Study and performances analysis of magnet design on rotor surface of permanent magnet synchronous machine (PMSM) based on finite element method (FEM) is presented. Three-phase PMSM has been investigated and numerical simulation performed using FEM with the aid of ANSYS Maxwell 2018.1 software. This research presents the positional variation of permanent magnets and their effects on the performance of the three-phase PMSM. The FEM is used as a technique for simulation besides the possibility of dealing with nonlinear equations. The PMSM involves a complex electromagnetic reaction, the authors used the ANSYS program to analyze and represent the performance of the motor under variable conditions. The case studied in this proposal is for three phases 220V, 50Hz, 0.55kW PMSM. Five rotor topologies namely, (i) spoke/tangential, (ii) saturable bridge/ U-shape (iii) V-shape (iv) radial, and (v) segmented bridge permanent magnet (PM) rotor is considered in the study. The aim of this research is to investigate the effect of a variety of rotor designs with different positions of magnets on efficiency, phase current, air gap magnetic flux density, and torque of PMSM. The ANSYS software has been used to model and simulate all topologies considered. In addition to the overall efficiency at steady state, electromagnetic and mechanical parameters are evaluated for each topology and comparative results are reported. The developed 2-D model shows the magnetic field distribution and performance of operational parameters under transient and steady-state conditions. The rotor shape with the smallest magnet volume is highly affecting the torque, magnetic flux, efficiency, and torque ripple. Radial force distribution with demagnetization of PM is also studied and results are reported. The obtained results show that significant changes in motor performance because of variation of PM design.
Research Article
Performance Analysis of Low Power Interior PMSM with different magnet Topology in Rotor Using FEM
https://doi.org/10.21203/rs.3.rs-1997552/v1
This work is licensed under a CC BY 4.0 License
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Electromagnetic and mechanical parameters
demagnetization
finite element method (FEM)
five rotor topologies
Permanent magnet synchronous motor (PMSM)
As induction motors (IMs) are pillar of industrial application, it considers the most widespread, but permanent magnet synchronous machine (PMSM) is coming into consideration which has dominated all types of markets such as industrial, electric vehicle, and hybrid electric vehicle (EV/HEV) application, aircraft, etc. This is due to its high-power density, extended flux weakening region, rugged construction, and high efficiency when compared with other traction motor technologies[1]. A comparative analysis of all types of motors for aircraft application was discussed to show the importance of PMSM [2]. IMs are characterized as robust compared to PMSM, but its limitation lies in its cooling system. The presence of excitation winding in the induction motor, creates more maintenance with extra power requirements. It increases the complexity operation of the motor. Similarly, synchronous reluctance motor (SRM) is also most widely used, and it is suitable for fault-tolerant operation and harsh environments. But it has high-acoustic noise and a low-power factor. To avoid limitations of IM and SRM, PMSM came into consideration for traction application[3], [4]. Insertion of permanent magnet (PM) in place of excitation winding reduces the size as well as the cost of the motor. Especially for electric vehicle applications, PMSM is used because of its high performance at a low cost[5], [6]. Including this, as compared to IM, PMSM has a higher power factor, higher power density in case of low rating. Not only IM, but it also replaced the DC motor. PMSM has longer life, less audible noise, sparkles with better heat transfer capacity than DC motor[7]. It reduced the complexity operation and design of the motor. There are two types of PMSM, (i) surface mounted and (ii) interior PM. The earlier one has some torque production limitations. Interior PM is mostly used in EV due to its high efficiency and variable speed operation[9]. In [10], the effects of dual-rotor axial flux are analyzed for surface-mounted permanent magnet (SPM), interior permanent magnet (IPM), and compared with consequent-pole PM motor. For traction applications in hybrid-electric vehicles, the basic demands of Interior permanent-magnet (IPM) machines include high-power density, high torque density, a wide constant power speed range (CPSR) with high efficiency, among which a wide constant power speed range is of particular importance[11].
In[12], it is noticed that the SPM rotor has better mechanical strength compared to IPM. This factor enables the SPM rotor to run higher speed. With the presence of relatively large physical air-gap length in the SPM motor, its flux weakening ability is deficient but IPM mitigates this. The rotor structure of the IPM motor has a vast impact on the CPSR. Thus, it is feasible to enhance CPSR by optimizing the rotor design. To analyze these properties, many numerical techniques have been developed. A numerical method has been extensively utilized to apprehend composite domain structure, FEM which is one of these techniques provides an accurate calculation for 2D/3D problems of electrical machines with complicated geometries. In [13], a three-phase PMSM is modeled with different designs for operation analysis of motor using ANSYS Maxwell software. All state of conditions are analyzed in this platform directly such as transient state, steady-state, magnetostatic condition, etc. To reduce the computation time, they adopted 2-D finite element analysis (FEA) additional with 3-D FEA. Hence, 2D FEM is considered an important apparatus for the simulation of electrical machines in the primary analysis. Solving issues using FEM desires data about the geometry, materials, sort of use, and boundary conditions that will be settled[14]. Several factors affect on because of rotor design variables such as power factor, phase current, output torque, and efficiency. Many advance PM-based electric machines developed by modifying stator mechanical parameters and using many optimization techniques are discussed in the literature [15], [16]. The present study mainly focuses limited to understanding the position of the PM on rotor and its effect on the performance of the output parameters of IPM. Some important parameters in the stator are slot fill factor, lamination factor, slot width, tooth height etc. For high-frequency application, the maximum slot filling factor is 0.75 to improve the power efficiency [17] For theoretical analysis, we consider the same in this study. Lamination factor is also important which is considered as 0.9 for low frequency application. For this study, we consider the same which reduces the eddy current. The position of the PM in the rotor core will have no effect on the distribution of air-gap magnetomotive force, hence the PM can move its place on the surface of rotor core under the same projection to obtained a different variety of motor[18]. Different types of rotor designs developed have been discussed in [19]-[21]. Designs are varying with respect to magnet alignment on the surface of rotor. This rotor design analysis is limited and not for all parameters of all rotor topology. For electromagnetic torque, it is necessary to understand the magnetic circuit alignment between teeth of the stator and the permanent magnet of rotors. Higher ripple factor in different output signal of the motor is mainly produced due to non-sinusoidal distribution of magnetic flux, its saturation; improper selection of slots etc., these harmful effects will also worsen the motor’s starting and steady-state performances. As these IPM motors are highly recommended for EV application which consists of many high/low voltage electrical components, its electromagnetic environment is so critical[22]. Hence, understanding of electromagnetic compatibility for all types of machine topology is necessary. In this proposal, such parameters are considered for analysis including demagnetization and saliency nature of IPM motors.
This paper, designing and performance comparison of five most common IPM rotor topologies (i) spoke/tangential, (ii) saturable bridge/ U-shape (iii) V-shape (iv) radial, and (v) segmented bridge permanent magnet (PM) are given. Spoke and radial shape is the basic design whereas rest three topologies are the modification of these basic. Furthermore, it is found that the literature discusses restricted basic design with examples. Precise magnetic circuits of IPMs are also introduced mainly when multi-layer or multi-segments interior magnets configurations are used. So, it is necessary to observe the characteristics of more basic designs before going to its modification under transient and steady-state condition. This will decrease the cost and timing of manufacturer. For performance analysis of these basic topologies, electromechanical, electromagnetic with PM demagnetization capability are considered. These parameters are clearly defining their uses under various applications. This article is organized as follows. Section 2 describes PMSM modeling, specifically IPMSM in ANSYS MAXWELL with requires mathematical expression used for electromagnetic analysis. The five topologies of IPM motor are discussed in Section 3 with its designing. The performances of all five topology are compared based on their electromagnetic and electromechanical properties in Section 4 to confirm the merit and demerit of each topology. Section 5 provides the numerical experimental results and conclusion, respectively.
The complete process of designing and analysis of PMSM is given in the form of a flowchart in Fig. 1.
Figure 1 described all the steps adopted for designing of the IPMSM machine, which includes selection of material property, resize the geometry of stator and rotor parameters such as slot width (Ws1), slot height (Hs1), opening base width (Bs0), stator teeth slant height (Hs2), magnet position from the shaft band. A partial differential form of Maxwell’s equations has discussed in [1] are solved in the processing part by using numerical method and the distribution of the magnetic field over the model is obtained. Stator phase currents with flux density and all other parameters of electromagnetic are found and modified as equilibrium equations. The equations for the whole model are obtained by including the equilibrium equation of every element such that continuity is ensured at each of the node.
The Maxwell’s equations are utilized to analyze the magneto static and magneto transient analysis of IPMSM in ANSYS Maxwell. The expression for the electromagnetic torque Eq. (1) developed can be obtained from the number of pole pairs of the PMSM (p), Flux density of PM (\({\varPsi }_{PM}\)) and other quantities along q- and d-axis as given in[22]
$$T=\frac{3}{2}p\left({\varPsi }_{PM}{i}_{q}+\left({L}_{q}-{L}_{d}\right){i}_{d}{i}_{q}\right)$$
1
Here d- and q-axis quantities such as inductance (Ld & Lq), current (Id & Iq) are calculated from three phase a, b, c quantities, and p is number of pole pair.
A motor having 24 number of stator slot with 4 number of rotor pole is selected, while the other designing parameters are restricted within the limits. Five PM rotor topologies of IPM machines were designed as shown in Fig. 2(a)-(e). As seen from Fig. 1, topologies are differentiated from each other based on the position of magnet, the magnet block number for each pole and their direction of magnetization. Based on these two basic topologies Fig. 2(a) and (d) other designs are modified. The multi-segment presented in Fig. 2(b), (c), and (e) has higher fabrication complexity and the magnet segmentation must be optimal, otherwise the motor’s output torque and the average air gap flux density will be decreased in addition to cogging torque. Each topology is examined with large number of ancillary geometrical parameters including thickness with total width of magnet poles for the purpose of determining the location, the flux barrier bridges, and the distance between them. More precisely, diameter D1 determines the distance from the circumference of the rotor that the magnet can expand in rotor region. O2 is the vertical distance between the midpoints of the magnetic poles and the motor shaft circumference for all magnet topologies. Similarly, except from the topologies with spoke, Rib denotes the closest distance between two adjacent poles for all the design. In spoke type, Rib is the distance between the magnet pole and the motor’s shaft. O1 defines the bridge length of each pole in U, V, and Segmented topology. In case of spoke magnet topology, B1 is the diameter from which expanding of magnet is take place while the width of the flux barrier bridges explains by the same parameter for U, V, radial with segmented magnets. The motor’s shaft (D-shaft) diameter is fixed with 65mm for all the topologies considered in this study.
The process of designing is increasing its complexity due to the huge number of geometrical features included and the lack of precise magnetic circuit designs. Therefore, in the first step, the maximum to minimum admissible values for each quantity is predicted at the preliminary design stage. Subsequently, a 2D parametric finite element (FE) model is developed for each topology. Analysis of the sensitivity and post-processing of the results generated shows an effect of the above parameters on the overall performance of the machine.
The five topologies consist of the same single-layer distributed-winding stator and were optimized to achieve a wide range of constant power operations. All topologies depicted in Fig. 2(a)–(e) are cross-sections of IPMSM, which have commonly been taken into consideration to be good candidates for achieving a wide operating speed at constant power, which is necessary to meet the performance requirements of hybrid electric vehicle applications.
The same nominal voltage and current limitations were applied to the five machine designs. The outer diameter of the rotor part of the motor is designed to be 74mm with an air gap of 1mm for all topologies. In many PMSM ferrite permanent magnets are emerged in rotor surfaces due to their lower cost. However, the lower energy product of ferrite PM has been seemed like a critical disadvantage to result in larger dimension [14]. In this design, the best performance of motor can be achieved by choosing neodymium–iron– boron (NdFeB35) based permanent magnets because they have high remanence and relatively larger coercive force compared to other PM [23].
For stator and rotor design, iron-based material having a good capacity for magnetic field capturing is selected. In stator, a copper coil with a number of turns and wire gauge is properly chosen to gain 75% of the fill factor. The outer diameter of an IPM motor stator is 120mm.
Based on the overall performance of the machines including the mechanical and electromagnetic performances, the design iteration of machines is evaluated. Output torque, efficiency, torque ripple, Cu-loss, eddy current loss, demagnetization ratio, and magnetic flux density are assessed underrated speed. Based on a series of simulations and analyses designs are estimated, after repeated refinements and adjustments. Comparison of maximum torque-speed characteristics has been done with respect to the design specifications to ensure the speed range of each motor. In addition, flux linkage, airgap flux density, and inductance are also studied and compared for all five topologies.
Performances of all five IPMSM topologies are analyzed based on 2D finite element models [24]. Table 1 shows the specifications of the stator model used in this study as the IPM motor.
|
Parameters |
Value |
Unit |
|---|---|---|
|
Output power |
550 |
W |
|
Output torque |
3.01 |
N-m |
|
Line voltage rating |
220 |
V |
|
Stator resistance |
2.16 |
Ohm |
|
Synchronous speed |
1500 |
rpm |
|
Frequency |
50 |
Hz |
|
Phase current (RMS) |
1.6 |
A |
|
Phase current (peak) |
2.4 |
A |
|
Relative permeability of NdFeB35 |
1.099 |
- |
|
Magnet width |
3.5 |
mm |
The stator design specification in Table 1 is used for all topologies considered in the study. To form a sinusoidal back electromotive force (BEMF) to the stator, distributed windings are designed. One forth section of all motors is considered for comparative study because of the symmetricity of the model. All the calculations in this study are carried out at a working temperature of 75°C. Using the static FEA, motor electromagnetic parameters are calculated at working temperatures and d-q current excitation. Hence, a statistical comparative study of parameters is proposed at the beginning, followed by an individual parameter analysis. The magnets are organized symmetrically with the magnet width comparable to pole pitch, for obtaining maximum fundamental component of BEMF with harmonic content causing significant torque ripples. The static torque decides the requirement of the torque necessary for the traction operations[25]. For such applications, it is necessary to observe torque at a different level during design.
The ripple torque(\({T}_{ripple}\)) is calculated using Eq. (2) which is defined in[5], [18]
$${ T}_{ripple}=\frac{{T}_{max}-{T}_{min}}{{T}_{avg}} \left(2\right)$$
Where, Tmax, Tmin, Tavg are maximum, minimum, and average values of torque under transient condition. The data generated with respect to each topology and comparative analysis between them are reported statistically in Fig. 3 to Fig. 6 in the form of bar charts. Figure 3 shows the comparison of airgap magnetic flux density for different PMSM rotor structure. From Fig. 3 it is observed that, radial topology motor airgap magnetic flux density is maximum (0.4425 T) compared with other motors under no-load condition. This is due to the nearest position of PM to the air gap compared to other rotors shape. Spoke type rotor has lowest flux density and it is 30.6% less compared with radial rotor.
Various mechanical anomalies like vibration, noise and rotor stress, harmonics in electromagnetic torque causes torque ripple. It is a dynamic oscillation during steady-state operation[26]. Using Eq. (2), the ripple torque of each machine topology at full load under transient condition is calculated and illustrated in Fig. 4. The rotor with segmented bridge PM has lowest torque ripple. From the Fig. 5, it is noticed that torque ripple of segmented bridge gives less than 50% torque ripple of spoke and saturable topology.
Coercive force of magnetic material is one of the important properties and necessary for a motor used in high speed applications. This comparison is illustrated in Fig. 5 for different rotor topologies studied in this work. From the Fig. 5, it is depicted that, V shape, and saturable bridge rotor of PMSM having highest coercive force compared with other topologies.
In this proposal, no load magneto-static analysis is performed to get coercive force and surface magnetic flux density which is generated due to the presence of PM. Its maximum value at different point of motor surface depends on the flux barrier present in rotor design and position of magnet design. From the study, maximum value of magnetic flux density occurs at a point in different rotor topologies are reported in Fig. 6. Under no-load, PMSM with radial rotor has maximum air gap flux density but when considering the magnetic flux density at the surface, V-shape PM rotor has maximum which is given in Fig. 6. Its ripple torque is also less which is already discussed.
Figure 7 shows the FFT analysis of flux density in air gap of different rotor topology. From Fig. 7, it is confirmed in frequency domain that, radial type has highest air gap flux density by comparing the fundamental component of each rotor topology. It is also verified that spoke-shape motor has lowest air gap flux density.
Air gap flux density is highly dependent on the volume of permanent magnet used in rotor design. Magnet thickness of the PM rotor is closely associated with the rotor yoke flux density, air-gap flux density[20], [27]. Magnetic force of the magnet has been defined by its volume. The variation in airgap flux density with magnet width is clearly depicted in Fig. 8. Here air gap magnetic field is considered under slot less condition. From the Fig. 8 it is clear that V- shape IPMSM has more flux density compared to others design. In every design, the value air gap flux density is increases with respect to width of magnet. Here value of magnet width depends on the inner diameter of rotor. In this study it considered from 2 to7mm.
Table 2 gives a comparison of no-load characteristics of the magnetic flux density and flux lines of the five topologies in the form of contour plots. Here thickness of magnet is considered as same in all five topologies. From the Table 2, it can be noticed that for a low rating machine under no load condition, there is no major differences in magnetic flux density among five topologies designs. Under the full load condition, because of the interaction between the magnetic field of stator and rotor, maximum magnetic flux density produces on the stator tooth those are situated between two rotor poles. In spoke shape magnet rotor, magnetic flux density is maximum at the region which has dense number of flux lines. The presence of magnetic shaft also attracts a minimum number of flux lines toward the shaft. This factor helps to improve magnetic flux density in the rotor shaft region. Overall performance of the machine has been improved by magnetic shaft[28].
In case of saturable bridge shaped magnet, both end edges are experience maximum flux density. Saturable bridge with small flux barrier in the lower region of magnet reduces the flux density in middle region of single pole. V-shape rotor topology has maximum value of flux density compared to radial and spoke type rotor due to the less amount of leakage flux. In case of V- shaped Magnet, there is less volume of flux barrier. In spoke type, shaft region is responsible for leakage flux whereas in radial structure, rotor region is responsible for leakage flux. Including this, here magnetic flux is repulsive in nature with single segment of PM. So that it has less flux density. In all type of motors have maximum flux density in the region of having dense flux lines. From the data in Table 2, it can be observed that, segmented bridge has maximum magnetic flux density compare with all other rotor topology.
Table 2 Magnetic flux density and flux lines comparison at no-load
The inductance of the SPM machine is typically low, and inductance of both axes are equal which results no reluctance torque unlike IPM Motor. It limits the SPM machine’s achievable constant power speed range (CPSR) whilst for the IPM machines, including the conventional and segmented PM rotor structures, the d and q-axis inductances (Ld & Lq) are large than the SPM machine. The behavior of PMSM is highly influenced by inductances in d-q axis. These are highly related to Id and Iq, also Lq is greater than Ld. This is a factor indicates good torque with efficiency of Motor. Here, spoke shape rotor only have Lq less than Ld. Their calculation is fundamental not only to access the performance such as torque and field attenuation power, but also to design the control system to improve performance with power factor [29]. Value of Ld and flux linkage of stator decides machine capability for wide speed applications. Under this study, comparative analysis of motor parameters including inductances along d- and q- axis under transient condition has been explained in Table 3. Data from Table 3 shows that d-axis inductance of spoke shaped magnet is highest among all. In addition, it has also lower flux linkage due to flux leakage through rotor shaft and air gap end of the magnet. It means, this is more suitable for wide speed application. Similar to spoke type, radial shape rotor has lowest flux linkage. In this case, flux leakage in the rotor as mentioned above. Saturable bridge shaped magnet has more flux linkage in stator among all rotor types. It is due to less region of flux barrier in rotor part. Saliency ratio indicates the torque capacity with power factor of motor[30]-[32]. Here, it is defined as Lq /Ld. It is also responsible for higher CPSR which is the vital parameter of traction application. It has large impact on flux weakening capacity of machines. From the Table 3, it is observed that saturable bridge segmented magnet shape rotor has better saliency ration than rest three topologies.
|
Rotor Topology |
Lq (mH) |
Ld (mH) |
Rotor Saliency ratio |
Flux linkage (Wb) |
Magnet Weight (kg) |
|---|---|---|---|---|---|
|
Spoke Shape |
11.1721 |
19.2916 |
0.5791 |
0.3201 |
0.1212 |
|
Saturable Bridge |
16.7925 |
13.5611 |
1.2573 |
0.3283 |
0.2693 |
|
V-shape |
14.7743 |
13.4591 |
1.0977 |
0.3215 |
0.2693 |
|
Radial Shape |
14.9057 |
14.4326 |
1.0327 |
0.3193 |
0.2693 |
|
Segmented Bridge |
16.8859 |
13.5554 |
1.2456 |
0.3291 |
0.2693 |
4.1 Losses and Efficiency
Iron loss or core loss strongly relies on the lamination cutting/punching, manufacturing process, welding and stacking. On each of the iron loss components, in addition to the saturation magnetization and the coercive field strength, the effect of these manufacturing processes is elaborated in this paper. Figure 9 compares the core loss and eddy current loss of the five optimized IPMSM motors under transient condition. It can be observed that radial type motor has the highest core loss and eddy current loss. Under low power application study, these losses are obtained due to ferromagnetic material M36 for the construction of rotor and stator cores. Lamination factor considered to be zero (i.e., without lamination of ferromagnetic material) for machine design. Compare with hysteresis loss, eddy current loss is more domination. Hence for comparative analysis eddy current losses is considered with core losses. From the Fig. 9., it is cleared that both core and eddy current losses are more in case of motor with radial shape PM rotor. It has 40.5%, 42.87% more core loss and 55.09%, 58.66% more eddy current loss than rotor with segmented and spoke shape respectively. Small interactive area of magnet from rotor to stator tooth results less eddy current loss.
Based on the losses, efficiency of all topologies considered in this study is also affected. The overall efficiency of each rotor topology is depicted in Fig. 10. As efficiency has proportional relation with losses in motor, here spoke shape has higher efficiency with 86.6355% as compared to other rotor topology. Here steady state of motor is considered. Under this condition spoke shape has maximum output torque and maximum average value of airgap flux density. Including this, here slot effect is also not considered for efficiency calculation.
4.2 Starting and Running State Characteristics
Under rated condition, all motor has higher value of performance characteristics. Figure 11 explains torque of all motor under rated condition. Here spoke shape has higher torque value as compare to other shape. So that it has higher efficiency also. The stable and dynamic model of the PMSM machine and its simulation play an essential role in validating the design process of motor drive systems. Also helps in eliminating unintended design errors and resulting errors in the construction and testing of the machine prototype [15]. As PMSM is used for electric vehicles applications, it is necessary to verify its starting and running torque. As electromagnetic torque determines the rotor position and speed, it is considered as the most important variable [33]. It is already discussed in the form of ripple torque in beginning of section 4. Figure 11 shows the details of maximum running torque of all rotor design under transient condition. From the Fig. 11, it is clear that saturable bridge, V-shape, and segmented bridge rotor design has nearly equal torque. Spoke shape rotor has least running torque with 16.2522 N-m for all topologies considered in the study. It has also low magnetic flux density already expressed in above. This is due to lack of Flux intensify region in spoke shape under magnetic field analysis.
Among all, V-shape rotor topology has a maximum running torque concerning torque angle. This running torque is found around 80o-110o of electrical torque angle under steady-state condition. Similarly, torque under transient conditions is also simulated directly under the ANSYS Platform for designing all types of rotor machines. Here voltage source type winding is considered with armature resistance 2.6573Ω. The results are compared and plotted in Fig. 12. From Fig. 12, it can be observed that the radial shape rotor has maximum starting torque among all.
Rotor with saturable bridge and V-shape permanent magnet has nearly equal starting torque at no-load condition. The motor synchronization is achieved within 20-25msfrom starting time.The primary element of electromagnetic torque is produced due to the interaction of the air gap magnetic field with stator armature reaction. The second harmonic component is reluctance torque which is produced due to the non-symmetric magnetic circuit of d and q-axis. IPMs have a better saliency ratio and it is already explained. The presence of reluctance torque in total electromagnetic torque leads to flux weakening, and it is highly affected the power density and overloading ability of IPM. Magnet torque is always negative which opposes reluctance torque. Higher the electromagnetic torque with respect to current excitation angle, depends on both magnetic and reluctance torque component. Under running condition when motor is accelerated load torque always less than electromagnetic torque. In Fig. 12, electromagnetic torque defines both magnetic torque and reluctance torque. Segregation of electromagnetic torque is illustrated in Table 4. Average values of all the torque is considered for this segregation.
|
Rotor Topology |
Electromagnetic Torque(N-m) |
Magnetic Torque (N-m) |
Reluctance Torque (N-m) |
|---|---|---|---|
|
Spoke Shape |
3.6977 |
-0.3953 |
4.0929 |
|
Saturable Bridge |
2.7551 |
-35.6004 |
38.3555 |
|
V-shape |
4.3341 |
-0.1110 |
4.4450 |
|
Radial Shape |
6.5906 |
7.6920 |
-1.1074 |
|
Segmented Bridge |
5.6303 |
-8.2351 |
13.8658 |
Electromagnetic torque is analyzed under mechanical loading condition. At load torque of 3.5Nm with starting rotation angle 30o with speed 1500 rpm, torque of all the five topology is considered for the analysis, and its results are shown in Fig. 13. Under mechanical transient condition, speed decreases result of which torque angle and driving torque increases. Effect of Load torque (Tl) reduces the ripple in the electromagnetic torque (Tem). Here saturable bridge has lower Tem characteristics than other topologies. V-shape, radial and segmented Bridge has better characteristics in this observation.
Here, rotor structures of all motors are considered without damping winding. So, it is possible to observe only transient and steady state conditions of all parameters. It is also possible to observe synchronous reactance along d-axis (Xd) and q-axis (Xq) of all types of motor considered in this study. It is important to analyze transient, steady state behavior of synchronous motor used for application. In this proposal torque characteristics of PMSM with different rotor topology are observed up to 0.2s to analyses its transient and the same is plotted in Fig. 14. From the Fig. 14, it is depicted that, electromagnetic torque reaches steady state within 25ms. Similar to torque, behavior of inductance along d and q-axis (Y1) is also simulated and reported in Fig. 14. These time characteristics are fully dependent on machine designing. So that all motor parameters are converged to steady state around same time. Initially, all signals have some transition period due to inrush current with presence of harmonics in motor.
Same transient duration is observed for both torque and inductive component because of dependency of torque on inductance along q-and d-axis, it is clearly seen in Fig. 14. Saliency nature of different topology is also clarified from both Inductance plots. Synchronous reactance data along d- and q- axis are reported in Table 5.
It clarified that under transient, only spoke shape PMSM having Xd ˃ Xq. From Fig. 12 it is observed that, the characteristic of torque is periodic under transient conditions. The time response of all motors is presented in Table 6.
|
Rotor Topology |
|
Xd(Ω) |
Xq(Ω) | ||
|---|---|---|---|---|---|
|
Spoke Shape |
7.4784 |
5.4221 |
|||
|
Saturable Bridge |
4.5545 |
8.8743 |
|||
|
V-shape |
7.5565 |
7.8724 |
|||
|
Radial Shape |
5.1534 |
7.6533 |
|||
|
Segmented Bridge |
4.2764 |
5.3757 |
|||
Table 6 Time response data of electromagnetic Torque(N-m)
Table 7 Torque under synchronous period
|
Rotor Topology |
Torque in Torque in Synchronous Period (Ts) in N-m Period (Ts) in N-m |
|
|
Spoke Shape |
12.0413 |
|
|
Saturable Bridge |
19.4458 |
|
|
V-shape |
23.6453 |
|
|
Radial Shape |
22.0925 |
|
|
Segmented Bridge |
23.4659 |
|
Magnitude of torque under synchronous of all the rotor topology is reported in Table 7. From the data in table 7, it is clear that V-shape and segmented bridge PM motor has highest toque compare to remaining rotor topology under synchronous condition. Also found that, spoke shape rotor has lowest synchronous torque.
In PMSM, there is only a breaking torque on the synchronous working zone [34], [35]. During the synchronous period, the cut-off torque behaves like an acceleration torque. Synchronous torque is elaborated in Fig. 15. Saturation in synchronous torque is occurring after 0.25s in all topologies of motors considered in the study.
Figure 16 shows the magnetic flux density of PMSM under synchronous condition. In this study, initial rotor position is considered at 15o and running for 3s. This initial position also defines the angular rotation, also affects magnetic flux density. Similar to torque performance, saturable bridge, V-shape, and segmented bridge rotor also have nearly equal maximum magnetic flux density with 3.1706T, 3.1930T, 3.1941T respectively. Radial shape rotor has lowest magnetic flux density among all.
4.3 Radial Force Analysis
In general, Radial forces are taken into account in the vibration estimation and analysis of acoustic noise in all types of machines. A typical way to examine the radial forces (Fr) is to analyze the components of the magnetic flux density vector B, which are obtained from the FEA. Generally Fr can be expressed by Eq. (3) as given in[13].
Fr = (1 /2µ0) (Br2 – Bt2) (3)
Where, Fr is radial force density, Br defines radial component of magnetic flux density, and Bt represents tangential component of magnetic flux density. The radial force density Fr is dependent on the radial and tangential component of the magnetic flux density vector. The tangential and axial components of the flux density are ignored to simplify the analysis, as they are typically much less than the radial component.
Here one forth section of whole model is considered for radial force observation. The changes in the radial force with respect to radial distance is simulated and reported in Fig. 17 for both full and no-load condition. At both sides of radial distance under study, spikes are obtained in no-load and full load condition for all type of topologies. Under no load condition, spikes occurring in the radial force is only at enter and exit point of the magnet with equal pulses in between for all type of PMSM rotor topology. But under full load condition spikiness of radial force at different part of the rotor is increases with non-uniformity of distribution. Spikiness in radial force at entry and exit edging point is more in case of spoke shape rotor under full load condition as shown in Fig. 17.
There is no pulse occurred continuously in middle section of this topology. The spikiness defines the roughness of the machine. Saturable and segmented bridge rotor has similar characteristics over radial force under full load condition that can be seen from Fig. 17(b) and Fig. 17(e). In these two rotors, under full load both have approximately equal magnitude of radial force and similar nature of pulses after the spikes of edging point. Also, non-uniformity of pulses is more as compare to that of V-shape and radial shape rotor. But in case of V-shape, magnitude of radial force is lower than radial shape which is observed in Fig. 17(c) and Fig. 17(d). Radial force distribution is also defining the sensitivity of motor under mechanical load condition. This spikiness reduces the performance capability of motor. Non uniform distribution of radial force create imbalance in the operation.
4.4 Torque-Speed Characteristics
The advantages of PM based machines include higher peak torque, best dynamic response, and lower maintenance requirement in all aspects of operation [36]. Constant torque, constant power, and decreasing power are the three distinct operational areas of these machines. Figure 18 shows the torque–speed characteristics for all five rotor topologies together in per unit (p.u.) under rated condition. Here speed varying from 500 to 4000 rpm. Each motor has different values of rated torque at rated speed 1500 rpm. Here per unit measurement is considered for analysis. Under rated condition torque of spoke shape is 2.18321Nm. It’s per unit value is also higher than other motor. Torque under rated condition for other motor has already mentioned.
From Fig. 18 it is cleared that, radial shape IPM rotor has wider range of speed. Also, in comparison to other types, it has good torque-speed performance for entire speed range. For the case of spoke type, it gives constant torque only up to rated speed then comes to torque reducing region. From the Fig. 18 it is observed that, PMSM V-shape, U-shape and segmented bridge rotors have nearly equal range of speed and constant torque region. In constant torque region, spoke shape IPM motor has higher value of torque. Because of higher speed, saturation level is come faster than others which cause its constant speed range upto per unit range of speed.
To widen the speed range, the high-speed field attenuation is applied so that more d-axis current is used in the armature current, which suppresses the magnetic field of the rotor and thus decreases the induced voltage. Figure 19 compares the induced phase voltage with current excitation angle of all five topology at 1.6A and 1500rpm under transient condition. Figure 19 depict that, radial shape IPM motor has highest and spoke shape rotor has lowest phase induced voltage.
Torque characteristics of the five different PMSM rotor topologies are determined by using FEA. Figure 20 shows the relation between maximum torque and current excitation angle under 2D transient analysis. From the Fig. 20, it is observed that, radial topology torque is more with respect to excitation angle compared with other topologies. All motors have declined characteristics when angle increasing. Maximum value of torque is achieved at zero current exciting angles. Under transient condition, voltage source leading by an angle ør. So that, total torque does not converged to zero value at 90o.
Under transient condition, characteristics of induced phase voltage are simulated for all rotor topologies and their comparisons are reported in Fig. 21(a). All rotor topologies have equal amplitude of induced phase voltage with respect to time except segmented bridge type. A FFT analysis of induced phase voltage of the five motors at the rated speed is compared and results are shown in Fig. 21(b). It shows that odd harmonic components are more compared with even harmonics, also observed that V-shape rotor topology has lowest fundamental component.
4.5 Demagnetization
Demagnetization analysis is an important and essential process in designing of PM motor. Irreversible PM demagnetization can arouse to a significant reduction in the output torque and consequently to declined reliability [36], [37]. The irreversible demagnetization of PM is defined as the loss of magnetization where the PM is not restored to the original curve, when a field is removed. This situation occurs when the strength of demagnetizing field reaches the intrinsic coercive field strength Hci and the operating point of a PM falls below the demagnetizing knee point[38]. So that it has maximum value flux density at no load condition. For demagnetization analysis in this proposal, operating temperature of machine at 75°C is considered. Temperature of PM is considered as 110°C. Demagnetization ratio is defined the magnet performance comparison before and after excitation current to motor. This is given in Eq. (4). This analysis is carried out under nonlinear permanent magnet.
Demagnetization ratio(%) = 100*(1-(B2/B1)) (4)
Where B1 is the magnet rasidual flux density at no currentloading and B2 is the magnetic flux density after loading of current. Demagnetization is also detrmined on the based of magnetic coercive force.
Zero value of demagnetization ratio represents magnet performance is same before and after the current loading. In this study, demagnetization measurement is considered based on flux density of permanent magnet at constant temperature of 110°C. Demagnetization highly affected the edges of the magnet. Table 8 shows the demagnetization analysis of PM of all topology considered.Table 8 also explains the magnetic flux density of PM before and after current loading.
In color bar, toward blue represents decrease of magnetic flux density. Under demagnetization condition, with increase of current, flux density decreases. This demagnetization analysis decides the life period of the motor. It affects torque, output power, efficiency of a machine. So in the analysis period, it is necessary to do test the magnet by defusion. From the demagnetization analysis as shown in Table 8, spoke shape motor has good demagnetization ratio compared to other shape motor. Saturable bridge, V-shape, radial shape and segmented shape has low demagnetization characteristics at given temperature of 110°C. This is because of volume and weight of the magnet used in rotor design. For the design, thickness is considered as constant with 3.5mm. In this analysis, the minimum point of operation is also explained which denotes demagnetization risk. Each edge points of PM is under the risk of demagnetization effectively.
Table 8 Magnetic flux density of PM under demagnetization
Demagnetization ratio of PM with different temperature (i.e., at 80°C, 110°C and 1400C) are elaborated in Table 9. With increase of temperature, demagnetization of PM is increases. In this paper NdFeB35 is considered for designing a PM rotor, whose operating range of temperature lies under 1500C. Maximum Operating temperature of standard NdFeB35 magnet is 800C. When temperature increases, it will experience irreversible demagnetization. A small variation in demagnetization ratio is observed from 800C to 1100C for saturable bridge, V- and radial rotor topology. But at 1400C, percentage of demagnetization is much higher. At this temperature, segmented and v-shape has lower demagnetization compare to rest topology of motors.
|
Rotor Topology |
Demagnetization Ratio(%) at 800C |
Demagnetization Ratio(%) at 1100C |
Demagnetization Ratio(%) at 1400C |
|---|---|---|---|
|
Spoke Shape |
28.8 |
56 |
70.33 |
|
Saturable Bridge |
30.00 |
32.49 |
56.44 |
|
V-shape |
28.35 |
28.60 |
49.39 |
|
Radial Shape |
39.05 |
39.06 |
66.11 |
|
Segmented Bridge |
27.00 |
32.31 |
46.09 |
4.6 Mechanical Stress Analysis
To know the mechanical stress distribution over the rotor surface and its total deformation with respect to original design at high speed under transient condition, it is necessary to do a mechanical stress analysis. It also provides the idea about the mechanical strength of rotor part. In this paper, 3000rpm is considered as a high speed of motor. Mechanical stress analysis also involves the magnetostatic force at different part of the machine. To ensure the rotor integrity, finite element analysis (FEA) is used for the analysis. Figure 22 shows the simulated von Mises stress distributions for the five different rotor topologies rotating with 3000rpm at 20◦C.
The first design consideration of a motor is the width of the flux bridges which buried Permanent Magnet on Rotor surface. The key point before designing the flux bridges in machine is sufficient magnetic saturation can be achieved in the bridges. As a result, it will minimize the magnet leakage flux in Rotor part. However, the mechanical rigidity will be compromised by reducing the bridge width too much. Second, distribution of the mechanical stress is not uniform in the rotor surface. In projected topology, four areas of rotor are highly sensitive for High mechanical stress distribution such that: 1) the upper bridges of permanent magnet pocket and rotor surface; 2) lower part of rotor surface of placed PM; 3) the center bridge between PM in the rotor back iron; and 4) inner edging surface of rotor at the shaft diameter.
Calculated maximum stress and corresponding deformation under reported conditions are listed in Table 10. As listed in Table 10, V-shape has minimum von Mises stress distribution over the surface of rotor compared to rest topologies.
|
Motors |
vonMises Stress(MPa) |
Deformation(mm) |
|---|---|---|
|
Spoke Shape |
461.97 |
0.0377 |
|
Saturable Bridge |
2185.30 |
1.7309 |
|
V-shape |
110.33 |
0.0095 |
|
Radial Shape |
232.15 |
0.0211 |
|
Segmented Bridge |
6847.80 |
4.1027 |
In all topology one factor is common that the mechanical stress is not uniformly distributed throughout the rotor surface. According to specific region, it is varying. In case of spoke shape, maximum stress occurs at upper edge of rotor which is shown in Fig. 22(a). Figure 22(b) represents mechanical stress distribution in saturable bridge rotor. Here maximum von Misses stress distribution occurred at central bridge situated between centralized magnets. At the center maximum mechanical stress is occurred in case of V-shape rotor as shown in Fig. 22(c). But it is very less compared to other proposed rotor topologies. Like V-shape, radial shape rotor also has less mechanical stress depicted in Fig. 22(d). But the stress is Maximum at inner edging surface of rotor. In segmented bridge case illustrated in Fig. 22(e), stress is maximum at the central bridge between both PM. It has maximum stress among all topology considered in the study.
Deformation is the result of displacement which is caused by centrifugal force. Including this, deformation will be permanently fixed when certain material strength limit is over crossed by stress. So, to know the limitation of deformation of each topology, all related data are elaborated in Table 10. As deformation is linearly proportional to mechanical stress, from stress distribution, it is easy to know the idea about deformation of each topology.
This paper represents the comparative study of five IPM rotor topologies on the basis of their designing and performance which includes magnet thickness, mass, and magnetic flux density. All motors considered in the study are having equal power rating. Performance of IPM rotor is compared under steady state, transient and synchronous mode. Parameters like torque, output power, inductance along d- and q- axis, core loss, and efficiency are analyzed for comparison purpose. Including this, demagnetization with mechanical stress is also considered for comparative study. 2D FEA method is used for performance analysis of all motors. From results, it is clear that spoke-shape PMSM rotor has high efficiency with 86.63% compared to others. But, when torque angle is greater than 900, degradation in efficiency is not smooth. Hence from overall, V-shape rotor gives good efficiency with maximum of 85.5256% for a wide range of torque angle. Radial shape IPMSM has maximum air gap flux density due to nearest position of magnet to the air gap. As here low power is considered for analysis, spoke shape IPMSM has less core loss of 18.70W compared to other. When considering overall surface of motor, V-shape has good flux density and magnetic force. Saturable bridge, V-shape and segmented bridge rotor have similar torque-speed characteristics. Among all, radial shape motor is more applicable for wide speed range application.
Conflict of interest The authors declare that there is no conflict of interest.
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