Analysis of the Mechanism of Variable Frequency Motor Shaft Voltage and Shaft Current (1)

**Analysis of the Mechanism of Shaft Voltage and Shaft Current in Variable Frequency Motors (Part 1)** Home > Bearing Knowledge > Analysis of the Mechanism of Shaft Voltage and Shaft Current of Variable Frequency Motor (1) Source: China Bearing Network | Time: June 26, 2014 --- When a motor is powered by a sine wave supply, shaft voltage is generated due to the alternating flux linkage in the motor's shaft. These flux linkages are formed by the rotor and stator slots, the connection between core pieces, and the magnetic material's orientation. Flux imbalance caused by power supply imbalance or other factors contributes to this phenomenon [1]. In the 1990s, with the use of IGBT-based PWM inverters as motor drives, the problem of shaft current became more severe, and its mechanism was completely different from that of sine wave power supplies. Literature [1] indicates that high carrier frequency IGBT inverters (e.g., above 10 kHz) cause faster bearing damage compared to those with lower frequencies. Busse further analyzed the relationship between bearing current density and bearing damage [2], and established a circuit model for PWM-driven bearings. However, this model does not fully reflect the relationship between bearing current and inverter switching frequency. This paper builds on the shaft voltage and current circuit model to analyze the conditions and modes under which shaft currents occur. It also observes overvoltage at the motor end when the inverter output voltage characteristics change. After simulation analysis, shaft voltage and bearing current waveforms under various conditions are obtained. To suppress bearing currents, the method in [1] converts PWM voltage into sine wave using a sine filter, allowing the motor to operate under sine wave conditions. However, this method involves large inductance, leading to slow system response, increased voltage drop, and higher power consumption. This article uses small inductance at the inverter output combined with an RC absorption network to effectively suppress shaft currents driven by PWM inverters. --- Common mode voltage and shaft voltage are often considered. Magnetic circuit imbalance, unipolar effect, and capacitor current are the main causes of shaft voltage in motors [3]. In grid-powered motors, magnetic circuit imbalance is usually the main factor, but in inverter-powered motors, the primary cause is voltage imbalance, specifically zero-sequence voltage. Due to imbalances in the circuit, components, and loop impedance, zero drift occurs in the power supply voltage, generating zero-sequence current in the system. Bearings form part of the zero-sequence loop. When driven by a sine wave supply, the inverter’s value depends on the switching condition, and the period is determined by the inverter’s carrier frequency. Common mode voltage can be expressed in different ways. Due to electrostatic coupling, there are scattered capacitances between the motor and ground, forming a zero-sequence loop. According to transmission line theory, a distributed parameter circuit can be replaced with an equivalent π network. Thus, the motor’s distributed parameter circuit can be simplified to a lumped parameter circuit. The windings responsible for shaft voltage—rotor coupling—are shown in Figure 2a). 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 a similar effect on the stator winding, influencing the bearing current. For simplicity, the coupling between the midpoint and the stator is not considered. Figure 2a) is simplified to the single-phase drive circuit model in Figure 2b). Z1 represents the power supply midpoint impedance, Z2 is the bypass impedance, characterizing common-mode reactance in the drive loop, including coils, line reactors, and long cables. R0 and L0 are the zero-sequence resistance and inductance of the stator. Csf, Csr, and Crf represent the stator-to-ground, stator-to-rotor, and rotor-to-ground capacitance of the motor. Rb is the bearing loop resistance, Cb and R1 are the bearing oil film capacitance and nonlinear impedance, and Usg and Urg are the neutral voltages of the stator and rotor windings. When the motor is powered by an inverter, if the bearing oil film is not broken down, the capacitive reactance of the capacitor is significantly reduced due to the high carrier frequency. Xcb is much smaller than Rb, and R1 is larger. Since the PWM driving voltage is non-sinusoidal, it is first divided during calculation, and then isolated. The effective values for the shaft voltage are calculated accordingly. --- Bearing models and bearing currents arise due to distributed capacitance and the excitation effect of high-frequency pulse input voltage, forming a coupled common-mode voltage on the motor shaft. The presentation of shaft voltage is not only related to these two elements but also depends on the layout. The front and rear ends of the rotor are supported by bearings, as shown in Figure 3. Taking a bearing in between as an example, the raceway consists of inner and outer rings. When the motor rotates, the balls in the bearing are surrounded by a smooth oil layer. Due to the insulating effect of the oil, a capacitor is formed between the raceway and the ball, as shown in Figure 3b). These capacitors exist in series in the rotor-stator loop (for simplicity, the ball impedance is ignored), and 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 the raceway exists in parallel, so the entire bearing can be modeled as a single capacitor Cb. According to bearing analysis, the bearing can be represented as a switch with internal inductance and resistance. When the ball is not in contact with the raceway, the switch is open, and the rotor voltage is set up. When the rotor voltage exceeds the oil film threshold voltage, the switch turns on, discharging the rotor voltage quickly and causing a large discharge current. Va, Vb, and Vc are the three-phase input voltages of the motor. L', R', and C' are the equivalent parameters of the input voltage coupled to the rotor shaft. Cg is the equivalent capacitance after parallel connection of Crf and Cb. When the ball and raceway touch or the oil layer breaks down, Cb no longer exists, and Cg only represents the coupling capacitance of the rotor shaft to the casing. The capacitance Cb is a function of multiple variables: Cb(Q, v, T, η, λ, Λ, εr) [2]. Here, Q represents power, v is the oil film velocity, T is temperature, η is the viscosity of the lubricant, λ is the additive, Λ is the oil film thickness, and εr is 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-case coupling capacitance Csf and the rotor-to-case coupling capacitance Crf. As a result, the voltage coupled to the motor bearing is not very large because the parallel combination of Crf and Cb is much larger than the series combination of Csr. In series capacitors, the larger the capacitance, the smaller the voltage. According to the characteristics of distributed capacitance, most of the common-mode current is transmitted to earth through the coupling capacitor Csf between the stator and core. Therefore, the bearing current is just a portion of the common-mode current. As shown in Figure 4, there are two basic methods for forming bearing currents. First, due to the existence of distributed capacitance, the stator winding and bearing form a voltage coupling loop. When the winding input voltage is a high-frequency PWM pulse voltage, a dv/dt current must occur in this loop, transmitted to earth through Crf. Part of it is transmitted through the bearing capacitor Cb, forming the so-called dv/dt bearing current, whose size depends on the input voltage and motor scattering parameters. Second, due to the presence of bearing capacitance, shaft voltage occurs on the motor shaft. When the shaft voltage exceeds the breakdown voltage of the bearing oil film, the raceway becomes equivalent to a short circuit, forming a large discharge current on the bearing, known as electric discharge machining (EDM) current. Similarly, during motor transitions, if the ball touches the raceway, a large EDM current can also be formed. To quantify the impact of EDM and dv/dt currents on the bearing, the current density in the bearing is crucial. To estimate the current density, it is necessary to determine the contact area between the ball and the raceway. According to Hertzian point contact theory, the bearing life can be calculated using the following formula [2]: Elec Life (hours) = (7) In the formula, represents the bearing current density. Generally, the dv/dt current has a significant impact on bearing life. The current density of EDM is very high, drastically reducing the bearing life. Additionally, bearing damage at no load is more severe than under load, as heavy loads increase the contact area, thereby reducing the current density. --- **Related Bearing Knowledge** Thrust angle touch ball bearing | Tumbling bearing fundamental production process ZT Metallurgical gearbox bearing application technology (2) FAG imported bearing cooperation in peeling damage and countermeasures Reasons for common cracks in NSK imported bearings and countermeasures This article links to http:// Please indicate the bearing network: http:// Previous: The basic type of one-way thrust angle touch ball bearing Next: Analysis of common faults of sliding bearings

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