1 Introduction

When the motor is driven by a sine wave power source, the shaft voltage is generated through the alternating magnetic flux of the motor shaft. These magnetic links are caused by factors such as the connection between the rotor and stator slots, the separation of iron core plates, the directional properties of magnetic materials, and the imbalance of the power supply, resulting in magnetic flux imbalance [1]. In the 1990s, when PWM inverters using IGBT as power devices were used as motor driving power sources, the problem of motor shaft current became more severe, and its generation mechanism was completely different from that of sine wave power sources. Reference [1] indicates that IGBT inverters with high carrier frequencies (such as 10kHz or above) cause faster damage to the bearings of the motor compared to inverters with low carrier frequencies. Busse analyzed in detail the generation of bearing current and the relationship between bearing current density and bearing damage [2], and established a bearing current circuit model under PWM drive. However, this model did not reflect the relationship between bearing current and inverter switching frequency. To discuss the generation mechanism of motor shaft voltage and shaft current when driven by high-frequency PWM pulse voltage, this article establishes a circuit model of shaft voltage and shaft current, analyzes the conditions and forms of shaft current generation, and obtains the waveform of shaft voltage and bearing current under different conditions through simulation analysis based on the characteristic changes of inverter output voltage and the presence or absence of overvoltage at the motor end.

In terms of suppressing bearing current, the method given in reference [1] uses a sine wave filter to convert PWM voltage into sine wave voltage, so that the motor operates in a sine wave power supply state. However, this method involves a large series inductance, slow system dynamic response, and an increase in voltage drop and power consumption on the inductance. This article effectively suppresses the shaft current caused by PWM inverter driving by serializing small inductors at the output end of the inverter and supplementing it with an RC absorption network.

2 Common mode voltage and shaft voltage

It is generally believed that unbalanced magnetic circuits, unipolar effects, and capacitive currents are the main causes of shaft voltage generation in motors [3]. In ordinary motors powered by the power grid, people generally attach great importance to the impact of magnetic circuit imbalance. However, in inverter-powered motors, the shaft voltage is mainly generated by voltage imbalance, which is the zero sequence component of the power supply voltage. Due to the imbalance of circuits, components, connections, and loop impedance, the power supply voltage will inevitably generate zero drift, which will generate zero sequence current in the system, and bearings are a part of the motor zero sequence circuit.

When driven by a sine wave power supply, it can be calculated that=0. Under the PWM inverter drive, the value of depends on the inverter switch state, and the change period is consistent with the inverter carrier frequency. In fact, it is only a manifestation of common mode voltage. Due to electrostatic coupling, there are distributed capacitors of varying sizes between various parts of the motor, thus forming the zero sequence circuit of the motor. 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 motor distributed parameter circuit can be equivalent to a lumped parameter circuit, forming the winding rotor coupling part of the shaft voltage circuit as shown in Figure 2a), where Vbrg is the shaft voltage, Ibrg is the bearing current, Va, Vb, and Vc are the motor input voltage. Although Iws does not flow through the bearings, it has the same path as the zirconia ceramic ball bearing current on the stator winding, which inevitably affects the bearing current. For the convenience of analysis, the coupling part from the center point of the winding to the stator will not be considered. For the convenience of calculation, Figure 2a) is simplified to the equivalent single-phase driving circuit model shown in Figure 2b). In the figure, Z1 represents the midpoint to ground impedance of the power supply, while Z2 represents 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 capacitance of the motor stator to ground, stator to rotor, and rotor to ground, respectively; Rb is the resistance of the bearing circuit; 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, due to the high carrier frequency, the capacitance reactance of the capacitor is greatly reduced. Compared with Xcb, Rb is very small and R1 is large. Due to the non sinusoidal driving voltage of PWM, it is first decomposed and then calculated separately. The effective value of the shaft voltage is:

3. Bearing Model and Generation of Bearing Current

Due to the presence of distributed capacitors and the excitation effect of high-frequency pulse input voltage, a coupled common mode voltage is formed 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, as shown in Figure 3.

Taking one of the bearings as an example, the raceway of the bearing is composed of an inner raceway and an outer raceway. When the motor rotates, the balls in the bearing are surrounded by a lubricating oil layer. Due to the insulation effect of the lubricating oil, capacitance is formed between the bearing raceway and the balls, as shown in Figure 3b). These two capacitors are located on the rotor The stator circuit exists in series (without considering the impedance of the ball for analysis), which can be equivalent to a capacitor Cbi, where i represents the i-th ball in the bearing. For the entire bearing, the capacitance between each ball and raceway exists in parallel. So the entire bearing can be equivalent to a capacitor Cb. According to the analysis of bearings, they can be equivalent to a switch with internal inductance and resistance. When the ball does not come into contact with the raceway, the switch opens and the rotor voltage is established; When the rotor voltage exceeds the oil film threshold voltage, the oil film breakdown switch conducts, and the rotor voltage rapidly discharges internally, forming a large discharge current in the bearing.

Va, Vb, and Vc are the three-phase input voltages of the motor, L ‘, R’, and C ‘are the equivalent concentrated parameters of the input voltage coupled to the rotor shaft, and Cg is the equivalent capacitance after parallel connection of Crf and Cb. When the bearing balls come into contact with the raceway or the oil layer inside the bearing is broken down, Cb does not exist, and Cg only represents the coupling capacitance of the rotor shaft to the casing. Capacitance Cb is a function of multiple variables: Cb (Q, v, T, η,λ, Λ, ε r) [2]. Q represents power, v represents oil film motion speed, and T represents temperature, η Represents the viscosity of the lubricant, λ Represents lubricant additive, Λ represents oil layer thickness, ε R represents the dielectric constant of the lubricant. 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.

In this way, the voltage coupled to the motor bearings will not be too high, because the capacitance of Crf and Cb in parallel is much larger than the Csr connected in series in the coupling circuit, and in the series capacitor circuit, the larger the capacitance, the smaller the voltage it bears. In fact, according to the characteristics of distributed capacitance, a large part of the common mode current is transmitted to the ground through the coupling capacitance Csf between the stator winding and the iron core, so the bearing current is only a part of the common mode current. From Figure 4, it can be seen that there are two basic ways to form bearing current.

One reason is that due to the presence of distributed capacitors, the stator winding and portfolio zirconia silicon ceramic bearing mr115ce form a voltage coupling circuit. When the input voltage of the winding is a high-frequency PWM pulse voltage, dv/dt current is inevitably generated in this coupling circuit. Part of this current is transmitted to the ground through Crf, and the other part is transmitted to the ground through the bearing capacity Cb, forming the so-called dv/dt bearing current, which is related to the input voltage and the distribution parameters inside the motor. The second reason is that 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 act as short circuits, forming a large discharge current on the bearing, which is called electric discharge machining (EDM) current. In addition, when the motor is rotating, if there is contact between the ball and raceway, a large EDM current will also form on the bearing.

In order to quantify the impact of EDM and dv/dt current on bearings, the current density inside the bearing is crucial. Estimating the current density requires estimating the point contact area between the ball and the inner surface of the raceway. According to Hertzian point contact theory, the electrical life of bearings can be calculated using the following formula [2]:

Elec Life (hrs)=(7)

In the equation, represents the bearing current density. Generally speaking, the impact of dv/dt current on bearing life is minimal, while the bearing current density generated by EDM is high, greatly reducing bearing life. In addition, the degree of bearing damage during no-load is much greater than during heavy load, because the contact area of the bearing increases during heavy load, invisibly reducing the current density of the bearing.

Simulation analysis of 4-axis voltage and bearing current

To further discuss the relationship between bearing current and the output voltage characteristics of PWM inverters, as well as the presence or absence of overvoltage at the motor end, this paper conducts simulation analysis on two forms of bearing current: dv/dt current and EDM current. The results show that the tin bronze motor spherical oil bearing current is not only related to the inverter carrier frequency, but also to the rise time of the inverter output pulse voltage. At the same time, when overvoltage occurs at the motor end, the bearing current significantly increases.

Assuming the cable length is zero, based on the existence form of bearing current, it can be seen that the dv/dt current is mainly caused by the input jump voltage. Therefore, the magnitude of dv/dt current is related to the inverter carrier frequency and voltage rise time. The higher the carrier frequency of the inverter, the more dv/dt currents generated within a sine wave cycle, but the current amplitude remains unchanged at this time. The rise time of pulse voltage is a decisive factor affecting the amplitude of dv/dt current, and the size of distributed capacitance also affects the amplitude of dv/dt current. The direct cause of EDM current generation is the existence of shaft voltage, so the magnitude of shaft voltage determines the amplitude of EDM current, and the magnitude of shaft voltage determines the magnitude of input voltage and the size of distributed capacitance in 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 not related to either, so there is no essential connection between EDM current and the two. This is the biggest difference between EDM current and 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 greater the EDM current generated. For the convenience of discussion, it is assumed that the bearing breakdown voltage is greater than or equal to the shaft voltage.

4.1 Changing the rise time tr

The simulated waveforms of shaft voltage and bearing current with different rise times are shown in Figure 5, where Figures a) and b) represent the shaft voltage waveform, while Figures c) and d) represent the bearing current waveform. The first oscillation in the current waveform is the EDM current, while the others are the dv/dt current. From the analysis, it can be seen that 1) increasing tr reduces the bearing current, including dv/dt current and EDM current. Especially, the decrease in dv/dt current amplitude is very significant, but tr has little effect on EDM current, mainly because EDM current is determined by shaft voltage and bearing impedance; 2) When tr is less than a certain value (about 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 when the voltage is broken down. TR does not affect the first oscillation, but affects the second oscillation, and the second oscillation decreases with the increase of TR. The reason is that the coupling path from the stator winding to the rotor still exists after the bearing short circuit, resulting in a dv/dt current oscillation.

Link to this article：Analysis of the Mechanism of Shaft Voltage and Shaft Current Generation in Variable Frequency Motors

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