Electromagnetic pulse welding effect perception regulation and control method based on current waveform characteristics

Abstract

The invention provides an electromagnetic pulse welding effect perception regulation and control method based on current waveform characteristics. The electromagnetic pulse welding effect perception regulation and control method comprises the following steps that S1, coil current is measured through an oscilloscope and a Rogowski coil; calculating mutual inductance M of the current waveform; according to the distance h between the workpiece and the coil, the frequency omega and the three-dimensional tensor M (h, omega, J) of the nonlinearity J, geometric distance calculation is carried out; s2, inverting a three-dimensional deformation field h (r, theta, z, t) of the workpiece by using a broadband current spectrum; s3, performing pulse adjustment constraint calculation through calculation of the elastic coefficient, the transverse stress and the longitudinal stress; and S4, predicting and controlling the MPC to adjust the capacitor charging voltage U0, the discharging time sequence delta t and the geometric pose of the coil in real time through the constraint model.

Description

Technical Field

[0001] This invention relates to the field of circuit control, and in particular to a method for sensing and controlling the effect of electromagnetic pulse welding based on current waveform characteristics. Background Technology

[0002] Dissimilar metal composite components are among the most widely used structures, commonly found in the automotive, aerospace, and instrumentation industries. However, dissimilar metals differ in their physical and chemical properties. When welding these two metals, defects such as stress concentration, porosity, and cracks can occur, affecting the strength and service life of the welded joint. Therefore, some researchers have proposed using electromagnetic pulse welding to achieve the welding of dissimilar metals.

[0003] The principle of electromagnetic pulse welding is as follows: the workpiece generates induced eddy currents, which interact with the pulsed magnetic field to form a Lorentz force. Driven by this Lorentz force, the workpiece accelerates towards the substrate and collides violently with it, forming a metallurgical bond. Therefore, the workpiece's motion speed is the most important physical parameter in electromagnetic pulse welding, determining the quality of the weld joint. However, currently, the motion speed of the workpiece in electromagnetic pulse welding is usually measured by Doppler sensors, high-speed cameras, or laser screens. But these methods are relatively expensive and easily affected by noise. Therefore, it is necessary to propose a convenient and rapid method for calculating the workpiece's motion speed to perceive the electromagnetic pulse welding effect. For example, in a method for electromagnetic pulse welding of magnesium alloy plates and steel plates (2022109554303), it is mentioned that a periodically oscillating time-varying high-intensity current is passed through the coil, causing the steel plate to rapidly impact the magnesium alloy plate under the action of electromagnetic force to complete the welding operation. However, this method cannot accurately perceive the specific Lorentz force during welding or control its force range, which urgently requires those skilled in the art to solve the corresponding technical problems. Summary of the Invention

[0004] This invention aims to at least solve the technical problems existing in the prior art, and in particular, it innovatively proposes a method for controlling the electromagnetic pulse welding effect based on current measurement and waveform characteristics.

[0005] To achieve the above-mentioned objectives of this invention, this invention provides an electromagnetic pulse welding effect sensing and control method based on current waveform characteristics, comprising the following steps:

[0006] S1. Measure the coil current using an oscilloscope and a Rogowski coil; calculate the mutual inductance M based on the current waveform; calculate the geometric distance based on the three-dimensional tensor M(h,ω,J) of the distance h between the workpiece and the coil, the frequency ω, and the nonlinearity J.

[0007] S2, use broadband current spectrum to invert the three-dimensional deformation field h(r,θ,z,t) of the workpiece;

[0008] S3, through calculation of elastic coefficient, transverse stress and longitudinal stress, performs pulse adjustment constraint calculation;

[0009] S4 uses a constraint model to predict and control the MPC in real time to adjust the capacitor charging voltage U0, discharge timing Δt, and coil geometric pose.

[0010] In a preferred embodiment of the above technical solution, S1 includes:

[0011] Calculate the mutual inductance M(*) between the coil and the workpiece:

[0012] M(h,ω,J)=μ0∫∫ A (1+jks)e -(h+ζ) / δ(ω,T,J) ·G(r,θ,z)dA

[0013] The mutual inductance M(*) is transformed from a scalar to a complex frequency domain tensor. The integration region of this double integral is A, and the integrand is a complex function (1+jks) multiplied by the exponential function e. -(h+ζ) / δ(ω,T,J) Then, taking the dot product with the Green's function G(r,θ,z) of the coil and the workpiece, in electromagnetism, the wave number k is used to characterize the propagation characteristics of electromagnetic waves, the physical quantity s specifically depends on the waveguide size of the electromagnetic pulse welding device, and ζ is the physical quantity of the plasma sheath thickness, determined by the sheath voltage U. sheath With electron density n e Let A be the coupling area between the workpiece and the coil, d(A) be the differential calculation, μ0 be the permeability in vacuum, h be the distance between the workpiece and the coil, i.e., the degree of deformation of the workpiece, r be the radial distance used to determine the position of the spatial point in the radial direction, and θ be the angle between the radial direction r and the reference direction rotated counterclockwise from the positive x-axis, in radians (rad). The polar angle θ, together with the radial distance r, determines the position of the spatial point in the plane, and the z-axis represents the axial direction of the waveguide, used to describe the propagation distance of the electromagnetic wave in the waveguide.

[0014] In a preferred embodiment of the above technical solution, S1 includes:

[0015]

[0016] Where ρ(T) represents the resistivity related to temperature T, μ r (J) represents the relative permeability related to the workpiece current density J; δ(*) is the skin depth of the workpiece, which varies with temperature T and workpiece current density J.

[0017] ρ(T)=ρ0[1+α(T-T0)]

[0018] Where ρ0 represents the resistivity at reference temperature T0; α is the temperature coefficient of resistance;

[0019]

[0020] In a preferred embodiment of the above technical solution, S1 includes:

[0021] The key to inferring workpiece speed from current lies in the fact that workpiece speed affects equivalent circuit parameters, which in turn affects the current. Due to the existence of induced eddy currents, there is a mutual inductance coefficient M between the workpiece and the coil. Furthermore, during the welding process, the farther the eddy current region of the workpiece is from the coil, the weaker the coupling relationship and the smaller the mutual inductance coefficient M.

[0022] Calculate plasma sheath thickness

[0023] Where ε0 is the vacuum permittivity, k B It is the Boltzmann constant, T e It is the electron temperature, e is the electron charge, and n e It is the electron number density, v drift It is the drift speed, v th It is the speed of thermal motion.

[0024] In a preferred embodiment of the above technical solution, step S2 includes:

[0025] S2-1, Nonlinear Circuit Equation

[0026] Substituting the mutual inductance M(*) between the coil and the workpiece into the decoupling equivalent circuit, we obtain the nonlinear frequency domain equations:

[0027]

[0028] Among them, Z coil (jω) is the complex impedance of the coil, R coil (T) is the coil resistance related to temperature T, L coil (T) represents the coil inductance related to temperature T. Z is the sum of the impedance components. n (h,ω,J) represents the impedance classification of the nth-order mirror current loop, which is a function of the distance h between the workpiece and the coil, the current angular frequency ω, and the workpiece current density J.

[0029]

[0030] Among them, I workpiece (jω) is the complex current in the workpiece, I coil (jω) is the complex current in the coil, R workpiece (T) represents the workpiece resistance in relation to temperature T, L workpiece (T) represents the workpiece inductance related to temperature T.

[0031] In a preferred embodiment of the above technical solution, step S2 includes:

[0032] Let be the reflected impedance of the nth-order mirror current loop;

[0033] By introducing the Volterra series, I coil Expanding to third-order nonlinear terms, we achieve an accurate solution under large-signal conditions:

[0034] I coil (jω)=Y1(jω)U(jω)+

[0035] ∫∫Y3(jω1,jω2,jω-ω1-ω2)U(jω1)U(jω2)U(jω-ω1-ω2)dω1dω2

[0036] Among them, I coil (jω) represents the complex current in the coil, Y1(jω) is the linear transfer function, U(jω) is the complex voltage applied across the coil, and Y3(jω1,jω2,jω-ω1-ω2) is the nonlinear transfer function. The interaction between ω1, ω2, and ω-ω1-ω2 at different frequency components affects the system response; ω1 and ω2 are two different angular frequency components participating in the nonlinear interaction.

[0037] U(jω1), U(jω2), and U(jω-ω1-ω2) are complex voltages with angular frequencies of ω1, ω2, and ω-ω1-ω2.

[0038] In a preferred embodiment of the above technical solution, step S2 includes:

[0039] S2-2, through the broadband current spectrum to three-dimensional deformable field inversion process, the oscilloscope samples at fs = 5GS / s to obtain Icoil(t). The time-frequency matrix S(t,f) is extracted using the Stockwell Transform.

[0040] For each frequency point f k Calculate the corresponding M k (h,ω k ,J) and establish a dictionary matrix

[0041] Ψ=[M(h1,ω k ),...,M(h m ,ω k ]], where the mutual inductance M varies with different workpiece distances h from the coil i (i = 1, ..., m) and the corresponding angular frequency ω k The value to be taken below.

[0042] Solving using Sparse Bayesian Learning (SBL):

[0043]

[0044] Minimum objective function argmin h ||h||1 Based on the distance vector h, minimize its L1 norm, that is, minimize the sum of the absolute values ​​of the vector elements; minimizing the L1 norm has the property of sparsity inducement, that is, it tends to make many elements in the distance vector h zero, thus obtaining a sparse solution; For quadratic constraints, ∥·∥2 represents the L2 norm; it measures the observed data S(t,f) k The difference between the predicted and observed values ​​is denoted by Ψh; the constraint requires that the square of this difference does not exceed a given threshold ∈, that is, to ensure that the error between the predicted and observed values ​​is within a certain range, where st indicates that it is constrained by;

[0045] A three-dimensional deformation field h(r,θ,z,t) with a spatial resolution of 0.1 mm was obtained.

[0046] In a preferred embodiment of the above technical solution, step S3 includes:

[0047] The instantaneous velocity is obtained from the deformed field based on the physical quantities related to the spatial coordinates (r, θ, z) and time t:

[0048]

[0049] in, Let h be the partial derivative of h with respect to time t, which is the rate of change of h with time. h·▽ is the differential operator.

[0050] The acceleration 'a' was obtained by smoothing the constraint using the optical flow method:

[0051]

[0052] Among them, the calculation of the correlation between the velocity vector v and time t

[0053] The Lorentz force density is given by the Maxwell stress tensor:

[0054] f L =J workpiece ×B coil =σ(E+v×B)×B

[0055] Among them, B coil The electric field intensity vector of E is obtained by measuring the voltage probe array on the workpiece surface through real-time calculation using the Biot-Savart integral. workpiece Let f be the current density vector in the workpiece. L Let σ be the Lorentz force density vector, and σ be the workpiece conductivity.

[0056] In a preferred embodiment of the above technical solution, step S3 includes:

[0057] S3-1, this output will be used as the expanded quantity of the MPC state vector x, and the material constitutive and elastic coefficients will be updated in real time;

[0058] Define the effective elasticity tensor

[0059]

[0060] Where C0 is the quasi-static elastic tensor of the workpiece and coil at room temperature, and β1 and β2 are the temperature rise and strain rate sensitivity coefficients; For the previous strain rate is and

[0061] Calculation of the given velocity and acceleration fields The reference strain rate is usually the standard strain rate or the initial strain rate, T is the current temperature, and T0 is the reference temperature.

[0062] The transverse and longitudinal stress fields are calculated in cylindrical coordinates (r, θ, z) using an incremental elastic-plastic update scheme:

[0063] First predict the total strain increment Let ▽v be the gradient of the velocity v, and (▽v) T It is the transpose of the velocity gradient v, where Δt is the time increment, and then the stress increment is calculated by trial and error. in, Let Δ be a fourth-order elastic tensor. P This represents the increment of plastic strain. This is a double dot product operation, representing the elastic tensor. The interaction between the total strain increment and the plastic strain increment (i.e., the elastic strain increment) yields the stress increment, which reflects the stress-strain relationship based on elasticity theory. That is, within the elastic deformation range of the workpiece, stress and elastic strain are related through the elastic tensor.

[0064] The radial echo algorithm is used to calculate the stress space function:

[0065]

[0066] If Φ>0, then Δ∈ is corrected according to the plastic flow rule. P To obtain the true stress increment When Φ≤0, the workpiece is in an elastic state; when Φ=0, the workpiece begins to yield; s is the stress deviator tensor, and s:s are the second-order invariants of the stress deviator tensor. This is a key part of the Mises yield criterion; taking the square root yields the Mises equivalent stress; the yield stress of the workpiece. It is temperature T and current strain rate The function; decomposed into horizontal and vertical components, σθθ (r,z,t) represents the transverse stress; σ zz (r,z,t) represents the longitudinal stress, and the average stress at the weld interface is obtained by area integral.

[0067] S3-2, Average transverse stress of the welded workpiece at time t The stress component σ of molecules in the θ direction at the interface S of the welded workpiece. θθ (r,z,t), where AS in the denominator is the area of ​​the interface S of the welded workpiece, because σ θθ The unit of (r, z, t) is Pa, and the unit of dA is m. 2 Multiplying the two gives the unit of force, N;

[0068] Longitudinal mean stress of the welded workpiece at time t The stress component σ in the z-direction of the molecule through the interface S of the welded workpiece. zz (r,z,t), A S Let S be the area of ​​the interface S of the welded workpiece.

[0069] By calculating the average stress of transverse and longitudinal stresses, the strength and stability of the welded workpiece can be determined, which is of great significance for the welding effect.

[0070] For dynamic stiffness and damping feedback, the effective stiffness k of the weld at time t is defined. eff and damping c eff :

[0071]

[0072] Among them, the longitudinal stress σ in the partial derivative calculation z With the area A of the welded workpiece S exist Take the value at that location. For a specific value of h,

[0073]

[0074] Where, m eff Let σ be the effective mass of the workpiece, and η be the material loss factor. The state vector and objective function are expanded by adding σ... h σ z k eff c eff Add the state vector.

[0075] In a preferred embodiment of the above technical solution, step S4 includes:

[0076] MPC-EMPW model prediction and regulation,

[0077] State vector x = [h,v,a,T,n]e ,σ h ,σ z ,k eff [], h is the distance between the workpiece and the coil, v is the velocity, a is the acceleration, T is the temperature, n e Let U be the electron density, and let the input vector be u = [U0, Δt, g(t)], where U0 is the initial voltage, Δt is the time step, and g(t) is the coil displacement function.

[0078] Predictive model:

[0079] x(t+1)=Ax(t)+Bu(t)+w(t)

[0080] The influence of state vector x and input vector u on the state x(t+1) at the next time step is given by w(k), where w(k) represents the process noise vector, A is the state transition matrix, and B is the input matrix.

[0081] Obtain the objective function D:

[0082]

[0083] The objective function aims to minimize the difference between the distance h(t) at time t and the reference distance h from t=0 to t=N-1. ref The velocity v(t) and the reference velocity v ref Lorentz force f L (t) and the reference Lorentz force f ref The sum of the differences between them; ||*|| Q For the weighted normal form, Q, R, and P are the weighted matrices of the corresponding differences, and w h w z w k These are the weights for calculating transverse stress, longitudinal stress, and effective stiffness, respectively, σ h,ref For the transverse reference stress, σ z,ref For the longitudinal reference stress, k eff,ref For reference effective stiffness.

[0084] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0085] This study extends the mutual inductance M from a traditional scalar to a three-dimensional tensor M(h,ω,J) of “h–ω–J”, and achieves nonlinear coupling of plasma sheath, temperature rise, and magnetic saturation in the complex frequency domain through Green's function-double integral. It uses broadband current spectrum + S-transform + sparse Bayesian learning to invert the 0.1mm-level three-dimensional deformation field h(r,θ,z,t) instead of single-point displacement. It also incorporates stress tensor and effective stiffness k. eff Damping c eff electron density n eBy directly embedding the MPC state vector, multi-physics constraint predictive control based on elasticity, plasticity, electromagnetics, and heat is achieved, enabling qualified welds to be produced with a single discharge. By using weld strength and defect rate as MPC optimization targets, the conventional approach of controlling only velocity and displacement is broken through.

[0086] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0087] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0088] Figure 1 This is the equivalent circuit diagram of electromagnetic pulse welding of the present invention;

[0089] Figure 2 This is the equivalent circuit diagram of the electromagnetic pulse welding decoupling of the present invention.

[0090] Figure 3 This is a schematic diagram of the working method steps of the present invention. Detailed Implementation

[0091] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0092] This invention designs an electromagnetic pulse welding effect sensing and control method based on current waveform characteristics. By measuring the pulse current of the coil, the workpiece deformation is calculated, and then the workpiece movement speed is calculated to sense the welding effect. The specific method is as follows:

[0093] like Figures 1 to 3 As shown, a real-time sensing and control method for electromagnetic pulse welding with multi-physics field-multi-frequency band-nonlinear coupling includes:

[0094] S1. Measure the coil current using an oscilloscope and a Rogowski coil; calculate the mutual inductance M based on the current waveform; calculate the geometric distance based on the three-dimensional tensor M(h,ω,J) of the distance h between the workpiece and the coil, the frequency ω, and the nonlinearity J.

[0095] S2, use broadband current spectrum to invert the three-dimensional deformation field h(r,θ,z,t) of the workpiece;

[0096] S3 performs pulse regulation constraint calculations based on the nonlinear effects of plasma sheath, temperature rise, and magnetic saturation;

[0097] S4 uses a constraint model to predict and control the MPC in real time to adjust the capacitor charging voltage U0, discharge timing Δt, and coil geometric pose.

[0098] To perform generalized mutual inductance tensor calculations for multi-frequency coupling, since traditional mutual inductance M only considers the distance h between the workpiece and the coil, this invention calculates the mutual inductance M by considering the distance h between the workpiece and the coil (also known as deformation), the current angular frequency ω, and the workpiece current density J.

[0099] Figure 1 This is the equivalent circuit for electromagnetic pulse welding, where C is the energy storage capacitor and R... line and L line These are the line resistance and line inductance, R. coil and L coil These are the coil resistance and coil inductance, R. workpiece and L workpiece These represent the workpiece resistance and inductance, respectively; M is the mutual inductance between the coil and the workpiece; j is an imaginary number; and the dots indicate the directions of the same-named and opposite-named terminals.

[0100] S1 includes, Figure 2 This is the equivalent circuit for decoupled electromagnetic pulse welding. Calculate the mutual inductance M(*) between the coil and the workpiece:

[0101] M(h,ω,J)=μ0∫∫ A (1+jks)e -(h+ζ) / δ(ω,T,J) ·G(r,θ,z)dA

[0102] The mutual inductance M(*) is transformed from a scalar to a complex frequency domain tensor. The integration region of this double integral is A, and the integrand is a complex function (1+jks) multiplied by the exponential function e. -(h+ζ) / δ(ω,T,J) Then, taking the dot product with the Green's function G(r,θ,z) of the coil and the workpiece, in electromagnetism, the wave number k is used to characterize the propagation characteristics of electromagnetic waves, the physical quantity s specifically depends on the waveguide size of the electromagnetic pulse welding device, and ζ is the physical quantity of the plasma sheath thickness, determined by the sheath voltage U. sheath With electron density n e Let A be the coupling area between the workpiece and the coil, d(A) be the differential calculation, μ0 be the permeability in vacuum, h be the distance between the workpiece and the coil, i.e., the degree of deformation of the workpiece; r be the radial distance, used to determine the position of the spatial point in the radial direction; θ be the angle between the radial direction r and the reference direction, rotated counterclockwise from the positive x-axis, in radians (rad). The polar angle θ, together with the radial distance r, determines the position of the spatial point in the plane; the z-axis represents the axial direction of the waveguide, used to describe the propagation distance of the electromagnetic wave in the waveguide.

[0103]

[0104] Where ρ(T) represents the resistivity related to temperature T, μ r (J) represents the relative permeability related to the workpiece current density J; δ(*) is the skin depth of the workpiece, which varies with temperature T and workpiece current density J.

[0105] ρ(T)=ρ0[1+α(T-T0)]

[0106] Where ρ0 represents the resistivity at reference temperature T0; α is the temperature coefficient of resistance;

[0107]

[0108] Among them, M s H represents saturation magnetization, measured in amperes per meter (A / m). k |J| represents the anisotropic field, measured in amperes per meter (A / m); |J| represents the absolute value of the workpiece current density J, measured in amperes per square meter (A / m). 2 ); γ is the levitation ratio, and the unit is radians per second per Tesla (rad / (s·T)).

[0109] The key to inferring workpiece speed from current lies in the fact that workpiece speed affects equivalent circuit parameters, which in turn affects the current. Due to the existence of induced eddy currents, there is a mutual inductance coefficient M between the workpiece and the coil. Furthermore, during the welding process, the farther the eddy current region of the workpiece is from the coil, the weaker the coupling relationship and the smaller the mutual inductance coefficient M.

[0110] Calculate plasma sheath thickness

[0111] Where ε0 is the vacuum permittivity, k B It is the Boltzmann constant, T e It is the electron temperature, e is the electron charge, and n e It is the electron number density, v drift It is the drift speed, v th It is the speed of thermal motion;

[0112] S2 includes:

[0113] S2-1, Nonlinear Circuit Equation

[0114] Substituting the mutual inductance M(*) between the coil and the workpiece into the decoupling equivalent circuit, we obtain the nonlinear frequency domain equations:

[0115]

[0116] Among them, Z coil (jω) is the complex impedance of the coil, R coil (T) is the coil resistance related to temperature T, L coil (T) represents the coil inductance related to temperature T. Z is the sum of the impedance components. n (h,ω,J) represents the impedance classification of the nth-order mirror current loop, which is a function of the distance h between the workpiece and the coil, the current angular frequency ω, and the workpiece current density J.

[0117]

[0118] Among them, I workpiece (jω) is the complex current in the workpiece, I coil (jω) is the complex current in the coil, R workpiece (T) represents the workpiece resistance in relation to temperature T, L workpiece (T) represents the workpiece inductance related to temperature T.

[0119] Let be the reflected impedance of the nth-order mirror current loop;

[0120] By introducing the Volterra series, I coil Expanding to third-order nonlinear terms, we achieve an accurate solution under large-signal conditions:

[0121] I coil (jω)=Y1(jω)U(jω)+

[0122] ∫∫Y3(jω1,jω2,jω-ω1-ω2)U(jω1)U(jω2)U(jω-ω1-ω2)dω1dω2

[0123] Among them, I coil (jω) represents the complex current in the coil, Y1(jω) is the linear transfer function, U(jω) is the complex voltage applied across the coil, and Y3(jω1,jω2,jω-ω1-ω2) is the nonlinear transfer function. The interaction between ω1, ω2, and ω-ω1-ω2 at different frequency components affects the system response; ω1 and ω2 are two different angular frequency components participating in the nonlinear interaction.

[0124] U(jω1), U(jω2), and U(jω-ω1-ω2) are complex voltages with angular frequencies of ω1, ω2, and ω-ω1-ω2.

[0125] S2-2, through the broadband current spectrum to three-dimensional deformable field inversion process, the oscilloscope samples at fs = 5GS / s to obtain Icoil(t). The time-frequency matrix S(t,f) is extracted using the Stockwell Transform.

[0126] For each frequency point f k Calculate the corresponding M k (h,ω k ,J) and establish a dictionary matrix

[0127] Ψ=[M(h1,ω k ),...,M(h m ,ω k ]], where the mutual inductance M varies with different workpiece distances h from the coil i (i = 1, ..., m) and the corresponding angular frequency ω k The value to be taken below.

[0128] Solving using Sparse Bayesian Learning (SBL):

[0129]

[0130] Minimum objective function argmin h ||h||1 Based on the distance vector h, minimize its L1 norm, that is, minimize the sum of the absolute values ​​of the vector elements; minimizing the L1 norm has the property of sparsity inducement, that is, it tends to make many elements in the distance vector h zero, thus obtaining a sparse solution; For quadratic constraints, ∥·∥2 represents the L2 norm; it measures the observed data S(t,f) k The difference between the predicted and observed values ​​is denoted by Ψh; the constraint requires that the square of this difference does not exceed a given threshold ∈, that is, to ensure that the error between the predicted and observed values ​​is within a certain range, where st indicates that it is constrained by.

[0131] A three-dimensional deformation field h(r,θ,z,t) with a spatial resolution of 0.1 mm was obtained.

[0132] S3 includes:

[0133] The instantaneous velocity is obtained from the deformed field based on the physical quantities related to the spatial coordinates (r, θ, z) and time t:

[0134]

[0135] in, Let h be the partial derivative of h with respect to time t, which is the rate of change of h with time. h·▽ is the differential operator.

[0136] The acceleration 'a' was obtained by smoothing the constraint using the optical flow method:

[0137]

[0138] Among them, the calculation of the correlation between the velocity vector v and time t

[0139] The Lorentz force density is given by the Maxwell stress tensor:

[0140] f L =J workpiece ×Bcoil =σ(E+v×B)×B

[0141] Among them, B coil The electric field intensity vector of E is obtained by measuring the voltage probe array on the workpiece surface through real-time calculation using the Biot-Savart integral. workpiece Let f be the current density vector in the workpiece. L Let σ be the Lorentz force density vector, and σ be the workpiece conductivity.

[0142] This output will serve as an expanded constant for the MPC state vector x, and the material constitutive and elastic coefficients will be updated in real time; the effective elastic tensor will be defined.

[0143]

[0144] Where C0 is the quasi-static elastic tensor of the workpiece and coil at room temperature, and β1 and β2 are the temperature rise and strain rate sensitivity coefficients; For the previous strain rate is and

[0145] Calculation of the given velocity and acceleration fields The reference strain rate is usually the standard strain rate or the initial strain rate, T is the current temperature, and T0 is the reference temperature.

[0146] The transverse and longitudinal stress fields are calculated in cylindrical coordinates (r, θ, z) using an incremental elastic-plastic update scheme:

[0147] First predict the total strain increment Let ▽v be the gradient of the velocity v, and (▽v) T It is the transpose of the velocity gradient v, where Δt is the time increment, and then the stress increment is calculated by trial and error. in, Let Δ be a fourth-order elastic tensor. P This represents the increment of plastic strain. This is a double dot product operation, representing the elastic tensor. The interaction between the total strain increment and the plastic strain increment (i.e., the elastic strain increment) yields the stress increment, which reflects the stress-strain relationship based on elasticity theory. That is, within the elastic deformation range of the workpiece, stress and elastic strain are related through the elastic tensor.

[0148] The radial echo algorithm is used to calculate the stress space function:

[0149]

[0150] If Φ>0, then Δ∈ is corrected according to the plastic flow rule. P To obtain the true stress increment When Φ≤0, the workpiece is in an elastic state; when Φ=0, the workpiece begins to yield; s is the stress deviator tensor, and s:s are the second-order invariants of the stress deviator tensor. This is a key part of the Mises yield criterion; taking the square root yields the Mises equivalent stress; the yield stress of the workpiece. It is temperature T and current strain rate The function; decomposed into horizontal and vertical components, σ θθ (r,z,t) represents the transverse stress; σ zz (r,z,t) represents the longitudinal stress, and the average stress at the weld interface is obtained through surface integral:

[0151] The average transverse stress of the welded workpiece at time t The stress component σ of molecules in the θ direction at the interface S of the welded workpiece. θθ (r,z,t), where AS in the denominator is the area of ​​the interface S of the welded workpiece, because σ θθ The unit of (r, z, t) is Pa, and the unit of dA is m. 2 Multiplying the two gives the unit of force, N;

[0152] Longitudinal mean stress of the welded workpiece at time t The stress component σ in the z-direction of the molecule through the interface S of the welded workpiece. zz (r,z,t), A S Let S be the area of ​​the interface S of the welded workpiece.

[0153] By calculating the average stress of transverse and longitudinal stresses, the strength and stability of the welded workpiece can be determined, which is of great significance for the welding effect.

[0154] For dynamic stiffness and damping feedback, the effective stiffness k of the weld at time t is defined. eff and damping c eff :

[0155]

[0156] Among them, the longitudinal stress σ in the partial derivative calculation z With the area A of the welded workpiece S exist Take the value at that location. For a specific value of h,

[0157]

[0158] Where, m eff Let η be the effective mass of the workpiece, and η be the material loss factor.

[0159] The state vector and objective function are expanded by adding σ. hσ z k eff c eff Add state vector:

[0160] MPC-EMPW model prediction and regulation,

[0161] State vector x = [h,v,a,T,n] e ,σ h ,σ z ,k eff [], h is the distance between the workpiece and the coil, v is the velocity, a is the acceleration, T is the temperature, n e Let U be the electron density, and let the input vector be u = [U0, Δt, g(t)], where U0 is the initial voltage, Δt is the time step, and g(t) is the coil displacement function.

[0162] Predictive model:

[0163] x(t+1)=Ax(t)+Bu(t)+w(t)

[0164] The influence of state vector x and input vector u on the state x(t+1) at the next time step is given by w(k), where w(k) represents the process noise vector, A is the state transition matrix, and B is the input matrix.

[0165] Obtain the objective function D:

[0166]

[0167] The objective function aims to minimize the difference between the distance h(t) at time t and the reference distance h from t=0 to t=N-1. ref The velocity v(t) and the reference velocity v ref Lorentz force f L (t) and the reference Lorentz force f ref The sum of the differences between them; ||*|| Q For the weighted normal form, Q, R, and P are the weighted matrices of the corresponding differences, and w h w z w k These are the weights for calculating transverse stress, longitudinal stress, and effective stiffness, respectively, σ h,ref For the transverse reference stress, σ z,ref For the longitudinal reference stress, k eff,ref For reference to effective stiffness,

[0168] Electrical safety: U0≤U max ,|dU0 / dt|≤S max

[0169] Mechanical limit: |g(t)|≤g max,|dg / dt|≤vg max

[0170] Temperature threshold: T≤T melt

[0171] By solving the quadratic programming (QP) problem online, closed-loop control at the 10μs level is achieved.

[0172] When σ h If the voltage is too high, reduce the discharge voltage U0 or turn off the field-effect transistor Δt earlier to decrease the transverse magnetic pressure; when σ z If the value is too large, adjust the longitudinal displacement g(t) of the coil to increase the longitudinal support;

[0173] When k eff By deviating from the set parameters and adjusting the current pulse width through fine-tuning capacitor group switching, the interface wave can form the optimal mechanical lock-in.

[0174] The elastic coefficient and transverse and longitudinal stress are embedded into a closed loop of sensing, prediction and control, directly participating in the online solution of MPC, and providing a precise means of controlling the sensing of welding effect.

[0175] The following conclusions were drawn through experimental verification and error compensation:

[0176] (1) The Green's function G in the formula was calibrated using a dual-laser Doppler vibration meter (LDV) and a high-speed X-ray synchronous measurement system;

[0177] (2) Use a hyperspectral thermometer to calibrate ρ(T) and μr(J) in real time;

[0178] (3) The model parameters are updated online using recursive least squares (RLS) to compensate for errors caused by coil ablation and workpiece surface oxidation.

[0179] MPC-EMPW closed-loop control: The "sensing-prediction-execution" closed loop is completed within 5-12μs, realizing controllable forming of weld interface waves.

[0180] Multiphysics calibration system: Combining LDV, X-ray, and hyperspectral thermometry, it enables online adaptive updating of model parameters to reduce drift.

[0181] Through the above innovations, this solution not only upgrades the single-point calculation of "current → speed" to a complete closed-loop system of "wide spectrum → three-dimensional field → multi-objective optimization", but also provides an scalable theoretical framework and engineering implementation path for the precision process control of electromagnetic pulse welding.

[0182] To verify the sensing and control effect of electromagnetic pulse welding, a comparative experiment was conducted on a 50kJ electromagnetic pulse welding machine platform.

[0183] The experimental material was a 1.0 mm thick Al1060 / Cu-T2 dissimilar lap joint (50 mm × 20 mm), and the coil was a 6-turn planar spiral (outer diameter 38 mm). All data were measured using a 12-bit, 1 GS / s oscilloscope with a 0.1 Ω coaxial shunt, and real-time X-ray imaging, LDV velocimetry, and SEM / EDS weld analysis were used for true value comparison. Key results are summarized below (mean ± 1σ, n = 30).

[0184] I. Waveform Inversion Accuracy

[0185] Mutual inductance M inversion error

[0186] Linear model: |ΔM| / M = 18.7%

[0187] The multi-frequency tensor model in this paper is: |ΔM| / M = 2.9%↓84%

[0188] Deformation amount h inversion error

[0189] Traditional single-frequency method: RMS = 0.19mm

[0190] This article uses the broadband-SBL method: RMS = 0.03mm↓84%.

[0191] II. Velocity-Acceleration Estimation

[0192] Maximum speed v max The measured speed was 286 m / s, while the algorithm in this paper estimated it to be 282 m / s, with an error of 1.4%.

[0193] Peak acceleration a max Measured value: 4.9 × 10^6 m / s 2 The estimated speed is 4.7 × 10^6 m / s 2 4% error

[0194] Verification via stress-stiffness closed-loop method:

[0195] Experiment 1: Fixed voltage 10kV, stress-free closed loop

[0196] Transverse mean stress σ h =132±11MPa

[0197] Longitudinal mean stress σ1=215±18MPa

[0198] Joint shear strength τ = 89 MPa

[0199] Experiment 2: Activating stress constraint MPC (σ_h,ref=90MPa,σ_l,ref=160MPa,k_eff,ref=1.5GN / m)

[0200] Real-time voltage regulation: U0 8.3–9.6kV, Δt 6–14μs

[0201] Measured σ h =91±5MPa (↓31%)

[0202] Measured σ1 = 158 ± 7 MPa (↓27%)

[0203] The joint shear strength τ = 118 MPa (↑32%)

[0204] The proportion of weld defects (X-ray void area fraction) decreased from 3.8% to 0.9%.

[0205] In 30 closed-loop tests C pk =1.87 (>1.67 High Reliability)

[0206] The single sensing-control closed-loop time is 9.1μs, which meets the real-time control requirements at the 200kHz level.

[0207] Compared with the traditional trial-and-error method, the number of convergence times of the process window was reduced from 8–12 times to 1 time, and the total cycle time was shortened by 68%. Through observation of microstructure and energy utilization, the wavelength λ of the wavy interface was 110±8μm after the closed loop, with a deviation of less than 5% from the set value of 105μm; the energy utilization rate η = (effective welding work / capacitor energy) increased from 14% to 21%, thus demonstrating that the characteristics of the multi-frequency current waveform can accurately invert transient mutual inductance, deformation, velocity and stress; the real-time closed loop of the elastic-plastic stress field improved the joint strength and reduced the defect rate; and the 5-11μs level closed loop control achieved "one-time discharge - qualified weld" for the first time in electromagnetic pulse welding, significantly shortening the process development cycle and improving energy utilization.

[0208] Therefore, by measuring the pulse current of the coil, the amount of workpiece deformation can be calculated, and then the workpiece movement speed can be calculated to perceive the welding effect.

[0209] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for sensing and controlling electromagnetic pulse welding effects based on current waveform characteristics, characterized in that, Includes the following steps: S1. Measure the coil current using an oscilloscope and a Rogowski coil; calculate the mutual inductance M based on the current waveform; calculate the geometric distance based on the three-dimensional tensor M(h,ω,J) of the distance h between the workpiece and the coil, the frequency ω, and the nonlinearity J. S2, use broadband current spectrum to invert the three-dimensional deformation field h(r,θ,z,t) of the workpiece; S3, through calculation of elastic coefficient, transverse stress and longitudinal stress, performs pulse adjustment constraint calculation; S4 uses a constraint model to predict and control the MPC in real time to adjust the capacitor charging voltage U0, discharge timing Δt, and coil geometric pose.

2. The electromagnetic pulse welding effect sensing and control method based on current waveform characteristics according to claim 1, characterized in that, S1 includes: Calculate the mutual inductance M(*) between the coil and the workpiece: M(h,ω,J)=μ0∫∫ A (1+jks)e -(h+ζ) / δ(ω,T,J) ·G(r,θ,z)dA The mutual inductance M(*) is transformed from a scalar to a complex frequency domain tensor. The integration region of this double integral is A, and the integrand is a complex function (1+jks) multiplied by the exponential function e. -(h+ζ) / δ(ω,T,J) Then, taking the dot product with the Green's function G(r,θ,z) of the coil and the workpiece, in electromagnetism, the wave number k is used to characterize the propagation characteristics of electromagnetic waves, the physical quantity s specifically depends on the waveguide size of the electromagnetic pulse welding device, and ζ is the physical quantity of the plasma sheath thickness, determined by the sheath voltage U. sheath With electron density n e Let A be the coupling area between the workpiece and the coil, d(A) be the differential calculation, μ0 be the permeability in vacuum, h be the distance between the workpiece and the coil, i.e., the degree of deformation of the workpiece, r be the radial distance used to determine the position of the spatial point in the radial direction, and θ be the angle between the radial direction r and the reference direction rotated counterclockwise from the positive x-axis, in radians (rad). The polar angle θ, together with the radial distance r, determines the position of the spatial point in the plane, and the z-axis represents the axial direction of the waveguide, used to describe the propagation distance of the electromagnetic wave in the waveguide.

3. The electromagnetic pulse welding effect sensing and control method based on current waveform characteristics according to claim 1, characterized in that, S1 includes: Where ρ(T) represents the resistivity related to temperature T, μ r (J) represents the relative permeability related to the workpiece current density J; δ(*) is the skin depth of the workpiece, which varies with temperature T and workpiece current density J. ρ(T)=ρ0[1+α(T-T0)] Where ρ0 represents the resistivity at reference temperature T0; α is the temperature coefficient of resistance; 4. The electromagnetic pulse welding effect sensing and control method based on current waveform characteristics according to claim 1, characterized in that, S1 includes: The key to inferring workpiece speed from current lies in the fact that workpiece speed affects equivalent circuit parameters, which in turn affects the current. Due to the existence of induced eddy currents, there is a mutual inductance coefficient M between the workpiece and the coil. Furthermore, during the welding process, the farther the eddy current region of the workpiece is from the coil, the weaker the coupling relationship and the smaller the mutual inductance coefficient M. Calculate plasma sheath thickness Where ε0 is the vacuum permittivity, k B It is the Boltzmann constant, T e It is the electron temperature, e is the electron charge, and n e It is the electron number density, v drift It is the drift speed, v th It is the speed of thermal motion.

5. The electromagnetic pulse welding effect sensing and control method based on current waveform characteristics according to claim 1, characterized in that, S2 includes: S2-1, Nonlinear Circuit Equation Substituting the mutual inductance M(*) between the coil and the workpiece into the decoupling equivalent circuit, we obtain the nonlinear frequency domain equations: Among them, Z coil (jω) is the complex impedance of the coil, R coil (T) is the coil resistance related to temperature T, L coil (T) represents the coil inductance related to temperature T. Z is the sum of the impedance components. n (h,ω,J) represents the impedance classification of the nth-order mirror current loop, which is a function of the distance h between the workpiece and the coil, the current angular frequency ω, and the workpiece current density J. Among them, I workpiece (jω) is the complex current in the workpiece, I coil (jω) is the complex current in the coil, R workpiece (T) represents the workpiece resistance in relation to temperature T, L workpiece (T) represents the workpiece inductance related to temperature T.

6. The electromagnetic pulse welding effect sensing and control method based on current waveform characteristics according to claim 5, characterized in that, S2 includes: Let be the reflected impedance of the nth-order mirror current loop; By introducing the Volterra series, I coil Expanding to third-order nonlinear terms, we achieve an accurate solution under large-signal conditions: I coil (jω)=Y1(jω)U(jω)+ ∫∫Y3(jω1,jω2,jω-ω1-ω2)U(jω1)U(jω2)U(jω-ω1-ω2)dω1dω2 Among them, I coil (jω) represents the complex current in the coil, Y1(jω) is the linear transfer function, U(jω) is the complex voltage applied across the coil, and Y3(jω1,jω2,jω-ω1-ω2) is the nonlinear transfer function. The interaction between ω1, ω2, and ω-ω1-ω2 at different frequency components affects the system response; ω1 and ω2 are two different angular frequency components participating in the nonlinear interaction. U(jω1), U(jω2), and U(jω-ω1-ω2) are complex voltages with angular frequencies of ω1, ω2, and ω-ω1-ω2.

7. The electromagnetic pulse welding effect sensing and control method based on current waveform characteristics according to claim 6, characterized in that, S2 includes: S2-2, through the broadband current spectrum to three-dimensional deformable field inversion process, the oscilloscope samples at fs = 5GS / s to obtain Icoil(t). The time-frequency matrix S(t,f) is extracted using the Stockwell Transform. For each frequency point f k Calculate the corresponding M k (h,ω k ,J) and establish a dictionary matrix Ψ=[M(h1,ω k ),...,M(h m ,ω k ]], where the mutual inductance M varies with different workpiece distances h from the coil i (i = 1, ..., m) and the corresponding angular frequency ω k The value to be taken below. Solving using Sparse Bayesian Learning (SBL): Minimum objective function arg min h ||h||1 Based on the distance vector h, minimize its L1 norm, that is, minimize the sum of the absolute values ​​of the vector elements; minimizing the L1 norm has the property of sparsity inducement, that is, it tends to make many elements in the distance vector h zero, thus obtaining a sparse solution; For quadratic constraints, ∥·∥2 represents the L2 norm; it measures the observed data S(t,f) k The difference between the predicted and observed values ​​is denoted by Ψh; the constraint requires that the square of this difference does not exceed a given threshold ∈, that is, to ensure that the error between the predicted and observed values ​​is within a certain range, where st indicates that it is constrained by; A three-dimensional deformation field h(r,θ,z,t) with a spatial resolution of 0.1 mm was obtained.

8. The electromagnetic pulse welding effect sensing and control method based on current waveform characteristics according to claim 1, characterized in that, S3 includes: The instantaneous velocity is obtained from the deformed field based on the physical quantities related to the spatial coordinates (r, θ, z) and time t: in, Let h be the partial derivative of h with respect to time t, which is the rate of change of h with time. It is a differential operator; The acceleration 'a' was obtained by smoothing the constraint using the optical flow method: Among them, the calculation of the correlation between the velocity vector v and time t The Lorentz force density is given by the Maxwell stress tensor: f L =J workpiece ×B coil =σ(E+v×B)×B Among them, B coil The electric field intensity vector of E is obtained by measuring the voltage probe array on the workpiece surface through real-time calculation using the Biot-Savart integral. workpiece Let f be the current density vector in the workpiece. L Let σ be the Lorentz force density vector, and σ be the workpiece conductivity.

9. The electromagnetic pulse welding effect sensing and control method based on current waveform characteristics according to claim 8, characterized in that, S3 includes: S3-1, this output will be used as the expanded quantity of the MPC state vector x, and the material constitutive and elastic coefficients will be updated in real time; Define the effective elasticity tensor Where C0 is the quasi-static elastic tensor of the workpiece and coil at room temperature, and β1 and β2 are the temperature rise and strain rate sensitivity coefficients; For the previous strain rate is and Calculation of the given velocity and acceleration fields The reference strain rate is usually the standard strain rate or the initial strain rate, T is the current temperature, and T0 is the reference temperature. The transverse and longitudinal stress fields are calculated in cylindrical coordinates (r, θ, z) using an incremental elastic-plastic update scheme: First predict the total strain increment Let v be the gradient of velocity v. It is the transpose of the velocity gradient v, where Δt is the time increment, and then the stress increment is calculated by trial and error. in, Let Δ be a fourth-order elastic tensor. P This represents the increment of plastic strain. This is a double dot product operation, representing the elastic tensor. The interaction between the total strain increment and the plastic strain increment (i.e., the elastic strain increment) yields the stress increment, which reflects the stress-strain relationship based on elasticity theory. That is, within the elastic deformation range of the workpiece, stress and elastic strain are related through the elastic tensor. The radial echo algorithm is used to calculate the stress space function: If Φ>0, then Δ∈ is corrected according to the plastic flow rule. P To obtain the true stress increment When Φ≤0, the workpiece is in an elastic state; when Φ=0, the workpiece begins to yield; s is the stress deviator tensor, and s:s are the second-order invariants of the stress deviator tensor. This is a key part of the Mises yield criterion; taking the square root yields the Mises equivalent stress; the yield stress of the workpiece. It is temperature T and current strain rate The function; decomposed into horizontal and vertical components, σ θθ (r,z,t) represents the transverse stress; σ zz (r,z,t) represents the longitudinal stress, and the average stress at the weld interface is obtained by area integral. S3-2, Average transverse stress of the welded workpiece at time t The stress component σ of molecules in the θ direction at the interface S of the welded workpiece. θθ (r,z,t), where AS in the denominator is the area of ​​the interface S of the welded workpiece, because σ θθ The unit of (r, z, t) is Pa, and the unit of dA is m. 2 Multiplying the two gives the unit of force, N; Longitudinal mean stress of the welded workpiece at time t The stress component σ in the z-direction of the molecule through the interface S of the welded workpiece. zz (r,z,t), A S Let S be the area of ​​the interface S of the welded workpiece. By calculating the average stress of transverse and longitudinal stresses, the strength and stability of the welded workpiece can be determined, which is of great significance for the welding effect. For dynamic stiffness and damping feedback, the effective stiffness k of the weld at time t is defined. eff and damping c eff : Among them, the longitudinal stress σ in the partial derivative calculation z With the area A of the welded workpiece S exist Take the value at that location. For a specific value of h, Where, m eff Let σ be the effective mass of the workpiece, and η be the material loss factor. The state vector and objective function are expanded by adding σ... h σ z k eff c eff Add the state vector.

10. The electromagnetic pulse welding effect sensing and control method based on current waveform characteristics according to claim 1, characterized in that, S4 includes: MPC-EMPW model prediction and regulation, State vector x = [h,v,a,T,n] e ,σ h ,σ z ,k eff [], h is the distance between the workpiece and the coil, v is the velocity, a is the acceleration, T is the temperature, n e Let U be the electron density, and let the input vector be u = [U0, Δt, g(t)], where U0 is the initial voltage, Δt is the time step, and g(t) is the coil displacement function. Predictive model: x(t+1)=Ax(t)+Bu(t)+w(t) The influence of state vector x and input vector u on the state x(t+1) at the next time step is given by w(k), where w(k) represents the process noise vector, A is the state transition matrix, and B is the input matrix. Obtain the objective function D: The objective function aims to minimize the difference between the distance h(t) at time t and the reference distance h from t=0 to t=N-1. ref The velocity v(t) and the reference velocity v ref Lorentz force f L (t) and the reference Lorentz force f ref The sum of the differences between them; ||*|| Q For the weighted normal form, Q, R, and P are the weighted matrices of the corresponding differences, and w h w z w k These are the weights for calculating transverse stress, longitudinal stress, and effective stiffness, respectively, σ h,ref For the transverse reference stress, σ z,ref For the longitudinal reference stress, k eff,ref For reference effective stiffness.

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