Design and analysis of a novel hybrid cooling method of high-speed high-power permanent magnet assisted synchronous reluctance starter/generator in aviation applications

Hong GUO, Xu HE, Jinquan XU,*, Wi TIAN, Xiaong DING,Laicai JU, Dhong LI

a School of Automation Science and Electrical Engineering, Beihang University, Beijing 100083, China

b Science and Technology on Aircraft Control Laboratory, Beihang University, Beijing 100083, China

c Ningbo Innovation Research Institute, Ningbo 315800, China

d School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China

e Beijing Shuguang Aviation Electric Co.LTD, Beijing 101300, China

f Aviation Industry Helicopter Design and Research Institute, Jingdezhen 333001, China

KEYWORDS Air gap friction loss;Oil spray cooling;Permanent magnet assisted synchronous reluctance starter/generator;Thermal analysis;Thermal network model

Abstract To improve the heat dissipation performance,this paper proposes a novel hybrid cooling method for high-speed high-power Permanent Magnet assisted Synchronous Reluctance Starter/Generator (PMaSynR S/G) in aerospace applications.The hybrid cooling structure with oil circulation in the housing, oil spray at winding ends and rotor end surface is firstly proposed for the PMaSynR S/G.Then the accurate loss calculation of the PMaSynR S/G is proposed, which includes air gap friction loss under oil spray cooling,copper loss,stator and rotor core loss,permanent magnet eddy current loss and bearing loss.The parameter sensitivity analysis of the hybrid cooling structure is proposed, while the equivalent thermal network model of the PMaSynR S/G is established considering the uneven spraying at the winding ends.Finally, the effectiveness of the proposed hybrid cooling method is demonstrated on a 40 kW/24000 r/min PMaSynR S/G experimental platform.

1.Introduction

The starter/generator is the core component of the power supply system in aviation applications.1,2The electrical machine with the characteristics of high power, high efficiency, high power factor and anti-short circuit capacity has attracted much attention in modern-aero-starter-generator fields,3–6and the PMaSynR machine is one of the required electrical machine choices.The PMaSynR S/G is characterized by a high-speed synchronous reluctance rotor topology by embedding permanent magnet, which has the advantage of high power density,high efficiency and high power factor.Furthermore, the PMaSynR S/G has the excellent anti-short-circuit capacity by the reasonable design of permanent magnet.However,with the increasing electrification of airborne equipment,the electrical power capacity of the PMaSynR S/G has increased remarkably, which also results in the significant increase of the machine loss.As a result, the heat dissipation design has become increasingly important for the high power PMaSynR S/G in aerospace applications.

In the past,considerable efforts have been conducted on the cooling methods of the starter/generator,which mainly include air cooling, oil circulation cooling in the housing, oil circulation cooling in stator slots,hollow shaft oil cooling,etc.Compared with the air-cooling method,the oil cooling method has the better heat dissipation performance, which helps to improve the power density of the starter/generator.In Refs.7–10, the housing oil circulation cooling methods with different spiral oil paths have been proposed to improve the heat dissipation of the machine.In Ref.11, a direct oil cooling method in stator slots was proposed by constructing an oil path in the slots with heat-conducting epoxy resin to improve the cooling performance of the traction motor,which was also verified by a 50 kW traction motor.In Ref.12,the oil cooling method by inserting cooling tubes into slots was proposed for an external rotor Permanent Magnet Starter/Generator(PMS/G).To solve the rotor overheat issue, the hollow shaft based oil cooling method was proposed to enhance the heat dissipation of the motor rotor.13,14The oil spray cooling has been a new emerging heat dissipation technology in electrical machine field in recent years, which is characterized by direct oil spray on the heating part.In Refs.15,16, the oil spray cooling method for the winding ends was proposed for a hairpin motor, in which the cooling effect of full cone nozzle and hollow cone nozzle was experimentally compared.However,there is little literature on the oil spray cooling of the PMaSynR S/G in aerospace applications.

Furthermore, the accurate thermal analysis is the essential tool for predicting the temperature distribution and heat dissipation of electrical machines,which can be mainly divided into three categories: Lumped Parameter Thermal Network(LPTN) method, Finite Element (FE) method and Computational Fluid Dynamics (CFD) method.The LPTN method has the simple structure and low computation burden, which has been widely applied to the thermal analysis of electrical machines.But its accuracy relies on the system parameters.In practical engineering, there inevitably exist various uncertainties due to materials properties, manufacturing tolerances and assembly process, which will cause the accuracy degradation of the LPTN method.17,18The FE method has the good robustness to the uncertainty,which can improve the accuracy of the thermal analysis.But it has the high computation cost,which cannot address the thermal analysis issue involving the fluid dynamics.19The CFD method can be accurate and offer more insights in the fluid dynamics behaviors of the thermal analysis of electrical machines,which also cost more computational time and efforts.20In aerospace application,the oil cooling method is generally adopted in the PMaSynR S/G for the requirement of the high power density.However, the accurate thermal analysis of the aerospace PMaSynR S/G is lacking,which remains a challenging problem.

This paper proposes a novel hybrid cooling method for high-speed high-power PMaSynR S/G in aerospace applications.The main contributions are fourfold.First, the hybrid cooling structure with oil circulation in the housing, oil spray at winding ends and rotor end surface is proposed for the PMaSynR S/G, which has the excellent heat dissipation performance.Second, the accurate loss calculation of the PMa-SynR S/G is proposed, especially, the air gap friction loss calculation under oil spray cooling.And the air gap friction empirical equation has been revised with the consideration of oil spray cooling.Third, the thermal network model of the PMaSynR S/G is established considering the uneven spray condition at the winding ends.The parameter sensitivity analysis of the hybrid cooling structure is proposed,which includes the flow rate distribution of two oil inlet paths, the nozzle number, the nozzle aperture, the flow rate, and the distance of nozzles to the spray surface.Finally, the effectiveness of the proposed hybrid cooling method is demonstrated on a 40 kW/24000 r/min PMaSynR S/G experimental platform.The results show that the proposed hybrid cooling method has the excellent cooling performance.

2.Hybrid cooling method for PMaSynR S/G

2.1.PMaSynR S/G topology

To meet the requirements of high power density, high speed and high reliability of aviation main power supply system,this paper proposes a novel PMaSynR S/G topological structure as shown in Fig.1.

The rated generation power is 40 kW@24000 r/min.The PMaSynR S/G adopts 24-slots/4-poles and double-layer structure with the dual-three-phase winding of 30° phase shift.In addition, the rotor core employs a topological structure of three-layer U-shaped magnetic barrier embedded with permanent magnet, which can enhance both electromagnetic and mechanical performance.Meanwhile, the ratio of shortcircuit current to rated power generation current is less than 1.As a result, the PMaSynR S/G will not cause the overheat issue during the short-circuit fault.The design specification of the PMaSynR S/G is shown in Table 1, while the corresponding design parameters are listed in Table 2.

Fig.1 PMaSynR SG topological structure.

2.2.Hybrid cooling method

For the high-speed high-power PMaSynR S/G,apart from the loss of stator core and winding, the loss caused by permanent magnet eddy current and air gap friction cannot be ignored.The traditional oil circulation cooling in the housing has the good heat dissipation for slot phase windings, while the cooling performance of the winding ends and the rotor core is poor.Although oil spray at winding ends can evidently reduce the temperature of the winding ends, the oil spray cooling method requires nozzles and connection device, which increases the structural complexity.Furthermore,the oil spray cooling from the hollow shaft cannot be applied for the highspeed PMaSynR S/G due to the friction and oil leakage between the tube and the hollow shaft.Therefore, this paper proposes a novel hybrid cooling structure with oil circulation in the housing,oil spray at winding ends and rotor end surface,which is shown in Fig.2, including 2 oil inlet paths and 1 oil outlet path.

The detailed structure of the oil inlet path 1 is shown in Fig.3, which consists of oil inlet 1, axial spiral hollow tube in the housing and oil spray nozzles through the first and last layer of the tube.The oil enters the tube from the oil inlet 1.A part of the oil sprays through the first layer oil nozzles, while the remaining part continues to flow in the tube and sprays through the last spiral layer oil nozzles.The nozzles are aligned with the front and back winding ends and evenly distributed along the circumferential direction.The structure of oil circulation in the housing and oil spray at the winding ends eliminates the oil nozzle devices, which can improve the power density of the PMaSynR S/G.Note that the end of the last layer spiral hollow tube of the oil path 1 is sealed,and no additional oil return path is set.The oil in the spiral hollow tube is finally sprayed from the nozzles.The process of oil flowing through the spiral hollow tube of oil path 1 can be regarded as the oil circulating cooling of in the housing.The process of oil spray from the nozzles to the winding ends and rotor end surface can be regarded as spraying cooling.

The oil inlet path 2 consists of the horizontal guidance tube in the housing and the L-shaped guidance tube in the front and rear end cap.The oil enters the horizontal and L-shaped oil guidance tube from the oil inlet 2 and sprays through the oil nozzles.The nozzles are aligned with the front and rear rotor end surface.

Oil return path consists of oil return inlet, oil return chute and oil return outlet at the bottom of the PMaSynR S/G shown as the blue block in Fig.3.The oil return outlet is connected with oil tank by oil return tube.

Table 1 Design specification of PMaSynR S/G.

Table 2 Design parameters of PMaSynR S/G.

Fig.2 PMaSynR S/G cooling structure.

The oil state and behavior should be discussed before analysis.The oil flowing through the spiral hollow tube of the oil path 1 and the horizontal guidance tube in the housing and the L-shaped guidance tube of the oil path 2 is in the state of liquid.The oil sprayed to the winding ends and rotor end surface is nearly all in the state of liquid, and little is in the state of gas due to evaporation of the liquid.During the analysis, the oil in the state of gas has little ratio of the total oil,and can be ignored.Therefore,only the heat exchange between oil in liquid state and winding ends and rotor end surface is considered.

Fig.3 Oil inlet path 1.

The spray process can be described as follows.All the oil is sprayed to the winding ends and rotor end surface first, and becomes oil mist.Due to the effect of gravity, the oil drops from the winding ends and rotor end surface to the bottom of the PMaSynR S/G.Then, the oil flows into the oil return chute from oil return inlet.Finally, the oil flows from the oil return outlet to the oil tank by a centrifugal pump to complete the oil recovery.

The proposed hybrid cooling method combines the advantages of oil circulation cooling and oil spray cooling,simplifies the cooling structure and improves the power density.In addition, there is no contact between the nozzles and the rotor when spraying on rotor end surface.The reliability of the PMaSynR S/G can be improved as well.

3.Loss calculation of PMaSynR S/G

The loss calculation is the premise and basis of thermal design and analysis of the PMaSynR S/G.The operation conditions of the PMaSynR S/G mainly include the following 4 states:constant torque starting state, constant power starting state,power generation state and short circuit fault state.Since the current of short-circuit fault is less than that of the rated power generation in the proposed PMaSynR S/G, its loss is much lower than that of the rated operation condition.Therefore,only the first three states need to be considered in loss calculation.The operation point with the most serious heating in each state are selected for analysis, namely 20 N?m@6000 r/min constant torque starting(State I),12.56 kW@12000 r/min constant power starting (State II) and rated power generation 40 kW@24000 r/min (State III).Furthermore, the loss types of the PMaSynR S/G mainly include core loss, copper loss,permanent magnet eddy current loss, bearing friction loss and air gap friction loss.Especially, the air gap friction loss calculation needs the consideration of spray cooling effect,which is introduced as follows.

3.1.Air gap friction loss considering oil spray effect

The air gap friction loss Pfis generated by rotor rotation.If the air is dry,the air gap friction loss is defined as the basic air friction loss Pair.Since the oil in the spray process is mixed into the internal air of the PMaSynR S/G in the state of atomization, the air becomes humid, and the loss caused by this is defined additional friction loss Padd.That is,

where k is the roughness coefficient of the rotor surface.For smooth rotor surface, k = 1.Here ρa(bǔ)iris the air density,Δρ is the difference value of oil mist density ρoiland air density ρa(bǔ)ir, ω, r and l are rotor angular velocity, rotor radius and rotor axial length,respectively,Cfis the gas friction coefficient,Reδis the radial Reynolds coefficient,Reais the axial Reynolds coefficient.Furthermore, Cf,Reδand Reacan be calculated as

where, δ is the air gap thickness, ρ is the gas density, μ is the gas dynamic viscosity, and v is the axial ventilation velocity.Since there is no axial ventilation for the proposed PMaSynR S/G, Reαcan be ignored.

Note that Paddis mainly associated with oil mist density and dynamic viscosity,which is difficult to be obtained by simulation, due to the unknown influence of different oil spray flow rate.As a result, this paper proposes the air gap friction loss calculation considering the oil spray effect by means of experimental test.

For the experiments, a torque sensor is installed on the shaft of the PMaSynR S/G to test the no-load torque at different speeds and flow rates.Then the no-load loss can be calculated as shown in Fig.4, which includes no-load core loss,bearing loss and air gap friction loss, where Q is flow rate in Fig.4.

Since the no-load core loss and the bearing loss are not affected by the flow rate.The no-load loss at different flow rate is compared with that at 0 L/min (dry air), and then Paddat different flow rates can be obtained as shown in Fig.5.

Therefore, Pfat different flow rates can be calculated according to the empirical equation and experimental test results as shown in Table 3.

According to the experimental data,the oil mist density ρoiland oil mist dynamic viscosity μoilat different flow rates can be obtained as shown in Fig.6.

Furthermore, the relationship between ρoil, μoiland flow rate Q can be formulized as

Fig.4 No-load loss at different flows and speeds.

Fig.5 Padd at different flows and speeds.

Table 3 Pf at different states and flow rates.

Fig.6 Relationship between ρoil, μoil and flow rate.

3.2.Other loss calculation

The other loss mainly consists of copper loss, stator and rotor core loss, permanent magnet eddy current loss and bearing loss.

For the copper loss calculation, considering the skin effect and the proximity effect, the total copper loss can be represented as

Fig.7 Comparison of Padd of fitting curves and experiment.

where I is the phase current RMS value, rris the phase resistance,kdis equivalent resistivity, Inis the multi-harmonic current, kd(2n-1)is the resistivity coefficient of the harmonic current.The relationship between resistivity coefficient kdand frequency is shown in Table 4.21

Note that with the increase of frequency,kdincreases sharply.Therefore, the total copper loss PCucan be calculated as shown in Table 5.

The loss of stator and rotor consists of hysteresis loss,eddy current loss and additional loss.Generally, when magnetic density is sinusoidal, the classical calculation model of core loss, namely Bertotti loss separation calculation model22,23can be adopted.In this paper, the flux density distribution of the stator and rotor can be calculated by finite element method, which is with the consideration of the magnetic field saturation.And then, the stator and rotor loss can be calculated by the Bertotti classical formula.Meanwhile, the permanent magnet loss can also be obtained by the FE analysis.

The bearing friction can be calculated as

where Pbis the bearing loss,M0is no-load bearing friction torque,M1is load bearing friction torque,ω is the angular velocity, f0is the coefficient of bearing lubrication types, vμis kinematic viscosity of lubricating material, Dmis bearing diameter, f1is coefficient of the bearing type and load, Fβis the load torque.

After calculation, each part of the PMaSynR S/G loss is shown in Table 6.

4.Parameter sensitivity analysis of hybrid cooling method

In the process of design of hybrid cooling structure, the number of nozzles at the single/dual sides of winding ends and single/dual sides of rotor end surface, the nozzle aperture at winding ends and rotor end surface, the flow rate and the distance of nozzles to the spray surface at winding ends and rotor end surface are indispensable parameters.These parameters are closely related to the PMaSynR S/G cooling effect and the efficiency.However,the influence law and influence degree of these parameters on the cooling effect and efficiency is not clear.Therefore, it is necessary to make parameter sensitivity analysis.The parameter sensitivity analysis is defined as the influence degree of the studied parameters on the PMaSynR S/G temperature change in this paper.

Table 5 Multi-harmonic current of PMaSynR S/G.

Table 6 Each part of PMaSynR S/G loss.

The parameter analysis of the hybrid cooling method is proposed in this section, which includes (A) the flow rate distribution of two oil inlet paths, (B) the number of nozzles at the single/dual sides of winding ends and single/dual sides of rotor end surface, (C) the nozzle aperture at winding ends and rotor end surface, (D) the flow rate, and (E) the distance of nozzles to the spray surface at winding ends and rotor end surface.

4.1.Thermal network model considering uneven spray condition

Based on the spray cooling model in Motor-CAD, this paper firstly proposes the improved thermal network model of winding ends considering the uneven spray at winding ends, as shown in Fig.8.Here leis the slot winding extension length,lweis 1/2 of the cross-slot winding length,wweis the equivalent width of one layer winding,hweis the equivalent height of one layer winding.Note that the even spray or uneven spray at the winding ends mentioned in this paper refers to the even spray on the upper surface of the winding ends(later referred as even spray) or uneven spray (later referred as uneven spray), the heat transfer among other areas of the winding ends mainly depends on heat conduction with winding and convection with air.The thermal resistance of the winding ends is mainly considered in the analysis of four kinds.For even spray,RWE-SPis the convection resistance with the oil spray, RWE-WEis the cross-slot lweconduction resistance, RWEis the slot- extension conduction resistance of le, RWE-Fis the convection resistancewith the air.For uneven spray, RWEis divided into RWEaand RWEb,RWE-WEis divided into RWE-WEaand RWE-WEb,RWE-Fis divided into RWE-Faand RWE-Fb.The distribution rule of thermal resistance equivalence is based on the ratio of sprayed area and unsprayed area.In addition, Sspis the spray cooling source,SCu1,SCu2,SCu3are the copper loss sources in different areas.

Table 4 Relationship between kd and frequency21.

In order to independently analyze the even and uneven spray cooling at the winding upper surface, we assume that x nozzles at one side winding ends are used to achieve even spray cooling, while the total area covered by spraying is A.When the number of nozzles is less than x, the relationship between the total area covered by spraying AN, and the number of nozzles N is as follows:

where, symbol‘‘//”means the thermal resistances are calculated in parallel.

The copper loss PCulegenerated by the part of the slot winding extension le.can be calculated as,

According to the winding structure of the PMaSynR S/G,RWEcan be equivalent to 48 parallel cross-slot winding ends resistance RWE1, which can be calculated as

Furthermore, RWEa, RWEbcan be calculated according to the spray coverage ratio.Similarly, RWE-F, RWE-Fa, RWE-Fb,RWE-WE, RWE-WEa, RWE-WEbcan be calculated according to the thermal resistance equivalent of spray coverage ratio.

The winding ends thermal network model with the consideration of uneven spray cooling condition is integrated into Motor-CAD, and LPNT model is established as shown in Fig.9.For even spray, the winding ends thermal network model in Fig.8(b) is adopted.Here ?is cooling or heating source, R is thermal resistance, and defined in Appendix B.Compared with the traditional oil circulation cooling in the housing,this paper adopts the oil spray cooling at the winding ends and rotor end surface on basis of it.

For the proposed PMaSynR S/G, the heat transfer of the components is by way of thermal conduction resistance between each other.The heat transfer of stator core, winding ends,rotor core,housing and end cap is by way of convection with oil/air.The oil in the hollow tube of the housing is convection heat transfer with the housing.The housing and end cap heat transfer with the outside environment is by convection and radiation.Considering the difference of the axial structure of the PMaSynR S/G, the housing can be divided into three parts of the front, middle and rear, in which each part is equipped with the oil circulation cooling source.The winding can also be divided into three parts of the front winding ends, slot winding and rear winding ends.The oil spray cooling source is set above the front and back winding ends.The rotor is divided into two parts,and each rotor end surface is equipped with the spray cooling source.Heat source of stator core, rotor core, winding, permanent magnet, air gap and bearing are set on the corresponding nodes.During the calculation process of spray cooling, the relationship between Nusselt number NuL, Prandtl number Pr, the aperture of spray nozzle d,area weighting Ar,and the length between the nozzle to the heat source surface L can be represented as

Fig.8 Winding ends structure and thermal network model.

Fig.9 LPTN of uneven spray cooling condition.

The spray cooling effect of the PMaSynR S/G can be judged by the convection coefficient at the spray area.The relationship between the convection coefficient hLand NuLis,

where LLis the characteristic length and koilis the oil mist thermal conductivity.Next, the parameter sensitivity analysis of convection coefficient, Nusselt number, convection heat transfer coefficient on the cooling performance of the proposed PMaSynR S/G will be conducted in the following.

4.2.Flow rate distribution

Since there are two oil inlet paths in the proposed hybrid cooling structure,the flow distribution of each path on the cooling performance will be analyzed firstly.

To avoid the interference of other factors, we assume that the total flow rate is 5 L/min,which means the total spray flow rate is 5 L/min.The initial structure conditions are set as follows.The number of the nozzles at front/rear (dual sides)winding ends is 10 along the circumferential direction with aperture of 1.5 mm.The number of the nozzle at front/rear(dual sides) rotor end surface is 1 with aperture of 1.5 mm.The distance between the nozzle and winding ends is 20 mm,while the distance between the nozzle and rotor end surface is 2.5 mm.The oil spray at the winding ends and rotor end surface is even.Since the operating time and loss of PMaSynR S/G are different in the starting and power generation process,the cooling effect should be analyzed separately.

During the short-time starting process,the operating time is generally within 1 min.Assume that the starting process consists of the constant torque 20 N?m starting for 30 s and the constant power 12.56 kW starting for 30 s.The initial oil temperature is 60°C,while the ambient temperature is 40°C.The temperature at different nodes of the PMaSynR S/G with different flow rate distribution can be calculated as shown in Fig.10.When the flow rate of path 1 is 0%, the PMaSynR S/G only performs oil spray cooling at the rotor end surface.When the flow rate of path 1 is 100%,the PMaSynR S/G only performs oil circulation in the housing and oil spray cooling at the winding ends.Here TWIis the average slot winding temperature, TWTis the winding ends temperature near the spray area, TWmaxis the maximum winding temperature, Tsis the average stator temperature, TWJis the average housing temperature,Tris the average rotor temperature,Trmaxis the maximum rotor temperature, Tbis the average shaft temperature.

Note that for the flow rate of path 1 in 0–20%, TWmaxand TWTdecrease with the increase of flow rate.When the flow rate exceeds 20%, the temperature rise of the proposed PMaSynR S/G will not change as the change of the flow rate.

Fig.11 shows the flow rate distribution on the heat transfer coefficient of the proposed PMaSynR S/G during the longtime power generation process, while Fig.12 shows the flow rate distribution on the corresponding cooling performance.The initial oil temperature is 60 °C, the average winding temperature is 80 °C, the stator and rotor average temperature is 70 °C.

Note that the flow rate distribution of two paths has a great influence on the steady-state temperature of rated power generation operation.The proposed hybrid cooling method has the excellent cooling performance with the flow rate of path 1 in 75%–85%.Furthermore, when the flow rate of path 1 is 80%,the maximum winding temperature is 110°C lower than that of rotor end surface spray, and the maximum rotor temperature is 75 °C lower than that of only oil circulation in the housing and oil spray at the winding ends.Due to small rotor end surface spray area and large convection heat transfer coefficient hrotor, only a small ratio of flow rate is needed for path 2 to significantly cool the rotor.Compared with the method of only path 1 cooling, the hybrid cooling method reduces the temperature of the rotor, increases the magnetic performance, reduces the rated current and the copper loss,and improves the efficiency by 0.3%.Compared with the mothed of only path 2 cooling, the hybrid cooling method reduces the winding temperature and the copper loss, and improves the efficiency of 0.6%.

4.3.Number of nozzles

For the analysis of the influence of the number of nozzles on the cooling effect, we assume that the total flow rate is set as 5 L/min, and the flow rate of path 1 is 85%.Only the number of nozzles at winding ends is changed with other initial thermal and structure conditions unchanged.

Fig.10 Temperature comparisons under different flow rate distribution.

Fig.11 Relationship between cooling parameters and flow rate distribution.

Fig.12 Relationship between PMaSynR S/G temperature,efficiency and flow rate distribution.

Fig.13 shows the temperature trajectory of the proposed PMaSynR S/G under different numbers of nozzles at single/dual winding ends.When the number of nozzles at one side of winding ends is more than 10, it is even spray at the upper of the winding ends,otherwise it is uneven spray.Here TWTnspis the average temperature of unsprayed area at the spray side of winding ends, TWTnsis the average temperature of the nozzle=0°C side of winding ends(unsprayed side),Nuwsingleand hwsingleare cooling coefficients of single side winding ends spray, Nuwdualand hwdualare the coefficients of dual sides spray.

Fig.14 shows the temperature trajectory of the proposed PMaSynR S/G under different numbers of nozzles at single/dual sides of rotor end surface.Here Nursand hrsare the cooling coefficients of single side rotor end surface spray,Nurdand hrdare the cooling coefficients at dual sizes.Note that the dual sides at the rotor end surface spray cooling effect is better than single side.When nozzle is 1,the maximum temperature difference of the winding is 5°C,the average temperature difference of the slot winding is 3°C,and the maximum temperature difference of the rotor is 6°C.With the increase in the number of nozzles,the Nusselt number and convection heat transfer coefficient will be decreased.The Nusselt number is positive correlation with the flow rate of the nozzle.For the total flow rate is certain,with the increase of the total nozzle number aligned to the rotor end surface, the flow rate of each nozzle decreases,and the Nusselt number decreases.However, due to the rotation of the rotor, the surface is sprayed evenly by the certain flow rate, the decrease of the Nusselt number leads to worse cooling effect.

Fig.13 Relationship between PMaSynR S/G temperature and nozzles at the winding ends.

4.4.Aperture of nozzles

The aperture of nozzles at the winding ends and rotor end surface is also one of the factors affecting the cooling effect.For aperture of nozzles analysis, considering the actual manufacturing process,the aperture cannot be infinitesimal,so the minimum aperture is selected as 0.5 mm.In addition, when the aperture is too large, the oil spraying through the nozzles becomes oil column rather than oil mist, which leads to the decrease of the spray cooling effect, so the maximum aperture is selected as 3 mm.

Fig.15 shows the temperature trajectory of the proposed PMaSynR S/G under different apertures of nozzles.

Here Nurd,w=1.5mm,hrd,w=1.5mm,are the Nusselt number and convection heat transfer coefficient at rotor end surface with the winding ends nozzles aperture of 1.5 mm,Nuwd,r=1.5mm,hwd,r=1.5mmare the Nusselt number and convection heat transfer coefficient of the winding ends nozzle aperture with the rotor end surface nozzles aperture of 1.5 mm.Note that with the increase of the nozzle aperture,the Nu and h decrease.The nozzle aperture at the end of the winding has little influence on the temperature of PMaSynR S/G.Furthermore, the rotor temperature increases 32 °C by increasing the nozzle aperture at rotor end surface from 0.5 mm to 3 mm.The larger the aperture,the worse the cooling effect at the range of 0.5–3 mm.

4.5.Flow rate

Fig.16 shows the temperature trajectory of the proposed PMa-SynR S/G under different flow rate.With the increase of flow rate, the overall temperature of the PMaSynR S/G decreases.When the flow rate increases from 2 L/min to 6 L/min, the reduction of copper loss is less than the increase of air gap friction loss, which makes the PMaSynR S/G efficiency decrease by 0.13%.From the point of view of efficiency, in the case of meeting the temperature requirements, minimize the flow will achieve higher efficiency.From the point of view of cooling effect,within a certain flow rate range,the greater the flow rate, the better the cooling effect.

4.6.Spray distance

Spray distance from nozzles to the winding ends or to the rotor end surface is mainly limited by the structure of the PMaSynR S/G.The distance from nozzles to the winding ends is mainly influenced by the height of the stator yoke and the housing inner diameter,which is in a small range of 15–25 mm.The distance from nozzles to the rotor end surface is mainly influenced by length the end cap extension,which is in a large range of 2–20 mm.The total flow is 5 L/min.

Fig.14 Relationship between PMaSynR S/G temperature and nozzles at the rotor end surface.

Fig.15 Relationship between PMaSynR S/G temperature and nozzles aperture.

Fig.16 Relationship between PMaSynR S/G temperature and flow rate.

Fig.17 Relationship between PMaSynR S/G temperature,hwinding and winding ends spray distance.

Fig.17 shows the temperature trajectory of the proposed PMaSynR S/G under different winding ends spray distance.With the increase of the spray distance from nozzles to winding ends from 15 mm to 25 mm, the maximum winding temperature raises 3 °C, which means that the spray distance from nozzles to winding ends surface has a little influence on the PMaSynR S/G temperature.Due to certain total flow rate and nozzle number, each nozzle flow rate is certain as well,which means the initial cooling conditions at the nozzle are the same.With the increase of the spray distance,spray surface increases while hwindingdecreases, which leads to a little increase of the thermal resistance from the nozzle to the winding ends.However, compared with the thermal resistance of other positions of the PMaSynR S/G, the thermal resistance from the nozzle and the sprayed winding ends surface is relatively low, and the heat exchange of oil spraying through this area is less.Even if the thermal resistance increases, the initial temperature of the sprayed winding ends surface increase slightly.It can be considered that the initial cooling conditions at the sprayed winding ends surface are nearly the same.Therefore,the steady temperature of the PMaSynR S/G raises a little with the increase of spray distance.

Fig.18 shows the temperature trajectory under different rotor end surface spray distances.With the increase of the spray distance at the rotor end surface, the temperature rises,and the other positions are also slightly increased.The maximum winding temperature increases by 8°C and rotor temperature increases by 23 °C.When the distance is more than 15 mm, the temperature change is not obvious.The cooling effect of winding end spray distance at 15–25 mm can be compared with that of rotor end spray distance at 15–20 mm,which is in the insensitive area of spray distance.

5.Experiment and analysis

Fig.18 Relationship between PMaSynR S/G temperature,hrotor and rotor end surface spray distance.

To verify the effectiveness of the proposed hybrid cooling method, a 40 kW/24000 r/min PMaSynR S/G prototype is manufactured as shown in Fig.19.Here 10 nozzles with the aperture of 1.5 mm are employed in oil inlet path 1, which is even along the circumference direction at the dual sides of winding ends.Moreover, 1 nozzle with the aperture of 1.5 mm is set at the rotor end surface.In addition, the PT100 is arranged in slot winding and winding ends respectively for temperature measurement.The PMaSynR S/G experimental platform is established as shown in Fig.20,which includes oil cooling tank, oil source controller, prime motor test bench,PMaSynR S/G,lab-view,power converter,flowmeter and load equipment.

5.1.Flow rate distribution experiment

Generally, the oil tank only has one oil outlet, while the proposed cooling structure needs two oil inlets.For the experiment, the three-way valve is used to generate two oil outlets with the flow sensors to measure the flow rate of the two oil outlets.By controlling the oil source controller,the oil is input from the tank to the PMaSynR S/G.The relationship between the two paths and total flow rate is shown in Fig.21.Note that the ratio of path 1 to total flow rate is 80%.

5.2.Verification of loss calculation

Fig.19 PMaSynR S/G prototype.

Fig.20 PMaSynR S/G system experimental platform.

Fig.21 Flow rate distribution.

During the experiment measurement of the loss, to avoid the additional friction loss interference, the PMaSynR S/G operates with the air cooling method at different speeds and loads at power generation state.The load equipment is set at different loads, and the input mechanical torque from prime motor to the PMaSynR S/G can be measured by the torque tester.The PMaSynR S/G system loss includes the PMaSynR S/G loss and the power convertor loss.The PMaSynR S/G system loss can be calculated by the difference between the input power from prime motor and the power generation load.The power convertor loss is relative with the phase current and the resistance of the power tube, according to the operation rule, the power convertor loss can be calculated.Finally,the PMaSynR S/G loss can be obtained.

Fig.22 shows the total loss (without additional friction loss) of the PMaSynR S/G in experiment and simulation at ω = 3000 r/min, 6000 r/min and 9000 r/min, where, LTtestis the experiment results of the total loss,LTsimuis the calculation results of the total loss.The results show the error of the PMa-SynR S/G loss in experiment measurement and calculation are all within 6%at ω=3000 r/min,all within 5.4%at ω=6000 r/min and all within 4.7% at ω = 9000 r/min.The error between experiment and calculation is mainly influenced by the PMaSynR S/G resistance, iron loss and the ignored stray loss.In spite of this,the error range is acceptable.The loss calculation can be regarded as accurate.

5.3.Verification of thermal network model

Fig.22 Experiment loss LTtest and simulation loss LTsimu at different speeds and loads.

The accuracy of proposed thermal network model is discussed by comparison of experiment and simulation in this part.The proposed thermal network model includes two model of uneven spray at the winding ends and even spray at the winding ends.The experiment includes the uneven spray and even spray of the thermal network model at starting and power generation state.

During the experiment process of starting, the initial temperature of the winding ends and slot ends is 24.5°C,the initial ambient temperature is 22°C,and flow rate is 4 L/min with the temperature of 24 °C.

As for even spray at the winding ends, Fig.23 shows the slot winding and winding ends temperature of experiment and simulation during starting process which consists of 30 s constant torque starting and then 30 s constant power starting.The results show the difference of the experimental and simulation temperature is within 3.6%.

Fig.23 Experiment and simulation temperature of even spray at the winding ends at starting state.

Fig.24 shows the temperature of experiment and simulation at 12000 r/min@20 kW power generation, the results show the differences of the experimental and simulation temperature are all within 6.7%.The temperature calculation of the thermal network model of even spray at the winding ends can be regarded as accurate.

Before the experiment of uneven spray at the winding ends,a metal ring sheet is manufactured whose outer diameter is equal to the inner diameter of the housing and with the thickness of 2 mm.The metal ring sheet with four parts of space area along the circumferential direction is embedded into the PMaSynR S/G housing internal space.Oil can only be sprayed to winding ends from four nozzles while other nozzles are plugged up by the metal ring sheet.In this way,the PMaSynR S/G with 4 nozzles aligned to the winding ends can make experiments of uneven spray at the winding ends condition.

During the experiment process of power generation,the initial temperature of the winding ends and slot ends is 31°C,the initial ambient temperature is 31 °C, and the flow rate is 4 L/min with the temperature of 24 °C.

As for the thermal network model of uneven spray at the winding ends, Fig.25 shows the temperature of slot winding,sprayed winding ends and unsprayed winding ends in both experiment and simulation at 30 s constant torque start and then 30 s constant power starting, where, absolute error is the difference of the experiment and simulation temperature,relative error is the ratio of the difference temperature to the experimental temperature raise.The results show the differences of the experimental and simulation temperature are all within 4.4%.Fig.26 shows the temperature of experiment and simulation at 12000 r/min@20 kW power generation.The results show the differences of the experimental and simulation temperature are all within 6.8%.The temperature calculation of the thermal network model of uneven spray at the winding ends can be regarded as accurate.

5.4.Verification of cooling effect

The advantages of the proposed hybrid cooling method cooling effect are discussed with the comparison of only oil path 1 cooling method, only oil path 2 cooling method and the air cooling method.The experiment temperature is measured at starting and power generation state about:

Fig.24 Experiment and simulation temperature of even spray at the winding ends at power generation state.

Fig.25 Experiment and simulation temperature of uneven spray at the winding ends at starting state.

Fig.26 Experiment and simulation temperature of uneven spray at the winding ends at power generation state.

Method 1.the proposed hybrid cooling method.

Method 2.only oil path 1 cooling method.

Method 3.only oil path 2 cooling method,

Method 4.air cooling method.

During the experiment process, the initial ambient temperature is 22°C,and flow rate is 4 L/min with the temperature of 24 °C, the initial temperature of the winding ends and slot winding at starting state is 24.5°C,and the initial temperature of that at power generation is 31 °C.

At the starting state, the PMaSynR S/G operates at 30 s 20 N?m constant torque and then 30 s constant power the temperature of the winding ends and slot winding is shown in Fig.27.The results show the cooling effect of the proposed hybrid cooling method is the best of the four methods.At the slot winding, the temperature of Method 1 is 1.0 °C,1.6°C and 4°C lower than that of Methods 2,3 and 4,respectively.At the winding ends, the temperature of Method 1 is 0.9 °C, 1.3 °C and 6.9 °C lower than that of Methods 2,3 and 4, respectively.

At the power generation state, the PMaSynR S/G operates 12000 r/min@20 kW,the temperature of the winding ends and slot winding is shown in Fig.28.For the temperature of the air cooling method raises sharply, only 10 min temperature is measured.Other method is measured until steady-state temperature.

The results show the effect of the proposed hybrid cooling method is the best of the four methods.At the slot winding,temperature raise of Method 1 is 4.8 °C, 24.3 °C and 46.3 °C lower than that of Methods 2, 3 and 4, respectively at the 10 min power generation and is 8.4°C and 42.2°C lower than that of Methods 2 and 3, respectively at the 120 min steadystate power generation.At the winding ends, the temperature of Method 1 is 3.3 °C, 19.5 °C and 67.6 °C lower than that of Methods 2,3 and 4,respectively at the 10 min power generation and is 5.7 °C and 33.8 °C lower than that of Methods 2 and 3, respectively at the 120 min steady-state power generation.The cooling effect of Methods 1,2 and 3 is far more effective than Method 4.During steady-state power generation,the temperature of slot winding with Method 1 decreases 10%and 35.7% compared with Methods 2 and 3, respectively.The cooling effect of Method 1 is obvious compared with other three cooling methods.

Fig.27 Experiment temperature of different cDesign specification of PMaSynR ooling methods at starting state.

Fig.28 Experiment temperature of different cooling methods at power generation.

Fig.29 shows the temperature of the winding ends and slot winding at power generation with Methods 1, 2 and 3.The results show that the difference of the slot winding and winding ends of Method 1 is lowest of these three methods.The temperature tolerance of Method 1 is higher than that of Methods 2 and 3.The temperature tolerance is defined as the maximum allowable design temperature of each part of the PMaSynR S/G.

Flow rate is also a cooling effect factor.The air cooling method can be regarded as 0 L/min of the hybrid cooling method.From Fig.27(b),the temperature difference of hybrid cooling method of 4 L/min and the air cooling method is within 7 °C.

For clear of the flow rate influence degree of the cooling effect, different flow rates are employed at the power generation of hybrid cooling method.Fig.30 shows the winding ends and slot winding temperature of 1–4 L/min flow rate.The results show the slot winding temperature of 4 L/min is 7.1 °C, 13.3 °C, and 22.4 °C lower than that of 3 L/min,2 L/min and 1 L/min, respectively.The winding ends temperature of 4 L/min is 7.7°C,14.4°C and 24.2°C lower than that of 3 L/min, 2 L/min and 1 L/min.The cooling effect is obviously improved with the increase of the flow rate.

The hybrid cooling structure with oil circulation in the housing, oil spray at winding ends and rotor end sur-face is proposed for the PMaSynR S/G, which has the excellent heat dissipation performance.

Fig.29 Experiment temperature of the winding ends and slot winding at power generation with different cooling methods.

Fig.30 Experiment temperature of the winding ends and slot winding with the flow rate of 1–4 L/min.

6.Conclusions

(1) This paper proposes a novel hybrid cooling method for high-speed high-power permanent magnet assisted synchronous reluctance starter/generator (PMaSynR S/G)in aerospace applications.The hybrid cooling structure consists of the oil circulation in the housing, oil spray at winding ends and rotor end surface.

(2) The accurate loss calculation of the PMaSynR S/G is proposed,especially,the air gap friction loss calculation under oil spray cooling.And the air gap friction empirical equation has been revised with the consideration of oil spray cooling.In addition, the calculation of copper loss,stator and rotor core loss, permanent magnet eddy current loss and bearing loss has been made as well.

(3) The parameter sensitivity analysis of the hybrid cooling structure is proposed, while the equivalent thermal network model of the PMaSynR S/G is established considering the uneven spraying at the winding ends.Note that the proposed hybrid cooling method has the excellent cooling performance with the flow rate of oil circulation in the housing and oil spray at the winding ends in 75%-85% to the total rate.Compared with only rotor end surface spray, the maximum winding temperature of the proposed method is 110 °C lower and the efficiency improves by 0.6%.Compared with only oil circulation in the housing and oil spray at the winding ends, the maximum rotor temperature is 75°C lower and the efficiency improves by 0.3%.The cooling effect of dual sides spray is obviously better than that of single side.The maximum winding temperature of dual sides spray is 21 °C lower than that of single side.The decrease of the aperture of nozzles in the range of 0.5–3 mm and the increase of the flow rate can improve the cooling effect of the proposed cooling method.However, when the flow rate increases from 2 L/min to 6 L/min, the reduction of copper loss is less than the increase of air gap friction loss, which makes the PMaSynR S/G efficiency decrease by 0.13%.From the point of view of efficiency, the appropriate reduction of flow rate is conducive to the improvement of efficiency with the guarantee of the temperature requirements.In addition,the spraying distance and aperture at the winding ends has little influence on the temperature of PMaSynR S/G, while the spraying distance at the end of rotor can be appropriately reduced to improve the cooling effect.The maximum winding temperature increases by 8 °C and rotor temperature increases by 23 °C.

(4) The loss calculation and the proposed hybrid cooling method is verified by a 40 kW/24000 r/min PMaSynR S/G experimental platform.The loss error is within allowable range, and the proposed hybrid cooling method cooling effect is obvious, which can decrease 10%and 35.7%temperature compared with the cooling method of the oil circulation in the housing,oil spray at winding ends and the cooling method of the oil spray at rotor end surface.The proposed hybrid cooling method is firstly proposed for the PMaSynR S/G.It provides a guideline for engineers to follow on the thermal design of the high-speed high-power density PMaSynR S/G in aviation applications.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China(No.52177028),in part by the Aeronautical Science Foundation of China (No.201907051002).

Appendix A.When the PMaSynR S/G operates, the heat generated by the winding is uneven, and the heat flow passes through both the copper wire and the insulation layer.

Therefore, in order to reflect the average temperature of the winding,the winding is equivalent to an isotropic material with the same thermal resistance to replace the winding with uneven heat.Suppose there is heat flow along the x-axis.Since the

thermal conductivity of copper is much higher than that of air,it can be assumed that the thermal resistance of copper is 0.The thermal path can be regarded as two insulation thermal resistances A and B in parallel, as shown in Fig.A1.

Fig.A1(a)is rectangle winding equivalent model,where llis the length along z axis,w1is the width of copper,dδis the distance between copper,h1is the height of copper,w2and h2are the width and height of the winding considering the insulation layer.Fig.A1(b) is circular wire winding equivalent model,where dCuis copper diameter, wwe and hwe are the width and length of the equivalent winding.

Resistance rA, rBis:

For circular wire winding analysis,the above results can be approximated by making dCu= h1= w1, dwe= h2, the total conductors Nc in the region of wWE×hWEcan be divided into wWE/(dCu+ dδ) columns and hwe/(dCu+ dδ) rows, then the equivalent thermal conductivity along x or y axis is

Appendix B.The thermal resistance at each position in Fig.9 is defined, including conduction thermal resistance, convection thermal resistance and radiant thermal resistance.

Conduction thermal resistance includes:

RWJis the housing conduction thermal resistance.

RWJ-ECis the housing and end cap conduction thermal resistance.

RWJ-Stis the housing and stator conduction thermal resistance.

RStis the stator conduction thermal resistance.

RSt-WIis the stator and slot winding conduction thermal resistance.

RWEis the slot extension winding ends conduction thermal resistance.

RWIis the slot winding conduction thermal resistance.

RECis the end cap conduction thermal resistance.

RRis the rotor conduction thermal resistance.

RRSis the rotor end surface conduction thermal resistance.

RPMis PM conduction thermal resistance.

RR-Shis the rotor and shaft conduction thermal resistance.

RShis the shaft conduction thermal resistance.

REC-Shis the end cap and the shaft conduction thermal resistance.

Convection thermal resistance includes:

RHcis the housing and ambient convection thermal resistance.

RO-WJis the hollow tube and housing convection thermal resistance.

RECcis the end cap and ambient convection thermal resistance.

RWJ-Fis the housing and PMaSynR S/G internal space liquid (air) convection thermal resistance.

RWE-Fis the winding ends and PMaSynR S/G internal space liquid (air) convection thermal resistance.

RSp-WEis the winding ends and oil spray convection thermal resistance.

REC-Fis the end cap and PMaSynR S/G internal space liquid (air) convection thermal resistance.

RR-Fis the rotor and PMaSynR S/G internal space liquid(air) convection thermal resistance.

RWI-F-Ris the air gap convection thermal resistance.

RSp-RSis the rotor end surface and oil spray convection thermal resistance.

RB-Fis the bearings and PMaSynR S/G internal space liquid (air) convection thermal resistance.

RShcis the shaft and ambient convection thermal resistance.

Radiant thermal resistance includes:

RHris housing to ambient radiant thermal resistance.

RECris end cap to ambient radiant thermal resistance.