Simulation and optimization method of magnetic suspension continuous casting process

Abstract

The present invention relates to the technical field of optimization of magnetic suspension continuous casting process, and specifically, to a simulation and optimization method of magnetic suspension continuous casting process. It includes the following steps: establishing boundary conditions of magnetic suspension continuous casting process and design constraints under multi-physical fields; combining multi-physical field coupling simulation technology with evolutionary topology optimization algorithm to establish a new multi-field evolutionary topology simulation model; using inverse optimization solution technology and evolutionary topology optimization algorithm to deduce current distribution, and gradually adjust the current configuration of electromagnetic coil to achieve the optimal coupling relationship with electromagnetic field distribution; real-time acquisition of temperature field and electromagnetic field data of the system, and evaluation of electromagnetic field distribution and cooling effect. The simulation and optimization method of magnetic suspension continuous casting process dynamically adjusts coil design by combining multi-physical field simulation and evolutionary topology optimization technology, and uses inverse optimization solution technology to accurately control current distribution, optimize electromagnetic field and cooling effect, and achieve stable suspension and uniform cooling in magnetic suspension continuous casting process.

Description

Technical Field

[0001] The invention relates to the technical field of magnetic suspension continuous casting process optimization, and in particular to a magnetic suspension continuous casting process simulation and optimization method. Background Art

[0002] The simulation and optimization method of the magnetic levitation continuous casting process aims to optimize the coupling between the electromagnetic field and the cooling process and improve the stability of the material solidification quality. By combining multi-physics field coupling simulation with evolutionary topology optimization algorithm, the electromagnetic field intensity distribution, current configuration and material cooling rate are controlled to achieve uniform cooling, stable suspension and optimization of material properties in the magnetic levitation continuous casting process.

[0003] Existing magnetic levitation continuous casting process optimization methods usually find it difficult to simultaneously optimize the synergy between the electromagnetic field and the cooling system. Due to the interaction between the temperature field, fluid field and electromagnetic field, the material is prone to uneven thermal stress during solidification, which in turn causes solidification cracks and instability between the current configuration and magnetic levitation. Therefore, a magnetic levitation continuous casting process simulation and optimization method is provided. Summary of the invention

[0004] The purpose of the present invention is to provide a simulation and optimization method for the magnetic levitation continuous casting process, so as to solve the problems raised in the above background technology that due to the interaction of temperature field, fluid field and electromagnetic field, the material is prone to uneven thermal stress during solidification, which in turn causes solidification cracks, as well as the instability between current configuration and magnetic levitation.

[0005] To achieve the above object, the present invention provides a method for simulating and optimizing a magnetic suspension continuous casting process, comprising the following steps:

[0006] S1. Establish boundary conditions of magnetic suspension continuous casting process and design constraints under multi-physics fields;

[0007] S2. Combine multi-physics field coupling simulation technology with evolutionary topology optimization algorithm to establish a new multi-field evolutionary topology simulation model that includes electromagnetic field, thermal field and fluid field coupling, and dynamically adjust the physical design of the coil;

[0008] S3, using inverse optimization solution technology and evolutionary topology optimization algorithm, reversely deduce the current distribution according to the predetermined magnetic field and cooling target, and gradually adjust the current configuration of the electromagnetic coil to achieve the optimal coupling relationship with the electromagnetic field distribution through optimization iteration;

[0009] S4. Collect the temperature field and electromagnetic field data of the system in real time to evaluate the electromagnetic field distribution and cooling effect.

[0010] As a further improvement of the technical solution, in S1, the boundary conditions of the magnetic suspension continuous casting process and the design constraints under the multi-physical field are established, which are as follows:

[0011] S1.1. Multi-physics fields include electromagnetic fields, thermal fields and fluid fields;

[0012] S1.2. Setting electromagnetic field strength limits:

[0013] ;

[0014] ;

[0015] in, Represents the inner normal component of the magnetic induction intensity and the outward normal component continuous at the border; Indicates the magnitude of magnetic induction Not exceeding the maximum magnetic field strength ;

[0016] S1.3. Set the maximum allowable temperature gradient of the thermal field:

[0017] ;

[0018] in, Indicates the temperature gradient of the thermal field Do not exceed the maximum temperature gradient ;

[0019] S1.4. Set the boundary conditions of the fluid field:

[0020] ;

[0021] ;

[0022] ;

[0023] in, Indicates fluid velocity Equal to the boundary fluid velocity ; Indicates that the fluid outlet pressure is equal to Environmental pressures; Indicates the velocity of the fluid Do not exceed the maximum fluid flow rate .

[0024] As a further improvement of the technical solution, in S2, the multi-physical field coupling simulation technology is combined with the evolutionary topology optimization algorithm to establish a new multi-field evolutionary topology simulation model including electromagnetic field, thermal field and fluid field coupling, and dynamically adjust the physical design of the coil. The specific steps are as follows:

[0025] S2.1. Based on the limitation of electromagnetic field strength and the initial design of the coil, the initial model of the electromagnetic field is described using Maxwell's equations:

[0026] ;

[0027] in, is the magnetic induction intensity The divergence of is the magnetic induction intensity; is the magnetic field strength The curl of This means that there are no magnetic monopoles at any point; is the magnetic field strength; is the current density;

[0028] Establish the initial thermal field model:

[0029] ;

[0030] in, is the thermal conductivity; is the temperature gradient; is the heat source term;

[0031] Establish the initial fluid field model:

[0032] ;

[0033] in, is the density of the fluid; is the fluid velocity; is the fluid velocity About Time The local derivative of is the convection term; is the pressure gradient; is the dynamic viscosity of the fluid; is the Laplace operator; is the driving force of the fluid field;

[0034] S2.2, coupling the electromagnetic field initial model, the thermal field initial model and the fluid field initial model to establish a multi-physics field coupling simulation;

[0035] S2.3. Based on the multi-physical field coupling simulation and the evolutionary topology optimization algorithm, a new multi-field evolutionary topology simulation model is established to dynamically adjust the coil geometry and material distribution to achieve the optimal coupling of electromagnetic field, thermal field and fluid field.

[0036] As a further improvement of the technical solution, in S2.2, the electromagnetic field initial model, the thermal field initial model and the fluid field initial model are coupled to establish a multi-physical field coupling simulation, and the specific steps are as follows:

[0037] S2.2.1. Current loss in electromagnetic field As a heat source, couple the electromagnetic field with the thermal field:

[0038] ;

[0039] S2.2.2. Using the Lorentz force in the electromagnetic field As the driving force of the fluid field, the electromagnetic field is coupled with the fluid field:

[0040] ;

[0041] S2.2.3. According to the temperature distribution in the thermal field , calculate the fluid buoyancy Act on the fluid field and modify the fluid field driving force to couple the thermal field with the fluid field:

[0042] ;

[0043] in, is the buoyancy of the fluid.

[0044] As a further improvement of the technical solution, in S2.3, a new multi-field evolutionary topology simulation model is established through an evolutionary topology optimization algorithm according to multi-physical field coupling simulation, and the coil geometry and material distribution are dynamically adjusted to achieve optimal coupling of electromagnetic field, thermal field and fluid field. The specific steps are as follows:

[0045] S2.3.1. Combine multi-physics coupling simulation with evolutionary topology optimization algorithm to construct coil optimization objective function:

[0046] ;

[0047] in, To control the weight of electromagnetic loss in the objective function; To control the weight of temperature gradient on the objective function; To control the weight of the fluid velocity field on the objective function; To optimize the area; is the temperature gradient; is the square of the fluid velocity;

[0048] S2.3.2, based on the coil optimization objective function and the boundary conditions of the magnetic suspension continuous casting process and the design constraints under multi-physics fields, the evolutionary topology optimization algorithm is used to dynamically adjust the coil geometry and material distribution;

[0049] S2.3.3. Initial design variables are the material distribution of the coil and geometric structures;

[0050] S2.3.4. Use the finite element method to solve the coupled equations of the electromagnetic field, thermal field and fluid field to obtain the electromagnetic field distribution , thermal field distribution and fluid field distribution , and calculate the coil optimization objective function value:

[0051] ;

[0052] in, To control the weight of electromagnetic loss in the objective function; To control the weight of temperature gradient on the objective function; To control the weight of the fluid velocity field on the objective function; To optimize the area;

[0053] S2.3.5. Calculate the Secondary design variables Impact on the coil optimization objective function and update the design variables:

[0054] ;

[0055] in, For the Iteration design variables; For the Iteration design variables; is the learning rate; For the The optimization objective function of the first iteration coil is relative to that of the Iteration design variables The gradient of

[0056] S2.3.6. When the change of the coil optimization objective function in two consecutive iterations is less than the set threshold , then the coil optimization objective function has converged:

[0057] ;

[0058] in, For the Iterative coil optimization objective function; Optimize the objective function convergence threshold for the coil;

[0059] S2.3.7. If the change of the design variable in two consecutive iterations is less than the set threshold, the design variable has converged:

[0060] ;

[0061] in, For the Iteration design variables With Iteration design variables The difference between

[0062] S2.3.8. When the coil optimization objective function and design variables meet the convergence conditions, the optimal coil physical design is output. :

[0063] ;

[0064] in, For optimal coil physical design; Represents the design variables that minimize the coil optimization objective function .

[0065] As a further improvement of the present technical solution, in S3, the inverse optimization solution technology and the evolutionary topology optimization algorithm are used to reversely deduce the current distribution according to the predetermined magnetic field and cooling target, and the current configuration of the electromagnetic coil is gradually adjusted through optimization iteration to achieve the optimal coupling relationship with the electromagnetic field distribution. The specific steps are as follows:

[0066] S3.1. According to the target magnetic induction intensity distribution And the target cooling requirements, establish the current distribution objective function:

[0067] ;

[0068] in, is the current distribution; The current distribution The generated magnetic induction intensity distribution; The current distribution Generates temperature gradient caused by electromagnetic field; is the influence weight of magnetic field on the current distribution objective function; is the weight of the influence of temperature gradient on the current distribution objective function;

[0069] S3.2. According to the target magnetic induction intensity distribution , using inverse optimization solution technology to calculate the target current distribution ;

[0070] S3.3. Gradually adjust the current distribution through sensitivity analysis , so that the current distribution The magnetic induction intensity distribution generated Gradually approach the target magnetic induction intensity distribution ;

[0071] S3.4, iteratively adjusting the current distribution for multiple times until the current distribution objective function converges and the current distribution converges;

[0072] S3.5. When the current distribution objective function and the current distribution both meet the convergence conditions, the optimal current distribution is output. .

[0073] As a further improvement of the technical solution, in S3.2, according to the target magnetic induction intensity distribution , using inverse optimization solution technology to calculate the target current distribution , the specific steps are as follows:

[0074] S3.2.1. According to the target magnetic induction intensity distribution , calculate the target magnetic field strength distribution :

[0075] ;

[0076] in, is the vacuum permeability;

[0077] S3.2.2. Calculate the target current density according to Ampere's law :

[0078] ;

[0079] S3.2.2. According to the target current density , integrate to get the target current distribution :

[0080] ;

[0081] in, is the target current distribution;

[0082] In S3.3, the current distribution is gradually adjusted by sensitivity analysis. , so that the current distribution The magnetic induction intensity distribution generated Gradually approach the target magnetic induction intensity distribution , the specific steps are as follows:

[0083] S3.3.1. Derivation of the current distribution objective function:

[0084] ;

[0085] in, is the sensitivity matrix of magnetic field with respect to current;

[0086] S3.3.2. Use the gradient descent method to iteratively calculate the Iteration current distribution :

[0087] ;

[0088] in, For the Iteration current distribution.

[0089] As a further improvement of the technical solution, in S3.4, the current distribution is adjusted iteratively for multiple times until the current distribution objective function converges and the current distribution converges, as follows:

[0090] S3.4.1. When the change of the current distribution objective function is less than the threshold, the current distribution objective function has converged:

[0091] ;

[0092] in, For the The current distribution objective function value of the iterative current distribution; For the The current distribution objective function value of the iterative current distribution; is the convergence threshold of the current distribution objective function;

[0093] S3.4.2. When the change in current distribution is less than the threshold, the current distribution has converged:

[0094] ;

[0095] in, is the convergence threshold of the current distribution objective function;

[0096] In S3.5, when the current distribution objective function and the current distribution both meet the convergence conditions, the optimal current distribution is output. , the specific method is as follows:

[0097] ;

[0098] in, is the optimal current distribution.

[0099] As a further improvement of the technical solution, in S4, the temperature field and electromagnetic field data of the system are collected in real time to evaluate the electromagnetic field distribution and cooling effect. The specific method is as follows:

[0100] S4.1. Use thermocouples to monitor the real-time temperature distribution on the material surface ; Use magnetic induction sensor to measure real-time magnetic induction intensity ;

[0101] S4.2, according to the real-time magnetic induction intensity , calculate the magnetic induction intensity error ;

[0102] S4.3, based on real-time temperature distribution , calculate the temperature gradient and temperature change rate .

[0103] As a further improvement of the technical solution, in S4.2, according to the real-time magnetic induction intensity , calculate the magnetic induction intensity error , the specific method is as follows:

[0104] ;

[0105] in, It is the real-time magnetic induction intensity; is the target magnetic induction intensity; is the magnetic induction intensity error;

[0106] In S4.3, according to the real-time temperature distribution , calculate the temperature gradient and temperature change rate , the specific method is as follows:

[0107] ;

[0108] ;

[0109] in, is the temperature gradient; is the gradient of the temperature field; For time; is the temperature change rate; For the spatial position Place, time The temperature value at .

[0110] Compared with the prior art, the present invention has the following beneficial effects:

[0111] 1. In the simulation and optimization method of the magnetic levitation continuous casting process, based on the combination of multi-physics field coupling simulation and evolutionary topology optimization algorithm, the geometric shape and material distribution of the electromagnetic coil can be dynamically optimized to ensure the synergistic effect of the electromagnetic field, thermal field and fluid field, improve the stability of magnetic levitation and cooling uniformity, and reduce solidification cracks.

[0112] 2. In the simulation and optimization method of the magnetic levitation continuous casting process, the dynamic adjustment of the current distribution is achieved through the iterative optimization of the inverse optimization solution technology and sensitivity analysis, so that the electromagnetic field distribution and the cooling process are optimally coupled, effectively reducing thermal stress and improving the solidification quality of the material. BRIEF DESCRIPTION OF THE DRAWINGS

[0113] Figure 1 The figure is a flow chart of the overall method of the present invention. DETAILED DESCRIPTION

[0114] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0115] Example:

[0116] See also Figure 1 As shown, this embodiment provides a simulation and optimization method for a magnetic suspension continuous casting process, comprising the following steps:

[0117] S1. Establish boundary conditions of magnetic suspension continuous casting process and design constraints under multi-physics fields;

[0118] In this embodiment S1, the boundary conditions of the magnetic suspension continuous casting process and the design constraints under the multi-physical field are established, as follows:

[0119] S1.1. Multi-physics fields include electromagnetic fields, thermal fields and fluid fields;

[0120] S1.2. Setting electromagnetic field strength limits:

[0121] ;

[0122] ;

[0123] in, Represents the inner normal component of the magnetic induction intensity and the outward normal component continuous at the border; Indicates the magnitude of magnetic induction Not exceeding the maximum magnetic field strength ;

[0124] S1.3. Set the maximum allowable temperature gradient of the thermal field:

[0125] ;

[0126] in, Indicates the temperature gradient of the thermal field Do not exceed the maximum temperature gradient ;

[0127] S1.4. Set the boundary conditions of the fluid field:

[0128] ;

[0129] ;

[0130] ;

[0131] in, Indicates fluid velocity Equal to the boundary fluid velocity ; Indicates that the fluid outlet pressure is equal to Environmental pressures; Indicates the velocity of the fluid Do not exceed the maximum fluid flow rate .

[0132] S2. Combine multi-physics field coupling simulation technology with evolutionary topology optimization algorithm to establish a new multi-field evolutionary topology simulation model that includes electromagnetic field, thermal field and fluid field coupling, and dynamically adjust the physical design of the coil;

[0133] In this embodiment S2, the multi-physics field coupling simulation technology is combined with the evolutionary topology optimization algorithm to establish a new multi-field evolutionary topology simulation model including electromagnetic field, thermal field and fluid field coupling, and dynamically adjust the coil physical design. The specific steps are as follows:

[0134] S2.1. Based on the limitation of electromagnetic field strength and the initial design of the coil, the initial model of the electromagnetic field is described using Maxwell's equations:

[0135] ;

[0136] in, is the magnetic induction intensity The divergence of is the magnetic induction intensity; is the magnetic field strength The curl of This means that there are no magnetic monopoles at any point; is the magnetic field strength; is the current density;

[0137] Establish the initial thermal field model:

[0138] ;

[0139] in, is the thermal conductivity; is the temperature gradient; is the heat source term;

[0140] Establish the initial fluid field model:

[0141] ;

[0142] in, is the density of the fluid; is the fluid velocity; is the fluid velocity About Time The local derivative of is the convection term; is the pressure gradient; is the dynamic viscosity of the fluid; is the Laplace operator; is the driving force of the fluid field;

[0143] S2.2, coupling the electromagnetic field initial model, the thermal field initial model and the fluid field initial model to establish a multi-physics field coupling simulation;

[0144] S2.3. Based on the multi-physical field coupling simulation and the evolutionary topology optimization algorithm, a new multi-field evolutionary topology simulation model is established to dynamically adjust the coil geometry and material distribution to achieve the optimal coupling of electromagnetic field, thermal field and fluid field.

[0145] In this embodiment S2.2, the electromagnetic field initial model, the thermal field initial model and the fluid field initial model are coupled to establish a multi-physics field coupling simulation, and the specific steps are as follows:

[0146] S2.2.1. Current loss in electromagnetic field As a heat source, couple the electromagnetic field with the thermal field:

[0147] ;

[0148] S2.2.2. Using the Lorentz force in the electromagnetic field As the driving force of the fluid field, the electromagnetic field is coupled with the fluid field:

[0149] ;

[0150] S2.2.3. According to the temperature distribution in the thermal field , calculate the fluid buoyancy Act on the fluid field and modify the fluid field driving force to couple the thermal field with the fluid field:

[0151] ;

[0152] in, is the buoyancy of the fluid.

[0153] In this embodiment S2.3, a new multi-field evolutionary topology simulation model is established through an evolutionary topology optimization algorithm according to multi-physical field coupling simulation, and the coil geometry and material distribution are dynamically adjusted to achieve optimal coupling of electromagnetic field, thermal field and fluid field. The specific steps are as follows:

[0154] S2.3.1. Combine multi-physics coupling simulation with evolutionary topology optimization algorithm to construct coil optimization objective function:

[0155] ;

[0156] in, To control the weight of electromagnetic loss in the objective function; To control the weight of temperature gradient on the objective function; To control the weight of the fluid velocity field on the objective function; To optimize the area; is the temperature gradient; is the square of the fluid velocity;

[0157] S2.3.2, based on the coil optimization objective function and the boundary conditions of the magnetic suspension continuous casting process and the design constraints under multi-physics fields, the evolutionary topology optimization algorithm is used to dynamically adjust the coil geometry and material distribution;

[0158] S2.3.3. Initial design variables are the material distribution of the coil and geometric structures;

[0159] S2.3.4. Use the finite element method to solve the coupled equations of the electromagnetic field, thermal field and fluid field to obtain the electromagnetic field distribution , thermal field distribution and fluid field distribution , and calculate the coil optimization objective function value:

[0160] ;

[0161] in, To control the weight of electromagnetic loss in the objective function; To control the weight of temperature gradient on the objective function; To control the weight of the fluid velocity field on the objective function; To optimize the area;

[0162] In this embodiment, is 0.6; is 0.4; is 0.1, and can be further fine-tuned according to specific physical fields and experimental results;

[0163] S2.3.5. Calculate the Secondary design variables Impact on the coil optimization objective function and update the design variables:

[0164] ;

[0165] in, For the Iteration design variables; For the Iteration design variables; is the learning rate; For the The optimization objective function of the first iteration coil is relative to that of the Iteration design variables The gradient of

[0166] S2.3.6. When the change of the coil optimization objective function in two consecutive iterations is less than the set threshold , then the coil optimization objective function has converged:

[0167] ;

[0168] in, For the Iterative coil optimization objective function; Optimize the objective function convergence threshold for the coil;

[0169] S2.3.7. If the change of the design variable in two consecutive iterations is less than the set threshold, the design variable has converged:

[0170] ;

[0171] in, For the Iteration design variables With Iteration design variables The difference between

[0172] S2.3.8. When the coil optimization objective function and design variables meet the convergence conditions, the optimal coil physical design is output. :

[0173] ;

[0174] in, For optimal coil physical design; Represents the design variables that minimize the coil optimization objective function .

[0175] S3, using inverse optimization solution technology and evolutionary topology optimization algorithm, reversely deduce the current distribution according to the predetermined magnetic field and cooling target, and gradually adjust the current configuration of the electromagnetic coil to achieve the optimal coupling relationship with the electromagnetic field distribution through optimization iteration;

[0176] In this embodiment S3, the inverse optimization solution technology and the evolutionary topology optimization algorithm are used to reversely deduce the current distribution according to the predetermined magnetic field and cooling target, and the current configuration of the electromagnetic coil is gradually adjusted through optimization iteration to achieve the optimal coupling relationship between the electromagnetic field distribution and the electromagnetic field distribution. The specific steps are as follows:

[0177] S3.1. According to the target magnetic induction intensity distribution And the target cooling requirements, establish the current distribution objective function:

[0178] ;

[0179] in, is the current distribution; The current distribution The generated magnetic induction intensity distribution; The current distribution Generates temperature gradient caused by electromagnetic field; is the influence weight of magnetic field on the current distribution objective function; is the weight of the influence of temperature gradient on the current distribution objective function;

[0180] S3.2. According to the target magnetic induction intensity distribution , using inverse optimization solution technology to calculate the target current distribution ;

[0181] S3.3. Gradually adjust the current distribution through sensitivity analysis , so that the current distribution The magnetic induction intensity distribution generated Gradually approach the target magnetic induction intensity distribution ;

[0182] S3.4, iteratively adjusting the current distribution for multiple times until the current distribution objective function converges and the current distribution converges;

[0183] S3.5. When the current distribution objective function and the current distribution both meet the convergence conditions, the optimal current distribution is output. .

[0184] In this embodiment S3.2, according to the target magnetic induction intensity distribution , using inverse optimization solution technology to calculate the target current distribution , the specific steps are as follows:

[0185] S3.2.1. According to the target magnetic induction intensity distribution , calculate the target magnetic field strength distribution :

[0186] ;

[0187] in, is the vacuum permeability;

[0188] S3.2.2. Calculate the target current density according to Ampere's law :

[0189] ;

[0190] S3.2.2. According to the target current density , integrate to get the target current distribution :

[0191] ;

[0192] in, is the target current distribution;

[0193] In this embodiment S3.3, the current distribution is gradually adjusted by sensitivity analysis method. , so that the current distribution The magnetic induction intensity distribution generated Gradually approach the target magnetic induction intensity distribution , the specific steps are as follows:

[0194] S3.3.1. Derivation of the current distribution objective function:

[0195] ;

[0196] in, is the sensitivity matrix of magnetic field with respect to current;

[0197] S3.3.2. Use the gradient descent method to iteratively calculate the Iteration current distribution :

[0198] ;

[0199] in, For the Iteration current distribution.

[0200] In this embodiment, when updating the current distribution, it is ensured that the current value does not exceed the current bearing capacity of the material and meets the safety requirements. The current must be between the minimum and maximum allowable current values;

[0201] In S3.4, the current distribution is adjusted iteratively for multiple times until the current distribution objective function converges and the current distribution converges, as follows:

[0202] S3.4.1. When the change of the current distribution objective function is less than the threshold, the current distribution objective function has converged:

[0203] ;

[0204] in, For the The current distribution objective function value of the iterative current distribution; For the The current distribution objective function value of the iterative current distribution; is the convergence threshold of the current distribution objective function;

[0205] S3.4.2. When the change in current distribution is less than the threshold, the current distribution has converged:

[0206] ;

[0207] in, is the convergence threshold of the current distribution objective function;

[0208] In this embodiment S3.5, when the current distribution objective function and the current distribution both meet the convergence conditions, the optimal current distribution is output. , the specific method is as follows:

[0209] ;

[0210] in, is the optimal current distribution.

[0211] S4, real-time acquisition of the temperature field and electromagnetic field data of the system, and evaluation of the electromagnetic field distribution and cooling effect. The above shows and describes the basic principles, main features and advantages of the present invention;

[0212] In this embodiment S4, the temperature field and electromagnetic field data of the system are collected in real time to evaluate the electromagnetic field distribution and cooling effect. The specific method is as follows:

[0213] S4.1. Use thermocouples to monitor the real-time temperature distribution on the material surface ; Use magnetic induction sensor to measure real-time magnetic induction intensity ;

[0214] S4.2, according to the real-time magnetic induction intensity , calculate the magnetic induction intensity error ;

[0215] S4.3, based on real-time temperature distribution , calculate the temperature gradient and temperature change rate .

[0216] In this embodiment S4.2, according to the real-time magnetic induction intensity , calculate the magnetic induction intensity error , the specific method is as follows:

[0217] ;

[0218] in, It is the real-time magnetic induction intensity; is the target magnetic induction intensity; is the magnetic induction intensity error;

[0219] In this embodiment S4.3, according to the real-time temperature distribution , calculate the temperature gradient and temperature change rate , the specific method is as follows:

[0220] ;

[0221] ;

[0222] in, is the temperature gradient; is the gradient of the temperature field; For time; is the temperature change rate; For the spatial position Place, time The temperature value at .

[0223] Those skilled in the art should understand that the present invention is not limited to the above-mentioned embodiments. The above-mentioned embodiments and descriptions are only preferred examples of the present invention and are not used to limit the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention, and these changes and improvements shall fall within the scope of the present invention to be protected.

Claims

1. A magnetic suspension continuous casting process simulation and optimization method, characterized in that: The following steps are involved: S1. Establish boundary conditions of magnetic suspension continuous casting process and design constraints under multi-physics fields; S2. Combine multi-physics field coupling simulation technology with evolutionary topology optimization algorithm to establish a new multi-field evolutionary topology simulation model that includes electromagnetic field, thermal field and fluid field coupling, and dynamically adjust the physical design of the coil; S3, using inverse optimization solution technology and evolutionary topology optimization algorithm, reversely deduce the current distribution according to the predetermined magnetic field and cooling target, and gradually adjust the current configuration of the electromagnetic coil to achieve the optimal coupling relationship with the electromagnetic field distribution through optimization iteration; S4, real-time acquisition of the system's temperature field and electromagnetic field data, evaluation of electromagnetic field distribution and cooling effect; In S2, the multi-physics field coupling simulation technology is combined with the evolutionary topology optimization algorithm to establish a new multi-field evolutionary topology simulation model including electromagnetic field, thermal field and fluid field coupling, and dynamically adjust the physical design of the coil. The specific steps are as follows: S2.

1. Based on the limitation of electromagnetic field strength and the initial design of the coil, the initial model of the electromagnetic field is described using Maxwell's equations: ； in, is the magnetic induction intensity The divergence of is the magnetic induction intensity; is the magnetic field strength The curl of This means that there are no magnetic monopoles at any point; is the magnetic field strength; is the current density; Establish the initial thermal field model: ； in, is the thermal conductivity; is the temperature gradient; is the heat source term; Establish the initial fluid field model: ； in, is the density of the fluid; is the fluid velocity; is the fluid velocity About Time The local derivative of is the convection term; is the pressure gradient; is the dynamic viscosity of the fluid; is the Laplace operator; is the driving force of the fluid field; S2.2, coupling the electromagnetic field initial model, the thermal field initial model and the fluid field initial model to establish a multi-physics field coupling simulation; S2.

3. Based on the multi-physics field coupling simulation and the evolutionary topology optimization algorithm, a new multi-field evolutionary topology simulation model is established to dynamically adjust the coil geometry and material distribution to achieve the optimal coupling of electromagnetic field, thermal field and fluid field; In S3, the inverse optimization solution technology and the evolutionary topology optimization algorithm are used to reversely deduce the current distribution according to the predetermined magnetic field and cooling target, and the current configuration of the electromagnetic coil is gradually adjusted through optimization iteration to achieve the optimal coupling relationship between the electromagnetic field distribution and the electromagnetic field distribution. The specific steps are as follows: S3.

1. According to the target magnetic induction intensity distribution And the target cooling requirements, establish the current distribution objective function: ； in, is the current distribution; The current distribution The generated magnetic induction intensity distribution; The current distribution Generates temperature gradient caused by electromagnetic field; is the influence weight of magnetic field on the current distribution objective function; is the weight of the influence of temperature gradient on the current distribution objective function; S3.

2. According to the target magnetic induction intensity distribution , using inverse optimization solution technology to calculate the target current distribution ; S3.

3. Gradually adjust the current distribution through sensitivity analysis , so that the current distribution The magnetic induction intensity distribution generated Gradually approach the target magnetic induction intensity distribution ; S3.4, iteratively adjusting the current distribution for multiple times until the current distribution objective function converges and the current distribution converges; S3.

5. When the current distribution objective function and the current distribution both meet the convergence conditions, the optimal current distribution is output. .

2. The magnetic suspension continuous casting process simulation and optimization method according to claim 1, characterized in that: In S1, the boundary conditions of the magnetic suspension continuous casting process and the design constraints under the multi-physical field are established, as follows: S1.

1. Multi-physics fields include electromagnetic fields, thermal fields and fluid fields; S1.

2. Setting electromagnetic field strength limits: ； ； in, Represents the inner normal component of the magnetic induction intensity and the outward normal component continuous at the border; Indicates the magnitude of magnetic induction Not exceeding the maximum magnetic field strength ; S1.

3. Set the maximum allowable temperature gradient of the thermal field: ； in, Indicates the temperature gradient of the thermal field Do not exceed the maximum temperature gradient ; S1.

4. Set the boundary conditions of the fluid field: ； ； ； in, Indicates fluid velocity Equal to the boundary fluid velocity ; Indicates that the fluid outlet pressure is equal to Environmental pressures; Indicates the velocity of the fluid Do not exceed the maximum fluid flow rate .

3. The magnetic suspension continuous casting process simulation and optimization method according to claim 2, characterized in that: In S2.2, the electromagnetic field initial model, the thermal field initial model and the fluid field initial model are coupled to establish a multi-physics field coupling simulation. The specific steps are as follows: S2.2.

1. Current loss in electromagnetic field As a heat source, couple the electromagnetic field with the thermal field: ； S2.2.

2. Using the Lorentz force in the electromagnetic field As the driving force of the fluid field, the electromagnetic field is coupled with the fluid field: ； S2.2.

3. According to the temperature distribution in the thermal field , calculate the fluid buoyancy Act on the fluid field and modify the fluid field driving force to couple the thermal field with the fluid field: ； in, is the buoyancy of the fluid.

4. The magnetic suspension continuous casting process simulation and optimization method according to claim 3 is characterized in that: In S2.3, a new multi-field evolutionary topology simulation model is established through an evolutionary topology optimization algorithm according to multi-physical field coupling simulation, and the coil geometry and material distribution are dynamically adjusted to achieve optimal coupling of electromagnetic field, thermal field and fluid field. The specific steps are as follows: S2.3.

1. Combine multi-physics coupling simulation with evolutionary topology optimization algorithm to construct coil optimization objective function: ； in, To control the weight of electromagnetic loss in the objective function; To control the weight of temperature gradient on the objective function; To control the weight of the fluid velocity field on the objective function; To optimize the area; is the temperature gradient; is the square of the fluid velocity; S2.3.

2. Based on the coil optimization objective function, boundary conditions of the magnetic suspension continuous casting process and design constraints under multi-physics fields, the evolutionary topology optimization algorithm is used to dynamically adjust the coil geometry and material distribution. S2.3.

3. Initial design variables are the material distribution of the coil and geometric structures; S2.3.

4. Use the finite element method to solve the coupled equations of the electromagnetic field, thermal field and fluid field to obtain the electromagnetic field distribution , thermal field distribution and fluid field distribution , and calculate the coil optimization objective function value: ； in, To control the weight of electromagnetic loss in the objective function; To control the weight of temperature gradient on the objective function; To control the weight of the fluid velocity field on the objective function; To optimize the area; S2.3.

5. Calculate the Secondary design variables Impact on the coil optimization objective function and update the design variables: ； in, For the Iteration design variables; For the Iteration design variables; is the learning rate; For the The optimization objective function of the first iteration coil is relative to that of the Iteration design variables The gradient of S2.3.

6. When the change of the coil optimization objective function in two consecutive iterations is less than the set threshold , then the coil optimization objective function has converged: ； in, For the Iterative coil optimization objective function; Optimize the objective function convergence threshold for the coil; S2.3.

7. If the change of the design variable in two consecutive iterations is less than the set threshold, the design variable has converged: ； in, For the Iteration design variables With Iteration design variables The difference between S2.3.

8. When the coil optimization objective function and design variables meet the convergence conditions, the optimal coil physical design is output. : ； in, For optimal coil physical design; Represents the design variables that minimize the coil optimization objective function .

5. The magnetic suspension continuous casting process simulation and optimization method according to claim 4, characterized in that: In S3.2, according to the target magnetic induction intensity distribution , using inverse optimization solution technology to calculate the target current distribution , the specific steps are as follows: S3.2.

1. According to the target magnetic induction intensity distribution , calculate the target magnetic field intensity distribution : ； in, is the vacuum permeability; S3.2.

2. Calculate the target current density according to Ampere's law : ； S3.2.

2. According to the target current density , integrate to get the target current distribution : ； in, is the target current distribution; In S3.3, the current distribution is gradually adjusted by sensitivity analysis. , so that the current distribution The magnetic induction intensity distribution generated Gradually approach the target magnetic induction intensity distribution , the specific steps are as follows: S3.3.

1. Derivation of the current distribution objective function: ； in, is the sensitivity matrix of magnetic field with respect to current; S3.3.

2. Use the gradient descent method to iteratively calculate the Iteration current distribution : ； in, For the Iteration current distribution.

6. The magnetic suspension continuous casting process simulation and optimization method according to claim 5, characterized in that: In S3.4, the current distribution is adjusted iteratively for multiple times until the current distribution objective function converges and the current distribution converges, as follows: S3.4.

1. When the change of the current distribution objective function is less than the threshold, the current distribution objective function has converged: ； in, For the The current distribution objective function value of the iterative current distribution; For the The current distribution objective function value of the iterative current distribution; is the convergence threshold of the current distribution objective function; S3.4.

2. When the change in current distribution is less than the threshold, the current distribution has converged: ； in, is the convergence threshold of the current distribution objective function; In S3.5, when the current distribution objective function and the current distribution both meet the convergence conditions, the optimal current distribution is output. , the specific method is as follows: ； in, is the optimal current distribution.

7. The magnetic suspension continuous casting process simulation and optimization method according to claim 1, characterized in that: In S4, the temperature field and electromagnetic field data of the system are collected in real time to evaluate the electromagnetic field distribution and cooling effect. The specific method is as follows: S4.

1. Use thermocouples to monitor the real-time temperature distribution on the material surface ; Use magnetic induction sensor to measure real-time magnetic induction intensity ; S4.2, according to the real-time magnetic induction intensity , calculate the magnetic induction intensity error ; S4.3, based on real-time temperature distribution , calculate the temperature gradient and temperature change rate .

8. The magnetic suspension continuous casting process simulation and optimization method according to claim 7, characterized in that: In S4.2, according to the real-time magnetic induction intensity , calculate the magnetic induction intensity error , the specific method is as follows: ； in, It is the real-time magnetic induction intensity; is the target magnetic induction intensity; is the magnetic induction intensity error; In S4.3, according to the real-time temperature distribution , calculate the temperature gradient and temperature change rate , the specific method is as follows: ； ； in, is the temperature gradient; is the gradient of the temperature field; For time; is the temperature change rate; For the spatial position Place, time The temperature value at .

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