The performance of core deterioration process analysis based on multiscale method and eddy current testing method

Abstract

In order to improve the reliability of high-voltage motor core, the deteriorated performance parameters of core structure under deteriorating condition are needed. However, the current research on performance reliability mainly focuses on entire motor system, the performance deterioration analysis and fault simulation of the local core structure have not been studied extensively. At the same time, based on the contradiction between calculation ability and accuracy, the calculation of laminated core modeling is large and time-consuming. In this paper, a reliability analysis method of core performance based on multi-scale method and eddy current testing method is proposed. Firstly, the equivalent circuit network is established according to the multi-scale structure of the core to simulate the performance deterioration process of the core. Then, the deterioration parameters are determined according to the analysis of insulation deterioration, and the three-dimensional eddy current field model and analysis of the core during insulation deterioration are carried out. Finally, the core sensor is designed based on eddy current testing method, and the performance deterioration experiment of the prototype is carried out, and the simulation data and experimental data are compared, the results show that the error between simulation parameters and experimental data is less than 5%, which verifies the validity of the performance reliability analysis method.

Keywords

Eddy current testing method insulation deterioration multiscale method performance deterioration

1. Introduction

With the rapid development of the intelligent production industry, the safe service and effective perception of products become more and more important. The degradation-failure state analysis and optimization design of key structures of large-scale power equipment is the key to ensure safety, improve service quality, and reduce maintenance cost. Accidents caused by insulation faults account for more than 50% of the total accidents involving large-scale power equipment [1–3]; Thus, the short circuit fault between iron core sheets is undoubtedly one of the major hidden dangers. How to quickly and accurately simulate the deterioration process of laminated core insulation, obtain the distribution of eddy current, eddy current loss and the variation law of short circuit current with the fault location, predict the possible location of short circuit fault and the development trend of deterioration area, so as to guide the fault diagnosis of laminated insulation area and the optimization design of core mechanical structure, and improve large-scale power equipment. The operation stability is very important to maintain the steady operation of the whole motor system [4,5].

Currently, the core reliability analysis is performed for the main body of the fault, and the reliability of the entire core is calculated by using the failure data of a single silicon steel sheet. However, as the reliability and life span of power equipment continue to increase, the lamination insulation deterioration should be accounted for a large proportion; this part of the deterioration data is difficult to obtain in a short amount of time. The multi-scale structure of stator core makes it difficult to realize software simulation and performance deterioration experiments.

Currently, in the simulation and analysis of core performance deterioration process, the current homogenization model was mainly used to replace the actual laminated core for performance deterioration simulation. In these models, a continuum of equivalent conductivities was used to simulate the eddy current in the short-circuit fault region [6–11]. Then, eddy-current and eddy-current losses were calculated on the basis of the theoretical research of reference [11] under multi-frequency conditions [12] and had been verified through the finite element method. Based on the ELCID method [13], indirectly obtained the fault by using direct and cross-axis vector decomposition of the fault current in the short-circuit region; and obtained the turbulent current at the fault point using the Chattock magnetic position meter. However, as this method didn’t consider the time-varying characteristics of the resistance of the inter-slab insulation layer during the insulation deterioration process, core fault was not considered as a gradually accumulating process when calculating the axial eddy-current effect and the thermal influence of the eddy-current on the insulation layer was ignored.

The heat loss of the insulation layer had been studied extensively; the analogy method was generally used to simulate the insulation faults of the core layer and internal insulation [14]. This provided a reference for the high-precision detection of a fault signal in the insulation area. Most fault diagnosis methods could diagnose the existence of faults in large-scale high-voltage motors; however, the judgment of the location of the fault often required dismantling and troubleshooting, it might take time, and also inevitably caused reducing the motor performance. Therefore, it was necessary to study the reliability analysis of the core performance. The equivalent circuit theory had been used to determine the resistance of the insulation layer between laminations [15–18]. Although this lumped parameter model could explain the basic principle of deterioration of the insulation layer between laminations, it could not calculate the fault current when the fault occurs at any position. However, the laminated sheet was relatively thin, and the finite element model for the actual core required a large calculation scale, consumed a significant amount of time, and made practical engineering applications difficult.

According to the multi-scale characteristics of the laminated core structure, the electrical and thermal aging of the insulation during the operation of the motor, the axial mechanical damage caused by the silicon steel sheet, and the impact damage between the inner winding of the slot to the iron core are considered. Combined with the multiscale method and the equivalent circuit theory, the anisotropic electromagnetic characteristics of the core in the degraded state, including the equivalent core resistance, equivalent conductivity, and permeability of the distribution parameters is derived. The conductivity and permeability tensors are used to represent the deterioration of the electromagnetic performance of the core, and a finite element calculation is performed on the performance-deteriorated core in the three-dimensional eddy-current field. Then, an excitation detection sensor based on the Eddy current testing method is used to obtain the deterioration parameters of the core. Finally, the simulation results are compared with the experimental data to verify the proposed degradation analysis method.

2. Multiscale parameter calculation of iron core

2.1. Eddy current analysis of the iron core under insulation deterioration

When the motor is running, the main flux flows in the laminate along the rolling direction of the silicon steel sheet. Because of their surface insulation, independent eddy currents are induced in each of the silicon steel sheets. The strong magnetic and high-temperature environment of the core causes the insulating material between laminations to gradually deteriorate. When the insulation deteriorates calculates to a certain threshold, local electrical connections occur on the core laminations, eddy currents between laminations suddenly increase, and additional eddy currents loss and heat will be generated. Then, the degradation between laminations is accelerated, and the fault of short-circuit between laminations is formed. Subsequently, the eddy-current loss of the silicon steel sheet at the fault point increases sharply while induced eddy currents of the remaining silicon steel sheets interact with each other through the fault point, thus a uniform short-circuit fault circulation path is formed.

When the iron core is in performance deteriorating condition, the insulation layer between the silicon steel sheets in the fault area still exists, except for the short-circuit fault point. Additionally, the electromagnetic characteristics of the remaining silicon steel sheets remain unchanged compared with the non-fault areas, and the electrical connection between them is only achieved by short-circuit the fault point.

2.2. Multiscale parameter calculation for non-faulty domains

Because of the magnitude difference between the mechanical structure of the core and the scale of the fault area, the multi-scale method was used to calculate which was called homogenization [19]. To do so, the inhomogeneous magnetic and electrical properties of the laminates are homogenized. Then, the macroscopic response of the composite can be obtained using the equivalent parameter method and continuous homogeneous model of the equivalent conductivity and permeability tensor of the macroscopic structure instead of the discontinuous core laminates.

Considering the rated operation of the motor, the value of iron loss at the tooth area of the stator is relatively large, and the top of the tooth is susceptible to mechanical damage. Thus, performance degradation is likely to occur between the laminations. Therefore, the stator tooth is selected as the research object. This homogenization process is shown in Fig. 1, where b is the thickness of the silicon steel sheet, b _t is the tooth width, h _s is the slot height, and l is the axial length of tooth.

Fig. 1.

Homogenization process of laminated iron core.

Actually the current skin depth of the non-fault area is far less than the thickness of a laminate, and σ_y ≪ σ_x and σ_z [20]. After homogenization, the conductivity of σ_y that is perpendicular to the plane of the laminate is 0 [9,21]. Thus, the eddy-current can be considered to be mainly distributed on the x–z plane near the insulated area.

Thus, the equivalent conductivity tensor can be calculated as follows: $\begin{eqnarray}\displaystyle [{\sigma}]=\left[\begin{array}{@{}ccc@{}}{\sigma}_{x} & & \\ & {\sigma}_{y} & \\ & & {\sigma}_{z}\end{array}\right]=\left[\begin{array}{@{}ccc@{}}k_{Fe}{\sigma} & & \\ & 0 & \\ & & k_{Fe}{\sigma}\end{array}\right]. & & \displaystyle\end{eqnarray}$ (1)

The equivalent permeability tensor can be described as [7] $\begin{eqnarray}\displaystyle [{\mu}]=\left[\begin{array}{@{}ccc@{}}{\mu}_{x} & & \\ & {\mu}_{y} & \\ & & {\mu}_{z}\end{array}\right]=\left[\begin{array}{@{}ccc@{}}k_{Fe}{\mu}_{fx} & & \\ & {\mu}_{fy}/(k_{Fe}+(1-k_{Fe}{\mu}_{fy}/{\mu}_{0})) & \\ & & k_{Fe}{\mu}_{fz}\end{array}\right] & & \displaystyle\end{eqnarray}$ (2) where 𝜇_fx, 𝜇_fy, and 𝜇_fz represent the relative permeability of the core laminations in the x, y, and z directions, respectively, and 𝜇₀ is the permeability of the air.

2.3. Multiscale parameter calculation for faulty domains

When the insulation between laminations deterioration occurs, in addition to its distribution in the x–z plane of laminations, the current in the core will flow along the axis of the core and pass through the insulation layer to form the fault current. At this time, the equivalent conductivity in the y direction of the core is not 0. Considering the influence of loss in the y direction on the damage of insulating layer, the equivalent circuit equation between insulating layer and adjacent silicon steel sheets is established to calculate the equivalent conductivity and permeability.

(1) Calculation of Actual Lamination Resistance: When short-circuit between laminations faults occur, the insulation between the silicon steel sheets is short-circuited, and the insulation circuit is replaced by the contact resistance of the fault point. The fault area of the tooth was assumed to be composed of n laminations, each lamination divided into m sections along the z direction, R _z is the resistance of silicon steel sheet lamination in the direction of z, and R _iy is the resistance of silicon steel sheet lamination in the direction of y, i.e., (i = 1, 2, 3, …m; j = 1, 2, 3, …n). Figure 2 shows the equivalent circuit of the core fault domain.

Fig. 2.

Equivalent circuit of interlamination short-circuit.

As the conductivity of the silicon steel sheet is much higher than that of the insulating layer, the skin depth of the fault current in silicon steel sheet is much smaller than that of the insulating layer. Thus, the eddy current in the silicon steel sheet to be distributed on both sides of the surface. The eddy current in the fault area will pass through the insulating layer along the axial direction.

To simplify the calculation of the lamination resistance, the following assumptions have been made:

1. The effects of higher harmonics in the power grid are negligible.

2. The fault current is evenly distributed in the damaged area of the insulation layer.

3. Under the condition of fault and non-fault, the variation law of magnetic flux of iron core is the same.

4. The volume resistivity of the insulation varies linearly with temperature.

5. There are no quality defects, such as burrs or bumps on the surface of the silicon steel sheet.

Thus, the equivalent resistances of R _ij and R _z can be calculated as follows: $\begin{eqnarray}\displaystyle & \displaystyle R_{ij}=R_{ave}({\theta})\times m & \displaystyle\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle & \displaystyle R_{z}=\frac{h_{s}}{{\sigma}_{z}\times b_{t}\times b\times (m-1)} & \displaystyle\end{eqnarray}$ (4) Where R _ave is the insulation resistance between two silicon steel sheets, the initial value of R _ave can be calculated according to the insulation grade and volume of the insulation coating, θ is the temperature coefficient, σ_z is the conductivity in the direction of z, (i = 1, 2, 3, …m; j = 1, 2, 3, …n).

During normal motor operation, the insulation between the lamination damages owing to the magnetic field and mechanical and thermal factors inside the motor. As the temperature of the fault area increases, the volume resistivity 𝜌_v and resistance of the insulation decrease, as shown in Fig. 3.

Fig. 3.

Change curve of volume resistivity.

The insulation resistance is mainly solved by the volume resistivity. The insulation resistance R _ij varies with time in the process of insulation deterioration. Therefore, the volume resistivity is adjusted in the above range to calculate the actual lamination resistance.

As shown in Fig. 2, the circuit subunits corresponding to the two silicon steel sheets in the dotted line box are used to process the T parameters in the two-port network: $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}T_{1}=\left\lfloor \begin{array}{@{}cc@{}}1 & 2R_{z}\\ 1/R_{11} & 2R_{z}/R_{11}+1\end{array}\right\rfloor \\[12.0pt] T_{2}=\left\lfloor \begin{array}{@{}cc@{}}1 & 2R_{z}\\ 1/R_{21} & 2R_{z}/R_{21}+1\end{array}\right\rfloor \\[9.0pt] \bullet \bullet \bullet \\ T_{m-1}=\left\lfloor \begin{array}{@{}cc@{}}1 & 2R_{z}\\ 1/R_{m-11} & 2R_{z}/R_{m-11}+1\end{array}\right\rfloor \\[10.0pt] T=T_{1}\times T_{2}\times T_{3}\times \bullet \bullet \bullet \times T_{m-1}=\left[\begin{array}{@{}cc@{}}A & B\\ C & D\end{array}\right]\end{array}\right. & & \displaystyle\end{eqnarray}$ (5) Where A, B, C, and D are matrix parameters and the actual equivalent resistance of the short-circuit between two silicon steel sheets is represented as follows: $\begin{eqnarray}\displaystyle R_{2}=\frac{B}{D-1}+B+\frac{B}{A-1}+R_{m1}. & & \displaystyle\end{eqnarray}$ (6)

The short-circuit fault between laminations develops along the axis, and the equivalent circuit in the direction of fault current diffusion is obtained in turn. According to this rule, the equivalent resistance R _q of the short-circuit fault between q silicon steel sheet can be obtained, q = 2, 3, … n.

(2) Conductivity and Permeability After Homogenization: For the core laminated continuum in the fault region, along the direction of fault current flow, the stator teeth are equivalent to a combination of thickness l and width b _t.

Thus, the equivalent resistance can be expressed as follows: $\begin{eqnarray}\displaystyle R_{q}=\frac{1}{{\sigma}_{y}}\times \frac{l}{{\delta}_{z}\times b_{t}} & & \displaystyle\end{eqnarray}$ (7) where δ_z represents the skin depth of the fault current in the z direction and can be calculated as ((8)) $\begin{eqnarray}\displaystyle {\delta}_{z}=\sqrt{\frac{k}{{\pi}f{\mu}_{r}{\sigma}_{y}}} & & \displaystyle\end{eqnarray}$ (8) where k is the temperature coefficient of conductivity, f is the frequency of the fault current, and 𝜇_r is the relative permeability of the silicon steel sheet.

Equation (8) can then be substituted into (7) to obtain the equivalent conductivity in the y direction: $\begin{eqnarray}\displaystyle {\sigma}_{y}=\frac{l^{2}\times {\pi}\times f\times {\mu}_{r}}{k\times R_{q}^{2}\times b_{t}^{2}}. & & \displaystyle\end{eqnarray}$ (9)

Considering that the equivalent resistance R _q is a value varying with temperature, it has time-varying characteristics. There is a deviation in the value of the solution in ((6)). Therefore, a combination of actual lamination resistance and homogenization method is adopted. According to the method described in Section 2.3(1), the evolution law of equivalent resistance in fault domain is found, and the equivalent conductivity with time-varying characteristics is obtained.

Then, the equivalent conductivity tensor of the fault domain can be expressed as follows: $\begin{eqnarray}\displaystyle [{\sigma}]=\left[\begin{array}{@{}ccc@{}}{\sigma}_{x} & & \\ & {\sigma}_{y} & \\ & & {\sigma}_{z}\end{array}\right]=\left[\begin{array}{@{}ccc@{}}k_{Fe}{\sigma} & & \\ & \displaystyle \frac{l^{2}\times {\pi}\times f\times {\mu}_{r}}{k\times R_{q}^{2}\times b_{t}^{2}} & \\ & & k_{Fe}{\sigma}\end{array}\right]. & & \displaystyle\end{eqnarray}$ (10)

Similarly, the equivalent permeability tensor of the fault domain can be expressed as follows: $\begin{eqnarray}\displaystyle [{\mu}]=\left[\begin{array}{@{}ccc@{}}{\mu}_{x} & & \\ & {\mu}_{y} & \\ & & {\mu}_{z}\end{array}\right]=\left[\begin{array}{@{}ccc@{}}k_{Fe}{\mu}_{fx} & & \\ & {\mu}_{fy} & \\ & & k_{Fe}{\mu}_{fz}\end{array}\right] & & \displaystyle\end{eqnarray}$ (11) where 𝜇_fx, 𝜇_fy and 𝜇_fz, are the relative magnetic permeability of the core lamination in the x, y, and z directions, respectively, thus, it is considered that the actual lamination and the uniform continuum 𝜇_fx = 𝜇_fy = 𝜇_fz = 𝜇_r the equivalent conductivity of the stator yoke is also treated as same as the magnetic permeability.

3. Modeling and analysis of three-dimensional eddy-current field in core insulation deterioration

3.1. Establishment of performance deterioration model

Based on the multi-scale method, the deterioration process of a complex laminated core is simulated; the actual core lamination was replaced by the continuum model of equivalent conductivity and permeability of the macrostructure.

The large high-voltage motor YR630-12/1430 with an F-grade motor insulation, a cooling mode of IC01, and a DR530-50 core silicon steel sheet was selected as the prototype.

Due to the symmetry of the laminated core, a core region V under a pair of poles was selected as the calculation region. The eddy-current density of this region can be calculated using T , 𝜓 −𝜓 and the 3D finite element method of equivalent conductivity and permeability [22].

As the insulation between the laminations deteriorates, the area V can be divided into the fault and non-fault areas V ₁ and V ₂, respectively. The current density J of region V can then be obtained using the potential T and magnetic potential 𝛹: $\begin{eqnarray}\displaystyle \begin{array}{@{}ll@{}}\boldsymbol{J}={\nabla}\times \boldsymbol{T} & V_{1}\text{ inside}\\ \boldsymbol{J}={\nabla}\times \boldsymbol{H}_{\boldsymbol{s}} & V_{2}\text{ inside}\end{array} & & \displaystyle\end{eqnarray}$ (12) where J is the current density, H _s is the magnetic field intensity produced by the external current density excitation source in infinite space. According to Boit-Savart law, H _s can be calculated as [23] $\begin{eqnarray}\displaystyle \boldsymbol{H}_{\boldsymbol{s}}=\frac{1}{4{\pi}}\int _{{\Omega}_{s}}\frac{\boldsymbol{J}_{\boldsymbol{s}}\times r}{r^{3}}d{\Omega}. & & \displaystyle\end{eqnarray}$ (13)

T and 𝛹 can be solved as follows: $\begin{eqnarray}\displaystyle \begin{array}{@{}l@{}}\left.\begin{array}{@{}l@{}}{\nabla}\times [{\sigma}]^{-1}{\nabla}\times \boldsymbol{T}-{\nabla}[{\sigma}]^{-1}{\nabla}\cdot \boldsymbol{T}+[{\mu}]\displaystyle \frac{\partial \boldsymbol{T}}{\partial t}-[{\mu}]{\nabla}\displaystyle \frac{\partial {\psi}}{\partial t}=0\\ {\nabla}\cdot ([{\mu}]\boldsymbol{T}-[{\mu}]{\nabla}{\psi})=0\end{array}\right\}V_{1}\\[15.0pt] \left.\begin{array}{@{}l@{}}-{\nabla}\cdot [{\mu}]{\nabla}{\psi}=0\end{array}\hspace{181.20007pt}\right\}V_{2}\end{array} & & \displaystyle\end{eqnarray}$ (14) where [σ] and [𝜇] represent the equivalent conductivity and permeability tensor of the core, respectively.

3.2. Simulation results and analysis

The fault area of the studied core comprised four 0.5 mm thick laminations, and the excitation current in the excitation winding was 175 A. Figure 4 shows the eddy current density simulation in the core under the continuous body model, actual lamination model. The corresponding errors are 1.429% and 1.846%, respectively. Figure 5 shows the vortex density comparison between the adaptive meshing and faults. From Fig. 5, the current density of the core tooth and yoke fault regions are much higher than those of other regions.

Fig. 4.

Eddy-current density in different models.

Fig. 5.

Eddy-current density in the adaptively generated model.

An area at the top of the tooth was selected as the simulation test point of the short-circuit fault between the laminations to obtain the axial fault current variation law. The comparison of current densities between the two models in simulation calculation is shown in Fig. 6.

Fig. 6.

Comparison of current density distribution at fault region of the short-circuit.

The eddy-current density at the fault point was significantly higher than the normal value, whereas the fault current density in the non-faulty domain was negligible. At the same fault point, the eddy-current effect, eddy-current distribution, and current distribution error at the fault point of the short-circuit fault were less than 5% in both models, which indicated the feasibility of using the homogenization model for the calculation of eddy currents.

Because of the limitation of the motor structure and the work environment, it is difficult to obtain the condition and the damage degree of short-circuit fault. The calculation simulation of the single event of a short-circuit fault between the laminations analyzed that results can be used to directly determine the degree of failure and the damage of the insulation deterioration between the laminations with respect to the motor reliability. The resulting data can be used as the reference for the reliability design in the later development of the iron core.

4. Fault parameter acquisition based on eddy current testing method

The experimental and simulation calculations use the same prototype, and the fault area detection point is same as the simulated area. Because the high-voltage motor short-circuit fault experiment requires a high excitation level over and a long time [24], a local welding method was used between laminations to simulate the short-circuit fault of the lamination. Then, the fault simulation errors between the two models could be judged by comparing the degree of short-circuit fault.

When the deterioration occurs between the laminations of the core in the axial direction and forms a closed loop with the positioning ribs, the alternating magnetic flux induces a fault current in the fault area. Thus, the degree and level of the short-circuit fault can be measured by the fault current value. To reduce the influence of the leakage current of the stator tooth and the end portion on the fault current and more accurately obtain the short-circuit fault between laminations, the low-frequency excitation method was adopted [25]. The excitation level used was only 4% of the rated excitation, and it is equivalent to rated excitation in simulation to obtain the degree of short-circuit fault.

4.1. Eddy current testing principle

The short circuit fault between the laminations primarily result from the mechanical damage and thermal aging of the insulation between the laminations, including the physical damage caused by physical collisions and the chemical damage caused by temperature rise during the motor operation. In this study, according to the Eddy current testing method based grinding burn detection mechanism of the metal specimens and the obtained scientific research results [26–28]. Based on the aspects of electromagnetic, magnetization, and magnetic domain theories, the damage details of the short-circuit fault between the laminations were obtained from a microscopic point of view, i.e., the state and attribute defect of the changed electrical conductivity and permeability in the iron core region. Additionally, an iron core sensor was designed to detect the deterioration of the fault domain based on the principles of Eddy current testing method and electromagnetic induction.

Under an external AC magnetic field, the local magnetic field at the fault location can be decomposed into two parts: the eddy-current field without deterioration and the disturbed magnetic field generated by the deterioration fault.

The eddy-current field without deterioration is represented by E ^U and H ^U, and σ^U represents the spatial conductivity distribution without deterioration. The eddy-current field E ^d and H ^d of the disturbed magnetic field caused by insulation deterioration can then be calculated by [29,30] $\begin{eqnarray}\displaystyle & \displaystyle E=E^{U}+E^{d} & \displaystyle\end{eqnarray}$ (15) $\begin{eqnarray}\displaystyle & \displaystyle H=H^{U}+H^{d}. & \displaystyle\end{eqnarray}$ (16)

According to the magnetic field changes of Maxwell’s equations and alternating magnetic fields, and ignoring the low-frequency displacement current, the governing equations of the degradation are established, as follows: $\begin{eqnarray}\displaystyle & \displaystyle {\nabla}\times H={\sigma}E+J_{s} & \displaystyle\end{eqnarray}$ (17) $\begin{eqnarray}\displaystyle & \displaystyle {\nabla}\times E=-j{\omega}{\mu}H & \displaystyle\end{eqnarray}$ (18) where σ is the distribution of spatial conductivity with deterioration, J _s is the density distribution of the coil current, 𝜇 is the permeability, and ω is the angular frequency of the exciting current.

The governing equations for the magnetic field distribution without deterioration are $\begin{eqnarray}\displaystyle & \displaystyle {\nabla}\times H^{U}={\sigma}^{u}E^{U}+J_{s} & \displaystyle\end{eqnarray}$ (19) $\begin{eqnarray}\displaystyle & \displaystyle {\nabla}\times E^{U}=-j{\omega}{\mu}H^{U}. & \displaystyle\end{eqnarray}$ (20)

Equations ((17)) and ((18)) can then be substituted into ((19)) and ((20)) to obtain $\begin{eqnarray}\displaystyle & \displaystyle {\nabla}\times H^{d}={\sigma}E^{d}+J^{d} & \displaystyle\end{eqnarray}$ (21) $\begin{eqnarray}\displaystyle & \displaystyle {\nabla}\times E^{d}=-j{\omega}{\mu}H^{d} & \displaystyle\end{eqnarray}$ (22) Where J ^d is the equivalent current density distribution for deteriorating disturbed fields, J ^d = (σ − σ^u)E ^U = σ^d E ^U.

According to Eq. (21), based on the equivalent source method, the disturbance magnetic field caused by insulation deterioration can be equivalent to the field caused by current source. Thus, the electrical parameters of equivalent current source can be obtained to determine the deterioration degree of fault area.

4.2. Design of core sensor

When the stator core of a large motor is excited, an alternating magnetic field will be generated in the silicon steel sheets of the iron core. If the insulation between the laminations is damaged, the damaged site and the pigeon tail positioning tendon on the back of the core will form a closed loop. Further, the magnetic field at the silicon steel sheet will be affected by the resulting short circuit current, which will lead to the distortion of the magnetic field lines passing across the damaged area.

According to Faraday’s law of electromagnetic induction, the characteristic parameters of the equivalent current source can be determined as the change in magnetic flux through the coil is known, that is, deterioration parameter.

Based on the Eddy current testing method and the low-frequency excitation method, the rotor is pulled out by an off-line fault testing method and the inner surface of stator core is scanned by sensor probe when the motor is in a machine halt. The experimental principle is shown in Fig. 7.

Fig. 7.

Experimental schematic diagram.

The black coil in the Fig. 7 is the excitation coil and is named as the first coil. And it is located at the axis of the stator cavity, the distance between the end of the stator core and excitation coil is more than 1 m, which can ensure the magnetic field generated at the end of the stator core does not interfere with the magnetic field in the stator core.

The AC excitation current signal is input to the first coil through the voltage regulator, and at this time, an induced eddy current magnetic field is generated in the circumferential direction of the core tooth portion, and from Ampere’s Law of Loops: $\begin{eqnarray}\displaystyle \int _{c}Hdl=\sum Ni & & \displaystyle\end{eqnarray}$ (23) where H is the magnetic field intensity, l is the integral path, N is the number of coil turns on the U-yoke, and i is the magnitude of the applied excitation current.

The 𝛷 0.1 mm Permalloy is used as the second coil to detect the fault on the top of the core tooth. That is, when the first coil is input to AC excitation, the alternating flux is obtained by the second coil and converted into voltage signal, and the deterioration parameter is $\begin{eqnarray}\displaystyle U=\frac{N_{w}{\varphi}_{w}}{\sqrt{2}}=4.44NfB_{m}S & & \displaystyle\end{eqnarray}$ (24) where N _w is the effective turns of the coil on the receiving rod, 𝜑_w is the magnetic flux, f is the frequency, B _m is the fundamental wave amplitude of magnetic density, and S is the area which the flux flows.

In order to reduce the eddy current loss in the permalloy and increase the measurement accuracy of the second coil, a 𝛷 0.1 mm permalloy wire was bundled in the same thickness, and each permalloy wire was coated with an insulating paint when the second coil was manufactured.

Considering that the detection of the second coil is carried out in the movement, the second coil was placed on the moving trolley with the aluminum alloy as the frame, and the screw-clamping base, the roller, and the permanent magnet were fixed on the base of the car for fixing the second coil. Further, a position encoder and its control box were installed on the side of the front and back of the car, respectively, which can ensure that the trolley could move smoothly along the axial direction of the tooth. The specific experimental platform is show in Fig. 8.

Fig. 8.

Experimental platform.

The AC excitation voltage is 1.4 V and the excitation current is about 1.6 A during the experiment.

4.3. Experimental design

Considering that the complex electromagnetic environment around the core will affect the measurement accuracy of the sensor during the experiment, the experimental core was placed inside a shielding box. An infrared thermometer was used to measure the temperature on both sides of the core.

1. The insulating paint on the corresponding fault location of the core was scraped and welded to the surrounding silicon steel sheet to simulate the actual laminated short-circuit fault.

2. According to the equivalent conductivity and the equivalent permeability in Section 2.1, a continuum model was manufactured to simulate the short-circuit fault between lamination.

3. Because the temperature influences on the core resistance value, the core was energized before the experiment and the short-circuit current was measured when the core temperature reached the steady state.

4. Then, a hole of diameter equal to the fault length was drilled at the top of the core and welded to the surrounding silicon steel sheet to ensure the formation of the fault current loop.

4.4. Experimental results and verification

A vehicle-mounted sensor probe collected the alternating magnetic field in the tooth top area, which can upload it to the recorder through Ethernet communication for waveform display in the real-time. The testing data of the iron core was recorded using the recorder. The deterioration voltage of the fault region is shown in Fig. 9 and compared with the simulation results. Table 2 summarizes the corresponding results.

Fig. 9.

Voltage waveform at the fault region.

Table 1

Silicon steel sheet parameter

Performance	Thickness b/mm	Relative permeability 𝜇_r	Conductivity σ/MS/m	Superimposed pressure coefficient
Parameter	0.5	2000	5	0.95

Table 2

Result contrast

	Model
Parameter	Homogenization continuum model/ A	Actual laminated model/ A	Error
Short-circuit fault current	1.68 A	1.626 A	3.21%

According to Fig. 9, when no short-circuit fault occurred, the induced voltage of the magnetic field was approximately 976 mV. When the car is scanned to the fault that is 10–14 cm away from the end of the stator core, and the voltage waveform has a larger bulge, and the amplitude of magnetic field induced voltage is 1435 mV and 1388.8 mV. Therefore, the position and fault degree of the short-circuit point of the core were consistent with the design before the experiment; the error of the corresponding current was less than 4% after the induction voltage was converted into current. Thus, the homogenization continuum model was determined to be capable of simulating the actual short-circuit fault.

5. Conclusions

1. A method of combining the multi-scale and finite element methods was proposed to replace the actual laminated model with the continuum model. The proposed model effectively reduced the computational resources and accurately calculated the short-circuit fault current. Additionally, the proposed model effectively calculated the fault current variation despite the varying fault positions of iron core.

2. For a complex laminated core structure, the equivalent core resistance, conductivity, and permeability can be obtained by the proposed equivalent circuit network with time-varying characteristics, which can provide the parameters for the simulation of the performance deterioration model.

3. The proposed model was verified using a designed core sensor based on the Eddy current testing method, which could effective obtain the insulation deterioration state and fault current of the laminated core. Additionally, a certain amount of data samples can be obtained, which can provide a reference for the reliability study and fault prediction of core, and has a certain engineering significance.

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