Solid Rotor Core vs. Lamination Rotor Core in Fractional-Slot PMSM Motor with High Power Density

The purpose of this study is to present a comparison of a high power density motor with a solid rotor and a laminated rotor core, considering the value of rotor losses, power density factor, efficiency and the range of rotational speed and range of current load. It should be emphasized here the importance of the analysis carried out in the context of applications in motors with high power density. The authors did not find similar publications linking these issues. These high power density motors operate in conditions incomparable to the operating conditions of other motors, i.e., when supplied with high frequency voltage (approx. 800 Hz), with very high values of magnetic flux density in the stator core and rotor yoke (approx. 1.9–2.2 T) and at very high current loads of 12–15 A/mm. All these factors significantly affect the value of losses in the rotor elements. It is also worth noting that such operating conditions may cause unfavorable phenomena in the motor, e.g., bearing currents [ 28 ]. The authors’ intention is also to assess the possibility of using a solid rotor core in motor operating in such demanding conditions, as well as to assess the real benefits of replacing it with a laminated rotor.

One of the known methods of limiting eddy current losses is laminating the rotor core. The external rotor with surface permanent magnet of the fractional-slot motor can be made as solid or laminated. The solid rotor simplifies the construction of the motor as it does not require additional elements to support the laminated core, but it causes higher values of losses in the rotor core. The laminated rotor core reduces eddy current losses but complicates the technological process and increases the rotor weight. As part of the work, the possibilities of using various types of materials in both the solid rotor and the laminated rotor were considered.

The selection of appropriate materials in the electromagnetic circuit is also important in reducing eddy current losses. In the publications [ 1 10 ], the authors present and describe the properties of a number of different materials used in the electromagnetic circuits of motors with high operating parameters (mainly traction motors), but they do not show or analyze the direct impact of their application on the values of losses in motors with high power density. The material properties of magnetic circuit elements in terms of limiting eddy current losses in the rotor are analyzed in publication [ 27 ]. However, they apply to special covers on permanent magnets, copper or other materials, which are not analyzed in this paper. Moreover, the use of this type of shield is intended mainly for high-speed machines, the operating conditions of which differ from those of motors with high power density.

There are methods known to limit the value of eddy current losses in rotor elements. The paper [ 11 ] presents the issue of the correct selection of the slot-pole combination, which allows the reduction of rotor losses. The articles [ 23 26 ] present methods of reducing eddy current losses in the rotor by segmentation of permanent magnets. Similarly, in the publications [ 19 ], the authors present various methods of reducing the negative effect of eddy current losses in the rotor based on the optimization of the shape of selected components of the electromagnetic circuit.

Motors with high power density (4 kW/kg and more) are sought in industries such as automotive, aviation or marine, which expect dedicated solutions with a high degree of technical advancement [ 1 9 ]. For these applications, rotational speeds are usually in the range up to 5000–6000 rpm; therefore, it should be understood that high power density is directly related to obtaining high shaft torque values. Fractional-slot PMSM motors are a particularly interesting solution that allows for obtaining very high operating parameters (torque, power) of the motor and, at the same time, low weight. One of the conditions is to work with high values of the supply frequency (500–1000 Hz), high magnetic flux density in the magnetic circuit elements (1.9–2 T) and high current load (>12 A/mm). In addition, the proper design of the electromagnetic circuit is very important, including the use of appropriate materials [ 4 11 ]. At the same time, fractional slot motors are usually characterized by the content of subharmonics and a high content of higher harmonics in the distribution of the magnetomotive force, which is one of the main causes of eddy current losses in the rotor elements—in the rotor yoke and permanent magnets [ 12 22 ]. These losses can demagnetize the permanent magnets or just limit the required operating range of rotational speed or shaft power of the motor. This is, therefore, one of the main issues at the design stage of this type of motor.

The electromagnetic circuit of the motor has been designed taking into account the key guidelines known from the literature [ 11 30 ] in the scope of limiting the value of eddy current losses in the rotor. One of them is the correct selection of the number of stator slotsto the number of magnetic polesin order to limit the content of subharmonics in theforce distribution. These subharmonics cause an increased content of eddy current losses in the rotor elements, and thus also the temperature, which in extreme cases may even lead to demagnetization of permanent magnets.

The object of the analysis is 20-pole, 24-slots PMSM motor with an external rotor, with surface permanent magnets (SPM) and concentrated winding. Figure 1 shows the cross-section of the fragment of the motor with a solid rotor ( Figure 1 a) and a laminated rotor ( Figure 1 b), which are analyzed in this paper. Table 1 presents the basic data for the analyzed motor model. NO27 sheets (0.27 mm) were used in the stator core and permanent magnets N45SH in the rotor. The permissible operating temperature for this type of magnet is 150 °C (catalog value). It was assumed that the motor is powered by a DC source through a sinusoidal AC motor controller. For all analyzed models, a highly efficient water cooling system was assumed, and the permissible rated current density in the winding would be= 15 A/mm. The end winding is also flooded with resin with good thermal conductivity. The laminated core rotor requires additional support, so the total motor weight is 11.4 kg, while the solid rotor motor weighs 10.2 kg. These differences were taken into account when determining the power density factorfor the analyzed solutions.

It is known from the literature [ 19 ] that the dominant losses in the solid rotor elements are eddy current losses. In papers [ 13 18 ], the theory of the eddy current phenomenon induced in the rotor elements is presented. It is known that the eddy current losses strictly depend on the resistivity of the material of a given element. The resistivity of NdFeB permanent magnets is approximately 0.625 MS/m, while the resistivity of the steel used in the solid rotor model is 1.95 MS/m; therefore, the eddy current losses cannot be ignored.

In using the developed calculation model, the total value of losses in the rotor core Δwas calculated as the sum of losses in permanent magnets Δand losses in the rotor yoke Δ. Magnet losses Δwere calculated as the sum of the losses in individual magnets within one full magnetic symmetry, multiplied by the number of magnetic symmetries.

4. FEM Analysis

The analysis was performed on the two-dimensional computational model of a motor with the use of the FEM method. Due to this fact, the end effect and segmentation of the permanent magnet were ignored. The ANSYS Electromagnetic and Octave FEMM software was used for simulations. Figure 3 shows the calculated distribution of the flux density from permanent magnets in the elements of the electromagnetic circuit of the motor model. The maximum value of the flux density in the stator teeth is approximately 2.0 T, in the stator yoke, it is 1.65 T, while the maximum value of the flux density in the rotor yoke is 1.8 T.

In order to extend the scope of the analysis, calculations were carried out for several types of materials in the solid core—S355j2 and Somaloy 700 3p, and for several materials in the laminated core—M400-50A, NO27 and Vacoflux48. It should be noted that the changes in individual calculation models concerned only the material properties of the rotor yoke. The geometric dimensions of the electromagnetic circuit and the rest of the data were the same in all models. The distribution of the magnetic flux density in the elements of the magnetic circuit and the values of the magnetic flux density, in particular in the rotor elements, are very similar for all solutions.

Kh

,

Kc

and

Ke

used in Equations (6)–(9) adopted for the calculations.Table 2 presents the basic properties of each analyzed material and the loss coefficientsandused in Equations (6)–(9) adopted for the calculations.

T

shaft and the shaft power

P

shaft are compared in accordance with Equations (11) and (12). The stator core losses Δ

P

Fes were calculated by FEMM using Equation (6). Mechanical losses Δ

P

mech were estimated on the basis of known bearing dimensions and rotational speed. Additional losses Δ

P

add were assumed as 1.5% of the electromagnetic power

P

Ψ. Stator winding losses Δ

P

Cu were calculated from the classical Joule loss equations. The efficiency of the motor was determined by Formula (14):

P shaft = P Ψ − Δ P Fes − Δ P T r − Δ P mech ,

(11)

T shaft = 30 π · n · P shaft ,

(12)

P in = P Ψ + Δ P Cu + Δ P add ,

(13)

η = P shaft P in ,  

(14)

The purpose of the FEM analysis is to identify and compare the operating parameters that are the most important from the point of view of the motor with high power density and the values of losses in the rotor elements. According to the guidelines described in [ 11 ], the values of the shaft torqueand the shaft powerare compared in accordance with Equations (11) and (12). The stator core losses Δwere calculated by FEMM using Equation (6). Mechanical losses Δwere estimated on the basis of known bearing dimensions and rotational speed. Additional losses Δwere assumed as 1.5% of the electromagnetic power. Stator winding losses Δwere calculated from the classical Joule loss equations. The efficiency of the motor was determined by Formula (14):

P Ψ —electromagnetic power,

Δ P Fes —power losses in laminated stator core,

Δ P mech —mechanical losses,

Δ P Cu —stator winding Joule losses,

Δ P add —additional losses,

P in —input power.

n

= 4800 rpm and for the nominal

J

= 15 A/mm2 and the maximum

J

= 30 A/mm2 current density in the stator winding. The power density factor

ξ

was calculated considering the differences in the densities of individual rotor materials and the need to use additional support elements for solutions with a laminated rotor core. Table 3 and Table 4 show the results of the FEM calculations for the analyzed variants, using different materials in the rotor yoke. The analysis was carried out for the nominal rotational speed= 4800 rpm and for the nominal= 15 A/mmand the maximum= 30 A/mmcurrent density in the stator winding. The power density factorwas calculated considering the differences in the densities of individual rotor materials and the need to use additional support elements for solutions with a laminated rotor core. Table 3 also shows the calculated value of the temperature of the permanent magnets as for the rated operating conditions.

Analyzing the results from Table 3 and Table 4 , we note that the change in the rotor yoke material has no significant effect on the main operating parameters of the motor. The differences in the obtained values of shaft torque and shaft power as well as in the efficiency are relatively small. The highest value of the shaft torque for the rated current was obtained for the Vacoflux48 core, which is 65 Nm, and the lowest for the solid core S355j2—63.3 Nm. The difference is less than 3%.

The SMC rotor has achieved particularly good results. However, it should also be taken into account that the mechanical properties of Somaloy 700 3p are much inferior to those of steel S355j2. After an additional strength analysis, it was decided that the use of the SMC rotor core, in this case, would be risky; therefore, the SMC rotor was not taken into account in the physical motor model.

J

= 15 A/mm2. In analyzing the results from

From the results presented in Table 3 and Table 4 , significant differences in the rotor core losses between the solid rotor core S355j2 steel and other solutions should be noticed. Both the use of the SMC core and the laminated cores allow for a drastic reduction of losses in the rotor yoke. Figure 4 shows a comparison of losses in the rotor yoke for the analyzed variants as a function of the frequency of the supply voltage for the rated current density in the winding= 15 A/mm. In analyzing the results from Figure 4 , it should be emphasized that the increased losses in the rotor yoke in the solid rotor core S355j2 do not disqualify this solution in the application in a high power density motor. The main decisive factor is the possibility and efficiency of discharging such a losses value, and thus the question of an efficient cooling system.

Another important issue that should be noticed when analyzing the results from Figure 4 is that for all other analyzed materials, except S355j2, the level of reduction of rotor losses in the whole range of supply frequencies is very similar. Therefore, the final selection should mainly take into account material costs and the necessary technological expenditure for the application of individual variants. It seems that among the analyzed solutions, the most advantageous in this respect is the use of classic M400-50A sheets.

PTr

as a function of the supply voltage frequency and the load current density for the solid rotor S355j2 solution. The calculated loss values do not consider the segmentation of the permanent magnets. Figure 5 a shows the dependence of the total rotor losses Δas a function of the supply voltage frequency and the load current density for the solid rotor S355j2 solution. The calculated loss values do not consider the segmentation of the permanent magnets. Figure 5 b shows the shaft power of the motor with a solid rotor core as a function of the supply frequency and the load current density in the stator winding. The rated operating point is marked with an opaque red color.2, is approximately 67 kW. For rated current density

J

= 15 A/mm2, the maximum possible motor shaft power is 39 kW.

When analyzing the results from Figure 5 b, it can be seen that the maximum shaft power of the motor, assuming a maximum power frequency of 1000 Hz and a maximum current density in the winding of 30 A/mm, is approximately 67 kW. For rated current density= 15 A/mm, the maximum possible motor shaft power is 39 kW.

P

shaft is very similar in the entire range of the supply frequency and the entire range of current loads (

J

= 15 A/mm2. For higher load values, the permissible temperatures in the stator winding were exceeded. Another factor that may limit the range of long-term operation is losses generated in the rotor. These losses cause deterioration of the operating parameters of the motor due to the increase in temperature of permanent magnets and thus their worse magnetic properties. Moreover, these losses may lead to demagnetization of the magnets in the event of exceeding the allowable temperatures.

For all analyzed variants, the value of the shaft poweris very similar in the entire range of the supply frequency and the entire range of current loads ( Table 3 and Table 4 ). From the point of view of a high power density motor, the basic question concerns the possible range of operation with continuous (long-term) power. From the conducted thermal simulations, the nominal current density was determined as= 15 A/mm. For higher load values, the permissible temperatures in the stator winding were exceeded. Another factor that may limit the range of long-term operation is losses generated in the rotor. These losses cause deterioration of the operating parameters of the motor due to the increase in temperature of permanent magnets and thus their worse magnetic properties. Moreover, these losses may lead to demagnetization of the magnets in the event of exceeding the allowable temperatures.

PTr

as a function of the supply frequency and the current load for all analyzed variants that are an alternative to the solid rotor core S355j2, for which the total rotor losses are presented in

PTr

for the rated current load is obtained at a supply frequency of 1000 Hz. In taking the above into account, it can be assumed that changing the solid rotor S355j2, e.g., to a laminated rotor M400 (due to the lowest material cost), will allow to increase the range of long-term operation to 1000 Hz, and thus increase the continuous power from 31.8 kW to 40 kW. Then the motor power density factor will increase from

ξ

= 3.06 kW/kg to

ξ

= 3.57 kW/kg. Figure 6 shows a comparison of the total rotor losses Δas a function of the supply frequency and the current load for all analyzed variants that are an alternative to the solid rotor core S355j2, for which the total rotor losses are presented in Figure 5 a. At the rated operating point, the value of the total rotor losses for the motor with a solid stator core is 1092 W. It can be seen that for the remaining solutions such value level of the total rotor losses Δfor the rated current load is obtained at a supply frequency of 1000 Hz. In taking the above into account, it can be assumed that changing the solid rotor S355j2, e.g., to a laminated rotor M400 (due to the lowest material cost), will allow to increase the range of long-term operation to 1000 Hz, and thus increase the continuous power from 31.8 kW to 40 kW. Then the motor power density factor will increase from= 3.06 kW/kg to= 3.57 kW/kg. Figure 7 shows the shaft power of the motor with the M400 rotor core as a function of the supply frequency and the load current density in the stator winding. The rated operating point is marked with an opaque green color.