Comparison of Temperature Characteristics of Outer Rotor Low-Speed PM Motors Considering Magnetic Load and Current Density

: In the electromagnetic design process of the outer rotor of a low-speed permanent magnet motor (LSPMM), due to the different heat dissipation conditions of the stator core and the stator winding, the selection of different magnetic loads and stator current densities will produce different temperature distributions even under the same efficiency. In the existing literature, the effects of magnetic load and current density on temperature distribution are rarely studied, which makes it difficult for designers to select optimal electromagnetic parameters to achieve better temperature performance. Therefore, in this paper, the comparison of temperature characteristics considering magnetic load and current density is conducted based on an outer rotor LSPMM. Firstly, the structure and parameters of an initial scheme of a 200 kW 56 rpm motor is determined, and the electro-magnetic and temperature characteristics of the initial scheme are obtained through two-dimensional finite element analysis (2D-FEA) using Ansys Maxwell and Motor-CAD software. Secondly, by comparing the temperature and loss characteristics under different magnetic loads and different current densities, the effect of magnetic load on temperature and the effect of current density on temperature are obtained. Furthermore, four different schemes are proposed, and the loss and temperature characteristics of the four schemes under rated load are also compared to obtain the comprehensive effects of magnetic load and current density on temperature. Next, a final scheme is determined based on the above analysis, and the temperature characteristics of the final scheme and the initial scheme are compared to verify the validity of the conclusions. Finally, a prototype is built and tested to verify the feasibility of the conclusions. For LSPMM design, the results and several measurements provided in this paper can help researchers to choose a better optimization scheme to achieve good temperature performance


Introduction
LSPMMs are widely used in industrial production, oil field exploration, wind power generation, port lifting, and ship propulsion [1,2].The traditional drive system of an induction motor plus a mechanical deceleration mechanism has disadvantages, such as complex structure, leakage of lubricating oil, poor operation reliability, high maintenance cost, and low overall efficiency of the system; thus, this system does not meet the requirements of economic development, energy saving, and environmental protection [3,4].The use of direct drive motors to replace traditional drive systems has become the consensus of scholars at home and abroad [5].In addition, the power factor and efficiency of permanent magnet motors are higher, and permanent magnet motors can maintain good performance over a wide range of load changes [6].Therefore, LSPMMs are wildly used.
However, an LSPMM needs to output a large torque, and it will generate a large electromagnetic torque, resulting in a large magnetic load and copper loss [7].On the other hand, the lower speed results in less effective self-fan cooling, causing the high-temperature rise of the motor [8].The higher motor temperature can result in the permanent magnet (PM) undergoing demagnetization and, ultimately, worse motor performance [9].Hence, for LSPMMs, the suitable temperature is significant for guaranteeing good motor operating conditions.
For LSPMMs, most of the literature focuses on motor design and performance optimization.An LSPMM with fractional concentrated winding used in a coal mine conveyor belt system was designed, of which the temperature distribution of different conductor turns and permanent magnet materials are presented in [10].A new stator cooling structure design was studied to achieve a lower temperature rise, and the results show that the larger magnetic load and lower current density can improve torque density [11].The Ushaped hybrid pole is proposed to improve motor torque density in [12].The effects of stator tooth shape on output torque and bearing stress have also been studied, based on a bearingless outer rotor of a permanent magnet synchronous motor [13].Furthermore, the effects of pole pair number and winding type on motor performance were investigated in [14]; a suitable embrace was found in order to obtain minimum cogging torque in [15]; and the influence of ratio of external diameter to stack length on torque and efficiency was analyzed in [16].In the electromagnetic design of LSPMMs, the selection of magnetic load and current density has a great influence on electromagnetic performance.Magnetic load mainly affects the rotor core loss, eddy current loss of the PM, and stator core loss.For LSPMMs, eddy current loss of the PM and rotor core loss change very little when the magnetic flux density changes [17,18].Therefore, stator core loss is mainly considered when the magnetic load is changing, and the copper loss of the stator winding is mainly considered when the current density is changing [19,20].These two losses will affect the efficiency and the temperature characteristics of the motor [21].In addition, for LSPMMs, due to the different heat dissipation characteristics of the core and winding, even at the same efficiency, different distributions of core loss and winding loss will result in different temperature distributions.However, in the existing literature, the electromagnetic properties are usually designed and optimized for maximum efficiency [22].When the efficiency is high, the temperature performance of the motor may not be the optimal due to different core loss and winding loss distributions.The temperature characteristics of some LSPMMs are also analyzed based on different cooling schemes [11,23,24].In these analyses, the effects of electromagnetic design parameters, especially the magnetic load and current density on the temperature, are not analyzed and summarized, which makes it difficult for designers to select optimal electromagnetic parameters to achieve better temperature performance.Therefore, comparative analysis of temperature characteristics considering magnetic load and current density should be studied and summarized for outer rotor LSPMMs.
In this paper, the temperature characteristics under different magnetic loads and stator current densities are compared and a final scheme is obtained, which has a lower temperature distribution than the initial scheme.In Section 2, the motor parameters and structure of the initial scheme are determined.In Section 3, the electromagnetic and temperature properties of the initial scheme are obtained through 2D-FEA using Motor-CAD and Ansys Maxwell software.In Section 4, by comparing the temperature and loss under different magnetic loads and different current densities, the effects of magnetic load and current density on temperature are revealed.Then, four different schemes are proposed, and the loss and temperature characteristics of these four schemes under rated load are compared.In Section 5, a final scheme is proposed and its temperature and loss characteristics are compared with the initial scheme, verifying the validity of our conclusions.In Section 6, a prototype is built and tested to verify the feasibility of our conclusions.For LSPMM design, the conclusions summarized in this paper can truly help researchers to choose a better scheme to realize better motor temperature performance.

Motor Parameters and Structure of Initial Scheme
A 200 kW 56 rpm motor is taken as the research object.The motor structure and parameters of initial scheme are provided in Figure 1 and Table 1.Considering the low speed, the motor adopts an outer rotor structure to meet the large torque [13].In addition, the surface-mounted permanent magnet (PM) structure is applied, because the surfacemounted permanent magnet structure has less flux leakage and simpler structure than the interior permanent magnet structure [17].In order to achieve a better cooling effect, the structure of axial spiral water cooling is adopted.

Electromagnetic and Temperature Characteristics of the Initial Scheme
On the basis of the initial scheme, the motor model is established using Ansys Maxwell software.Zero current is set during no-load analysis, and a three-phase rated current is set during load simulation.After the boundary conditions are set, the electromagnetic properties under no-load state and rated load are calculated and analyzed by 2D-FEA.
The magnetic flux density distributions of the motor under no-load state and rated load conditions are shown in Figure 2. In these two states, a small part of the stator teeth region is saturated in magnetic flux density, but the magnetic flux density of the other part behaves well.
Figure 3 shows the variation of radial air-gap magnetic flux density with mechanical angle waveform and Fourier transform results under no-load state.As shown, the peak value of the radial air-gap magnetic flux density is 1.14 T. In addition, the 5th and 7th harmonic amplitudes of the radial air-gap flux density are small compared to the fundamental amplitude of the radial air-gap flux density.The waveform and Fourier transform result of line-to-line back electromotive force (back-EMF) under no-load state are shown in Figure 4.The amplitude of the no-load back-EMF line-to-line voltage is about 520 V, and its image is very smooth.Figure 5 shows the cogging torque and the output torque under rated load.As shown in the figure, the output torque under rated load is 34,700 N•m, and the ripple of the output torque is only 2%.The core loss and eddy current loss of PM under rated load are shown in Figure 6.After entering the steady state, the average values of core loss and eddy In order to obtain the temperature characteristics of the initial scheme, an FEA of temperature is conducted using Motor-CAD software.The axial spiral water cooling, inlet velocity, and inlet temperature are also set in the FEA.In addition, in order to consider the influence of the air-gap and rotational speed on the heat transfer characteristics of the motor, the rotational speed of the motor is set to 56 rpm, the length of the air-gap is set to 3 mm in the FEA.The temperature distribution of the initial scheme is shown in Figure 7.The lowest temperature occurs at the rotor yoke, which is 69.4 °C.The highest temperature occurs at the stator winding caused by the large copper loss of winding, which is 122.7 °C.The temperature of the stator teeth is higher than that of the stator yoke.

Influence of Magnetic Load on Motor Temperature
This section studies the effect of magnetic load on temperature, and the stator core loss is used to reflect the change in magnetic load.The relationship between stator core loss and stator magnetic flux density can be obtained by the following equations [19,20]: (1) where _ is the core loss of stator yoke， is the core loss coefficient of stator yoke， is the weight of the stator yoke， is the magnetic flux density of the stator yoke, _ is the core loss of stator teeth， is the core loss coefficient of stator teeth, is the weight of the stator teeth， is the magnetic flux density of the stator teeth, is the frequency of the magnetic field.
From Equations ( 1) and ( 2), the stator core losses under different stator magnetic flux densities are obtained, and the results are shown in Figure 8.The stator core loss increases from 2724 W to 4843 W, and the stator magnetic flux density increases from 1.2 T to 1.6 T. The temperature distribution and comparison of the motor under different stator magnetic flux densities are shown in Figures 9 and 10.As shown in Figure 9, the highest temperature still occurs at the winding, and the lowest temperature appears at the rotor yoke.When the stator magnetic flux density increases from 1.2 T to 1.6 T, the temperature of each part increases.Among them, the temperature rise at the stator winding is the highest, which is only 9 °C.The temperature rise at PM is the smallest, which is 2.7 °C.Therefore, changes in magnetic flux density have a mild effect on temperature.

Influence of Current Density on Motor Temperature
The effect of current density on temperature is explored in this section.The relationship between copper loss of winding and current density can be obtained using the following equations [17]: where is the copper loss of the valid part, is the phase number, is the phase current, is the effective partial resistance of each phase conductor, is the conductor's effective cross-sectional area, is the core length, is the resistivity of conductor materials, is the current density.Temperature (℃) Stator magnetic flux density (T)

Stator teeth Winding
The copper losses at different current densities are obtained via Equation ( 6), as shown in Figure 11.From the figure, it can be seen that the copper loss of winding increases by 12,127 W when the current density increases from 2 A/mm 2 to 6 A/mm 2 .

Combined Effect of Magnetic Load and Current Density on Temperature
Four schemes are proposed to explore the combined effects of magnetic load and current density on temperature under rated load.Among them, the current density of Case 1 and Case 2 remains unchanged, while the magnetic load is changed.The air-gap magnetic flux densities of Case 3 and Case 4 are unchanged, and the current densities are changed.In addition, the back-EMF, stator outer diameter, and slot fill rate of the four schemes also remain unchanged.
The parameters of the four schemes are shown in Table 2.As shown, the permanent magnet thickness and pole embrace of Case 1 are increased to achieve higher magnetic load, while the pole embrace of Case 2 is decreased to reduce the magnetic load.Furthermore, to maintain the same back-EMF, the core length of Case 1 is shortened, while the core length of Case 2 is increased.For Case 3 and Case 4, in order to achieve higher current density, the parallel winding number is reduced in Case 3, and in Case 4, the parallel winding number is increased to reduce the current density.To guarantee the same slot fill rate of 75%, the slot area of Case 3 is reduced and the slot area of Case 4 is increased.Figure 14 shows the magnetic flux density distribution for the four schemes.From the figure, the air-gap flux density and stator teeth flux density of Case 1 are the largest, and its air-gap magnetic flux density and stator teeth magnetic flux density are 0.92 T and 1.53 T, respectively.The magnetic load in Case 2 is the smallest, and its air-gap magnetic flux density and stator teeth magnetic flux density are 0.84 T and 1.2 T.Although the airgap magnetic flux densities of Cases 2, 3, and 4 are the same, the stator magnetic flux densities of Case 3 and Case 4 are different due to the change in the slot area.The stator teeth magnetic flux density of Case 3 is 1.34 T, and the stator teeth magnetic flux density After 2D-FEA simulation using Ansys Maxwell software, the stator core loss, rotor core loss, eddy current loss of the PM, and copper loss under rated load are obtained, as shown in Figure 15.It can be seen that Case 4 has the largest stator core loss, which is 4548 W. This is because, among the four schemes, Case 4 has the same maximum stator teeth magnetic flux density as Case 1, and the core length of Case 4 is longer than that of Case 1.The stator core loss of Case 3 is the smallest, which is 2978 W, because although the stator magnetic flux density of Case 3 is larger than that of Case 2 (which has the smallest stator magnetic flux density), the core length of Case 3 is shorter than that of Case 2. In addition, the stator core losses for Case 1 and Case 2 are 3923 W and 3284 W, respectively.The stator core loss of Case 1 is larger than that of Case 2; this is because although the core length of Case 1 is shorter than Case 2, the magnetic load is larger.For the rotor core loss, the maximum value is 58 W in Case 2. For eddy current loss of the PM, Case 3 has the largest eddy current loss at 700 W. The smallest eddy current loss of the PM is 527 W, which occurs in Case 2. In addition, the maximum copper loss is 16,005 W, which appears in Case 3; this is because Case 3 has the highest current density.The copper loss of Case 4 is the smallest, at 9407 W, because the current density of Case 4 is the smallest.For Case 1 and Case 2, since the core length of Case 2 is longer than that of Case 1, and the current densities of the two cases are the same, the copper loss of Case 2 is larger.Figures 16 and 17 show the temperature distribution and comparison under the four schemes.From the figure, the temperature of each part of Case 3 is the highest: temperature of the stator winding is 150 °C, and the temperature of PM is 75.6 °C.In contrast, Case 4 has the lowest temperature: the stator winding temperature is 102.2 °C, and the PM temperature is 66 °C.For Case 1 and Case 2, Case 1 (with the higher magnetic load) has the lower temperature.This is because compared with Case 2, although Case 1 has a larger magnetic load, resulting in greater stator core loss, the reduction in copper loss due to the reduction in the core length is greater than the increase in stator core loss.Therefore, the increase in the magnetic load does not necessarily lead to an increase in the temperature, because the shortening of the core length may counteract this by reducing the temperature.In addition, among the four schemes, Case 4 has the smallest current density and copper loss, and has the largest stator magnetic flux density and stator core loss.Compared to the other schemes, the current density of Case 4 decreases, respectively, by 1 A/mm 2 , 1 A/mm 2 , and 2.2 A/mm 2 , resulting in a reduction in copper loss by 1510 W, 4267 W, and 6598 W, while the stator core loss increases by 625 W, 1264 W, and 1610 W. Furthermore, compared with the other three schemes, the stator winding temperature of Case 4 is reduced by 18.1 °C, 20.7 °C, and 48.8 °C, respectively.Obviously, with the further decrease in the current density, although the stator core loss increases, the copper loss due to the changes in current density decreases further, and the temperature still drops significantly.Therefore, for LSPMMs, the motor temperature is significantly affected by current density.

Final Scheme
Based on the above analysis, a final scheme is determined.Compared with Case 4, which had the lowest temperature, the magnetic load of the final scheme is further increased to achieve lower temperature rise and smaller motor volume.Furthermore, the final scheme has higher magnetic load and lower current density compared to the initial scheme.
The parameter comparison between the final scheme and the initial scheme is shown in Table 3.The PM thickness and pole embrace of the final scheme are increased to obtain higher magnetic load, and the parallel winding number is increased to obtain a smaller current density.In addition, the core length of the final scheme is shortened to ensure the same back-EMF.In order to realize the same slot fill rate, the slot area of final scheme is also reduced.Moreover, in final and initial schemes, the back-EMF, the stator outer diameter, and the slot fill rate remain unchanged.Figure 18 shows the magnetic flux density distribution of the final scheme obtained by 2D-FEA using Ansys Maxwell software.As shown, the magnetic flux densities of the stator teeth and yoke are 1.6 T and 0.97 T, respectively, and the air-gap magnetic flux density is 0.88 T; these values are increased compared to the initial scheme.Although the magnetic load of the final scheme has increased significantly, the stator magnetic flux density still does not exceed 1.8 T, and does not reach saturation.The core loss and eddy current loss of the PM in the final scheme at rated load are shown in Figure 19.After entering the steady state, the average core loss of the final scheme is 4870 W, the average eddy current loss of the PM is 602 W, and the average copper loss is 8655 W. Compared with the initial scheme, the core loss of the final scheme increases by 1122 W, caused by the increase in magnetic load.In addition, due to the reduction in current density and core length of the final scheme, the copper loss has dropped by 3775 W. The eddy current loss of the PM has not changed substantially in two schemes.Figures 20 and 21 show the temperature distribution and comparison at rated load for the final and initial schemes.Compared with the initial scheme, since the copper loss of final scheme decreases more than the stator core loss increases, the temperature of each part of the motor has dropped considerably in the final scheme.The temperature of the stator winding part has dropped the most, reaching 21 °C.Therefore, in the design of outer rotor LSPMMs, lower current density and higher magnetic load can effectively improve temperature characteristics and reduce the size of the motor.

Experimental Test
A 22 kW 56 rpm prototype is made to verify the feasibility of the previous conclusions.The prototype is shown in Figure 22.The prototype adopts an outer rotor structure and surface-mounted permanent magnets, and double-layer windings are applied.The winding temperature is measured by Pt100 resistance temperature detectors in the end windings.The efficiency of the prototype and the stator winding temperature are obtained after the prototype is run.At rated load, the measured efficiency of the prototype is 94.2%, which is slightly lower than the calculated value.In addition, the stator winding temperature of the prototype is 109 °C, which is 3 °C higher than the calculated value.Furthermore, the continuous normal operation and good temperature performance of the prototype verify the feasibility of our conclusions.

Conclusions
In this paper, the temperature and loss characteristics under different magnetic loads and current densities are compared and investigated.The comprehensive effects of magnetic load and current density on temperature are further revealed.On the basis of the conclusions obtained, the temperature characteristics of the final scheme and the prototype are analyzed to verify the validity and feasibility of our conclusions.The key points are summarized as follows: 1.When the stator magnetic flux density increases from 1.2 T to 1.6 T, although the temperature of each part of the motor increases, the highest temperature rise is only 9 °C, which appears at the stator winding.In addition, the temperature of the PM only increases by 2.7 °C.Therefore, an increase in the magnetic load does not cause a significant increase in the temperature for LSPMMs.2. Case 1 and Case 2 have the same current density.However, compared with Case 2, the core loss of Case 1 increases by 639 W due to the higher magnetic load.In addition, in order to ensure the same back-EMF, the core length of Case 1 is shortened while increasing the magnetic load, resulting in lower copper loss of Case 1.The copper loss of Case 1 is reduced by 2757 W compared with Case 2, which is about five times the increase in stator core loss.Therefore, Case 1, with a higher magnetic load, has a lower temperature under rated load compared with Case 2. The winding and PM temperatures of Case 1 are 120.3°C and 78.8 °C, respectively, and the temperature of the corresponding parts of Case 2 are 122.9°C and 68.5 °C.Thus, for LSPMM design, an increase in the magnetic load may not lead to an increase in the temperature, because the core length will also be shortened, resulting in lower copper loss and the possibility of a temperature drop.3.Among the four schemes, Case 4 has the smallest current density, but has the largest stator magnetic flux density and stator core loss.Compared with the other three schemes, the current density of Case 4 is reduced by 1 A/mm 2 , 1 A/mm 2 , 2.3 A/mm 2 in turn, resulting in a reduction in copper loss by 1510 W, 4267 W, and 6598 W, while the stator core loss increases by 625 W, 1264 W, and 1610 W, respectively.However, the temperature of Case 4 is the lowest.Compared with the other three cases, the stator winding temperature of Case 4 drops by 18.1 °C, 20.7 °C, and 48.8 °C.It can be summarized that although the stator core loss keeps increasing, the copper loss due to the decrease in current density decreases more sharply; thus, the temperature still decreases.Therefore, for LSPMMs, the motor temperature is significantly affected by current density.4.After comparing the final scheme with the initial scheme, the final scheme with higher magnetic flux density and lower current density has a lower temperature.The stator winding temperature of the final scheme is 101.7 °C, and the stator winding temperature decreases by 21 °C compared to the initial scheme.In addition, the temperature performance of the manufactured prototype is also very good, and the error between the measured and calculated results of the temperature is only 2%.Therefore, in the design of outer rotor LSPMMs, lower current density and higher magnetic load can indeed lead to better temperature performance.

Figure 2 .Figure 3 .
Figure 2. Magnetic flux density distributions under no-load state and rated load: (a) no-load state; (b) rated load.

Figure 7 .
Figure 7. Temperature distribution of motor under rated load: (a) whole temperature distribution; (b) partial temperature distribution.

4 .
Influence of Magnetic Load and Current Density on Temperature

Figure 8 .
Figure 8. Stator core loss under different stator magnetic flux density.

Figure 9 .Figure 10 .
Figure 9. Temperature distributions under 1.2 T and 1.6 T: (a) whole temperature distribution under 1.2 T; (b) partial temperature distribution under 1.2 T; (c) whole temperature distribution under 1.6 T; (d) partial temperature distribution under 1.6 T.

Figure 15 .
Figure 15.Loss of four schemes under rated load: (a) stator core loss; (b) rotor core loss; (c) eddy current loss of the PM; (d) copper loss.

Figure 18 .
Figure 18.The magnetic flux density distribution of the final scheme.

Figure 19 .
Figure 19.The core loss and eddy current loss of PM in final scheme: (a) core loss; (b) eddy current loss of the PM.

Figure 20 .Figure 21 .
Figure 20.Whole and partial temperature distribution of final scheme: (a) whole temperature distribution; (b) partial temperature distribution.

Table 1 .
The parameters of initial scheme.

Table 2 .
The parameters of four schemes.

Table 3 .
The parameters comparisons of the final and initial schemes.