CN115130348A - Method for calculating maximum temperature rise rate of after-local welding heat treatment of medium-frequency induction heating of 9% Cr hot-strength steel thick-wall pipeline - Google Patents
Method for calculating maximum temperature rise rate of after-local welding heat treatment of medium-frequency induction heating of 9% Cr hot-strength steel thick-wall pipeline Download PDFInfo
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Abstract
The invention discloses a method for calculating the maximum temperature rise rate of medium-frequency induction heating local postweld heat treatment of a 9% Cr hot-strength steel thick-wall pipeline. The method comprises the following steps: firstly, establishing a transient model of a heat treatment temperature field after partial welding of medium-frequency induction heating of a 9% Cr hot-strength steel thick-wall pipeline to obtain the maximum axial temperature gradient of different characteristic points in the whole heat treatment process; then obtaining the maximum axial temperature gradient allowed by each axial characteristic point of the pipeline through an equation of the axial temperature gradient and the induced stress; and finally, calculating the maximum heating rate of the pipelines with different wall thicknesses under the temperature gradient according to the maximum axial temperature gradient allowed by each axial characteristic point of the pipeline, fitting to obtain a maximum heating rate formula, and calculating to obtain the maximum heating rate according to the wall thickness of the pipeline. The calculation method is suitable for the medium-frequency induction heating process, the maximum temperature rise rate can be calculated, the heat treatment time is shortened as far as possible under the condition that safe operation is guaranteed, the construction period is shortened, and the heat treatment cost is reduced.
Description
Technical Field
The invention belongs to the technical field of heat-resistant steel welding, and particularly relates to a method for calculating the maximum heating rate of a 9% Cr hot-strength steel thick-wall pipeline during local postweld heat treatment in a medium-frequency induction heating mode, which is applicable to welding of novel 9% Cr hot-strength steel thick-wall pipelines such as P91, P92 and G115.
Background
The novel 9% Cr thermal-strength steel has good high-temperature oxidation resistance and high-temperature creep resistance, high thermal conductivity and low linear expansion coefficient, and is an ideal material for manufacturing thick-wall parts such as a high-parameter thermal power generating unit header, a main steam pipe and the like. However, the weldability of the novel 9% Cr hot strength steel is poor, the welded joint of the steel is subjected to phase transformation under the action of a welding thermal field, and forms a hard and brittle martensite structure after cooling, so that the toughness of the welded state is low, and the joint structure must be improved through postweld heat treatment in engineering, and residual stress is eliminated. At present, a commonly used postweld heat treatment method during field construction is flexible ceramic resistance heating, and the method has the advantages of low heating power, poor heating uniformity, large heating width and large heat damage to a base material. In addition, the method has poor heating control, so the engineering generally selects a smaller heating rate, which increases the construction period. In view of the above disadvantages, the application of the medium frequency induction heating method in the heat treatment of the novel 9% Cr hot strength steel pipeline is attracting attention, and the medium frequency induction heating method has the advantages of good heating uniformity, high temperature rise rate, controllable process and less damage to the base metal.
The heating rate is an important parameter to be selected during the postweld heat treatment. The temperature rise rate is improved, so that the temperature rise time of postweld heat treatment can be shortened, the construction period is shortened, the heat treatment efficiency is improved, and the cost is saved. However, if the temperature rise rate is too high, an obvious temperature gradient is generated in the axial direction of the pipeline, and if the axial temperature gradient is too large, new residual stress is generated, so that the safe operation of the pipeline is influenced. Therefore, the heating rate has an optimal value, namely the maximum heating rate, and the efficiency and the safe operation of the pipeline can be considered. Although some studies exist on the optimization method of the post-weld heat treatment temperature rise rate of the 9% Cr hot strength steel pipeline at present, for example, patent 2019111714440 proposes an optimization calculation method of the post-weld heat treatment temperature rise rate of the 9% Cr hot strength steel pipeline, but the optimization calculation method is only suitable for flexible ceramic resistance heating. For medium-frequency induction heating, the heating power is high, the temperature rising process is well controlled, the axial temperature distribution of the pipeline is more uniform under the same heat treatment parameters, and higher temperature rising rate can be allowed. The power industry standard DL/T819-2019 provides a calculation formula 8000/delta (DEG C/h, delta is the wall thickness of the pipeline, mm) for selecting the temperature rise rate according to the wall thickness, but the calculation result of the formula is conservative. In order to shorten the construction period in the engineering, it is necessary to increase the temperature rise rate as much as possible and shorten the heat treatment time. Therefore, the method for calculating the maximum temperature rise rate of the medium-frequency induction heating local postweld heat treatment of the 9% Cr hot-strength steel pipeline has obvious practical value.
Disclosure of Invention
The invention aims to provide a method for calculating the maximum heating rate of the medium-frequency induction heating local postweld heat treatment of a 9% Cr hot-strength steel pipeline, which is suitable for the medium-frequency induction heating process, can obtain the maximum heating rate, and can reduce the heat treatment time, shorten the construction period and reduce the heat treatment cost as much as possible under the condition of ensuring safe operation.
In order to solve the technical problem, the invention adopts the following technical scheme:
the method for calculating the maximum heating rate of the local postweld heat treatment of the medium-frequency induction heating of the 9% Cr hot-strength steel thick-wall pipeline comprises the following steps of:
step 1: establishing a transient temperature field model of the after-local induction heating heat treatment of the hot-strength steel thick-wall pipeline with 9% of Cr to obtain the maximum axial temperature gradient of different characteristic points in the whole heat treatment process;
step 2: obtaining the maximum axial temperature gradient allowed by each axial characteristic point of the pipeline through an equation of the axial temperature gradient and the induced stress;
and step 3: and (3) calculating the maximum temperature rise rate of the pipelines with different wall thicknesses under the temperature gradient according to the maximum axial temperature gradient allowed by each characteristic point in the axial direction of the pipeline obtained in the step (2), fitting the calculation result to obtain a maximum temperature rise rate formula, and calculating to obtain the maximum temperature rise rate according to the wall thickness of the pipeline.
According to the scheme, in the step 1, a transient model is established through finite element software.
According to the scheme, in the step 1, the characteristic points are as follows: the edge of the heating zone of the outer wall of the pipeline and the middle point from the center of the welding seam of the outer wall of the pipeline to the edge of the heating zone.
According to the scheme, in the step 1, a concrete method for suggesting the transient model comprises the following steps:
step 1.1, selecting a pipeline with a certain specification, selecting parameters according to the electric power industry standard DL/T819-2019, and modeling the pipeline specification and the parameters by using finite element software;
step 1.2, coupling an electromagnetic model and a heat transfer model, inputting transient time domain excitation, applying extra heating power excitation after a temperature control point reaches Curie temperature, and enabling the temperature control point to reach temperature control temperature to obtain a medium-frequency induction heating local postweld heat treatment temperature field transient model;
and step 1.3, selecting corresponding characteristic points of the outer wall of the pipeline by using the obtained intermediate frequency induction heating local postweld heat treatment temperature field transient model, determining time nodes of the maximum axial temperature gradients of the characteristic points in the whole heat treatment process, and obtaining the maximum axial temperature gradients of different characteristic points in the whole heat treatment process.
Preferably, in the step 1.1, the pipe specification is wall thickness; the parameters of the pipeline comprise heating width, heat preservation width, alternating current frequency, the number of turns and the turn interval of the induction coil and heating rate.
Preferably, in step 1.3, when the central point of the weld of the outer wall of the pipeline just reaches the steady-state temperature, the axial temperature gradient of the characteristic point is the maximum, that is, the time node at which the maximum axial temperature gradient occurs in the whole heat treatment process of the characteristic point.
According to the scheme, in the step 2, the specific method for obtaining the maximum axial temperature gradient allowed by each axial characteristic point of the pipeline comprises the following steps:
step 2.1, calculating the deflection of the axisymmetric cylinder, which is generated due to the axial temperature gradient, and solving the deflection according to the Fourier heat transfer theorem to obtain the maximum bending stress of the axisymmetric cylinder;
step 2.2, solving according to the maximum bending stress formula obtained in the step 2.1 to obtain the relation between the maximum stress and the axial temperature gradient of each characteristic point of the outer wall of the pipeline;
and 2.3, carrying out value calculation on the formula obtained in the step 2.2, and calculating to obtain the maximum axial temperature gradient allowed under the condition of safe operation of each characteristic point of the outer wall of the pipeline.
Preferably, in step 2.1, the maximum bending stress formula is:
wherein E is elastic modulus, h is coefficient, R is radius of inner wall of the pipeline, upsilon is Poisson ratio, and T (x) is axial temperature distribution of the pipeline.
According to the scheme, in the step 3, the formula of the maximum heating rate is as follows:
v＝0.03081t 2 -6.8416t+454.73273 (12)
wherein v (DEG C/h) is the heating temperature rise rate; t (mm) is the tube wall thickness.
According to the scheme, in the step 3, the specific method comprises the following steps:
step 3.1, calculating the maximum heating rates of pipelines with different specifications (wall thicknesses) according to the temperature field transient model obtained in the step 1 and the maximum axial temperature gradient allowed by each characteristic point obtained in the step 2;
and 3.2, fitting the data obtained in the step 3.1 to obtain a selection curve of the maximum heating rate and a calculation formula.
The invention has the following beneficial effects:
the invention provides a method for calculating the maximum heating rate of local postweld heat treatment of medium-frequency induction heating of a 9% Cr hot-strength steel thick-wall pipeline, which is suitable for the medium-frequency induction heating process, can obtain the maximum heating rates of pipelines with different wall thicknesses on the premise of ensuring the axial temperature gradient, can reduce the heat treatment time as far as possible on the basis of ensuring the safe operation, shortens the construction period, improves the heat treatment efficiency, reduces the heat treatment cost, has important industrial application value, and can be suitable for welding novel 9% Cr hot-strength steel thick-wall pipelines such as P91, P92, G115 and the like.
Drawings
FIG. 1 shows a maximum temperature rise rate fitted curve for pipes of different wall thicknesses obtained in an example of the present invention.
FIG. 2 is a flow chart of a simulation of a heating phase of an induction heating postweld heat treatment in an embodiment of the present invention.
Detailed Description
The technical solution of the present invention is further specifically described below by way of examples with reference to the accompanying drawings.
The embodiment of the invention provides a method for calculating the maximum heating rate of the medium-frequency induction heating local postweld heat treatment of a 9% Cr hot-strength steel pipeline, which comprises the steps of firstly establishing a temperature field transient model of the medium-frequency induction heating local postweld heat treatment of the 9% Cr hot-strength steel pipeline, and finding out the node of the maximum axial temperature gradient in the whole heat treatment process; and then determining the maximum axial temperature gradient allowed under the safe operation condition through an equation of the axial temperature gradient and the induced stress. Calculating the maximum heating rate of pipelines with different specifications under the maximum axial temperature gradient allowed based on the established transient model, fitting the calculation result, and finally obtaining a calculation formula of the maximum heating rate of the medium-frequency induction heating local postweld heat treatment; the method specifically comprises the following steps:
in the step 1, establishing a medium-frequency induction heating local postweld heat treatment temperature field transient model, taking the edge of a heating area of the outer wall of the pipeline and the midpoint between the center of a welding seam of the outer wall of the pipeline and the edge of the heating area as characteristic points, and calculating the maximum axial temperature gradient time node of the characteristic points in the whole heat treatment process, wherein the specific method comprises the following steps:
step 1.1, modeling the specification and parameters of a P91 pipeline in a finite element software, wherein the specification is OD540 multiplied by 85mm, the heating width is 800mm, the heat preservation width is 1000mm, the frequency of introduced alternating current is 1500Hz, the number of turns and the turn-to-turn distance of an induction coil are 17 and 30mm, and the heating rate is controlled to be 100 ℃/h;
step 1.2, coupling an electromagnetic model and a heat transfer model, inputting transient time domain excitation to obtain a medium-frequency induction heating local postweld heat treatment transient model, and applying heating power adjusted in real time according to temperature control point temperature to enable the temperature control point temperature to reach 760 ℃ after the temperature control point temperature reaches 750 ℃;
and step 1.3, using the obtained intermediate frequency induction heating local postweld heat treatment temperature field transient model, taking the edge of a heating area of the outer wall of the pipeline and the midpoint between the center of a welding seam of the outer wall of the pipeline and the edge of the heating area as characteristic points, and determining the time node of the maximum axial temperature gradient of each characteristic point in the whole heat treatment process, specifically, when the center point of the welding seam of the outer wall of the pipeline just reaches the steady-state temperature, the axial temperature gradient of the characteristic point is maximum.
In step 2, the maximum axial temperature gradient allowed under the safe operation condition is determined through an equation of the axial temperature gradient and the induced stress, and the specific method is as follows:
step 2.1, calculating the deflection omega of the axisymmetric cylinder generated by the axial temperature gradient can be expressed as:
ω″′(x)+4β 4 ω(x)＝-4β 4 αR[T(x)-T] (1)
wherein alpha is the heat transfer coefficient of the material, R is the radius of the inner wall of the pipeline, T is the ambient temperature, and T (x) is the temperature distribution along the axial direction of the pipeline.
β 4 Can be expressed as:
wherein upsilon is Poisson's ratio, and t is the wall thickness of the pipeline;
the maximum bending stress for an axisymmetric cylinder can be expressed as:
σ xmax ＝6M x /t (3)
in the formula:
M x ＝-Dω″(x) (4)
in the formula:
wherein E is the modulus of elasticity;
from the fourier heat transfer law, equation 2 can be solved:
ω(x)＝-αR[T(x)-T] (6)
by taking the second derivative of equation 6 and substituting equation 3, the maximum bending stress can be expressed as:
step 2.2, calculating the relation between the bending stress and the axial temperature gradient of each characteristic point of the outer wall of the pipeline, and recording the temperature of the central point of the welding seam of the outer wall of the pipeline as T 0 The characteristic point temperature is T 1 And T 2 Wherein T is 1 Refers to the temperature, T, of the edge of the heating zone of the outer wall 2 Refers to the temperature from the center of the outer wall weld to the midpoint of the edge of the heating zone. The distance of pipeline outer wall welding seam central point to the edge of the heating area is recorded as s, and the distance of outer wall surface to outer wall welding seam central point is x, then the upward temperature distribution of pipeline axial can be expressed as:
the second derivative of equation 8 is substituted for equation (7) to obtain:
because the pipeline is a cylinder, the following components are provided:
and 2.3, taking a value of the formula obtained in the step 2.2, wherein the reciprocal of the axial temperature gradient can be expressed as:
the maximum bending stress is twice of the yield strength at constant temperature (namely temperature control temperature), and is substituted into other material attribute values, so that the allowable maximum axial temperature gradient at the edge of a heating area of the pipeline is about 2.1; will be T in the formula 1 Substitution to T 2 That is, the maximum allowable axial temperature gradient from the center of the weld of the outer wall of the pipe to the midpoint of the edge of the heating zone of the outer wall of the pipe is about 1.26.
In step 3, calculating the maximum temperature rise rate of the pipelines with different specifications (wall thicknesses) under the condition according to the maximum axial temperature gradient allowed by each axial characteristic point of the pipeline obtained in step 2, and fitting the calculation result, wherein the specific method comprises the following steps:
step 3.1, obtaining the maximum allowable axial temperature gradient of about 2.1 at the edge of the heating area of the pipeline according to the transient model obtained in the step 1 and the step 2, obtaining the maximum allowable axial temperature gradient of about 1.26 at the middle point from the center of the welding seam of the outer wall of the pipeline to the edge of the heating area of the outer wall of the pipeline, and calculating the maximum temperature rise rate of pipelines (20mm-120mm) with different wall thicknesses;
step 3.2, fitting the data obtained in the step 3.1 to obtain a selection curve of the maximum heating rate, wherein the obtained fitting formula is as follows:
v＝0.03081t 2 -6.8416t+454.73273 (12)
wherein v (DEG C/h) is a heating temperature rise rate; t (mm) is the pipe wall thickness. The maximum heating rate under different wall thicknesses can be calculated through a fitting formula.
Examples
For P91 pipelines with specifications of OD540 x 35mm and OD540 x 55mm, the allowable maximum value of the axial temperature gradient and the maximum heating rate during the after-welding heat treatment of the medium-frequency induction heating local part are calculated according to the method. The maximum heating rate obtained by calculation is used for carrying out post-welding heat treatment tests on pipelines with two specifications, the axial temperature gradient is actually measured, and the allowable maximum calculation result of the axial temperature gradient is compared with the actually measured value, so that the accuracy of the method can be verified. The comparison result is shown in table 1, and it can be seen that, under the maximum temperature rise rate given by the method, the deviation between the calculated value and the measured value of the axial temperature gradient of the pipeline with the two specifications of P91 is very small, which indicates the accuracy of the calculation result of the method.
TABLE 1 verification of the accuracy of the maximum heating rate calculation results of the present invention
The maximum heating rates of the two pipelines with the specifications of P91 obtained by the invention are compared with the maximum heating rate obtained according to the electric power industry standard DL/T819-2019, and are shown in the table 2.
TABLE 2 comparison of the present invention with the maximum heating Rate calculation of the existing Standard
| Pipe specification/mm | OD540×35mm | OD540×55mm |
| The maximum temperature rise rate/DEG C/h obtained by the invention | 253.0 | 171.7 |
| Temperature rise rate/° C/h recommended by DL/T819- | 228.6 | 145.5 |
The result shows that the maximum heating rates obtained by using the invention are all larger than the electric power industry standard, and the improvement range is very obvious for pipelines with two specifications. Therefore, the invention can save the heat treatment time, shorten the construction period and reduce the cost.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (9)
1. A method for calculating the maximum temperature rise rate of the medium-frequency induction heating local postweld heat treatment of a 9% Cr hot-strength steel thick-wall pipeline is characterized by comprising the following steps:
step 1: establishing a transient temperature field model of the after-local induction heating heat treatment of the hot-strength steel thick-wall pipeline with 9% of Cr to obtain the maximum axial temperature gradient of different characteristic points in the whole heat treatment process;
step 2: obtaining the maximum axial temperature gradient allowed by each axial characteristic point of the pipeline through an equation of the axial temperature gradient and the induced stress;
and step 3: and (3) calculating the maximum temperature rise rate of the pipelines with different wall thicknesses under the temperature gradient according to the maximum axial temperature gradient allowed by each axial characteristic point of the pipeline obtained in the step (2), fitting the calculation result to obtain a maximum temperature rise rate formula, and calculating the maximum temperature rise rate according to the wall thickness of the pipeline.
2. The method of claim 1, wherein in step 1, the transient model is established by finite element software.
3. The method according to claim 1, wherein in step 1, the characteristic points are: the heating area edge of the outer wall of the pipeline and the middle point from the center of the welding seam of the outer wall of the pipeline to the heating area edge.
4. The method according to claim 1, wherein in the step 1, the concrete method for suggesting the transient model is as follows:
step 1.1, selecting a pipeline with a certain specification, selecting parameters according to the electric power industry standard DL/T819-2019, and modeling the pipeline specification and the parameters by using finite element software;
step 1.2, coupling an electromagnetic model and a heat transfer model, inputting transient time domain excitation, and applying additional heating power excitation after a temperature control point reaches the Curie temperature to enable the temperature control point to reach the temperature control temperature so as to obtain a temperature field transient model of the medium-frequency induction heating local postweld heat treatment;
and step 1.3, selecting corresponding characteristic points of the outer wall of the pipeline by using the obtained intermediate frequency induction heating local postweld heat treatment temperature field transient model, determining time nodes of the maximum axial temperature gradients of the characteristic points in the whole heat treatment process, and obtaining the maximum axial temperature gradients of different characteristic points in the whole heat treatment process.
5. The method of claim 4, wherein in step 1.1, the pipe gauge is wall thickness; the parameters of the pipeline comprise heating width, heat preservation width, alternating current frequency, the number of turns and the turn interval of the induction coil and heating rate.
6. The method according to claim 4, wherein in the step 1.3, when the central point of the welding seam of the outer wall of the pipeline just reaches the steady-state temperature, the axial temperature gradient of the characteristic point is the maximum, namely, the time node of the maximum axial temperature gradient of the characteristic point in the whole heat treatment process is obtained.
7. The method according to claim 1, wherein in the step 2, the specific method for obtaining the maximum axial temperature gradient allowed by each characteristic point in the axial direction of the pipeline is as follows:
step 2.1, calculating the deflection of the axisymmetric cylinder generated by the axial temperature gradient, and solving the deflection according to the Fourier heat transfer theorem to obtain the maximum bending stress of the axisymmetric cylinder;
step 2.2, solving according to the maximum bending stress formula obtained in the step 2.1 to obtain the relation between the maximum stress and the axial temperature gradient of each characteristic point of the outer wall of the pipeline;
and 2.3, carrying out value calculation on the formula obtained in the step 2.2, and calculating to obtain the maximum axial temperature gradient allowed under the condition of safe operation of each characteristic point of the outer wall of the pipeline.
8. The method according to claim 1, wherein in step 3, the formula of the maximum temperature rise rate is as follows:
v＝0.03081t 2 -6.8416t+454.73273 (12)
wherein v (DEG C/h) is a heating temperature rise rate; t (mm) is the pipe wall thickness.
9. The method according to claim 1, wherein in the step 3, the specific method is as follows:
step 3.1, calculating the maximum heating rates of pipelines with different wall thicknesses according to the temperature field transient model obtained in the step 1 and the maximum axial temperature gradient allowed by each characteristic point obtained in the step 2;
and 3.2, fitting the data obtained in the step 3.1 to obtain a selection curve of the maximum heating rate and a calculation formula.
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