The usage of the interior permanent magnet (IPM)-type brushless DC motors (BLDCMs) is increasing in industrial applications and electrical machines because of its high power density and efficiency . In these systems, shaft voltage has become a serious problem owing to occurrence of bearing current, which reduces the lifetime and reliability of the motor. If shaft voltage is constantly maintained for a long time, it eventually leads to breakdown of the motor.
There are four generation causes of shaft voltage in a motor: electrostatic shaft voltage, magnetic unbalanced shaft voltage, electromagnetic shaft voltage and shaft voltage from the external power supply. Among these four generation causes, shaft voltage for electromagnetic reason and external power-supply is the primary causes of shaft voltage. In case of the electromagnetic reason, magnetic unbalanced is primary reason for shaft voltage generation. It is usually caused by modification of the stator core and eccentricity between the stator and rotor. On the other hand, shaft voltage by the external power supply is caused by the common mode voltage, which is due to a parasitic component and leakage flux from the high input voltage and high frequency of the inverter [2, 3].
In addition, when the rotor is rotating under non-inverter-driven condition, linkage flux is induced at the shaft by main magnetic flux of PM. For this reason, shaft voltage is induced by the linkage flux between main magnetic flux and shaft. We named it inherent shaft voltage because it depends on the rotor configuration. In particular, high voltage IPM-type BLDCM using neodymium PM should be considered the effect on inherent shaft voltage to prevent the reduction of their lifetime.
In the previous, many studies on insulated bearings, shaft grounding rings, grounding brushes, Faraday shields, conductive grease, insulated rotors and etc. have been conducted to suppress the shaft voltage [2, 3]. Although there are many ways to suppress the shaft voltage, they cannot be used in special circumstances. For example, a motor using the fragile insulating material cannot withstand in high-temperature and in the deep sea conditions because of high hydraulic pressure. Thus, the study for robust design method against high-temperature and hydraulic pressure should be conducted.
In this study, we proposed method for suppressing shaft voltage, which is robust in high-temperature and hydraulic pressure conditions through the design of flux-path. In order to change the flux-path, we modified the magnet-type from parallel magnet-type to V-shape magnet-type. In addition, we inserted barriers surrounding shaft to reduce the flux flow through the shaft. Based on this method, we optimized IPM-type high-voltage BLDCM within a range to maintain output torque of initial motor. Consequently, we validated shaft voltage suppression in IPM-type high-voltage motors through simulation and experiment.
2. Occurrences of Inherent Shaft Voltage
Fig. 1 shows the flux lines for parallel-shape and V-shape IPM-type BLDCMs under non-inverter-driven condition. The flux lines of both motors are flow through the shaft. For these flux components, linkage flux between the main magnetic flux and shaft is generated, and therefore shaft voltage is induced. We named it inherent shaft voltage.
Fig. 1.Flux lines for IPM-type BLDCMs
Inherent shaft voltage depends on the rotor configuration because influence of inherent shaft voltage is decided according to geometry and arrangement of the rotor and PM, respectively. In addition, inherent shaft voltage affects and reflects on the extrinsic shaft voltage under inverter-driven condition. Therefore, design for preventing the inherent shaft voltage should be taken into account in order to improve the lifetime and durability of the PM motors.
3. Occurrences of Extrinsic Shaft Voltage
3.1 Electrostatic shaft voltage
Static electricity by the friction in the motor-driven systems includes electrostatic capacity. Thus, it leads to occurrence of an electrostatic shaft voltage. In addition, the electrostatic shaft voltage in motor driven-system work as a direct current component, and it mostly occurs in the drive belts connected between the motor and loads.
3.2 Magnetic unbalanced shaft voltage
Magnetic unbalanced shaft voltage is induced by structure, material, and deviation of the motors. For example, the commissure of the segmented stator core, the segment-contact of the core, transformation of the stator core and the eccentricity between the rotor and stator are cause of the magnetic unbalanced shaft voltage. Thus, the linkage magnetic flux of the shaft occurred by magnetic unbalances.
3.3 Shaft voltage from the external power supply
High frequency and leakage current from external power supply generates the common mode voltage. It not only occurs between the inverter and motor but also lead to generation of the shaft voltage. Therefore, the common mode voltage by external power supply has become a serious problem.
3.4 Electromagnetic shaft voltage
Electromagnetic shaft voltage under inverter-driven condition occurs by the magnetic field that rotates with the shaft, the stationary magnetic field in the casing, combination with the magnetic field of the rotor and stator, and the residual magnetism of components. The magnetic-induced voltage causes vibration and instability of the rotated axis.
4. Calculation of the Inherent and Extrinsic Shaft Voltage
4.1 Calculation of the inherent shaft voltage
Inherent shaft voltage can be calculated by the Faraday’s law as (1) because it is induced by linkage flux between the main magnetic flux and shaft.
where eshaft is the inherent shaft voltage, and λshaft is the linkage flux between the main magnetic flux and the shaft.
The linkage flux between the shaft and main magnetic flux can be expressed as
where N is the number of windings, φshaft is the magnetic flux at the shaft, Bshaft is the magnetic flux density at the shaft, and Ashaft is the cross-sectional area of the shaft.
Therefore, the inherent shaft voltage can be rewritten as
Here, N is indicated the shaft and assumed parallel single coil because the shaft has only on path and is not winded.
4.2 Calculation of the extrinsic shaft voltage
When the motor is operating, the parasitic component and leakage flux occur chiefly because of the high input voltage and the high frequency of the inverter. In order to calculate extrinsic shaft voltage, first, the parasitic component should be calculated. A detailed mathematical analysis will be carried out to determine the effects on these parameters of the motor shaft voltage. Fig. 2 (a) shows the structure of a high-voltage motor. Fig. 2 (b) shows the equivalent circuit including the common mode voltage for calculating shaft voltage [4-7].
Fig. 2.Schematics of an IPM-type high voltage motor.
4.2.1 Composite capacitance between the winding and the stator core (Cs)
There are 4 surfaces which surround the winding in the slot. The Cs can be calculated as
where, Ns is the number of slots, wd is the slot width, wf is the slot height, Ls is the stator length, gin is the insulation thickness and εrc is the dielectric constant of the coil.
4.2.2 Composite capacitance between the winding and the rotor (Cr)
By considering the air-gap to be much smaller than the outer diameter of the rotor, a capacitance coupling between rotor and stator frame in stator slot can be calculated as (5), and slot design factors are shown in Fig. 3 (a).
Fig. 3.Parameters of an IPM-type motor.
4.2.3 Electrostatic capacity between the stator core and the rotor core (Cg)
Electrostatic capacitance of the stator and the rotor surface were measured. Cg can be calculated as follows
where, Lr is the rotor length, a is the radius of the rotor, and b is the radius of the inside stator.
4.2.4 Magnet capacitance (Cmg)
The magnet capacitance between the rotor surface and the shaft (Cmg) can be calculated as
where, Nm is the number of magnets, wm is the magnet width and dm is the distance between the magnet and the shaft.
4.2.5 Ball bearing capacitance (CB)
The ball bearing capacitance is calculated as (8), and ball bearing factors are shown in Fig. 3 (b).
where, Lb is the roller length of the bearing, k is the inner radius of the bearing outer race, m is the outer radius of the bearing inner race, j is the ball radius of the bearing and εrb is the dielectric constant of the coil.
4.2.6 Extrinsic shaft voltage by common mode voltage
Eq. (9) shows the shaft voltage of the motor. Eq. (10) is another form of Eq. (9). Eq. (11) shows common mode voltage, which is obtained by adding the three voltages from the three inverter legs.
5. Design of Proposed Model
Numerous papers have been published by both motor manufacturers and drive manufacturers in the last several years that attempt to understand the causes of shaft voltage in motors and to find a solution to eliminate electrical bearing damage. The bearing can be protected from shaft voltage in the following ways: insulated bearings, shaft grounding rings, grounding brushes, Faraday shield, conductive grease, and insulated rotors. There are many methods of suppressing shaft voltage, but some of these cannot be used in special circumstances. For example, fragile insulating materials cannot be used at extreme temperature because they are easily broken or melted. In addition, the vessel cannot be earthed. In such cases, there is no option to suppress shaft voltage by modifying the magnetic and electric circuits [2-4].
Therefore, we re-designed magnetic circuit of the motor and used an optimization technique to suppress shaft voltage. Fig. 4 shows the design variable applied in the optimization. From (4)-(11), these design variables mainly affect shaft voltage as shown (12) and (13). Figs. 5, 6, and 7 show the design results for the position and thickness of the magnetic flux barrier and the arc radius, respectively. The average torque of the applied model has almost the same value. As shown in Fig. 5, for 4.3 mm, we get the lowest value of the magnetic flux density on the shaft. However, when the motor rotates in the case of 4.3 mm, the rotor core can get ruptured because the thickness between the barrier and the shaft is thin. Therefore, 5.3 mm is the optimal result. As shown in Fig. 6, for 1 mm, we get the lowest value of the magnetic flux density on the shaft. For 26 mm, we can get the lowest value of the magnetic flux density on the shaft as shown in Fig. 7. In addition, the arc shape is modified to reduce the cogging torque. Table I shows the final optimized results for the proposed motor. We did not change the size of the magnet [8-11].
Fig. 4.Structure of the design variables
Fig. 5.The optimization results for flux barrier position
Fig. 6.The optimization results for flux barrier thickness.
Fig. 7.The optimization results for arc size.
Table 1.Final optimized results
Fig. 8 shows the initial motor and the proposed motors. In the case of the proposed motors, shaft voltage is suppressed by increasing the Cmg value and reducing the Cr value. When Cmg, increases, the distance between the magnet and the shaft (dm) decreases. When the Cr decreases, the air-gap length of the arc part (g1) is increases. So, shaft voltage is suppressed by decreasing the linkage magnetic flux on the shaft.
Fig. 8.The initial motor and the proposed motors
Fig. 9 shows the torque characteristics for each motor type. The average torques for each motor is almost same because we focused on motor design which can maintain output characteristics when we applied V-shape magnet and flux barriers. Fig. 10 shows the manufactured models.
Fig. 9.Torque characteristics for each motor type
Fig. 10.The proposed rotors
6. Analysis and Results
Figs. 10(a), (b), and (c) show the experimental results for the shaft voltage of the initial and the proposed motors. Fig. 10(d) shows the simulation results for the total magnetic flux density of the shaft. The shaft voltage of the proposed motors is lower than the shaft voltage of initial model.
The permissible range of the shaft voltage of the ball bearing is 2 V. Therefore, the V-shaped and flux barrier motors can be prevented bearing fault. Fig. 11(a) shows the cogging torques. The shaft voltages of the proposed models are lower than for the initial motor. The reduced cogging torque can be checked by an applied arc in the rotor. Fig. 11(b) shows the commutation torques. The ripple of the commutation torque is reduced by the arc-shaped rotor and V-shaped magnet. The simulation results for the shaft voltage are without the bearing.
Fig. 11.The experimental result of shaft voltage and the magnetic flux
Fig. 12.The commutation torque and the cogging torque
In this study, in order to detail analysis of the shaft voltage, we divided the shaft voltage into two types of shaft voltages such as inherent and extrinsic shaft voltage. First, inherent shaft voltage depends on rotor configuration because it is induced by linkage flux between main magnetic flux and shaft. Thus, it should be considered when design the motor. In addition, it was calculated by Faraday’s law. On the other hand, extrinsic shaft voltage is induced by several external factors such as electrostatic, unbalanced magnetic field, external power supply and electromagnetic factors. All of occurrences of shaft voltage could lead to bearing fault, and then the industrial production will be stopped.
Therefore, we proposed method for suppressing shaft voltage through an improved PM shape from the parallel-shape PM to V-shape PM and inserting barriers surrounding shaft.