Introduction When a motor is driven by a sinusoidal power supply, a shaft voltage is generated through the alternating magnetic flux of the motor shaft. These magnetic fluxes are generated by the magnetic flux imbalance caused by factors such as the connection between the rotor and stator slots, the connection between the separated iron core plates, the directional properties of the magnetic material, and the imbalance of the power supply [1]. In the 1990s, when PWM inverters with IGBTs as power devices were used as the motor drive power supply, the problem of motor shaft current became more serious, and its generation mechanism was completely different from that of sinusoidal power supply drive. IGBT inverters with high carrier frequencies (e.g., above 10kHz) cause the motor bearings to be damaged faster than those driven by inverters with low carrier frequencies. Busse analyzed the generation of bearing current and the relationship between bearing current density and bearing damage in more detail, and established a bearing current circuit model under PWM drive, but the model failed to reflect the relationship between bearing current and inverter switching frequency. In order to discuss the generation mechanism of motor shaft voltage and shaft current when driven by high frequency PWM pulse voltage, this paper analyzes the conditions and forms of shaft current generation based on the establishment of shaft voltage and shaft current circuit model, and obtains the shaft voltage and bearing current waveforms under different conditions through simulation analysis based on the characteristic changes of inverter output voltage and whether there is overvoltage at the motor end. In terms of suppressing bearing current, the method given in reference [1] is to use a sine wave filter to convert PWM voltage into sine wave voltage so that the motor works in the sine wave power supply state. However, the inductor in this method is large, the dynamic response of the system is slow, and the voltage drop and power consumption on the inductor are increased. In this paper, a small inductor is connected in series at the inverter output end and supplemented with an RC absorption network, which can effectively suppress the shaft current that appears under PWM inverter drive. Common mode voltage and shaft voltage It is generally believed that magnetic circuit imbalance, unipolar effect and capacitor current are the main causes of shaft voltage in motor [3]. In ordinary motors powered by the grid, people generally pay more attention to the influence of magnetic circuit imbalance. However, in motors powered by inverter, shaft voltage is mainly generated by voltage imbalance, that is, the zero-sequence component of power supply voltage. Due to the imbalance of circuit, components, connections, and loop impedance, the power supply voltage will inevitably experience zero-point drift, which will generate zero-sequence current in the system. The bearing is part of the motor's zero-sequence loop. When driven by a sinusoidal power supply, it can be calculated that = 0. Under PWM inverter drive, the value of depends on the inverter switching state, and the change period is consistent with the inverter carrier frequency. In fact, is just a manifestation of common-mode voltage. Due to electrostatic coupling, there are distributed capacitances of varying sizes between different parts of the motor, thus forming the motor's zero-sequence loop. According to transmission line theory, a distributed parameter circuit can be replaced by an equivalent lumped parameter π network model with the same input-output relationship. Therefore, the distributed parameter circuit of the motor can be equivalently represented by a lumped parameter circuit, forming the winding-rotor coupled part circuit of the shaft voltage as shown in Figure 2a), where Vbrg is the shaft voltage, Ibrg is the bearing current, and Va, Vb, and Vc are the motor input voltages. Although Iws does not flow through the bearing, it has the same path as the bearing current in the stator winding, which will inevitably affect the bearing current. For ease of analysis, the coupling from the winding center point to the stator will not be considered. For calculation convenience, Figure 2 a) is simplified to the equivalent single-phase drive circuit model shown in Figure 2 b). In the figure, Z1 is the power supply neutral point to ground impedance, Z2 is the bypass impedance, representing the common-mode reactance coil, line reactor, and long cable in the drive circuit; R0 and L0 are the zero-sequence resistance and inductance of the stator; Csf, Csr, and Crf are the stator-to-ground, stator-to-rotor, and rotor-to-ground capacitances, respectively; Rb is the bearing circuit resistance; Cb and R1 are the capacitance and nonlinear impedance of the bearing oil film; Usg and Urg are the stator winding and rotor neutral point to ground voltages, respectively. For motors powered by inverters, when the bearing oil film is not broken down, the capacitive reactance of the capacitor is greatly reduced due to the high carrier frequency. Compared with Xcb, Rb is very small while R1 is very large. Since the PWM drive voltage is a non-sinusoidal voltage, it is first decomposed during calculation, and then the shaft voltage is calculated separately. The bearing model and the generation of bearing current are due to the presence of distributed capacitance and the excitation effect of high-frequency pulse input voltage, resulting in a coupled common-mode voltage on the motor shaft. In fact, the occurrence of shaft voltage is not only related to the above two factors, but also directly related to the bearing structure. The front and rear ends of the rotor are supported by a bearing. Taking one bearing as an example, the bearing raceway consists of an inner raceway and an outer raceway. When the motor rotates, the balls in the bearing are surrounded by a layer of lubricating oil. Due to the insulating effect of the lubricating oil, a capacitance is formed between the bearing raceway and the balls. These two capacitances exist in series in the rotor-stator circuit (for ease of analysis, the impedance of the balls is not considered), and can be equivalent to a capacitor Cbi, where i represents the i-th ball in the bearing. For the entire bearing, the capacitances between each ball and the raceway exist in parallel. Therefore, the entire bearing can be equivalent to a capacitor Cb. Based on the analysis of the bearing, it can be equivalently represented by a switch with internal inductance and resistance. When the balls are not in contact with the raceway, the switch is open, and the rotor voltage is established. When the rotor voltage exceeds the oil film threshold voltage, the oil film breakdown switch is activated, and the rotor voltage rapidly discharges internally, forming a large discharge current within the bearing. Vb and Vc are the three-phase input voltages of the motor, L', R', and C' are the equivalent lumped parameters of the input voltage coupled to the rotor shaft, and Cg is the equivalent capacitance after Crf and Cb are connected in parallel. When the bearing balls are in contact with the raceway or the oil layer inside the bearing is broken down, Cb does not exist; in this case, Cg only represents the coupling capacitance of the rotor shaft to the housing. The capacitance Cb is a function of multiple variables: Cb(Q, v, T, η, λ, Λ, εr). Where Q represents power, v represents the oil film movement speed, T represents temperature, η represents lubricant viscosity, λ represents lubricant additives, Λ represents oil layer thickness, and εr represents the lubricant dielectric constant. The bearing capacitance Cb and the stator-to-rotor coupling capacitance Csr are much smaller than the stator-to-casing coupling capacitance Csf and the rotor-to-casing coupling capacitance Crf. This prevents the voltage coupled to the motor bearing from becoming excessive, because the capacitance of Crf and Cb in parallel is much larger than that of Csr connected in series in the coupling circuit. In a series capacitor circuit, a larger capacitance results in a smaller voltage across the load. In fact, due to the characteristics of distributed capacitance, a large portion of the common-mode current is transmitted to ground through the coupling capacitance Csf between the stator winding and the core; therefore, the bearing current is only a part of the common-mode current. Figure 4 shows that there are two basic pathways for the formation of the bearing current. First, due to the presence of distributed capacitance, the stator winding and the bearing form a voltage coupling circuit. When the winding input voltage is a high-frequency PWM pulse voltage, a dv/dt current will inevitably be generated in this coupling circuit. Part of this current is transmitted to ground through Crf, and the other part is transmitted to ground through the bearing capacitance Cb, forming the so-called dv/dt bearing current. Its magnitude depends on the input voltage and the distributed parameters within the motor. Secondly, due to the presence of bearing capacitance, a shaft voltage is generated on the motor shaft. When the shaft voltage exceeds the breakdown voltage of the bearing oil layer, the inner and outer raceways of the bearing are equivalent to a short circuit, thus forming a large discharge current on the bearing, which is the so-called electric discharge machining (EDM) current. In addition, when the motor is rotating, if there is contact between the balls and the raceways, a large EDM current will also be generated on the bearing. In order to quantify the influence of EDM and dv/dt current on the bearing, the current density inside the bearing is crucial. To establish the current density, it is necessary to estimate the point contact area between the balls and the inner surface of the raceways. According to Hertzian point contact theory, the bearing electrical life can be obtained by the following formula: (hrs) = (7) where represents the bearing current density. Generally speaking, the dv/dt current has little effect on the bearing life, while the bearing current density generated by EDM is very large, which greatly reduces the bearing life. In addition, the bearing damage is much greater when unloaded than when heavily loaded, because the bearing contact area increases under heavy load, which reduces the bearing current density. To further discuss the relationship between bearing current and the output voltage characteristics of the PWM inverter, as well as the presence of overvoltage at the motor terminals, this paper conducts simulation analyses of bearing current in two forms: dv/dt current and EDM current. The results show that the bearing current is related not only to the inverter carrier frequency but also to the rise time of the inverter output pulse voltage. Furthermore, the bearing current increases significantly when overvoltage occurs at the motor terminals. Assuming zero cable length, based on the form of bearing current, the dv/dt current is mainly caused by the input voltage jump, therefore its magnitude is related to the inverter carrier frequency and voltage rise time. A higher inverter carrier frequency results in a greater amount of dv/dt current generated within one sine wave cycle, but the current amplitude remains unchanged. The pulse voltage rise time is the decisive factor affecting the dv/dt current amplitude; additionally, the size of the distributed capacitance also affects the dv/dt current amplitude. The direct cause of EDM current is the presence of shaft voltage; therefore, the magnitude of the shaft voltage determines the EDM current amplitude, which in turn depends on the input voltage and the size of the distributed capacitance within the motor. Although the inverter carrier frequency and pulse voltage rise time both affect the shape of the shaft voltage, the peak value of the shaft voltage is unrelated to either. Therefore, the EDM current is not fundamentally related to either, which is the biggest difference between the EDM current and the dv/dt current. Of course, the EDM current is also related to the breakdown voltage of the bearing oil layer; the higher the breakdown voltage, the larger the generated EDM current. For ease of discussion, we assume that the bearing breakdown voltage is greater than or equal to the shaft voltage. Simulations with varying rise times yielded shaft voltage and bearing current waveforms as shown in Figure 5, where Figures a) and b) are shaft voltage waveforms, and Figures c) and d) are bearing current waveforms. The first oscillation in the current waveform represents the EDM current, and the others represent the dv/dt current. Analysis shows that: 1) Increasing tr decreases the bearing current, including both the dv/dt current and the EDM current. In particular, the amplitude of the dv/dt current decreases significantly, but the tr has little effect on the EDM current. This is mainly because the EDM current is determined by the shaft voltage and bearing impedance. 2) When tr is less than a certain value (approximately 200ns), the dv/dt current is even higher than the EDM current. 3) Changing the rise time has little effect on the shaft voltage. 4) Special phenomenon: The shaft voltage oscillates twice during voltage breakdown. tr does not affect the first oscillation but does affect the second oscillation, and the second oscillation decreases as tr increases. This is because the coupling path from the stator winding to the rotor still exists after the bearing short circuit, resulting in a dv/dt current oscillation. Changing the coupling parameters and bearing parameters: The larger the coupling capacitance of the stator winding to the rotor, the higher the shaft voltage, and both the dv/dt current and the EDM current increase. Decreasing the bearing capacitance decreases the dv/dt current; however, the EDM current remains basically unchanged, and the shaft voltage increases. The reason is that in a common-mode circuit, the shaft voltage is caused by the voltage coupling of the stator winding to the rotor core, and the existence of this voltage is maintained by the bearing capacitance and the coupling capacitance of the rotor to the casing. Since the latter two are connected in parallel and then in series with the former, the shaft voltage is distributed according to the capacitance value; the larger the capacitance, the smaller the voltage drop. Generally, the bearing capacitance and rotor-to-casing coupling capacitance are much larger than the stator winding-to-rotor coupling capacitance. When only the bearing capacitance is changed, the smaller the bearing capacitance, the lower the equivalent value of the entire parallel capacitance, and the shaft voltage actually increases. Since the dv/dt current on the bearing is proportional to the capacitive reactance and dv/dt, when dv/dt remains constant, the capacitive reactance decreases, and the dv/dt current decreases. The simulation results are shown in Figure 6. Csr is the stator winding-to-rotor coupling capacitance, and Cg is the parallel equivalent capacitance of the rotor-to-casing coupling capacitance Crf and the bearing capacitance Cb. Suppression Methods: From the previous theoretical research and simulation analysis, it can be seen that a major cause of motor bearing current is the excessively high dv/dt leading and trailing edges of the high-frequency pulses output by the inverter. Therefore, an effective way to suppress bearing current is to reduce the dv/dt of the inverter output voltage. However, the rise time of the inverter's output pulse voltage is determined by the switching characteristics of the power devices. Therefore, the only way to change the dv/dt of the output voltage is to add a device to the inverter output terminal. One of the most direct ways to reduce the rise time dv/dt of the inverter output voltage is to connect a large reactor in series at the inverter output terminal, thus forming a so-called "sine wave filter." The pulse voltage output by the inverter becomes a completely sinusoidal voltage after passing through the large reactor, thereby eliminating shaft voltage and bearing current. However, this method comes at the cost of high power loss, large size, and high cost of the reactor, making it unsuitable for ordinary variable frequency speed control systems. This paper adopts a compromise approach: connecting an inductor with a small inductance value in series at the inverter output terminal to suppress rapid current changes, and simultaneously setting an RC reactor between the output lines to absorb high-order harmonics of the output voltage. This appropriately reduces the dv/dt value of the output pulse voltage rise time, achieving the purpose of suppressing bearing current. The inverter output filter reduces the voltage rise rate of the motor input pulse voltage. This significantly weakens the voltage coupling effect of the distributed capacitors within the motor, leading to a decrease in shaft voltage and the resulting EDM current. Simultaneously, the dv/dt current caused by the voltage change rate is also significantly reduced. Therefore, the filter effectively suppresses bearing current. Figure 8 shows the simulated waveforms of the motor bearing current before and after adding the filter (ungrounded). The inverter carrier frequency is 5kHz, the pulse voltage rise time is 200ns, and the cable length is 100m. The figure shows a significant reduction in both EDM current and dv/dt current. The simulation also revealed that grounding the filter significantly reduces both dv/dt current and EDM current compared to ungrounded operation. This is because the RC branch has a stronger absorption effect on higher harmonics, better improving the voltage waveform. Conclusion Under high-frequency PWM pulse input, the voltage coupling effect of the distributed capacitors within the motor forms a common-mode loop, causing shaft voltage and bearing current issues. Bearing current exists primarily in three forms: dv/dt current, EDM current, and loop current. The magnitude of shaft voltage depends not only on the coupling capacitance parameters of various parts within the motor but also on the rise time and amplitude of the pulse voltage. This paper focuses on the bearing current in the first two scenarios. The dv/dt current is mainly related to the rise time tr of the PWM; the smaller tr is, the larger the amplitude of the dv/dt current. The higher the inverter carrier frequency, the more dv/dt current component appears in the bearing current. The occurrence of EDM current is somewhat random, only appearing when the bearing lubricating oil layer is broken down or internal contact occurs in the bearing; its amplitude mainly depends on the magnitude of the shaft voltage. Based on the principle of reducing the pulse voltage rise rate, a method is designed to suppress shaft voltage and bearing current by connecting a small inductor in series at the inverter output and supplementing it with an RC absorption network. Simulation results verify the effectiveness of this method.