Thermal Network Model Research Articles

Non-Newtonian Thermo-Elastohydrodynamics and Sub-Surface Stress Field of High-Performance Racing Spur Gears

Meshing teeth pairs of involute spur gears often form the final drive of high-performance motorsport transmissions. They are subject to high normal and shear loading. Under transient conditions pertaining to a meshing cycle, the contact conditions alter from the onset of teeth pair engagement through to maximum normal loading, followed by contact separation. Sliding motion only ceases instantaneously at the pitch point. The regime of lubrication remains mostly in non-Newtonian thermo-elastohydrodynamic conditions. The results show that a starved inlet boundary is attained throughout most of the meshing cycle which leads to the diminution of the pressure spike at the exit from the contact conjunction. The reversing sub-surface shear stresses are the main source of the onset of any inelastic deformation, which is dominated by the primary pressure peak in compliance with the Hertzian maximum pressure. The shear stress field is supplemented by an induced field due to the presence of the pressure spike. Under starved conditions this secondary stress field is diminished. The combined solution of elastohydrodynamics with a thermal network model, non-Newtonian lubricant traction, and sub-surface stress evaluation provides for a comprehensive solution not hitherto reported in the literature.

A thermal network model for hydrocarbon heat pump systems: A coupling analysis of configuration, working condition, and refrigeration distribution

The ambition of zero emission neighborhood has been set out to operate the building components with zero life cycle greenhouse gas emissions. Hydrocarbon heat pumps as the building components with nearly zero greenhouse gas emissions are faced with the problem of simultaneously reducing refrigerant charges and maintaining competitive capacities. These must be resolved by formulating an effective modeling tool for detailed design and optimization. To develop a resistance–capacitance network model, interdisciplinary knowledge (including graph theory, heat and mass transfer, local moving boundary modeling, and algebraic multigrid) is integrated. The model simultaneously considers heat exchanger circuitries with a high detail level and component behaviors at a holistic system level. Based on experimental validation, the model’s error is ∼ 10%. In an R290 heat pump case study, the coupling mechanism of the system’s configuration, working conditions, and refrigerant distribution are analyzed. Results indicate that the refrigerant charge can be reduced by 11.6% at the expense of a 4.2% reduction in the coefficient of performance, by varying the compressor displacement alone. In response to the variation in the system’s refrigerant, 46.8%, 7.85%, and 44.2% of the total amount of refrigerants are allocated to the condenser, evaporator, and compressor, respectively. The distribution of the refrigerant quality in the heat exchanger is also visualized to indicate the direction of refrigerant reduction.

Dynamic, thermal, and vibrational analysis of ball bearings with over-skidding behavior

The term “over-skidding” indicates that the cage rotational speed ratio exceeds the theoretical value as ball purely rolls on the raceway. Different from the skidding phenomenon that occurs in low-load and high-speed bearing, over-skidding usually occurs in large-size angular contact bearings, and it is still difficult to suppress under high load conditions. The main forms of damage to the raceway by over-skidding are spinning and gyro slip. To further explore the vibration characteristics and thermal effects of this phenomenon, a set of over-skidding tests of an angular contact bearing with a bore diameter of 220 mm were conducted on an industrial-size test bench. Through the experiment, the influence of axial load, rotational speed, and lubrication conditions on the occurrence of over-skidding were determined. Based on a previous dynamics model, the heat generation and thermal network models were integrated in the present study to predict the over-skidding and its thermal behavior. The model was validated in terms of the measured degree of over-skidding and temperature rise. The results showed that the degree of over-skidding reaches up to 12% of the theoretical value, and the friction power loss of the ball-pocket accounts for 30% of the total power loss. The analysis of the vibration signal showed a strong correlation between the bearing vibration characteristics and over-skidding behavior, thereby providing a way to indirectly measure the degree of over-skidding.

Parametric study of evacuated tube collector solar air heater with inserted baffles on thermal network for low-temperature applications

The great challenge in the evacuated tube solar air heater for the industrial application is choosing the optimum thermal networks to get target temperature for the desired air flow rate. In this work, theoretical analysis is done to investigate the influence of the significant design parameters such as evacuated tube length, diameter and number of tubes in a collector on the thermal performance and to design a thermal network model for achieving the desired temperature at specified flow rate of air for industrial process heat applications. Further, establishing an empirical correlation to simplify the thermal network design process. Based on the results of design parametric study, optimal parameters identified for a collector system are 20 numbers of evacuated tubes having dimensions of 1.8 m length, 58 and 47 mm outer and inner diameters. It is noticed that a considerable drop in temperature rise attained in each collector while increasing the number of collectors in series network. The enviro-economic analysis reveals that the overall useful energy gain per annum can be achieved around 8252 kWh which will reduce 17.16 tonne of carbon dioxide emission through the utilization of a thermal network comprising six modules working at 500 kg/h mass flow rate of air. The correlation relates the attainable effective thermal with the non-dimensional operating parameters such as mass flow number, temperature ratio, and number of collectors. The correlation can be used to design a solar evacuated tube thermal network and the proposed solar evacuated tube thermal network can be effectively employed for fulfilling the industrial process heating applications require hot air between 80 and 120 °C.

A quasi-dynamic model and thermal analysis for vapor chambers with multiple heat sources based on thermal resistance network model

The heat and mass transfer mechanism in a vapor chamber is a complex process. The thermal resistance network model is an effective tool to describe the heat transfer behavior of a vapor chamber (VC). An improved quasi-dynamic multi heat source model has been developed in this study to analyze the temperature distribution of a vapor chamber with multiple heat sources under dynamic operating conditions. The accuracy of the proposed model has been validated by experiments. The influence of the VC thickness and thickness ratio has also been analyzed. Different heat source inputs have been used to study the startup characteristics of the vapor chamber. The results from simulations reveal that the optimum thickness ratio for a VC depends on the thermal resistance as well as heat transfer limit. Under the same cooling conditions, a longer startup time for a VC was observed with the increase in heating power. In addition to this, the thermal resistance of a vapor chamber was found to increase slightly at a higher temperature. The model in this study has certain guiding significance for the analysis of heat transfer and the design of a VC under various working conditions. • Thermal resistance network model for vapor chambers with multiple heat sources is established. • Quasi-dynamic approach for transient analysis with high accuracy. • The influences of thickness and optimum thickness ratio are analyzed. • Startup characteristics and thermal resistance are analyzed.

Design and energy flexibility analysis for building integrated photovoltaics-heat pump combinations in a house

This paper considers three configurations of air source heat pumps and building-integrated photovoltaic (BIPV) systems in a solar house. This study evaluates energy efficiency and flexibility when interacting with a smart grid. The reference case is a 5 kW BIPV system on the roof with a separate air-source heat pump water heater (HPWH). In the two more novel options we have: first, a 5 kW BIPV/thermal (BIPV/T) roof system where the heated air from the BIPV/T system is ducted to the air source of the HPWH, which also contains integrated thermal storage (hot water); in the second case we have an attached solarium with a 5 kW semi-transparent photovoltaic façade, with the solar heated air in the solarium connected to the air source of the HPWH with integrated water thermal storage. The three cases are modelled with an explicit finite difference thermal network model, and energy performance is determined and compared over a typical heating season in Montreal, Canada. The energy flexibility potential of the options is compared for different scenarios, such as heating the thermal water storage during the daytime (e.g. using the solar heat in the novel options) and using it for space heating during the time that the grid is under stress (and may have price incentives). Results show that the second novel case utilizing the solarium air as the source of the heat pump resulted in an over 80% energy use reduction relative to the reference. In comparison, the BIPV/T configuration had around 20% reduction compared to the reference case. The tank volume and solarium size had the highest impact on the flexibility of the system. Optimal sizes for the tank volume were typically between 300 and 600 L for the house with a floor area of 116 m2.

An Online SOC-SOTD Joint Estimation Algorithm for Pouch Li-Ion Batteries Based on Spatio-Temporal Coupling Correction Method

An SOC (state of charge)-SOTD (state of temperature distribution) joint estimation algorithm is established for a pouch lithium-ion battery. This method integrates the first-order RC model, distributed heat generation model, thermal resistance network model, and spatio-temporal coupling correction based on spatial restoration algorithm and dual Kalman filter (DKF). Unlike the traditional 1-D SOT estimation model, the proposed algorithm can accurately estimate the temperature distribution in the battery online by restoring the battery surface temperature distribution, calculating the battery internal temperature distribution, and jointly correcting the SOC and average internal temperature. Then, the proposed method is used for the SOC-SOTD estimation of a 25-Ah pouch battery at the ambient temperatures of 10, 20, and 30 °C under the worldwide light-duty test cycle and new european driving cycle driving cycles, and the estimated values are verified by experiment and 3-D simulation. According to the verification results, calculation errors of SOC are no more than 2.12%, and the maximum average calculation errors are 0.16 °C for the surface temperature and 0.24 °C for the internal temperature. However, the DKF is needed for the SOC-SOTD joint estimation because the single KF can only correct SOC or average internal temperature but cannot handle the inconsistency in temperature distribution.

Analytical Modeling for Rotor Eddy Current Loss of a Surface-Mounted PMSM With Both Non-Ferromagnetic Conductive Retaining Sleeve and Shielding Cylinder

It is recognized that the rotor with shielding cylinder (SC) is one of the effective measures to restrain the rotor eddy current loss (RECL) for high-speed surface-mounted permanent magnet synchronous motors (PMSMs). At present, the RECL of PMSMs with multilayer composite rotor structure is mainly analyzed by the finite element method (FEM), which has obvious shortcomings in time-consumption and the mesh generation of thin SC. In this paper, a multi-layer subdomain analytical model for calculating the RECL of high-speed PMSMs with both non-ferromagnetic retaining sleeve and SC is proposed by taking the effects of eddy current reaction, stator slotting and current harmonics into account. Moreover, the 3-D distribution coefficient of eddy current in the SC is derived by the equivalent impedance method and the effects of temperature on the conductivity of the SC and RECL are obtained through equivalent thermal network (ETN) model. Based on the analytical model, the SC parameters are calculated to obtain the variation ranges when the RECL is minimum. Finally, the C-shape core experiment was built up to verify the correctness of the multilayer analytical model under different shielding layer conductivities and thicknesses.

A Temperature-Dependent Cauer Model Simulation of IGBT Module With Analytical Thermal Impedance Characterization

In pursuit of high power density and high reliability of power converters, the junction temperature of power devices becomes an essential indicator for heath condition monitoring and thermal management. Particularly under high-temperature operating conditions, the temperature-dependent thermal properties of the chip and ceramic materials must be incorporated to enhance the prediction accuracy. In this article, an improved temperature-dependent Cauer-type thermal network of insulated-gate bipolar transistor (IGBT) module is established. The temperature dependence of thermal parameters for the chip layer and ceramic layer is meticulously considered. More importantly, finite-element method (FEM) simulation is used to yield the heat flux curve of the power module at the center line in order to better imitate the real heat-spreading scenario. In this way, the effective heat transfer area of each layer can be calculated accurately and analytically. By this analytic method, the temperature-dependent thermal impedance can be efficiently determined. Compared with prior-art fully FEM-based temperature-dependent thermal impedance characterization method, the method proposed in this article reduces the FEM simulation time cost approximately 20 times under the same computing hardware facilities and considerably simplifies the parameter extraction process. Finally, experimental results based on two commercial IGBT modules successfully validate the usefulness, effectiveness, and accuracy of the proposed thermal network model.

Identification of High Resolution Transient Thermal Network Model for Power Module Packages

A transient thermal network model is utilized to design and evaluate the transient thermal characteristics of power modules. Static test method identifies the transient thermal network model from the time response of the junction temperature, which is obtained by using the temperature dependency of I-V characteristics for power devices. This paper experimentally evaluates the effect of the sampling frequency and the resolution of the AD conversion on the accuracy of the obtained transient thermal network model. The high sampling frequency and the high resolution in the obtained time response of the junction temperature enable to clearly identify the transient thermal network model of the power module with the direct bonding copper substrate.

Improvements on permanent magnet synchronous motor by integrating heat pipes into windings for solar unmanned aerial vehicle

The successful market uptake of all-electric propulsion systems is closely related to the performance metrics of the electrical motor used within. In light of this, various road-maps have been set for the next two decades by aerospace and automotive bodies targeting ambitious future targets of the motor's power densities and efficiencies. In achieving motors with such step-improvement performance metrics, often the thermal management is a key challenge. In this paper, a cooling structure for a propulsion motor of solar unmanned aircraft is proposed which combines the stator windings with heat pipes, and which is shown to simultaneously improve the heat dissipation as well as the efficiency. This paper firstly determines the heat transfer characteristic of the heat pipe experimentally which is then used in the development of a bespoke thermal network model of the motor. The effects of the cooling structure on the motor's temperature rise, copper losses, torque, and efficiency are studied in detail. Finally, a prototype is developed and a test platform is built. The experimental results are consistent with the analytical result, verifying the correctness of the thermal network model and the benefits of the proposed mechanism. Compared to the motor without heat pipes, the temperature rise of the motor is reduced by 35%, while its efficiency is improved by a significant 1.5%.

A graph-theory based directed network feature for thermal anisotropy

The effective thermal conductivity of a granular material varies with the predominant heat transfers direction. The anisotropic effective thermal conductivity is known to be dominated by the microstructure in a dry material. However, no microstructural parameters that are well related to thermal anisotropy have been proposed. After analysing the heat transfer mechanisms at the particle scale, this work constructs new directed weighted thermal networks for both lattice and randomly distributed sphere packings, by considering particles as nodes and local heat transfer paths with thermal resistance as directed edges. With the implementation of graph theory to the directed weighted thermal networks, the shortest preferential heat transfer paths between nodes paired at opposite faces of a sample across the driving temperature gradient direction are identified. Based on the shortest heat transfer paths, a new sample-scale feature named “directed network thermal resistance” is computed for each sample. This new parameter accounts for particle connectivity, interparticle contact orientation and contact quality simultaneously. After computing the effective thermal conductivity of each sample in different directions using a weighted thermal network model, it is found that directed network thermal resistance is inversely proportional to anisotropic effective thermal conductivity.

Thermal Network Model for an Assessment of Summer Indoor Comfort in a Naturally Ventilated Residential Building

Costs of cooling installations cause them to be very rarely used in residential buildings in countries located in heating-dominated climates, like Poland. Hence, there arises the need to assess indoor thermal comfort during summer and to indicate ways to reduce possible overheating. This paper presents an attempt to use the thermal network model of the building zone of EN ISO 13790 to assess indoor operative temperature during four warm months from June to September. The model of the naturally ventilated single-family residential building located in central Poland was used. Performed calculations for the base case resulted in 38 and 63 days within the comfort zone at 80% acceptance level in a total of 122 days in the analyzed period for EN 15251 and ASHRAE standards, respectively. Use of external shading on windows and the roof with lower solar absorptance resulted in 46 and 70 days with acceptable conditions, respectively. Further application of night ventilation resulted in the 38 and 63 days, respectively. From the considered solutions in Polish climate conditions, windows shading seems to be the most efficient solution when controlling indoor comfort in residential buildings with no cooling system. A comparison of hourly operative temperature from that model with the detailed simulation in EnergyPlus showed a strong correlation with R2 = 0.934.

Entropy per Rapidity in Pb-Pb Central Collisions using Thermal and Artificial Neural Network (ANN) Models at LHC Energies

The entropy per rapidity produced in central Pb-Pb ultra-relativistic nuclear collisions at LHC energies is calculated using experimentally identified particle spectra and source radii estimated from Hanbury Brown-Twiss (HBT) correlations for particles π, k, p, Λ, Ω, and and π, k, p, Λ, and at and TeV, respectively. An artificial neural network (ANN) simulation model is used to estimate the entropy per rapidity at the considered energies. The simulation results are compared with equivalent experimental data, and a good agreement is achieved. A mathematical equation describing the experimental data is obtained. Extrapolation of the transverse momentum spectra at is required to calculate ; thus, we use two different fitting functions, the Tsallis distribution and hadron resonance gas (HRG) model. The success of the ANN model in describing the experimental measurements leads to the prediction of several spectra values for the mentioned particles, which may lead to further predictions in the absence of experiments.

Electric Aircraft Fueled by Liquid Hydrogen and Liquefied Natural Gas

The paper is a review of the opportunities and challenges of cryogenic power devices of electric aircraft, and the ongoing research and development efforts of the government agencies and the industry. Liquid Hydrogen (LH2) and Liquefied Natural Gas (LNG) are compared to support high temperature superconducting (HTS) and normal metal devices, respectively. The power devices were assumed to operate at the normal boiling point of the fuel used. The efficiencies of the electrical devices are estimated based on state-of-the-art technology. The mass flow rates and total fuel requirements for both the cryogenic fuels required to maintain the operating temperatures of the devices were simulated using thermal network models. A twin-aisle, 300 passenger aircraft with a 5.5 h flight duration was used for the models. The results show that the required masses of LH2 and LNG are 744 kg and 13,638 kg, respectively for the cooling requirement. The corresponding volumes of LH2 and LNG required are 9,760 and 30,300 L, respectively. In both cases, the estimated mass of the fuel needed for the aircraft is more than what is needed to maintain the cryogenic environment of the power devices. It was concluded that an electric aircraft with LNG cooled normal metal devices is feasible. However, an aircraft with HTS devices and cooled with LH2 is more attractive if the ongoing R&D efforts on HTS devices and LH2 infrastructure are successful. The emission reductions would be substantially higher with LH2, particularly when H2 is produced using renewable energy sources.

Impact of Air Density Variation on a Simulated Earth-to-Air Heat Exchanger’s Performance

Due to their simple design and reliable operation, earth-to-air heat exchangers (EAHE) are used in modern buildings to reduce ventilation heat losses. EAHE operation in atmospheric conditions results in variation in ambient air temperature and pressure affecting air density. The paper presents the study on the impact of ambient air density variation on the calculated hourly air temperature at the EAHE outlet and the resulting energy use for space heating and cooling of an exemplary residential building. The ground temperature was computed from the model given in EN 16798-5-1. Then, air density was obtained using five various methods. Energy use for space heating and cooling of the building was computed using the 5R1C thermal network model of EN ISO 13790. Depending on the chosen method and concerning the base case without EAHE, a reduction in annual heating and cooling needs was obtained from 7.5% to 8.8% in heating and from 15.3% to 19% in cooling. Annual heating and cooling gain from EAHE were 600.9 kWh and 628.3 kWh for heating and 616.9 kWh and 603.5 kWh for cooling for the Typical Meteorological Years (TMY) and International Weather for Energy Calculation (IWEC) files, respectively. Unit heating and cooling gains per heat exchanger area were from 34.9 kWh/m2 to 36.8 kWh/m2 and from −35.1 kWh/m2 to −36.3 kWh/m2. Density variation with temperature from the relevant typical Polish meteorological year at constant pressure, in comparison to the method of EN 16798-5-1, resulted in an hourly difference of that unit gain up to 4.3 W/m2 and 2.0 W/m2 for heating and cooling, respectively. The same was true inthe case of IWEC files that resulted in differences of 5.5 W/m2 and 1.1 W/m2.

JT-60SA TF coil quench model and Analysis: Joule energy estimation with SuperMagnet and STREAM

In the framework of JT-60SA Tokamak commissioning (Japan, 2021), all coils have to be cooled with supercritical helium forced-flow at the temperature of 4.5 K in order to reach superconducting state before energization. An important issue is to predict the Joule energy dissipated in Cable-In-Conduit Conductors (CICC) and the maximal temperature reached in case of an incidental quench occurrence. Therefore, quench simulations were performed on the Toroidal Field Coil (TFC) with the STREAM (Superconductor Thermal hydraulic and Resistive Electrical Analytical Model) code and with the SuperMagnet code (CryoSoft), coupling THEA (thermal hydraulic and electrical 1-D CICC model) and Flower (thermal hydraulic network model). The quench event was simulated for one TFC at nominal conditions of tokamak operation. External energy deposition over each pancake’s first turn of the coil at the peak magnetic field location was applied for initiating the resistive transition. This way, the computed Joule energy dissipated by one TFC is conservatively evaluated to be 5.65 MJ. The Joule energy dissipation depends strongly on quench initiation conditions and on the number of fully and rapidly quenched pancakes (maximal quench propagation velocity of 19.5 m/s). Some further analyses were performed on the acceptance quench test realized at the Cold Test Facility (CEA Saclay, 2018) on TFC02. The different calculation results (helium temperature, mass flow rate in upstream and downstream manifolds, normal length propagation) are presented in the following study and are consistent with the measurements. This analysis brings information on the limits and the ability of STREAM code to model quench behaviour in CICC coils cooled by forced flow of supercritical helium. This tool could be useful for tokamak magnets protection during quench event and safe operation, notably thanks to its fast computing time.

Thermal Analysis of Axial-Flux Permanent Magnet Motors for Vehicles Based on Fast Two-Way Magneto-Thermal Coupling

Axial-flux permanent magnet motor (AFPMM) have small size and high power density. It has a good application prospect in the field of new energy vehicle driving. In this paper, based on a 56 kW AFPMM, the magnetic circuit characteristics are calculated by the split loop method, considering the influence of pulse width modulated (PWM) power supply. The loss is taken as the heat source, combined with the motor structure characteristics and cooling conditions, the lumped-parameter thermal network model of the motor is established to solve the steady-state and transient temperature distribution of each structure. By this way, fast and accurate thermal calculation of the motor is realized in design stage. The accuracy of the lumped-parameter thermal network model is verified by experiment. At the same time, the effects of spliting the permanent magnet (PM) into pieces, flow rate of cooling water, and loss distribution on temperature rise are analyzed. This research work provides an effective fast thermal calculation method for AFPMM and provides a reference basis for the design of similar motors. It has important value of theoretical significance and engineering practical.

Improvement and Validation of the System Analysis Model and Code for Heat-Pipe-Cooled Microreactor

Heat-pipe-cooled microreactors (HPMR) use a passive high-temperature alkali metal heat pipe to directly transfer the heat of solid core to the hot end of the intermediate heat exchanger or thermoelectric conversion device, thus avoiding a single point failure. To analyze and evaluate the transient safety characteristics of an HPMR system under accident conditions, such as heat pipe failure in the core or a loss of system heat sink and other accidents, a previously developed model for transient analysis of a heat-pipe-cooled space nuclear reactor power system (HPSR) was improved and validated in this study. The models improved mainly comprise: (1) An entire 2-D solid-core heat transfer model is established to analyze the accident conditions of core heat pipe failure and system heat sink loss. In this model, radial and axial Fourier heat conduction equations are used to divide the core into r-θ direction control volumes. The physical parameters of the material in the control volume are calculated according to the volume-weighted average. (2) By coupling the heat transfer limit model and the two-dimensional thermal resistance network model, the transient model of a heat pipe for HPMR system analysis is improved. (3) Conversion system models are established to simulate the system characteristics of the advanced HPMR concept, such as thermoelectric conversion, Stirling conversion, and the open Brayton conversion analysis model. Based on the improved models, the HPMR system analysis program TAPIRSD was developed, which was verified by experimental data of the separated conversion components and the ground nuclear test device KRUSTY. The maximum deviation of the power output predicted by the energy conversion model is less than 8%. The accident conditions of the KRUSTY tests, such as load change, core heat pipe failure, and heat sink loss accident, were studied by using TAPIRSD. The results show that the simulation results of the TAPIRSD code agree well with the experimental data of the KRUSTY prototype reactor. The maximum error between the TAPIRSD code prediction and the measured value of the core temperature under accident conditions is less than 10 K, and the maximum deviation is less than 2%. The results show that the developed code can predict the transient response process of the HPMR system well. At the same time, the accuracy and reliability of the improved model are proved. The TAPIRSD is suitable for system transient analysis of different types of HPMRs and provides an optional tool for the system safety characteristics analysis of HPMR.

Thermal analysis of the cooling system with the circulation between rotor holes of enclosed PMSMs based on modified models

• Novel cooling structure of circulation between rotor holes is designed. • The deflector pressure is calculated based on the element-momentum theory. • The air friction pressure drop is modified by introducing a spiral correction coefficient. • The convective heat transfer coefficient of each heat transfer surface is refined. • Adopting the designed cooling structure, the temperature rise is greatly reduced. Accurate temperature predictions and cooling structure design for permanent magnet machines are essential to ensure safe and stable operation. In this paper, a cooling system with circulation between rotor holes for enclosed permanent magnet synchronous machines is proposed. The modified lumped parameter models of airflow network and thermal network are established, respectively, so as to predict the air velocity and temperature distribution quickly and accurately. In the airflow network model, the calculation method of deflector pressure is proposed based on blade element theory. The equation for the pressure drops in the rotor holes is modified, and the influence of rotor rotation on air velocity is better considered. To improve the accuracy of the thermal network model, each part of the motor is equivalent to three typical heat transfer surfaces, and the corresponding calculation methods of the convective heat transfer coefficient are listed. The parameters of the cooling structure are analyzed and designed based on the lumped parameter models. Compared with the original motor without the deflector, the maximum temperature-rise of the rotor is decreased by 16%. The accuracy of the calculation models is verified by experiment and simulation.