A simulation fitting method for the cooling curve of the annealing stage of a butt welding machine

Abstract

The present application relates to the technical field of butt welding annealing simulation, and discloses a simulation fitting method for a cooling curve in an annealing stage of a butt welding machine, comprising: establishing an initial energy field benchmark according to electrical parameters in a top forging stage; mapping energy density to equivalent values of splash latent heat by using instantaneous acoustic emission wave velocity, and deducing a basic environmental thermal disturbance factor; extracting a frequency drift gradient by changing a sampling frequency of adjacent cycles, which is used for quantifying a phase change hysteresis index; constructing a dynamic compensation factor of lattice expansion to correct acoustic wave velocity and spatial latent heat distribution; combining the corrected thermal field parameters to deduce an effective heat dissipation coefficient and a transient thermal resistance, and calculating an instantaneous cooling rate in a cooling process; and finally generating a fitting cooling curve sequence through time domain integration. The present application solves the problems of monitoring distortion caused by optical interference and nonlinear cooling fitting deviation caused by metal phase change in the butt welding annealing process.

Description

Technical Field

[0001] This invention relates to the field of welding annealing simulation technology, specifically to a simulation fitting method for the cooling curve of the welding machine during the annealing stage. Background Technology

[0002] The annealing and cooling stage after upsetting in butt welding is a critical period that determines the metallographic structure and mechanical properties of the weld joint. Accurately obtaining the cooling curve during this stage is crucial for optimizing annealing process parameters and preventing joint embrittlement. Existing methods for monitoring and simulating cooling curves mainly rely on infrared thermometers or pre-set heat conduction models. In actual welding conditions, the intense arc light, dense welding fumes, and high-speed metal spatter generated during upsetting can severely shield and interfere with optical sensors, leading to significant distortion in the initial cooling data. Traditional thermodynamic simulation models often assume a quasi-steady state in the welding microenvironment. However, in reality, the latent heat carried by a large amount of metal spatter alters the heat dissipation conditions of the local microenvironment, generating significant thermal disturbances. Current technologies lack effective methods for quantifying the energy distribution of spatter, making it difficult to accurately assess the impact of these disturbances on the cooling curve. Furthermore, the base metal undergoes complex solid-state transformations during cooling. These microscopic changes at the lattice scale cause nonlinear lattice expansion and the release of latent heat from phase transitions. Existing simulation algorithms typically employ simplified linear cooling models, failing to objectively describe the energy hysteresis effect resulting from phase transitions. While acoustic emission technology has been attempted to monitor internal states, the density of the medium continuously changes during cooling, causing phase shifts in the sound wave propagation path. Without spatial mapping correction, acoustic characteristics cannot be accurately reconstructed into macroscopic thermodynamic parameters. Furthermore, existing simulation schemes, lacking consideration of dynamic compensation factors, are prone to showing deviations between calculated results and actual temperature drop trends when handling acoustic-thermal mapping.

[0003] For the aforementioned complex operating conditions, existing technologies cannot comprehensively consider the combined effects of spatter thermal disturbance and phase transition nonlinear hysteresis on the annealing cooling process under strong interference environments. Therefore, a simulation fitting method for the cooling curve of the welding machine annealing stage is needed, which can couple acoustic and electrical characteristics and has phase transition hysteresis compensation capabilities. Summary of the Invention

[0004] This invention provides a simulation fitting method for the cooling curve of the annealing stage of a welding machine, which helps to solve the problems mentioned in the background art.

[0005] This invention provides the following technical solution: a simulation fitting method for the cooling curve of a welding machine during the annealing stage, comprising:

[0006] Calculate the initial welding volume energy density based on the electrical parameters during the upsetting stage;

[0007] The initial welding volume energy density is converted into an equivalent value of spatter latent heat by using the instantaneous acoustic emission wave velocity, and the thermal disturbance factor of the basic environment is deduced.

[0008] The frequency drift gradient of the acoustic signal is calculated based on the sampling frequency change between adjacent periods;

[0009] The phase transition hysteresis index is calculated by combining the characteristic cooling time constant and the frequency drift gradient, and then a dynamic compensation factor for lattice expansion is constructed.

[0010] The compensated acoustic velocity is calculated using the lattice expansion dynamic compensation factor, and the corrected splash latent heat equivalent value is calculated based on this mapping.

[0011] The effective heat dissipation coefficient is calculated by combining the basic environmental thermal disturbance factor and the corrected splash latent heat equivalent value, and then the transient thermal resistance is obtained.

[0012] The instantaneous cooling rate during the cooling process is calculated based on transient thermal resistance and the current instantaneous temperature.

[0013] The instantaneous cooling rate and the phase transition hysteresis index are integrated in the time domain to generate a sequence of fitted cooling curves.

[0014] Optionally, the calculation of the initial welding volumetric energy density based on the electrical parameters during the upsetting stage includes:

[0015] Obtain the upsetting current and upsetting time, and obtain the preset fixture contact resistance and effective welding volume corresponding to the current material;

[0016] The total input heat is obtained by multiplying the square of the upsetting current by the fixture contact resistance and the upsetting time.

[0017] The initial welding volume energy density is obtained by calculating the ratio of the total input heat to the effective welding volume.

[0018] Optionally, the step of converting the initial welding volume energy density into an equivalent value of spatter latent heat using the instantaneous acoustic emission wave velocity, and deriving the basic environmental thermal disturbance factor, includes:

[0019] The instantaneous acoustic emission velocity and ambient temperature are obtained through direct measurement, and the basic acoustic wave propagation velocity, metal density, and specific heat capacity of the metal weldment body are also obtained.

[0020] The square of the ratio of the instantaneous acoustic emission wave velocity to the fundamental acoustic wave propagation velocity is multiplied by the initial weld volume energy density.

[0021] The calculation result is multiplied by the reciprocal of the metal density to obtain the equivalent value of the splashing latent heat;

[0022] The basic environmental thermal disturbance factor is obtained by comparing the equivalent value of splash latent heat with the product of specific heat capacity and ambient temperature.

[0023] Optionally, calculating the frequency drift gradient of the acoustic signal based on the sampling frequency change between adjacent periods includes:

[0024] Obtain the current sampling frequency and the sampling frequency at the previous moment, and obtain the fundamental resonant frequency of the metal weldment body; set the sampling time interval of the system controller.

[0025] Calculate the difference between the current sampling frequency and the sampling frequency at the previous moment;

[0026] The frequency drift gradient is obtained by taking the ratio of this difference to the product of the sampling time interval and the fundamental resonant frequency.

[0027] Optionally, the step of combining the characteristic cooling time constant and the frequency drift gradient to calculate the phase transition hysteresis exponent, and then constructing the lattice expansion dynamic compensation factor, includes:

[0028] Obtain the weld quality, reference natural heat dissipation coefficient, effective weld surface area, and equivalent elastic modulus density;

[0029] Calculate the product of specific heat capacity and weldment mass, and then compare it with the product of reference natural heat dissipation coefficient and effective weld surface area to obtain the characteristic cooling time constant.

[0030] The phase transition hysteresis exponent is obtained by taking the negative of the product of the frequency drift gradient and the characteristic cooling time constant and then performing an exponential operation.

[0031] The product of the phase transformation hysteresis index and the initial welding volume energy density is compared with the equivalent elastic modulus density, and then added to the constant term to obtain the lattice expansion dynamic compensation factor.

[0032] Optionally, the step of calculating the compensated acoustic velocity using the lattice expansion dynamic compensation factor and mapping it accordingly to calculate the corrected splash latent heat equivalent value includes:

[0033] The compensated acoustic velocity is obtained by multiplying the instantaneous acoustic emission velocity with the lattice expansion dynamic compensation factor.

[0034] Calculate the square of the ratio of the compensated acoustic wave velocity to the instantaneous acoustic emission wave velocity, and multiply this squared value with the equivalent value of splash latent heat to obtain the corrected equivalent value of splash latent heat.

[0035] Optionally, the step of calculating the effective heat dissipation coefficient by combining the basic environmental thermal disturbance factor and the corrected splash latent heat equivalent value, and then obtaining the transient thermal resistance, includes:

[0036] The basic environmental thermal disturbance factor is summed with the constant term and then multiplied with the reference natural heat dissipation coefficient.

[0037] The result of this calculation is multiplied by the corrected splash latent heat equivalent value, and then the ratio is calculated relative to the product of specific heat capacity and ambient temperature to obtain the effective heat dissipation coefficient.

[0038] The transient thermal resistance is obtained by multiplying the effective heat dissipation coefficient with the effective welding surface area and taking the reciprocal of the product.

[0039] Optionally, the calculation of the instantaneous cooling rate during the cooling process based on transient thermal resistance and the current instantaneous temperature includes:

[0040] Acquire the current transient temperature data of the weld and its heat-affected zone;

[0041] Calculate the difference between the current transient temperature and the ambient temperature;

[0042] The instantaneous cooling rate is obtained by comparing this difference with the product of transient thermal resistance, specific heat capacity, and weldment mass.

[0043] Optionally, the step of performing time-domain integration calculation of the instantaneous cooling rate and the phase transition hysteresis exponent to generate a fitted cooling curve sequence includes:

[0044] Obtain the initial temperature after welding is completed;

[0045] The instantaneous cooling rate function, which varies with time, is multiplied in the time domain with the phase transition hysteresis exponential function, which varies with time.

[0046] Integrate the product result over the target fitting time range;

[0047] Subtracting the integral result from the initial temperature after welding yields a sequence of fitted cooling curves that vary with time.

[0048] The present invention has the following beneficial effects:

[0049] 1. By collecting electrical parameters during the upsetting stage of the welding machine, an initial energy field benchmark is established, and instantaneous acoustic emission signals are introduced into the cooling monitoring system. This technical solution utilizes acoustic characteristics such as sound wave velocity and frequency drift to deduce the thermal disturbance of the spatter microenvironment and the lattice expansion effect caused by metal phase transformation, thereby dynamically correcting transient thermal resistance and cooling rate, and finally integrating and fitting the cooling curve of the annealing stage. During the annealing cooling stage after the welding machine completes the upsetting action, the working environment contains strong welding arc light, metal vapor, and dense fumes. This physical environment can block and interfere with the propagation of optical signals, resulting in extraction errors in direct temperature measurement data based on optical sensors. In addition, the high-temperature metal particles spewed from the welding machine can change the local heat dissipation boundary conditions, and the microscopic lattice distortion and latent heat release accompanying the solid-phase transformation of the weldment base material during cooling can cause nonlinear physical hysteresis in the macroscopic cooling process. For this specific working environment with optical shielding and complex microscopic changes in matter, this solution changes the conventional thermodynamic monitoring path and constructs a mapping relationship between acoustic and thermal cross-modal physical fields. In terms of beneficial effects, this scheme uses acoustic emission signals, which are less affected by ambient light and smoke interference, as the characterization medium for the microscopic thermodynamic state. It quantifies the initial equivalent distribution of spatter latent heat through the relative change of sound wave velocity, achieving objective extraction of thermodynamic boundary conditions under specific environments with strong light and smoke obscuring the surface. Addressing the nonlinear cooling characteristics caused by phase transitions in metallic materials, this scheme utilizes the frequency drift gradient of the acoustic signal to construct a phase transition hysteresis index, and uses this to dynamically compensate for the sound velocity and latent heat of the heat transfer medium. It integrates the heat capacity retention effect caused by microscopic lattice deformation into the dynamic solution process of transient thermal resistance and cooling rate. This processing logic couples high-frequency acoustic characteristic distortion with the physical equations of heat conduction, enabling the fitting calculation in complex welding microenvironments to comprehensively consider the combined effects of spatter thermal shock and internal phase transition hysteresis on the heat dissipation process. This reduces the bias of conventional linear temperature models when dealing with complex phase transitions, and the output fitted cooling curve sequence more closely matches the actual objective thermodynamic evolution law of the butt welding annealing stage.

[0050] 2. By acquiring the current and time parameters during the upsetting stage, combined with the fixture contact resistance and effective welding volume, the initial welding volume energy density is calculated, establishing a fundamental correlation between electrical input and thermodynamic state. This transforms the transient electrical work process into initial heat source parameters in three-dimensional space, providing a quantitative energy benchmark constraint for subsequent thermodynamic field inversion. This processing mechanism eliminates the physical interference of the complex lighting environment at the initial stage of welding machine startup on conventional optical temperature measuring instruments, transforming the transient arc heating behavior, which is difficult to measure directly, into a macroscopic volume energy distribution with determinable boundaries. The deduction based on objective electrical parameters ensures the rationality of the initial heat source field extraction, enabling subsequent complex simulation fitting calculations to be built on an energy foundation that conforms to the objective physical laws of electrothermal conversion. This establishes physically meaningful source input data for analyzing the heat transfer state at the initial stage of annealing cooling, improving the reliability of initial state assessment.

[0051] 3. By introducing directly measured instantaneous acoustic emission wave velocity, comparing its ratio with the basic sound velocity of the metal weldment, and combining it with metal density and initial energy density to convert it into an equivalent value of spatter latent heat, and then combining specific heat capacity and ambient temperature to deduce the basic environmental thermal disturbance factor; this mechanism uses the dynamic changes in the propagation characteristics of sound waves under different media states to characterize the latent heat carried away and dissipated by the spatter, bypassing the limitations of strong light and smoke during upsetting that obscure the thermal field observation, converting the disordered sputtering behavior of the microscopic physical environment into macroscopically measurable thermodynamic equivalent characteristics, quantifying the degree of initial thermal shock caused by the local microenvironment to conventional natural heat dissipation, enabling the fitted simulation model to truly consider the actual changes in the surrounding convective heat transfer boundary conditions caused by the heat dissipated by the spatter, reducing the misjudgment of the state caused by environmental interference, and improving the objectivity of the construction of complex microscopic thermal fields under special working conditions.

[0052] 4. By obtaining the difference between the current sampling frequency and the sampling frequency at the previous moment, and combining the system's sampling time interval with the fundamental resonant frequency of the metal body, the frequency drift gradient of the acoustic signal is calculated. This processing method utilizes the Doppler frequency shift phenomenon of high-frequency acoustic signals to extract the dynamic physical characteristics of the microscopic deformation of the metal's internal lattice, and peels off the trend of internal physical state changes caused by temperature drop and phase transition contraction. It maps the macroscopic thermal expansion and contraction physical effects into continuous gradient variables in the acoustic frequency domain, providing an intuitive physical observation dimension for quantifying the invisible microscopic phase transition evolution process. This enables the monitoring system to capture the minute stiffness changes of the metal base material in the early stage of annealing and cooling due to internal stress release and lattice distortion. It establishes a highly sensitive underlying monitoring parameter for subsequent dynamic compensation of the physical property deviation of the heat transfer medium, and refines the granular characterization of the evolution of the physical state.

[0053] 5. By combining the specific heat capacity and mass of the metal with the baseline natural heat dissipation coefficient, the characteristic cooling time constant is solved. The phase transition hysteresis index is obtained by exponentially calculating this time constant with the frequency drift gradient. Then, a dynamic compensation factor for lattice expansion is constructed by combining parameters such as energy density. This design uses a time-scale benchmark to measure the objective decay law of lattice distortion characteristics, quantifies the nonlinear hysteresis effect of the solid phase transition process inside the metal on conventional heat dissipation, integrates the lumped parameter model in macroscopic heat transfer with the microscopic phase transition mechanical characteristics, and transforms the release of latent heat of phase transition and changes in lattice stress into specific dynamic compensation coefficients. This corrects the limitation of treating material properties as constants in conventional thermal simulations, reflects the dynamic correlation characteristics of the evolution of the internal physical properties of the material over time in the annealing cooling process, and improves the fidelity of the characterization of the phase transition hysteresis effect of the material.

[0054] 6. The compensated acoustic velocity is obtained by multiplying the acquired instantaneous acoustic emission velocity with the lattice expansion dynamic compensation factor. The equivalent value of the splash latent heat is then calculated based on the ratio of the compensated acoustic velocity to the original acoustic velocity. This process injects the lattice density change caused by the micro-phase transition into the calculation link of the acoustic velocity to complete the physical calibration at the phase level. This reduces the acoustic transmission observation error caused by the nonlinear changes in thermal expansion and density of the metal medium, restores the inherent velocity of acoustic wave transmission at the scale of the real physical environment, and uses the calibrated wave velocity to perform spatial scale energy realignment and distribution correction on the previously mapped local latent heat field. This reduces the spatial distortion rate in the cross-modal physical quantity mapping process, ensures that the extracted microenvironmental thermodynamic field characteristic parameters conform to the actual thermodynamic spatial distribution law inside the metal at the current specific moment, and enhances the accuracy of the mapping parameters.

[0055] 7. By integrating the basic environmental thermal disturbance factor with the equivalent value of the corrected spatter latent heat, and combining it with the benchmark natural heat dissipation coefficient and environmental parameters to calculate the effective heat dissipation coefficient, and then combining it with the effective welding surface area to obtain the transient thermal resistance; this calculation logic reshapes the complex convection boundary conditions that include the combined effects of spatter thermal shock and micro-phase change, transforming the externally dynamically changing convection heat transfer capacity into the internal transient thermodynamic impedance parameter that hinders heat loss. This breaks the inherent mode of directly using the static convection heat transfer constant in traditional thermal fitting, enabling the thermal resistance parameter to evolve synchronously with the thermal energy fluctuations of the microenvironment and the release state of the internal phase change latent heat. It truly reflects the actual heat dissipation capacity attenuation or enhancement trend caused by the complex environmental alternation during the welding machine annealing process, and establishes a boundary constraint resistance index with time-varying adaptive characteristics for subsequent solutions to continuous temperature drop gradient changes.

[0056] 8. By obtaining the temperature difference between the current transient temperature and the ambient temperature, and performing a logical ratio calculation with the transient thermal resistance, metal mass, and specific heat capacity, the instantaneous cooling rate is obtained. This mechanism strictly follows the transient energy conservation law to extract the real-time microscopic rate of temperature change in the variable parameter thermal resistance network model. It transforms the previously accumulated boundary heat transfer resistance characteristics and the internal thermal energy storage properties of the medium into a macroscopically continuous cooling derivative, realizing a smooth logical transition from steady-state thermodynamic field parameters to transient temperature drop dynamic variables. This ensures that the cooling slope calculated for the current moment can objectively cover the splash heat compensation and the thermal inertia resistance effect of the medium itself in the actual working environment. It provides a rate guide with objective physical driving force for the subsequent extension of temperature parameters to the time dimension, avoiding the fitting deviation of relying solely on external temperature measurement nodes and improving the rationality of rate prediction.

[0057] 9. By obtaining the initial temperature after welding completion as the boundary value for the calculation, the instantaneous cooling rate function and the phase transition hysteresis exponential function output by dynamic calculation are continuously integrated in the time domain to generate a fitted cooling curve sequence. This step transforms the microscopic thermodynamic state derivative at discrete time nodes into a macroscopic continuous fitted prediction curve. The internal phase transition hysteresis effect is introduced in the time domain integration operation to perform nonlinear smoothing and temporal constraints on the basic cooling amplitude, so that the curvature shape of the final generated curve can objectively reflect the physical characteristics of the slowing temperature drop caused by the release of lattice energy inside the metal. This completes the convergence of the calculation from the underlying microscopic acoustic characteristic parameters to the macroscopic specific thermodynamic continuous time sequence, and finally produces a global cooling time domain data feature sequence covering the entire annealing stage, ensuring that the time sequence fitting result fits the true performance of metal physical annealing. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the basic process of the present invention.

[0059] Figure 2 This is a detailed data flow diagram illustrating the initial energy field and splash thermal disturbance derivation of this invention.

[0060] Figure 3 This is a detailed data flow diagram of acoustic frequency shift extraction and phase transition dynamic compensation of the present invention.

[0061] Figure 4 This is a detailed data flow diagram of the dynamic thermal resistance network and macroscopic time-domain integral of the present invention. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] Example 1, refer to Figure 1 A simulation fitting method for the cooling curve during the annealing stage of a welding machine, comprising:

[0064] Calculate the initial welding volume energy density based on the electrical parameters during the upsetting stage;

[0065] The initial welding volume energy density is converted into an equivalent value of spatter latent heat by using the instantaneous acoustic emission wave velocity, and the thermal disturbance factor of the basic environment is deduced.

[0066] The frequency drift gradient of the acoustic signal is calculated based on the sampling frequency change between adjacent periods;

[0067] The phase transition hysteresis index is calculated by combining the characteristic cooling time constant and the frequency drift gradient, and then a dynamic compensation factor for lattice expansion is constructed.

[0068] The compensated acoustic velocity is calculated using the lattice expansion dynamic compensation factor, and the corrected splash latent heat equivalent value is calculated based on this mapping.

[0069] The effective heat dissipation coefficient is calculated by combining the basic environmental thermal disturbance factor and the corrected splash latent heat equivalent value, and then the transient thermal resistance is obtained.

[0070] The instantaneous cooling rate during the cooling process is calculated based on transient thermal resistance and the current instantaneous temperature.

[0071] The instantaneous cooling rate and the phase transition hysteresis index are integrated in the time domain to generate a sequence of fitted cooling curves.

[0072] The calculation of the initial welding volumetric energy density based on the electrical parameters during the upsetting stage includes:

[0073] Obtain the upsetting current and upsetting time, and obtain the preset fixture contact resistance and effective welding volume corresponding to the current material;

[0074] The total input heat is obtained by multiplying the square of the upsetting current by the fixture contact resistance and the upsetting time.

[0075] The initial welding volume energy density is obtained by calculating the ratio of the total input heat to the effective welding volume.

[0076] The method of converting the initial welding volume energy density into an equivalent value of spatter latent heat using the instantaneous acoustic emission wave velocity, and deriving the basic environmental thermal disturbance factor, includes:

[0077] The instantaneous acoustic emission velocity and ambient temperature are obtained through direct measurement, and the basic acoustic wave propagation velocity, metal density, and specific heat capacity of the metal weldment body are also obtained.

[0078] The square of the ratio of the instantaneous acoustic emission wave velocity to the fundamental acoustic wave propagation velocity is multiplied by the initial weld volume energy density.

[0079] The calculation result is multiplied by the reciprocal of the metal density to obtain the equivalent value of the splashing latent heat;

[0080] The basic environmental thermal disturbance factor is obtained by comparing the equivalent value of splash latent heat with the product of specific heat capacity and ambient temperature.

[0081] The calculation of the frequency drift gradient of the acoustic signal based on the sampling frequency change of adjacent periods includes:

[0082] Obtain the current sampling frequency and the sampling frequency at the previous moment, and obtain the fundamental resonant frequency of the metal weldment body; set the sampling time interval of the system controller.

[0083] Calculate the difference between the current sampling frequency and the sampling frequency at the previous moment;

[0084] The frequency drift gradient is obtained by taking the ratio of this difference to the product of the sampling time interval and the fundamental resonant frequency.

[0085] The method of calculating the phase transition hysteresis exponent by combining the characteristic cooling time constant and the frequency drift gradient, and then constructing the lattice expansion dynamic compensation factor, includes:

[0086] Obtain the weld quality, reference natural heat dissipation coefficient, effective weld surface area, and equivalent elastic modulus density;

[0087] Calculate the product of specific heat capacity and weldment mass, and then compare it with the product of reference natural heat dissipation coefficient and effective weld surface area to obtain the characteristic cooling time constant.

[0088] The phase transition hysteresis exponent is obtained by taking the negative of the product of the frequency drift gradient and the characteristic cooling time constant and then performing an exponential operation.

[0089] The product of the phase transformation hysteresis index and the initial welding volume energy density is compared with the equivalent elastic modulus density, and then added to the constant term to obtain the lattice expansion dynamic compensation factor.

[0090] The calculation of the compensated acoustic wave velocity using the lattice expansion dynamic compensation factor, and the mapping calculation of the corrected splash latent heat equivalent value based on this, includes:

[0091] The compensated acoustic velocity is obtained by multiplying the instantaneous acoustic emission velocity with the lattice expansion dynamic compensation factor.

[0092] Calculate the square of the ratio of the compensated acoustic wave velocity to the instantaneous acoustic emission wave velocity, and multiply this squared value with the equivalent value of splash latent heat to obtain the corrected equivalent value of splash latent heat.

[0093] The calculation of the effective heat dissipation coefficient by combining the basic environmental thermal disturbance factor and the corrected splash latent heat equivalent value, and then obtaining the transient thermal resistance, includes:

[0094] The basic environmental thermal disturbance factor is summed with the constant term and then multiplied with the reference natural heat dissipation coefficient.

[0095] The result of this calculation is multiplied by the corrected splash latent heat equivalent value, and then the ratio is calculated relative to the product of specific heat capacity and ambient temperature to obtain the effective heat dissipation coefficient.

[0096] The transient thermal resistance is obtained by multiplying the effective heat dissipation coefficient with the effective welding surface area and taking the reciprocal of the product.

[0097] The calculation of the instantaneous cooling rate during the cooling process based on transient thermal resistance and the current instantaneous temperature includes:

[0098] Acquire the current transient temperature data of the weld and its heat-affected zone;

[0099] Calculate the difference between the current transient temperature and the ambient temperature;

[0100] The instantaneous cooling rate is obtained by comparing this difference with the product of transient thermal resistance, specific heat capacity, and weldment mass.

[0101] The step of integrating the instantaneous cooling rate with the phase transition hysteresis exponent in the time domain to generate a sequence of fitted cooling curves includes:

[0102] Obtain the initial temperature after welding is completed;

[0103] The instantaneous cooling rate function, which varies with time, is multiplied in the time domain with the phase transition hysteresis exponential function, which varies with time.

[0104] Integrate the product result over the target fitting time range;

[0105] Subtracting the integral result from the initial temperature after welding yields a sequence of fitted cooling curves that vary with time.

[0106] Example 2, based on Example 1, combined with Appendix Figures 2 to 4 This paper provides a detailed explanation of the specific sub-processes and data calculation procedures for simulating and fitting the cooling curve during the annealing stage of the welding machine, including:

[0107] Reference Figure 2 This figure illustrates the logical path from the acquisition of underlying electrical parameters to the deduction of the spatter thermal disturbance factor, providing a basis for establishing boundary conditions; the calculation of the initial welding volume energy density based on the electrical parameters of the upsetting stage includes:

[0108] High-frequency acoustic emission sensors are rigidly mounted on the cold ends of the fixed and moving fixtures of the welding machine, a high-frequency current transformer is connected in series in the power circuit of the welding fixture, and an infrared thermometer is placed 0.5 meters away from the weld.

[0109] The purpose of this step is to establish the initial heat source magnitude inside the weldment. The principle is to use Joule's law to convert the electrical energy in the upsetting stage into volumetric heat energy constraint.

[0110] First, the system performs an acquisition action to obtain the upsetting current. and upsetting time ;

[0111] And retrieve the preset clamp contact resistance corresponding to the current material from the memory. and effective welding volume ;

[0112] To obtain the total heat source substrate input into the workpiece by the welding machine during the upsetting stage, the initial weld volumetric energy density is then calculated using the following formula:

[0113] In the formula, This represents the initial weld volume energy density; Indicates the upsetting current; Indicates the contact resistance of the clamp; Indicates the upsetting time; Indicates the effective welding volume.

[0114] By acquiring the current and time parameters during the upsetting stage, combined with the fixture contact resistance and effective welding volume, the initial welding volume energy density is calculated, establishing a fundamental correlation between electrical input and thermodynamic state. This transforms the transient electrical work process into initial heat source parameters in three-dimensional space, providing a quantitative energy benchmark constraint for subsequent thermodynamic field inversion. This processing mechanism eliminates the physical interference of the complex lighting environment at the initial stage of welding machine startup on conventional optical temperature measuring instruments, transforming the transient arc heating behavior, which is difficult to measure directly, into a macroscopic volume energy distribution with determinable boundaries. The deduction based on objective electrical parameters ensures the rationality of the initial heat source field extraction, enabling subsequent complex simulation fitting calculations to be built on an energy foundation that conforms to the objective physical laws of electrothermal conversion. This establishes physically meaningful source input data for analyzing the heat transfer state at the initial stage of annealing cooling, improving the reliability of initial state assessment.

[0115] The method of converting the initial welding volume energy density into an equivalent value of spatter latent heat using the instantaneous acoustic emission wave velocity, and deriving the basic environmental thermal disturbance factor, includes:

[0116] The purpose of this step is to bypass optical distortion and directly assess splash thermal disturbance;

[0117] First, the system performs an acquisition action to obtain the directly measured instantaneous acoustic emission velocity. and ambient temperature ;

[0118] And obtain the basic acoustic wave propagation speed of the metal weldment body. Metal density and specific heat capacity ;

[0119] To accurately obtain the latent heat distribution of the local microenvironment generated by splashes under strong light and smoke interference, it is necessary to calculate the equivalent value of splash latent heat using the characteristics of sound wave propagation. The equivalent value of splash latent heat is calculated using the following formula:

[0120] In the formula, This represents the equivalent value of splash latent heat; This represents the initial weld volume energy density; Indicates the instantaneous acoustic emission wave speed; The basic sound wave propagation speed of the metal weldment body; This indicates the metal density of the metal weldment body;

[0121] After obtaining the splash latent heat, in order to quantify the initial thermal shock caused by this latent heat to the conventional cooling environment, it is then necessary to calculate the basic environment thermal disturbance factor, which is calculated using the following formula:

[0122] In the formula, Indicates the basic environmental thermal disturbance factor; This represents the equivalent value of splash latent heat; Indicates the specific heat capacity of the metal weldment body; Indicates ambient temperature.

[0123] By introducing directly measured instantaneous acoustic emission wave velocity and comparing it with the basic sound velocity of the metal weldment, and combining it with metal density and initial energy density to convert it into an equivalent value of spatter latent heat, and then combining specific heat capacity and ambient temperature to deduce the basic environmental thermal disturbance factor; this mechanism uses the dynamic changes in the propagation characteristics of sound waves under different media states to characterize the latent heat carried away and dissipated by the spatter, bypassing the limitations of strong light and smoke during upsetting that obscure the thermal field observation, and converting the disordered sputtering behavior of the microscopic physical environment into macroscopically measurable thermodynamic equivalent characteristics, it quantifies the degree of initial thermal shock caused by the local microenvironment to conventional natural heat dissipation, so that the fitted simulation model can truly consider the actual changes in the surrounding convective heat transfer boundary conditions caused by the heat dissipated by the spatter, reduce the misjudgment of the state caused by environmental interference, and improve the objectivity of the construction of complex microscopic thermal fields under special working conditions.

[0124] Reference Figure 3 The figure details the process of acoustic frequency shift feature capture, phase transition coefficient construction, and latent heat correction, achieving microscopic state quantization; the calculation of the acoustic signal frequency drift gradient based on the sampling frequency change of adjacent periods includes:

[0125] The purpose of this step is to capture the dynamic trend of microscopic deformation of the internal lattice of the metal;

[0126] First, the system performs an acquisition action to obtain the current sampling frequency for direct measurement. and the sampling frequency of the previous moment ;

[0127] Simultaneously, obtain the standard physical constant of the fundamental resonant frequency of the metal weldment body. ;

[0128] This step begins by performing a setup action, which sets the sampling time interval for the system controller. Its value is set based on the highest characteristic frequency of the acoustic emission signal and satisfies the Nyquist sampling theorem. If the value is too large, it will cause the short-time high-frequency signal of the transient deformation of the lattice to be missed. If the value is too small, it will cause the microprocessor data stack to overflow and introduce high-frequency calculation noise.

[0129] To isolate the internal state changes purely caused by lattice contraction, the frequency drift gradient needs to be calculated using the rate of change of frequency between the preceding and following sampling periods. The frequency drift gradient is calculated using the following formula:

[0130] In the formula, Represents the frequency drift gradient; Indicates the current sampling frequency; Indicates the sampling frequency at the previous moment; Indicates the sampling time interval; It represents the fundamental resonant frequency of the metal weldment body.

[0131] By obtaining the difference between the current sampling frequency and the previous sampling frequency, and combining the system's sampling time interval with the fundamental resonant frequency of the metal body, the frequency drift gradient of the acoustic signal is calculated. This processing method utilizes the Doppler frequency shift phenomenon of high-frequency acoustic signals to extract the dynamic physical characteristics of the microscopic deformation of the metal's internal lattice, and peels off the trend of internal physical state changes caused by temperature drop and phase transition contraction. It maps the macroscopic thermal expansion and contraction physical effects into continuous gradient variables in the acoustic frequency domain, providing an intuitive physical observation dimension for quantifying the invisible microscopic phase transition evolution process. This enables the monitoring system to capture the minute stiffness changes of the metal base material in the early stage of annealing and cooling due to internal stress release and lattice distortion. It establishes a highly sensitive underlying monitoring parameter for subsequent dynamic compensation of the physical property deviation of the heat transfer medium, and refines the granular characterization of the evolution of the physical state.

[0132] Reference Figure 4 The figure details the logic of thermal resistance network construction, cooling rate calculation, and full-time integration to synthesize a cooling curve; the calculation of the phase transition hysteresis exponent by combining the characteristic cooling time constant and frequency drift gradient, and then constructing the lattice expansion dynamic compensation factor, includes:

[0133] The purpose of this step is to quantify the nonlinear hysteresis effect of metal phase transformation on thermal shrinkage;

[0134] First, the system performs an acquisition action to obtain the weldment quality. Reference natural heat dissipation coefficient Effective welding surface area and the standard physical constant of equivalent elastic modulus density ;

[0135] To provide a baseline time reference for comparing transient changes, the characteristic cooling time constant needs to be calculated using inherent physical properties. The characteristic cooling time constant is calculated using the following formula:

[0136] In the formula, Indicates the characteristic cooling time constant; Indicates the specific heat capacity of the metal weldment body; Indicates the quality of the welded parts; Indicates the reference natural thermal conductivity; Indicates the effective welded surface area;

[0137] After obtaining the reference time, to characterize the deviation of the phase transition process from the normal natural cooling law, the phase transition hysteresis index is then calculated using the following formula:

[0138] In the formula, Indicates the phase transition hysteresis index; Represents the frequency drift gradient; Indicates the characteristic cooling time constant;

[0139] To convert this hysteresis effect into a stiffness correction factor for the physical propagation medium of sound waves, it is further necessary to calculate the dynamic compensation factor for lattice expansion, which is calculated using the following formula:

[0140] In the formula, Indicates the dynamic compensation factor for lattice expansion; Indicates the phase transition hysteresis index; This represents the initial weld volume energy density; It represents the equivalent elastic modulus density.

[0141] By combining the specific heat capacity and mass of the metal with the baseline natural heat dissipation coefficient, the characteristic cooling time constant is solved. This time constant is then used to perform an exponential operation with the frequency drift gradient to obtain the phase transition hysteresis exponent. Subsequently, a dynamic compensation factor for lattice expansion is constructed by combining parameters such as energy density. This design uses a time-scale benchmark to measure the objective attenuation law of lattice distortion characteristics, quantifies the nonlinear hysteresis effect of the solid-state phase transition process inside the metal on conventional heat dissipation, integrates the lumped parameter model in macroscopic heat transfer with the microscopic phase transition mechanical characteristics, and transforms the release of latent heat of phase transition and changes in lattice stress into specific dynamic compensation coefficients. This corrects the limitation of treating material properties as constants in conventional thermal simulations, reflects the dynamic correlation characteristics of the evolution of the internal physical properties of the material over time in the annealing cooling process, and improves the fidelity of the characterization of the phase transition hysteresis effect of the material.

[0142] The calculation of the compensated acoustic wave velocity using the lattice expansion dynamic compensation factor, and the mapping calculation of the corrected splash latent heat equivalent value based on this, includes:

[0143] The purpose of this step is to eliminate acoustic spatial mapping errors caused by changes in medium density;

[0144] To recreate the true propagation speed of sound waves at a real physical scale, it is necessary to extract the existing data stream and calculate the compensated sound wave velocity using the following formula:

[0145] In the formula, Indicates compensation for the speed of sound; Indicates the instantaneous acoustic emission wave speed; Indicates the dynamic compensation factor for lattice expansion;

[0146] Based on the true wave velocity after error elimination, in order to spatially align and redistribute the previously mapped latent heat field, it is then necessary to calculate the corrected splash latent heat equivalent value. The corrected splash latent heat equivalent value is calculated using the following formula:

[0147] In the formula, This indicates the corrected value for the splash latent heat equivalent; This represents the equivalent value of splash latent heat; Indicates compensation for the speed of sound; This indicates the instantaneous acoustic emission wave speed.

[0148] The compensated acoustic velocity is obtained by multiplying the acquired instantaneous acoustic emission velocity with the lattice expansion dynamic compensation factor. The equivalent value of splash latent heat is then calculated based on the ratio of the compensated acoustic velocity to the original acoustic velocity. This process injects the lattice density change caused by the micro-phase transition into the calculation link of the acoustic velocity to complete the physical calibration at the phase level. This reduces the acoustic transmission observation error caused by the nonlinear changes in thermal expansion and density of the metallic medium, restores the inherent velocity of acoustic wave transmission at the scale of the real physical environment, and uses the calibrated wave velocity to perform spatial scale energy realignment and distribution correction of the previously mapped local latent heat field. This reduces the spatial distortion rate in the cross-modal physical quantity mapping process, ensures that the extracted microenvironmental thermodynamic field characteristic parameters conform to the actual thermodynamic spatial distribution law inside the metal at the current specific moment, and enhances the accuracy of the mapping parameters.

[0149] The calculation of the effective heat dissipation coefficient by combining the basic environmental thermal disturbance factor and the corrected splash latent heat equivalent value, and then obtaining the transient thermal resistance, includes:

[0150] The purpose of this step is to establish the actual thermal conductivity boundary capability in the current complex microenvironment;

[0151] To obtain the convective heat transfer capacity after the superposition of thermal disturbance and latent heat of phase change, it is necessary to calculate the effective heat dissipation coefficient, which is calculated using the following formula:

[0152] In the formula, Indicates the effective heat dissipation coefficient; Indicates the reference natural thermal conductivity; Indicates the basic environmental thermal disturbance factor; This indicates the corrected value for the splash latent heat equivalent; Indicates the specific heat capacity of the metal weldment body; Indicates ambient temperature;

[0153] After determining the system boundary heat transfer capacity, in order to quantify the transient barriers within the system that impede heat loss, the transient thermal resistance is then calculated using the following formula:

[0154] In the formula, Indicates transient thermal resistance; Indicates the effective heat dissipation coefficient; This indicates the effective welded surface area.

[0155] By integrating the basic environmental thermal disturbance factor with the equivalent value of the corrected spatter latent heat, and combining it with the benchmark natural heat dissipation coefficient and environmental parameters to calculate the effective heat dissipation coefficient, and then combining it with the effective welding surface area to obtain the transient thermal resistance, this calculation logic reshapes the complex convective boundary conditions that include the combined effects of spatter thermal shock and micro-phase change. It transforms the externally dynamically changing convective heat transfer capacity into the internal transient thermodynamic impedance parameter that hinders heat loss. This breaks the inherent mode of directly using the static convective heat transfer constant in traditional thermal fitting, allowing the thermal resistance parameter to evolve synchronously with the thermal energy fluctuations of the microenvironment and the release state of the internal phase change latent heat. It truly reflects the actual heat dissipation capacity attenuation or enhancement trend caused by the complex environmental alternation during the welding machine annealing process, and establishes a boundary constraint resistance index with time-varying adaptive characteristics for subsequent solutions to continuous temperature drop gradient changes.

[0156] The calculation of the instantaneous cooling rate during the cooling process based on transient thermal resistance and the current instantaneous temperature includes:

[0157] The purpose of this step is to convert the accumulated boundary and internal thermodynamic conditions into transient temperature derivatives;

[0158] First, the system performs an acquisition action to obtain the current transient temperature data of the weld and its heat-affected zone directly measured by the infrared thermometer;

[0159] To accurately output the degree of temperature drop experienced by the weld and heat-affected zone at the current moment, it is necessary to calculate the instantaneous cooling rate, which is calculated using the following formula:

[0160] In the formula, Indicates instantaneous cooling rate; Indicates the current transient temperature; Indicates ambient temperature; Indicates transient thermal resistance; Indicates the specific heat capacity of the metal weldment body; Indicates the quality of the welded parts.

[0161] By acquiring the temperature difference between the current transient temperature and the ambient temperature, and performing a logical ratio calculation with the transient thermal resistance, metal mass, and specific heat capacity, the instantaneous cooling rate is obtained. This mechanism strictly follows the transient energy conservation law to extract the real-time microscopic rate of temperature change in the variable parameter thermal resistance network model. It transforms the previously accumulated boundary heat transfer resistance characteristics and the internal thermal energy storage properties of the medium into a macroscopically continuous cooling derivative, realizing a smooth logical transition from steady-state thermodynamic field parameters to transient temperature drop dynamic variables. This ensures that the cooling slope calculated for the current moment can objectively cover the splash heat compensation and the thermal inertia resistance effect of the medium itself in the actual working environment. It provides a rate guide with objective physical driving force for the subsequent extension of temperature parameters to the time dimension, avoiding the fitting bias of relying solely on external temperature measurement nodes and improving the rationality of rate prediction.

[0162] The step of integrating the instantaneous cooling rate with the phase transition hysteresis exponent in the time domain to generate a sequence of fitted cooling curves includes:

[0163] The purpose of this step is to transform the microscopic evolution into a macroscopically continuous simulation prediction curve;

[0164] First, the system performs an acquisition action to obtain the initial temperature after welding when the welding is completed;

[0165] To generate a continuous set of curve data covering the entire annealing process that can be directly accessed by the auxiliary design simulation platform, the fitted cooling curve sequence needs to be output in integral form. The fitted cooling curve sequence is calculated using the following formula:

[0166] In the formula, This represents the fitted cooling curve sequence; Indicates the initial temperature after welding; The instantaneous cooling rate function represents the rate of change over time; This represents the phase transition hysteresis exponential function that changes over time.

[0167] By obtaining the initial temperature after welding completion as the boundary value for the calculation, the instantaneous cooling rate function and the phase transition hysteresis exponential function, which are dynamically calculated and change over time, are continuously integrated in the time domain to generate a fitted cooling curve sequence. This step transforms the microscopic thermodynamic state derivative at discrete time nodes into a macroscopic continuous fitted prediction curve. In the time-domain integration operation, an internal phase transition hysteresis effect is introduced to perform nonlinear smoothing and temporal constraints on the basic cooling amplitude, so that the curvature of the final generated curve can objectively reflect the physical characteristics of the slowing temperature drop caused by the release of lattice energy inside the metal. This completes the convergence of the calculation from the underlying microscopic acoustic characteristic parameters to the macroscopic specific thermodynamic continuous time sequence, and finally produces a global cooling time domain data feature sequence covering the entire annealing stage, ensuring that the time-series fitting results closely match the true performance of metal physical annealing.

[0168] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0169] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A simulation fitting method for the cooling curve during the annealing stage of a welding machine, characterized in that, include: Calculate the initial welding volume energy density based on the electrical parameters during the upsetting stage; The initial welding volume energy density is converted into an equivalent value of spatter latent heat by using the instantaneous acoustic emission wave velocity, and the thermal disturbance factor of the basic environment is deduced. The frequency drift gradient of the acoustic signal is calculated based on the sampling frequency change between adjacent periods; The phase transition hysteresis index is calculated by combining the characteristic cooling time constant and the frequency drift gradient, and then a dynamic compensation factor for lattice expansion is constructed. The compensated acoustic velocity is calculated using the lattice expansion dynamic compensation factor, and the corrected splash latent heat equivalent value is calculated based on this mapping. The effective heat dissipation coefficient is calculated by combining the basic environmental thermal disturbance factor and the corrected splash latent heat equivalent value, and then the transient thermal resistance is obtained. The instantaneous cooling rate during the cooling process is calculated based on transient thermal resistance and the current instantaneous temperature. The instantaneous cooling rate and the phase transition hysteresis index are integrated in the time domain to generate a sequence of fitted cooling curves.

2. The simulation fitting method for the cooling curve of the annealing stage of a welding machine according to claim 1, characterized in that, The calculation of the initial welding volumetric energy density based on the electrical parameters during the upsetting stage includes: Obtain the upsetting current and upsetting time, and obtain the preset fixture contact resistance and effective welding volume corresponding to the current material; The total input heat is obtained by multiplying the square of the upsetting current by the fixture contact resistance and the upsetting time. The initial welding volume energy density is obtained by calculating the ratio of the total input heat to the effective welding volume.

3. The simulation fitting method for the cooling curve of the annealing stage of a welding machine according to claim 2, characterized in that, The method of converting the initial welding volume energy density into an equivalent value of spatter latent heat using the instantaneous acoustic emission wave velocity, and deriving the basic environmental thermal disturbance factor, includes: The instantaneous acoustic emission velocity and ambient temperature are obtained through direct measurement, and the basic acoustic wave propagation velocity, metal density, and specific heat capacity of the metal weldment body are also obtained. The square of the ratio of the instantaneous acoustic emission wave velocity to the fundamental acoustic wave propagation velocity is multiplied by the initial weld volume energy density. The calculation result is multiplied by the reciprocal of the metal density to obtain the equivalent value of the splashing latent heat; The basic environmental thermal disturbance factor is obtained by comparing the equivalent value of splash latent heat with the product of specific heat capacity and ambient temperature.

4. The simulation fitting method for the cooling curve of the annealing stage of a welding machine according to claim 3, characterized in that, The calculation of the frequency drift gradient of the acoustic signal based on the sampling frequency change of adjacent periods includes: Obtain the current sampling frequency and the sampling frequency at the previous moment, and obtain the fundamental resonant frequency of the metal weldment body; set the sampling time interval of the system controller. Calculate the difference between the current sampling frequency and the sampling frequency at the previous moment; The frequency drift gradient is obtained by taking the ratio of this difference to the product of the sampling time interval and the fundamental resonant frequency.

5. The simulation fitting method for the cooling curve of the annealing stage of a welding machine according to claim 4, characterized in that, The method of calculating the phase transition hysteresis exponent by combining the characteristic cooling time constant and the frequency drift gradient, and then constructing the lattice expansion dynamic compensation factor, includes: Obtain the weld quality, reference natural heat dissipation coefficient, effective weld surface area, and equivalent elastic modulus density; Calculate the product of specific heat capacity and weldment mass, and then compare it with the product of reference natural heat dissipation coefficient and effective weld surface area to obtain the characteristic cooling time constant. The phase transition hysteresis exponent is obtained by taking the negative of the product of the frequency drift gradient and the characteristic cooling time constant and then performing an exponential operation. The product of the phase transformation hysteresis index and the initial welding volume energy density is compared with the equivalent elastic modulus density, and then added to the constant term to obtain the lattice expansion dynamic compensation factor.

6. The simulation fitting method for the cooling curve of the annealing stage of a welding machine according to claim 5, characterized in that, The calculation of the compensated acoustic wave velocity using the lattice expansion dynamic compensation factor, and the mapping calculation of the corrected splash latent heat equivalent value based on this, includes: The compensated acoustic velocity is obtained by multiplying the instantaneous acoustic emission velocity with the lattice expansion dynamic compensation factor. Calculate the square of the ratio of the compensated acoustic wave velocity to the instantaneous acoustic emission wave velocity, and multiply this squared value with the equivalent value of splash latent heat to obtain the corrected equivalent value of splash latent heat.

7. The simulation fitting method for the cooling curve of the annealing stage of a welding machine according to claim 6, characterized in that, The calculation of the effective heat dissipation coefficient by combining the basic environmental thermal disturbance factor and the corrected splash latent heat equivalent value, and then obtaining the transient thermal resistance, includes: The basic environmental thermal disturbance factor is summed with the constant term and then multiplied with the reference natural heat dissipation coefficient. The result of this calculation is multiplied by the corrected splash latent heat equivalent value, and then the ratio is calculated relative to the product of specific heat capacity and ambient temperature to obtain the effective heat dissipation coefficient. The transient thermal resistance is obtained by multiplying the effective heat dissipation coefficient with the effective welding surface area and taking the reciprocal of the product.

8. The simulation fitting method for the cooling curve of the annealing stage of a welding machine according to claim 7, characterized in that, The calculation of the instantaneous cooling rate during the cooling process based on transient thermal resistance and the current instantaneous temperature includes: Acquire the current transient temperature data of the weld and its heat-affected zone; Calculate the difference between the current transient temperature and the ambient temperature; The instantaneous cooling rate is obtained by comparing this difference with the product of transient thermal resistance, specific heat capacity, and weldment mass.

9. The simulation fitting method for the cooling curve of the annealing stage of a welding machine according to claim 8, characterized in that, The step of integrating the instantaneous cooling rate with the phase transition hysteresis exponent in the time domain to generate a sequence of fitted cooling curves includes: Obtain the initial temperature after welding is completed; The instantaneous cooling rate function, which varies with time, is multiplied in the time domain with the phase transition hysteresis exponential function, which varies with time. Integrate the product result over the target fitting time range; Subtracting the integral result from the initial temperature after welding yields a sequence of fitted cooling curves that vary with time.

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