Mitigating Eccentricity in PMSM Motors for Enhanced Performance

Introduction

For the past few decades, the automotive industry has been searching for alternatives to internal combustion engine (ICE) vehicles to reduce pollution, leading to a significant trend in electrification. Various electric motor categories have been proposed, with most relying on an electric motor as a traction source. The two main types of electric machines used in the passenger car industry are induction motors (IMs) and permanent magnet synchronous motors (PMSMs), with the latter being preferred due to their high efficiency and power density. PMSMs can be designed with different configurations, classified by flux direction and magnet positioning. Among these, the interior permanent magnets synchronous machine (IPMSM) architecture is the most employed for electric traction motors in electrified vehicles. However, the noise and vibration produced by electric motors pose a challenge to designers and engineers, as they can affect riding comfort [1-4]. 

In this blog post, we will discuss the concept of eccentricity and its impact on PMSM machines. We will explore how simulation software can be used to analyze the effects of eccentricity and optimize PMSM motor performance.

Impact of Eccentricity

In a perfect motor, the rotor's center coincides with the stator's center, and the air gap between them is uniform. However, in real-world motors, the rotor's center often deviates from the stator's center, which leads to a non-uniform air gap and introduces a series of unwanted effects. Eccentricity can cause unbalanced magnetic forces, which create vibrations that can result in mechanical failure, noise, and reduced efficiency.

The impact of eccentricity on PMSM machines is dependent on the type and severity of eccentricity. There are mainly three types of eccentricity: static, dynamic, and mixed eccentricity. Static eccentricity refers to a constant displacement of the rotor's center from the stator's center, resulting in a steady-state condition. Dynamic eccentricity, on the other hand, refers to a time-varying displacement of the rotor's center from the stator's center. Finally, mixed eccentricity is a combination of both static and dynamic eccentricity.

One of the major problems that can result from eccentricity in PMSM is electromagnetic noise and vibration (eNVH) as shown in Figure 1. It is generated by the radial force produced by the electromagnetic field, which acts on the stator and rotor. This force results from the non-uniformity of the air gap between the rotor and stator due to eccentricity. The resulting eNVH can lead to several negative impacts, such as increased acoustic noise, mechanical stress on the motor components, and reduced efficiency. In addition, the resulting vibration can lead to reduced bearing life and potential failures. Therefore, it is essential to accurately analyze the effects of eccentricity on PMSM machines [5]. The analysis of eccentricity in PMSM machines is a challenging task, and it requires sophisticated simulation tools to accurately predict the behavior of the motor under different conditions.

Fig. 1. Source of Noise and Vibration in an Electric Motor

A Simulation-Based Approach

EMWorks’ eccentricity analysis uses electromagnetic simulation to predict the motor's behavior under different types of eccentricity, including static, dynamic, and mixed. By performing a simulation-based approach, motor designers can optimize the motor's performance and avoid potential issues caused by eccentricity. Figure 2 illustrates the location of the stator and rotor cross sections relative to the stator reference frame in three different situations: static, dynamic, and mixed eccentricity. The stator's symmetry center is labelled as O_s, the rotor rotation center as O_ω, and the rotor symmetrical axis as O_r.

Static eccentricity refers to the scenario where there is a shift in the rotation axis, while the air gap length remains constant in space as shown in Figure 2(a). The ratio is given as

ε_st=|O_s O_ω |/g

where g is the uniform air gap length, O_s O_ω is the static vector which is fixed for all the angular positions of the rotor. Next, dynamic eccentricity is a situation where the stator axis and the rotor rotation axis are the same, but the rotor axis is slightly shifted as shown in Figure 2(c). The ratio is given as

ε_dyn=|O_ω O_r |/g

where O_ω O_r is the dynamic vector and fixed for all angular positions of the rotor, however, its angle varies. Finally, the combination of static and dynamic eccentricity leads to mixed eccentricity as shown in Figure 2 (d) and which is given as:

ε_st+ε_dyn=|O_s O_r |/g=|(O_s O_ω)/g+(O_ω O_r)/g|

where O_s O_r is the mixed vector.

Fig. 2. Location of the Stator and Rotor Cross Sections Relative to the Stator Reference Frame in Three Different Situations

The designer can set up the simulation scenario with the desired eccentricity type and magnitude. The simulation results provide the motor's electromagnetic behavior, including the flux density, magnetic field, torque, stator tooth forces, etc.

Create a study with eccentricity

To analyze the impact of eccentricity on a PMSM machine, the designer needs to create a new study by clicking on the "New Study" button in the EMWorks software. Within this study, the designer can choose the type of eccentricity to be analyzed: static, dynamic, or mixed eccentricity.

Define static eccentricity parameters

If the designer chooses to analyze the impact of static eccentricity, they need to enter the shift in the rotor rotation axis and the angle based on the percentage of the air gap magnitude. The designer can do this by inputting the parameters into the software's interface.

Define dynamic eccentricity parameters

If the designer chooses to analyze the impact of dynamic eccentricity, they need to enter the shift in the rotor motion based on the percentage of the air gap magnitude. Similar to static eccentricity, the designer can input these parameters into the software's interface.

Define mixed eccentricity parameters

If the designer chooses to analyze the impact of mixed eccentricity, they need to enter the parameters used in both static and dynamic eccentricity. The designer can input these parameters in the same manner as for static and dynamic eccentricity.

Run the simulation

Once the study and parameters have been defined, the designer can run the simulation in EMWorks. The software will use the parameters entered by the designer to create a model of the PMSM machine with the selected eccentricity type. The simulation will then generate results for the designer to analyze and interpret.

Fig. 3. Illustration of Different Types of Eccentricity - with Air Gap Length Extended for Enhanced Visualization

EMWorks software provides a powerful tool for analyzing the impact of eccentricity on PMSM machines through animations. These animations enable motor designers to visualize the effects of eccentricity on the magnetic field, rotor position, and motor performance, providing valuable insights for optimizing motor designs.

In these animations, the three types of eccentricity are depicted: static, dynamic, and mixed. Static eccentricity, which occurs when the center of the rotor is offset from the center of the stator, is represented in the animation by a shift in the rotor rotation axis and an angle based on the percentage of the air gap magnitude. Dynamic eccentricity, which occurs when the rotor deviates from its circular motion, is shown in the animation by a shift in the rotor motion based on the percentage of the air gap magnitude. Finally, mixed eccentricity, which is a combination of static and dynamic eccentricity, is represented by a combination of the parameters used in the above static and dynamic eccentricity.

Fig. 6. Animated Magnetic Flux Density Plot with Mixed Eccentricity

These 2D animations of eccentricity are more than just a visual aid; they are a product of sophisticated mathematical computations and electromagnetic field simulations that consider the intricate interactions among the stator, rotor, and air gap. Motor designers can leverage these animations to gain a more profound comprehension of the impact of eccentricity on PMSM performance. Armed with this knowledge, designers can optimize motor designs, mitigating the adverse effects of eccentricity, such as increased noise and vibration levels, reduced efficiency, and shorter motor lifespan. By utilizing these powerful tools, designers can make informed decisions to deliver superior motor performance and reliability.

Tooth Force Calculation

There has been significant research interest in developing accurate and efficient tooth force calculation techniques. One common approach is to use the finite element method (FEM) to model and analyze the electromagnetic field distribution and resulting tooth forces. This method involves discretizing the machine geometry into small elements and solving the governing electromagnetic equations numerically. FEM has proven to be a powerful tool for analyzing tooth forces under various fault conditions, including eccentricity. Tooth force analysis can be used to optimize machine design by identifying areas of high stress and minimizing material usage and cost.

Let's consider a surface-mounted PMSM design with 12 slots, each containing a coil, while the rotor has 4 poles with permanent magnets attached to it. The rated current of the machine is 25 A, and the rated speed is 1500 rpm.

Table 1. Specification of the Surface-Mounted PMSM

Under healthy conditions, the tooth forces in a PMSM are generally balanced and evenly distributed around the rotor. However, in the presence of an eccentricity fault, the tooth forces can become unbalanced and vary significantly from one tooth to another.

In a 12-slot, 4-pole PMSM, tooth 1 and tooth 7 are located at opposite ends of the stator and rotor, and therefore, experience different air gap lengths. Under eccentricity fault conditions, the air gap length can vary significantly around the circumference of the rotor, leading to uneven tooth forces. Tooth 1, which is located near the maximum air gap length, experiences a lower force than tooth 7, which is located near the minimum air gap length. In dynamic eccentricity, where the rotor centerline oscillates around the stator centerline, both tooth 1 and tooth 7 experience cyclic variations in force. In mixed eccentricity, where the rotor centerline is both displaced and oscillating, tooth 1 and tooth 7 forces are affected by both types of eccentricity, resulting in complex and uneven force distributions. Therefore, accurate and comprehensive tooth force analysis under different fault conditions is crucial for the proper functioning and optimal design of electrical machines.

         

Fig. 8.  Healthy Rotor

 

Fig. 9. Static Eccentricity [50% at 0°] 

  

 

Fig. 10. Dynamic Eccentricity [50%] 

 

Fig. 11. Mixed Eccentricity [Static 25% at 0° | Dynamic 25%]                

Conclusion

In conclusion, the analysis of eccentricity is a crucial step in optimizing the performance of PMSM machines. Eccentricity can lead to various negative impacts, including electromagnetic noise and vibration, mechanical stress on the motor components, reduced efficiency, and potential failures. Therefore, it is essential to accurately analyze the effects of eccentricity on PMSM machines using sophisticated simulation tools. EMWorks' eccentricity analysis uses electromagnetic simulation to predict the motor's behavior under different types of eccentricity, including static, dynamic, and mixed. With this simulation-based approach, motor designers can optimize the motor's performance and avoid potential issues caused by eccentricity.

The benefits of simulation-based approaches are numerous. They enable designers to optimize the design before building the prototype, reducing costs and time to market. The simulation also provides the opportunity to test different design configurations and scenarios, leading to a better understanding of the motor's behavior under different operating conditions. Moreover, simulation-based approaches allow designers to explore the impact of changes in design parameters on the motor's performance, providing valuable insights that can be used to improve the overall design.

References

[1] B. M. Ebrahimi, J. Faiz and M. J. Roshtkhari, "Static-, Dynamic-, and Mixed-Eccentricity Fault Diagnoses in Permanent-Magnet Synchronous Motors," in IEEE Transactions on Industrial Electronics, vol. 56, no. 11, pp. 4727-4739, Nov. 2009

[2] M. Cheng, J. Hang and J. Zhang, "Overview of fault diagnosis theory and method for permanent magnet machine," in Chinese Journal of Electrical Engineering, vol. 1, no. 1, pp. 21-36, Dec. 2015

[3] Mohamed Moustafa Mahmoud Sedky. (2014). Diagnosis of Static, Dynamic and Mixed Eccentricity in Line Start Permanent Magnet Synchronous Motor by Using FEM. International Journal of Electrical, Electronic and Communication Sciences, 7.0(1)

[4] B. M. Ebrahimi and J. Faiz, "Configuration Impacts on Eccentricity Fault Detection in Permanent Magnet Synchronous Motors," in IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 903-906, Feb. 2012

[5] N. Remus et al., "Electromagnetic Noise and Vibration in PMSM and Their Sources: An Overview," 2020 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), London