Motor Bearing Damage Induced by Bearing Current: A Review

: The occurrence of the motor shaft voltage and bearing current caused by the inverter will aggravate bearing damage and lead to the premature failure of bearings. Many types of equipment are being shut down due to bearing currents, such as ﬁlters, insulated bearings and grounding brushes. Traditional suppression measures cannot eliminate the bearing current and the bearing damage mechanism under the bearing current is not clear. In this paper, the damage caused by the bearing current to bearings is analyzed in detail. The inﬂuences of different working conditions on the bearing current and the damage caused are discussed. The source of bearing currents is introduced and the bearing current model under different working conditions is reviewed. An outlook for future studies is proposed, based on the current research status and challenges.


Introduction
The roller bearing is the crucial component of the motor and determines its performance.With the extensive use of the pulse width modulation (PWM) inverter in electric motors, the occurrence of the bearing current in the motor has become non-negligible.It will lead to corrosion damage to the bearing, shortening the motor service life and consequently causing motor failure [1,2].
Practically, the voltage frequency and amplitude on the output of the PWM inverter are controlled by the fast switching supply of the power electronics controls.The time taken to turn the thyristor on/off results in an unbalanced output from the inverter and generates a common-mode voltage with a high frequency at the neutral terminal of the motor windings.The motor winding, rotor, frame, bearing rollers and raceways act as capacitive electrodes, which form a coupling capacitance in the motor and provide a grounding path for the common-mode voltage [3][4][5][6].In addition, the asymmetric magnetic flux inside the motor can induce the non-zero voltage at the shaft, which causes the circulating current to move through the "one end bearing-frame-other end bearing-rotor".
The bearing currents will cause the electrical discharge machining (EDM) between the roller and raceway [7][8][9][10].The surface materials of these components will melt and pitting defects will form [11][12][13][14].Meanwhile, bearing currents will reduce the surface hardness of the bearing rollers and raceway.Combined with the stress concentration caused by corrosion pits, frosting damage will appear in the bearing raceways [15][16][17].Under the action of the long-term bearing current, the surface of the bearing rollers and the raceway will present as bright and dark with corrugated damage [18][19][20][21][22]. Furthermore, the high temperature and the debris generated by the current discharge lead to the performance degradation of the bearing's lubricating grease [23].
Currently, research on bearing current damage mainly includes the mechanism and the crucial influence parameters of the bearing current generation, the circuit model of bearing currents, and the damage to bearing performance [24,25].In the study of current damage to bearings, many studies have shown that bearing current damage is mainly affected by the motor speed [26][27][28], load [29], lubricating grease composition [30,31] and insulation layer [32,33].However, bearing failure is a diverse field under current investigation, and the mechanism analysis of the damage processing production is as yet unknown.
Based on a comprehensive literature survey, the bearing damage caused by bearing currents is reviewed in this paper.Section 2 introduces the different classifications of bearing current damage, the conditions of bearing current discharge and the process of bearing current damage.Section 3 describes the generation forms, types and circulation path of bearing currents, and the influences of motor structure, grease and operating parameters on the bearing current.Section 4 discusses the motor bearing current models, including the characteristics of the models, different ways to obtain model parameters and the establishment of equivalent models.Discussions on the current research status and outlooks for future investigations are highlighted in Section 5. Finally, conclusions of the present study are drawn.The relationship between the contents is shown in Figure 1.
Currently, research on bearing current damage mainly includes the mechanism and the crucial influence parameters of the bearing current generation, the circuit model of bearing currents, and the damage to bearing performance [24,25].In the study of current damage to bearings, many studies have shown that bearing current damage is mainly affected by the motor speed [26][27][28], load [29], lubricating grease composition [30,31] and insulation layer [32,33].However, bearing failure is a diverse field under current investigation, and the mechanism analysis of the damage processing production is as yet unknown.
Based on a comprehensive literature survey, the bearing damage caused by bearing currents is reviewed in this paper.Section 2 introduces the different classifications of bearing current damage, the conditions of bearing current discharge and the process of bearing current damage.Section 3 describes the generation forms, types and circulation path of bearing currents, and the influences of motor structure, grease and operating parameters on the bearing current.Section 4 discusses the motor bearing current models, including the characteristics of the models, different ways to obtain model parameters and the establishment of equivalent models.Discussions on the current research status and outlooks for future investigations are highlighted in Section 5. Finally, conclusions of the present study are drawn.The relationship between the contents is shown in Figure 1.

Damage of Bearings Caused by Bearing Currents
Bearing current may flow through the bearing in several states: (1) When the bearing is in full film lubrication, the roller, raceway, and grease from an equivalent capacitance; there is a weak current flowing through the equivalent capacitance of the bearing from the motor shaft to the frame under the effect of rapid alternating common-mode voltage; (2) The bearing forms a resistance on the circuit when the roller and raceway are in contact.The current will flow through the contact area, which is extremely small, and the heat generated by the current may melt the surface material of the bearing rollers and raceways, making them stick together.(3) When the oil film is formed, the common-mode voltage will create an electric field between the inner and outer ring of the bearing until the bearing voltage exceeds the oil film breakdown voltage.In addition, the separation of the roller and raceway or the approach of the roller to the raceway may also cause the discharge phenomenon due to the electric field between the inner and outer rings of the bearing.Bearing current will cause early pitting damage to the bearing, medium-term frosting and eventually forms fluting as well as lubricant degradation.

Damage of Bearings Caused by Bearing Currents
Bearing current may flow through the bearing in several states: (1) When the bearing is in full film lubrication, the roller, raceway, and grease from an equivalent capacitance; there is a weak current flowing through the equivalent capacitance of the bearing from the motor shaft to the frame under the effect of rapid alternating common-mode voltage; (2) The bearing forms a resistance on the circuit when the roller and raceway are in contact.The current will flow through the contact area, which is extremely small, and the heat generated by the current may melt the surface material of the bearing rollers and raceways, making them stick together.(3) When the oil film is formed, the common-mode voltage will create an electric field between the inner and outer ring of the bearing until the bearing voltage exceeds the oil film breakdown voltage.In addition, the separation of the roller and raceway or the approach of the roller to the raceway may also cause the discharge phenomenon due to the electric field between the inner and outer rings of the bearing.Bearing current will cause early pitting damage to the bearing, medium-term frosting and eventually forms fluting as well as lubricant degradation.
In the process of bearing current damage, the bearing current density J b = i b /A H (where i b is bearing current, A H is Hertz contact area) can be used to determine the degree of bearing current harm [34].References [35][36][37][38] concluded that small shaft voltages and bearing currents do not cause damage.However, Xie et al. [13] and Shoji et al. [39] found that weak currents can still cause damage to the bearings.Because the electrical contact area between the bearing roller and raceway is significantly smaller than the Hertz contact area when the bearing current passes through the bearing, the local current density flowing through the roller and raceway may be high [40].Even if the current is very low, it will cause degradation of lubricating grease, shortening the bearing life.

Pitting
When the bearing is lubricated with a full film, the common mode voltage will form an electric field between the roller and the raceway, until the voltage value exceeds the oil film voltage threshold and a discharge occurs between the roller and the raceway [41,42], as shown in Figure 2. The discharge current generates a transient high temperature above the melting point of the bearing material, causing the bearing roller and raceway surface material to melt and form crater defects [11,12,14], and welding beads on the metal subsurface [17].Xie et al. [13] applied gentle currents to a glycerin-lubricated bearing and discovered slope pits on the roller surface, presumably caused by the collapse of lubricant bubbles.
In the process of bearing current damage, the bearing current density (where b i is bearing current, H A is Hertz contact area) can be used to determine the degree of bearing current harm [34].References [35][36][37][38] concluded that small shaft voltages and bearing currents do not cause damage.However, Xie et al. [13] and Shoji et al. [39] found that weak currents can still cause damage to the bearings.Because the electrical contact area between the bearing roller and raceway is significantly smaller than the Hertz contact area when the bearing current passes through the bearing, the local current density flowing through the roller and raceway may be high [40].Even if the current is very low, it will cause degradation of lubricating grease, shortening the bearing life.

Pitting
When the bearing is lubricated with a full film, the common mode voltage will form an electric field between the roller and the raceway, until the voltage value exceeds the oil film voltage threshold and a discharge occurs between the roller and the raceway [41,42], as shown in Figure 2. The discharge current generates a transient high temperature above the melting point of the bearing material, causing the bearing roller and raceway surface material to melt and form crater defects [11,12,14], and welding beads on the metal subsurface [17].Xie et al. [13] applied gentle currents to a glycerin-lubricated bearing and discovered slope pits on the roller surface, presumably caused by the collapse of lubricant bubbles.Pitting is an early type of bearing damage caused by bearing current, as shown in Figure 3.The current forms pits surrounded by melted material on the babbitt's surface and material transfer between the two electrodes can be detected by energy dispersive spectroscopy [43].This suggests that during the electrical corrosion process, the materials of the two electrodes (rollers and raceways) may be connected to create a resistance circuit.The pits generated by the current increase the roughness of the rollers and runways and increase bearing wear [44].It is necessary to measure the degree of pit damage caused by bearing current to provide a basis for monitoring the running state and service life of bearings.The size of the pits can be estimated by the energy generated by the bearing current, and the dissipation of grease and energy in the air must be considered in the calculation.Prasad [45,46] investigated the energy accumulation and release of high-resistivity lubricants to determine the time it takes for electrical sparks to form a pitting on the raceway surface, and the time it takes to charge accumulation in grease [47].Tischmacher et al. [16] also calculated the energy needed to evaporate the material.The electro-corrosion area Pitting is an early type of bearing damage caused by bearing current, as shown in Figure 3.The current forms pits surrounded by melted material on the babbitt's surface and material transfer between the two electrodes can be detected by energy dispersive spectroscopy [43].This suggests that during the electrical corrosion process, the materials of the two electrodes (rollers and raceways) may be connected to create a resistance circuit.The pits generated by the current increase the roughness of the rollers and runways and increase bearing wear [44].It is necessary to measure the degree of pit damage caused by bearing current to provide a basis for monitoring the running state and service life of bearings.The size of the pits can be estimated by the energy generated by the bearing current, and the dissipation of grease and energy in the air must be considered in the calculation.Prasad [45,46] investigated the energy accumulation and release of high-resistivity lubricants to determine the time it takes for electrical sparks to form a pitting on the raceway surface, and the time it takes to charge accumulation in grease [47].Tischmacher et al. [16] also calculated the energy needed to evaporate the material.The electro-corrosion area showed a positive correlation with the discharge power, and the calculation of pitting was focused on a fault, which cannot predict the overall damage of the bearing raceway and roller.

Votage
showed a positive correlation with the discharge power, and the calculation of pitting was focused on a fault, which cannot predict the overall damage of the bearing raceway and roller.

Frosting
Under mechanical wear, as shown in Figure 4, the bearing raceway along the rolling direction shows light grey wear marks (frosting).The scanning electron microscope shows that there are many traces of bearing current damage in this area, and the hardness of this area is low [15,17].The pit damage caused by the bearing current on the surface of the bearing roller and raceway will reduce the contact area in this area, and when the bearing current melts the surface material, it will soften the material near the pitting damage, and the frosting will be caused by mechanical wear.
The formation of frosting damage may be related to the load on the bearing.Tischmacher et al. [16,48] discovered that under heavier loads, the bearing current formed a light grey frosted raceway on the bearing raceway, with intensive material melting traces visible with the scanning electron microscopy; under lighter loads, the bearing raceway formed corrugated damage.This may be due to the bearing oil film thickening under lighter radial loads, allowing it to withstand higher shaft voltages and generate higher bearing currents, thus causing more damage.In addition, lighter loads may result in larger vibrations of the rollers in the raceway, which can cause the rollers to contact the raceway at a certain frequency and eventually form corrugated damage.

Corrugated Damage
The inner raceway surface of a 5.5 kw motor bearing is shown in Figure 5.As shown in Figure 5a, scanning electron microscopy was used to examine the microscopic morphology of the surface of the bright and dark areas.When compared to the bearing raceway without corrugated damage area (Figure 5d), it was discovered that the dark zone area organization structure was relatively dense, with low roughness.In contrast, the

Frosting
Under mechanical wear, as shown in Figure 4, the bearing raceway along the rolling direction shows light grey wear marks (frosting).The scanning electron microscope shows that there are many traces of bearing current damage in this area, and the hardness of this area is low [15,17].The pit damage caused by the bearing current on the surface of the bearing roller and raceway will reduce the contact area in this area, and when the bearing current melts the surface material, it will soften the material near the pitting damage, and the frosting will be caused by mechanical wear.

Frosting
Under mechanical wear, as shown in Figure 4, the bearing raceway along the rolling direction shows light grey wear marks (frosting).The scanning electron microscope shows that there are many traces of bearing current damage in this area, and the hardness of this area is low [15,17].The pit damage caused by the bearing current on the surface of the bearing roller and raceway will reduce the contact area in this area, and when the bearing current melts the surface material, it will soften the material near the pitting damage, and the frosting will be caused by mechanical wear.
The formation of frosting damage may be related to the load on the bearing.Tischmacher et al. [16,48] discovered that under heavier loads, the bearing current formed a light grey frosted raceway on the bearing raceway, with intensive material melting traces visible with the scanning electron microscopy; under lighter loads, the bearing raceway formed corrugated damage.This may be due to the bearing oil film thickening under lighter radial loads, allowing it to withstand higher shaft voltages and generate higher bearing currents, thus causing more damage.In addition, lighter loads may result in larger vibrations of the rollers in the raceway, which can cause the rollers to contact the raceway at a certain frequency and eventually form corrugated damage.

Corrugated Damage
The inner raceway surface of a 5.5 kw motor bearing is shown in Figure 5.As shown in Figure 5a, scanning electron microscopy was used to examine the microscopic morphology of the surface of the bright and dark areas.When compared to the bearing raceway without corrugated damage area (Figure 5d), it was discovered that the dark zone area organization structure was relatively dense, with low roughness.In contrast, the The formation of frosting damage may be related to the load on the bearing.Tischmacher et al. [16,48] discovered that under heavier loads, the bearing current formed a light grey frosted raceway on the bearing raceway, with intensive material melting traces visible with the scanning electron microscopy; under lighter loads, the bearing raceway formed corrugated damage.This may be due to the bearing oil film thickening under lighter radial loads, allowing it to withstand higher shaft voltages and generate higher bearing currents, thus causing more damage.In addition, lighter loads may result in larger vibrations of the rollers in the raceway, which can cause the rollers to contact the raceway at a certain frequency and eventually form corrugated damage.

Corrugated Damage
The inner raceway surface of a 5.5 kw motor bearing is shown in Figure 5.As shown in Figure 5a, scanning electron microscopy was used to examine the microscopic morphology of the surface of the bright and dark areas.When compared to the bearing raceway without corrugated damage area (Figure 5d), it was discovered that the dark zone area organization structure was relatively dense, with low roughness.In contrast, the microstructure of the bright region was sparse and the roughness was high.When looking at the status of the surface material in the damaged region of the bearing, the raceway surface was covered with a layer of melted material, with the melted layer in the bright band area being thicker than the melted layer in the dark area, as shown in Figure 6.
Machines 2022, 10, x FOR PEER REVIEW 5 of 23 microstructure of the bright region was sparse and the roughness was high.When looking at the status of the surface material in the damaged region of the bearing, the raceway surface was covered with a layer of melted material, with the melted layer in the bright band area being thicker than the melted layer in the dark area, as shown in Figure 6.Corrugated damage occurs in the middle and late life of bearings, accompanied by the phenomenon of increased bearing vibration.Corrugated damage is thought to be caused by the bearing current [21] or by the slip band [49].However, corrugated damage is not caused by a single factor.EDM craters on the bearing raceway surface reduce the actual contact area between the rolling element and the raceway surface, resulting in higher contact pressure and the formation of corrugated damage [22].Liu [50] discovered scratches from abrasive wear in the corrugated damage in the bearing raceway between bright and dark.As a result, the combined influence of mechanical wear and bearing currents cannot be isolated from the production of corrugated damage.In addition, corrugated damage has two forms; one is induced by sinusoidal AC bearing current and the high-frequency non-sinusoidal current [50].The pitch of corrugations on the inner race is lower than on the outer race and is much greater on the rolling components, according to Prashad [19], and the breadth of corrugations on the bearing surface depends on the load.In 1991, Prashad [18] analyzed the corrugated damage width and spacing of bearing raceways under different operating conditions and found that the corrugated damage width depends on load, velocity, roller diameter, etc.In 1994, he studied the failure mechanism microstructure of the bright region was sparse and the roughness was high.When looking at the status of the surface material in the damaged region of the bearing, the raceway surface was covered with a layer of melted material, with the melted layer in the bright band area being thicker than the melted layer in the dark area, as shown in Figure 6.Corrugated damage occurs in the middle and late life of bearings, accompanied by the phenomenon of increased bearing vibration.Corrugated damage is thought to be caused by the bearing current [21] or by the slip band [49].However, corrugated damage is not caused by a single factor.EDM craters on the bearing raceway surface reduce the actual contact area between the rolling element and the raceway surface, resulting in higher contact pressure and the formation of corrugated damage [22].Liu [50] discovered scratches from abrasive wear in the corrugated damage in the bearing raceway between bright and dark.As a result, the combined influence of mechanical wear and bearing currents cannot be isolated from the production of corrugated damage.In addition, corrugated damage has two forms; one is induced by sinusoidal AC bearing current and the high-frequency non-sinusoidal current [50].The pitch of corrugations on the inner race is lower than on the outer race and is much greater on the rolling components, according to Prashad [19], and the breadth of corrugations on the bearing surface depends on the load.In 1991, Prashad [18] analyzed the corrugated damage width and spacing of bearing raceways under different operating conditions and found that the corrugated damage width depends on load, velocity, roller diameter, etc.In 1994, he studied the failure mechanism Corrugated damage occurs in the middle and late life of bearings, accompanied by the phenomenon of increased bearing vibration.Corrugated damage is thought to be caused by the bearing current [21] or by the slip band [49].However, corrugated damage is not caused by a single factor.EDM craters on the bearing raceway surface reduce the actual contact area between the rolling element and the raceway surface, resulting in higher contact pressure and the formation of corrugated damage [22].Liu [50] discovered scratches from abrasive wear in the corrugated damage in the bearing raceway between bright and dark.As a result, the combined influence of mechanical wear and bearing currents cannot be isolated from the production of corrugated damage.In addition, corrugated damage has two forms; one is induced by sinusoidal AC bearing current and the high-frequency non-sinusoidal current [50].The pitch of corrugations on the inner race is lower than on the outer race and is much greater on the rolling components, according to Prashad [19], and the breadth of corrugations on the bearing surface depends on the load.In 1991, Prashad [18] analyzed the corrugated damage width and spacing of bearing raceways under different operating conditions and found that the corrugated damage width depends on load, velocity, roller diameter, etc.In 1994, he studied the failure mechanism of bearings under the influence of an electric field and discovered that the load has a significant effect on the corrugated damage width [19].In 1998, he computed the energy needed to generate corrugated damage in the bearing racetrack based on the bearing size and working conditions and established a model for calculating the corrugated damage width of the bearing raceway [20].The degree of corrugated damage is related to the axial stress, the contact area of the roller and raceway, and the direction of current flow.In addition, the width and pitch of the corrugated damage may be related to the machine operating frequency and machine resonance.

Grease Degradation
When the bearing is in full-film lubrication, the common-mode voltage in the motor establishes a shaft voltage between the bearing inner and outer rings through a coupling circuit, and once the shaft voltage reaches the oil film breakdown threshold (dozens of volts [34]), the bearing current passes through the bearing.As the current passes through the gap between the bearing raceway and the rollers, heat is discharged into the surrounding area, causing the components in the grease to degrade and the grease to spoil [51].As shown in Figure 7, increasing the shaft voltage can lead to more severe bearing grease degradation [52,53].In addition, lubricant with discharge breakdown reduces dielectric strength; molecules in the grease may be polarized by the current, leading to lower dielectric constants and a lower threshold for shaft voltage penetration of the oil film [54].Through X-ray analysis, Ost et al. [15] found a large amount of iron in the grease, indicating that bearing wear and bearing current cause the material on the raceway and roller surface to fall off and enter the grease, affecting grease performance and increasing friction between the roller and the raceway [55].It can be observed that the bearing current degrades the lubrication grease in the bearing, thereby reducing its lubricating efficacy and reducing the bearing's service life.So the motor's bearing grease is required to withstand degradation from bearing wear and bearing currents [56].
Machines 2022, 10, x FOR PEER REVIEW 6 of 23 of bearings under the influence of an electric field and discovered that the load has a significant effect on the corrugated damage width [19].In 1998, he computed the energy needed to generate corrugated damage in the bearing racetrack based on the bearing size and working conditions and established a model for calculating the corrugated damage width of the bearing raceway [20].The degree of corrugated damage is related to the axial stress, the contact area of the roller and raceway, and the direction of current flow.In addition, the width and pitch of the corrugated damage may be related to the machine operating frequency and machine resonance.

Grease Degradation
When the bearing is in full-film lubrication, the common-mode voltage in the motor establishes a shaft voltage between the bearing inner and outer rings through a coupling circuit, and once the shaft voltage reaches the oil film breakdown threshold (dozens of volts [34]), the bearing current passes through the bearing.As the current passes through the gap between the bearing raceway and the rollers, heat is discharged into the surrounding area, causing the components in the grease to degrade and the grease to spoil [51].As shown in Figure 7, increasing the shaft voltage can lead to more severe bearing grease degradation [52,53].In addition, lubricant with discharge breakdown reduces dielectric strength; molecules in the grease may be polarized by the current, leading to lower dielectric constants and a lower threshold for shaft voltage penetration of the oil film [54].Through X-ray analysis, Ost et al. [15] found a large amount of iron in the grease, indicating that bearing wear and bearing current cause the material on the raceway and roller surface to fall off and enter the grease, affecting grease performance and increasing friction between the roller and the raceway [55].It can be observed that the bearing current degrades the lubrication grease in the bearing, thereby reducing its lubricating efficacy and reducing the bearing's service life.So the motor's bearing grease is required to withstand degradation from bearing wear and bearing currents [56].

Insulation Breakdown
For insulated bearings, bearing currents still occur.Malec et al. [57] and Zhang et al. [58] did a breakdown experiment on alumina and analyzed the breakdown channel morphology.When the current passes through the insulation, it creates a breakdown channel on the inside (as shown in Figure 8).Neusel et al. [59] showed that ceramic samples exhibit ohmic conduction at low pressure and space charge limited conduction at higher pressure.Insulation breakdown of insulated bearings may be related to inherent defects in the insulation and the electric field generated by local electron concentration.The original defects in the insulation layer are available for current flow and cause local Joule heating, according to Ref. [60], and when the applied electric field exceeds the insulation layer's withstanding voltage value, the current increases until thermal runaway occurs, resulting in a material breakdown.Touzin et al. [61] analyzed the influence of the microstructure and temperature of materials on electron injection into alumina.The present breakdown

Insulation Breakdown
For insulated bearings, bearing currents still occur.Malec et al. [57] and Zhang et al. [58] did a breakdown experiment on alumina and analyzed the breakdown channel morphology.When the current passes through the insulation, it creates a breakdown channel on the inside (as shown in Figure 8).Neusel et al. [59] showed that ceramic samples exhibit ohmic conduction at low pressure and space charge limited conduction at higher pressure.Insulation breakdown of insulated bearings may be related to inherent defects in the insulation and the electric field generated by local electron concentration.The original defects in the insulation layer are available for current flow and cause local Joule heating, according to Ref. [60], and when the applied electric field exceeds the insulation layer's withstanding voltage value, the current increases until thermal runaway occurs, resulting in a material breakdown.Touzin et al. [61] analyzed the influence of the microstructure and temperature of materials on electron injection into alumina.The present breakdown of the insulation layer will result in permanent damage, which will degrade the insulation layer's insulating effectiveness and may result in additional crack flaws around the breakdown channel.Malec et al. [62] examined the breakdown sites of alumina samples using spherical and flat electrodes and found that the breakdown was more frequent in areas with high electric field strength and initial electrode defects.Liebault et al. [63] investigated the variation curves of current absorption during the breakdown of alumina ceramics with different parameters and described the breakdown strength of alumina ceramics with different charge aggregation or diffusion parameters.Aside from the effect of the applied electric field, the thickness [57,[59][60][61][62]64,65], porosity [64,65] and impurity [60] of the insulating layer directly impact the insulating properties of the insulating layer.
Machines 2022, 10, x FOR PEER REVIEW 7 of 23 of the insulation layer will result in permanent damage, which will degrade the insulation layer's insulating effectiveness and may result in additional crack flaws around the breakdown channel.Malec et al. [62] examined the breakdown sites of alumina samples using spherical and flat electrodes and found that the breakdown was more frequent in areas with high electric field strength and initial electrode defects.Liebault et al. [63] investigated the variation curves of current absorption during the breakdown of alumina ceramics with different parameters and described the breakdown strength of alumina ceramics with different charge aggregation or diffusion parameters.Aside from the effect of the applied electric field, the thickness [57,[59][60][61][62]64,65], porosity [64,65] and impurity [60] of the insulating layer directly impact the insulating properties of the insulating layer.

White Etching Cracks (WECs)
In recent years, it has been found that the formation of white etched cracks may be related to bearing discharges [38], and the high temperatures generated during discharge may lead to the production of hydrogen ions or hydrogen atoms in lubricating oil, making the material on the bearing surface fragile [54].In addition, the defects caused by bearing currents can lead to the accumulation of local stresses, eventually causing cracks in the fragile material.A study showed that WECs were more likely to occur in statically loaded bearings than in those which are dynamically loaded [38].In Ref. [66], the input DC amplitude was changed from 0 to 750 mA, and the time required to generate the WECs was decreased with the increase in the current amplitude.Gould et al. [67] found that the crack originated in a central inclusion and extends in other directions.In addition to the inclusions left inside the bearing material during the manufacturing process of the bearing, the welding beads created by the bearing current will also cause inclusions on the bearing subsurface [17].
The amplitude of the bearing current plays a role in the formation of WECs, primarily by producing initial defects on the bearing subsurface and embrittlement of the bearing surface material in some way, and the stress concentration under heavy bearing load causes the WECs to extend from the location of the initial defects to the bearing surface embrittlement.

Influencing Factors of Bearing Currents
The operating environment affects the inverter output voltage and current and the bearing voltage (bearing current) [68].The magnitude of the current has a significant effect on the area of the bearing current damage [41,43,44].However, bearing current is not the only measure of bearing damage; bearing type and size, application fields (high-power motors, generator), working conditions (grease, speed, load, size, inverter parameters), etc., can all affect bearing current damage [37].Different discharge energy levels can cause different degrees of damage to the lubricated surface [55].Shoji et al. [39,53] found that increasing the bearing voltage will exacerbate the current's damage to the grease and

White Etching Cracks (WECs)
In recent years, it has been found that the formation of white etched cracks may be related to bearing discharges [38], and the high temperatures generated during discharge may lead to the production of hydrogen ions or hydrogen atoms in lubricating oil, making the material on the bearing surface fragile [54].In addition, the defects caused by bearing currents can lead to the accumulation of local stresses, eventually causing cracks in the fragile material.A study showed that WECs were more likely to occur in statically loaded bearings than in those which are dynamically loaded [38].In Ref. [66], the input DC amplitude was changed from 0 to 750 mA, and the time required to generate the WECs was decreased with the increase in the current amplitude.Gould et al. [67] found that the crack originated in a central inclusion and extends in other directions.In addition to the inclusions left inside the bearing material during the manufacturing process of the bearing, the welding beads created by the bearing current will also cause inclusions on the bearing subsurface [17].
The amplitude of the bearing current plays a role in the formation of WECs, primarily by producing initial defects on the bearing subsurface and embrittlement of the bearing surface material in some way, and the stress concentration under heavy bearing load causes the WECs to extend from the location of the initial defects to the bearing surface embrittlement.

Influencing Factors of Bearing Currents
The operating environment affects the inverter output voltage and current and the bearing voltage (bearing current) [68].The magnitude of the current has a significant effect on the area of the bearing current damage [41,43,44].However, bearing current is not the only measure of bearing damage; bearing type and size, application fields (high-power motors, generator), working conditions (grease, speed, load, size, inverter parameters), etc., can all affect bearing current damage [37].Different discharge energy levels can cause different degrees of damage to the lubricated surface [55].Shoji et al. [39,53] found that increasing the bearing voltage will exacerbate the current's damage to the grease and bearing, and Plazenet et al. [69] revealed that the higher the shaft voltage, the less the discharge phenomenon occurs, but the energy of a single discharge increases.Modeling of bearing currents in motors can benefit in examining their amplitude, frequency, and other features, investigating the bearing current damage, and developing bearing current monitoring and suppression technologies.Using DC, AC and high-frequency pulsed currents to erode bearings and evaluate the damage to bearing raceways electrically, Zika et al. [70] found that high-frequency pulsed currents were more harmful to bearings than continuous currents, despite having less total dissipated energy.

Sources of Bearing Currents
Circulating currents are often seen in large motors, but the high-frequency current of inverters magnifies the motor's structural asymmetry.Asymmetrical flux inside the motor will cause additional magnetic fields to induce voltages on the motor shaft [71].Pratt et al. [72] and Torlay et al. [73] showed that the stator or rotor eccentricity and asymmetry in motor structure cause this flux.In addition, inverter unbalanced power output can also cause the asymmetric flux of current in the motor windings [74].Finally, the shaft voltage driven by the circulating current generated by the magnetic circuit asymmetry passes through "one end of the bearing-frame-another end of bearing-rotor" (blue line in Figure 9) [75][76][77].
bearing, and Plazenet et al. [69] revealed that the higher the shaft voltage, the less the discharge phenomenon occurs, but the energy of a single discharge increases.Modeling of bearing currents in motors can benefit in examining their amplitude, frequency, and other features, investigating the bearing current damage, and developing bearing current monitoring and suppression technologies.Using DC, AC and high-frequency pulsed currents to erode bearings and evaluate the damage to bearing raceways electrically, Zika et al. [70] found that high-frequency pulsed currents were more harmful to bearings than continuous currents, despite having less total dissipated energy.

Sources of Bearing Currents
Circulating currents are often seen in large motors, but the high-frequency current of inverters magnifies the motor's structural asymmetry.Asymmetrical flux inside the motor will cause additional magnetic fields to induce voltages on the motor shaft [71].Pratt et al. [72] and Torlay et al. [73] showed that the stator or rotor eccentricity and asymmetry in motor structure cause this flux.In addition, inverter unbalanced power output can also cause the asymmetric flux of current in the motor windings [74].Finally, the shaft voltage driven by the circulating current generated by the magnetic circuit asymmetry passes through "one end of the bearing-frame-another end of bearing-rotor" (blue line in Figure 9) [75][76][77].In a PWM inverter-driven motor, the motor inverter driver transmits sinusoidal voltages of different amplitudes and frequencies to the motor winding through a thyristor in the inverter circuit.Figure 10 shows the motor windings in a star configuration with three terminals linked to the driver output.Vdc is the DC bus voltage, V1-V6 are thyristors, and A, B, C denote the three-phase winding of the motor.The common-mode voltage at the motor winding's neutral point is computed as [4]: where A V , B V , C V are the phase-to-ground-voltages of the inverter output.
If the inverter's thyristor is switched on or off at the same time, the common-mode voltage is zero at the neutral point of the motor winding.Otherwise, due to the lost time of the thyristor switch, there will be a non-zero common mode voltage.The capacitance coupling in the motor with common-mode voltage is shown in Figure 11, where wr C is the capacitive coupling between the stator winding and the rotor, wf C is the capacitive coupling between the stator winding and the frame, and rf C is the capacitive coupling between the rotor and the frame [78,79].The coupling capacitor inside the motor provides In a PWM inverter-driven motor, the motor inverter driver transmits sinusoidal voltages of different amplitudes and frequencies to the motor winding through a thyristor in the inverter circuit.Figure 10 shows the motor windings in a star configuration with three terminals linked to the driver output.Vdc is the DC bus voltage, V1-V6 are thyristors, and A, B, C denote the three-phase winding of the motor.The common-mode voltage at the motor winding's neutral point is computed as [4]: where V A ,V B ,V C are the phase-to-ground-voltages of the inverter output.
Machines 2022, 10, x FOR PEER REVIEW 9 of 23 a low-impedance ground path for common-mode currents, as shown in Figure 9 [24].The leakage current that flows from the motor windings to the ground through capacitance wf C (purple line in Figure 9) creates an encircling magnetic flux inside the motor which induces shaft voltage and the circulating current [80].When the impedance of the winding to the ground through the rotor is low, the leakage current will reach the rotor through capacitive coupling between the rotor and the winding, and the bearing flows to the ground (red line in Figure 9) [81].If the motor frame is poorly grounded or insulated bearings are used, current flows to the ground through the load end (green line and yellow in Figure 9) [82].Boucenna et al. [83] analyzed the "zigzag" way on the motor stator laminations due to the skin effect of the high-frequency current.If the inverter's thyristor is switched on or off at the same time, the common-mode voltage is zero at the neutral point of the motor winding.Otherwise, due to the lost time of the thyristor switch, there will be a non-zero common mode voltage.The capacitance coupling in the motor with common-mode voltage is shown in Figure 11, where C wr is the capacitive coupling between the stator winding and the rotor, C wf is the capacitive coupling between the stator winding and the frame, and C rf is the capacitive coupling between the rotor and the frame [78,79].The coupling capacitor inside the motor provides a low-impedance ground path for common-mode currents, as shown in Figure 9 [24].The leakage current that flows from the motor windings to the ground through capacitance C wf (purple line in Figure 9) creates an encircling magnetic flux inside the motor which induces shaft voltage and the circulating current [80].When the impedance of the winding to the ground through the rotor is low, the leakage current will reach the rotor through capacitive coupling between the rotor and the winding, and the bearing flows to the ground (red line in Figure 9) [81].If the motor frame is poorly grounded or insulated bearings are used, current flows to the ground through the load end (green line and yellow in Figure 9) [82].Boucenna et al. [83] analyzed the "zigzag" way on the motor stator laminations due to the skin effect of the high-frequency current.
a low-impedance ground path for common-mode currents, as shown in Figure 9 [24].The leakage current that flows from the motor windings to the ground through capacitance wf C (purple line in Figure 9) creates an encircling magnetic flux inside the motor which induces shaft voltage and the circulating current [80].When the impedance of the winding to the ground through the rotor is low, the leakage current will reach the rotor through capacitive coupling between the rotor and the winding, and the bearing flows to the ground (red line in Figure 9) [81].If the motor frame is poorly grounded or insulated bearings are used, current flows to the ground through the load end (green line and yellow in Figure 9) [82].Boucenna et al. [83] analyzed the "zigzag" way on the motor stator laminations due to the skin effect of the high-frequency current.

Motor Structure Parameters
The structural characteristics of the motor will affect the equivalent capacitance inside the motor, which will affect the shaft voltage and bearing current.Schuster et al. [84] investigated the bearing current of two types of permanent magnet synchronous machines (PMSM, 90 kW) with different stator slots and geometric shapes, and discovered that the voltage division ratio (BVR) of motor bearings with the longer axial core length is higher and keeping the stator windings away from the rotor surface can reduce coupling capacitance and the peak value of bearing current.Peng et al. [85] investigated the impact combinations of magnetic poles and stator slots on the shaft voltage of magnet machines and discovered that stator slots can reduce the induced shaft voltage.It is worth noting that the 8-pole 12-slot combination has a high induction shaft voltage.
Han et al. [86] used a coupled field-circuit electromagnetic finite element analysis (FEA) to study the effect of winding distribution on bearing voltage and bearing current.Muetze et al. [87] found that the stator slot and cooling duct frame have a large effect on the common-mode flux, which will cause circulating bearing currents.By studying the

Motor Structure Parameters
The structural characteristics of the motor will affect the equivalent capacitance inside the motor, which will affect the shaft voltage and bearing current.Schuster et al. [84] investigated the bearing current of two types of permanent magnet synchronous machines (PMSM, 90 kW) with different stator slots and geometric shapes, and discovered that the voltage division ratio (BVR) of motor bearings with the longer axial core length is higher and keeping the stator windings away from the rotor surface can reduce coupling capacitance and the peak value of bearing current.Peng et al. [85] investigated the impact combinations of magnetic poles and stator slots on the shaft voltage of magnet machines and discovered that stator slots can reduce the induced shaft voltage.It is worth noting that the 8-pole 12-slot combination has a high induction shaft voltage.
Han et al. [86] used a coupled field-circuit electromagnetic finite element analysis (FEA) to study the effect of winding distribution on bearing voltage and bearing current.Muetze et al. [87] found that the stator slot and cooling duct frame have a large effect on the common-mode flux, which will cause circulating bearing currents.By studying the influence of motor structure on shaft voltage and bearing current, the design and manufacture of the motor can be improved and the bearing current can be reduced.

Lubricant Grease
When the motor operates at high speeds, bearing rollers are separated from the raceway by non-conductive lubrication, and the non-zero common-mode voltage applies a voltage on the bearing, causing a small capacitive bearing current i bcap = C b dv/dt [88].Once the bearing voltage exceeds the oil film's threshold value, EDM current will break through the oil film, and heat generated by electric sparks will melt the material on the roller and the raceway surface to form a defect [29,89,90].
Because of the non-conductive nature of lubricating grease, it makes the bearing grease directly affect the bearing voltage and bearing current.The base oil of grease has a significant impact on bearing current discharge and bearing damage [91,92].By using lowresistivity lubricating grease, Prashad [93] detected the magnetic flux density (indicating current passing through) on bearing surfaces.The bearing acts electrically as an ohmic resistance when bearing rollers and raceways are in contact or there are conductive greases; the current flows directly through the bearing and heats the rollers and raceways [94].According to Tischmacher et al. [95], the shaft voltage of conductive greases is lower than that of non-conductive greases, but their qualities are similar to non-conductive greases after the operation.Zheng et al. [96] found that the high-frequency dv/dt bearing current amplitude increased with the degradation of the bearing grease.
The dielectric strength of the grease and the minimum oil film thickness are now used to determine the breakdown voltage of the bearing oil film.Bhattacharya et al. [97] and Niskanen [98] discovered that the breakdown voltage of the bearing oil film decreases when the voltage frequency increases.Khan et al. [28] showed that high temperature reduces the viscosity of the grease, which thins the oil film and lowers the oil film breakdown voltage.The greater the bearing temperature, the more time the bearing spends in the ohmic state, which might be due to the temperature causing a reduction in the thickness of the oil coating, according to Refs.[26,95,98,99].The rotational speed and temperature have effects on the oil film thickness and dielectric strength.The dielectric strength of the lubricating grease is higher at high temperatures than at low temperatures, and rotational speed decreases the dielectric strength while increasing the oil film thickness.Lin et al. [11] reported that when the concentration of MoS 2 (a lubricating oil ingredient that improves wear performance) and current amplitude increased, the insulating effect of the oil film decreased.Noguchi et al. [100] found that bearings with low raceway roughness vibrated more severely during the latter part of the experiment.This may be because a smooth surface is more likely to form a full oil film and therefore can withstand higher voltage, but a rough raceway can directly contact the oil film or reduce the breakdown voltage of the oil film, causing less bearing current damage than a smooth surface.Therefore, it may cause an error to calculate the breakdown voltage of the bearing lubricating film based on the thickness of the bearing lubricating film and its dielectric strength.

Rotational Speed
In the motor operation process, the speed of the motor changes the running state of the bearings and the average output voltage of the inverter, which in turn affects the bearing current damage to the bearings.Some research showed that when motor speed increased, the peak value of bearing current increased as well and that at a particular speed, the peak value reached its maximum and subsequently fell [26][27][28].When testing the peak discharge current of a motor, Magdun et al. [29] found that as the load increased, the rotational speed at which the highest bearing current appeared decreased.Khan et al. [28] found that the discharge activity of the motor is more significant at low speeds than at high speeds.They reasoned that when the rotational speed rose after passing a certain threshold, the oil film thickness grew, preventing the discharge phenomena and supplying more resistance to the bearing current loop, lowering the peak bearing current.This was also demonstrated by the frequency of discharge phenomena seen in [29,95] at varied rotating speeds.
During the motor operation, it may be in a state of frequent speed change and startstop due to the evolution of load or application environment, which will also contribute to the formation of damage to the bearing current.In comparison to constant speed operations, Tischmacher et al. [16,69] indicated that variable speed operations that frequently start and stop cause more bearing current damage pits for the motor than constant speed operations.

Inverter Parameters
The power parameters determine the frequency and the motor's neutral voltage.The carrier frequency of the inverter, the thyristor's switching frequency and the bus voltage all affect the bearing voltage and current of the motor.Statistical data on bearing currents collected by Smolenski et al. [101] revealed that increasing the inverter carrier frequency also increases the number of bearing current discharges as well as the current amplitude.Inverter switching frequency and inverter DC bus voltage are positively linked with the number of discharges [26,28].Xu et al. [102] also pointed out that the increase in switching frequency of the inverter increases the dv/dt current amplitude, but it has a nonlinear effect on the current discharge frequency of EDM.It is surmised that the increase in switching frequency may increase the common-mode voltage amplitude and the electric field of the oil film.Moreover, the increase in frequency reduces the time required for the electric field to break through the oil film and cause discharge.
To determine the impact of inverter types on shaft voltage and bearing current, Reddy et al. [103] and Chandrashekar et al. [104] compared the common-mode voltage, shaft voltage, and bearing current generated by two-level and three-level inverters and found that the common-mode voltage, shaft voltage, and bearing current generated by three-level inverters were smaller than those caused by two-level inverters.Collin et al. [105] compared the shaft voltage and bearing current amplitudes of silicon-and silicon carbidebased PWM inverters, and discovered that SiC inverters have higher shaft voltage and bearing current than Si inverters.

Connection Cable
The use of long cable connections between frequency converters and the motor can easily lead to transient overvoltage at the motor terminals [106].Weicker et al. [107] measured the common-mode voltage of motors at different lengths of three types of cables, and data revealed that the 300-m-long cable contains more high-frequency components.Compared with unshielded cables, shielded cables showed lower common-mode voltage amplitudes, smaller bearing current peaks, and a part of the common-mode voltage waveform was suppressed.Muetze et al. [108] measured the influence of cable shielding on EDM currents, high-frequency circulating currents, and rotor ground currents, and found that using shielded cables only affects the high-frequency circulating currents of large motors.Because of the long cable voltage reflection phenomena and the asymmetry of the long cable, the motor bearings may be exposed to higher voltages, increasing the risk of bearing current damage.

Modeling
An electrical model is established for different states of bearings to describe the states of shaft voltage and bearing current.The existing shaft current models are summarized in Table 1.The bearing current lumped parameter model can predict the shaft voltage and shaft current.Based on this model, the three-phase windings model of the motor can be studied independently to reveal the effect of each phase winding on the shaft current.The motor distribution parameter model divides the motor winding into several pieces and establishes the electrical connection between each motor winding and the motor rotor and frame.The high-frequency model can analyze the high-frequency component of the motor shaft current and the bearing current when the motor is connected to a long cable, but the models are more complex and have more parameters.
Non-insulated bearings RLC circuit Analytical calculation [24,25,133] Nonlinear resistance model at the breakdown

Lumped Parameter Model
Based on the distribution of coupling capacitance inside the motor and the electrical characteristics of the bearing under common-mode voltage, Chen et al. [25] developed equivalent lumped parameter circuit models to describe the motor ground current and bearing current generated by the coupling from the windings to the frame and the rotor.As shown in Figure 12, Erdman et al. [24] built a model of the current equivalent circuit of the motor bearing by considering capacitance coupling between the motor rotor, winding and frame.Park et al. [7] considered the electrical effects of the three-phase windings of the motor to establish an equivalent circuit model.In addition to the motor structure, Mäki-Ontto et al. [111] constructed a model of the motor system including the power supply, inverter, wires and filters.Mirafzal et al. [112] further considered stator resistance, core loss resistance, magnetizing inductance, etc., to build a three-phase motor model.Tagami et al. [113] developed a motor shaft voltage model describing the imbalance between the stator winding and the frame and rotor.Duan et al. [110] modelled the shaft voltage of the surface permanent magnet (SPM) motor and the interior permanent magnet (IPM) motor.Wang et al. [114] developed a model of the motor that includes the insulation of the outer ring and the wire that connects the outer ring of the bearing to the frame.structure parameters.Jun et al. [140,141] analyzed the impedance of the motor windings, rotor and frame, and the coupling capacitance in the motor by the finite element model.Magdun et al. [142] studied the equivalent capacitance between winding and frame for random wound round wire winding motors and wound profile copper winding motors.

Circulating Current Model
The leakage current in the motor and the axial flux generated by the unbalanced flux cause a voltage at the motor shaft, forming a high-frequency circulating current that causes damage to the bearings at both ends of the motor [117], as shown in Figure 13.Muetze et al. [116] and Postariu et al. [119] proposed an eddy-current model for the circulating bearing current based on the circulation loop of circulating bearing currents.Magdun et al. [120,143] also consider the motor rotor impedance in the circulating bearing current model.Maki-Ontto et al. [115,144] investigated the phenomenon of the skin effect causing the high-frequency current to propagate in a zigzag pattern on the motor stator laminations by refining the electrical model of the motor stator core and windings.Jaritz et al. [121] considered the electromagnetic coupling between the common mode current and the circulating current in their circulating bearing current model.Muetze et al. [118] developed a circulating bearing current model for insulated bearings and insulated housings.The status of the bearings at both ends of the motor during operation is not always the same, and the above model may be used to investigate the difference in bearing damage at both ends caused by a circulating current.

High-Frequency Model
The influence of common mode and differential mode voltages on bearing current at a high-frequency state may be studied by using a high-frequency motor model, which can then be used to develop shaft voltage suppression strategies.Naik et al. [79] developed RLC circuits for the electrical connection between the motor winding and frame and rotor, the air-gap impedance, and the bearing to meet the response of the motor model at different frequencies.Cacciato et al. [122] refined the connection of each winding coil to the frame and rotor to form a high-frequency motor model.Bubert and Quabeck et al.According to the parameters in the bearing current model, researchers [7,109,139] have calculated the value of coupling capacitance in the machine based on the machine structure parameters.Jun et al. [140,141] analyzed the impedance of the motor windings, rotor and frame, and the coupling capacitance in the motor by the finite element model.Magdun et al. [142] studied the equivalent capacitance between winding and frame for random wound round wire winding motors and wound profile copper winding motors.

Circulating Current Model
The leakage current in the motor and the axial flux generated by the unbalanced flux cause a voltage at the motor shaft, forming a high-frequency circulating current that causes damage to the bearings at both ends of the motor [117], as shown in Figure 13.Muetze et al. [116] and Postariu et al. [119] proposed an eddy-current model for the circulating bearing current based on the circulation loop of circulating bearing currents.Magdun et al. [120,143] also consider the motor rotor impedance in the circulating bearing current model.Maki-Ontto et al. [115,144] investigated the phenomenon of the skin effect causing the high-frequency current to propagate in a zigzag pattern on the motor stator laminations by refining the electrical model of the motor stator core and windings.Jaritz et al. [121] considered the electromagnetic coupling between the common mode current and the circulating current in their circulating bearing current model.Muetze et al. [118] developed a circulating bearing current model for insulated bearings and insulated housings.The status of the bearings at both ends of the motor during operation is not always the same, and the above model may be used to investigate the difference in bearing damage at both ends caused by a circulating current.
Machines 2022, 10, x FOR PEER REVIEW 13 of 2 structure parameters.Jun et al. [140,141] analyzed the impedance of the motor windings rotor and frame, and the coupling capacitance in the motor by the finite element model Magdun et al. [142] studied the equivalent capacitance between winding and frame fo random wound round wire winding motors and wound profile copper winding motors

Circulating Current Model
The leakage current in the motor and the axial flux generated by the unbalanced flu cause a voltage at the motor shaft, forming a high-frequency circulating current tha causes damage to the bearings at both ends of the motor [117], as shown in Figure 13 Muetze et al. [116] and Postariu et al. [119] proposed an eddy-current model for the circu lating bearing current based on the circulation loop of circulating bearing currents.Mag dun et al. [120,143] also consider the motor rotor impedance in the circulating bearing current model.Maki-Ontto et al. [115,144] investigated the phenomenon of the skin effec causing the high-frequency current to propagate in a zigzag pattern on the motor stato laminations by refining the electrical model of the motor stator core and windings.Jarit et al. [121] considered the electromagnetic coupling between the common mode curren and the circulating current in their circulating bearing current model.Muetze et al. [118 developed a circulating bearing current model for insulated bearings and insulated hous ings.The status of the bearings at both ends of the motor during operation is not alway the same, and the above model may be used to investigate the difference in bearing dam age at both ends caused by a circulating current.

High-Frequency Model
The influence of common mode and differential mode voltages on bearing current a a high-frequency state may be studied by using a high-frequency motor model, which can then be used to develop shaft voltage suppression strategies.Naik et al. [79] developed RLC circuits for the electrical connection between the motor winding and frame and rotor the air-gap impedance, and the bearing to meet the response of the motor model at differ ent frequencies.Cacciato et al. [122] refined the connection of each winding coil to th frame and rotor to form a high-frequency motor model.Bubert and Quabeck et al

High-Frequency Model
The influence of common mode and differential mode voltages on bearing current at a high-frequency state may be studied by using a high-frequency motor model, which can then be used to develop shaft voltage suppression strategies.Naik et al. [79] developed RLC circuits for the electrical connection between the motor winding and frame and rotor, the air-gap impedance, and the bearing to meet the response of the motor model at different frequencies.Cacciato et al. [122] refined the connection of each winding coil to the frame and rotor to form a high-frequency motor model.Bubert and Quabeck et al. [124,125] characterized the electrical characteristics of motor windings and built a more comprehensive model for motor windings.Magdun et al. [123] compared several motor winding high-frequency models and found that the equivalent capacitance between the winding and the frame, the stator leakage inductance, and the eddy currents loss resistance have a large impact on the accuracy of the model and proposed the corresponding motor model.
Because the voltage and current distribution in the motor winding are not constant in high-frequency alternating voltage [116,145,146], Gersem and Vivo et al. [126][127][128] developed the transmission line model to describe the effects of electromagnetic wavepropagation and reflection in cables and motor windings, as well as the frequency-dependent distributed losses in the system.However, the transmission line model must account for skin and proximity effects and dielectric losses, which adds to the complexity of the model.
The transmission line effect of the cable may raise the values of common-mode voltage, shaft voltage, and bearing current in systems when the inverter is connected to the motor with a long cable.Moreira et al. [129] modelled the high frequency per unit length of the cable.In Refs.[111,130,147] established the motor equivalent electrical model with long cables.Asymmetrical cables connecting the motor to the inverter will result in a high frequency zero system voltage at the motor terminals [106].Magdun et al. [132] developed transmission line models for the motor-inverter cable (long cable, cable asymmetry).Dahl et al. [131] modelled the system circuit for back-feeding bearing currents due to cable asymmetry.

Bearing Model
The equivalent bearing model can be described as an equivalent circuit model with a capacitor composed of an oil film and a bearing resistor connected in series and parallel [133].The circuit models of insulated bearing and non-insulated bearing are shown in Figure 14, where R_b is the bearing resistance, R_break is the nonlinear resistance when the bearing breaks down, C-oil is the equivalent capacitance of bearing oil film, C_ins is the equivalent capacitance of the bearing insulation layer, S1 and S2 represent the state switching when the bearing is broken.Ren et al. [134] pointed out that the bearing resistance is not constant when the bearing current is generated.Erdman et al. [24] and Bubert et al. [124] added the bearing nonlinear resistance to the model.In addition, for insulated bearings, Wang et al. [135] and Quabeck et al. [125] added to the bearing model the equivalent capacitance used to describe the insulation layer.Bearing equivalent capacitance is calculated by the Hertzian contact area [148] of the roller and raceway and the thickness of the oil film [149].Moreover, the grease near the Hertzian contact area between the roller and the raceway is also involved in the composition of the equivalent capacitance of the bearing [150,151].In addition, the bearing equivalent model will be affected by motor speed [151,152] and load [153,154], the temperature-dependent dielectric constant of the lubricant [133,150], raceway surface roughness [151,155], and bearing type [156].Prediction of bearing currents for different parameters of bearing rollers and raceway surfaces can be performed by the finite element software [136][137][138].

Discussions and Outlook
Failures associated with significant bearing damage induced by bearing currents have been commonly reported.Some studies have focused on bearing current damage to bearings.For example, Chiou et al. [41] and Xie et al. [13] studied the craters generated on the lubricated surfaces of bearings under bearing currents.Tischmacher et al. [16] and Raadnui et al. [17] analyzed the frosting damage caused by bearing currents to the bearings.Prashad [18,49] studied the corrugated damage caused by bearing currents to bearings and developed a model for calculating the width of corrugated damage.However, few studies have focused on modeling the early microdamage of bearing currents, and most of them tend to observe and analyze the damage of bearing currents rather than develop mathematical models of the damage of bearing currents.This leads to the incapability of existing models to effectively predict the length of a bearing life under the bearing currents.The reason for the existence of the bearing currents research status is that there are still more difficulties in the study of early micro-damage of bearing currents, which are summarized as follows: (1) The mechanism of bearing current generation is not clear.Many existing studies have used the bearing oil film breakdown voltage threshold proposed by Doyle et al. [90] as the condition for bearing current generation.However, insulated bearings with an insulating layer are not compatible with this method.The insulating properties of each bearing grease may vary considerably and will change as the grease deteriorates.In addition, there are factors such as load changes and grid disturbances during motor operation, and the bearing currents appear for very short periods and are more difficult to monitor.Therefore, it is very challenging to identify the conditions in which bearing currents occur.(2) The damage process of the bearing current to the bearing cannot be directly observed.
The bearings are installed inside the motor and the discharge phenomenon of the bearing current occurs between the bearing rollers and the raceway, so the motor components and the roller cage of the bearings will limit visibility.In addition, the emergence of the bearing current process is very short.Thus, it is difficult to observe the damage process of bearing current on the bearing.Because of this, it is hard to determine how bearing current damage occurs.(3) The single damage area caused by the bearing current to the bearing is at the micron level and cannot be directly observed.Therefore, scanning electron microscopy is needed to observe the micro damage.Moreover, in the initial bearing current damage bearing roller and raceway surface will not be covered with bearing current damage traces, which adds difficulty to the observation of damage.

Discussion and Outlook
Failures associated with significant bearing damage induced by bearing currents have been commonly reported.Some studies have focused on bearing current damage to bearings.For example, Chiou et al. [41] and Xie et al. [13] studied the craters generated on the lubricated surfaces of bearings under bearing currents.Tischmacher et al. [16] and Raadnui et al. [17] analyzed the frosting damage caused by bearing currents to the bearings.Prashad [18,49] studied the corrugated damage caused by bearing currents to bearings and developed a model for calculating the width of corrugated damage.However, few studies have focused on modeling the early microdamage of bearing currents, and most of them tend to observe and analyze the damage of bearing currents rather than develop mathematical models of the damage of bearing currents.This leads to the incapability of existing models to effectively predict the length of a bearing life under the bearing currents.The reason for the existence of the bearing currents research status is that there are still more difficulties in the study of early micro-damage of bearing currents, which are summarized as follows: (1) The mechanism of bearing current generation is not clear.Many existing studies have used the bearing oil film breakdown voltage threshold proposed by Doyle et al. [90] as the condition for bearing current generation.However, insulated bearings with an insulating layer are not compatible with this method.The insulating properties of each bearing grease may vary considerably and will change as the grease deteriorates.
In addition, there are factors such as load changes and grid disturbances during motor operation, and the bearing currents appear for very short periods and are more difficult to monitor.Therefore, it is very challenging to identify the conditions in which bearing currents occur.(2) The damage process of the bearing current to the bearing cannot be directly observed.
The bearings are installed inside the motor and the discharge phenomenon of the bearing current occurs between the bearing rollers and the raceway, so the motor components and the roller cage of the bearings will limit visibility.In addition, the emergence of the bearing current process is very short.Thus, it is difficult to observe the damage process of bearing current on the bearing.Because of this, it is hard to determine how bearing current damage occurs.(3) The single damage area caused by the bearing current to the bearing is at the micron level and cannot be directly observed.Therefore, scanning electron microscopy is needed to observe the micro damage.Moreover, in the initial bearing current damage bearing roller and raceway surface will not be covered with bearing current damage traces, which adds difficulty to the observation of damage.
In order to establish early micro-damage models of bearing currents and to achieve effective prediction of the length of motor bearing life under the action of bearing currents, further research should be conducted in the following areas: (1) Consider the effect of power supply frequency on the breakdown voltage of the bearing oil film and insulation layer.The high-frequency component of the commonmode voltage and the extremely high rate of voltage change accelerate the injection of electrons into the oil film and insulation layer, increasing the density of highenergy charged particles in the oil film and insulation layer and increasing the chance of breakdown.(2) Accurate modeling of the bearing currents helps to analyze the extent of bearing current damage to the bearings.Electric vehicles have used permanent magnet synchronous motors instead of induction motors, but at high speeds, the permanent magnets in the rotor may be close to the stator winding and cut the magnetic field, thus creating the back electromagnetic fields (EMF).Inside the motor, electromagnetic interference may affect the bearing currents.Therefore, when modeling the bearing current, the electromagnetic interference between the current in the winding, and the leakage current should be considered.(3) Establish the heat source model of bearing current discharge using the heat source model of electrical discharge machining (EDM).The bearing damage caused by bearing current may be calculated by energy analysis and with the help of finite element software.

Concluding Remarks
According to the literature, the effects of different operating conditions on bearing currents have been analyzed and the corresponding models of bearing currents have been developed to describe the bearing current characteristics.However, the bearing current generation conditions in these models do not apply to the commonly used insulated bearings.Furthermore, the damage morphology and extent of bearing current damage at different periods have been investigated.Although models for late corrugated damage are available, they have limitations for predicting bearing service life.In general, it is still difficult to predict the length of bearing life due to the absence of a clear mechanism of bearing current generation and early micro-damage models.
The mechanism of bearing current generation and bearing current damage process to bearings are not clear.As an important part of electric motors, the prediction of bearing life under the action of currents is still a necessary research direction in this field, and the above problems will be gradually solved.So, the purpose of this paper was to give a review of the bearing currents, from the origins of bearing current, and bearing fault caused by bearing current, to the model of bearing current.The content of this paper will assist researchers in quickly grasping the hotspots and challenges of current research.

Figure 1 .
Figure 1.Relationship diagram of bearing current research content.

Figure 1 .
Figure 1.Relationship diagram of bearing current research content.

Figure 3 .
Figure 3. Pitting damage micromorphology (a) SEM image of the rolling elements in the bearing with the passage of the electrical current; (b) the magnified image of a typical pit [13].

Figure 4 .
Figure 4. Frosting on the inner raceway ring and a magnified view of the running track [17].

Figure 3 .
Figure 3. Pitting damage micromorphology (a) SEM image of the rolling elements in the bearing with the passage of the electrical current; (b) the magnified image of a typical pit [13].

Figure 3 .
Figure 3. Pitting damage micromorphology (a) SEM image of the rolling elements in the bearing with the passage of the electrical current; (b) the magnified image of a typical pit [13].

Figure 4 .
Figure 4. Frosting on the inner raceway ring and a magnified view of the running track [17].

Figure 4 .
Figure 4. Frosting on the inner raceway ring and a magnified view of the running track [17].

Figure 5 .
Figure 5. Bearing corrugated damage and its microstructure (a) Corrugated damage of raceway surface (b) Micro-morphology of dark area (c) Micro-morphology of bright area (d) No damage area.

Figure 5 .
Figure 5. Bearing corrugated damage and its microstructure (a) Corrugated damage of raceway surface (b) Micro-morphology of dark area (c) Micro-morphology of bright area (d) No damage area.

Figure 5 .
Figure 5. Bearing corrugated damage and its microstructure (a) Corrugated damage of raceway surface (b) Micro-morphology of dark area (c) Micro-morphology of bright area (d) No damage area.

Figure 7 .
Figure 7. Changes in bearing grease after 500 h of operation at different voltages [53].

Figure 7 .
Figure 7. Changes in bearing grease after 500 h of operation at different voltages [53].

Figure 9 .
Figure 9. Bearing current paths in an inverter-driven induction motor system.

Figure 9 .
Figure 9. Bearing current paths in an inverter-driven induction motor system.

Figure 11 .
Figure 11.Capacitance coupling in an induction motor.

Figure 14 .
Figure 14.Models of insulated and non-insulated bearings.

Figure 14 .
Figure 14.Models of insulated and non-insulated bearings.

Table 1 .
Classification of motor shaft current model.