Design Factors of High-Speed Turbo-Electric Distributed Propulsion System

Turbo-electric Distributed Propulsion (TeDP) is a promising concept to achieve the operational goals of more electric aircraft. The application of TeDP architecture can achieve the desired weight reduction of an aircraft power system. The use of a superconducting machine is expected to provide the workaround for the weight issue, but its current state of technology has not yet been extensively tested for aircraft applications. Another more practical option is to directly couple the aircraft's propeller system to a high-speed permanent magnet (PM) electrical machine, eliminating the gear part that also contributes to the total weight. A critical part of the design for a high-speed PM machine is choosing the optimum magnet configurations. This study used finite element modelling to analyze the impact of scaling the PM’s critical parameters on the weight and machine speed. A prototype testing of a 2-KW high-speed machine, suitable for a Remotely Piloted Aircraft System (RPAS), was developed and tested. The results confirmed the following critical parameters that should be carefully designed to achieve the optimum output, such as the (a) number of winding turns, (b) stack length, (c) sleeve thickness, and (d) terminal voltage.


Introduction
The design of the next generation aircraft targets less fuel consumption, noise, and emissions [1,2].This could be made possible with full electrification using high-density energy storage.However, the energy density of the batteries and the power-to-weight ratio of existing electric motors undermine the requirements of long-range aircraft.The main problem is their weight, which is well over the weight of the gas turbines used to generate electricity on the ground [3].A way to overcome the weight problem is to migrate to a hybrid electric aircraft (HEA) or a more electric aircraft (MEA) [4].Doing so could take advantage of the high energy density of conventional fuel-powered gas turbine engines [4,5], and the flexibility of electrical motors [6,7].The design of electric aircraft employs a lot of aerodynamics concepts.Such is the case with the Turbo-electric Distributed Propulsion (TeDP).
B Mithun Eqbal mithun.eqbal@rmit.edu.au;mithun.eqbal@adelaide.edu.auThis paper will present theoretical design factors of a highspeed TeDP, that will be subsequently applied to a prototype.
TeDP systems are based on electricity generation through a directly-coupled gas-turbine-electric-generator and distribute propulsive power through small electrical motors located in aircraft wings and tips [8], known as Distributed Electric Propulsion (DEP).The coupling between the aircraft's propulsion system and its airframe creates a Boundary Layer Ingestion (BLI), allowing the propulsion system to ingest and re-energize a portion of the boundary layer created on the body of the aircraft [9,10].The combined effect of DEP and BLI increases the propulsive efficiency of the aircraft and lift while reducing the drag, power, and fuel consumption [9,10].
To take advantage of the benefits of TeDP, the electric machine should be specifically designed with the primary objective of optimizing its weight.Otherwise, the result would be comparable only to a low-range aircraft powered by a conventional gas turbine [11,12].The discovery of a superconducting machine is expected to provide the workaround for the weight issue since it could deliver the required power at a lesser weight [13].However, superconducting machine technology is still in its infancy and is yet to be adapted to airborne applications.An option is to replace some sections of the electronics and motors with superconducting parts to increase efficiency.This would require the use of cryogenic coolers to reduce the system temperature, which also adds weight to the system [1,14].
Other studies considered the use of high-speed machines to potentially achieve lower weight compared to a low-speed electrical machine of the same power rating [15,16].Eqbal et al. [17] studied the effect of replacing the starter motor and gear of a turboprop with a high-speed electrical machine using a permanent magnet and achieved a 31% reduction in overall weight.A typical gas turbine engine shaft rotates at extreme speeds, e.g., a turboshaft used in a conventional aircraft typically rotates up to 40,000 rpm, and a micro gas turbine up to 600,000 rpm [18,19].Whereas, the aircraft propeller requires a much lower rotational speed, typically under 10,000 rpm to operate at optimum efficiency and below the speed of sound [17,20].Higher propeller speed increases the tip speed and creates shock waves that result in high structural loads while reducing efficiency [21,22].To solve this issue, aircraft makers use a large gear system, with an additional weight of around 75% of the total gas turbine weight.A better alternative, then, is to eliminate the gearing system, which could be made possible through direct coupling with a high-speed electric machine [17,23].
High-speed electric machines are used for a wide range of applications, such as military, civil aviation, high-speed turbochargers, space engineering, and high-speed machine tools [17,24,25].The different types of electric machines suited for high-speed operation are the switched reluctance machine, flux switching machine, induction machine, and permanent magnet (PM) machine.The switched reluctance machines and flux switching machines have robust rotor construction and are more suited for high-speed operation.These machines have been proposed for more electric aircraft and waste heat recovery systems [26][27][28].Switched reluctance machines and induction machines do not have magnets and therefore can be used for applications requiring hightemperature operation [17,24,27,29].The application of TeDP power generation requires low weight and high-speed operation.The PM machines have low weight and are typically designed to operate in high-speed conditions, which makes them the most suitable option for application in TeDP [17,25,30,31].
PM machines are based on different factors such as current, synchronization, flux, rotor arrangements, winding, and slot [32].Alternating Current (AC) is more efficient than Direct Current (DC) and incurs less energy loss [32].Easy regulation and synchronized output make synchronous machines more suitable for high-speed applications [33,34].External rotor machines are more compact and have lower power output, excessive vibration, lower efficiency, higher armature thermal load, higher rotor instabilities, and higher current density than internal rotor machines [35,36].Since the application needs higher torque density, the internal rotor machine is more suitable for high-speed applications.For an internal rotor configuration, radial inner flux is a better choice, as well as a slotted stator [37].
Considering such factors as high-power density, lower weight, compactness, simple structure, high efficiency, and being able to be used as a starter motor, the Permanent Magnet Synchronous Machine (PMSM) is the optimum choice for aerospace applications.Its other advantages include inherent PM excitation, less complicated designs requiring fewer support systems, improved power electronics, and the use of the stator structure [17,38,39].It also generates less heat, since the externally coupled spool provides enough cooling from the flowing wind.A jacket cooling using fuel as in a rocket potential engine is of potential future interest [40,41].The PMSM technology is already mature, and there are several prototypes available.For example, the group led by Prof. Kolar at ETH-Zurich has developed a 500,000 rpm, 100W PM machine [42,43].Based on this machine, another PM machine with a maximum speed of 1,000,000 rpm was designed and tested, setting the current world record for the maximum speed achieved by an electrical drive system [42][43][44].
This paper aims to design a novel permanent-magnetbased, high-speed, turboelectric generator that can provide a lightweight hybrid power source for emerging electric aircraft in terms of weight reduction, design simplicity and methods for novel electrical power generation.This paper creates a systems-based link between aerodynamics, electrical power generation, high-speed gas turbine mechanics and the general propulsion system to create relatively higher propulsive efficiency.This helps link high-speed machine manufacturing, gas turbine designing and aircraft integration; as for gas turbines and electric machine increase in rotational speed reduces the weight and makes a compact power plant, but with the impact of less power output [17].However, the compact power plant provides other advantages, such as less aircraft drag, wing structures, more design complexities and reduced aircraft weight.So electric machines' different design and power aspects help to design a gas turbine electric power plant and aircraft in tandem for higher efficiency [4,13,17,24].

Machine Parameters
A typical selection of machine parameters is given as follows:

Stator
The stator is an integral part of the machine design as it provides housing for winding, acts as the main structural component, and completes flux paths for the magnetic circuit [45][46][47].A diagram of the slotted design is given in Fig. 1, where D IS stands for the inner diameter of the stator and D OS for the outer diameter.
Various types of slot geometry are available that can affect performance.A low number of slots creates significant rotor losses and a large amount of vibration and noise.Goss et al. [48] investigated 12-36 slots, with the 33-slot design found to have marginally better performance than the 36-slot.However, it also generated some unbalanced magnetic pull on the rotor, leading to mechanical issues at higher speeds.Xing et al. [49,50] also found that a higher number of slots reduces the risk of overheating and demagnetization.But they were not able to increase the slot design beyond 36 as it would require excessively thin teeth that are difficult to manufacture.Therefore, a 36-slot stator design was selected [49,50].

Distributed Winding
Concentrated and distributed windings are among the most common types of winding used [51].Concentrated winding is small, lightweight, and has higher productivity and advantages in terms of the short-end coil and easy winding operation.However, it has a large PM eddy current loss at high speeds.On the other hand, the PMSM with a distributed winding, while having disadvantages in terms of copper and core losses, was found to have the advantage of low PM eddy current loss.Hence, the distributed winding should be selected for frequent high-speed operation, and for an environment where rotor cooling is difficult [51].
The winding factors is a parameter that describes how well the windings of an electrical machine are distributed along the stator slots.Lower order magnitude in the harmonics is preferred as it would result in lower losses mainly due to eddy current and core losses that are frequency-dependent [51].The calculation of winding factors is well known and can be found in [61][62][63] The table below highlights the winding factor in percentages for different coil throw values from 18 to 14: With a coil throw of 18, the winding harmonics are at approximately 19.7%, 14.5%, and 10.2% winding factor, with a 95.6% fundamental winding factor.However, by reducing the coil throw to 15, the higher order harmonics were reduced to 5.1%, 3.8%, and 8.8% winding factor respectively, with a trade-off of the fundamental winding factor to 92.4%.A coil throw of 14 would result in a higher 7th order harmonic and is counterproductive.Compared with a coil throw of 16, the winding factor at the 5th harmonic with a coil throw of 15 reduced from 12.7 to 5.1% with a drop in fundamental from 94.2 to 92.4%.Therefore, a double layer distributed winding with a coil throw of 15 shown in Fig. 2 is selected, after considering the trade-off of higher order harmonics with a fundamental winding factor.

Sleeve Retention for Magnets
The high-speed operation creates extensive stress on the rotor and the magnets [52], which can damage the rotor and the PM.PMs are typically brittle, with their tensile and compression strengths low, and cannot stand the high rotational stress [53].To retain magnets to the rotor, a sleeve made of carbon-fibre bandage or nonmagnetic high-strength metals is considered the most suitable solution [52,53].

Rotor Mechanical Design
For a shaft, one of the critical parameters is the rotor aspect ratio, which is defined as the length-to-diameter ratio.For a PM machine, the rotor aspect ratio has to be between 1 and 3 so that it will be relatively more dynamically stable than other machines.Since the rotor centrifugal force of the PM machine is directly proportional to the rotor diameter, the rotor diameter cannot be excessive.The rotor radius and rotational speed of the shaft are limited by tip speed, which is the surface velocity [47].

Magnet Sizing
The magnet dimension has prime significance in machine design as it creates the excitation to generate electric power in the winding and is limited by the air gap and magnet height.Correct computations of these two parameters will yield the required magnetic field, induced machine voltage, and air gap flux density.To maximize the air gap flux density, it is recommended to make the radial air gap as small as possible, although using a higher-flux density rare-earth permanent magnet allows flexibility in the air gap sizing.The magnet height can be computed upon selection of the material for the permanent magnet.Selecting a very large magnet height will reduce machine performance, so the minimum amount of magnet should be used.The usual proportion of magnet height to air gap is between five to ten times larger [47].

Slot-Per-Pole Phase
The slot-per-pole-per-phase is the design parameter that determines the relationship of interactions between the rotor poles and stator windings.It also shapes the generated back-electromotive force (Back-EMF) of the machine.The slot-per-pole-per-phase is given by where, S ph , slots per pole per phase; p, pole pairs; q , number of phases; N s , number of slots.
For a 36-slot 3-phase machine, where the pole number is selected at 2 to lower the frequency, the computed S ph = 6.

Inner Diameter of the Stator
Once the appropriate rotor radii are selected for a given sleeve thickness, at a given operating speed, the corresponding rotor inner radius, the needed sleeve thickness, and the air gap are selected.Equation ( 2) is used to calculate the inner diameter of the stator as shown in Fig. 1a and b and as described for the base machine in Table 1.
where D I S , stator inner diameter; r outer , outer diameter.

Split Ratio
To accommodate a comfortable area for winding and anchoring the stator, the outer diameter is set at 3 times the inner diameter.The factor is called a split ratio in higher-speed machines.The split ratio changes with the design speed, and it can be higher for higher-speed machines [54].Another reason for this is to have a consistent machine ratio, although rotor limitations and stator limitations have to be separately considered.would not make it suitable for air-cooled applications.Its maximum power output will be 200 kW, considering the structural integrity of the machine.For higher power output, multiple small generators integrated into the turbine tip should be deployed, where the turbine will help produce a higher output ratio.Table 2 shows the materials selected for the 1 MW surface permanent-magnet synchronous machine.Carbon Fibre 4020 is chosen because it can withstand tangential stress of up to 4020 MPa.A magnet thickness of 10 mm is considered for the sleeve stress analysis.Figure 3 shows the flow chart of the methodology for the machine design.
Compared to an interior PM machine, a sleeved PM machine is mechanically safe.The eddy current losses, which is an issue with the sleeved PM machine, are addressed by selecting a carbon fiber sleeve.To reduce the stresses within the sleeve, the usual course of action is increasing the sleeve thickness, but this is known to reduce the machine's power density [25].Figure 4 shows the variation of sleeve tangential stress for varying outer radius of the rotor for different sleeve thicknesses.
This analysis is patterned after the research paper of Fernando and Gerada [25] and considers operating points where the contact pressure between the sleeve and magnets approaches zero at a fixed speed of 60,000 rpm.For a given sleeve thickness, the rotor radius at which maximum stress occurs can be obtained by reading the intersection point of the corresponding thickness curve with the horizontal line at 4020 MPa, as shown in Fig. 4.However, the selection of the rotor radius takes into account a 20% safety margin to allow for speed overshoot conditions.For variable motor speed, Fig. 5 shows the variation of sleeve maximum stress for varying outer radius of the rotor for different operating speed conditions, and a fixed sleeve thickness of 2 mm.The rotor radius at which maximum stress occurs can be obtained by reading the intersection point of the corresponding speed curve with the horizontal line at 3216 MPa.After the sleeve thickness is selected, the radial scaling factor (K scale ) is introduced, which can change with the design [55].The slot dimensions given in Fig. 1 should be multiplied by K scale to give a similar ratio design for other machines.Next, the scaling factor is used to set the exact sleeve thickness and dimensions, as shown in Fig. 3. Then the slot area is calculated after minimizing the number of slots, and the area from the measured stator area.The computed slot area can be used to calculate the phase current to achieve the optimum current density with a random default stack length.Next, the torque data is extracted from the Ansys Fig. 4 Carbon 4020 sleeve tangential stress against rotor radius at 60,000 rpm Fig. 5 Carbon 4020 sleeve tangential stress against rotor radius for a 2-mm thick sleeve Maxwell software, and used in the power equation in Eq. 3 [25].
where ï, efficiency; N 1 , number of series turns per phase; K w , winding factor; I ph , phase current; q, number of phases; B g , air-gap flux density; l stk , stack length; D s,I , stator internal diameter; ω, rotation speed.The scaled stator length, stack length, and terminal voltage are also computed.Core loss and solid loss are used to calculate the efficiency, where the total efficiency is the sum of the core efficiency and the solid efficiency.The total area is the sum of the area of individual factors, such as rotor area, stator area, copper area, sleeve area, and magnet area.The total weight can be calculated from the sum of the weights of all materials used, or from the materials' densities.4 High-Speed Machine Designs

Scaling and Performance of High-Speed PM Machines at Different Rated Speeds
An analysis of the variation of output power with different rated speeds of high-speed machine designs is presented in this section by using the methodology as given in the Fig.
3 [25].In Table 3, the given factors such as terminal voltage, line current, current density, sleeve thickness, and stator outer diameter are kept constant to provide comparable dimensional changes with the radial scaling factor.When the radial scaling factor changes, so do the dimensions of the machine.
To reiterate, the machine design considered here has a fixed rotor sleeve thickness of 2 mm and a magnet thickness of 10 mm.For each of the designs with different rated speeds, the rotor outer diameter can be adjusted such that the sleeve stresses are at the same level, as shown in Fig. 6a, where the section above the red mark is dynamically unstable, as discussed in Sect.2.3.Figure 6b shows the variation of speed against the stator length.The section below the red mark in Fig. 6b is dynamically unstable.For the same scale, the turns are increased to maintain the specified terminal voltage for low speed, as shown in Fig. 6c.The section above the red mark in Fig. 6c is dynamically unstable.In the following figures, the rotor's dynamic stability is marked with orange line, which is the ratio of the length of the rotor to the diameter of the rotor.
Figure 6d shows the change in power output with rotor speed, i.e., as the speed increases, the power output also increases.Similarly, the length of the stator increase with the increase in turns.On the other hand, the outer diameter and the number of turns show an inverse relationship with speed.Due to variation in turns, weight comparison cannot be considered for the current section.However, the increase in speed increases the efficiency and power-to-weight ratio, as shown in Fig. 7a and b.This is a factor favorable to TeDP as it has a higher power-to-weight ratio than low-speed machines and an increase in efficiency close to 100%.However, it is difficult to reach 100% efficiency due to mechanical and structural losses.

Single-Turn-Per-Coil Design for High-Speed Operation
This section shows a high-speed machine with the same characteristics as in Table 2, but with a winding similar to the coil arrangement in Figs. 1, 2. As the rated speed increases, the number of turns reduces for the 36-slot stator arrangement [25].Higher power output can be obtained from the design with a single turn per coil, as shown in Fig. 6c.Another way to increase the power output is to increase the voltage.Figure 8a-d describe the electric machine design characteristics for a single turn.
As shown in Fig. 8a-d, with the number of turns fixed at one turn per coil, the plotted machine parameters vary above the speed of 80 kRPM.With an increase in the rated speed, the weight of the machine reduces, which is favorable for TeDP power generator applications.For aircraft applications, the machine diameter reduces when the power-to-weight ratio increases.The lower the diameter, the lower the drag [56].
Figure 9 shows that the outer diameter of the machine reduces with an increase in speed, as well as the stack length Fig. 9 Variation of speed against stator diameter for a single-turn of the machine, which is between 80 and 88 mm.This shows that a compact machine with an increased speed is possible.The smaller machine will allow direct integration of the electric machine into the existing gas turbine without affecting the flow of air into the gas turbine.The increase in weightto-power ratio with speed also allows the use of multiple high-speed generators in a single gas turbine.A one-speed Stator OD/ID ratio 3 high-speed output gear can be used in a regular gas turbine, which is normally designed to run under 40 kRPM.Compared to Sect.4.1 where the number of turns varies, a single turn allows a better comparison of machine characteristics.With an increase in speed, there is a reduction in power output due to lower torque, but the advantages include a reduction in weight, an increase in efficiency, and a powerto-weight ratio.

Turns Per Coil for a Fixed Speed of 25 kRPM
For this section, the machine speed is kept at 25 kRPM, and the sleeve thickness is at 2 mm, as shown in Table 4. Turns are made to vary, the rated terminal voltage is kept constant at 311 V, and the diameter is kept constant [25].Since the diameter is the same, there is no need to scale for each analysis.The graphs are given in Fig. 10a-d.
Figure 10a-d show how machine characteristics change when turns are varied for the same speed of 25 kRPM.When the turns are increased, the power output is reduced, while the weight is increased.This implies that turns should be kept at a minimum.However, increased length and reduced efficiency  Stator OD/ID ratio 3 are also factors to consider when the turns are kept at a minimum.In Fig. 10c, machines below six turns do not appear to be feasible due to impractical length.Figure 10a shows how the increase in turns can affect the power output while keeping the diameter constant.Therefore, the number of turns should be kept as low as possible and should be increased only when the terminal voltage is high.The optimum number of turns should be derived from the power requirement for a specific aircraft.

Changes in Sleeve Thickness for a Fixed Speed of 100 kRPM
In an aircraft, the power plant needs to be as compact as possible.If the machine is designed with a thinner sleeve, the rotor diameter, as well as the outer diameter of the machine, will be affected [25].This section discusses the sleeve thickness variations for 100 kRPM machines, as given in Table 5.The terminal voltage is kept constant at 311 V, with a constant air gap of 1 mm. Figure 11a-d show the power, weight, outer diameter, and length changes for a constant speed of 100 kRPM.In Fig. 11a, an increasing sleeve thickness up to 6.5 mm shows corresponding increase in power output.Beyond 6.5 mm sleeve thickness, the power output attains a plateau.Additionally, an increase in sleeve thickness also increases the outer diameter but reduces the length.The weight also increases proportionately with increasing sleeve thickness.Since the goal is to keep the machine compact and power dense, it is advantageous to keep the sleeve thickness as low as possible.

Stack Length Changes for a Fixed Speed of 100 kRPM
As discussed previously, the power plant of the aircraft should be as compact as possible.The issue of large outer diameter can be overcome by increasing the length, but length cannot be increased uncontrollably due to mechanical and space constraints [25].A balance between the length and diameter is necessary.In this section, the stack length is varied, but the outer diameter is kept constant, causing the rated voltage to change.The speed, current density, air gap, and sleeve thickness are also kept constant.Figure 12a-c shows that increasing the stack length produces linear increases in the power output, weight, and terminal voltage.The increase in terminal voltage causes a constant electrical efficiency of 90%.Therefore, the stack length selection should be aircraft specific.If the line and terminal voltages need to be increased without much modification, a better option would be to increase the stack length.One thing to note is that when the stack length is significantly low, the end windings will cause higher copper losses, causing a lower efficiency.

Variable Design Voltage for a Fixed Speed of 100 kRPM
In this section, the design voltage of the electric machine is made to vary.The design voltage variation can change the output and performance of a high-speed machine at 100 kRPM.The description of the machine is given in Table 6, where the magnetic sleeve retention, stator diameter, and shaft diameter are fixed (Table 7).Stator OD/ID ratio 3 Figure 13a-d show how the voltage will change when power output, weight, length, and efficiency change.An increase in the root means square (RMS) of voltage entails a linear increase in power output, but a reduction in efficiency.Additionally, higher voltage RMS subsequently increases the length, which is not good.The machine should be limited to a voltage under 400 V since higher-voltage machines are not necessary for MW applications [57].While a design above 400 V is unnecessary, the graphs of higher voltages were plotted to show the trend.Hence, maintaining the RMS voltage at the minimum acceptable level is considered a good design.

Prototype
For the prototype, a smaller 2 kW machine is selected, as discussed by Eqbal et al. [17] for a gas turbine with a speed of 120 kRPM.Next, the voltage output is selected, which should be specific for the operation.In the case of Remotely Piloted Aircraft Systems (RPAS), a 12S LiPo (Lithium Polymer) powered propeller motor gives the desired voltage output of 44 V. Since the power needed for the aircraft is under 2 kW, the sleeve material is changed to a more common Inconel 718, as shown in Table 8 [17].The graphs show that the number of turns should be lower so the output could be set at 1. To achieve the desired voltage and power output, the stator length can be increased, while reducing the sleeve thickness and air gap.Based on these conditions, three machines of similar power output are analyzed in Ansys Maxwell [17].
The resulting data are summarized in the following tables.A comparison of the three different versions of machines (Tables 8, 9, 10 and 11) [17] shows that the higher the diameter, the more weight of the machine can be reduced.However, the generator is placed directly on the path of the inlet airflow, circumcircling the turbine.The outer diameter of the machine  For the prototype, some changes are made that increased the weight and reduced the power output.The changes and rationale are explained in Tables 12 and 13.
The picture of the prototype is given in Fig. 14, and the testing setup is given in Fig. 15.
Figure 15 shows the test setup for the machine.Due to a lack of high-speed coupling and prime mover, the machine was tested under 10,000 RPM, with open circuit and close circuit modes.The rest of the data is extrapolated as testing was limited.The test results are shown in Figs. 16, 17, 18 and 19.From Fig. 16, voltage output for 6700 RPM shows a wave pattern, as expected [24,52].However, the peak voltage of around 1.18 Volt is less than 50% of the expected power output.The reasons for this are: (1) the magnet used is N42 instead of N52; (2) the magnet needs to be 10 mm thick, the one used is only 6 mm thick; and (3) the custom-made magnets were not concentric enough, so cylindrical grinding was used to make them concentric, affecting the magnet output.
Figure 17 shows the current sensor measurement output at 2876 RPM.A short circuit apparatus that includes a shunt resistor and relay, was used for the test.When the relay was activated, the current flowed through the shunt and generated a voltage drop.The current output was then measured using the sensor.The current was initially measured at a set speed of roughly 2900 RPM.Below this, the BLDC motor stalled due to the resistance from the electric machine.When the machine was started at 2900 RPM, it created some resistance, Figure 18 shows that the voltage output at various speeds has a linear trend [24,52].The reasons for the reduced voltage were explained in Fig. 16.It is important to use an N52 magnet and increase the magnet's size to increase the power output.
Figure 19 shows the combined current output for different speeds.As expected, power output increases linearly with speed [24,52].
Figure 20 shows the tested and extrapolated voltage output, as rotational speed is increased.The graph showed a linear trend [24,52].To increase power output, a precision concentric magnet should be made without any cylindrical grinding.By using a thicker N52 magnet and changing the shaft material, power output can also be increased.Another way to increase power output is to use a composite sleeve, but it can lead to heating issues.
The weight of electric machines can be reduced by reducing the shaft length and maintaining an acceptable power-to-weight ratio without sacrificing dynamic stability.The prototype proves that the design mechanism can develop a high-speed machine, gas turbine and aircraft structure in tandem, leading to a more compact, lightweight and higher-range aircraft with the existing technology.Additionally, electric machines can use low-weight materials to reduce their weight [24,27,48,55,59,60].A precision-made highspeed machine should be tested at higher rotational speeds once these issues are fixed.As part of future work, the bus and power distribution mechanisms should also be designed and tested, as well as the cooling mechanisms for machines with a high-power output.

Conclusion
A prototype for a 2-kW machine was made and tested, to find ways to come up with a lighter alternative to the existing turbo-electric distributed propulsion (TeDP) system.The various trend analyses presented showed how the different machine design factors can impact the weight and the power output of a high-speed TeDP machine.The results revealed that to get the optimum output, the winding turns should be kept to a minimum, the stack length should be increased proportionately, the sleeve thickness should be kept as low as possible, and the terminal voltage should be increased.But considering the weight and dimensional constraints, it is recommended to find the optimum balance for each machine.The current density and packing factor are kept constant for the study but can be increased based on the manufacturing and the cooling capabilities.Although the analysis is based on synchronous PM machines, the data can be used for other electric machines.Further, the data derived from this study can be used for the combined development of high-speed machines and gas turbines, since both aimed to reduce the size, while increasing the rotational speed.The prototype data identified the design considerations for high-speed machine manufacturing.Recommendations were given to fix the limitations observed, and possible methods to increase the power output.

Fig. 1 a
Fig. 1 a Stator.b Stator slot geometry

Fig. 3
Fig. 3 Flow chart of the methodology

Fig. 6 aFig. 7 aFig. 8 a
Fig. 6 a: Variation of speed against the outer diameter of the stator.b: Variation of speed against length.c: Variation of speed against the number of turns

R²Fig. 10 a
Fig. 10 a: Variation of number of turns against power for 25 kRPM speed.b: Variation of number of turns against weight for 25 kRPM Speed.c: Variation of number of turns to length for 25kRPM.d: Variation of number of turns to efficiency for 25KRPM

Fig. 11 aFig. 12 a
Fig. 11 a Variation of sleeve thickness against Power for 100 kRPM machine.b: Variation of sleeve thickness against weight for 100 kRPM machine.c: Variation of sleeve thickness against diameter for 100 kRPM

Fig. 13 a
Fig. 13 a: Variation of voltage against power for 100 kRPM.b Variation of voltage against weight for 100 kRPM.c: Variation of voltage against length for 100 kRPM.d: Variation of voltage against efficiency for 100 kRPM

Table 1
Winding factor in percentages

Table 2
Material selection for the 1 MW machine

Table 3
Scaling and performance of High-speed PM machines at different rated speeds

Table 4
Machine design for variable turns per coil

Table 5
Machine design for variable sleeve thickness

Table 6
Machine design for a variable stack length

Table 7
Machine design with variable terminal voltage

Table 8
Prototype machine specifications

Table 9
a The bearing loss for the given shaft diameter is not included

Table 12
Changes in the materials for the prototype

Table 13
Parts and weight distribution of the prototype