.Table IV also shows experimental modal analysis results.Results of the study on the rotor dimensions under thermal conditions are given in Table V.
The 1st and 2nd bending modes in the FE modal analysis of the S355MC (1.0976)-Inconel 600 (2.4816) rotor do not show  any major differences either in the perpendicular (⊥) direction or in the parallel (||) direction.The experimental modal analysis results are in line with the FE analysis results for the first bending mode (Fig. 6(c)), but the experimental modal analysis shows an orientation-dependent change in the 2nd bending mode (Fig. 6(d)) frequencies.Possible causes for this might be different material parameters in the real materials compared with the material parameters used in the FE model.A sensitivity analysis for the sensitivity of the structure to changes in Young's modulus was conducted to study this effect.The results suggest a difference in natural frequencies in different orientations if the materials have much different Young's moduli.Further, the joint stiffness may have an effect on the natural frequency of the real rotor if the vacuum-brazed joint is not equally formed and bonded.The mechanical FE analysis revealed that in Load case I the maximum principal stress occurs in the middle of the active part of the rotor on the first nonmagnetic layer (Fig. 6(a)).The maximum principal stress is less than the material yield limits given in Tables I and II and the measured ones in [26].This is the most critical condition for the machine in which both thermal and rotational stresses reach maximal values.Despite this, the maximum stress inside the rotor is far from its theoretical limit, with a safety factor of 4 considering the material's yield strength and 7 considering the tensile strength.When no rotational load is considered (Load case II), the maximum principal stress occurs on the same layer but at the end of the rotor (Fig. 6(b)).The thermal expansion of the rotor diameter corresponds to the analytical estimation provided earlier.
Measurement results of the rotor diameters at elevated temperatures are shown in Table V.The experimental results show a slightly higher thermal expansion of the rotor diameter as opposed to the analytical or FE analysis estimations.However, the measurements suggest that the rotor diameter expands approximately the same amount in both directions (||-dir.and ⊥-dir.).No difference greater than the measurement accuracy could be noticed in the experimental measurements.

B. Electromagnetic Results
Because ALASynRM rotors are electrically well-conducting, the typical self-commissioning procedures of the commercial inverters for parameter estimation are not possible, making it necessary to adopt custom solutions.The standard procedures provide the supply of an alternating current, which causes an alternating flux in the air gap and the rotor core.This causes eddy currents in the rotors with a consequent modification (in particular, reduction) of the flux inside the machine and of the estimated inductance.The error in the inductance estimation introduces a mismatch between the suitable coefficients for the current PI regulator, which can lead to an unstable control.Another problem for the full load test of this machine is the low switching frequencies of present-day commercial IGBT converters, typically lower than 10 kHz which can lead to a high current ripple because of the very low q-axis inductance of the motor.Because of that a full test of the machine is planned to verify the performance of this kind of machine at the rated load and speed, and a custom converter with SiC power elements is under preparation to run the machine (with switching frequency above 50 kHz) to avoid large ripples in the supply current.For this reason, to verify the simulation results, the inductance measurement method described and presented in [27] was adopted.The method exploits the mutual inductance between each phase; because of the nonconventional winding supply of two phases, it is possible to produce a flux in the same direction as the third one, in which it is possible to measure it.The technique provides a quasi-static supply for this evaluation to minimize the effects of rotor eddy currents.It is possible to repeat the procedure for different rotor positions to obtain the behavior of the phase inductance and its harmonic spectrum.Thus, it is also possible to estimate the torque behavior of the machine and compare it with the experimental one.In this case, the torque was evaluated in static conditions by supplying the machine with three DC power supplies, one for each phase, generating a current linkage in the desired directions as a function of rotor position.By averaging this value, it is possible to evaluate the mean torque of the motor.These tests are carried out considering a star connection (the sum of the currents of the DC power supplies is zero), while the machine is designed for a delta connection, which leads to the introduction of the third and its multiple harmonics; therefore, the results of the torque ripple could be quite different with the simulated one but not the mean one.The combination S355MC/Inconel600 was tested for inductance and torque measurements.The results of the inductance measurements are shown in Figs.7 and 8.The comparison clearly shows a good match between the experimental and simulated results, thus Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.validating the adopted finite element model.The THD of the inductance is computed referring to the 2nd harmonic (the main one); therefore, only the higher-order harmonics are used for its computation.At the rated current, in the simulations the average value of the torque is equal to 4.832 Nm, and the peak-to-peak value is 0.99 Nm, while the experimental results show values equal to 4.885 Nm and 1.264 Nm.Referring to the mean value, the difference is small (less than 1%), but when referred to the peak-to-peak value, the difference is higher (around 20%).This can be justified considering that the torque ripple is more sensitive to the manufacturing tolerances in the stator and layer thickness.Other possible reasons for these differences should be investigated related to the deviation of magnetic properties due to heat and mechanical treatments, end winding effects, and measurement tolerances.The end-coil leakage inductance is not considered in FEM simulations and its value can be associated with the difference shown in the q-axis inductance value between experimental tests and simulations.In order to have a good approximation of the end-coil leakage inductance, an additional test, removing the rotor, is made to evaluate the difference in the experimental results and simulations.This difference can be fully associated with end-winding effects.Without a rotor, the magnetic reluctance is very high and the stator is far from the saturation; because its permeability is much higher than the one of the air it allows to neglect possible deviation in magnetic materials properties.Therefore, the results in terms of inductance should be the same.From this difference, it is possible to evaluate the end-coil inductance and the new value for the saliency ratio.Without the rotor, the measured inductance is 0.2610 mH, while the simulated one is 0.1313 mH.Adding this term to the inductance profile, there is a reduction of the error between simulation and experimental results, especially in the q-axis.These comparisons verify the results obtained by the simulations.From the torque results, it was possible to verify the model from a macroscopic point of view (the mean value of the inductance is correctly simulated), while from the inductance profile, it is possible to verify the model in terms of flux harmonics and high-frequency losses.Because the rotor is made of solid elements, the main contributor to the losses are the eddy current ones which depend on the material resistivity and the flux harmonics.Differently by the magnetic properties of the materials, which can be strongly impacted by the manufacturing, the resistivity of the material is typically not affected.Thanks to the good agreement of these two results, it is possible to consider good for comparison also the efficiency and the power factor computed with simulations.

V. COMPARISON OF THE SIMULATION RESULTS
Table VI shows the comparison results for different combinations of nonmagnetic and magnetic materials in terms of efficiency.
The materials that show the highest efficiency are the ones with the highest magnetic permeability; this is due to the high achievable average torque with these materials (Table VII).The results of the efficiency is reported as graphs in Fig. 9 in order to better understand the comparison between the different material combinations.
Comparing materials with similar values of permeability (AISI 1010, AISI 1018, AISI 1020, and S355MC), the difference in the efficiency is mainly due to the value of electrical resistivity.The S355MC material is the one with the highest electrical resistivity, and it shows the highest efficiency.If 40CrMoV5-1 is considered, despite its lower permeability compared with the other materials, because of its very high resistivity (54.3 µΩcm vs 20.0 µΩcm of the S355MC), it shows the highest efficiency, which is due to a significant reduction in the rotor eddy current losses.The effect of the nonmagnetic material is a variation in the rotor eddy current losses as a function of its electrical resistivity.The effects are similar to various magnetic materials.The highest values of efficiency are reached with the materials with the highest electrical resistivity (Inconel 600, Inconel 718, or Titanium (Grade 5)).Titanium has also the advantage of having a lower density, and thus, it can reduce rotor inertia and mechanical stress in the rotor.The peak-to-peak torque, shown in Table VIII, mainly depends on the value of the average torque, and the torque ripple of the machine (the ratio between the peak-to-peak torque and the average one) is slightly dependent on the combination of different materials, the maximum variation being 5%.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The results in terms of power factor when using different combinations of materials are given in Table IX, which shows that the power factor mainly depends on the magnetic material, whereas changing the nonmagnetic material has a negligible effect.The best material maximizing the power factor is, again, the one with the highest permeability (AISI 1020 or S355MC).The same effects are shown for the values of average torque and peak-to-peak torque, shown in Tables VII and VIII.All of these comparisons are made using the same value of input currents, but according to the material curve, also other considerations are possible.Rotors that have S355MC and AISI 1020 as the magnetic steel show a similar electromagnetic performance (power factor and average torque).A comparison of the BH curves of the materials indicates that AISI 1020 can reach a higher value of magnetic flux, resulting in a better overloading performance.This is because it guarantees a higher magnetic permeability, a higher d-axis inductance value, and a higher saliency ratio when a higher current (and flux inside the machine) is required to increase the torque capability.Because all the materials show similar values in terms of power factor and due to the voltage limitation, if a higher speed has to be reached without modifications in the stator and the winding arrangement (for mass production issues), a low-permeability material provides an opportunity to reach a higher speed while maintaining a similar level of power compared with the other solution.For example, considering the IMACRO M steel, from the electromagnetic point of view, it is possible to reach a speed of 33000 rpm with similar values of power compared with S355MC or AISI 1020.With a high permeability, it is possible to reach that speed, but operating in the flux weakening region with a higher current control angle.This is possible but introduces a lot of problems for this kind of machine as reported in [28]; when a higher current angle control is applied, the high-order flux density harmonics will increase, and with them also the eddy current losses, the stator losses, and the torque ripple.Of course, field weakening operation with higher permeability material can be avoided if the motor geometry is redesigned (e.g.air gap is increased).
Another important aspect that should be considered in the choice of the material is the mechanical integrity of the structure at a high speed and considering the possible temperature variations.This kind of rotor has two different materials bonded together.They are affected by the losses inside the rotor and the thermal heat exchange from the stator.This increases the temperature of these materials, which typically have a different thermal coefficient of linear expansion.This produces additional stress in the rotor, which may cause its bending, bowing, and eventually breaking.For this reason, in addition to the electromagnetic aspects of the materials, the choice of their combination should cover these aspects, as discussed in the previous section.
Titanium as a nonmagnetic material shows the highest electrical resistivity, which leads to the highest performance of the material with a low value of density.It cannot, however, be combined with the magnetic materials analyzed here because it has a very low thermal expansion coefficient compared with magnetic materials.The combinations that show similar values of thermal coefficient of linear expansion are Inconel 718 (12.8 µm/(m • C)) with AISI 1010 (12.2 µm/(m • C)), IMACRO M (12.0 µm/(m • C)), MoCN315 (12.0 µm/(m • C)), S335 (12.0 µm/(m • C)), and 40CrMoV5-1 (12.3 µm/(m • C)).Between these materials, the one that shows the highest torque is S335, while the one that shows the best efficiency is 40CrMoV5-1.These are the two most suitable candidates for the combination with Inconel 718.40CrMoV5-1 also shows higher mechanical properties with a tensile strength of around 2000 MPa, but this material would be too expensive for some applications compared with the structural steel S355MC; therefore, the choice compromise between these two depends on the maximum strength required by the motor, the maximum torque, and the cost.Further, the bonding method for each material pair must be carefully studied to select the most suitable one for each material combination.In this study, S335MC-Inconel 600 was bonded successfully by vacuum brazing.However, previous studies have shown that vacuum brazing of, e.g., Inconel 718 is not possible with the copper-based braze material [24], but with a suitable brazing material it is possible to vacuum braze Inconel 718 [29].
The FE modal analysis results given in Table IV show that the resulting structure has isotropic stiffness, i.e., the modulus of elasticity is not orientation dependent.However, the EMA showed a small difference between the different orientations of the rotor.This suggests and verifies that the joint between the metal sheets of the vacuum-brazed rotor is formed well.The simulated results for modal analysis are within 0.2-1.6%accuracy to the measured one thereby representing the real case with good accuracy.
The thermal expansion simulation and measurements shown in Tables IV and V suggest that in the operating condition, the rotor is expanding evenly, and thus, bowing of the rotor should not be expected.Moreover, according to the FE analysis, at the nominal operating point, the stresses do not exceed the yield limits of the selected material pair.Further theoretical analyses suggest that the maximum rotational speed of this particular rotor is 42 000 rpm, which equals approximately a 214 m/s rotor surface speed with a safety factor of 1.5 to yield the limit of Inconel 600.

VI. CONCLUSION
In the study, nine magnetic plates of steel and five nonmagnetic materials and their suitability for ALASynRM high-speed electric machines were investigated with 2D electromagnetic FEM.In the comparison, the power factor, efficiency, peak-topeak torque, and average torque were evaluated in addition to the electromagnetic properties, and also the mechanical and thermal properties were considered.The study shows that the individual performance criteria are strongly correlated, and the final selection of the most suitable pair of materials is highly applicationspecific, i.e., which compromise leads to the best performance.The best solution in terms of efficiency, maximum torque per ampere, and torque density is the adoption of S355MC as the magnetic material because of its high magnetic permeability and high saturation level.The selection of the nonmagnetic material needs some additional consideration.From an economic point of view, titanium presents a higher price per mass compared with Inconel 718, but considering its lower density, the total cost for rotor production is the same.However, there has been a recent increase in the Ni price, which can lead to different considerations.Because the electromagnetic performance of Inconel 600 (with a reduced amount of Ni compared with Inconel 718) is still good compared with the other materials, it could be a valid alternative in the rotor production, and it was selected as a case study for this analysis.The adoption of titanium allows a higher efficiency because of its higher electrical resistivity, and a higher torque density because of its lower density.The limit of this material is the thermal coefficient of linear expansion, which is quite different from that of S335MC.The selection of materials could also depend on stator shape, air gap length, and layer thickness because they can modify the rotor harmonics, and the losses in the rotor could increase or decrease, affecting the efficiency of the analyzed combinations.However, the presented analyses lead to evaluating the best material combination in terms of performance.Also, modifying the stator structure, the solution which shows the best efficiency remains the same.Therefore, if the motor cost of the solution is included in the optimization process, the best material combination, which adopts expensive materials, could have a low value of efficiency increase which does not justify the cost increase compared to the other solutions.The best compromise, which includes economic, performance, and manufacturability aspects, is the adoption of Inconel 600, because it has a notably higher performance compared with 40CrMoV5-1 with a reduced price.With this combination (Inconel 600/S335MC), an experimental campaign verifies the analytical results.The manufacturing process of this machine is not ordinary and the comparison in terms of cost with the traditional SynRM and PM motors should be made in terms of active materials.The solution that adopts S355MC as magnetic material and Inconel 600 as a nonmagnetic one (considering also the processing waste) is around $40. Considering the AISI 316 as nonmagnetic material, the price is around $13, comparable to the ones of traditional SynRM.Regarding the PM motors, depending on the country in which the motor is manufactured, the cost of the rotor's raw materials could be in the range of $55-$85.The stator is made with standard manufacturing, and for this application, it has been used the same as a commercial induction motor in terms of shape and winding; therefore, the price of this element is comparable with the other motor types.

Fig. 1 .
Fig. 1.B-H curves of the magnetic materials with field strengths from 0 to 5000 A/m.

Fig. 2 .
Fig. 2. B-H curves of the magnetic materials with field strengths from 5000 to 50000 A/m.

Fig. 4 .
Fig. 4. Eddy current loss density distribution in the rotor.

Fig. 5 (
a) displays the setup used in the diameter measurement and Fig. 5(b) the EMA setup.

Fig. 7 .
Fig. 7. Simulated and experimentally tested inductance as a function of rotor position.

Fig. 8 .
Fig. 8. Simulated and experimentally tested inductance as a function of rotor position.

TABLE III DETAILS
OF THE FE ANALYSIS FOR THE S355MC (1.0976)-INCONEL 600 (2.4816) ROTOR