A heat treatment temperature control system for stainless steel seamless pipes

Abstract

This invention relates to the field of heat treatment technology for stainless steel seamless tubes, and discloses a heat treatment temperature control system for stainless steel seamless tubes. The system includes: a data processing unit that establishes a non-uniform geometric distribution model, combines the material's temperature-dependent thermophysical properties, and calculates the wall thickness heat absorption weighting factor modulated by the power supply frequency and the circumferential heat flow migration factor determined by the tube's rotation speed; further, it solves for the critical morphological frequency that cancels out the wall thickness heat absorption effect and the gap fluctuation effect under the action of heat flow migration. A multivariable execution unit monitors the circumferential temperature curvature in the thinnest wall direction in real time, uses the critical morphological frequency as the control benchmark, and coordinates the power supply frequency and rotation speed to make the local temperature curvature closed loop follow the preset target, achieving dynamic balance of the circumferential temperature field of the tube body, thereby improving the uniformity of heat treatment and process stability.

Description

Technical Field

[0001] This invention relates to the field of heat treatment technology for stainless steel seamless tubes, and more specifically, to a heat treatment temperature control system for stainless steel seamless tubes. Background Technology

[0002] During solution treatment or bright annealing, seamless stainless steel tubes require induction heating or roller bottom heating to achieve comprehensive material heating and microstructure recovery. Because these tubes are hollow cylindrical structures, and due to the uneven wall thickness easily formed axially and circumferentially during the earlier piercing, cold rolling, and cold drawing processes, significant differences in heat absorption occur during heating. In actual production, high-frequency or medium-frequency induction heating is typically used to improve efficiency, coupled with rotary conveying to improve temperature distribution. However, due to variations in wall thickness, ellipticity, and the gap between the coil and the outer surface of the tube, the circumferential temperature of the tube body is still difficult to achieve completely uniformity, often resulting in overheating or underheating in localized areas, leading to fluctuations in grain size, phase composition, and surface condition.

[0003] In continuous heat treatment processes, temperature control systems often rely on average temperature or single-point temperature measurements for adjustment. For seamless tubes with wall thickness variations, this control method struggles to reflect the actual circumferential temperature distribution. As the frequency changes, the electromagnetic penetration depth of induction heating alters, causing a shift in heat distribution across the tube's thickness. When the frequency or power is improperly adjusted, thin-walled areas may heat up rapidly due to concentrated current, while thick-walled areas may experience insufficient heat absorption, creating localized temperature differences. Simultaneously, the balancing effect of tube rotation has a time-delay effect; if the frequency and rotation speed are not properly matched, abrupt changes in the temperature field structure may occur in a certain temperature range. These abrupt changes can reverse the previously stable circumferential temperature distribution, leading to drastic alterations in the surface oxide layer, grain size, and even the phase ratio of the microstructure.

[0004] In summary, existing control methods cannot identify and prevent abrupt changes in circumferential temperature morphology at specific heating frequencies. When process parameters cross this critical frequency, the local temperature distribution of the tube suddenly changes its dominant direction: thin-walled areas that previously heated rapidly become cooling areas, or vice versa, leading to localized overheating, abnormal microstructure growth, and uneven performance. This problem directly affects the solution uniformity and surface quality of seamless tubes and is a key factor restricting the precision and stability of heat treatment. Summary of the Invention

[0005] This invention provides a temperature control system for heat treatment of stainless steel seamless tubes, which solves the technical problems mentioned in the background art.

[0006] This invention provides a heat treatment temperature control system for seamless stainless steel tubes, comprising a data processing unit and a multivariable execution unit:

[0007] The data processing unit is configured to: construct a non-uniform geometric distribution model that includes the eccentric amplitude of the pipe wall thickness, the amplitude of the coil gap fluctuation, and the target phase difference; and combine the thermal property parameters of the material with temperature changes to calculate the wall thickness heat absorption weight factor modulated by the power supply frequency and the circumferential heat flow migration factor determined by the pipe rotation speed.

[0008] The data processing unit further solves the problem based on the non-uniform geometric distribution model, which makes the wall thickness heat absorption weight factor and the gap fluctuation effect cancel each other out under the action of the circumferential heat flow migration factor, thereby causing the temperature distribution in the thinnest wall direction of the pipe to exhibit the critical morphological frequency of curvature polarity reversal.

[0009] The multivariable execution unit is configured to monitor the local circumferential temperature curvature in the thinnest wall direction of the tube in real time during the heating process, and drive the local circumferential temperature curvature to follow the preset process target value by coordinating the adjustment of the power supply frequency and the tube rotation speed.

[0010] The beneficial effects of this invention include: by establishing a non-uniform geometric distribution model incorporating the amplitude of wall thickness eccentricity, the amplitude of coil gap fluctuations, and the target phase difference, and combining this with the temperature-dependent thermal properties of the material, the critical morphological frequency is used as the control benchmark for the heating process for the first time, achieving coordinated control of the power supply frequency and the tube rotation speed. This invention can monitor the local circumferential temperature curvature in the thinnest wall direction in real time and automatically adjust based on feedback results, ensuring a balanced and stable temperature field throughout the heating and holding stages. This effectively prevents circumferential overheating and underheating caused by wall thickness deviations, ellipticity, and uneven induction gaps, significantly improving the microstructure uniformity and surface quality of the solution treatment of stainless steel seamless tubes, and ensuring precise control and optimal energy efficiency in the heat treatment process. Attached Figure Description

[0011] Figure 1 This is a diagram showing the coupling relationship between the local curvature of the present invention and the power supply frequency and rotational speed;

[0012] Figure 2 This is a diagram showing the evolution of the circumferential temperature distribution near the critical frequency of this invention.

[0013] Figure 3 This is a schematic diagram of the cooperative control closed-loop performance based on the critical morphological frequency of the present invention.

[0014] Figure 4 This is a block diagram of a heat treatment temperature control system for stainless steel seamless tubes according to the present invention. Detailed Implementation

[0015] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0016] like Figure 1 As shown, Figure 1 The figure displays the steady-state characteristic curves of the local circumferential temperature curvature along the thinnest wall direction as a function of power supply frequency under different pipe rotation speeds. The three solid lines of different colors represent low, medium, and high rotation speeds, respectively. All three lines intersect the black horizontal dashed line representing the point of curvature polarity reversal, visually confirming the existence of the critical morphological frequency—that is, at a specific frequency, the wall thickness effect balances the gap and convection effects. As the rotation speed increases, the intersection point of this curve with the zero line shifts significantly towards higher frequencies, indicating that the heat transfer effect caused by rotation significantly alters the thermal equilibrium state of the system.

[0017] like Figure 2 As shown, Figure 2 Focusing on the local temperature distribution around the thinnest wall of the pipe, the diagram illustrates its evolution with varying power supply frequency. The red dotted line indicates that when the power supply frequency is low and hasn't reached the critical point, the thinnest wall exhibits a bulging pattern with excessively high local temperatures, dominated by wall thickness. The blue dashed line shows that when the power supply frequency is high and exceeds the critical point, the gap and convection factors dominate, resulting in a concave pattern with locally lower temperatures. In contrast, the solid green line in the middle highlights the ideal feature of an extremely flat temperature curve at the thinnest wall when the power supply frequency is precisely aligned with the critical frequency. This verifies that by locking this critical state, the proposed solution effectively eliminates extreme local temperature differences and achieves excellent local temperature uniformity.

[0018] like Figure 3 As shown, Figure 3 This demonstrates the dynamic closed-loop response capability of the control system during process stage transitions and its internal coordinated adjustment mechanism. The top chart shows that when the preset curvature process target value abruptly switches from a specific bias value in the heating stage to zero in the heat preservation stage, the curvature actually monitored by the system can quickly and stably track this change and closely adhere to the target value during the subsequent heat preservation process. The middle and bottom charts further reveal the process of achieving this excellent tracking performance: the power supply frequency, as the main regulating variable, is significantly adjusted to find a new thermal equilibrium point, while the pipe rotation speed is adjusted in an auxiliary coordinated manner at the moment of target switching to optimize the dynamic transition process.

[0019] like Figure 4 As shown, a heat treatment temperature control system for seamless stainless steel tubes includes a data processing unit and a multivariable execution unit.

[0020] The data processing unit is configured to: construct a non-uniform geometric distribution model that includes the eccentric amplitude of the pipe wall thickness, the amplitude of the coil gap fluctuation, and the target phase difference; and combine the thermal property parameters of the material with temperature changes to calculate the wall thickness heat absorption weight factor modulated by the power supply frequency and the circumferential heat flow migration factor determined by the pipe rotation speed.

[0021] The data processing unit further solves the problem based on the non-uniform geometric distribution model, which makes the wall thickness heat absorption weight factor and the gap fluctuation effect cancel each other out under the action of the circumferential heat flow migration factor, thereby causing the temperature distribution in the thinnest wall direction of the pipe to exhibit the critical morphological frequency of curvature polarity reversal.

[0022] The multivariable execution unit is configured to monitor the local circumferential temperature curvature in the thinnest wall direction of the tube in real time during the heating process, and drive the local circumferential temperature curvature to follow the preset process target value by coordinating the adjustment of the power supply frequency and the tube rotation speed.

[0023] In one embodiment of the present invention, a non-uniform geometric distribution model is constructed, including the amplitude of pipe wall thickness eccentricity, the amplitude of coil gap fluctuation, and the target phase difference, comprising:

[0024] Collect the set of measured wall thickness values ​​and the set of measured coil gap values ​​at multiple circumferential discrete points on the outer surface of the pipe.

[0025] Calculate the sum of the products of each measured wall thickness and the corresponding cosine and sine values ​​of the angle at the circumferential discrete point. Multiply the sum by twice the reciprocal of the total number of sampling points to obtain the wall thickness cosine coefficient and wall thickness sine coefficient. Take the square root of the sum of the squares of the wall thickness cosine coefficient and wall thickness sine coefficient as the pipe wall thickness eccentricity amplitude, and take the four quadrant arguments of the wall thickness sine coefficient and wall thickness cosine coefficient as the direction of maximum wall thickness.

[0026] Calculate the sum of the products of the measured gap value of each coil and the cosine and sine values ​​of the corresponding circumferential discrete point angles. Multiply the sum by twice the reciprocal of the total number of sampling points to obtain the gap cosine coefficient and gap sine coefficient. Take the square root of the sum of the squares of the gap cosine coefficient and gap sine coefficient as the coil gap fluctuation amplitude. Take the angle obtained by superimposing the four quadrant arguments of the gap sine coefficient and gap cosine coefficient with the constant pi as the gap minimum direction.

[0027] Calculate the angle difference between the direction of maximum wall thickness and the direction of minimum gap, and perform sine and cosine projection on this angle difference. Determine the target phase difference based on the four-quadrant arctangent calculation results of the projection values.

[0028] The set of measured wall thickness values ​​is a series of wall thickness data obtained by uniformly selecting multiple discrete angle points along the circumference of the outer surface of the pipe and measuring them using an ultrasonic or eddy current thickness gauge.

[0029] The set of measured values ​​for coil gap is a one-to-one correspondence with the wall thickness measurement points, and is the distance data between the coil and the outer surface of the pipe obtained by measuring with a feeler gauge or laser displacement sensor.

[0030] The wall thickness cosine coefficient is a parameter that quantifies the distribution characteristics of wall thickness in the circumferential cosine direction, reflecting the magnitude of the wall thickness variation along the circumferential cosine law. Specifically, the first step is to calculate the product of each measured wall thickness value and the corresponding circumferential discrete point angle cosine value; the second step is to add all the products together to obtain the cumulative sum; the third step is to multiply the cumulative sum by two and then divide it by the total number of sampling points, and the result is the wall thickness cosine coefficient.

[0031] The wall thickness sine coefficient is a parameter that quantifies the distribution characteristics of the wall thickness in the circumferential sine direction. Together with the wall thickness cosine coefficient, it can completely describe the circumferential first harmonic distribution of the wall thickness. Specifically, the first step is to calculate the product of each measured wall thickness value and the corresponding circumferential discrete point angle sine value; the second step is to add all the products together to obtain the cumulative sum; the third step is to multiply the cumulative sum by two and then divide it by the total number of sampling points. The result is the wall thickness sine coefficient.

[0032] The eccentricity amplitude of pipe wall thickness is a core parameter reflecting the degree of circumferential non-uniformity of pipe wall thickness. The larger the value, the more serious the eccentricity of the wall thickness. Specifically, the first step is to calculate the squares of the cosine coefficient and the sine coefficient of the wall thickness respectively; the second step is to add the two squared values ​​to get the sum; the third step is to calculate the arithmetic square root of the sum, and the result is the eccentricity amplitude of the pipe wall thickness.

[0033] The direction of maximum wall thickness refers to the angular position where the maximum circumferential wall thickness of the pipe is located. Specifically, it is determined by the four-quadrant argument calculation method. The cosine coefficient of the wall thickness is used as the abscissa and the sine coefficient of the wall thickness is used as the ordinate. The quadrant is determined according to the positive and negative signs of the two. Then, the angle between the line connecting the point to the origin and the positive direction of the abscissa is calculated. This angle is the direction of maximum wall thickness.

[0034] The gap cosine coefficient is a parameter that quantifies the distribution characteristics of the coil gap in the circumferential cosine direction, reflecting the amplitude of the gap variation along the circumferential cosine law. Specifically, the first step is to calculate the product of the measured value of the coil gap for each coil and the corresponding circumferential discrete point angle cosine value; the second step is to add all the products together to obtain the cumulative sum; the third step is to multiply the cumulative sum by two and then divide it by the total number of sampling points, and the result is the gap cosine coefficient.

[0035] The gap sine coefficient is a parameter that quantifies the distribution characteristics of the coil gap in the circumferential sine direction. Together with the gap cosine coefficient, it can completely describe the circumferential first harmonic distribution of the gap. Specifically, the first step is to calculate the product of the measured value of the coil gap for each coil gap and the sine value of the angle of the corresponding circumferential discrete point. The second step is to add all the products together to obtain the cumulative sum. The third step is to multiply the cumulative sum by two and then divide it by the total number of sampling points. The result is the gap sine coefficient.

[0036] The amplitude of coil gap fluctuation is a core parameter reflecting the degree of circumferential non-uniformity of the gap between the coil and the tube, which directly affects the uniformity of induction heating. Specifically, the first step is to calculate the squares of the gap cosine coefficient and the gap sine coefficient respectively; the second step is to add the two squared values ​​to get the sum; the third step is to calculate the arithmetic square root of the sum, and the result is the amplitude of coil gap fluctuation.

[0037] The minimum gap direction refers to the angular position where the minimum gap between the coil and the tube is located. Adding pi is the key process to convert the maximum gap direction into the minimum gap direction. Specifically, the first step is to obtain the four-quadrant argument of the gap (i.e., the maximum gap direction) according to the calculation method of the maximum wall thickness direction. The second step is to add the angle value corresponding to pi to this argument, and the result is the minimum gap direction.

[0038] The target phase difference is a parameter characterizing the relative positional relationship between wall thickness eccentricity and gap undulation in the circumferential angle. Specifically, the first step is to subtract the angle value in the direction of minimum gap from the angle value in the direction of maximum wall thickness to obtain the angle difference. The second step is to calculate the sine and cosine values ​​of this angle difference (i.e., sine projection and cosine projection). The third step is to use the cosine projection value as the abscissa and the sine projection value as the ordinate, and obtain the angle by performing arctangent calculation in the four quadrants. The value range is controlled between negative and positive pi.

[0039] In one embodiment of the present invention, calculating the wall thickness heat absorption weighting factor modulated by the power supply frequency includes:

[0040] Obtain the material resistivity and relative permeability as the pipe temperature changes, calculate the square root of the ratio of resistivity to the product of vacuum permeability, relative permeability, power frequency and pi, and obtain the skin depth.

[0041] Obtain the average wall thickness in the non-uniform geometric distribution model, calculate the ratio of the average wall thickness to the skin depth as negative two, and then raise the power of this ratio to the natural constant to obtain the thickness attenuation exponent.

[0042] Multiply the thickness attenuation index, the pipe wall thickness eccentricity amplitude, and the preset equipment calibration constant together, and divide the resulting product by the square of the skin depth to obtain the wall thickness heat absorption weighting factor modulated by the power supply frequency.

[0043] Material resistivity is a parameter that characterizes the ability of stainless steel to impede the passage of electric current, and its value changes with the heat treatment temperature of the pipe.

[0044] Relative permeability is the ratio of the permeability of stainless steel to the permeability of vacuum. In the commonly used temperature range for heat treatment of stainless steel, this value is approximately 1, and it fluctuates only slightly with temperature.

[0045] Vacuum permeability is a physical constant with a fixed value.

[0046] The power supply frequency is a core control parameter of induction heating equipment, which determines the electromagnetic penetration depth. The value range must match the frequency adjustable range of the equipment.

[0047] Skin depth is a parameter characterizing the penetration depth of induced current in a material, determining the range of heat deposition in the pipe wall thickness direction. Specifically, the first step is to calculate the product of vacuum permeability, relative permeability, power frequency, and pi; the second step is to divide the material resistivity by this product to obtain a ratio; the third step is to calculate the arithmetic square root of this ratio, and the result is the skin depth.

[0048] The average wall thickness is the arithmetic mean of the measured wall thickness values ​​at all circumferential discrete points when constructing the geometric model. It is a benchmark parameter reflecting the overall wall thickness of the pipe.

[0049] The thickness attenuation index is a parameter that quantifies the degree of heat attenuation in the pipe wall thickness direction, reflecting the influence of the skin effect on heat deposition. Specifically, the first step is to calculate the ratio of the average wall thickness to the skin depth; the second step is to multiply this ratio by negative two; the third step is to obtain the power value of this product with the natural constant as the base, and the result is the thickness attenuation index.

[0050] The equipment calibration constant is a fixed coefficient adapted to a specific induction heating equipment and coil structure, used to correct the deviation between theoretical calculations and actual heating effects. Specifically, it is determined through a single calibration test. A pipe with a standard wall thickness is selected, and the actual heat input is measured at a known power frequency. The ratio of the actual heat input to the theoretical calculation value is used as the equipment calibration constant.

[0051] In one embodiment of the present invention, calculating the circumferential heat flow migration factor determined by the pipe rotation speed includes:

[0052] Obtain the number of revolutions per second of the pipe, multiply it by twice pi, and get the angular velocity of the pipe's rotation;

[0053] Obtain the thermal diffusivity and outer radius of the pipe as the pipe temperature changes, and divide the thermal diffusivity by the square of the outer radius of the pipe to obtain the circumferential diffusivity;

[0054] Dividing the angular velocity of the pipe rotation by the circumferential diffusivity yields the circumferential heat transfer factor.

[0055] Rotations per second (RPS) refers to the number of times the pipe rotates per second during induction heating. It is obtained in real time through a speed sensor and is a fundamental physical quantity characterizing the rotational speed of the pipe.

[0056] The pipe rotational angular velocity is a parameter that converts the number of rotations of the pipe into the rate of change of angle, and is used to quantify the intensity of circumferential heat flow migration. Specifically, the pipe rotational angular velocity is obtained by multiplying the collected number of rotations per second of the pipe by twice the value of pi.

[0057] Thermal diffusivity is a parameter characterizing the ability of stainless steel to conduct heat, and it varies with heat treatment temperature.

[0058] The outer radius of the pipe refers to the radius of the outer circle of the stainless steel seamless pipe. It is obtained by measuring the average value of multiple points on the same cross section of the pipe with a laser diameter gauge. It is the geometric reference parameter for calculating the circumferential diffusion capacity.

[0059] Circumferential diffusivity is a parameter characterizing the rate at which heat diffuses in the circumferential direction of a pipe, realizing the coupling and quantification of the material's thermal diffusivity and the pipe's geometric dimensions; specifically, the circumferential diffusivity is obtained by dividing the obtained thermal diffusivity by the square of the outer radius of the pipe.

[0060] The circumferential heat transfer factor is a dimensionless parameter used to quantitatively compare the strength of the circumferential convection effect caused by pipe rotation and the thermal diffusion effect of the material itself. Specifically, the circumferential heat transfer factor is obtained by dividing the calculated pipe rotation angular velocity by the circumferential diffusivity.

[0061] In one embodiment of the present invention, solving for the critical morphological frequency includes:

[0062] The arithmetic mean of the set of measured coil gap values ​​is calculated and defined as the average coil gap value. The amplitude of the coil gap fluctuation is divided by the average coil gap value and multiplied by a preset gap sensitivity calibration constant to obtain the gap effect amplitude.

[0063] The initial power supply frequency is obtained by dividing the resistivity of the pipe by the product of the squares of pi, vacuum permeability, relative permeability, and the average wall thickness.

[0064] Iterative calculations are initiated based on the initial power frequency:

[0065] The residual function value is obtained by adding the products of the wall thickness heat absorption weighting factor, the gap effect amplitude and the target phase difference cosine value, and the circumferential heat flow migration factor, the gap effect amplitude and the target phase difference sine value.

[0066] Multiply the equipment calibration constant, the pipe wall thickness eccentricity amplitude and the reciprocal of the current power frequency, and then multiply by the thickness attenuation exponent, the negative cube of the skin depth, and the difference between the skin depth and the average wall thickness to obtain the derivative value of the weighting factor.

[0067] The updated power frequency is obtained by subtracting the ratio of the residual function value to the derivative value of the weighting factor from the current power frequency.

[0068] Repeated iterative calculations are performed until the absolute value of the residual function or the change in the power supply frequency is less than a preset threshold. The final power supply frequency is then defined as the critical morphological frequency.

[0069] The average coil gap is a benchmark parameter that reflects the overall size of the circumferential gap between the coil and the pipe. Specifically, the average coil gap is obtained by adding up all the data in the set of measured coil gap values ​​and dividing the sum by the total number of measured values.

[0070] The gap sensitivity calibration constant is a fixed coefficient adapted to a specific coil structure and is used to quantify the influence of coil gap changes on the induction heating effect. Specifically, it is determined through a single calibration test. A standard gap specimen is selected, and the actual heating effect under different gap fluctuations is measured. The ratio of the actual heating effect to the theoretical calculation value is used as the gap sensitivity calibration constant.

[0071] The gap effect amplitude is a parameter that comprehensively reflects the degree of gap fluctuation and coil sensitivity, and is used to quantify the impact of gap changes on heat source distribution. Specifically, the first step is to divide the coil gap fluctuation amplitude by the average coil gap to obtain the relative value of gap fluctuation; the second step is to multiply the relative value by the gap sensitivity calibration constant, and the result is the gap effect amplitude.

[0072] The initial power supply frequency is the starting reference value for the iterative calculation. It is selected based on the material properties and pipe geometry parameters to ensure rapid convergence of the iteration. Specifically, the first step is to calculate the product of pi, vacuum permeability, relative permeability and the square of the average wall thickness. The second step is to divide the pipe resistivity by this product, and the result is the initial power supply frequency.

[0073] Iterative calculation is a numerical calculation process that gradually approaches the critical morphological frequency by continuously updating the power supply frequency. The core is to use the residual function value to judge the degree of approximation.

[0074] The target phase difference cosine value is the cosine trigonometric function value corresponding to the target phase difference, which is used to quantify the coupling relationship between wall thickness and gap in phase; specifically, by inputting the target phase difference through a trigonometric function calculation tool, the corresponding cosine value is obtained, which is the target phase difference cosine value.

[0075] The target phase difference sine value is the sine trigonometric function value corresponding to the target phase difference, which, together with the cosine value, completes phase coupling quantization. Specifically, by using a trigonometric function calculation tool, inputting the target phase difference, the corresponding sine value is obtained, which is the target phase difference sine value.

[0076] The residual function value is the core indicator for judging whether the current power supply frequency is close to the critical morphological frequency. The closer the value is to zero, the closer the current frequency is to the critical value. Specifically, the first step is to calculate the product of the gap effect amplitude and the cosine of the target phase difference, and then calculate the product of the circumferential heat flow migration factor, the gap effect amplitude and the sine of the target phase difference. The second step is to add the wall thickness heat absorption weighting factor to the above two product results one by one, and the sum is the residual function value.

[0077] The derivative value of the weighting factor is the basis for adjusting the gradient of the power supply frequency in the iterative calculation, and determines the step size of each iteration. Specifically, the first step is to multiply the equipment calibration constant, the eccentricity amplitude of the pipe wall thickness, and the reciprocal of the current power supply frequency. The second step is to multiply this product by the thickness attenuation exponent, the negative cube of the skin depth, and the difference between the average skin depth and the average wall thickness in sequence. The final result is the derivative value of the weighting factor.

[0078] The updated power frequency is a new frequency value obtained after one iteration, which is an intermediate result of gradually approaching the critical morphological frequency; specifically, the updated power frequency is obtained by subtracting the ratio of the residual function value to the derivative value of the weighting factor from the current power frequency.

[0079] The preset threshold is the critical criterion for determining whether the iterative calculation has terminated. It includes two types: the residual function value threshold and the frequency change amplitude threshold. Specifically, the preset threshold for the residual function value is set to 0.001, and the preset threshold for the power supply frequency update change amplitude is set to per kilohertz. It can be finely adjusted according to the process accuracy requirements.

[0080] The critical morphological frequency is the core reference frequency that makes the wall thickness heat absorption effect and the gap fluctuation effect cancel each other out and the temperature curvature polarity reverse in the thinnest wall direction. Specifically, when the absolute value of the residual function is less than the residual preset threshold, or the power supply frequency update change amplitude is less than the frequency change preset threshold, the iteration stops, and the power supply frequency at this time is the critical morphological frequency.

[0081] In one embodiment of the present invention, real-time monitoring of the local circumferential temperature curvature in the thinnest wall direction of the pipe includes:

[0082] By superimposing the constant pi in the direction of maximum wall thickness, the circumferential angle in the direction of thinnest wall thickness is obtained;

[0083] Set the circumferential angle spacing. At each sampling period, collect the temperature value of the outer surface of the pipe at the circumferential angle in the thinnest wall direction as the center temperature value, collect the temperature value of the outer surface of the pipe at the circumferential angle in the thinnest wall direction plus the circumferential angle spacing as the positive offset temperature value, and collect the temperature value of the outer surface of the pipe at the circumferential angle in the thinnest wall direction minus the circumferential angle spacing as the negative offset temperature value.

[0084] Add the positive offset temperature measurement value to the negative offset temperature measurement value, and subtract twice the center temperature measurement value to obtain the temperature difference value; divide the temperature difference value by the square of the circumferential angular spacing to obtain the local circumferential temperature curvature.

[0085] The circumferential angle in the direction of the thinnest wall is a key angular parameter for determining the core location of temperature monitoring, providing an accurate orientation reference for three-point temperature measurement. Specifically, the circumferential angle in the direction of the thinnest wall is obtained by adding the angle value corresponding to the constant pi to the angle value corresponding to the direction of the maximum wall thickness.

[0086] The circumferential angle spacing is the angular interval between the circumferential angle in the thinnest wall direction and the temperature measuring points on both sides. It is used to construct a three-point temperature measuring structure to calculate the curvature. Specifically, it is set between 20 and 30 degrees according to the process accuracy requirements. The commonly used value is 25 degrees, which can be finely adjusted according to the pipe size.

[0087] The sampling period is the time interval between two consecutive temperature data acquisitions, which determines the real-time nature of temperature monitoring. Specifically, it is set between 0.1 seconds and 0.5 seconds according to the rhythm of the heat treatment process, with 0.1 seconds for high-frequency heating scenarios and 0.5 seconds for heat preservation scenarios.

[0088] The temperature reading at the center is the temperature data at the core location in the direction of the thinnest wall.

[0089] The positive offset temperature measurement value is the temperature data on the side of the circumferential angle in the thinnest wall direction. It is used in conjunction with the negative offset temperature measurement value to reflect the circumferential trend of temperature change.

[0090] The negative offset temperature measurement value is the temperature data on the other side of the circumferential angle in the thinnest wall direction, which together with the positive offset temperature measurement value forms the basis for temperature gradient calculation.

[0091] The temperature difference value is an intermediate parameter that quantifies the temperature distribution gradient at three points and directly reflects the curvature trend of the temperature curve. Specifically, the positive offset temperature measurement value and the negative offset temperature measurement value are added together to obtain a sum, and then twice the center temperature measurement value is subtracted from the sum. The result is the temperature difference value.

[0092] Local circumferential temperature curvature is a core parameter characterizing the bending shape of temperature distribution in the thinnest wall direction. Its positive and negative values ​​correspond to temperature bulges or depressions, while zero values ​​correspond to an ideal flat state. Specifically, the calculated temperature difference value is divided by the square of the circumferential angular spacing to obtain the local circumferential temperature curvature.

[0093] In one embodiment of the present invention, using the critical morphological frequency as the control benchmark, the local circumferential temperature curvature is driven to follow a preset process target value by coordinating the adjustment of the power supply frequency and the tube rotation speed, including:

[0094] Obtain the preset process target value, calculate the difference between the process target value and the local circumferential temperature curvature, and define it as curvature deviation;

[0095] The curvature adjustment command is obtained by adding the product of curvature deviation and preset curvature loop proportional gain, as well as the product of historical cumulative curvature deviation and preset curvature loop integral gain.

[0096] Obtain the preset adjustment allocation factor, calculate the product of the curvature adjustment command and the adjustment allocation factor, and define it as the power frequency increment; calculate the ratio of the difference between the value and the adjustment allocation factor to the preset equivalent gain conversion coefficient, and multiply the ratio by the curvature adjustment command, and define it as the rotational angular velocity increment.

[0097] The critical mode frequency is added to the power frequency increment, and the addition result is subjected to saturation truncation based on the preset upper and lower limits of the power frequency to obtain the power frequency setting value at the next moment.

[0098] Obtain the actual value of the pipe's rotational angular velocity at the current moment, add it to the increment of the rotational angular velocity, and perform saturation truncation processing on the addition result based on the preset upper and lower limits of the allowable rotational angular velocity to obtain the set value of the rotational angular velocity at the next moment.

[0099] The preset process target value is a local circumferential temperature curvature target value set according to the heat treatment process requirements of stainless steel seamless tubes, which determines the ideal shape of temperature distribution; specifically, the heating section is set to a value greater than zero, the heat preservation section is set to zero, and the cooling section is set to a value greater than or equal to zero. The commonly used heat preservation section target value is zero.

[0100] Curvature deviation is a core indicator for measuring the difference between the actual temperature shape and the ideal target shape. Its positive or negative sign reflects the direction of deviation, and its absolute value reflects the degree of deviation. Specifically, the curvature deviation is obtained by subtracting the local circumferential temperature curvature from the preset process target value.

[0101] The preset curvature loop proportional gain is a control parameter used to amplify curvature deviation and quickly respond to deviation; specifically, it is set between 0.1 and 1.0 according to the process response requirements, with 0.8 for the heating stage, 0.3 for the holding stage, and 0.6 for the cooling stage.

[0102] The historical cumulative sum of curvature deviation is the sum of the curvature deviations accumulated in each sampling period from the start of control, and is used to eliminate static deviations in the system.

[0103] The preset curvature loop integral gain is a control parameter used to eliminate static deviations and improve control accuracy; specifically, the value ranges from 0.01 to 0.1, with 0.08 for the heating stage, 0.03 for the heat preservation stage, and 0.05 for the cooling stage.

[0104] The curvature adjustment command is a control output that combines proportional and integral actions, directly determining the adjustment intensity of the subsequent power supply frequency and rotation speed. Specifically, the first step is to calculate the product of the curvature deviation and the preset curvature loop proportional gain; the second step is to calculate the product of the historical cumulative sum of the curvature deviation and the preset curvature loop integral gain; the third step is to add the two product results together, and the sum obtained is the curvature adjustment command.

[0105] The preset adjustment allocation factor is a parameter used to allocate the adjustment weight of the curvature adjustment command between the power supply frequency and the rotation speed; specifically, the value ranges from 0 to 1, with 0.7 to 0.9 when the frequency is adjusted first, 0.1 to 0.3 when the rotation speed is adjusted first, and 0.5 when the balance is adjusted.

[0106] The power frequency increment is the adjustment range of the power frequency, used to move closer to the critical state frequency and correct temperature curvature deviation; specifically, the result of multiplying the curvature adjustment command by the preset adjustment allocation factor is the power frequency increment.

[0107] The preset equivalent gain conversion factor is an adaptation factor that converts the curvature adjustment command into the unit of rotational angular velocity increment, used to unify the adjustment dimensions; specifically, it is determined through equipment calibration, taking the ratio of the rotational angular velocity adjustment range to the frequency adjustment range, with commonly used values ​​ranging from 0.5 to 2.0.

[0108] The rotational angular velocity increment is the adjustment range of the rotational angular velocity, which serves as an auxiliary means of power frequency regulation to correct temperature curvature deviation. Specifically, the first step is to subtract the preset adjustment allocation factor from the numerical value, and divide the difference by the preset equivalent gain conversion coefficient. The second step is to multiply the result by the curvature adjustment command amount, which gives the rotational angular velocity increment.

[0109] The preset power frequency upper and lower limits are frequency boundary values ​​set according to the capabilities of the induction heating equipment to prevent the frequency from exceeding the equipment's operating range. Specifically, the lower limit is set to the equipment's minimum rated frequency, and the upper limit is set to the equipment's maximum rated frequency, with a common range of 2 kHz to 10 kHz.

[0110] The power frequency setting value for the next moment is the final frequency command to drive the induction heating equipment, ensuring that the frequency is within a safe and effective range. Specifically, the first step is to add the critical state frequency to the power frequency increment. The second step is to take the lower limit value if the result is lower than the preset power frequency allowable lower limit value, and the upper limit value if it is higher than the upper limit value. If it is within the range, the sum is taken, which is the power frequency setting value for the next moment.

[0111] The actual value of the pipe's rotational angular velocity at the current moment is the angular velocity data of the pipe's current rotation, which is collected in real time by the speed sensor and serves as the reference value for adjusting the rotational speed.

[0112] The preset upper and lower limits of the rotational angular velocity are angular velocity boundary values ​​set according to the capacity of the pipe conveying equipment to avoid equipment overload; specifically, the lower limit is set to the minimum rated rotational angular velocity of the equipment, and the upper limit is set to the maximum rated rotational angular velocity of the equipment, with a common range of 2 radians per second to 8 radians per second.

[0113] The rotational angular velocity setting value for the next moment is the final angular velocity command that drives the pipe rotation equipment, ensuring safe and effective rotation adjustment. Specifically, the first step is to add the actual value of the pipe rotational angular velocity at the current moment to the rotational angular velocity increment. The second step is to take the lower limit value if the result is lower than the preset allowable lower limit of rotational angular velocity, take the upper limit value if it is higher than the upper limit, and take the upper limit value if it is within the range. The sum is the rotational angular velocity setting value for the next moment.

[0114] The embodiments of this example have been described above. However, this example is not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms based on the guidance of this example, and all of them are within the protection scope of this example.

Claims

1. A heat treatment temperature control system for seamless stainless steel tubes, comprising a data processing unit and a multivariable execution unit, characterized in that: The data processing unit is configured to: construct a non-uniform geometric distribution model that includes the eccentric amplitude of the pipe wall thickness, the fluctuation amplitude of the coil gap, and the target phase difference; and combine the thermal property parameters of the material with temperature changes to calculate the wall thickness heat absorption weight factor modulated by the power supply frequency and the circumferential heat flow migration factor determined by the rotational angular velocity of the pipe. The data processing unit further uses a non-uniform geometric distribution model to solve for the critical frequency of temperature distribution along the thinnest wall direction where the wall thickness heat absorption weighting factor and the gap undulation effect cancel each other out under the influence of the circumferential heat flow migration factor. This results in the critical frequency of the curvature polarity reversal of the temperature distribution along the thinnest wall direction of the pipe, including: The arithmetic mean of the set of measured coil gap values ​​is calculated and defined as the average coil gap value. The amplitude of the coil gap fluctuation is divided by the average coil gap value and multiplied by a preset gap sensitivity calibration constant to obtain the gap effect amplitude. The initial power supply frequency is obtained by dividing the resistivity of the pipe by the product of the squares of the constant pi, the permeability of vacuum, the relative permeability, and the average wall thickness. Iterative calculations are initiated based on the initial power frequency: The residual function value is obtained by adding the products of the wall thickness heat absorption weighting factor, the gap effect amplitude and the target phase difference cosine value, and the circumferential heat flow migration factor, the gap effect amplitude and the target phase difference sine value. Multiply the preset equipment calibration constant, the pipe wall thickness eccentricity amplitude and the reciprocal of the current power frequency, and then multiply by the thickness attenuation exponent, the negative cube of the skin depth, and the difference between the skin depth and the average wall thickness to obtain the derivative value of the weighting factor. The updated power frequency is obtained by subtracting the ratio of the residual function value to the derivative value of the weighting factor from the current power frequency. Repeat the iterative calculation until the absolute value of the residual function value or the update change of the power frequency is less than the preset threshold, and define the final power frequency as the critical morphological frequency. The multivariable execution unit is configured to: monitor the local circumferential temperature curvature in the thinnest wall direction of the tube in real time during the heating process, and use the critical morphological frequency as the control reference, drive the local circumferential temperature curvature closed loop to follow the preset process target value by coordinating the adjustment of the power supply frequency and the tube rotation angular velocity; The preset gap sensitivity calibration constant is a fixed coefficient adapted to a specific coil structure, used to quantify the impact of coil gap changes on the induction heating effect; The preset process target value is a local circumferential temperature curvature target value set according to the heat treatment process requirements of stainless steel seamless tubes.

2. The heat treatment temperature control system for stainless steel seamless tubes according to claim 1, characterized in that, A non-uniform geometric distribution model is constructed, including the amplitude of pipe wall thickness eccentricity, the amplitude of coil gap fluctuation, and the target phase difference, comprising: Collect the set of measured wall thickness values ​​and the set of measured coil gap values ​​at multiple circumferential discrete points on the outer surface of the pipe. Calculate the sum of the products of each measured wall thickness and the corresponding cosine and sine values ​​of the angle at the circumferential discrete point. Multiply the sum by twice the reciprocal of the total number of sampling points to obtain the wall thickness cosine coefficient and wall thickness sine coefficient. Take the square root of the sum of the squares of the wall thickness cosine coefficient and wall thickness sine coefficient as the pipe wall thickness eccentricity amplitude, and take the four quadrant arguments of the wall thickness sine coefficient and wall thickness cosine coefficient as the direction of maximum wall thickness. Calculate the sum of the products of the measured gap value of each coil and the cosine and sine values ​​of the corresponding circumferential discrete point angles. Multiply the sum by twice the reciprocal of the total number of sampling points to obtain the gap cosine coefficient and gap sine coefficient. Take the square root of the sum of the squares of the gap cosine coefficient and gap sine coefficient as the coil gap fluctuation amplitude. Take the angle obtained by superimposing the four quadrant arguments of the gap sine coefficient and gap cosine coefficient with the constant pi as the gap minimum direction. Calculate the angle difference between the direction of maximum wall thickness and the direction of minimum gap, and perform sine and cosine projection on this angle difference. Determine the target phase difference based on the four-quadrant arctangent calculation results of the projection values.

3. A heat treatment temperature control system for stainless steel seamless tubes according to claim 2, characterized in that, Calculate the wall thickness heat absorption weighting factor modulated by the power supply frequency, including: Obtain the material resistivity and relative permeability as the pipe temperature changes, calculate the square root of the ratio of resistivity to the product of vacuum permeability, relative permeability, power supply frequency and pi constant, and obtain the skin depth. Obtain the average wall thickness in the non-uniform geometric distribution model, calculate the ratio of the average wall thickness to the skin depth as negative two, and then raise the power of this ratio to the natural constant to obtain the thickness attenuation exponent. Multiply the thickness attenuation index, the pipe wall thickness eccentricity amplitude, and the preset equipment calibration constant together, and divide the resulting product by the square of the skin depth to obtain the wall thickness heat absorption weighting factor modulated by the power supply frequency.

4. A heat treatment temperature control system for stainless steel seamless tubes according to claim 3, characterized in that, Calculate the circumferential heat transfer factor determined by the pipe's rotational angular velocity, including: Obtain the number of revolutions per second of the pipe, multiply it by twice the constant of pi, and get the angular velocity of the pipe's rotation; Obtain the thermal diffusivity and outer radius of the pipe as the pipe temperature changes, and divide the thermal diffusivity by the square of the outer radius of the pipe to obtain the circumferential diffusivity; Dividing the angular velocity of the pipe rotation by the circumferential diffusivity yields the circumferential heat transfer factor.

5. A heat treatment temperature control system for stainless steel seamless tubes according to claim 4, characterized in that, Real-time monitoring of the local circumferential temperature curvature along the thinnest wall direction of the pipe, including: By superimposing the constant pi in the direction of maximum wall thickness, the circumferential angle in the direction of thinnest wall thickness is obtained; Set the circumferential angle spacing. At each sampling period, collect the temperature value of the outer surface of the pipe at the circumferential angle in the thinnest wall direction as the center temperature value, collect the temperature value of the outer surface of the pipe at the circumferential angle in the thinnest wall direction plus the circumferential angle spacing as the positive offset temperature value, and collect the temperature value of the outer surface of the pipe at the circumferential angle in the thinnest wall direction minus the circumferential angle spacing as the negative offset temperature value. Add the positive offset temperature measurement value to the negative offset temperature measurement value, and subtract twice the center temperature measurement value to obtain the temperature difference value; divide the temperature difference value by the square of the circumferential angular spacing to obtain the local circumferential temperature curvature.

6. A heat treatment temperature control system for stainless steel seamless tubes according to claim 5, characterized in that, Using the critical morphological frequency as the control benchmark, the local circumferential temperature curvature is driven to follow the preset process target value by coordinating the adjustment of the power supply frequency and the tube rotation angular velocity, including: Obtain the preset process target value, calculate the difference between the process target value and the local circumferential temperature curvature, and define it as curvature deviation; The curvature adjustment command is obtained by adding the product of curvature deviation and preset curvature loop proportional gain, as well as the product of historical cumulative curvature deviation and preset curvature loop integral gain. Obtain the preset adjustment allocation factor, calculate the product of the curvature adjustment command and the preset adjustment allocation factor, and define it as the power frequency increment; calculate the ratio of the difference between the value and the preset adjustment allocation factor to the preset equivalent gain conversion coefficient, and multiply the ratio by the curvature adjustment command, and define it as the rotational angular velocity increment. The critical mode frequency is added to the power frequency increment, and the addition result is subjected to saturation truncation based on the preset upper and lower limits of the power frequency to obtain the power frequency setting value at the next moment. Obtain the actual value of the pipe rotation angular velocity at the current moment, add it to the rotation angular velocity increment, and perform saturation truncation processing on the addition result based on the preset upper and lower limits of the pipe rotation angular velocity to obtain the set value of the pipe rotation angular velocity at the next moment. The preset adjustment allocation factor is a parameter used to allocate the adjustment weight of the curvature adjustment command between the power frequency and the pipe rotation angular velocity; The preset equivalent gain conversion factor is an adaptation factor that converts the curvature adjustment command into the unit of rotational angular velocity increment. The preset curvature loop integral gain is a control parameter used to eliminate static deviations and improve control accuracy. The preset curvature loop proportional gain is a control parameter used to amplify curvature deviation and quickly respond to deviation.

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