Optimization of tangential interior brushless DC motor rotor for hybrid vehicles (2025)

The interior brushless DC motor has the advantages of simple structure, low material cost, and high mechanical strength. Currently, this type of motor is widely used in traditional fuel vehicles and hybrid vehicles. Compared with the surface mounted rotor, the interior brushless DC motor generates reluctance torque due to the asymmetric structure of its AC/DC axis magnetic circuit, which increases the motor output torque. The permanent magnet is placed inside the rotor, which increases the robustness of the motor rotor, makes the dynamic performance smoother, and has stronger weak magnetic expansion ability^1,2,3,4,5.

The flux per pole of the tangent interior brushless DC motor is provided by two permanent magnets, which is greatly improved compared with the magnetic flux and air-gap density of the radial interior rotor structure, and plays a “magnetic gathering” role. However, the tangential interior brushless DC motor leakage flux coefficient is large, it needs to focus on optimizing the rotor magnetic isolation structure to improve the performance of the motor⁶. Reference⁷ analyzes the suppression effect of different magnetic structures on the armature reaction; Reference⁸ proposes a special-shaped magnetic isolation slot, which effectively improves the distortion degree of air gap magnetic field and improves the electromagnetic torque; Reference⁹ introduces the structure of the interval magnetic bridge rotor, which effectively eliminates the one-way magnetic flux leakage; Reference¹⁰ designs a block-type non-conducting rotor isolation structure, which effectively improves the performance of the motor rotor and verifies the feasibility of the method.Reference¹¹ proposes the installation of wedge-shaped permanent magnet materials on the rotor iron core, aimed at reducing torque ripple and cogging torque.Reference¹² analyzes the impact of different protective structures on the electromagnetic performance of permanent magnet synchronous motors and addresses the challenge of accurately calculating the magnetic field in tangential permanent magnet motors with multilayer winding structures.Reference¹³ improves the magnetic isolation bridge based on segmented slotted rotor design to enhance output torque, and certain work is conducted to investigate the effects of segmented slotted rotors on cogging torque, no-load back electromotive force, and torque ripple.However, the process is not very workable. Reference¹⁴ performs finite element analysis and experimental validation, resulting in significantly reduced cogging torque for half-inset fault-tolerant permanent magnet steering motors after selecting the optimal slotted angle for the segmented slotted rotor, thereby improving performance such as vibration noise.However, the output torque is reduced. Reference¹⁵ Topology design and optimisation of permanent magnet motor rotor structure isolation structure has been carried out. It has higher electromotive force but increased cogging torque compared to conventional structure motor. The above researches have considered the optimisation of permanent magnet motor in terms of optimisation of the magnetic isolation structure, improvement of electromagnetic torque, reduction of cogging torque, etc., but they have not considered the process feasibility and manufacturing cost. Therefore, it is of high research value to solve the above problems at the same time.

The permanent magnets in interior permanent magnet brushless DC motors are commonly made of sintered neodymium iron boron. Although the magnetic performance is high, the negative temperature coefficient of the material itself makes it prone to high-temperature demagnetization, which weakens the high-temperature performance of oil pump motors in the field of hybrid vehicles and reduces product safety and stability.

In order to solve the above problems, this article proposes a new structure of rotor air magnetic isolation injection molding using low-cost and high-temperature performance stability, positive temperature coefficient of ferrite permanent magnet material (without rare earth materials), and proposes the optimised structure of rotor air-isolated injection moulding. Through finite element magnetic field analysis of a new motor model, the relationship between different magnetic bridge widths and leakage flux coefficient was obtained. The mechanical characteristic curves of traditional magnetic bridge and air magnetic bridge motors were compared, effectively reducing leakage flux coefficient, improving the mechanical stiffness and electromagnetic torque of the motor, and reducing the cost of the motor. The mechanical strength of the new injection molded rotor structure was verified through 3D simulation, and the stress was within the allowable range of the material. The first ‘mirror image’ segmented rotor structure in this paper effectively reduces the motor cogging torque and the harmonic content of the reverse potential, and finally the feasibility of the above new structure and the validity of the calculation method are verified through prototype tests respectively. The new structure motor maintains the high performance of the motor and reduces the risk of demagnetisation while significantly reducing the cost, meets the requirements for the use of high-temperature working conditions in hybrid vehicles, and reduces the reliance on expensive rare-earth materials for hybrid vehicle motors, and its design has significant novelty.

The stator of the hybrid car oil pump motor adopts a centralized winding. When operating stably, the influence of winding inductance can be ignored in the simplified model. The time constant is much smaller than the commutation period, so the voltage balance equation is¹⁶:

In the formula, U is the output voltage of the inverter, E_eq is the back electromotive force of the motor, i is the armature current, and R_eq is the winding resistance.

According to formula (2) and the law of energy conservation, the electromagnetic power is equal to the mechanical power output by the rotor. The open-loop mechanical characteristic equation of the interior brushless DC motor is:

In Eq.(2),Ω is the mechanical angular velocity (rad/s) of the motor, Ω₀ is the ideal no-load mechanical angular velocity (rad/s) of the motor, T_av is the average torque of the motor, and K_E is the back electromotive force coefficient,

K_rms is the effective value coefficient of the back electromotive force during the conduction period, K_av is the average value coefficient of the back electromotive force during the conduction angle conduction period, K_eq is the equivalent back electromotive force coefficient, and K_T is the torque coefficient,

According to formula (2), it can be concluded that the mechanical characteristics of the interior brushless DC motor are similar to those of a brushless motor. Ignoring inductance, the mechanical characteristics are an approximately linear line.

According to formulas (2), (3), (4), it can be concluded that the back electromotive force coefficient determines the no-load speed of the motor, and the back electromotive force coefficient and winding resistance determine the stiffness of the motor’s mechanical characteristics. In response to the characteristics of leakage flux in tangential interior brushless motors, the back electromotive force coefficient and torque coefficient of the motor are improved by optimizing the rotor structure and reducing the leakage flux coefficient, while keeping the stator size and stator winding parameters unchanged. Furthermore, it improves the mechanical stiffness and electromagnetic power of the tangential interior brushless DC motor.

In order to reduce the leakage flux on the inner surface of the rotor of a tangential interior brushless DC motor, two optimization methods of non-magnetic material and magnetic isolation bridges are generally adopted. As shown in the traditional magnetic isolation bridge in Fig.1 (A), has a narrow magnetic isolation bridge at point A of the rotor core, where the magnetic circuit is saturated to achieve magnetic isolation. Due to the bottleneck in the stamping process of rotor silicon steel sheet, the width of the magnetic isolation bridge needs to be strictly controlled, so the magnetic isolation effect is general, and the leakage flux coefficient is still relatively large¹⁷. This article conducts a brand - new optimization of the magnetic isolation structure for the motor rotor, as shown in Fig.1 (b). The rotor core is cut off (point B), and the rotor core consists of two main parts (core 1 and core 2).The rotor magnetic isolation bridge material is changed from silicon steel sheet to air magnetic isolation of high reluctance, which increases the leakage flux path reluctance, inhibits the magnetic line of flux from the path formed by the permanent magnets, the rotor iron core A, the rotor iron core B, the rotating shaft, and reduces the leakage coefficient. The leakage coefficient is reduced. At the same time using nylon pure material and positioning tooling on the rotor structure integrated injection moulding, the rotor assembly to form a whole, to ensure the reliability of the motor rotor operation.

The simulation model is a 12-slot, 8-pole, tangentially interior brushless DC motor. Based on the main parameters provided in Table1, a 2D model of the motor was created using CAD and imported into Maxwell, as shown in Fig.2. The simulation working temperature is set at 25℃. To optimize computer resource allocation and reduce simulation time while ensuring accuracy, a 1/4 model of the motor was selected for simulation, considering the symmetry of the motor and the characteristics of the magnetic circuit. The two rectangular boundaries of the model were set as master and slave boundaries, respectively. Key air gap region, the mesh was made sufficiently fine around the magnetic bridge, avoiding excessively long or sharp mesh elements, ensuring good mesh uniformity. A three-phase bridge inverter circuit for the brushless DC motor was constructed, and a coupled field-circuit simulation was performed to obtain the no-load magnetic field distribution and magnetic flux density distribution of the motor.

It can be observed from Fig.3 that the new structure of the air-isolated injection-molded rotor significantly suppresses the leakage magnetic flux on the inner surface of the rotor. The magnetic flux density at the rotor magnetic isolation bridge is reduced to ≤ 0.3 T, effectively lowering the iron core losses and improving the efficiency of the motor.

Analysis of leakage flux coefficient

In order to measure the effect of different magnetic bridge widths on the leakage flux coefficient of the motor, a parameterized finite element model of a tangential interior brushless DC motor was established. The width of the magnetic bridge in the rotor core was parameterized, with an initial value of 1mm (in which case the material property was set to silicon steel sheet) and an ending width of 0mm (in which case the material property was set to vacuum). The step size was − 0.1mm, with a total of 11 steps. Brushless DC motors with different magnetic bridge widths were simulated. The brushless DC motor with different widths of the magnetic isolation bridge is simulated respectively. Using Fig.3 obtained from maxwell software and the post-processing capabilities of maxwell, the leakage flux coefficient of the motor was calculated using the magnetic flux density integration method. Figure4 illustrates the relationship between the width of the rotor core’s magnetic bridge and the leakage flux coefficient.

It can be seen from Fig.4 that the width of the magnetic isolation bridge in the rotor core of the hybrid vehicle motor is reduced from 1mm to 0mm (when the width of the spacer bridge is 0mm, the rotor core is divided into 9 parts), and the leakage magnetic coefficient of the motor is reduced from 1.53 to 1.18, with an amplitude reduction of 25.3%.The reduction of the spacer width effectively enhances the per-pole magnetic flux of the motor, improves magnetic field utilization, and indirectly enhances the back electromotive force coefficient and motor performance. The reduction of the spacer the width of the spacer bridge effectively enhances the per-pole flux of the motor, and the magnetic field utilisation is improved, which indirectly improves the motor reverse potential coefficient and motor performance. The relationship between the leakage coefficient σ and the width of the spacer bridge b is obtained through simulation as in formula (5), which further simplifies the calculation time of the leakage magnetic coefficient.

Comparison of mechanical characteristic curves

The load condition simulations were conducted for two types of tangentially mounted brushless DC motors: one with a magnetic isolation bridge width of 0.8mm (the limit of rotor core stamping width) and the other with a magnetic isolation bridge width of 0mm (air-gap magnetic isolation structure). The inverter circuit was configured for a three-phase symmetrical load. The speed was ramped up from 0rpm to a stable state. The load torque was parameterized, starting from 0 Nm and ending at 1.4 Nm with a step size of 0.1 Nm, resulting in a total of 15 steps, with the initial speed set at 0rpm. The simulations provided the motor speed and current corresponding to different torque values for both structures. The post-processing script functionality was utilized to obtain the torque-speed and torque-current characteristic curves for both structures, with the comparison shown in Figs.5 and 6.

The comparison curves of the two motor structures in Figs.5 and 6 indicate that the brushless DC motor with the tangentially mounted air-isolated injection-molded rotor structure shows a 14.5% increase in back electromotive force coefficient compared to the traditional magnetic isolation bridge structure. The torque coefficient is increased from 0.0253 Nm/A to 0.0312 Nm/A, resulting in a 21.7% improvement. The viscous damping coefficient is raised from 0.00318 Nm/(rad/s) to 0.00456 Nm/(rad/s), which represents a 43% increase. The new air-isolated injection-molded rotor structure enhances the mechanical characteristic stiffness of the motor. At the rated torque of 0.9 Nm, the power of the traditional magnetic isolation structure motor is 250W, while that of the air-gap structure motor is 275W, reflecting a 10% increase in motor power. In summary, through the novel design of tangential interior rotor air-isolated injection molding structure, the leakage flux coefficient is effectively reduced, the reverse potential coefficient, torque coefficient and viscous damping coefficient of the motor are improved, and the performance of the motor is increased by more than 10% under the same volume.

Strength analysis of air magnetic isolation injection molded rotor structure

Using an air magnetic isolation structure, it is not possible to form a whole between rotor core 1, rotor core 2, and permanent magnet. In order to ensure the reliability of the oil pump motor operation in this structure¹⁸,this article adopts an integrated injection molded rotor structure, fixing the rotor core 1, rotor core 2, and permanent magnet as a whole to improve the mechanical strength of the motor rotor, as shown in Fig.6.

As shown in Fig.7, the strength and deformation analysis of the injection molded rotor assembly is performed using workbench simulation software. Based on the symmetry of the motor, the simulation model is a 1/8 rotor model. The boundaries on both sides of the model are constrained using frictionless supports to restrict normal displacement. The centrifugal force and magnetic pull experienced by the rotor are applied as loads, with a maximum rotational speed of 5500r/min. The rotor core material is B50A470, the permanent magnet material is DM4545, and the injection molding material is PA66. The material properties of each component are listed in Table2, and the stress and strain distribution of the rotor are shown in Fig.8.

As shown in Figs.8, 9 and 10, the maximum stress of the rotor assembly is located at the middle position of the rotor core, where it bears the weight of the external core. The maximum stress value is 18.32MPa, which is much lower than the yield strength of silicon steel sheets, which is 241MPa. The maximum deformation of the rotor assembly is found in the injection molded part, with a deformation amount of 7.9μm, located on the outer side of the rotor, blocking the middle position of the magnet injection, as indicated in Fig.8b. The maximum stress of the injection molded part is located at the junction of the outer diameter of the magnet, with a maximum stress value of 8.9MPa, which is significantly lower than the tensile yield strength of PA66, which is 70MPa. Therefore, the strength of the tangential injection structure rotor is deemed to meet the requirements, and the design margin is considered appropriate, allowing the oil pump motor to operate stably and enhancing safety.

Hybrid vehicle oil pump motors commonly employ permanent magnet brushless DC motors. Due to the presence of rotor permanent magnets, it inevitably generates cogging torque, which seriously affects the low-speed performance of the motor¹⁹. Domestic R&D personnel have achieved good results in suppressing and reducing the cogging torque of permanent magnet motors through methods such as stator slots, rotor permanent magnet eccentricity, unequal pole arc coefficient, and adding auxiliary slots.

Small power brushless DC motors often adopt a segmented iron core structure in their stator, which effectively improves the power density of the motor by increasing the slot filling rate of the stator winding; Surface-mounted rotor structures commonly employ segmented oblique pole methods to reduce the motor’s cogging torque. However, due to the inherent structural characteristics of the interior tangential brushless DC motor, traditional improvement methods such as rotor skewing are difficult to implement in the process, and automated production and product beat cannot be achieved^20,21,22.

Building upon the rare-earth-free tangential interior air-insolated injection-molded rotor structure, this article is based on the overall idea of weakening the cogging torque with uneven air gaps, and adopts the method of peak shaving and valley filling. By combining the optimization of the rotor core with the ‘mirror image’ of the rotor core, a new “segmented” rotor optimization structure is designed, as shown in Fig.11. Under the technical constraints preventing manufacturability of permanent magnet segmented oblique poles, Under the constraints where the segmented oblique pole of permanent magnets (via circumferential rotation angles) is manufacturing-infeasible, an unequal width air gap is used to chamfer one side of the rotor core. The dimensions of rotor core A and rotor core B are completely the same, and rotor core B is the mirror image of A (rotor core A flipped 180 ° along the axial direction is the rotor core B). The motor rotor core is divided into two axial sections, and the two iron cores are assembled in mirror image as shown in Fig.11 (a). The axial direction of the permanent magnet is not segmented. By using peak shaving and valley filling methods, the amplitude of torque peaks and valleys in the circumferential direction is reduced, and the magnetic field waveform of the motor is optimized to weaken the cogging torque. L in the figure represents the axial length of the permanent magnet of the motor rotor.

Analytical analysis of tooth slot torque weakening

The tooth trough torque is an inherent property of permanent magnet brushless DC motors, which is generated by the interaction between the iron core and the permanent magnet under non energized operating conditions^23,24,25. Its value is the magnetic field energy W relative to the relative position angle of the stator and rotor α Negative derivative of:

Relative position angle of motor stator and rotor α It is the specified circumference angle between the centerline of a stator tooth and the centerline of the rotor permanent magnet, as shown in Fig.12. The set position is on the centerline of the permanent magnet of the rotor, θ angle of variation of air gap magnetic induction intensity along the circumference of the motor.

The magnetic field energy W in Eq.(6) is determined by the size of the motor structure. To derive the analytical expression for the cogging torque of a interior permanent magnet motor, it is assumed that the magnetic permeability of the motor core is infinite, the magnetic permeability of the permanent magnet is the same as that of the air, the core stacking coefficient is 1, and the shape and performance of the permanent magnet in the same motor are the same. Therefore, compared with the magnetic field energy stored in the air gap of the motor, the magnetic field energy stored in the stator and rotor cores can be approximately ignored.

Therefore, when analyzing and calculating the cogging torque, the magnetic field energy stored in the motor can be expressed as:

In the formula, W_air represents the magnetic field energy contained in the motor air gap; W_PM is the magnetic field energy in the permanent magnet, µ₀ is the air permeability, B(θ,α) is the distribution of air gap magnetic flux density along the circumferential direction when the relative position of the rotor changes. The distribution function B(θ,α) of the air gap flux density along the circumference can be approximated as:

In Eq.(8), B_r(θ), h_m(θ), δ(θ,α) represents the distribution of residual magnetism of the permanent magnet, length in the direction of permanent magnet magnetization, and effective air gap length along the circumferential direction.

Substituting Eq.(8) into Eq.(7) yields

Perform fourier series expansion on \(B_{r}^{2}\left( \varvec{\varvec{\uptheta}} \right)\) and \({\left[ {\frac{{{h_m}\left( \varvec{\varvec{\uptheta}} \right)}}{{{h_m}\left( \varvec{\varvec{\uptheta}} \right)+\varvec{\varvec{\updelta}}\left( {\varvec{\varvec{\uptheta},\varvec{\upalpha}}} \right)}}} \right]^2}\) respectively to obtain

In Eqs.(10) and (11), B_r is the residual magnetism of the permanent magnet,α_p is the pole arc coefficient, p is the number of motor poles, G_n is the fourier coefficient of the square of relative air gap magnetic permeability, and z is the number of stator slots in the motor.

By substituting Eqs.(9), (10), (11) into Eq.(6) and utilizing the integral properties of trigonometric functions, the expression for the torque of non-oblique tooth slots can be obtained as

In Eq.(12), R₂ is the inner radius of the stator core, R₁ is the outer radius of the rotor yoke, and n is an integer that makes the nz/2p term an integer.

As shown in Fig.12, the relative position diagram between the tangential interior mirror image segmented rotor permanent magnet and the stator is divided into two axial sections.The rotor core A (referred to as section A) is used for 0-L/2, and the rotor core B (referred to as section B) is used for 0-L/2 in the axial direction. Due to the uniform distribution of permanent magnet poles, the remaining B_r(θ) magnetic field of the permanent magnet corresponding to sections A and B is the same as the length h_m(θ) of the magnetization direction of the permanent magnet. From Fig.12, it can be seen that due to the difference in assembly between the iron core and the permanent magnet in the circumferential direction, the distribution of the effective air gap length δ(θ,α) along the circumferential direction is not the same for the A and B rotors. The corresponding effective air gap lengths for A and B segments are δ_A(θ,α) and δ_B(θ,α), respectively. Therefore, the expression for the torque of the non oblique pole tooth slot in A segment can be obtained as:

The expression for the torque of the B segment non oblique tooth slot is:

The expression for the torque of the tangential Interior “segmented” rotor slot is:

By comparing Eq.(12) and Eq.(15), a reasonable air gap magnetic permeance is achieved through the mirror imaged segmentation structure of the rotor and the parametric design of unilateral chamfering on the rotor core.As long as (G_nA+G_nB)/2≪G_n is used, that is, under this structure, although the iron core size of sections A and B is the same, the air gap magnetic permeability of the two sections is changed through mirror assembly, that is, the amplitude and phase of G_nA and G_nB are not the same. The peak shaving and valley filling approach is adopted to effectively reduce the cogging torque and thereby reduce the torque ripple of the motor.

Simulation calculation of cogging torque

The simulation object is a 12-slot, 8-pole tangential interior brushless DC motor model, and the finite element simulation and calculation of the no-load backpotential and cogging torque of the original structure and the interior motor with mirror image segmente structure are carried out. The motor speed is set to a constant speed of 1rpm and the stator armature winding current is set to zero. The simulation of the motor with mirror image segmente structure is divided into three steps, which are to establish the motor model of A-section (axial length L/2) and B-section (axial length L/2) respectively; To calculate the back electromotive force and cogging torque of the A-section and B-section motors individually; And to statistically process the data of the simulation parameters by using the post-processing function of the script file, and Fig.13 shows a comparison of the no-load back potential between the original structure and the mirror image segmente structure.

From Figs.13, 14 and 15, it can be concluded that the 5th harmonic content of the no-load back electromotive force in the original structure is relatively large, accounting for 5.7%, with a voltage waveform sine distortion rate of 6.4%. In contrast, the 7th harmonic content of the no-load back electromotive force in the “mirror image” segmente structure is the highest, accounting for 3%, and the voltage waveform sine distortion rate is 4.1%, representing a reduction of 35%. The mirror image segmente structure has effectively improved the no-load back electromotive force of the motor, resulting in a more sinusoidal waveform. This has effectively reduced the noise and vibration generated during motor operation, enhancing the comfort of the oil pump motor and extending the lifespan of the equipment.

Figure 16 presents the finite element simulation results of cogging torque for both the original structure and the mirror image segmente structure. The simulated cogging torque value for the original structure motor is 130 mNm, while the cogging torque value for the motor using the mirror image segmente structure has been reduced to 32 mNm, indicating a reduction of 75.4%. This effectively reduces the wear rate of components caused by cogging torque, increases the motor’s effective output, and ensures more stable output torque, aligning with the prevailing environmental trend of energy conservation and emission reduction. Thus, it can be concluded that the mirror image segmente structure is an effective method for reducing the cogging torque of interior brushless DC motors, with good manufacturability. The next section will focus on online testing of the motor’s T-n curve and cogging torque, with the effectiveness of the new structure and the validity of the method being verified through comparison of simulation results and experimental outcomes.

The mechanical performance of the tangential interior motor was tested using a hysteresis dynamometer, as shown in Fig.17. An open-loop control mode was employed for the driver, and the T-n curves of both the traditional magnetic isolation structure and the air magnetic isolation structure were tested. The loading torque ranged from 0.1 Nm to 0.8 Nm, with a step size of 0.1 Nm, and each testing point lasted no more than 3s. The results are presented in Figs.18 and 19.

The measured data from Fig.18 (a), (b) indicate that the back electromotive force coefficient of the tangential interior air magnetic isolation structure motor has been increased by 15.1% compared to the conventional magnetic bridge structure (with a magnetic bridge width of 0.8mm). The torque coefficient has risen from 0.0242 Nm/A to 0.03 Nm/A, reflecting a 23% improvement, while the viscous damping coefficient has increased by 46.5%, resulting in a stiffer slope of the motor’s mechanical characteristic curve.Under rated load (rated torque of 0.9 Nm), the motor power has been enhanced by 11%. Cost analysis shows that the cost of components has been reduced by 8%, while process costs have increased by 3%. At the same power level, the price of the new structure can be lowered by 5%.

The comparison between the simulation data and the measured data reveals that the measured no-load speed of the motor is slightly lower than the simulated no-load speed. At the same torque, the measured motor current is slightly higher than the simulated current value. The influencing factors include the additional torque from the testing system shown in Fig.19, as well as environmental factors such as humidity and vibration affecting motor performance. In particular, the increase in temperature during the motor operation testing has led to a decrease in the torque coefficient. Additionally, the simulation model’s inverter circuit is overly idealized and does not account for factors such as actual harmonic currents, which contributes to the discrepancies between the simulation and experimental results. However, the back electromotive force coefficient, torque coefficient, and viscous damping coefficient obtained from the simulation are all within 3.5% of the measured data, verifying the accuracy of the simulation results. This also confirms the effectiveness of the air magnetic isolation rotor’s new structure, which significantly improves the performance metrics of the tangential interior brushless DC motor and enhances mechanical characteristic stiffness.

The motor cogging torque testing system is shown in Fig.19, in which a servo motor is used to drive both the original structure motor and the mirror image segmente rotor new structure motor. Under the condition of 1rpm, no less than 2000 test points are established to measure the no-load torque fluctuations of both motors. The test results are presented in Fig.20.

Torque decomposition through differential-common mode analysis has been conducted on the no-load torque fluctuation test results of the two motor configurations depicted in Fig.20. The differential mode component corresponds to the motor’s cogging torque, whereas the common mode component represents the friction torque. For the baseline motor structure, the cogging torque measures 138 mNm with a friction torque of 21.3 mNm. In contrast, the mirror-image segmented configuration demonstrates significant improvement, achieving a cogging torque of 36.5 mNm (73.5% reduction) and a friction torque of 18.2 mNm. The simulation results exhibit close alignment with experimental data, showing deviations within 2%. The slight underestimation in simulations primarily originates from: (1) Assembly and measurement system tolerances; (2) Material property variations in permanent magnets and ancillary components; (3) Overly idealized magnetic saturation thresholds in the simulation model.By implementing the peak-shaving and valley-filling strategy, the optimized mirror-image segmented rotor architecture effectively reduces cogging torque in the tangential interior brushless DC motor while simultaneously decreasing manufacturing complexity. This innovation yields a 5% reduction in process costs and enhances mass production feasibility. By synergistically integrating innovative designs including the application of rare-earth-free materials, optimized air-isolated injection-molded rotor structure, and a novel mirror-image segmented configuration, the motor demonstrates an 11% increase in power output, a 75.4% reduction in cogging torque, and a 10% decrease in production costs.

This article designs a new type of tangential interior brushless DC motor without rare earth materials, and provides the influence of leakage flux coefficient on the mechanical characteristics of the brushless DC motor. A new structure of rotor air-isolated injection-molding is proposed, and the relationship between the width of the magnetic isolation bridge and the leakage flux coefficient of the motor is obtained. The mechanical characteristics of the two types of motors are compared, and the strength of the air-isolated injection-molding structure is analyzed; Secondly, a novel mirror-image segmented rotor optimization structure is proposed using waveform equivalence method, which effectively reduces the cogging torque of the motor, good processability; Finally, the feasibility of the above optimization method was verified through experimental and simulation comparisons, and the conclusions are as follows:

1. (1)

   The width of the magnetic isolation bridge of the tangential interior brushless DC motor from 1mm to 0mm, and the rotor leakage coefficient gradually decreases by about 25.3%;When the stator dimensions are identical, compared with traditional structure motors, the no-load back electromotive force coefficient and torque coefficient of the air magnetic bridge structure motor increase by 14.5% and 21.7%, respectively, effectively enhancing the mechanical stiffness and output power of the motor.11% increase in motor output.Additionally, the overall injection-molded rotor structure and the stress on the components remain within the allowable range of the materials, ensuring the reliability and safety of the tangential interior permanent magnet air magnetic bridge structure motor.

2. (2)

   On the basis of the air-isolated injection-molded rotor structure, the method of peak shaving and valley filling is adopted to verify through simulation that the new ‘mirror image’ segmented rotor structure can effectively reduce the cogging torque of the motor by up to 75.4%, with good workmanship, effectively reduce the noise and vibration of the motor in operation, and reduce the wear rate of the motor components. This approach holds certain reference significance for reducing the cogging torque of tangential interior permanent magnet motors.

3. (3)

   Through the comparison of motor tests and simulations, the testing results are found to be highly consistent with the finite element simulation values. This validates the innovative feasibility of the air-isolated structure and the mirror-image segmented rotor structure, as well as the accuracy of the simulation method. The observed deviation is mainly caused by the additional torque of the test system. Through the synergistic integration of rare-earth-free material implementation, air-isolated magnetic circuit optimization, and novel mirror-image segmented structural design, this motor achieves performance parity with equivalent-volume rare-earth-based radial interior brushless DC motors while demonstrating enhanced manufacturability. This design also addresses the issues of performance degradation and irreversible demagnetization of motors under high-temperature conditions in hybrid vehicles, significantly reduces motor costs, and meets the current requirements for hybrid vehicle motors, enhancing reliability.

4. (4)

   This study has not yet addressed the multi-objective optimization of motor parameters. Future research will optimize multiple objectives, including the back electromagnetic fields coefficient, motor power, cogging torque, torque ripple and rotor strength, to achieve the maximum cost-effectiveness.

Authors and Affiliations

1. Hebei Petroleum University of Technology, 2 Xueyuan Road, Shuangqiao District, Chengde, 067000, Hebei Province, China

   Xiaojing Li,Yingbo Zhang&Jiale Wu

Contributions

X.L. contributed to the conception, supervision, review and editing of the study. Y.Z. made substantial contributions to developing the methodology, conducting experiments, and preparing the manuscript. J.W. provided project supervision, focusing on analyzing experimental data. All authors discussed the results and contributed to the final manuscript.

Corresponding author

Correspondence to Yingbo Zhang.

Competing interests

The authors declare no competing interests.

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