2.1

Motor design procedure

Based on the high speed and high frequency operating characteristics of permanent magnet motors, this paper takes the design of an ultra-high-speed permanent magnet motor (maximum speed of 150,000 RPM) of an automotive ETC system as an example, adopts a combination of electromagnetic and structural analyses, starting from the design of the magnetic circuit of the motor, analysis of the strength of the rotor, and the motor temperature and loss. The design steps are shown in Figure 2.

Figure 2.

Flowchart of motor design procedure

2.1.4

Define the stator size and winding arrangement

As a key component of the motor, the design and arrangement of stator has a significant influence on the performance and operating characteristics of the motor. In this case, a fractional-slot concentrated winding arrangement is adopted to further reduce the torque ripple and losses. On the other hand, since the output torque of the motor is proportional to the axial length of the stator, thus, as soon as the parameters such as the winding arrangement, the number of turns, the number of conductors per slot are determined, a suitable active length can be defined based on the output characteristics of the motor.

If the motor efficiency η is set to 0.9, its three-phase power P_3∅ can be expressed as:

In the formula above, V₀ and i₀ represent the amplitude of the three-phase voltage and three-phase current of the motor respectively, and can be expressed as:

The back emf constant K_e of the motor can be expressed as:

Where, K_t is the torque constant of the motor, K_J represents the ratio of the torque to the current density, and A_w is the cross-sectional area of the copper wire.

Where, T_mot represents the output torque of the motor, and denotes the root mean square value of the current density as input to the motor.

In the formula above, K_cp is the slot filling factor of the motor, A_s represents the cross section area of the tooth slot of the motor, and N_t is the number of coil turns; the magnetic flux λ_p of the motor can be expressed by the product of the magnetic flux constant K_λ, the number of coil turns N_t, and the stator length l_m:

Therefore, all the relevant parameters such as the back emf constant, the torque constant, the inductance, and the magnetic flux, etc. can be obtained through the formulas above to satisfy the specification requirements of the designed motor.

2.2

Simulation results

According to the analysis above, the designed motor has a 2-pole/3-slot configuration with fractional-slot concentrated windings. (copper wire diameter of 0.5 mm, and the number of turns per coil is 40), and the main design parameters of the motor are listed in Table 2. The winding arrangement and the cloud diagram of flux density distribution of the motor are shown in Figure 3 and Figure 4, respectively.

Figure 3.

Winding arrangement

Figure 4.

FEM result of magnetic flux density

Table 2.

Design parameters of ultra-high-speed permanent magnet motor

3.1

Analysis of rotor structure and force

The motor rotor adopts a surface-mounted structure, the permanent magnets were divided into four arc segments to reduce the circumferential stress inside the magnets. The permanent magnet is made of N45SH high-temperature sintered neodymium-iron-boron (NdFeB) material, which shows a high compressive strength. However, its bending strength and tensile strength are relatively low [5]. In any case it is necessary to use a retainment sleeve to avoid the rupture of the magnets due to excessive centrifugal forces. When the material density and rotation speed are known, the centrifugal stress can be calculated.

3.2

Rotor sleeve design

For surface-mounted permanent magnet motors, two strategies are often used: one is to use high-strength composite materials, such as high-modulus carbon fiber; the other one is to use high-strength non-magnetic metals, such as nonmagnetic stainless steel or titanium alloys. A number of researches have been carried out on the material, thickness and interference of the sleeve [6]. Compared with non-magnetic stainless-steel materials, the use of high modulus carbon fiber can avoid the problem of demagnetization of permanent magnets, and theoretically, it allows to reach higher rotation speed without generating high-frequency eddy current losses, however, the shortcomings mainly lie in the high manufacturing cost, complicated installation and unfavorable to the heat dissipation of the permanent magnet rotor; the advantages of adopting non-magnetic stainless steel sleeve lie in the convenience of the installation process and the controllable value of interference, while the shortcomings are mainly due to its large mass and relatively large eddy current losses. Different material properties are shown in Table 3.

Table 3.

Material properties of the rotor sleeve

The sleeve is installed on the outer surface of the permanent magnet through interference fit. When the motor rotates at high speed, the radial compressive stress p on the contact surface between the sleeve and the permanent magnet counteracts the centrifugal stress 𝜎_c suffered by the permanent magnet.

In terms of thickness, if the thickness of sleeve is too thick, it will affect the electromagnetic characteristics of the motor; while a too thin sleeve cannot resist the centrifugal force during high-speed rotation, etc. Therefore, the mechanical analysis of the sleeve is carried out using the Thick-Wall cylinder model and Lame’s equation. At this time, the radial stress 𝜎_t applied to the sleeve can be expressed as:

Where, d is the nominal diameter of the interference fit, and h_t is the thickness of the sleeve.

Once the safety factor is defined based on the yield strength of the material, the radial stress 𝜎_t and the thickness of the sleeve h_t of the above-mentioned sleeve can be obtained accordingly.

3.3

FEM simulation results

In this case, a non-magnetic stainless steel (06Cr25Ni20) material is chosen to construct the rotor sleeve, which has a yield strength of 600 MPa and a tensile strength of 900-1150 MPa as shown in Table 3. From the analysis above, the thickness of the sleeve is obtained as 1.5 mm, and the interference between the permanent magnet and the sleeve is set to 20 μm. According to the symmetry of the rotor structure, the permanent magnet and the sleeve can be further simplified by establishing a 2D equivalent model in COMSOL Multiphysics, in addition, the two edges of the permanent magnet are set as free boundaries, the simulation is carried out under maximum speed condition, and the stress distribution simulation result of the sleeve is shown in Figure 5.

Figure 5.

Internal stress distribution

From the simulation result, it can be seen that when the thickness of the rotor sleeve is set to 1.5 mm and the interference is set to 20 μm, the maximum stress at maximum rotational speed is about 334 MPa, which is still smaller than the yield strength (600 MPa). Also there is no relative displacement in the radial direction between the sleeve and the permanent magnet as shown in Figure 6. Which means, the designed sleeve can guarantee the stability of the rotor structure of the motor under maximum speed.

Figure 6.

Relative displacement

4.1

Loss analysis

When the motor is running at high speed, the generated internal loss P will heat up the motor, increase the temperature:

Where, P_Copper denotes the copper loss in the windings, and the energy consumption generated in the wires due to the wire resistance can be further expressed as:

Where, R_ph is the phase resistance of the winding, and i₀ is the three-phase input current.

P_Iron in Equation (8) represents the iron loss of the stator, which consists of eddy current loss P_e, hysteresis loss P_h and stray loss P_a [7]:

Among them, the eddy current loss P_e is the loss generated by the induced current based on Faraday’s Law; the hysteresis loss P_h is the loss generated by the mutual friction of multiple magnetic domains inside the ferromagnetic material; and the anomalous loss P_a is the energy loss caused by the micro vortex currents generated within the walls of the magnetic domains. According to the material properties, when the three loss coefficients K_e, K_h and K_a of the material are determined, the corresponding losses can be calculated respectively.

P_PM in Eq. (8) denotes the eddy current loss of the permanent magnet, which is generated inside the permanent magnet due to the presence of a large number of harmonics in the input current of the motor, which also causes the temperature rise of the motor. The eddy current loss of the permanent magnet can be calculated by simulating with a single-turn coil in finite element simulation software.

In order to reduce the eddy current loss of the motor, the stator of the motor is made of non-oriented NO20 silicon steel with a thickness of 0.2 mm by using sheet stamping technique, the iron loss coefficients are shown in Table 4. At the same time, in order to describe the loss values precisely, the influence of temperature on the loss is also considered in the design process, and the error can be further reduced by introducing correction factors [8].

Table 4.

Iron loss coefficients

Based on the equations above, the copper loss, iron loss and eddy current loss of permanent magnets corresponding to the motor at different input currents and rotational speeds can be calculated respectively. When the input current of the motor is 20A, and the rotational speed is 150,000 RPM, the calculation results of the losses inside the motor are shown in Table 5, and the total loss density distribution of the motor stator is shown in Figure 7.

Figure 7.

Loss distribution of motor stator

Table 5.

Calculation results of motor internal losses (input current 20 A, speed 150,000 RPM)

From the results, it is shown that when the motor is running at high speed, the proportion of iron loss is about 62 % of the total loss, and more than 60 % of the iron loss comes from anomalous loss. The temperature rise of the stator is mainly concentrated in the tooth tip region. The variation of each loss inside the motor with rotational speed is shown in Figure 8. It can be seen that in the low rotational speed region, the loss of the motor is mainly due to copper loss, and with the increase of the speed, iron loss gradually dominates when the rotational speed exceeds 60000 RPM.

Figure 8.

Different losses variation with speed

4.2

Thermal analysis

In order to simplify the model, the influence of heat radiation is ignored in the thermal analysis of the motor, only the steady state heat dissipation of the motor under rated working condition is considered. In addition, a water jacket cooling system is also designed outside the motor, while for the internal part of the motor, only air cooling is considered. The cooling conditions of the motor are shown in Table 6.

Table 6.

Boundary conditions for water cooling of ultra-high speed permanent magnet motor

The loss data of the motor are imported into MotorCAD software as inputs, and the temperature of each part of the motor is obtained through simulation when the motor is running at different speeds. The maximum temperature of the motor winding under different working conditions are registered and shown in Table 7. From the results, it can be seen that the maximum temperature of the winding is about 155 ℃, and the heat is transferred from the winding to the stator, and then conducted along the radial direction and finally taken away by the cooling water. The temperature distribution inside the motor is shown in Figure 9 and Figure 10.

Figure 9.

Temperature distribution inside the motor

Figure 10.

Maximum winding temperature distribution

Table 7.

Temperature distribution of motor winding