In order to improve the air-gap flux density of the permanent magnet synchronous motor and reduce the cogging torque, a novel structure with asymmetric magnetic poles for automobile was proposed. Based on the characteristics of the parallel magnetic circuit, the magnetic flux path diagram is established. And the equivalent magnetic circuit model is established by the equivalent magnetic circuit method. The Taguchi method is used to be a multiobjective optimization algorithm. The total harmonic distortion of the air-gap flux density is the first optimization goal. The second and third optimization goals are the cogging torque and the average of output torque, respectively. And the torque ripple is a constraint condition. The optimized parameter combination is obtained by the Taguchi method. Finite element simulation analysis and prototype test are carried out for the optimized motor structure. The results show that the total harmonic distortion of air-gap flux density is reduced by 36.7% comparing with the initial structure. The cogging torque is reduced by 26.0%. And the average output torque is increased by 4.8%.

Electric automobile has been widely concerned around the world because of the superiority of energy saving and environmental protection. As one of the core technologies of electric automobiles, the driving motor system has become the key component. High power density, high efficiency, and wide speed range have become current research directions. At present, driving motors of electric automotive include induction motor, direct current motor, and permanent magnet synchronous motor (PMSM). PMSM has become the most promising drive motor due to its advantages of high power density, high efficiency, and simple structure [

According to the relative position of the permanent magnet and the rotor core, PMSM can be divided into surface mount type and interior type. The interior type can be divided into three types: radial type, tangential type, and hybrid type. Their magnetization directions of the permanent magnets are different. At present, the interior PMSM is used widely in industrial engineering. Many automotive companies such as Daimler, Toyota, and BYD have widely applied interior PMSM to their electric automobile [

However, the air-gap flux density waveform of PMSM is similar to a square wave. It has many higher harmonics. And high cogging torque is not conducive to the output performance [

In view of above disadvantages, domestic and foreign scholars carried out studies on the influence of output performance and different magnetic pole shapes. It is determined that the air-gap flux density and the cogging torque are greatly affected by the shape of the magnetic poles. Appropriate magnetic pole shape can improve the air-gap flux density and reduce cogging torque [

In order to improve the air-gap flux density and the cogging torque, this paper proposes a PMSM structure with asymmetric magnetic poles. The equivalent magnetic circuit model is established. And the effective magnetic flux is analyzed by the equivalent magnetic circuit method. The rotor structure is improved. Optimization goals are selected. Some key parameters are selected to be optimization variables. Using the Taguchi method, a multiobjective optimization scheme is proposed. And a two-dimensional finite element method and prototype experiment are used to verify.

This paper proposes PMSM structure asymmetric magnetic poles. Its three-dimensional structure is shown in Figure

PMSM structure of asymmetric poles.

Motor structure parameters.

Parameters | Value |
---|---|

Outer diameter of stator (mm) | 145 |

Inner diameter of stator (mm) | 89.5 |

Outer diameter of rotor (mm) | 88 |

Inner diameter of rotor (mm) | 30.5 |

Axial length (mm) | 120.3 |

Permanent magnet material | N35SH |

Silicon steel sheet grade | DW310-35 |

Pole slot matching | 8/12 |

This paper takes a traditional V-type structure as comparing structure. Each pole effective magnetic flux of two motor structures is analyzed. Figure

Comparison diagrams of flux paths.

Schematic diagrams of flux paths have been shown above. The equivalent magnetic circuit models of two motor structures are established, respectively, by the equivalent magnetic circuit method. And they are shown in Figure

The equivalent magnetic circuit models: (a) traditional V-type; (b) asymmetrical magnetic poles.

In Figure

In Figure

According to the superposition principle,

In order to obtain a better geometric motor shape, this paper makes some improvements on the rotor structure. The shape of rotor edge is changed. The auxiliary slots are used inside the rotor. The length of the air gap becomes nonuniform. The parameters are optimized by an appropriate optimization method. And the performance of the rated operating point is selected for research and analysis.

The method of changing the air-gap length is used in this paper. The air-gap length becomes nonuniform. And the effective magnetic flux direction is adjusted. The specific measures are as follows. The auxiliary slots are used inside the rotor. It can enhance the magnetization ability and reduce the rotational inertia. The distance between auxiliary slots and a permanent magnet is

Rotor structure optimization.

The above improvement method can improve the air-gap flux density waveform. The schematic diagram of the expected waveform can be represented in Figure

Schematic diagrams of the air-gap magnetic density waveform: (a) initial structure and waveform; (b) improved structure and expected waveform.

This paper uses the Taguchi method to optimize the parameters. The Taguchi method was first proposed by Dr. Genichi Taguchi who is a Japanese quality control expert. It is a local optimization method based on orthogonal experiments. It can quickly determine the combination of multiobjective optimization with the least number of experiments. The basic design process is as follows:

Determine optimization goals according to requirements

Determine optimization variables and corresponding level values

Establish an orthogonal experimental matrix

Use the finite element method to solve the orthogonal experiment matrix

Analyze the influence of each optimization variable and determine the optimal parameters

Verify the optimization results by finite element analysis

In this paper, the Taguchi method is used to optimize the air-gap flux density waveform, the cogging torque, and the output torque. And it must ensure that the torque ripple does not increase. Therefore, the total harmonic distortion of the air-gap flux density (THD) is the first optimization goal. The cogging torque (

In addition,

Motor optimization parameters and level values.

Level | |||
---|---|---|---|

1 | 2 | 6 | None |

2 | 4 | 6.5 | 4 |

3 | 6 | 4 | 4.5 |

4 | 8 | \ | \ |

5 | 10 | \ | \ |

6 | 12 | \ | \ |

The optimization goals, optimization variables, and corresponding level values have been determined above. The number of level values is not exactly the same. The traditional standard orthogonal experiment matrix cannot be established. According to principles of the Taguchi method experiment designing, the nonstandard orthogonal experimental matrix is established as shown in Table

Nonstandard orthogonal experimental matrix.

Experiment number | |||
---|---|---|---|

1 | 1 | 1 | 1 |

2 | 2 | 1 | 2 |

3 | 3 | 1 | 3 |

4 | 4 | 1 | 2 |

5 | 5 | 1 | 3 |

6 | 6 | 1 | 1 |

7 | 1 | 2 | 3 |

8 | 2 | 2 | 1 |

9 | 3 | 2 | 2 |

10 | 4 | 2 | 1 |

11 | 5 | 2 | 2 |

12 | 6 | 2 | 3 |

13 | 1 | 3 | 2 |

14 | 2 | 3 | 3 |

15 | 3 | 3 | 1 |

16 | 4 | 3 | 3 |

17 | 5 | 3 | 1 |

18 | 6 | 3 | 2 |

The rated operating point performance of each experiment can be calculated by using the two-dimensional finite element analysis method. The orthogonal experimental results are shown in Table

Orthogonal experimental results.

Experiment number | THD (%) | ||
---|---|---|---|

1 | 40.35 | 298.86 | 13.32 |

2 | 37.93 | 294.42 | 13.57 |

3 | 37.25 | 286.83 | 13.58 |

4 | 33.91 | 277.12 | 13.60 |

5 | 35.86 | 280.57 | 13.59 |

6 | 38.68 | 284.29 | 13.46 |

7 | 40.23 | 297.56 | 13.32 |

8 | 36.95 | 286.89 | 13.54 |

9 | 37.06 | 281.55 | 13.57 |

10 | 31.01 | 274.46 | 13.78 |

11 | 35.67 | 277.92 | 13.65 |

12 | 37.47 | 282.65 | 13.61 |

13 | 40.62 | 364.42 | 13.45 |

14 | 38.27 | 324.96 | 13.56 |

15 | 37.72 | 314.61 | 13.56 |

16 | 34.95 | 297.53 | 13.71 |

17 | 36.82 | 304.35 | 13.69 |

18 | 37.73 | 302.57 | 13.61 |

In the previous section, the results of each experiment were obtained by the two-dimensional finite element method. The overall average value of the experimental results can be calculated by formula (

The overall average value of experimental results.

THD (%) | |||
---|---|---|---|

Average value | 37.734 | 302.570 | 13.606 |

The average value of each optimization variable can be calculated, respectively, at a certain level value. To give an example, the average value can be obtained by the following formula when the optimization variable

The average value of THD.

Level | |||
---|---|---|---|

1 | 40.40 | 36.33 | 36.92 |

2 | 37.72 | 36.40 | 36.15 |

3 | 37.34 | 37.68 | 36.34 |

4 | 33.29 | \ | \ |

5 | 36.11 | \ | \ |

6 | 37.96 | \ | \ |

The average value of

Level | |||
---|---|---|---|

1 | 320.28 | 287.02 | 294.02 |

2 | 302.09 | 283.51 | 295.67 |

3 | 294.33 | 318.07 | 293.91 |

4 | 283.04 | \ | \ |

5 | 287.61 | \ | \ |

6 | 289.84 | \ | \ |

The average value of

Level | |||
---|---|---|---|

1 | 13.36 | 13.52 | 13.56 |

2 | 13.56 | 13.60 | 13.57 |

3 | 13.57 | 13.68 | 13.65 |

4 | 13.70 | \ | \ |

5 | 13.64 | \ | \ |

6 | 13.56 | \ | \ |

If a single goal is optimized, the optimization combination can be selected in Table

It is necessary to analyze the influence of each optimization variable when multiobjective optimization is carried out. Based on the previous calculation, the proportions can be calculated by formula (

The proportions of the influence of each optimization variable on the optimization goal.

Optimization variables | THD | |||||
---|---|---|---|---|---|---|

SS | Proportion | SS | Proportion | SS ( | Proportion | |

4.95 | 82.66% | 265.53 | 46.48% | 12.78 | 73.17% | |

0.65 | 10.89% | 281.93 | 49.35% | 2.84 | 16.28% | |

0.39 | 6.45% | 23.83 | 4.17% | 1.84 | 10.55% | |

Total | 5.99 | 100% | 571.28 | 100% | 17.46 | 100% |

In the above, the experimental results of the Taguchi method optimization are analyzed. And the proportions of the influence of each variable on the optimization goal are obtained. It can be seen that optimization variable

According to the above optimization scheme, the motor structure after optimization is obtained and designed. The structure is shown in Figure

Motor structure after optimization.

Static magnetic field analysis.

The optimized motor structure is analyzed by finite element simulation. The air-gap flux density waveform and harmonic analysis are compared and analyzed in Figure

Air-gap flux density waveform and harmonic analysis: (a) before optimization; (b) after optimization.

Cogging torque comparison is shown in Figure

Cogging torque comparison.

Output torque comparison.

It can be seen from Figure

The performance comparison before and after optimization is shown in Figure

Performance comparison before and after optimization.

In order to verify the effectiveness of the simulation analysis, the rotor structure after optimization is manufactured. It is shown in Figure

Rotor structure.

The cogging torque test platform.

The cogging torque experimental curve is shown in Figure

The cogging torque experimental curve.

In order to obtain the maximum torque and efficiency of asymmetrical magnetic pole PMSM, it is necessary to test the characteristic curve of the motor. The prototype is placed on the dynamometer test platform for a full load test. It is shown in Figure

Dynamometer test platform.

Motor characteristic curve.

In Figure

This paper proposes a novel asymmetric magnetic pole PMSM for automobiles. The equivalent magnetic circuit model is established. Many improvements have been made to the rotor structure. The Taguchi method is used to obtain the optimal solution of each optimization variable. Combined with finite element analysis and prototype experiment, the effectiveness of the structure and optimization method is verified. In addition, some conclusions are drawn as follows:

The novel asymmetric magnetic pole permanent magnet synchronous motor has parallel effective magnetic flux. Compared with the traditional V-type structure, the total permeance is reduced. And the effective magnetic flux content is increased

The Taguchi method is used to optimize the motor structure. A nonstandard orthogonal experimental matrix is established. The original 54 sets of experiments are replaced by 18 combinations of experiments. The number of experiments is reduced obviously. And the finite element method verifies the effectiveness of the method

The eccentric distance of the rotor has the greatest influence on the total harmonic distortion of the air-gap flux density and the average output torque. The eccentric distance and the length of the straight line both have influence on the cogging torque. The proportions are approximately 50%

Compared with the performance before optimization, the total harmonic distortion of the air-gap flux density reduced by 36.7%. The cogging torque is reduced by 26.0%. The average output torque is increased by 4.8%. And the output torque ripple is reduced by 16.4%

All data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there is no conflict of interest regarding the publication of this paper.

This research work is partially supported by the National Natural Science Foundation of China (Grant Nos. 51975340 and 51875327).