First-person overview. I treated the water-cooled interior PMSM electric motor as a coupled electromagnetic and thermal system because the reliability, efficiency, and continuous power capability of a PMSM electric motor are strongly limited by the spatial distribution of electromagnetic loss and the ability of the cooling circuit to remove that loss. In my workflow, I did not separate the electromagnetic calculation from the thermal calculation as two unrelated tasks. Instead, I used the loss density computed in the electromagnetic field as the volumetric heat source for the thermal-fluid model, and I then evaluated how the temperature field of the PMSM electric motor changed when the coolant velocity was increased. This approach allowed me to connect the magnetic design, the winding arrangement, the insulation system, the stator core, the rotor core, the permanent magnets, the housing, and the water channel in one numerical framework.
I focused on an interior permanent magnet synchronous motor because the interior magnet arrangement provides a combination of permanent-magnet torque and reluctance torque, which is attractive for electric vehicle traction. In a PMSM electric motor of this type, the magnets are buried inside the rotor, so the rotor structure is mechanically robust and can operate over a wide speed range. However, the buried magnet topology also creates localized saturation, harmonic content, and eddy-current loss in solid conductive parts. These effects influence the thermal behavior of the PMSM electric motor. Therefore, I built a coupled simulation in which the electromagnetic loss was not assumed uniform, but was mapped from the magnetic solution into the thermal solution according to the actual geometry.
Physical model and assumptions. I constructed the three-dimensional geometry of the PMSM electric motor and then imported it into a finite-volume environment for thermal and flow analysis. The stator slot contains many conductors, impregnation material, insulation layers, and small air regions. Modeling every strand individually would be numerically expensive and would introduce many uncertain contact resistances. Therefore, I homogenized the slot region and represented the winding and insulation as an equivalent solid with direction-dependent thermal conductivity. This simplification preserved the total copper loss and the dominant thermal path from the winding to the stator core while keeping the mesh size practical. The same logic was applied to thin insulation layers between the slot and the winding and between the magnets and the rotor laminations.
The main dimensions and operating point of the PMSM electric motor that I analyzed are listed below. I selected a rated power of 30 kW and a rated speed of 3000 r/min because this operating point produces a representative traction load for a compact electric drive. The rotor has eight poles and the stator has forty-eight slots. The air gap is small, so the electromagnetic torque production is strong, but the small gap also requires careful thermal management because heat must cross several interfaces before reaching the coolant.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Rated power | 30 kW | Stator outer diameter | 190 mm |
| Rated speed | 3000 r/min | Stator inner diameter | 125 mm |
| Number of poles | 8 | Rotor outer diameter | 123.8 mm |
| Number of stator slots | 48 | Rotor inner diameter | 74 mm |
| Core length | 110 mm | Permanent magnet thickness | 5.5 mm |
| Air gap length | 0.6 mm | Permanent magnet width | 16 mm |
I assigned material properties to each region of the PMSM electric motor according to the dominant physical role of that region. The copper winding has high thermal conductivity in the axial direction and much lower effective conductivity in the transverse direction because of insulation and air voids. The electrical steel core has a laminated structure, so its thermal conductivity is anisotropic. The permanent magnets have moderate thermal conductivity and a relatively low specific heat compared with copper, which means that the magnets can respond quickly to changes in loss. The housing is aluminum and is directly cooled by the water channel, so it acts as a major heat sink. The air gap has very low thermal conductivity, so heat transfer across the gap is limited, although convection and radiation can still provide a secondary path.
| Component | Material | Density in kg/m3 | Specific heat in J/kg K | Thermal conductivity in W/m K |
|---|---|---|---|---|
| Air gap | Air | 1.225 | 1006.43 | 0.0242 |
| Slot insulation | Insulation | 1400 | 1000 | 0.2 |
| Permanent magnet | NdFe30 | 7600 | 420 | 9 |
| Shaft | Low-carbon steel | 7800 | 460 | 60.5 |
| Housing | Aluminum | 2700 | 830 | 168 |
| Core | Silicon steel | 7800 | 460 | 30, 30, 0.9384 in lamination direction |
| Winding | Copper | 8954 | 400 | 0.1, 0.1, 174.66 in axial direction |
For the homogenized slot, I estimated the equivalent thermal conductivity from the volume fractions of copper, insulation, and air. If the copper volume fraction is denoted by \(f\), and if the transverse conduction path is approximated by a combination of conducting and insulating paths, then the equivalent conductivity can be written as
$$
k_{eq} = \frac{1}{\frac{1-f}{k_{air}} + \frac{f}{k_{cu}}}
$$
where \(k_{air}\) is the thermal conductivity of air and \(k_{cu}\) is the thermal conductivity of copper. This expression captures the fact that the transverse thermal path in a slot is limited by the insulation and voids, even though the copper itself conducts heat very well. In the axial direction, I used a much larger effective conductivity because the copper conductors are continuous along the machine length. This directional treatment is important in a PMSM electric motor because the end-winding region can become the hottest part of the machine, while the active slot region may remain cooler.
Electromagnetic field formulation. I solved the low-frequency electromagnetic field in the PMSM electric motor using a magnetic vector potential formulation. The governing equations are the Maxwell equations in their differential and integral forms. The material relations close the system together with the nonlinear magnetic permeability of the electrical steel. The table below summarizes the equations that I used in the electromagnetic solution.
| Name | Differential form | Integral form |
|---|---|---|
| Ampere law | \(\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\) | \(\oint \mathbf{H}\cdot d\mathbf{l} = \int_s \left(\mathbf{J}+\frac{\partial \mathbf{D}}{\partial t}\right)\cdot d\mathbf{s}\) |
| Faraday law | \(\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}\) | \(\oint \mathbf{E}\cdot d\mathbf{l} = -\frac{\partial}{\partial t}\int_s \mathbf{B}\cdot d\mathbf{s}\) |
| Gauss law for electric field | \(\nabla \cdot \mathbf{D} = \rho\) | \(\oint \mathbf{D}\cdot d\mathbf{s} = \int_V \rho dV\) |
| Gauss law for magnetic field | \(\nabla \cdot \mathbf{B} = 0\) | \(\oint \mathbf{B}\cdot d\mathbf{s} = 0\) |
| Constitutive relations | \(\mathbf{B}=\mu\mathbf{H}, \mathbf{D}=\varepsilon\mathbf{E}, \mathbf{J}=\sigma\mathbf{E}\) | Material-dependent closure |
In the magnetic vector potential form, I introduced \(\mathbf{A}\) such that
$$
\mathbf{B} = \nabla \times \mathbf{A}
$$
and I then solved
$$
\nabla \times \left(\frac{1}{\mu}\nabla \times \mathbf{A}\right) = \mathbf{J}_s – \sigma \left(\frac{\partial \mathbf{A}}{\partial t} + \nabla V\right)
$$
where \(\mathbf{J}_s\) is the source current density, \(\sigma\) is the electrical conductivity, and \(V\) is the electric scalar potential. For the nonlinear steel, the permeability depends on the local magnetic flux density, so I updated \(\mu(B)\) during the iterative solution. This nonlinear treatment is necessary for a PMSM electric motor because the stator teeth and yoke operate near saturation in some regions, while other regions remain relatively linear.
I first computed the no-load field to verify the magnetic circuit of the PMSM electric motor. The flux lines formed closed paths from one magnet pole to the adjacent magnet pole, and the periodic symmetry of the eight-pole rotor produced eight repeated magnetic circuits. In the no-load state, the peak flux density reached about 2750 mT. The regions with closely spaced flux lines corresponded to high flux density, while the regions with sparse flux lines had lower flux density. This distribution confirmed that the rotor bridge and stator tooth tips were the most saturated parts of the magnetic circuit.
After the no-load check, I applied a three-phase alternating current at the rated condition and calculated the transient loss. I separated the loss into stator core loss, rotor core loss, solid eddy-current loss in large conductive parts, and copper loss in the winding. The core loss was further divided into hysteresis loss, classical eddy-current loss, and anomalous loss. The general form that I used is
$$
P_{core} = k_h f B_m^\alpha + k_e f^2 B_m^2 + k_a f^{1.5} B_m^{1.5}
$$
where \(f\) is the electrical frequency, \(B_m\) is the peak flux density, and \(k_h\), \(k_e\), \(k_a\), and \(\alpha\) are material-dependent coefficients. For the solid conductive parts, I computed the eddy-current loss from the induced current density as
$$
P_{solid} = \int_V \frac{|\mathbf{J}|^2}{\sigma} dV
$$
The copper loss in the winding was calculated from the current density and the effective resistance of the winding:
$$
P_{cu} = \int_V \frac{|\mathbf{J}|^2}{\sigma} dV
$$
At the rated operating point, the transient loss reached a stable periodic state after the initial electrical transient. The stator core loss was the dominant component. The rotor core loss and solid eddy-current loss were much smaller, but they were still included in the thermal model because they are generated in components that are difficult to cool. The loss breakdown that I obtained is summarized below.
| Loss component | Symbol | Value in W | Share of core loss |
|---|---|---|---|
| Stator core loss | \(P_{fe,s}\) | 247.194 | 92.254% |
| Rotor core loss | \(P_{fe,r}\) | 20.755 | 7.746% |
| Total core loss | \(P_{fe,tot}\) | 267.949 | 100% |
| Solid eddy-current loss | \(P_{solid}\) | 19.806 | Not applicable |
I observed that the stator core loss accounted for more than ninety-two percent of the total core loss. This result is consistent with the fact that the stator experiences the fundamental and harmonic components of the air-gap field, while the rotor field rotates more synchronously with the rotor in the fundamental reference frame. In a PMSM electric motor with buried magnets, however, the rotor harmonics, flux barriers, and bridge saturation can still create local loss concentrations that influence magnet temperature. I therefore retained the rotor loss and the solid loss in the thermal calculation instead of neglecting them.
Thermal-fluid model. I modeled the water-cooled housing as a conjugate heat transfer problem. The solid domains of the PMSM electric motor conducted heat by conduction, and the coolant domain transferred heat by convection. The steady-state energy equation in the solid regions was
$$
\nabla \cdot (k \nabla T) + Q = 0
$$
where \(k\) is the thermal conductivity and \(Q\) is the volumetric heat source obtained from the electromagnetic loss calculation. In the fluid domain, I solved the continuity equation, the momentum equation, and the energy equation. The continuity equation was
$$
\nabla \cdot \mathbf{u} = 0
$$
The momentum equation for the incompressible coolant was
$$
\rho (\mathbf{u}\cdot \nabla)\mathbf{u} = -\nabla p + \mu \nabla^2 \mathbf{u}
$$
and the energy equation was
$$
\rho c_p \mathbf{u}\cdot \nabla T = \nabla \cdot (k \nabla T)
$$
At the fluid-solid interface, I imposed continuity of heat flux and temperature:
$$
T_s = T_f
$$
$$
k_s \frac{\partial T_s}{\partial n} = k_f \frac{\partial T_f}{\partial n}
$$
The convective heat transfer at the channel wall was represented by
$$
q” = h (T_s – T_f)
$$
where \(h\) is the convective heat transfer coefficient. I estimated the thermal performance of the water channel using the Reynolds number, the hydraulic diameter, and the Nusselt number. The Reynolds number was
$$
Re = \frac{\rho u D_h}{\mu}
$$
and the hydraulic diameter was
$$
D_h = \frac{4 A_c}{P_w}
$$
where \(A_c\) is the channel cross-sectional area and \(P_w\) is the wetted perimeter. For the baseline inlet velocity of 0.65 m/s and an inlet area of 314.159 mm2, the flow remained in a range where forced convection was significant. The pressure drop along the channel was estimated from
$$
\Delta p = f \frac{L}{D_h} \frac{\rho u^2}{2}
$$
The hydraulic pumping power required to circulate the coolant was
$$
P_{pump} = \Delta p Q
$$
where \(Q\) is the volumetric flow rate. I used these relations to interpret the trade-off between lower winding temperature and higher pumping loss. In a PMSM electric motor, the coolant velocity cannot be increased indefinitely because the pressure drop grows approximately with the square of velocity, while the temperature reduction tends to saturate as the flow becomes more effective.
| Boundary condition | Value |
|---|---|
| Inlet velocity | 0.65 m/s |
| Inlet cross-sectional area | 314.159 mm2 |
| Inlet temperature | 25 °C |
| Initial temperature | 25 °C |
| Outlet boundary | Pressure outlet |
| Outlet gauge pressure | 0 Pa |
| Coolant | Water-compatible coolant |
| Solid-fluid interface | Coupled thermal wall |
Baseline temperature results. I imported the electromagnetic loss into the thermal model as a volumetric heat source and solved for the steady temperature field. The highest temperature appeared at the end winding of the stator. The end winding is located outside the stator core, so it has a long thermal path to the water-cooled housing. In addition, the end winding is close to other loss-producing regions and has a relatively small surface area for heat transfer. For this reason, the end winding is often the limiting component in a liquid-cooled PMSM electric motor. The maximum temperature that I obtained was approximately 101.5 °C. The insulation layer between the slot and the winding reduced the heat flow from the winding to the stator core, which helped to lower the average slot temperature but also contributed to the local end-winding temperature rise.
The lowest temperature appeared in the housing because the housing is directly adjacent to the water channel. The stator core was cooler than the winding, with a maximum of about 55.56 °C. The rotor core and permanent magnets were in the range of about 50 to 58 °C. The permanent magnet temperature is especially important in a PMSM electric motor because the remanent flux density and coercivity of the magnet depend on temperature. A high magnet temperature can reduce the torque capability and increase the risk of irreversible demagnetization. In my baseline result, the magnet temperature remained moderate, but the margin depends on the coolant temperature and the duty cycle.
| Component | Minimum temperature in °C | Maximum temperature in °C | Temperature span in °C |
|---|---|---|---|
| Full model | 24.92 | 101.5 | 76.58 |
| Winding | 37.94 | 101.5 | 63.56 |
| Stator | 33.30 | 55.56 | 22.26 |
| Rotor | 50.87 | 58.63 | 7.76 |
| Permanent magnet | 51.77 | 57.71 | 5.94 |
| Water channel | 24.92 | 29.02 | 4.10 |
The water channel temperature distribution was relatively narrow, with a span of about 4.10 °C. This indicates that the coolant heated gradually as it passed through the channel, but the total temperature rise was not large at the baseline flow rate. The pressure distribution in the channel showed a maximum at the inlet and a minimum at the outlet. The inlet pressure reached about \(1.734 \times 10^4\) Pa, while the outlet pressure was about \(-4.709 \times 10^2\) Pa. The pressure difference was about \(1.781 \times 10^4\) Pa. The velocity field showed higher values at the bends and lower values near sharp corners. In some corner zones, the velocity was almost zero, which can create local hot spots if the heat flux is high in those regions.
| Quantity | Value |
|---|---|
| Maximum inlet pressure | \(1.734 \times 10^4\) Pa |
| Outlet pressure | \(-4.709 \times 10^2\) Pa |
| Pressure difference | \(1.781 \times 10^4\) Pa |
| Maximum coolant velocity | 2.62 m/s |
| Inlet area | 314.159 mm2 |
| Baseline inlet velocity | 0.65 m/s |
Effect of coolant velocity. I repeated the thermal-fluid solution at inlet velocities of 0.65 m/s, 1.0 m/s, and 1.35 m/s. The pressure and velocity distributions followed the same general pattern at all three flow rates, but the maximum pressure and maximum velocity increased with the inlet velocity. The temperature of the PMSM electric motor decreased as the flow rate increased, although the reduction in the maximum winding temperature was modest. The most noticeable improvement was the reduction in the temperature span along the water channel. At 0.65 m/s, the channel temperature span was 4.10 °C. At 1.0 m/s, it decreased to 2.51 °C, and at 1.35 m/s, it decreased to 1.91 °C. This means that a higher flow rate made the cooling more uniform along the axial direction, which is beneficial for reducing thermal stress and local hot spots.
| Component | 0.65 m/s | 1.0 m/s | 1.35 m/s |
|---|---|---|---|
| Full model | 24.92 to 101.5 °C | 24.95 to 101.4 °C | 21.88 to 101.2 °C |
| Winding | 37.94 to 101.5 °C | 36.88 to 101.4 °C | 36.02 to 101.2 °C |
| Stator | 33.30 to 55.56 °C | 32.09 to 54.70 °C | 31.23 to 53.98 °C |
| Rotor | 50.87 to 58.63 °C | 50.38 to 58.33 °C | 50.02 to 58.12 °C |
| Permanent magnet | 51.77 to 57.71 °C | 51.26 to 57.35 °C | 50.90 to 57.10 °C |
| Water channel | 24.92 to 29.02 °C | 24.95 to 27.46 °C | 24.96 to 26.87 °C |
I also estimated the pumping power associated with each flow rate using the pressure difference and the volumetric flow rate. The inlet area was \(3.14159 \times 10^{-4}\) m2. Therefore, the volumetric flow rate was \(Q = A u\). At 0.65 m/s, \(Q\) was about \(2.042 \times 10^{-4}\) m3/s. Using the baseline pressure difference of \(1.781 \times 10^4\) Pa, the pumping power was about 3.64 W. At higher velocities, the pressure drop increased approximately with the square of velocity, so the pumping power increased more rapidly than the flow rate. This is an important design trade-off in a PMSM electric motor because the coolant pump consumes part of the vehicle energy, and excessively high flow rates may not produce a proportional thermal benefit.
| Inlet velocity in m/s | Volumetric flow rate in m3/s | Estimated pressure difference in Pa | Estimated pumping power in W |
|---|---|---|---|
| 0.65 | \(2.042 \times 10^{-4}\) | \(1.781 \times 10^4\) | 3.64 |
| 1.00 | \(3.142 \times 10^{-4}\) | \(4.105 \times 10^4\) | 12.90 |
| 1.35 | \(4.241 \times 10^{-4}\) | \(7.478 \times 10^4\) | 31.72 |
The temperature reduction from increasing the flow rate was not uniform across all components. The winding maximum temperature decreased from 101.5 °C to 101.2 °C when the velocity increased from 0.65 m/s to 1.35 m/s. This small reduction shows that the end-winding hot spot is not controlled only by the channel convection resistance. It is also controlled by the internal conduction resistance from the end winding to the stator core and housing. In other words, even if the housing is cooled more aggressively, the heat must first travel through the insulation and the stator structure. For this reason, improving the end-winding thermal path can be more effective than simply increasing the flow rate in a PMSM electric motor.
I used a simple thermal resistance network to interpret this behavior. The temperature rise from the coolant to the hottest winding point can be expressed as
$$
\Delta T = Q_{loss} R_{th,total}
$$
where \(Q_{loss}\) is the heat generation rate and \(R_{th,total}\) is the sum of the conduction and convection resistances. The total thermal resistance can be written as
$$
R_{th,total} = R_{th,cond} + R_{th,conv}
$$
The convection resistance is
$$
R_{th,conv} = \frac{1}{h A}
$$
and the conduction resistance through a layer of thickness \(t\) and area \(A\) is
$$
R_{th,cond} = \frac{t}{k A}
$$
When the flow rate increases, \(h\) increases and \(R_{th,conv}\) decreases. However, if \(R_{th,cond}\) is large, the total resistance is dominated by conduction. This explains why the end-winding temperature only decreased slightly while the channel temperature span decreased more noticeably. In my model, the insulation layer and the air voids in the slot created a significant conduction resistance. The slot insulation helped to reduce the temperature of the stator core, but it also limited the heat flow from the winding to the core.
| Thermal path element | Dominant resistance | Effect of increasing coolant velocity | Effect on PMSM electric motor |
|---|---|---|---|
| Water channel convection | Convection | Strongly reduced | Lower housing and stator temperature |
| Housing to stator core | Conduction and contact | Moderately reduced | Improved heat spreading |
| Stator core to slot insulation | Conduction | Weakly reduced | Limited by insulation thickness |
| Slot insulation to winding | Conduction | Weakly reduced | Controls slot winding temperature |
| End winding to ambient | Convection and radiation | Weakly affected | Main hot spot in PMSM electric motor |
| Rotor to shaft and air gap | Conduction and convection | Weakly affected | Moderate magnet temperature |
Electromagnetic and thermal coupling observations. The most important coupling observation that I made is that the loss distribution is not uniform, and the temperature distribution inherits that nonuniformity. The stator core loss was concentrated in the teeth and yoke, where the flux density and its harmonics were largest. The stator winding loss was distributed in the slot and end-winding regions. The solid eddy-current loss was concentrated in large conductive parts near the air gap. As a result, the temperature field of the PMSM electric motor was not symmetric in a simple radial sense. The end winding was hotter than the slot winding, the stator teeth were hotter than the yoke in some locations, and the rotor magnets had a relatively narrow temperature span but still required attention because of their temperature-sensitive magnetic properties.
I also noted that the insulation layer plays a dual role. Electrically, it separates the winding from the stator core and prevents short circuits. Thermally, it adds resistance between the copper loss source and the cooled stator core. In a high-power-density PMSM electric motor, the insulation thickness and the impregnation quality can therefore have a measurable effect on the hot spot temperature. A better impregnation process can reduce void content and increase the effective thermal conductivity of the slot, which lowers the winding temperature without changing the electromagnetic design. Similarly, a thin but robust insulation layer can improve heat transfer while maintaining dielectric strength.
The water channel design also influences the thermal behavior. The axial Z-shaped channel that I modeled provides a long cooling path along the housing and promotes heat transfer near the stator outer diameter. However, sharp bends and corners can create recirculation zones where the local velocity is low. These zones can become local hot spots if they coincide with high heat flux. I observed that the velocity was highest at the bends and almost zero in some sharp corner regions. Therefore, a channel design with smoother transitions and fewer stagnant corners can improve the uniformity of cooling in a PMSM electric motor. The pressure drop must also be considered, because a more complex channel may increase the required pumping power.
Design implications. Based on the coupled results, I identified several design directions for a water-cooled PMSM electric motor. First, the end-winding region should be treated as a critical hot spot. Improving the thermal contact between the end winding and the housing, or adding a local potting material with high thermal conductivity, can reduce the maximum temperature more effectively than increasing the coolant velocity alone. Second, the slot insulation should be optimized to balance dielectric strength and thermal resistance. Third, the water channel should be designed to avoid stagnant corners while keeping the pressure drop acceptable. Fourth, the magnet temperature should be monitored because it affects the torque capability and demagnetization margin. Fifth, the electromagnetic design should consider loss harmonics, because harmonic loss in the rotor and solid parts can create local heating even when the total loss is small.
| Design parameter | Thermal benefit | Electromagnetic benefit | Possible penalty |
|---|---|---|---|
| Higher coolant velocity | Lower channel temperature span | No direct electromagnetic change | Higher pump power |
| Thinner slot insulation | Lower winding temperature | No direct change | Dielectric risk |
| Improved impregnation | Higher effective slot conductivity | No direct change | Manufacturing complexity |
| End-winding potting | Lower hot spot temperature | No direct change | Additional mass and cost |
| Smoother channel bends | More uniform cooling | No direct change | Manufacturing complexity |
| Lower harmonic content | Lower rotor and solid loss | Higher efficiency and lower magnet heating | May require more stator material |
I also examined how the temperature field would respond if the loss were assumed uniform instead of mapped from the electromagnetic solution. A uniform loss assumption would underestimate the local temperature near the stator teeth and end winding and would overestimate the temperature in regions with low loss. This is why the electromagnetic-thermal coupling is essential for a PMSM electric motor. The magnetic field determines where the heat is generated, and the thermal field determines whether that heat can be removed. The two fields are linked through the temperature-dependent properties of the materials, especially the permanent magnet remanence and the electrical conductivity of copper and aluminum.
In principle, a fully coupled solution could also update the electromagnetic loss after each thermal iteration, because the electrical conductivity of copper changes with temperature and the magnet flux density changes with magnet temperature. In my workflow, I used a sequential coupling in which the electromagnetic loss was computed first and then imported into the thermal model. This sequential approach is computationally efficient and is often sufficient when the temperature change is moderate. However, for a PMSM electric motor that operates near its thermal limit, the temperature dependence of copper resistivity and magnet remanence can be important. A future extension of my model would be to iterate between the electromagnetic and thermal solutions until the loss and temperature converge.
Quantitative summary. The table below summarizes the main quantitative findings from my coupled analysis. The baseline maximum winding temperature was 101.5 °C, and the maximum water channel temperature was 29.02 °C. The channel temperature span was 4.10 °C at 0.65 m/s and decreased to 1.91 °C at 1.35 m/s. The stator core loss was 247.194 W, which was 92.254% of the total core loss. The solid eddy-current loss was 19.806 W. The pressure difference at the baseline flow rate was \(1.781 \times 10^4\) Pa, and the maximum coolant velocity was 2.62 m/s.
| Metric | Value | Unit |
|---|---|---|
| Rated power of PMSM electric motor | 30 | kW |
| Rated speed | 3000 | r/min |
| Stator core loss | 247.194 | W |
| Rotor core loss | 20.755 | W |
| Total core loss | 267.949 | W |
| Solid eddy-current loss | 19.806 | W |
| Stator core loss share | 92.254 | % |
| Maximum winding temperature | 101.5 | °C |
| Maximum stator temperature | 55.56 | °C |
| Maximum rotor temperature | 58.63 | °C |
| Maximum magnet temperature | 57.71 | °C |
| Maximum water channel temperature | 29.02 | °C |
| Water channel span at 0.65 m/s | 4.10 | °C |
| Water channel span at 1.35 m/s | 1.91 | °C |
| Baseline pressure difference | \(1.781 \times 10^4\) | Pa |
| Maximum coolant velocity | 2.62 | m/s |
Conclusions. I performed an electromagnetic-thermal coupling analysis of a water-cooled interior PMSM electric motor using a finite-volume thermal model driven by a finite-element electromagnetic loss calculation. The main conclusions that I draw from this work are as follows. The stator winding end region is the hottest part of the PMSM electric motor under the rated condition because the end winding has a long conduction path to the cooled housing and a limited convection area. The water channel effectively lowers the housing and stator temperatures, but the channel temperature span and the local velocity distribution must be designed carefully to avoid stagnant zones. Increasing the coolant velocity reduces the channel temperature span and slightly reduces the maximum winding temperature, but the pumping power increases rapidly, so the flow rate should be selected as a compromise between thermal margin and hydraulic loss. The stator core loss is the dominant heat source, accounting for more than ninety-two percent of the total core loss, while the rotor core loss and solid eddy-current loss are smaller but still relevant for magnet temperature and local heating. The insulation layer between the winding and the stator core is thermally significant because it limits the heat flow from the copper loss source to the cooled core. Finally, the electromagnetic and thermal fields of a PMSM electric motor are strongly coupled through the spatial loss distribution and through the temperature-dependent properties of the materials. A coupled numerical approach is therefore essential for accurate thermal management, efficiency optimization, and reliability assessment of a PMSM electric motor.