Magnetic saturation state radial magnetic suspension bearing modeling method based on deep neural network

Abstract

The invention relates to a magnetic saturation state radial magnetic suspension bearing modeling method based on a deep neural network, and the method comprises the following steps: 1, calculating magnetic resistance expressions of a stator magnet yoke, a rotor, a stator magnetic pole, an air gap and magnetic leakage of a magnetic suspension bearing through a magnetic circuit model and a magnetic resistance theory, and building a static magnetic resistance equation; 2, learning magnetic saturation data of the ferromagnetic materials of the stator and the rotor by using a deep neural network, so as to carry out mathematical modeling of absolute magnetic permeability change during magnetic saturation; and 3, recalculating the magnetic resistance of the ferromagnetic material by using the magnetic conductivity containing the neural network, and solving a nonlinear magnetic resistance equation for replacing a magnetic resistance expression. And 4, updating the incremental magnetic conductivity by using the neural network, freezing and replacing the absolute magnetic conductivity to solve the static magnetic resistance equation, and calculating the incremental inductance. According to the method, a dynamic magnetic circuit method is improved, stator and rotor magnetic resistance, magnetic leakage and the like are incorporated into a model, modeling of magnetic pulling force and magnetic flux density under complex working conditions is achieved, and the precision and practicability of the model are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the field of magnetic levitation technology and relates to a method for modeling a radial magnetic levitation bearing in a magnetic saturation state based on a deep neural network. Background Art

[0002] Magnetic bearings are widely used today and have extensive research in both industrial and medical fields. Compared to traditional bearings, magnetic bearings have no direct contact with the rotor, eliminating frictional losses. This significantly reduces maintenance costs and extends service life. Active magnetic bearings (AMBs), which utilize magnetic fields generated by energized coils to intelligently control rotor vibration displacement, have become a hot research topic.

[0003] Modeling the dynamic parameters of magnetic bearings is crucial for their design and development. While traditional finite element modeling methods can account for factors such as magnetic leakage, magnetic saturation, eddy current losses, and edge effects, achieving high modeling accuracy, they impose high demands on equipment performance, incur high computational costs, and lack real-time performance, making them typically used only for design verification. Another widely used linear simplification method, while highly efficient, ignores various nonlinear factors and models only the air gap reluctance, making it difficult to meet the modeling requirements for complex magnetic bearing operating conditions.

[0004] Self-sensing magnetic bearings (SMBs) exploit the variation of the inductance of the active magnetic bearing coil with rotor eccentricity to demodulate rotor vibration displacement, offering the advantage of saving sensor space and cost. However, existing methods lack modeling of the incremental inductance under magnetic saturation conditions, limiting displacement demodulation accuracy and easily leading to control instability. Therefore, a SMB modeling method that comprehensively considers factors such as magnetic saturation is urgently needed to expand the operating range of SMBs and improve their performance under complex operating conditions. Summary of the Invention

[0005] In order to solve the problems existing in the above-mentioned technology, such as the lack of accuracy in radial magnetic bearing modeling and the inability to model the relationship between incremental inductance and eccentric displacement, the present invention provides a modeling method for radial magnetic bearings in a magnetic saturation state based on a deep neural network.

[0006] The specific technical solution of the magnetic saturation state radial magnetic bearing modeling method based on deep neural network of the present invention is as follows:

[0007] A method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network comprises the following steps:

[0008] Step 1. Calculate the magnetic reluctance expressions of the stator yoke, rotor, stator pole, air gap and leakage magnetic field of the magnetic levitation bearing through the magnetic circuit model and reluctance theory, and establish a static reluctance equation; reluctance theory is to equate each part of the magnetic field to the resistance of the circuit and the magnetic flux to the current, which is convenient for solving. The magnetic circuit theory is an equivalent circuit.

[0009] Step 2: Use a deep neural network to learn the magnetic saturation data of the stator and rotor ferromagnetic materials, which is used to mathematically model the change in absolute magnetic permeability during magnetic saturation. The magnetic saturation data is the calibration data of the ferromagnetic material, that is, the BH curve of the ferromagnetic material.

[0010] Step 3: Recalculate the magnetic resistance of the ferromagnetic material using the magnetic permeability containing the neural network, and solve the nonlinear magnetic resistance equation that replaces the magnetic resistance expression.

[0011] Step 4: Use the neural network to update the incremental permeability, freeze and replace the absolute permeability to solve the static magnetic resistance equation and calculate the incremental inductance.

[0012] Furthermore, the step 1 includes the following steps:

[0013] Step 1.1, mathematically model the magnetic reluctance of ferromagnetic materials such as the stator yoke, rotor, and stator poles;

[0014] Step 1.2, mathematically model the air gap between the stator pole and the rotor, and the leakage magnetic reluctance;

[0015] Step 1.3, set the magnetomotive force of each magnetic pole of the magnetic bearing and establish the static reluctance equation; the static reluctance equation is

[0016] R*Φ=U (1)

[0017] Where Φ is the 5n-dimensional magnetic flux matrix to be determined, n is the number of magnetic poles of the magnetic bearing, R is the reluctance coefficient matrix, and U is the magnetomotive force matrix of the magnetic pole coil.

[0018] The magnetoresistance equation requires the magnetoresistance of each part as the equation coefficient. Therefore, the magnetoresistance of each part must be modeled and solved in the first two steps before the magnetoresistance equation can be calculated.

[0019] Furthermore, the step 2 includes the following steps:

[0020] Step 2.1: Organize the correlation data of the magnetic flux density B and magnetic field intensity H of the ferromagnetic material, and use interpolation technology between data points to increase valid data for training;

[0021] Interpolation is a technique that inserts new data between two adjacent points to increase the amount of data. Because the original BH curve data volume is not large enough, training the neural network requires more data, so interpolation is required.

[0022] Step 2.2: Build a deep neural network model NetBH to learn the mapping from magnetic flux density B to magnetic field intensity H in the BH curve; the error calculation of the neural network takes the maximum error between the original data; and the error back propagation method is used to update the network parameters.

[0023] Furthermore, the step 3 includes the following steps:

[0024] Step 3.1, replace the magnetic permeability of the magnetoresistance matrix with a form containing a neural network expression;

[0025] Step 3.2, recalculate the reluctance coefficient of the stator and rotor ferromagnetic materials;

[0026] Step 3.3, update the nonlinear magnetoresistance equation and solve the flux matrix including the saturation effect;

[0027] Step 3.4, solve the air gap magnetic flux density and magnetic pull of each magnetic pole;

[0028] Step 3.5. Calculate the apparent inductance of each coil winding.

[0029] Furthermore, the absolute permeability expression updated in step 3.1 is:

[0030]

[0031] Where w is the effective width of the ferromagnetic material magnetic circuit, φ is the magnetic flux of the ferromagnetic material, μ is the effective width of the ferromagnetic material magnetic circuit, a The absolute permeability is updated to take into account the magnetic saturation effect.

[0032] Furthermore, the stator yoke reluctance expression in the same magnetic circuit updated in step 3.2 is:

[0033]

[0034] Where R si ′ is the updated stator yoke reluctance in the same magnetic circuit, φ s is the stator yoke flux, w s is the stator yoke magnetic circuit width; the updated stator yoke reluctance expression between different magnetic circuits is

[0035]

[0036] Where R so ′ is the stator yoke reluctance between different magnetic circuits; the updated rotor reluctance expression is:

[0037]

[0038] Where R r ′ is the magnetic resistance of the rotor, φ ris the rotor flux, w r is the rotor magnetic circuit width; the updated reluctance expression of the stator pole is:

[0039]

[0040] Where R p ′ is the magnetic resistance of the stator pole, φ p is the stator pole flux, w p is the stator pole width.

[0041] Furthermore, the nonlinear magnetoresistance equation updated in step 3.3 is expressed as:

[0042] R′(φ)*Φ=U (13)

[0043] Where R′(φ) represents the nonlinear parameter matrix after updating the magnetoresistance expression of the ferromagnetic material in the magnetoresistance matrix, which is converted into a nonlinear equation system about the magnetic flux. Solving the equation system can obtain the magnetic flux considering the saturation effect.

[0044] The air gap flux density expression updated in step 3.4 is:

[0045]

[0046] Where, l g (θ) refers to the air gap length at angle θ, B g (θ) is the air gap flux density corresponding to angle θ, φg k is the magnetic flux of the kth magnetic pole, Rg k is the magnetic resistance of the kth magnetic pole; the magnetic pull expression of each magnetic pole is:

[0047]

[0048] Where A0 is the pole air gap area, F k is the magnetic pull of the kth magnetic pole.

[0049] Furthermore, the apparent inductance expression of the coil solved in step 3.5 is:

[0050] L a =T′R -1 N (16)

[0051] Where T is the coil turns matrix with a dimension of (5n, 4), where the (i, j) element represents the number of turns of the j-th coil around the i-th magnetic flux, and n represents the number of magnetic poles of the magnetic bearing; N represents the coil turns matrix with a dimension of (5n, 1), where the number of turns corresponding to the magnetic pole position is not 0; L a Represents the apparent inductance of the coil winding.

[0052] Furthermore, step 4 includes the following steps:

[0053] Step 4.1. Input the magnetic flux density B of each node and use the neural network to solve the incremental magnetic permeability.

[0054] Step 4.2, replace the absolute magnetic permeability with the incremental magnetic permeability to solve the static magnetic resistance equation;

[0055] Step 4.3: Control the current to increase to a minimum value, freeze the magnetic permeability, and solve the static reluctance equation;

[0056] Step 4.4. Calculate the incremental inductance using the flux matrix under the two currents.

[0057] Furthermore, the incremental permeability expression solved in step 4.1 is:

[0058]

[0059] μ in the formula i is the incremental permeability, lim is the limit symbol, and Δ is the infinitesimal symbol. According to the definition of incremental permeability, the slope of the tangent line of the BH curve of the ferromagnetic material is the incremental permeability.

[0060] The magnetic resistance equations solved in steps 4.2 and 4.3 are:

[0061] R′(φ)*Φ=U(I) (18)

[0062] R′(φ)*Φ=U(I+Δi) (19)

[0063] Where U(I) represents the magnetomotive force matrix under the initial control current, and U(I+Δi) represents the magnetomotive force matrix after the control current increases to the minimum value; respectively solve the coil winding magnetic flux matrix Φ I and Φ I+Δi , which lays the foundation for solving the incremental inductance;

[0064] The incremental inductance expression solved in step 4.4 is:

[0065]

[0066] L in the formula i Indicates the incremental inductance, Φ I and Φ I+Δi represent the coil flux before and after the current is increased, respectively, and Δi represents the increased current value. After the above steps are completed, the dynamic modeling of the radial magnetic bearing considering magnetic saturation, leakage flux, and edge flux is completed.

[0067] Beneficial effects

[0068] (1) The present invention improves the dynamic magnetic circuit method and incorporates the stator and rotor magnetic resistance, leakage flux, eddy current effect and magnetic saturation effect into the model, thereby realizing the modeling of magnetic pull and magnetic flux density under complex working conditions, and significantly improving the model accuracy and practicality.

[0069] (2) This paper introduces a deep neural network to learn and fit the nonlinear BH curve of ferromagnetic materials to output the magnetic permeability in real time. Combined with the frozen permeability technique, the incremental inductance of the coil can be solved under magnetic saturation, thus providing a solid modeling foundation for the displacement demodulation of self-sensing magnetic suspension bearings.

[0070] (3) The modeling method of the present invention has higher robustness and applicability than existing technologies. A comprehensive comparison with finite element modeling and linear simplification methods proves that the modeling accuracy of this method is significantly better than that of existing methods under complex working conditions such as magnetic saturation, magnetic leakage, and eddy current. It does not require iterative solutions, has high computational efficiency, and can meet the needs of real-time control. This method provides a new solution for the application of self-sensing technology in complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a structural schematic diagram of the radial magnetic bearing in the present invention;

[0072] Figure 2 Schematic diagram of the magnetoresistance model established by the present invention;

[0073] Figure 3 This is the basic flow chart of BH neural network training and reasoning in the present invention;

[0074] Figure 4 This is the basic flow chart of the magnetic saturation solution algorithm in the present invention;

[0075] Figure 5 This is a diagram showing the modeling results of the air gap magnetic flux density of the present invention;

[0076] Figure 6 1 is a diagram showing radial magnetic tension modeling results of the present invention and other methods used for comparison;

[0077] Figure 7 1 is a diagram of incremental inductance modeling results of the present invention and other methods for comparison.

[0078] Figure Numbers

[0079] 1 stator yoke between two magnetic circuits, 2 stator yoke within the same magnetic circuit, 3 rotor, 4 stator pole coil of magnetic bearing, 5 magnetic pole of magnetic bearing, 6 reluctance of stator yoke within the same magnetic circuit, 7 reluctance of stator yoke between two magnetic circuits, 8 magnetomotive force of stator pole coil of magnetic bearing, 9 reluctance of stator pole of magnetic bearing, 10 leakage reluctance of magnetic bearing, 11 air gap reluctance of magnetic bearing, 12 rotor reluctance of magnetic bearing, a1-a16 stator yoke-coil-stator pole-leakage magnetic circuit, b1-b16 leakage magnetic-air gap-rotor magnetic circuit, c large circuit of stator yoke of all outer poles, d large circuit of leakage magnetic path in the middle, e large circuit of inner rotor. DETAILED DESCRIPTION

[0080] The following will describe in detail the implementation of the present invention in conjunction with the accompanying drawings and specific implementation cases.

[0081] A method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network of the present invention comprises the following steps:

[0082] Step 1: Use the magnetic circuit model and reluctance theory to calculate the expressions of the magnetic bearing stator yokes 1 and 2, rotor 3, stator poles 5, air gap reluctance 11, and leakage reluctance 10, and establish a static reluctance equation. Reluctance theory equates each part of the magnetic field to the resistance of the circuit, the magnetic flux generated by the pole coil 4 to the current, and the pole coil 4 to the magnetomotive force 8 of the reluctance model, which facilitates the solution. The magnetic circuit is the equivalent circuit. Specifically, the following steps are included:

[0083] Step 1.1, mathematically modeling the magnetic resistance of ferromagnetic materials such as the stator yoke, rotor, and stator poles (reference numerals 6, 7, 9, and 12);

[0084] Step 1.2, mathematically modeling the air gap between the stator pole and the rotor, and the leakage magnetic reluctance (reference numerals 10 and 11);

[0085] Step 1.3, set the magnetomotive force of each magnetic pole of the magnetic bearing (see Figure 8) and establish the static reluctance equation; the static reluctance equation is

[0086] R*Φ=U (1)

[0087] Where Φ is the 5n-dimensional magnetic flux matrix to be determined, n is the number of magnetic poles of the magnetic bearing, R is the reluctance coefficient matrix, and U is the magnetomotive force matrix of the magnetic pole coil.

[0088] Step 1.4: Complete the construction of the magnetic flux loop for the entire electromagnetic bearing model. This includes the stator yoke-coil-stator pole-leakage flux loop (reference numerals a1-a16), the leakage flux-air gap-rotor magnetic loop (reference numerals b1-b16), the outer stator yoke loop for all magnetic poles (reference numeral c), the central leakage flux path loop (reference numeral d), and the inner rotor loop (reference numeral e).

[0089] The magnetoresistance equation requires the magnetoresistance of each part as the equation coefficient. Therefore, the magnetoresistance of each part must be modeled and solved in the first two steps before the magnetoresistance equation can be calculated.

[0090] Step 2: Use a deep neural network to learn the magnetic saturation data of the stator and rotor ferromagnetic materials to mathematically model the change in absolute magnetic permeability during magnetic saturation. The magnetic saturation data is the calibration data of the ferromagnetic material, that is, the BH curve of the ferromagnetic material. The specific steps include the following:

[0091] Step 2.1: Organize the correlation data of the magnetic flux density B and magnetic field intensity H of the ferromagnetic material, and use interpolation technology between data points to increase valid data for training;

[0092] Interpolation is a technique that inserts new data between two adjacent points to increase the amount of data. Because the original BH curve data volume is not large enough, training the neural network requires more data, so interpolation is required.

[0093] Step 2.2: Build a deep neural network model NetBH to learn the mapping from magnetic flux density B to magnetic field intensity H in the BH curve; the error calculation of the neural network takes the maximum error between the original data; and the error back propagation method is used to update the network parameters.

[0094] Step 3: Use the magnetic permeability with neural network to recalculate the magnetic resistance of the ferromagnetic material and solve the nonlinear magnetic resistance equation that replaces the magnetic resistance expression. The specific steps include the following:

[0095] Step 3.1, replace the magnetic permeability of the magnetoresistance matrix with a form containing a neural network expression;

[0096] The absolute permeability expression updated in step 3.1 is:

[0097]

[0098] Where w is the effective width of the ferromagnetic material magnetic circuit, φ is the magnetic flux of the ferromagnetic material, μ is the effective width of the ferromagnetic material magnetic circuit, a The absolute permeability is updated to take into account the magnetic saturation effect.

[0099] Step 3.2, recalculate the reluctance coefficient of the stator and rotor ferromagnetic materials; the updated reluctance expression of the stator yoke in the same magnetic circuit is:

[0100]

[0101] Where R si ′ is the updated stator yoke reluctance in the same magnetic circuit, φ s is the stator yoke flux, w s is the stator yoke magnetic circuit width; the updated stator yoke reluctance expression between different magnetic circuits is

[0102]

[0103] Where R so ′ is the stator yoke reluctance between different magnetic circuits; the updated rotor reluctance expression is:

[0104]

[0105] Where R r ′ is the magnetic resistance of the rotor, φ r is the rotor flux, w r is the rotor magnetic circuit width; the updated reluctance expression of the stator pole is:

[0106]

[0107] Where R p ′ is the magnetic resistance of the stator pole, φ p is the stator pole flux, w p is the stator pole width.

[0108] Step 3.3: Update the nonlinear magnetoresistance equation and solve the flux matrix including the saturation effect. The updated nonlinear magnetoresistance equation is expressed as:

[0109] R′(φ)*Φ=U (13)

[0110] Where R′(φ) represents the nonlinear parameter matrix after updating the magnetoresistance expression of the ferromagnetic material in the magnetoresistance matrix, which is converted into a nonlinear equation system about the magnetic flux. Solving the equation system can obtain the magnetic flux considering the saturation effect.

[0111] Step 3.4, solve the air gap magnetic flux density and magnetic pull of each magnetic pole; the updated air gap magnetic flux density expression is:

[0112]

[0113] Where, l g (θ) refers to the air gap length at angle θ, B g (θ) is the air gap flux density corresponding to angle θ, φg k is the magnetic flux of the kth magnetic pole, Rg kis the magnetic resistance of the kth magnetic pole; the magnetic pull expression of each magnetic pole is:

[0114]

[0115] Where A0 is the pole air gap area, F k is the magnetic pull of the kth magnetic pole.

[0116] Step 3.5. Calculate the apparent inductance of each coil winding. The expression for the apparent inductance of the coil is:

[0117] L a =T′R -1 N (16)

[0118] Where T is the coil turns matrix with a dimension of (5n, 4), where the (i, j) element represents the number of turns of the j-th coil around the i-th magnetic flux, and n represents the number of magnetic poles of the magnetic bearing; N represents the coil turns matrix with a dimension of (5n, 1), where the number of turns corresponding to the magnetic pole position is not 0; L a Represents the apparent inductance of the coil winding.

[0119] Step 4: Use the neural network to update the incremental permeability, freeze and replace the absolute permeability to solve the static magnetic resistance equation and calculate the incremental inductance. The specific steps include the following:

[0120] Step 4.1. Input the magnetic flux density B of each node and use the neural network to solve the incremental magnetic permeability. The expression of the solved incremental magnetic permeability is:

[0121]

[0122] μ in the formula i is the incremental permeability, lim is the limit symbol, and Δ is the infinitesimal symbol. According to the definition of incremental permeability, the slope of the tangent line of the BH curve of the ferromagnetic material is the incremental permeability.

[0123] Step 4.2, replace the absolute magnetic permeability with the incremental magnetic permeability to solve the static magnetic resistance equation;

[0124] Step 4.3: Control the current to increase to a minimum value, freeze the magnetic permeability, and solve the static reluctance equation;

[0125] The expressions of the magnetic resistance equations solved in steps 4.2 and 4.3 are:

[0126] R′(φ)*Φ=U(I) (18)

[0127] R′(φ)*Φ=U(I+Δi) (19)

[0128] Where U(I) represents the magnetomotive force matrix under the initial control current, and U(I+Δi) represents the magnetomotive force matrix after the control current increases to the minimum value; respectively solve the coil winding magnetic flux matrix Φ I and Φ I+Δi , which lays the foundation for solving the incremental inductance;

[0129] Step 4.4. Calculate the incremental inductance using the flux matrix under the two currents. The incremental inductance expression is:

[0130]

[0131] L in the formula i Indicates the incremental inductance, Φ I and Φ I+Δi represent the coil flux before and after the current is increased, respectively, and Δi represents the increased current value. After the above steps are completed, the dynamic modeling of the radial magnetic bearing considering magnetic saturation, leakage flux, and edge flux is completed.

[0132] Example

[0133] The structural diagram of the radial magnetic bearing selected in this embodiment is as follows Figure 1 As shown, the magnetic bearing has 16 magnetic poles and adopts the currently commonly used C-type magnetic pole arrangement. The input is the coil winding control current in the four directions of up, down, left, and right and the eccentricity of the rotor. The target output is the magnetic pull of the magnetic bearing pole, the air gap magnetic flux density distribution, the apparent inductance and incremental inductance of the coil winding when considering the magnetic saturation effect, that is, to achieve the magnetic saturation state modeling of the radial magnetic bearing. The modeling steps are as follows:

[0134] First, according to step 1 Figure 1 Mathematically model the magnetic reluctance of the stator yoke, stator poles, rotor, air gap, and leakage path in the magnetic bearing. Calculate the reluctance of each component and sort them by pole number from 1 to 16 to use them as the coefficients of the static reluctance matrix. Given 16 poles, the reluctance matrix R has a dimension of (80,80).

[0135] Figure 2 It is a drawn reluctance model. The energized coil acts as the magnetomotive force. Each magnetic pole corresponds to 5 reluctances: stator yoke reluctance R s , stator pole reluctance R p , leakage magnetic resistance R l , air gap magnetic resistance R g and rotor reluctance R r The initial static magnetic resistance form is the same as above and will not be repeated here.

[0136] To determine the coefficient matrix of the magnetic resistance equation, it is necessary to list the magnetic circuit equations of each magnetic closed loop according to Kirchhoff's magnetic circuit law.

[0137] Figure 2 The a1-a16 stator yoke-coil-stator pole-leakage magnetic circuit equation is:

[0138] Rp k *φp k +Rp k+1 *φp k+1 +Rl k *φl k +Rs k *φs k =Ni k +Ni k+1 (41)

[0139] Where φp is the magnetic flux of the magnetic pole circuit, φl is the magnetic reluctance of the leakage magnetic circuit, φs is the magnetic flux of the rotor magnetic circuit, N is the number of coil turns of a single magnetic pole, and i is the coil current. When the loop number k is an even number, that is, it is located between adjacent magnetic circuits, the magnetic circuit equation is:

[0140] Rp k *φp k -Rp k+1 *φp k+1 +Rl k *φl k +Rs k *φs k =Ni k -Ni k+1 (42)

[0141] The left side of the above formula is the magnetic voltage drop, and the right side is the magnetomotive force generated by the coil.

[0142] Then, derive Figure 2 Similarly, when the loop number k is an odd number, that is, it is located in the same magnetic circuit, the magnetic circuit equation is:

[0143] Rl k *φl k -Rg k *φg k -Rr k *φr k -Rg k+1 *φg k+1 =0 (43)

[0144] When the loop number k is an even number, that is, it is located between adjacent magnetic circuits, the magnetic circuit equation is:

[0145] Rl k *φl k -Rg k *φgk -Rr k *φr k +Rg k+1 *φg k+1 =0 (44)

[0146] In the above formula, φg is the air gap magnetic flux, and φr is the rotor magnetic flux.

[0147] Furthermore, each magnetic circuit has three nodes: the stator yoke, the magnetic poles, and the rotor. According to Kirchhoff's laws for magnetic circuits, the magnitude of the input flux at each node should be equal to the magnitude of the output flux. Therefore, we first list the magnetic circuit equations at the stator yoke nodes. When the pole number k is an odd number, each flux satisfies:

[0148] φs k-1 +φp k -φs k =0 (45)

[0149] When the pole number k is an even number, each magnetic flux satisfies:

[0150] φs k-1 -φp k +φs k =0 (46)

[0151] The magnetic circuit equations at the magnetic pole nodes are then listed. When the magnetic pole number k is an odd number, the magnetic flux satisfies:

[0152] φl k-1 +φp k -φg k -φl k =0 (47)

[0153] When the pole number k is an even number, each magnetic flux satisfies:

[0154] φl k-1 -φp k +φg k +φl k =0 (48)

[0155] Finally, the magnetic circuit equations at the rotor nodes are listed. When the pole number k is an odd number, the magnetic flux satisfies:

[0156] φr k-1 +φg k -φr k =0 (49)

[0157] When the pole number k is an even number, each magnetic flux satisfies:

[0158] φr k-1 -φg k +φrk =0 (50)

[0159] At this point, theoretically, 80 magnetic circuit equations of 5 equation groups have been established. Combining the equation groups on the left and right sides can obtain the magnetic resistance equation:

[0160] R*Φ=U (51)

[0161] Where R is the reluctance matrix, Φ is the magnetic flux matrix, and U is the magnetomotive force matrix.

[0162] In some cases, the above magnetoresistance matrix is ​​not full rank, then it is necessary to add Figure 2 The magnetic circuit equations of the c, d, and e large loops in the figure. Assuming that the magnetic pressure drop is 0 after one circle of the magnetic circuit, the equations of the magnetic circuits c, d, and e are listed respectively:

[0163]

[0164] Where ∑ represents the summation symbol and n is the counter. Substituting any of the three equations for the magnetoresistance coefficient in the last row achieves the full rank of the magnetoresistance matrix.

[0165] After the static magnetic circuit equation is established, according to Figure 3 The training algorithm is used to train the deep neural network to realize the modeling of ferromagnetic material characteristics. The error back propagation algorithm is used to iteratively update the network parameters until the mapping error of the neural network from magnetic flux density B to magnetic field intensity H is less than 10 -6 The error calculation uses the maximum error from the original data point to ensure that the neural network passes through the original data point as much as possible.

[0166] according to Figure 3 The permeability update algorithm with neural network recalculates the reluctance of ferromagnetic materials and solves the nonlinear reluctance equation with the replaced reluctance expression. The updated absolute permeability expression is:

[0167]

[0168] Where w is the effective width of the ferromagnetic material magnetic circuit, φ is the magnetic flux of the ferromagnetic material, μ is the effective width of the ferromagnetic material magnetic circuit, a The absolute permeability is updated to take into account the magnetic saturation effect.

[0169] according to Figure 3 The stator yoke reluctance expression in the same magnetic circuit updated with the new magnetic permeability is:

[0170]

[0171] Where R si ′ is the updated stator yoke reluctance in the same magnetic circuit, φ s is the stator yoke flux, w sis the stator yoke magnetic circuit width.

[0172] according to Figure 3 The stator yoke reluctance expression between different magnetic circuits after the new magnetic permeability is updated is:

[0173]

[0174] Where R so ' is the stator yoke reluctance between different magnetic circuits.

[0175] according to Figure 3 The updated rotor reluctance expression for the new magnetic permeability is:

[0176]

[0177] Where R r ′ is the magnetic resistance of the rotor, φ r is the rotor flux, w r is the rotor magnetic circuit width.

[0178] according to Figure 3 The reluctance expression of the stator pole after the new magnetic permeability is updated as:

[0179]

[0180] Where R p ′ is the magnetic resistance of the stator pole, φ p is the stator pole flux, w p is the stator pole width.

[0181] according to Figure 4 The magnetic saturation state magnetic bearing modeling method is used to bring the updated ferromagnetic material reluctance expression back to the static reluctance equation, and the obtained nonlinear reluctance equation expression is:

[0182] R′(φ)*Φ=U (58)

[0183] Where R′(φ) represents the nonlinear parameter-containing matrix after updating the magnetoresistance expression of the ferromagnetic material in the magnetoresistance matrix, which is converted into a nonlinear equation system about the magnetic flux. Solving the equation system can obtain the magnetic flux considering the saturation effect.

[0184] according to Figure 4 The magnetic bearing modeling algorithm is used to determine the air gap flux density expression of the 16-pole radial magnetic bearing:

[0185]

[0186] Where, l g (θ) refers to the air gap length at angle θ, B g(θ) is the air gap flux density corresponding to angle θ, φg k is the magnetic flux of the kth magnetic pole, Rg k is the magnetic resistance of the kth magnetic pole. The magnetic flux density curve of each magnetic pole of the magnetic bearing calculated by this method is plotted on Figure 5 The magnetic flux density modeling error of the present invention is maintained within 3%.

[0187] The magnetic pull expression of each magnetic pole of the 16-pole radial magnetic bearing can be further solved as:

[0188]

[0189] Where A0 is the pole air gap area, F k is the magnetic pull of the kth magnetic pole. The relationship curve between the radial magnetic pull of the magnetic bearing calculated by this method and the rotor eccentricity and control current is plotted on Figure 6 The magnetic tension modeling error of the present invention is maintained within 5%.

[0190] Using the solved magnetic flux matrix, determine the nonlinear magnetic resistance matrix R'. Figure 4 The modeling algorithm of the magnetic bearing is used to find the apparent inductance expression of the 16-pole radial magnetic bearing coil:

[0191] L a =T′R′- 1 N (61)

[0192] Where T is the coil turns matrix, with a dimension of (80, 4), where the (i, j) element represents the number of turns of the j-th coil around the i-th magnetic flux, and n represents the number of magnetic poles in the magnetic bearing. N represents the coil turns matrix, with a dimension of (80, 1), where only the number of turns corresponding to the magnetic pole position is not zero. L a represents the apparent inductance of the 16-pole radial magnetic bearing coil winding to be determined.

[0193] use Figure 4 The frozen permeability algorithm is shown to solve the incremental inductance. The incremental permeability is updated using a neural network, and the expression for the incremental permeability of ferromagnetic materials considering magnetic saturation is:

[0194]

[0195] μ in the formula i is the incremental permeability, lim is the limit symbol, and Δ is the infinitesimal symbol.

[0196] Next, we use incremental permeability to replace absolute permeability and solve the static reluctance equation. We use the definition of incremental inductance to solve it, increase the control current of each pole coil to a minimum value, and freeze the permeability to solve the reluctance equation separately:

[0197] R′(φ)*Φ=U(I) (63)

[0198] R′(φ)*Φ=U(I+Δi) (64)

[0199] Where U(I) represents the magnetomotive force matrix under the initial control current, and U(I+Δi) represents the magnetomotive force matrix after the control current increases to the minimum value. The two solve the coil winding magnetic flux matrix Φ I and Φ I+Δi , laying the foundation for solving the incremental inductance.

[0200] Finally, the incremental inductance is calculated using the flux matrix under the two currents and the definition of incremental inductance. The incremental inductance expression is:

[0201]

[0202] Where, L i Indicates the incremental inductance, Φ I and Φ I+Δi The incremental inductance of the magnetic bearing coil calculated by this method is plotted on Figure 7 In the present invention, the incremental inductance modeling error is maintained within 1% before entering the magnetic saturation state, and is maintained within 3% when reaching the magnetic saturation state.

[0203] After completing the above steps, the modeling of a 16-pole radial magnetic bearing example considering magnetic saturation, leakage flux, and fringing flux can be completed.

[0204] The method of the present invention is not limited to 16-pole radial magnetic bearings, but can also be used with all radial magnetic bearings with similar structures, without requiring the number of magnetic poles. In addition, the modeling method for magnetic saturation can be applied to all active magnetic bearings.

[0205] The above contents of the present invention are only preferred embodiments of the present invention and are not intended to limit the implementation scheme of the present invention. Ordinary technicians in this field can easily make corresponding changes or modifications based on the main concepts and spirit of the present invention. Therefore, the scope of protection of the present invention shall be based on the scope of protection required by the claims.

Claims

1. A modeling method for radial magnetic bearings in magnetic saturation state based on deep neural network, characterized in that: The following steps are involved: Step 1: Calculate the magnetic reluctance expressions of the stator yoke, rotor, stator pole, air gap and leakage magnetic flux of the magnetic suspension bearing through the magnetic circuit model and reluctance theory, and establish the static reluctance equation; Step 2: Use a deep neural network to learn the magnetic saturation data of the stator and rotor ferromagnetic materials to mathematically model the change in absolute magnetic permeability during magnetic saturation. Step 3: Recalculate the magnetic reluctance of the ferromagnetic material using the magnetic permeability including the neural network, and solve the nonlinear magnetic reluctance equation that replaces the magnetic reluctance expression; Step 4: Use the neural network to update the incremental permeability, freeze and replace the absolute permeability to solve the static magnetic resistance equation and calculate the incremental inductance.

2. The method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network according to claim 1 is characterized in that: The step 1 comprises the following steps: Step 1.1, mathematically model the magnetic reluctance of ferromagnetic materials such as the stator yoke, rotor, and stator poles; Step 1.2, mathematically model the air gap between the stator pole and the rotor, and the leakage magnetic reluctance; Step 1.3: Set the magnetomotive force of each magnetic pole of the magnetic bearing and establish the static reluctance equation; The static magnetoresistance equation is R*Φ=U (1) Where Φ is the 5n-dimensional magnetic flux matrix to be determined, n is the number of magnetic poles of the magnetic bearing, R is the reluctance coefficient matrix, and U is the magnetomotive force matrix of the magnetic pole coil.

3. The method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network according to claim 1 is characterized in that: The step 2 comprises the following steps: Step 2.1: Organize the correlation data of the magnetic flux density B and magnetic field intensity H of the ferromagnetic material, and use interpolation technology between data points to increase valid data for training; Step 2.2: Build a deep neural network model to learn the mapping from magnetic flux density B to magnetic field intensity H in the BH curve; the error calculation of the neural network takes the maximum error between the original data; and the network parameters are updated using the forward or back propagation method.

4. The method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network according to claim 1 is characterized in that: The step 3 comprises the following steps: Step 3.1, replace the magnetic permeability of the magnetoresistance matrix with a form containing a neural network expression; Step 3.2, recalculate the reluctance coefficient of the stator and rotor ferromagnetic materials; Step 3.3, update the nonlinear magnetoresistance equation and solve the flux matrix including the saturation effect; Step 3.4, solve the air gap magnetic flux density and magnetic pull of each magnetic pole; Step 3.

5. Calculate the apparent inductance of each coil winding.

5. The method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network according to claim 4 is characterized in that: The absolute permeability expression updated in step 3.1 is: Where w is the effective width of the ferromagnetic material magnetic circuit, φ is the magnetic flux of the ferromagnetic material, μ is the effective width of the ferromagnetic material magnetic circuit, a The absolute permeability is updated to take into account the magnetic saturation effect.

6. The method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network according to claim 4 is characterized in that: The stator yoke reluctance expression in the same magnetic circuit updated in step 3.2 is: Where R si ′ is the updated stator yoke reluctance in the same magnetic circuit, φ s is the stator yoke flux, w s is the stator yoke magnetic circuit width; the updated stator yoke reluctance expression between different magnetic circuits is Where R so ′ is the stator yoke reluctance between different magnetic circuits; the updated rotor reluctance expression is: Where R r ′ is the magnetic resistance of the rotor, φ r is the rotor flux, w r is the rotor magnetic circuit width; the updated reluctance expression of the stator pole is: Where R p ′ is the magnetic resistance of the stator pole, φ p is the stator pole flux, w p is the stator pole width.

7. The method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network according to claim 4 is characterized in that: The nonlinear magnetoresistance equation updated in step 3.3 is expressed as follows: R′(φ)*Φ=U (13) Where R′(φ) represents the nonlinear parameter matrix after updating the magnetoresistance expression of the ferromagnetic material in the magnetoresistance matrix, which is converted into a nonlinear equation system about the magnetic flux. Solving the equation system can obtain the magnetic flux considering the saturation effect. The air gap flux density expression updated in step 3.4 is: Where, l g (θ) refers to the air gap length at angle θ, B g (θ) is the air gap flux density corresponding to angle θ, φg k is the magnetic flux of the kth magnetic pole, Rg k is the magnetic resistance of the kth magnetic pole; the magnetic pull expression of each magnetic pole is: Where A0 is the pole air gap area, F k is the magnetic pull of the kth magnetic pole.

8. The method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network according to claim 4 is characterized in that: The apparent inductance expression of the coil solved in step 3.5 is: L a =T′R -1 N (16) Where T is the coil turns matrix with a dimension of (5n, 4), where the (i, j) element represents the number of turns of the j-th coil around the i-th magnetic flux, and n represents the number of magnetic poles of the magnetic bearing; N represents the coil turns matrix with a dimension of (5n, 1), where the number of turns corresponding to the magnetic pole position is not 0; L a Represents the apparent inductance of the coil winding.

9. The method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network according to claim 1, characterized in that: The step 4 comprises the following steps: Step 4.

1. Input the magnetic flux density B of each node and use the neural network to solve the incremental magnetic permeability. Step 4.2, replace the absolute magnetic permeability with the incremental magnetic permeability to solve the static magnetic resistance equation; Step 4.3: Control the current to increase to a minimum value, freeze the magnetic permeability, and solve the static reluctance equation; Step 4.

4. Calculate the incremental inductance using the flux matrix under the two currents.

10. The method for modeling a radial magnetic bearing in a magnetic saturation state based on a deep neural network according to claim 9, characterized in that: The incremental permeability expression solved in step 4.1 is: Where μ i is the incremental permeability, lim is the limit symbol, and Δ is the infinitesimal symbol. According to the definition of incremental permeability, the slope of the tangent line of the BH curve of the ferromagnetic material is the incremental permeability. The magnetic resistance equations solved in steps 4.2 and 4.3 are: R′(φ)*Φ=U(I) (18) R′(φ)*Φ=U(I+Δi) (19) Where U(I) represents the magnetomotive force matrix under the initial control current, and U(I+Δi) represents the magnetomotive force matrix after the control current increases to the minimum value; Solve the coil winding magnetic flux matrix Φ separately I and Φ I+Δi , which lays the foundation for solving the incremental inductance; The incremental inductance expression solved in step 4.4 is: Where, L i Indicates the incremental inductance, Φ I and Φ I+Δi represent the coil flux before and after the current is increased, respectively, and Δi represents the increased current value. After the above steps are completed, the dynamic modeling of the radial magnetic bearing considering magnetic saturation, leakage flux, and edge flux is completed.

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