Cooling Systems for High-Speed Machines—Review and Design Considerations

Abstract

High-speed machines are attractive to many industries due to their small size and light weight, but present unique cooling challenges due to their increased loss and reduced surface area. Cooling system advancements are central to the development of faster, smaller machines, and as such, are constantly evolving. This paper presents a review of classical and state-of-the-art cooling systems. Each cooling method—air cooling, indirect liquid cooling, and direct liquid cooling—has potential use in cooling high-speed machines, but each comes with unique considerations, which are discussed. An example design process highlights the interdependence of the electromagnetic and thermal design choices, illustrating the necessity of integrating the electromagnetic and thermal designs in a holistic approach.

1. Introduction

High-speed machines are smaller and lighter than slower machines for the same power rating [1,2]. At the same time, fast machines can eliminate gear or belt drives in high-speed applications [3,4], further reducing size and weight in addition to reducing system complexity [5]. As a result, high-speed machines are desirable in any application where small size and light weight are desirable, notably in the transportation and aerospace industries, as well as in high-speed machining apparatus. Smaller, lighter machines also reduce material costs and require less total magnetic material. Due to their high frequencies, high-speed machines can often employ ferrite magnets [6,7] while maintaining similar power densities to slower, larger machines using rare-earth magnets, further reducing cost.

High-speed machines (with speeds in excess of 10 krpm) present two thermal challenges. First, losses increase with speed. Both hysteresis and eddy current losses in the core increase with electrical frequency [8], and so high-quality steel with thinner laminations is required. In the windings, high frequencies decrease skin depth, and so litz wire is often used, but the use of litz wire decreases slot fill [9]. Second, the cooling system must reject this loss through a smaller surface area. Increasing the coolant flow increases the heat rejection [10], but the incremental improvement diminishes with increased flow.

Therefore, as machine speeds increase, the load on the cooling system increases twofold. The accelerated demand for improved cooling systems is addressed in this paper. First, a review of existing cooling systems is presented in three sections, organized by cooling type, with considerations specific to high-speed machines: Section 2 presents air cooling methods, Section 3 presents indirect liquid cooling, and Section 4 presents direct liquid cooling, while Section 5 presents a general discussion on how architecture selection affects cooling for high-speed machines. In the second part, Section 6 presents a listing of architectures and cooling methods for reference, and an example design process is presented to illustrate an example of how the machine architecture and cooling system are interrelated, with a summary of conclusions in Section 7.

2. Air Cooling

Air cooling is generally the least effective method for cooling a machine, as air has a lower volumetric heat capacity than liquids, and therefore, is less capable of removing heat. However, air cooling is also simple: air is readily available in most applications, and even in liquid-cooled systems, it is typically the final sink for thermal energy in the system. In addition, forced air systems can cool all parts of the machine simultaneously [11], which is an advantage over many liquid-cooled systems.

2.1. Closed Frame, Convection Only

This cooling method is best illustrated by the totally-enclosed, non-ventilated (TENV) motor frame common in industrial induction machines. The housing is constructed so that no external air can enter the frame, and there is no forced air either internal or external to the machine. This is typical in applications where any ingress of dust, air, or other environmental debris would be detrimental to the operation of the machine. Heat from the rotor can be rejected through the shaft to the external environment, or it can pass into the air gap and surrounding internal air. The stator can pass heat through the housing to the external environment directly, or through the internal air to the end bells. Closed-frame machines often employ fins on the outer surfaces of the housing to increase the surface area for heat transfer to the environment, and the housing can be constructed with minimal clearance to the active components of the machine, as there is no shaft-mounted cooling fan.

While convection-only cooling systems are less effective than forced air, convection is still induced by the motion of the rotor. The Taylor and Reynolds numbers at the rotor surface govern whether flow remains laminar, vortices form, or flow becomes turbulent, which in turn, determines whether thermal transfer is conductive (in laminar flow) or convective (in turbulent flow). In the air gap, the Taylor and Reynolds numbers are a function of rotor size and rotational speed, and [12] provides a thorough description of the conditions for conductive and convective transfer in the air gap. Moreover, the transitions between laminar and turbulent flow depend on the surface smoothness of the stator and rotor [13] and the relative diameter and air gap length [14].

Similarly, the external design of the housing affects overall heat rejection. The thermal effects of free convection on cylindrical and finned surfaces have been studied extensively [15,16,17], and analysis has demonstrated that the size of the external fins and their orientation play a role in the air flow over the surface, affecting convection cooling to the environment. Reference [18] presents an analysis of the passive cooling in a fan-cooled machine in the case when the shaft is moving too slowly to effect enough air flow to cool the machine, effectively analyzing a convection-only system. By presenting a subdivided analytical approach to calculating the cooling from the housing, the paper enables a path for the improvement of the standard radial fin housing shown in Figure 1a [19,20].

In traction applications, or in applications where the motor is moving in an air stream, further improvement can be realized by embedding cooling channels in the stator [21]. This can be conducted strategically so that the internal components are not exposed to the environment, and the internal air and external air never mix. While this is not strictly convection-only cooling, it is not grouped with forced air cooling because a blower or fan is not employed to move the air across the machine; rather, the natural environment is the only source of air movement.

2.2. Closed Frame, Forced Air

This category has two mechanisms for cooling: External cooling and internal cooling. Figure 1b shows a section view of a totally-enclosed, fan-cooled (TEFC) machine, which uses a fan mounted on the shaft external to the sealed housing to generate air movement over the external surfaces of the machine with an internal fan to promote internal air movement. The housing is equipped with fins designed to maximize cooling [22]. As machines have become more powerful and more power-dense, improved air movement has become more important. At the same time, the blower design can affect both the parasitic drag and the ambient noise in these designs [23].

In these designs, cooling the end windings is the biggest challenge, as the thermal path from the end windings is predominantly into the stator slots and radially through the machine housing. As a result, most TEFC designs use fins on the rotor to promote air movement. The machine-air and air-housing thermal transfer improves with increased surface air velocity, while the transfer from the machine to the end bells via convection improves with increased bulk air flow, resulting in an alternative heat path from the end windings through the external housing of the machine to the environment [24]. The fan wafters, fins, or blades affect the air flow, resulting in cooling [24,25,26], and the intentional design of these features provides an improvement over past designs. If the blade geometry is optimized for operation in one direction, then it will be less effective in the opposite direction [27], so if the machine is to be run in both directions, then the overall cooling efficacy may be sacrificed to provide more balanced cooling in both directions. Even without changing the fan design, significant improvements can be made simply by adding deflectors and baffles in the air space [28].

Eliminating the external fan reduces the operating noise, while cooling the machine solely with internal air movement improves cooling compared to a non-forced air machine [29]. Similarly to [21,30] proposes a design that uses improved cooling channels external to the machine to take advantage of the ambient air flow in a tractive application, while simultaneously using an internal fan to further improve cooling. At the same time, the internal fan is designed with an uneven blade pitch to further reduce internal noise.

Segmenting the machine to provide air channels improves the heat distribution inside the machine [31]. The separation of the stator segments in the axial direction, as in Figure 2, allows air to flow between segments and around sections of exposed windings, while rotor segmentation provides air flow to the interior of the rotor, which is one of the hottest parts of a fully-enclosed machine. Ref. [32] demonstrates that selecting the optimal number of segments reduces both the maximum magnet temperature and the total temperature gradient in the magnets. Similarly, the circumferential segmentation provides a similar benefit while also allowing for the use of oriented steels, improving the electromagnetic operation of the machine [33].

2.3. Open Frame, Forced Air

An open frame for an air-cooled machine improves the cooling efficacy by providing a direct path for heat transfer between the active components and the external air, and while this typically improves overall cooling, the overall housing design depends on how protected the internal components must be from the environment [29,34]. For example, a weatherproof housing may have a long, serpentine inlet to prevent dust and large particles from entering the machine.

The blower can be shaft-mounted, as in [35], or it can also be a separate fan, as in [36]. A disadvantage of the shaft-mounted design is that the blower will always spin at the shaft speed, incurring the necessary energy input to keep the blower moving at all times. However, when the torque load is low, cooling may be altogether unnecessary [35]. Moreover, the fan will supply no cooling when the machine is not rotating, so a shaft-mounted blower is less appropriate in an application with large speed and torque operating ranges.

In the case where the motor is designed to drive a blower or blade as the mechanical load, the forced air can be used to cool the machine as well [37,38]. In this case, both the load and air flow will increase with the shaft speed, balancing the need for additional cooling as the shaft speed increases while avoiding the conditions where cooling is needed at low speeds, or not needed at high speeds.

Regardless of the fan location, the inlet and outlet designs play a role in the efficacy of the cooling, which is affected by air speed, inlet and outlet locations, and the angle of the incoming air [36,37]. Ensuring that the internal air moves through the air gap further improves the system performance [39]. A strategic design for the air flow paths can provide superior cooling while excluding debris, both of which are necessary for machines in dirty environments.

2.4. Considerations for Air Cooling in High-Speed Machines

While the cooling surface area is reduced in high-speed machines, there is still potential for the use of natural convection in a high-speed machine. The small size of the machine also means that the heat path to the exterior of the active machine volume is short. If heat can be effectively extracted to the exterior of the machine, then it is possible that a well-designed, passively-cooled aluminum housing will provide both weight and space savings over a liquid-cooled assembly, without the need for an additional fan. If the ultimate goal is light weight, high speed, and simplicity, then natural convection can still be viable.

For both internal and external cooling, shaft-mounted fans create a unique challenge in high-speed machines. First, the fan must withstand the high stresses that come with high speeds. Second, if the machine is not intended for fixed-speed operation, high-speed machines have a potential for much larger dynamic range than low-speed machines. Because the power input to the fan is $P=k{w}^3$, if there is a need for cooling at low speeds, the input power may become unreasonable at full speed. Thus, an external, non-shaft-mounted air source may be necessary.

The turbulence that develops in the air gap depends on the machine slotting, air gap surfaces, and air gap length [40,41]. While the turbulence in the air gap improves the heat transfer between the rotor and stator and is beneficial in a convection-cooled machine, the bulk air flow in the air gap is more effective at cooling the machine than heat transfer across the gap. Because high-speed machines also have small air gaps (often less than 0.5 mm), the pressure required to force air through the gap is already high, and this pressure is increased further when turbulence is introduced. On the other hand, as the air gap decreases, laminar flow in the air gap becomes more likely [14], reducing friction. This balance must be considered when designing the mechanical surfaces of the air gap.

3. Indirect Liquid Cooling

Indirect liquid cooling is used when the application requires that the coolant be contained within the active parts of the machine. Consequently, there must be a barrier between the coolant and the heat sources, so while these systems are more effective than air cooling, they are typically less effective than direct liquid cooling. Moreover, the design and efficacy of a liquid cooling system are dependent on the machine’s architecture, e.g., axial-flux vs. radial-flux. The development of evaporative, or phase-change, cooling has improved the efficacy of indirect cooling systems, and these will be discussed here alongside their corresponding liquid cooling systems. This section is divided by the location of the coolant.

3.1. Cooling Jacket or Plate on Stator Yoke

External, fully-enclosed cooling jackets attached to the stator are simple, well-studied, and effective. They are also easy to implement, and so are the most common indirect cooling methods.

The efficacy of the cooling mechanism can be improved by adding a thermal path, through epoxy or thermally conductive potting, from the end windings to the outer jacket. Integrating cooling in the end bells of the machine further improves cooling, even if the thermal path is only through the internal air, as in a TEFC or TENV motor [42].

3.1.1. Radial Cooling Jackets

In radial-flux machines, a cylindrical sleeve is typically attached to the stator, and coolant is forced through the assembly. Because most machines are built with laminated steel in the stator, the cooling passages must be entirely enclosed in the jacket or plate, as laminated stacks do not remain liquid-tight over time. Two-part assemblies are still possible with the use of seals.

The thermal contact between the lamination stack and the jacket is determined by the regularity of the lamination stack, the presence of any thermal compound, and the contact pressure between the stator and the cooling jacket [43]. High pressures in radial jackets are realized with interference fits, while the jacket may also transmit torque to the mounting assembly, so structural analysis must be considered to ensure the integrity of the jacket [44,45].

3.1.2. Attached Cooling Plate

In axial-flux applications, a plate is attached to the axial face of the stator, as in Figure 3b, and high contact pressures may not be feasible. However, cooling plates are nevertheless effective even with the reduced thermal transfer coefficient. The shape of the cooling channel and the coolant path play a role in the heat distribution in the machine, due to the increase in coolant temperature along its path as well as the effect of induced turbulence [46,47,48]. This variation in temperature distributions is shown for axial-flux cooling plates in Figure 4.

3.1.3. Leakage Flux

Care must be taken with an external cooling jacket if the machine has leakage flux, as time-varying flux may intersect the metal cooling jacket, as in Figure 5, introducing eddy current losses in the cooling jacket [49]. This is more important if the coils are in direct contact with the jacket, as leakage flux is greater in this area, and in the case of a coreless design, the risk of leakage flux is even greater.

3.1.4. Phase Change Coolant

Phase-change coolants change between liquid and gas, taking advantage of the high latent heat of vaporization of the coolant. As the liquid is heated, it vaporizes and moves away from the heat source, where it condenses as it rejects its heat to the environment. This provides an improvement over liquid-filled cooling jackets [50,51], although this may limit the orientation of the machine [52], as there is potential for the gas phase to become trapped, or for the liquid phase to pool in low areas.

3.2. Embedded Cooling in Core and Windings

Moving the coolant closer to the heat source improves the cooling system. In the stator, the heat is generated in the stator core and the stator windings, so adding cooling channels in these areas improves heat rejection.

3.2.1. Tubes in Stator Core

Within the stator, coolant can be circulated through tubes embedded in the stator teeth and yoke [53], as illustrated in Figure 6. As most of the winding heat also exits through the stator core, this shortened heat path also improves winding cooling. If the tubes are embedded in the teeth, then the end windings must leave sufficient space for the cooling apparatus.

Tubes in the stator core occupy some of the flux-carrying cross-section of the machine, reducing the total flux and, therefore, torque. The net effect depends on the flux density in the machine and the tubing size. Machines that are run at magnetic saturation, with the tubes occupying a large cross-section, will be the most affected, while machines that are run below the saturation point of the steel will be relatively unaffected.

3.2.2. Tubes in Windings

Effective cooling can also be realized by embedding cooling tubes in the windings. Locating the coolant in the windings provides multiple additional benefits over coolant channels in the teeth and yoke. First, the windings are often the hottest part of the machine because the windings are the furthest point from the heat sink. Second, the winding insulation is often the most temperature-sensitive component in the machine, except in some permanent magnet designs. Third, the winding losses increase with temperature; therefore, improving winding cooling can also reduce machine losses, providing a double benefit to the machine. This can be accomplished in two main ways. Ref. [54] demonstrates the effectiveness of embedding a single tube in the slot, separate from the coils. Ref. [55] demonstrates a similar method, except that the cooling tubes are flexible and enmeshed in a bundle of litz wire. Both have been shown to be effective.

This cooling method reduces the available slot area, potentially reducing the fill factor of the machine. In distributed windings, the overlapping endturns may require the tubing to form a convoluted shape, or the end turns may have to be routed in an alternative path to avoid the tubing, increasing the endturn volume and manufacturing costs. However, many production machines leave some slot areas unfilled. For example, needle winders need space in the slot for the winding head. In these cases, cooling tubes could be added after the winding is complete, having no effect on the slot fill.

This method provides a more pronounced improvement in a slotless machine. In a slotted machine, heat flows from the coils to the yoke via two paths: Radially, directly to the yoke, and circumferentially into the teeth and then radially to the yoke. The thermal conductivity in the teeth is higher than the transverse thermal conductivity in the windings, and so heat is conducted through the teeth. In a slotless machine, this low-impedance path is not present, and so the embedded cooling design is particularly useful in these machines [56,57].

3.3. Phase Change Coolant

Further improvement can be realized by embedding phase-change pipes in the machine instead of coolant-carrying tubes [52,58]. In each case, the thermal transfer between the stator and tubes is dependent on contact pressure, the thermal compound, and the regularity of the contact surface, similar to the case with the external jacket. In machines with long heat paths, such as long, narrow, radial-flux machines, heat pipes can be particularly effective due to their rapid thermal transfer from one end of the pipe to another [59].

In machines with high transient loads, the phase-change medium can be used as a buffer to absorb excess heat during operation, letting the heat dissipate slowly when the machine is under light loads [60]. In this case, a solid-liquid phase change is utilized to eliminate the need for large chambers for the gas phase. Although the latent heat of fusion is less than that of vaporization, it is still relatively high compared with the specific heat of the liquid. This method improves the peak loading of the machine, allowing either heavier duty cycles or a smaller machine design without adding external cooling mechanisms.

3.4. Rotor Cooling

Rotors can be cooled in an indirect system by pumping coolant through the shaft. This system requires shaft seals, adding complexity. The inlet and outlet can be on the same end, with concentric inlet and outlet, or opposite ends, as shown in Figure 7. Having concentric feeds in and out of the shaft can produce centrifugal effects, eliminating the need for a pump in cases where cooling is not needed at low speeds. On the other hand, the layout of the system also affects the mechanical drag [61], due to the acceleration of the coolant within the rotor, and the induced drag increases with speed.

Similarly to the stator, the rotor can employ phase change cooling, and the rotation of the rotor can be utilized to aid in the separation of the phases [62,63], improving their heat transfer properties. If the internal chambers are accordingly designed, the centripetal forces will cause the condensate to pool in the hot end of the shaft while the vapor releases heat to the environment at the opposite end, as in Figure 8.

3.5. Considerations for Indirect Cooling in High-Speed Machines

Liquid cooling systems must provide enough coolant flow and surface area to effectively remove heat from the machine. In small machines, the relative size of the cooling system is increased, and the containment mechanism takes up proportionally more volume in small machines.

When using a cooling jacket on the stator, the jacket’s radial thickness is determined in part by the required volumetric flow, along with manufacturing and structural limitations, and occupies a larger percentage of the machine volume as the machine diameter decreases. The technology studied in [64,65,66] for radiators could be employed in the cooling jacket to reduce its size. However, manufacturing is further complicated by the required tolerances to achieve a good fit between the jacket and stator.

The thermal transfer to the jacket depends on the contact pressure at the interface between the stator and the cooling jacket. Approximating the stator as a solid cylinder and the jacket as a solid sleeve, the pressure at the interface is given by

$$P={\displaystyle \frac{\delta }{\frac{r_j}{E_j}(\frac{r_j^2+r_s^2}{r_j^2-r_s^2}+{\mu }_j)+\frac{r_s}{E_s}(1-{\mu }_s)}}$$

(1)

where $\delta$ is the radial interference between the jacket and stator, $r_s$ and $r_j$ are the outer diameters of the stator and jacket. $E_s$ and $E_j$ are the modulus of elasticity for the stator and jacket, while ${\mu }_s$ and ${\mu }_j$ are Poisson’s ratio of the stator and jacket, respectively.

Table 1. Interference fit vs. diameter for aluminum cooling jacket, 8 MPa.

Stator OD (mm)	Radial Interference (μm)
100	62
80	40
60	23
40	11
20	3.1

shows the radial interference for a 5 mm-thick aluminum jacket on a steel stator to attain 8 MPa contact pressure for a stator outer diameter (OD) between 20 mm and 100 mm.

Therefore, for a given contact pressure in an interference fit, as diameters decrease, the diametric interference also decreases. The reduction in interference at smaller diameters requires progressively tighter machining tolerances, increasing manufacturing costs.

Both additive manufacturing and soft magnetic composites are being used in high-speed machines [67,68] for their reduced core loss potential, but they have lower mechanical strength than other steel cores. As a result, further care must be taken to ensure the mechanical integrity of the machine with an interference-fit jacket.

In the case of windings with embedded tubes, the minimum tube diameter and number of tubes are determined by the required heat rejection and corresponding coolant flow. However, as the machine size decreases, so does the slot area, and with embedded tubes in the windings, the relative slot area further decreases, as shown in Figure 9. Therefore, either the number of tubes must be decreased or the slot current density must be increased, or else the machine size must grow to accommodate a larger slot.

On the other hand, high-speed machines often operate below the saturation flux density in the steel, either due to the use of ferrite magnets or to maintain the structural integrity of the core, especially with soft magnetic composite (SMC) or additive manufacturing materials. In these cases, the reduction in the stator cross-section due to embedded tubing in the stator core may be tolerable except in cases where the machine is very small.

When cooling the rotor in an indirect cooling system, coolant must be pumped through the rotor cavity or shaft. The coolant from the pump is stationary relative to the rotor’s rotation, but upon entering the rotor, the fluid will accelerate to the rotational speed of the machine. This creates more loss at high speeds [61]. Moreover, this may induce turbulence, requiring more effort to push fluid through the shaft. However, this also improves the heat transfer to the coolant. Ref. [69] details the effect of turbulence on rotor cooling in both direct-through and recirculating architectures. Specifically, above the critical speed, where Taylor vortices begin to form, the heat transfer to the coolant improves to the point that the increased friction is worth the cost.

On the other hand, the shaft seals must be able to operate at the rotational speed of the machine, and the shaft seals in a recirculating system are particularly complex. The use of air seals [70] may make the realization of shaft cooling more practical at high speeds. Air seals utilize similar technology to air bearings, which have been shown to operate at up to ten times the speed of traditional contact bearings [71].

4. Direct Liquid Cooling

In direct cooling systems, the coolant is distributed in direct contact with the active parts of the machine. Because they eliminate a thermal boundary between the heat source and coolant, they are typically more effective than indirect cooling systems.

Direct cooling systems also offer superior cooling of the end windings when compared with indirect cooling systems. The end windings produce loss, but the thermal path to an indirect cooling system usually has a high impedance. Direct cooling systems enable the liberal application of the coolant to the end windings, overcoming one of the primary challenges in motor thermal design.

4.1. Friction and Drag

Direct cooling systems are susceptible to additional drag from the coolant in contact with the rotor. In some cases, coolant ingress to the air gap can be eliminated completely [72] while still pumping coolant in direct contact with the windings in the slots, providing both the benefits of a direct cooling system and the reduced drag of an indirect cooling system. The coolant is usually oil-based, as water-based coolant should be kept away from the windings, and in all cases, the coolant’s compatibility with the machine materials must be considered. At the same time, the drag is related to the surface speed and viscosity of the coolant, and so low-viscosity coolants are preferred if possible.

4.2. Flooded Cooling

Among the simplest systems is the machine immersed in coolant, or partially submerged in a coolant sump, and the rotor’s rotation carries coolant up to the upper parts of the stator. This can be the most effective option, with the added benefit of the coolant providing a thermal buffer for transient operation [73]. This system has an advantage in traction applications because the motor case can be shared with the gearbox, and the gear lubricant can serve a secondary purpose as the motor coolant, and research in dual-function lubricants is being driven by this application [74]. This can also be particularly effective in systems where the machine also serves to drive a fluid pump, as the motor can be immersed in the working fluid [75].

4.3. Pumped Coolant

Coolant can be selectively pumped to various parts of the machine. Coolant distribution can be as simple as pumping the coolant onto the windings and allowing gravity to distribute the coolant [76] while still cooling the machine, or hoses and distribution manifolds can be used to distribute the coolant as desired.

Similar to any of the indirect cooling systems, coolant can also be pumped through an external jacket or through channels in the slots, stator teeth, and yoke. In each case, the coolant can be more widely distributed in the machine than in the indirect system, improving the thermal circuit. Moreover, the thermal barrier between the active components and the coolant containment system, which is one of the largest thermal barriers in the system, is eliminated.

Further benefits are realized beyond the thermal circuit. External jackets are simpler to manufacture if they only need to contain coolant within a cylindrical region as opposed to between two sleeves. Eliminating the inner wall of the jacket reduces the jacket’s radial thickness and reduces the potential for eddy current losses due to flux leakage at the stator OD. Moreover, the tight machining tolerances required for an interference fit can be relaxed, reducing the manufacturing costs. Manifolds for distribution through the slots do not need to seal to the tubes that see thermal cycling, and removing the tubing increases the available winding area, improving the net slot fill.

The rotor can also be used as a fluid pump. Incorporating radial channels for fluid allows the coolant to be centripetally pulled in through the rotating shaft, as shown in Figure 10. These channels provide excellent thermal contact between the coolant and the internal parts of the rotor, which then subsequently expel the coolant to cool the stator [77]. Because magnet temperature and motor performance are closely linked, and because magnets are sensitive to heat, this cooling method is particularly effective, and this method can approach the efficacy of spray cooling with respect to the stator components.

4.4. Spray Coolant

Spray cooling is typically the most effective direct cooling system [78]. The forced spray can produce coolant flow in parts of the machine that may develop stagnant regions in a fully-immersed design, and the velocity developed with spray cooling improves the thermal transfer coefficient to the coolant. With spray cooling, the speed of the coolant, its degree of atomization, incident angle, and viscosity affect how well a direct cooling system will function [79,80,81,82,83]. In addition, the specific coolant chosen has an impact on the cooling efficacy [84], as various coolants have different thermal properties, but some coolants are poor choices for contact with motor materials. Finally, high-viscosity coolants present additional challenges when designing nozzles for spray cooling [85], as added pressure is required to reach the degree of atomization required for effective cooling, and a fine nozzle that functions well for low-viscosity coolants may not pass enough volume of a higher-viscosity coolant.

4.5. Phase Change

Phase-change cooling can also be applied in direct cooling systems. The relatively high latent heat of vaporization can be employed to improve heat removal to an external heat exchanger, as in [86,87,88], and is a promising mechanism for the high-power, low-weight cooling required for aviation systems.

4.6. Considerations for Direct Cooling in High-Speed Machines

The primary concern for direct liquid cooling in a high-speed machine is friction from the contact between the coolant and rotor, as the friction increases with surface speed. Refs. [72,89] use a shield to isolate the coolant from the rotor, effectively creating an isolated cooling system with the efficacy of flooded direct cooling on the stator. However, this system requires a sleeve to be inserted through the gap; the thickness of the proposed sleeve in [89] is 0.75 mm, larger than the total air gap of many high-speed machines. Thinner sleeves may not withstand the fluid pressure without deformation or provide adequate sealing capability. Yet, this is promising as an area of study because laminar air flow in the air gap is improved with narrower physical air gaps, and the added sleeve can improve the windage in the air gap [90], reducing losses.

Advances in manufacturing have also enabled the benefits of direct cooling in a self-contained cooling system. In a core made with either additive manufacturing or soft magnetic composites, the cooling jacket wall can be eliminated on the side contacting the stator yoke, putting coolant in direct contact with the stator without introducing leaks [91], effectively creating an indirect cooling system without the drag induced by coolant in contact with the rotor. Similar functionality can be realized with additive manufacturing processes [92]. Hollow conductors similarly eliminate the boundary between the coils and coolant while also creating an indirect system [67,93]. Ref. [93] has demonstrated that this method, owing to the coolant reaching into the center of the machine, can provide improvement over direct liquid cooling.

While fluid in the air gap is detrimental, it may be tolerable to allow some splash; in the case of an axial-flux machine or short axial-length machine, the fluid will likely be expelled by the machine’s rotation. In addition, machines for underwater generation and propulsion and for fluid pumps intentionally flood the air gap with coolant [94,95,96]. The introduction of coolant into the air gap increases drag. However, the flooding of the machine, including the air gaps, improves cooling over other methods, and Ref. [96] showed the accompanying drag to be practical with surface speeds up to 40 m/s, which would result in a ∼10 krpm machine at 40 mm diameter.

5. Additional Cooling Considerations Based on Machine Architecture

Beyond the general considerations for cooling, the selected machine architecture will have an effect on the cooling system. As such, the selection of the cooling system must be an integral part of the machine design process. This section outlines the basic machine design options and how the specific design will affect the cooling system selection.

5.1. Flux Orientation

The orientation of flux (radial inside-rotor, radial outside-rotor, axial, etc.) determines the geometry of the stator, rotor, and air gap, and therefore, will affect the efficacy of the cooling system. The above designs and considerations were outlined for radial-flux designs with the rotor inside the stator. As such, the above considerations generally apply to inside-rotor radial-flux machines. Outside-rotor radial-flux and axial-flux machines are presented below. Other flux paths are neglected here due to them not being widespread in production environments.

5.1.1. Radial-Flux, Outside-Rotor

In an outside-rotor, radial-flux machine, at least one end of the stator must be covered by the end of the rotor, blocking the end windings and stator end on that side. It is possible for the end housing to be open, and even for it to integrate a fan, promoting cooling on that side of the machine, but this must be designed for the full speed range, and will also create drag.

Air can, however, be pumped through the stator shaft and through the air gap, cooling the end windings along the way (see Figure 11). The rotor itself is directly exposed to the environment, and if the rotor is cantilevered, then one set of end windings is also exposed. While not as free to stator cooling as an open frame with an inside rotor, the added rotor cooling may provide an advantage despite the increased rotor losses in a high-speed machine.

Cooling the stator with a closed, liquid cooling system becomes more difficult for two reasons. First, as the surface area for cooling is at the minor diameter of the stator core, the surface area for a cooling jacket is reduced, making a cooling jacket less effective. In addition, any cooling system with embedded tubes in the slots or stator core must either have its inlets and outlets on the same side, or one of the ports must be through the stator shaft, complicating the mechanical construction.

Open cooling systems are similarly complicated by the construction, as any coolant that enters the enclosed side will be trapped by the rotor and generate additional friction. Because the rotor will centripetally accelerate the coolant, the rotor construction can include features to aid in extracting the coolant from the air gap, although again, this still increases drag over a system where the coolant is isolated from the rotor.

5.1.2. Axial-Flux

Axial-flux machines have larger end windings at the OD than the inner diameter (ID), resulting in more loss at the OD, but the OD is also closer to the cooling source, presenting a possible advantage for cooling the end windings. Further, in a single-stator, single-rotor design, both the stator yoke and one rotor face are exposed to the environment in an open-frame machine, providing improved cooling to the rotor. However, in an arrangement with multiple stators, e.g., a two-stator, one-rotor configuration, the rotor surface is almost entirely obscured by the two stators, making rotor cooling particularly challenging.

There are two considerations for a closed liquid cooling system. First, a stator-attached cooling jacket is less effective because, in the axial-flux case, a stator-attached cooling plate cannot leverage the high pressure developed by a radial interference fit. As a result, the thermal impedance to the cooling plate in an axial-flux machine is higher than the thermal impedance to the cooling jacket in a radial-flux machine. Second, any embedded tubes in the radial direction must either exit back through the machine’s OD or through the center shaft, increasing the mechanical complexity. However, if heat pipes can be used to extract heat to the outer diameter of the machine, there is a sufficient surface area to reject heat to the environment.

In an open cooling system, the rotation of the rotor naturally propels coolant centripetally outward, away from the air gap. Thus, the risk of coolant accumulating in the air gap is low, unless excess coolant is perpetually being directed to the air gap, although any incident coolant will still produce drag. Meanwhile, the larger losses in the OD endwindings provide a similar advantage compared with the air-cooled system.

5.2. Winding Configuration—Concentrated vs. Distributed Windings

In a machine with concentrated windings, the total endwinding length is reduced, reducing the total winding loss. This reduces the net load on the cooling system, which is generally loaded more than in a slower machine. Moreover, the simple geometry of a concentrated winding makes insertion of heat pipes or coolant tubes easier when compared to distributed windings. Thus, concentrated windings provide better cooling options for high-speed machines.

5.3. Rotor

The selection of rotor architecture has a role in the cooling system for two reasons. First, the rotor losses are dependent on the rotor type and the design details, so the rotor design affects the amount of cooling required. Second, the rotor architecture can also affect the cooling system itself.

5.4. Induction Machines

Induction machines are attractive for high-speed applications because their rotors are very robust. However, induction machines also have high rotor losses that increase with frequency, and the skin effect increases the loss in the rotor conductors. Solid rotor designs are attractive for their mechanical integrity, but also produce large losses at high speeds.

Aside from the losses, induction motor rotors are generally amenable to any of the available cooling systems, and they offer few, if any, additional challenges unique to induction motor rotors.

Reluctance Machines

Reluctance machines (both switched reluctance and synchronous reluctance) have losses that are dependent on the flux space harmonics in the air gap, which increase with frequency. These harmonics are reduced with synchronous reluctance machines, and can be further mitigated with the use of low-loss electrical steels.

Like induction machines, the cooling challenges are not further complicated by reluctance rotors beyond the above discussion.

5.5. Permanent Magnet Machines

In a permanent-magnet machine, two architectures are common: Surface-mounted permanent magnets (SPM) and interior permanent magnets (IPM). SPM machines produce trapezoidal back electromotive force (EMF), and therefore, increase the core losses in the stator compared to IPM machines. In addition, magnets in an SPM are exposed to space harmonics from the stator. In small, high-speed machines, where concentrated windings and open slots are often selected, the space harmonics create flux harmonics in the magnets of an SPM.

As a consequence, SPM magnets in high-speed machines will have eddy current losses if they are conductive, such as solid rare earth magnets. Bonded rare earth magnets have less conductivity but lower flux densities, and ferrite magnets are non-conductive but also have very low flux densities. Ultimately, the magnet selection in an SPM affects the losses in several places in the machine, and also affects the machine size, both due to the surface area required to reject the losses and also the magnetic flux density from the magnets.

Finally, an SPM requires the magnets to be adhered to the rotor surface, but at high speeds, the adhesive may not be strong enough to retain the magnets, and bonded magnets may not be strong enough to maintain their structural integrity. As a result, high-speed SPM machines are often wrapped with banding or encased in a sleeve. Maintaining the mechanical air gap then increases the magnetic air gap, reducing the air gap magnet flux, and therefore, making the machine larger. The banding itself is frequently made of conductive material, and so the banding choices compared with conventional machines are limited, and non-conductive banding is often thicker than using metal banding. Finally, the banding also impedes the cooling of the rotor [97], as it provides an additional thermal barrier between the rotor and the air gap, which is the primary cooling surface unless the rotor is cooled internally. Moreover, the banding may limit the direct cooling options (e.g., it may not be possible for the rotor to act as a centrifugal pump for coolant if the rotor is banded).

While an IPM still has structural integrity challenges, it offers advantages to the SPM for high-speed machines. The mechanical concern for an IPM in high-speed machines is that the structural support bridges (see Figure 12) must be strong enough to retain the magnets while small enough to prevent shorting of the magnet flux. The same concerns are present in low-speed machines, but the increased stresses in high-speed machines make the problem more consequential. Even so, if additional banding is required, it is thinner, reducing the net impact on the machine and the cooling system. The recession of the magnets from the surface reduces the induced eddy currents, allowing more conductive (and stronger) magnets to be used in the machine while also reducing loss. Only an SPM with ferrite magnets would have less loss, as the IPM has laminated steel exposed to the air gap space harmonics.

6. Existing Design Summary and Example Design Process

The combinations of architectures and cooling systems, and considerations for high-speed operation, are numerous, and a summary listing is informative when narrowing down the design choices.

Table A1. Option 2—list of high-speed machines, architectures, and cooling methods.

Source	Citation	Speed	Power	Rotor Type	Cooling Method
Schiefer, M	[100]	15 krpm	70 kW	IPM	Cooling jacket
Schiefer, M	[100]	15 krpm	70 kW	IPM	Embedded tubes in windings
McLaren	[101]	15 krpm	100 kW	SPM	Embedded tubes in windings
Tesla	[102]	18 krpm	190 kW	SPM	Embedded tubes in windings
Xu, Z	[89]	32 krpm	45 kW	SPM	Direct stator cooling with air gap sleeve
Venturini, Giada	[103]	22 krpm	245 kW	IPM	Embedded in windings
Luo, Hao	[104]	20 krpm	100 kW	SPM	Open forced air
Huang, Ziyuan	[105]	32 krpm	100 kW	Induction	Open forced air
Duan, Chongwei	[50]	18 krpm	120 kW	SPM	Evaporative cooling jacket
Dong, Baotian	[106]	60 krpm	30 kW	SPM	Open forced air and cooling jacket
Choudhary, Dikhsita	[42]	20 krpm	150 kW	SPM	Open forced air and cooling jacket
Qi, Zhenning	[107]	30 krpm	30 kW	SPM	Cooling jacket
Nagorny, A.S.	[108]	50 krpm	7 kW	SPM	Radiation on rotor; convection on stator
Wang, Xiaoguang	[109]	24 krpm	150 W	SPM	Convection
Jankowski, B.	[110]	18 krpm	100 W	SPM	Convection
Zhang, Leyue	[37]	10 krpm	30 kW	SPM	Enclosed, forced air
Meier, Matt	[1]	80 krpm	500 W	SPM	Direct stator cooling with integrated channel
Hong, Do-Kwan	[111]	100 krpm	3 kW	IPM	Open, forced air
Boxberg, F.	[36]	29 krpm	100 kW	IPM	Open, forced air
Nachouane, A. B.	[14]	500 krpm	100 W	IPM	Convection
Nachouane, A. B.	[14]	70 krpm	120 kW	IPM	Convection
Dong, Jianning	[35]	36 krpm	75 kW	IPM	Enclosed, forced air
Zhu, Gaojia	[31,32]	30 krpm	15 kW	IPM	Enclosed, forced air
Du, Guanghui	[112]	15 krpm	800 kW	IPM	Cooling jacket
La Rocca, A.	[90]	32 krpm	150 kW	SPM	Direct stator cooling with air gap sleeve
Herrault, Florian	[113]	200 krpm	1.9 W	SPM	Open convection

in Appendix A lists machines from literature and industry, provides their power and speed ratings, and identifies their general architecture and cooling methods. All designs except [1] are radial-flux with internal rotors.

From this list, few high-speed machines are produced in anything but the traditional radial-flux arrangement, and few use classic direct cooling, although some do use a hybrid system where the coolant is excluded from the air gap. Yet, there are ample examples of machines that have been produced successfully with air cooling and indirect liquid cooling.

Therefore, while the listing in Table A1 is thorough, and should help to reduce the number of design choices, many choices still remain. To illustrate how some of the design decisions in a high-speed machine affect the cooling system, a 2 kW, 100 krpm machine design is presented with several general architectures, and each is compared for several cooling system options.

6.1. Electromagnetic Design

A rough machine design was performed for three basic electromagnetic designs. To avoid the complexity of rotor cooling, SPMs with rare earth magnets (even segmented or bonded magnets) were avoided. Thus, an SPM with Y30 (equivalent to C5) ferrite magnets, an IPM with C5 magnets, and an IPM with N40 NdFeB magnets. The IPM machines still will have rotor loss, but it is assumed that this can be minimized by selecting high-quality electrical steel.

For the SPM, in particular, the stresses on the magnet must be considered to determine if banding is required for the rotor. Using the method described in Appendix B.1, for a ferrite magnet with density $4.8{\displaystyle \frac{\mathrm{g}}{{\mathrm{cm}}^3}}$ and radial thickness 2 mm on a 10 mm shaft, the radial stress is roughly 10 MPa. This is the same order as the maximum stress from a typical magnet adhesive. Moreover, although the shear stress for a high-speed machine like this is often trivial (less than 100 kPa in our example), it was not included as part of the calculation, so rotor banding must be added.

To provide a 1.5× safety factor from the banding, the banding must have an additional 7 MPa applied radially to the magnets. From Appendix B.2, using Poly Glas®H200 kevlar banding, manufactured by Von Roll [98], the required banding thickness is less than two layers thick, so the banding will be increased to 0.5 mm (two layers) to ensure banding integrity.

Each machine was designed to be evaluated with three cooling systems: A convection cooling system, a forced air cooling system, and a closed liquid cooling system; each of these will be fitted to the OD of the stator, and the machine housing will be closed on the end bells.

Table 2. Magnetic and mechanical design parameters.

Design Parameter	Ferrite SPM	Ferrite IPM	NdFeB IPM
Br (T)	0.39	0.39	1.25
Mechanical Air Gap (mm)	0.5	0.5	0.5
Banding Thickness (mm)	0.5	NA	NA
Magnet Thickness to Electrical Air Gap Ratio	0.5	0.5	0.6
Air Gap Length/Diameter Ratio	1	1	1

and

Table 3. Cooling and applied current design parameters.

Design Parameter	Convection	Forced Air	Liquid Jacket
Copper Current Density (A/mm2)	3	6	12
Linear Air Gap Current Density (A/mm)	30	60	120

show the basic design parameters for each design architecture and cooling system.

The SPM machines were designed based on the process presented in [99]. The IPM machines followed a similar process based on the following criteria to provide a more direct comparison between the different designs.

• The magnet thickness in the Ferrite IPM was chosen to reach the same magnetic flux density in the air gap as the SPM.
• The linear current density in the ferrite IPM was chosen so that the net flux density in the core matched the SPM.
• The linear current density in the NdFeB IPM was chosen to match that of the ferrite IPM.

Table 4. Electromagnetic machine dimensions.

Dimension	FSC	FSA	FSL	FIC	FIA	FIL	NIC	NIA	NIL
Stack length (mm)	28.0	22.2	17.7	39.6	31.5	25.0	27.7	22.0	17.5
Total length (mm)	52.9	43.2	35.3	66.3	53.5	43.1	47.5	38.4	31.1
Stator outside radius (mm)	38.4	32.7	28.0	38.1	31.8	26.6	28.8	24.2	20.4
Air gap mean radius (mm)	14.0	11.1	8.82	19.8	15.7	12.5	13.9	11.0	8.73
Magnet volume (mL)	13.0	6.02	2.75	37.5	17.4	7.9	11.3	5.03	2.16
Coil volume (mL)	97.2	62.5	40.3	62.9	40.1	25.5	31.3	20.0	12.8
Total volume (mL)	244	145	86.8	303	170	95.9	124	70.5	40.5
Weight (g)	1070	616	359	1540	834	455	631	343	189

shows the final machine dimensions for each design, with dimensions illustrated in Figure 13. The design acronyms are designated in

Table 5. Electromagnetic machine acronym identifiers.

Machine	ID
Ferrite SPM, Convection	FSC
Ferrite SPM, Forced Air	FSA
Ferrite SPM, Liquid	FSL
Ferrite IPM, Convection	FIC
Ferrite IPM, Forced Air	FIA
Ferrite IPM, Liquid	FIL
NdFeB IPM, Convection	NIC
NdFeB IPM, Forced Air	NIA
NdFeB IPM, Liquid	NIL

.

6.2. Assessing the Cooling Systems

Assuming the rotor losses to be negligible, the stator losses were estimated and reported in

Table 6. Stator losses.

Machine	Tooth Loss	Yoke Loss	Slot Loss	Endturn Loss	Total Loss
FSC	32.4	31.4	4.44	4.31	72.5
FSA	23.2	21.1	11.2	11.3	66.8
FSL	19.8	17.1	18.2	30.0	94.9
FIC	38.0	60.5	3.14	2.52	104
FIA	27.7	39.9	7.91	6.51	81.9
FIL	24.0	31.5	19.9	16.9	92.3
NIC	127	174	1.54	1.28	303
NIA	75.6	94.4	3.87	3.33	177
NIL	47.4	54.5	9.75	8.65	120

.

Assuming the majority of heat is extracted through the stator OD, the general lumped parameter thermal model for the machine is given in Figure 14. Nodes are described in

Table 7. Node descriptions for Figure 14.

Node	Description
1	Endturns
2	Slot Windings
3	Stator Teeth
4	Stator Yoke
5	Stator Housing/Cooling Jacket
6	Coolant

. Nodes are placed at the center of each body, with the exception of the end turns. The end turns were modeled as a double-layer concentrated winding, and the nodes are at the zenith of the endturn arc, at the center of the cross-section.

The thermal impedances to the left of Node 5 were calculated from the stator geometry and the thermal parameters provided in

Table 8. Thermal parameters for lumped parameter calculations.

Parameter	Description	Value
Kst	Steel Thermal Conductivity	45 W/mK
KCu,l	Copper Longitudinal Thermal Conductivity	200 W/mK
KCu,t	Copper Transverse Thermal Conductivity	2 W/mK
hjacket	Thermal Transfer Coefficient, Stator to Jacket	2 mW/mm2K
hslot	Thermal Transfer Coefficient, Windings to Stator	0.2 mW/mm2K

. The nine models were then evaluated based on this thermal circuit to determine the required temperature at Node 5 in order to keep the endturn temperature below 180 °C, the maximum temperature for class H insulation. The results are provided in

Table 9. Maximum jacket temperatures.

Machine	Tmax, °C
FSC	162
FSA	138
FSL	53
FIC	167
FIA	153
FIL	105
NIC	133
NIA	130
NIL	97.6

.

To the right of Node 5, $R_{jc}$ is derived from the stator outer geometry and the Nusselt number. For the air-cooled designs, the temperature source is the temperature of the environment, while for the closed liquid cooling system, it is the average coolant temperature in the cooling channel.

The thermal circuit to the right of Node 5 is dependent on the coolant flow and surface area at the coolant interface. Each cooling system is evaluated as described in the following subsections.

Convection

For convection, the machine was assumed to be mounted horizontally. Using the method described in Equation (A6), the Nusselt number, h is calculated between the surface of the machine and the air, and the required surface area for each of the designs was calculated.

6.3. Forced Air

In each of the forced air cases, the required air velocity to maintain the maximum machine temperature was calculated using the Nusselt number calculated according to Appendix C.2.

6.4. Liquid Cooling

For an enclosed cooling jacket, the channel was set to roughly a 4:1 width/length ratio, the full active width of the stator. In the liquid-cooled cases, the required flow velocity and volumetric flow to maintain the maximum machine temperature were calculated using the Nusselt number in Appendix C.3.

6.5. Cooling System Results

For the nine designs, the three liquid-cooled machines were able to be cooled with the available outer surface area. None of the air-cooled designs were functional without providing fins for improved thermal transfer to the air, but some of the designs were potentially viable.

Table 10. Summary of cooling system requirements.

Machine	Required Coolant Surface Velocity ($\frac{\mathbf{m}}{\mathbf{s}}$)	Volumetric Flow ($\frac{\mathbf{mL}}{\mathbf{min}}$)	Required Surface Area (%)
FSC	NA	NA	8.1
FSA	5	NA	4.2
FSL	0.3	1400	1
FIC	NA	NA	8.0
FIA	5	NA	3.2
FIL	0.04	94	1
NIC	NA	NA	52.5
NIA	10	NA	9
NIL	0.13	149	1

provides the required air or coolant speed and added surface area as a ratio to the original outer machine cooling surface. The volumetric flow rate is provided for the liquid-cooled machines.

The two air-cooled designs with rare earth magnets are not viable due to their high air flow and surface area requirements. The remaining machines all could be built and kept cool with, at minimum, a finned housing. In each case, there is no cooling from the end turns to the environment, either directly or through the housing. As a result, any added air flow would improve these designs.

Ultimately, the specific design is dependent on many factors, including cost and coolant availability. However, the basic design comparison highlights a few considerations.

First, the advantage of neodymium-iron-boron (NdFeB) magnet designs wanes as speeds increase, and not only due to their potential for increased magnet losses. As speeds increase, the loss distribution shifts toward the steel cores in the machine, and so NdFeB machines have higher stator core losses than ferrite machines. Because the flux densities are higher, they are also smaller—an advantage of rare earth magnets. However, if the cooling system cannot reject the heat as designed, the machine must be made larger to reduce loss and increase surface area, offsetting the size advantage.

Second, the proposed cooling jacket had a 4 mm radial thickness, leaving a 1 mm wall. This is approaching the practical limit for fabrication and may also not be manufacturable to achieve the assumed contact pressure with the stator yoke. On the other hand, by increasing the forced air flow, the required increase in surface area can be further reduced. In the case of FIA and FIL, the ultimate radius of FIL with the cooling jacket is 30.6 mm, while FIA has an outer radius of only 31.8 mm without the added fins. If the fins are incorporated into the lamination stack, and the air flow is increased to 10 m/s, the ultimate outer radius of FIA could be kept within 33 mm. Thus, due to the minimum manufacturing limits of the cooling jacket, the air-cooled design may be similar in size to the liquid-cooled design.

Comparing the SPM to the IPM, the banding in the rotor is a disadvantage to a small, high-speed machine. While the machines were designed for the same flux densities, the larger electrical air gap in the SPM machines required more slot current to produce enough q-axis flux, ultimately requiring larger slots. The advantage of the cooling system in IPM designs is that the slots are smaller and the teeth are shorter and wider, producing a lower-impedance path from the coils and teeth to the cooling source.

7. Conclusions

The demand for high-speed machines is expanding due to their lighter weight and smaller size for the same power, and new technologies have overcome the reduced efficiency, increased stresses, and limitations in manufacturing that accompany small, fast machines. Furthermore, a cooling system for a high-speed machine takes into consideration factors beyond those of a low-speed machine, and new methods have been developed to meet the increased cooling requirements.

Specifically, advances in air cooling, indirect liquid cooling, and direct liquid cooling have made each general cooling type viable for high-speed machines. New fan designs and improved manufacturing have allowed air flow through machines in new ways. Improved manufacturing has allowed the circulation of coolant through the stator and rotor in an indirect system. Advances in construction have enabled direct coolant contact with the machine while still containing the coolant, providing the benefit of direct cooling in a closed-cooling system. Each of these has proven promising for use in various high-speed machine architectures, despite their differences in efficacy.

Yet, the continued advancement of high-speed machine technology requires further improvement to cooling, which can only be achieved when the cooling system design is an integral part of the machine design process. This paper has established, through analysis, the interrelationship between the electromagnetic design and thermal design for high-speed machines, and reinforced this relationship through a collection of example designs. Fundamental architecture decisions, such as rotor structure, pole count, magnet material, cooling fluid, and cooling application, all affect the final machine dimensions and weight for a given power and speed target, and must be considered in concert.

The finding is that, for high-speed machines, the most effective system might not be achieved via rare earth magnets and direct cooling, although these would produce the most compact machine at low speeds. Therefore, designers should not split responsibilities for thermal management and electromagnetic design. Instead, they should apply a unified approach, considering both the electromagnetic design and thermal system from the very beginning of the design process.

Finally, while high-speed machines present unique challenges to cooling, as technology advances, the range of viable options will continue to expand, increasing the importance of the machine designer’s integral knowledge of cooling systems.