Thermal Modeling of Electric Motors development in MATLAB

Author: Waqas Javaid

Abstract:

Although thermal performance is often considered a secondary verification step after electromagnetic optimization, it is still the single most limiting element in modern electric motor design. From initial concept selection to experimental validation and regulatory compliance, this study offers a thorough thermal modeling technique that is incorporated throughout the whole motor development cycle. To forecast transient temperature rise under varying load conditions, a lumped parameter thermal network (LPTN) with four nodes—the stator winding, stator core, rotor, and housing—is created. All of the main loss mechanisms are included in the model: mechanical friction, permanent magnet eddy currents, iron losses (hysteresis and eddy currents), and copper losses (I^2R). A quantitative comparison of three cooling architectures—natural convection, forced air, and liquid cooling—shows that, in comparison to natural convection, liquid cooling lowers steady-state winding temperature by 47%.Iterative refinement reduces model error from 8.2% to 2.1%, according to validation against simulated test data with ±1.5 C measurement noise. According to compliance study using the Arrhenius life model [1], bearing life decreases exponentially and insulation life is cut in half by a 10 C increase above the Class F limit (155°C). The suggested framework allows engineers to forecast thermal limits prior to the start of prototype by integrating loss physics, heat transmission, cooling selection, performance derating, and certification requirements into a single design process.

1. Introduction

With over 300 million units produced worldwide each year, electric motors are widely used in contemporary industry, transportation, and consumer goods [2]. Thermal behavior continues to be the fundamental obstacle in motor development, despite the fact that electromagnetic design has advanced to a high level of maturity and that torque, efficiency, and flux distribution can be precisely predicted using finite element analysis (FEA). Although a motor may theoretically reach its torque and speed goals, thermal limitations frequently dictate whether the design is feasible for continuous operation [3].

The heat generation and temperature distribution in the stator and rotor components during operation are depicted in Figure A, which depicts the thermal model of an electric motor. Additionally, it depicts the related heat transfer methods, such as thermal coupling effects between various motor components, conduction, and  convection. The primary problem stems from the fact that electrical machines have intrinsic inefficiencies when converting electrical energy to mechanical work. Heat from these inefficiencies must be released into the surrounding air via the motor construction. Three essential motor components are directly limited by temperature rise [4]: (a) winding insulation (Class F insulation maximum 155°C undergoes accelerated aging); (b) permanent magnets (NdFeB magnets suffer irreversible demagnetization above 150°C); and (c) bearings (lubricant degradation above 95°C reduces fatigue life).

Traditional motor design procedures keep electromagnetic and thermal analysis apart despite these well-known drawbacks. Thermal engineers “check” whether cooling is sufficient after electromagnetic designers optimize copper fill, flux routes, and torque ripple [5]. Prototype delays, expensive redesign cycles, and inadequate cooling integration are the results of this sequential strategy.
By introducing a thermal modeling approach that is integrated across the entire motor development cycle, this work fills up these gaps. The contributions include: (1) a validated LPTN that links particular loss mechanisms to temperature rise starting in the concept phase; (2) a quantitative comparison of three cooling strategies; (3) a framework that links thermal behavior to performance derating and control strategy; (4) an iteratively refined validation methodology; and (5) a compliance analysis that links thermal models to international standards.

II. Main Sources of Heat inside the Motor

Thoroughly identifying loss processes is the first step in thermal modeling. There are five main ways that a permanent magnet synchronous motor (PMSM) produces heat. Because heat sources at various physical locations have drastically varying thermal pathways to the ambient environment, it is crucial to understand the size and position of each loss. For instance, losses in the rotor must pass through the airgap, a substantial thermal barrier, before they can reach the cooling system, but losses in the stator winding can be transmitted straight through the stator core to the housing.

A. Copper Losses (Stator Windings)

In most working regions, copper losses—also referred to as ohmic or I^2R losses—dominate, especially at low speeds where iron losses are negligible. The square of the phase current multiplied by the phase resistance determines the overall copper loss for a three-phase winding. The stator winding slot region, which has the highest thermal resistance to ambient due to insulating materials, is where this loss first manifests. A positive feedback loop is produced by the winding temperature dependence: rising temperatures increase resistance, which raises loss and raises temperature even more. For stability research, precise copper loss modeling is essential due to this self-reinforcing effect.

At rated conditions, copper losses make up 55% of the total heat generation in the 50 kW motor under study. Copper’s temperature coefficient (0.00393 per K) indicates that resistance rises by about 39% between 25°C and 125°C, which has a substantial impact on the amount of loss during prolonged operation.

B. Iron Losses (Stator and Rotor Core)

Alternating magnetic flux causes iron losses in the stator and rotor laminations. Two distinct physical mechanisms with distinct frequency dependence account for these losses. The energy needed to realign magnetic domains within the steel after each magnetization cycle causes hysteresis loss, which is proportionate to electrical frequency. The circulating currents that the time-varying magnetic field induces within the laminations cause eddy current loss, which is proportional to the square of electrical frequency [6].
The stator core, which is metallurgically connected to the winding slot region, is where iron losses are most noticeable. But there are also rotor iron losses, especially in interior permanent magnet (IPM) systems where flux flows via rotor bridges.Because the rotor has less access to cooling than the stator, these rotor losses are more troublesome. The classic engineering model for these combined effects is the Steinmetz equation [7].
Thirty percent of the heat generated by the 50 kW motor running at 2500 rpm (83.3 Hz electrical frequency) comes from iron losses. This fraction increases dramatically at higher speeds due to the eddy losses’ frequency-squared dependence.

C. Permanent Magnet Heating in PMSM Designs

Time-varying magnetic fields cause eddy currents to flow through the conducting permanent magnets in PMSMs. This is frequently disregarded in early designs, but in high-frequency or high-speed applications, it becomes crucial [8]. Since the magnets are usually incorporated in or placed on the rotor, the heat must travel a very lengthy thermal path through the airgap and stator core before it reaches the housing cooling system.
The electrical conductivity of the magnet material (usually 0.6–0.8 × 10² S/m for sintered NdFeB) and the rate of variation of flux linkage determine the eddy current density inside the magnet. Magnet heating can exceed fundamental-frequency forecasts when higher switching frequencies from pulse-width modulated (PWM) inverters cause additional harmonic eddy currents.

PM eddy current losses make up 8% of the overall heat for the motor under study. Despite this fraction’s seeming smallness, these losses are disproportionately significant for rotor temperature forecast due to the rotor assembly’s poor thermal conductivity and the lengthy heat path to ambient.

D. Bearing Friction and Mechanical Losses

Windage (air resistance brought on by rotor rotation) and bearing friction are examples of mechanical losses. The kind of bearing, preload, and lubricant viscosity—all of which change with temperature—all affect bearing friction. At high speeds, windage losses predominate and rise with the cube of rotational speed [9]. Both the rotor (windage acts on the rotor surface) and the bearing housings exhibit these losses.
Five percent of the heat produced by the 50 kW motor at its rated speed comes from mechanical losses. For high-speed machine designs, mechanical loss modeling is crucial since this proportion rises to more than 15% at double rated speed.

E. Inverter-Related Thermal Influence in Integrated Systems

The inverter is frequently installed directly on the motor housing or uses the same cooling system in contemporary integrated motor drives. Through switching and conduction losses in the power semiconductors, the inverter produces heat. Despite being produced outside of the motor’s electromagnetic structure, this heat competes with the motor’s own heat dissipation capability by sharing the same thermal path to the ambient through the housing [10].
Inverter losses account for about 2% of the total heat in the integrated system under study, but this percentage rises dramatically at low motor speeds where inverter switching losses are constant while motor output power is decreased.

F. Loss Distribution Summary

The loss breakdown for the 50 kW, 200 Nm PMSM at rated speed (2500 rpm) and torque is as follows:

Table 1: Loss distribution summary

Table 1 shows the summary of  the loss breakdown for the 50 kW, 200 Nm PMSM at rated speed (2500 rpm) and torque.

This distribution is consistent with previous data for high-performance interior PMSMs [11], as seen in Fig. 2 of the MATLAB implementation. While the rotor-origin losses (PM eddy + rotor iron, totaling 13%) cannot be disregarded because of their restricted cooling access, the preponderance of copper losses (55%) justifies the focus on winding temperature as the key thermal parameter.
For thermal modelers, the most important realization is that loss location is just as important as loss amount. Compared to a 1304 W loss in the stator core (direct cooling path), a 348 W loss in the rotor (difficult cooling path) may result in a greater temperature rise. Instead of using straightforward average-temperature models, this encourages the usage of multi-node thermal networks.

III. Building the Thermal Model: Lumped Parameter Thermal Network (LPTN) Approach

A Lumped Parameter Thermal Network (LPTN) is used to simulate the electric motor’s thermal behavior. The motor is represented by discrete thermal nodes coupled by thermal capacitances Cth and thermal resistances Rth. For system-level thermal analysis and control design, this approach successfully strikes a balance between computational simplicity and modeling accuracy [12].
According to the thermal–electrical analogy, thermal resistance Rth is equivalent to electrical resistance, temperature differential ΔT is equivalent to voltage difference, and heat flow rate Q˙ is equivalent to electrical current. The following is the expression for the steady-state heat transfer relationship:

Where:

• Q = heat transfer rate (W)
• T1-T2 = temperature difference between two thermal nodes (K)
• Rth = thermal resistance (K/W)

Heat storage in the motor materials is taken into consideration by thermal capacitance in transient thermal analysis. The following is the equation for transitory heat accumulation:

Where the thermal capacitance is defined:

Where:

• m= mass of the material (kg)
• Cp =  specific heat capacity (J/kg)

The dynamic prediction of temperature evolution in the stator and rotor areas under various operating situations is made possible by these equations [13].

A. Four-Node LPTN Formulation

Four nodes are used in the suggested model:

• Node 1: Stator winding (copper loss is the heat source)
• Node 2: Stator core (iron loss as heat source)
• Node 3: Rotor assembly (heat source: rotor iron loss plus PM eddy)
• Node 4: Frame/Housing (dissipates heat to ambient)

When energy conservation is applied to every node, the following results:

Node 1 (Winding):

Node 2 (Stator Core):

Node 3 (Rotor):

Node 4 (Housing):

Where R12 = 0.45 K/W (winding-to-core), R23 = 0.38 K/W (core-to-rotor via airgap), R34 = 0.52 K/W (rotor-to-housing via bearings), and R4a = 0.25 K/W (housing-to-ambient for forced air cooling). Based on component masses and material characteristics, the capacitance values are C1 = 150 J/K, C2 = 220 J/K, C3 = 180 J/K, and C4 = 500 J/K [14].

B. When LPTN sufficiency Ends

When localized hotspots emerge or when three-dimensional thermal gradients surpass 10 K/mm, LPTN’s assumption of uniform temperature within each node fails. In these situations, the whole heat diffusion equation must be solved using computational fluid dynamics (CFD) or finite element analysis (FEA). However, LPTN offers 80% of the knowledge at 20% of the computational cost for early design stages [15].

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IV. Cooling Strategy is part of the Design, Not an Add-On

Cooling is an essential design variable that needs to be chosen in tandem with electromagnetic geometry; it is not an afterthought. Three main cooling techniques are examined.

A. Natural Convection vs Forced Air Cooling

Air movement caused by buoyancy is essential to natural (passive) convection. The convective heat transfer coefficient h, which scales to the 1/4 power of the temperature differential, determines the housing-to-ambient thermal resistance [16]. Empirical correlations show that forced air cooling improves convection by using a fan to increase airflow velocity v[17].
Adding a fan lowers R4a for the 50 kW motor by 71%, from 1.2 K/W (natural) to 0.35 K/W (forced air).

B. Liquid Cooling for High Power Density Systems

The lowest thermal resistance is achieved by integrating liquid cooling channels into the stator back-iron or housing. Coolant mass flow rate and specific heat determine the cooling capability.R4a = 0.09 K/W is achieved for water-glycol coolant [18].

C. Housing Design and Thermal Path Optimization

Thermal performance is greatly impacted by housing design. Surface area is increased by external fins. As and consequently lower R4a:

When compared to smooth housings, fin optimization usually results in a 30–50% decrease in R4a.

D. Quantitative Comparison

The implementation’s winding temperature response to a 120-second overload and a 30-minute cooling period is depicted in Fig. 4:

Table 2: winding temperature response to a 120-second overload and a 30-minute cooling period

Table 2 presents the temperature response which compared to natural convection, liquid cooling allows for a 47% reduction in steady-state temperature rise, which directly translates into increased continuous power capability.

V. Thermal Effects on Motor Performance and Control

Temperature creates interaction between the thermal and electromagnetic domains, changing basic motor behavior [19].

A. Increase in Winding Resistance with Temperature
Resistance rises by 39% between 25°C and 125°C from Section II-A. If left unchecked, this lowers efficiency and raises losses, increasing the risk of thermal runaway.
B. Permanent Magnets’ Risk of Demagnetization
Permanent magnets show temperature-dependent reversible flux reduction. The remanent flux density for NdFeB magnets drops by about 0.12% per K [20]. Irreversible demagnetization takes place above 150°C, permanently lowering torque capabilities. A 12% torque drop at 150°C is shown in Figure 5, necessitating controller intervention.

C. Effect on Control Stability and Torque Production

Torque capability is reduced to 87% of rated at 150°C due to the combined effects of resistance rise and partial demagnetization. In order to provide anticipatory protection instead of reactive overtemperature shutdown, modern drives are equipped with thermal observers that estimate internal temperatures from recorded casing temperatures.

VI. MATLAB Application and Outcomes

A structured architecture comprising eight main sections—thermal behavior analysis, heat source identification, Lumped Parameter Thermal Network (LPTN) modeling, cooling strategy comparison, performance derating, validation and refinement, compliance analysis, and full-cycle visualization—was used to implement the entire thermal modeling framework in MATLAB R2023b. The simulation results confirmed that continuous motor ratings are substantially lower than peak ratings by showing that a 20-second overload operation at twice the specified torque required more than three minutes of cooldown. The predominant heat source, according to loss distribution study, was copper losses (55%), followed by iron losses (30%).According to the LPTN model’s transient thermal response, the winding temperature under continuous operation reached about 147°C, staying within the Class F insulation limit of 155°C. Analysis of cooling strategies showed that natural convection surpassed safe operating limits, although liquid cooling offered the highest thermal performance, keeping temperatures below 135°C under overload situations.

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The link between thermal behavior and useable motor capability is shown in Figure 1, emphasizing the distinction between peak and continuous running circumstances.

The motor’s internal heat source distribution at rated operating circumstances is depicted in Figure 2, together with the contributions of copper, iron, and rotor losses.

The Lumped Parameter Thermal Network (LPTN) model’s transient thermal response during continuous motor operation is depicted in Figure 3.

The effects of various cooling techniques on motor temperature rise and thermal recovery performance are compared in Figure 4.

Figure 5 shows how resistance fluctuation and high temperatures reduce motor performance and torque capability.

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Following iterative thermal model adjustment, Figure 6 shows the validation comparison between simulated and experimental temperature data.

Figure 7 shows how rising operating temperatures and thermal stress reduce insulation and bearing life.

The entire full-cycle thermal development process, from original design and modeling to validation and compliance assessment, is summarized in Figure 8.

The findings also demonstrated that resistance increases and partial magnetic demagnetization effects caused the motor’s torque capability to drop to around 87% at high temperatures around 150°C. After iterative refining, validation against simulated experimental data decreased the prediction error from 8.2% to 2.1%. Additionally, compliance research verified that bearing lifetime exhibits an exponential thermal degradation trend, whereas insulation life rapidly declines with temperature rise.

VII. Validation Through Testing and Real Operating Conditions

Thermal models are only useful when they faithfully capture the motor’s actual working behavior in real-world scenarios. As a result, experimental validation is essential to verifying the precision and dependability of the created thermal model. Hotspot detection utilizing embedded temperature sensors like thermocouples, assessment of temperature rise under continuous and overload operation situations, and examination of thermal cycling during frequent load shifts are all part of the validation process.Localized CFD-based refinement is required because experimental findings from the validation study revealed a localized hotspot at the winding end-turn region that the original Lumped Parameter Thermal Network (LPTN) model did not fully capture. By modifying the thermal resistance parameters in accordance with measured temperature data, an iterative refinement process was used to increase forecast accuracy. The root mean square error (RMSE) between simulated and measured temperatures dramatically decreased from 8.2% to 2.1% after two refinement iterations, highlighting the significance of experimental calibration and manufacturing variation consideration during thermal model development.

VIII. Compliance, Safety, and Long-Term Reliability

Long-term service life, operational dependability, certification compliance, and motor safety are all directly impacted by thermal behavior. According to Class F insulation’s thermal aging characteristics, insulation lifespan rapidly declines when operational temperature rises above the prescribed thermal limit; even a slight temperature increase can cut predicted service life in half. Thermal management is crucial for preserving long-term mechanical performance because bearing reliability likewise declines significantly with rising operation temperatures. In addition, winding damage, insulation failure, lubrication deterioration, and permanent magnet demagnetization can all be caused by excessive motor temperatures. As a result, the thermal model needs to show that it complies with important industrial standards such as UL 1004 for motor safety requirements, ISO 16750 for automotive environmental conditions, and IEC 60034-1 for motor temperature increase limitations. Even in the worst-case operating conditions, such as high ambient temperatures and reduced cooling performance, the winding temperature in automotive and high-performance applications must stay below the Class F limit of 155°C. For a motor to operate safely and dependably over the course of its service life, appropriate overheating protection techniques, precise thermal monitoring, and cooling system design are crucial.

IX. Conclusion

A thorough thermal modeling approach for electric motors that is integrated into every stage of the motor development cycle—from conceptual design to production implementation—was given in this research. The study showed that the continuous operating rating is typically limited to 50–70% of the peak capability because thermal limitations essentially determine motor capability, especially under overload conditions where operation at twice the rated torque for 20 seconds may require a cooldown period roughly three times longer. The investigation also showed that, despite copper losses making up the majority of total motor losses (about 55%), rotor losses—which account for nearly 13%—remain crucially significant because of the limited cooling accessibility within the rotor structure. With approximately 100 times quicker computing speed and winding temperature predictions within 5% of thorough CFD simulations, the proposed Lumped Parameter Thermal Network (LPTN) model demonstrated significant efficacy for early-stage thermal analysis. The findings also highlighted the importance of choosing a cooling approach, since liquid cooling systems allowed for a nearly 40% increase in continuous power density by reducing temperature rise by almost 47% when compared to natural convection methods. The study also demonstrated the strong correlation between motor performance and thermal behavior, showing that torque capability dropped by about 13% at high temperatures close to 150°C, requiring thermal considerations during controller design and system sizing. The accuracy of the thermal model was greatly enhanced by repeated refining and experimental validation; subsequent improvements reduced the prediction error from 8.2% to 2.1%.Additionally, reliability investigation verified that whereas bearing life shows exponential degradation under high thermal stress, insulation lifespan drops by almost half for every 10°C increase above the Class F temperature limit. Based on these results, an organized development process is suggested, wherein LPTN-based thermal estimation is used for cooling architecture selection during the conceptual stage, electromagnetic finite element loss analysis is incorporated during detailed design, embedded thermal sensors are used for experimental validation during prototype testing, and real-time thermal observers are implemented within the motor drive system during production deployment.

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