The global push towards industrialization and electrification has brought the dual challenges of energy security and environmental pollution to the forefront. The electric vehicle car, with its efficient conversion of electrical energy into propulsion, stands as a strategic solution to this dilemma. Statistics from industry associations reveal that the market for new energy vehicles continues to expand rapidly, with production and sales volumes consistently breaking records, solidifying a leading global position for over a decade. At the heart of this transformation lies the electric drive motor, the core actuator responsible for electromechanical energy conversion. Within this motor, bearings are a critical component whose operational lifespan is intrinsically linked to the safe and reliable operation of the entire vehicle. Studies indicate that bearing-related faults can account for a significant percentage of motor failures in electric vehicle car applications. While faults stemming from mechanical issues like improper assembly or excessive load can often be mitigated through monitoring and maintenance, a more insidious threat exists: “bearing electrical erosion” induced by shaft currents.
These shaft currents are primarily excited by the common-mode voltage (CMV) generated by the pulse-width modulation (PWM) inverters that drive electric vehicle car motors. With the industry trend towards higher switching frequencies, higher DC-link voltages (such as 800V platforms), and increased power density in electric vehicle car powertrains, the problem of bearing currents is becoming increasingly severe. Elevated switching frequencies proportionally increase the rate of high-frequency voltage pulses, higher voltages amplify the induced shaft voltage, and greater power levels increase the energy available for discharge events. This synergistic effect accelerates bearing degradation through electrical discharge machining (EDM), leading to operational noise, reduced bearing life, and in severe cases, bearing seizure—posing significant risks to motor operation and driving safety in an electric vehicle car. Therefore, precise modeling of shaft currents is of paramount importance for enhancing the safety and reliability of electric vehicle cars, predicting the risk of bearing electrical erosion, and formulating effective mitigation strategies.
Shaft currents in inverter-fed motors are generally categorized by their conduction path: dv/dt currents, EDM discharge currents, circulating bearing currents, and rotor ground currents. The first two types originate from the capacitive coupling of the inverter’s CMV through the motor’s stray capacitances, inducing a high-frequency voltage between the rotor shaft and the stator frame (bearing voltage). When this voltage remains below the dielectric breakdown threshold of the bearing lubricant film, a displacement (dv/dt) current flows. If the threshold is exceeded, a spark discharge occurs, causing EDM. These are collectively termed capacitive bearing currents. In contrast, inductive circulating bearing currents are induced electromagnetically. The high-frequency common-mode current flowing in the stator laminations creates an alternating环形 magnetic flux. According to Faraday’s law, this flux induces a voltage along the shaft, driving a current that circulates through a loop comprising the shaft, bearings, and frame. In a typical electric vehicle car motor without specific countermeasures, both capacitive and inductive bearing currents can coexist.
Existing research offers various modeling approaches. For capacitive currents, models range from behavioral “black-box” models using resonant units to physics-based circuit models. While distributed parameter models offer high accuracy, their complexity limits practical use. Lumped parameter models remain prevalent due to their simplicity. For inductive circulating currents, models exist that consider only the inductive loop, joint models combining capacitive and inductive shaft voltages, and comprehensive lumped parameter models. However, these often have limitations: some use overly simplified lumped parameters for the capacitive common-mode path, failing to accurately represent high-frequency impedance; others may misinterpret the physical meaning of impedances in the inductive loop.
Addressing these gaps, this paper proposes a high-precision comprehensive modeling method for both capacitive and inductive bearing currents in electric vehicle car motors. The key improvements of the proposed model are: 1) The capacitive circuit accurately reflects the motor’s internal impedance across a broad frequency spectrum, enabling precise calculation of the common-mode current. 2) The inductive loop employs ladder equivalent circuits to represent the frequency-dependent surface impedance of the stator and rotor laminations, accurately simulating skin effect. 3) By properly interconnecting the capacitive and inductive loops, the model can simulate the combined effect of both CMV and the inductively generated shaft voltage on the total bearing current.
Proposed Comprehensive Bearing Current Model
The proposed comprehensive model integrates four subsystems: the inverter (source), the motor’s capacitive path, the inductive circulating path, and the bearing circuit. The inverter provides the CMV excitation, \( v_{com} \).
The capacitive circuit models the common-mode path from the stator windings to the frame and rotor. It accounts for the frequency-dependent behavior of parasitic capacitances (\( C_{wf1}, C_{wf2} \) winding-to-frame; \( C_{wr1}, C_{wr2} \) winding-to-rotor; \( C_{rf} \) rotor-to-frame) and their associated resistances (\( R_{wf1}, R_{wf2}, etc. \)). It also includes the common-mode inductance \( L_{CM} \), eddy current resistance \( R_e \), and lead inductance \( L_E \). This refined circuit offers a more accurate representation of motor impedance than simpler lumped models.
The bearing circuit models the three bearings (non-drive end, drive end, and gearbox end) with their lubricant film capacitance (\( C_{b}, C_{nb}, C_{b1} \)) and breakdown resistance (\( R_{b}, R_{nb}, R_{b1} \)), along with insulation layer capacitance \( C_{iso} \). Switches (\( S_1, S_2, S_3 \)) simulate the transition from capacitive to resistive state during oil film breakdown.
The inductive circuit models the path for circulating currents. Key elements include the rotor impedance \( Z_{r,b} \), the internal AC impedance of the stator laminations for bearing current flow \( Z_{Fe,b} \), and the equivalent common-mode impedance \( Z_c \) representing the voltage drop due to common-mode current in the laminations. The electromotive force \( v_c \) is related to the inductively generated shaft voltage \( v_{sh} \). A crucial innovation is the derivation of the relationship between these voltages based on electromagnetic theory:
$$ Z_g = \frac{V_{sh}}{I_{com}} = \frac{Z_c}{3} = \frac{Z_{Fe,b}}{2} $$
$$ V_{sh} = \frac{3}{2} V_c $$
where \( Z_g \) is the excitation impedance. This relationship, \( v_{sh} = (3/2) v_c \), serves as the essential link coupling the inductive loop to the capacitive circuit at the center of the rotor-to-frame capacitance \( C_{rf} \). The impedances \( Z_c \), \( Z_{Fe,b}/2 \), and \( Z_{r,b}/2 \) are all modeled using four-stage R-L ladder circuits to accurately capture their frequency-dependent behavior due to the skin effect in the laminations and rotor shaft.
Parameter Extraction and Model Validation
The model parameters were extracted for a 220kW asynchronous motor used in an electric vehicle car. Port impedance measurements (1 kHz – 10 MHz) were performed to determine the capacitive circuit parameters. The common-mode and differential-mode impedance characteristics were measured, and key frequency points were identified for parameter calculation.
For example, the total low-frequency winding-to-frame capacitance \( C_{wf} \) is calculated from the impedance at the point of near -90° phase angle:
$$ C_{wf} = C_{wf1} + C_{wf2} = \frac{1}{2\pi f_A |Z_A|} $$
where \( f_A \) and \( |Z_A| \) are the frequency and impedance magnitude at point A. The high-frequency branch capacitance \( C_{wf1} \) is found using the phase angle at a high-frequency point C:
$$ C_{wf1} = \frac{-\sin\theta_C}{\omega_C |Z_C|}, \quad C_{wf2} = C_{wf} – C_{wf1} $$
The lead inductance \( L_E \) and resistance \( R_{wf1} \) are solved using the measurements at a very high-frequency point D:
$$ L_E = \frac{|Z_D| \cos\theta_D}{\omega_D} – \frac{1}{\omega_D^2 C_{wf1}}, \quad R_{wf1} = |Z_D| \sin\theta_D $$
Other parameters like \( L_{CM} \), \( R_{wf2} \), and \( R_e \) are extracted similarly. The winding-to-rotor and rotor-to-frame capacitances are found via a short-circuit measurement technique. The final extracted parameters for the capacitive circuit are summarized below.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| \( C_{wf1} \) | 8.15 nF | \( R_{wf1} \) | 3.212 Ω |
| \( C_{wf2} \) | 3.35 nF | \( R_{wf2} \) | 18.89 Ω |
| \( C_{wr1} \) | 42.59 pF | \( C_{wr2} \) | 17.51 pF |
| \( C_{rf} \) | 0.807 nF | \( L_E \) | 0.46 μH |
| \( C_{iso} \) | 450 pF | \( R_e \) | 386 Ω |
| \( L_{CM} \) | 44.88 μH | k | 0.709 |
For the inductive circuit, the impedances \( Z_{Fe,b}/2 \), \( Z_c \), and \( Z_{r,b}/2 \) were determined by direct measurement on the stator core (with rotor removed) and the rotor shaft across multiple frequencies (e.g., 2.3 kHz, 23 kHz, 230 kHz, 2.3 MHz). The four-stage R-L ladder circuit parameters for each impedance were then extracted from these four frequency-point measurements using a systematic formula. The extracted parameters are shown in the following table.
| Impedance | Stage 1 | Stage 2 | Stage 3 | Stage 4 | ||||
|---|---|---|---|---|---|---|---|---|
| L (μH) | R (Ω) | L (μH) | R (Ω) | L (μH) | R (Ω) | L (μH) | R (Ω) | |
| \( Z_{Fe,b}/2 \) | 1.225 | 0.028 | 0.222 | 0.088 | 0.122 | 0.183 | 0.029 | 0.680 |
| \( Z_{c} \) | 0.827 | 0.019 | 0.153 | 0.058 | 0.082 | 0.122 | 0.019 | 0.452 |
| \( Z_{r,b}/2 \) | 0.755 | 0.024 | 0.129 | 0.040 | 0.057 | 0.095 | 0.100 | 0.254 |
The validation of the extracted parameters was performed by comparing the simulated port impedance of the capacitive circuit and the impedance-frequency curves of the ladder circuits against the measured data. The results showed excellent agreement across the entire frequency range, confirming the accuracy of the parameter extraction process for both the capacitive and inductive parts of the comprehensive electric vehicle car motor model.
Experimental Verification and Model Performance
The comprehensive model was implemented in MATLAB/Simulink and validated against experimental data from the 220kW electric vehicle car asynchronous motor test bench, driven by an 800V SiC inverter. Two key operational scenarios were tested.
Scenario 1: Purely Capacitive Bearing Current. All three bearings were insulated to block any circulating current path. The measured CMV was used as the input to the model. The simulated common-mode current \( i_{com} \) and non-drive end bearing voltage \( v_b \) were compared with measurements at various speeds. The waveforms showed high fidelity. The peak-to-peak values at different speeds are compared below, with the relative error \( \epsilon \) calculated as:
$$ \epsilon = \frac{|\text{Measured Value} – \text{Simulated Value}|}{\text{Measured Value}} \times 100\% $$
| Speed (rpm) | Quantity | Simulated | Measured | Error \( \epsilon \) % |
|---|---|---|---|---|
| 2000 | \( I_{com} \) (A) | 32.00 | 33.48 | 3.82 |
| \( V_b \) (V) | 29.00 | 28.07 | 3.31 | |
| \( I_{com} \) (A) | 28.39 | 29.46 | 3.63 | |
| \( V_b \) (V) | 36.18 | 35.39 | 2.23 | |
| 12000 | \( I_{com} \) (A) | 26.98 | 27.79 | 2.91 |
| \( V_b \) (V) | 39.67 | 38.45 | 3.17 |
Scenario 2: Combined Capacitive and Inductive Bearing Currents. To create a small circulating loop, the non-drive and drive-end bearings were made conductive (modeled with small resistances), while the gearbox-end bearing remained insulated (capacitive). The measured CMV was again used as the model input. The simulated common-mode current and the bearing currents at the drive end \( i_b \) and non-drive end \( i_{nb} \) were compared with test results. The simulated waveforms closely matched the measurements, showing equal magnitude and opposite phase for \( i_b \) and \( i_{nb} \), confirming a circulating path. The bearing current ratio (BCR), a key metric for erosion risk assessment in an electric vehicle car motor, is defined and compared:
$$ \text{BCR} = \frac{I_{CB}}{I_{CM}} $$
where \( I_{CB} \) is the bearing current and \( I_{CM} \) is the common-mode current.
| Speed (rpm) | Quantity | Simulated | Measured | Error \( \epsilon \) % |
|---|---|---|---|---|
| 2000 | \( I_{com} \) (A) | 29.01 | 28.10 | 3.24 |
| \( I_{b} \) (A) | 2.54 | 2.48 | 2.42 | |
| \( I_{nb} \) (A) | 2.85 | 2.78 | 2.52 | |
| BCR\(_b\) (%) | 8.76 | 8.83 | 0.79 | |
| BCR\(_{nb}\) (%) | 9.82 | 9.89 | 0.71 | |
| 6000 | \( I_{com} \) (A) | 27.38 | 26.40 | 3.72 |
| \( I_{b} \) (A) | 2.19 | 2.11 | 3.79 | |
| \( I_{nb} \) (A) | 2.21 | 2.20 | 0.50 | |
| BCR\(_b\) (%) | 7.80 | 7.99 | 2.38 | |
| BCR\(_{nb}\) (%) | 8.07 | 8.31 | 2.89 | |
| 12000 | \( I_{com} \) (A) | 27.31 | 28.18 | 3.09 |
| \( I_{b} \) (A) | 2.38 | 2.47 | 3.64 | |
| \( I_{nb} \) (A) | 2.29 | 2.38 | 3.74 | |
| BCR\(_b\) (%) | 8.72 | 8.77 | 0.57 | |
| BCR\(_{nb}\) (%) | 8.39 | 8.45 | 0.67 |
Conclusion
This paper presents a high-precision comprehensive modeling method for capacitive and inductive bearing currents in electric vehicle car motors. The proposed model corrects misconceptions in existing models and achieves significantly higher accuracy. The key findings are:
1. The capacitive circuit of the model, with parameters extracted from port impedance measurements, accurately simulates the motor’s internal impedance characteristics across all relevant frequency bands. This is crucial for correctly predicting the common-mode current, which is the driver for both types of bearing currents.
2. The inductive loop employs R-L ladder circuits to model the frequency-dependent impedance of stator laminations and the rotor shaft, effectively capturing skin effect phenomena over a wide frequency range.
3. The model successfully interconnects the capacitive and inductive circuits based on derived electromagnetic relationships, enabling accurate simulation under the combined excitation of common-mode voltage and inductively generated shaft voltage.
4. Experimental validation on a 220kW electric vehicle car asynchronous motor demonstrates the model’s effectiveness. Under conditions with only capacitive currents and with both capacitive and inductive currents present, the simulation error for key quantities like common-mode current, bearing voltage, and bearing current is consistently below 4% across a wide speed range.
This comprehensive model provides a powerful tool for analyzing bearing electrical erosion risks in electric vehicle car drive systems. It can be used to predict bearing currents under various operating conditions and to evaluate the effectiveness of different mitigation strategies (e.g., insulated bearings, conductive rings) during the design phase, thereby enhancing the reliability and safety of electric vehicle car powertrains.