CN117542459A - Transient temperature field calculation method and system for metal forming process - Google Patents
Transient temperature field calculation method and system for metal forming process Download PDFInfo
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Abstract
The invention discloses a transient temperature field calculation method and a system in a metal forming process, wherein the calculation of the transient temperature field by a numerical manifold method and a golden section ratio optimization method and correction factors are combined to be used for the prediction and correction of the temperature field in the metal forming process; the calculation and the prediction of the temperature field in the metal forming are completed efficiently and accurately, the temperature field in the transient process can be obtained rapidly, the calculation accuracy is ensured, the calculation resource consumption is reduced, and the calculation efficiency is improved greatly.
Description
Technical Field
The invention relates to the field of metal forming computer simulation research, in particular to a transient temperature field calculation method and a transient temperature field calculation system for a metal forming process.
Background
In the current part of technologies, only commercial general finite element analysis software is used for temperature field analysis, and specific mathematical model establishment is lacked. Some techniques use finite difference methods to predict the temperature field, but do not use numerical manifold and golden section ratio optimization methods to correct. Studies on numerical manifold temperature field discrete formats do not include prediction and correction. Some techniques use finite impulse integration and golden section methods to predict thermal conductivity, but do not involve the use of golden section methods in addition to predictive calculation of thermal conductivity.
None of the above techniques relates to the prediction and correction of temperature fields based on numerical manifold methods. The application prospect before the invention is to predict the temperature field in the metal forming process so as to have a preliminary predictive analysis on the global forming process; by combining a numerical manifold method and a discrete idea, the metal forming process is predicted and analyzed, so that the process parameter improvement process can be corrected in time, and metal forming failure caused by inaccurate temperature prediction in the metal forming process due to temperature is avoided.
The prior art provides a high-efficiency high-precision calculation method for a fluid-solid temperature field of a flight wrapping line, and belongs to the field of heat transfer. The method comprises the following steps: adopting conjugate heat transfer calculation aiming at a fluid-solid coupling temperature field in a transition stage in the flight envelope to obtain a fluid-solid coupling temperature field in the transition stage; decoupling fluid and solid after the transition phase conjugate heat transfer calculation in the flight envelope is completed, and extracting parameters; performing finite element reduced order efficient calculation on the solid temperature field aiming at a steady-state stage in the flight envelope to obtain an all-time-domain solid temperature field of the steady-state stage; extracting solid temperature at the last moment, re-coupling the fluid-solid temperature field, and taking the parameters as an initial field for calculating the fluid-solid coupling temperature field at the next transition stage; carrying out fluid-solid coupling temperature field conjugate heat transfer calculation again aiming at the second transition stage; and similarly, the calculation of the fluid-solid transient temperature field of the full flight envelope is completed.
Disclosure of Invention
The invention provides a transient temperature field calculation method and a transient temperature field calculation system for a metal forming process, which aim to overcome the defect of inaccurate temperature prediction in the metal forming process.
In order to solve the technical problems, the technical scheme of the invention is as follows:
the invention provides a transient temperature field calculation method in a metal forming process, which comprises the following steps:
s1: acquiring material parameters of a metal blank and an initial temperature field of a forming process;
s2: setting total forming time and time step intervals, and judging whether the current time step is a first time step or not; if yes, calculating a first time step predicted temperature field according to the material parameters of the metal blank and the initial temperature field, and taking the first time step predicted temperature field as a current time step predicted temperature field; otherwise, calculating a current time step predicted temperature field by using a hybrid interpolation method according to the previous time step actual temperature field;
s3: calculating a current time step calculation temperature field according to the current time step prediction temperature field and the material parameters of the metal blank;
s4: calculating an error reference of the current time step predicted temperature field and the current time step calculated temperature field, and comparing the error reference with a preset error threshold; if the error reference is greater than the preset error threshold, executing step S5; otherwise, executing step S6;
s5: correcting the current time step predicted temperature field to obtain a corrected current time step predicted temperature field serving as a new current time step predicted temperature field, and returning to the step S3;
s6: taking the corresponding calculated temperature field of the current time step as the actual temperature field of the current time step;
s7: judging whether the current time step is smaller than the total forming time or not; if yes, repeating the steps S2-S6; otherwise, the actual temperature field for each time step is obtained as the temperature during the metal forming process.
Preferably, the initial temperature field comprises an initial temperature of the metal blank and an initial temperature of the die;
the first time step predicted temperature field is:
T 1 ＝T blank material -(Δt*(T Blank material -T Mould )*0.1)
Wherein T is 1 Predicting a temperature field for a first time step; t (T) Blank material Is the initial temperature of the metal blank; Δt is the set time step interval; t (T) Mould Is a dieInitial temperature.
Preferably, in S2, the current time-step predicted temperature field is calculated by using a hybrid interpolation method according to the previous time-step actual temperature field, wherein the method comprises a linear interpolation method and a parabolic interpolation method;
the formula of the linear interpolation method is as follows:
wherein n is a sample point in a linear interpolation method; k is the number of time steps; x is x k Sample points for the current time step; x is x k-1 Sample points for a previous time step; x is x k+1 Sample points for the next time step; t (T) k-1 A predicted temperature field for a previous time step; t (T) k A predicted temperature field for the current time step; t (T) k+1 Predicting a temperature field for the next time step;
the formula of the parabolic interpolation method is as follows:
T k-2 ＝T k-1 *L k-1 (x)+T k *L k (x)+T k+1 *L k+1 (x)
wherein x is a sample point in a parabolic interpolation method; x is x k-2 Sample points for the first two time steps; t (T) k-2 Predicted temperature fields for the first two time steps; l (L) k+1 (x) Interpolation basis functions for the next time step; l (L) k (x) Interpolation basis functions for the current time step; l (L) k-1 (x) Interpolation basis function for previous time step。
Preferably, in S3, the heat flux density and the heat convection coefficient of the predicted temperature field are calculated before the temperature field is calculated according to the predicted temperature field of the current time step and the material parameters of the metal blank; the material parameters of the metal blank comprise the heat flux density of the metal blank, the height of the metal blank, the heat conductivity coefficient of the metal blank, the density of the metal blank and the specific heat capacity of the metal blank;
and calculating the heat flux density of the predicted temperature field, wherein the calculation formula is as follows:
wherein q s The heat flux density of the metal blank; lZ is the height of the metal blank; ks is the heat conductivity coefficient of the metal blank; t (T) Blank material Is the initial temperature of the metal blank; t (T) Mould Is the initial temperature of the mold;
and calculating the heat convection coefficient of the predicted temperature field, wherein the calculation formula is as follows:
pr is the Plandter number, and represents the relative thickness of the fluid thermal boundary layer and the flow boundary layer; c Air-conditioner Is the specific heat capacity of air; μ is aerodynamic viscosity; ks (ks) Air-conditioner Is the heat conductivity coefficient of air; c is a first constant; LT is a characteristic length; g is gravity acceleration; alpha is the bulk expansion coefficient; v is the air kinematic viscosity; n is a second constant.
Preferably, the specific method of S3 is as follows:
s31: calculating a current time step predicted temperature field by using a numerical manifold method to obtain a plurality of unit shape functions;
s32: calculating a shape function matrix based on the obtained cell shape function;
s33: calculating a shape function matrix according to the heat flux density and the convective heat transfer coefficient of the current time step prediction temperature field to obtain a B matrix, a heat load array matrix and a heat capacity matrix;
s34: calculating a cell stiffness matrix based on the obtained B matrix;
s35: and (3) bringing the unit stiffness matrix, the unit heat load array matrix and the unit heat capacity matrix obtained by all the unit shape functions into a recursive formula to obtain a current time step calculation temperature field.
Preferably, in S35, the calculation formula of the unit stiffness matrix is:
the calculation formula of the unit heat capacity matrix is as follows:
the calculation formula of the unit thermal load array matrix is as follows:
wherein T is A An air temperature that is in contact with the calculation region;a transpose of the shape function matrix for the second boundary condition cell; t (T) S3 T A transpose of the shape function matrix for the third boundary condition cell; t (T) Ω T A transpose of the shape function matrix for all cells; b (B) x T The transposed matrix of the bias derivative of the strain rate B matrix of all the units to x is calculated; b (B) y T Y-biasing for strain rate B matrix of all cellsIs a transposed matrix of (a); k is the heat conductivity coefficient of the metal blank; q is an internal heat source value; q is the heat flux density of the metal blank; h is the convective heat transfer coefficient of the metal blank; ρ is the density of the metal blank; c is the specific heat capacity of the metal blank.
Preferably, in S35, the recursive formula is:
wherein T is Calculation of Calculating a temperature field for the current time step; t (T) Prediction A predicted temperature field for the current time step; Δt is a set time interval; c is a unit heat capacity matrix; k is a unit stiffness matrix; f is a unit thermal load array matrix; k is the number of steps in the current time; θ is a weighting coefficient.
Preferably, in S4, the error reference is a two-norm of the difference between the calculated temperature field and the predicted temperature field.
Preferably, in S5, the specific method for correcting the predicted temperature field of the current time step is:
setting golden section coefficients m and n; when the error reference is greater than a preset error standard value, the golden section coefficient m is used for correction, and when the error reference is less than or equal to the preset error standard value, the golden section coefficient n is used for correction.
The invention also includes a transient temperature field computing system for a metal forming process for implementing the method described above, the system comprising:
the data acquisition module acquires material parameters of the metal blank and an initial temperature field of a forming process;
the prediction temperature field calculation module is used for setting the total forming time and the time step interval and judging whether the current time step is a first time step or not; if yes, calculating a first time step predicted temperature field according to the material parameters of the metal blank and the initial temperature field, and taking the first time step predicted temperature field as a current time step predicted temperature field; otherwise, calculating a current time step predicted temperature field by using a hybrid interpolation method according to the previous time step actual temperature field;
the calculation temperature field calculation module calculates a current time step calculation temperature field according to the current time step prediction temperature field and the material parameters of the metal blank;
the error judging module is used for calculating an error reference of the current time step predicted temperature field and the current time step calculated temperature field and comparing the error reference with a preset error threshold; if the error reference is larger than the preset error threshold, the method goes to a correction feedback module; otherwise, turning to an actual temperature field updating module;
the correction feedback module corrects the current time step predicted temperature field to obtain a corrected current time step predicted temperature field, and the corrected current time step predicted temperature field is used as a new current time step predicted temperature field and returns to the calculation temperature field calculation module;
the actual temperature field updating module is used for calculating a temperature field corresponding to the current time step as an actual temperature field of the current time step;
judging and executing a module in a time step, wherein whether the current time step is smaller than the total forming time or not; if yes, returning to a predicted temperature field calculation module; otherwise, the actual temperature field for each time step is obtained as the temperature during the metal forming process.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention provides a transient temperature field calculation method and a system, which are used for predicting and correcting a temperature field in a metal forming process by combining calculation of a transient temperature field by a numerical manifold method with a golden section ratio optimization method and a correction factor; the calculation and the prediction of the temperature field in the metal forming are completed efficiently and accurately, the temperature field in the transient process can be obtained rapidly, the calculation accuracy is ensured, the calculation resource consumption is reduced, and the calculation efficiency is improved greatly.
Drawings
FIG. 1 is a flow chart of a transient temperature field calculation method of a metal forming process described in example 1;
fig. 2 is a schematic diagram of a transient temperature field calculation system of a metal forming process described in embodiment 3.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
for the purpose of better illustrating the embodiments, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the actual product dimensions;
it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
Example 1
The embodiment provides a transient temperature field calculation method in a metal forming process, as shown in fig. 1, the method includes:
s1: acquiring material parameters of a metal blank and an initial temperature field of a forming process;
s2: setting total forming time and time step intervals, and judging whether the current time step is a first time step or not; if yes, calculating a first time step predicted temperature field according to the material parameters of the metal blank and the initial temperature field, and taking the first time step predicted temperature field as a current time step predicted temperature field; otherwise, calculating a current time step predicted temperature field by using a hybrid interpolation method according to the previous time step actual temperature field;
s3: calculating a current time step calculation temperature field according to the current time step prediction temperature field and the material parameters of the metal blank;
s4: calculating an error reference of the current time step predicted temperature field and the current time step calculated temperature field, and comparing the error reference with a preset error threshold; if the error reference is greater than the preset error threshold, executing step S5; otherwise, executing step S6;
s5: correcting the current time step predicted temperature field to obtain a corrected current time step predicted temperature field serving as a new current time step predicted temperature field, and returning to the step S3;
s6: taking the corresponding calculated temperature field of the current time step as the actual temperature field of the current time step;
s7: judging whether the current time step is smaller than the total forming time or not; if yes, repeating the steps S2-S6; otherwise, the actual temperature field for each time step is obtained as the temperature during the metal forming process.
Example 2
The embodiment provides a transient temperature field calculation method in a metal forming process, which comprises the following steps:
s1: acquiring material parameters of a metal blank and an initial temperature field of a forming process;
s2: setting total forming time and time step intervals, and judging whether the current time step is a first time step or not; if yes, calculating a first time step predicted temperature field according to the material parameters of the metal blank and the initial temperature field, and taking the first time step predicted temperature field as a current time step predicted temperature field; otherwise, calculating a current time step predicted temperature field by using a hybrid interpolation method according to the previous time step actual temperature field;
the initial temperature field comprises the initial temperature of the metal blank and the initial temperature of the die;
the first time step predicted temperature field is determined by adopting a quadratic spline interpolation function, and the function of two segments is obtained according to three data points by using the quadratic spline interpolation, wherein the first data point t of the three data points 1 For an initial temperature field before cooling has not been started and for the first data point t 1 The y-coordinate of (2), the x-coordinate, i.e. 0, the second data point t 2 Is infinitely close to the first data point t 1 Where the value is the first data point t 1 Subtracting 0.001 and being the second data point t 2 The y-coordinate, x-coordinate, i.e. 1, third data point t 3 Then based on the second data point t 2 Slope k formed by angle a between the data points (angle a here is 5 degrees, which corresponds to the trend of temperature drop in this case) 12 ，
And the slope is given by:
according to the slope formulaSolving to obtain a third data point t 3 The y-coordinate of (2) and the x-coordinate of (2); finally solving all coefficients to be solved to obtain a function expression, substituting the function expression into a fourth data point, namely a first time step predicted temperature field T, according to the function of the last segment of line segment 1 To obtain a first time-step predicted temperature field T 1 The formula for obtaining the first time step predicted temperature field by applying the quadratic spline interpolation is as follows:
k 12 ＝tan(a)
t 3 ＝t 2 -k 12
the function of the first segment is: f (x) =a 1 x 2 +b 1 x+c 1
The function of the second segment is: f (x) =a 2 x 2 +b 2 x+c 2
Wherein a is 1 、b 1 、c 1 、a 2 、b 2 、c 2 All are belt solving coefficients;
the 6 coefficients to be solved need 6 equations to be solved, and the solving formula is as follows:
1)c 1 ＝f(x 1 )
2)a 1 +b 1 +c 1 ＝f(x 2 )
3)a 2 +b 2 +c 2 ＝f(x 2 )
4)a 1 ＝0
5)2a 1 +b 1 ＝2a 2 +b 2
6)4a 2 +2b 2 +c 2 ＝f(x 3 )
wherein the first equation is directly substituted into the first data point t 1 X, y coordinates of (c);
the second equation is that the first segment function passes through the second data point t 2 Directly substituting the second data point t 2 X, y coordinates of (c);
the third path second segment function passes through the second data point t 2 Directly substituting the second data point t 2 X, y coordinates of (c);
the fourth pass is due to the first data point t 1 And a second data point t 2 Infinitely close, the line segment between the two is almost similar to a straight line, so that the first-order derivative is 0;
second data point t of fifth equation 2 The slopes of the left end and the right end, namely the first-order derivation, are required to be continuous, and all the first-segment line segment functions and the second-segment line segment functions are equal in first-order derivation at the point;
the sixth equation is that the second segment function passes through the third data point t 2 Directly substituting the second data point t 3 X, y coordinates of (c);
solving the above 6 equations to obtain a 1 、b 1 、c 1 、a 2 、b 2 、c 2 Obtaining a functional expression of a second segment after obtaining all coefficients to be solved, substituting the x coordinate of a fourth data point into the functional expression to obtain f (x) 4 )，f(x 4 ) I.e. the first time step predicts the temperature field T 1 。
Calculating a current time step predicted temperature field by utilizing a hybrid interpolation method according to the previous time step actual temperature field, wherein the method comprises a linear interpolation method and a parabolic interpolation method;
the formula of the linear interpolation method is as follows:
wherein n is a sample point in a linear interpolation method; k is the number of time steps; x is x k Sample points for the current time step; x is x k-1 Sample points for a previous time step; x is x k+1 Sample points for the next time step; t (T) k-1 A predicted temperature field for a previous time step; t (T) k A predicted temperature field for the current time step; t (T) k+1 Predicting a temperature field for the next time step;
the formula of the parabolic interpolation method is as follows:
T k-2 ＝T k-1 *L k-1 (x)+T k *L k (x)+T k+1 *L k+1 (x)
wherein x is a sample point in a parabolic interpolation method; x is x k-2 Sample points for the first two time steps; t (T) k-2 Predicted temperature fields for the first two time steps; l (L) k+1 (x) Interpolation basis functions for the next time step; l (L) k (x) Interpolation basis functions for the current time step; l (L) k-1 (x) The interpolation basis function for the previous time step.
S3: calculating a current time step calculation temperature field according to the current time step prediction temperature field and the material parameters of the metal blank;
calculating the heat flux density and the heat convection coefficient of the predicted temperature field before calculating the temperature field according to the predicted temperature field of the current time step and the material parameters of the metal blank; the material parameters of the metal blank comprise the heat flux density of the metal blank, the height of the metal blank, the heat conductivity coefficient of the metal blank, the density of the metal blank and the specific heat capacity of the metal blank;
and calculating the heat flux density of the predicted temperature field, wherein the calculation formula is as follows:
wherein q s The heat flux density of the metal blank; lZ is the height of the metal blank; ks is the heat conductivity coefficient of the metal blank; t (T) Blank material Is the initial temperature of the metal blank; t (T) Mould Is the initial temperature of the mold;
and calculating the heat convection coefficient of the predicted temperature field, wherein the calculation formula is as follows:
pr is the Plandter number, and represents the relative thickness of the fluid thermal boundary layer and the flow boundary layer; c Air-conditioner Is the specific heat capacity of air; μ is aerodynamic viscosity; ks (ks) Air-conditioner Is the heat conductivity coefficient of air; c is a first constant; LT is a characteristic length; g is gravity acceleration; alpha is the bulk expansion coefficient; v is the air kinematic viscosity; n is a second constant.
The specific method of the S3 is as follows:
s31: calculating a current time step predicted temperature field by using a numerical manifold method to obtain a plurality of unit shape functions;
s32: calculating based on the obtained unit shape function to obtain a shape function matrix;
s33: calculating a shape function matrix according to the heat flux density and the convective heat transfer coefficient of the current time step prediction temperature field to obtain a B matrix, a heat load array matrix and a heat capacity matrix;
s34: calculating based on the obtained B matrix to obtain a unit stiffness matrix;
s35: and (3) bringing the unit stiffness matrix, the unit heat load array matrix and the unit heat capacity matrix obtained by all the unit shape functions into a recursive formula to obtain a current time step calculation temperature field.
The calculation formula of the unit stiffness matrix is as follows:
the calculation formula of the unit heat capacity matrix is as follows:
the calculation formula of the unit thermal load array matrix is as follows:
wherein T is A An air temperature that is in contact with the calculation region;a transpose of the shape function matrix for the second boundary condition cell; t (T) S3 T A transpose of the shape function matrix for the third boundary condition cell; t (T) Ω T A transpose of the shape function matrix for all cells; b (B) x T The transposed matrix of the bias derivative of the strain rate B matrix of all the units to x is calculated; b (B) y T A transposed matrix of the bias derivative of the strain rate B matrix of all the units on y is obtained; k is the heat conductivity coefficient of the metal blank; q is an internal heat source value; q is the heat flux density of the metal blank; h is the convective heat transfer coefficient of the metal blank; ρ is the density of the metal blank; c is the specific heat capacity of the metal blank.
S4: calculating an error reference of the current time step predicted temperature field and the current time step calculated temperature field, and comparing the error reference with a preset error threshold; if the error reference is greater than the preset error threshold, executing step S5; otherwise, executing step S6;
the error reference is a two-norm of the difference between the calculated temperature field and the predicted temperature field.
S5: correcting the current time step predicted temperature field to obtain a corrected current time step predicted temperature field serving as a new current time step predicted temperature field, and returning to the step S3;
the specific method for correcting the current time step predicted temperature field comprises the following steps:
setting correction factor β includes golden section factor m (m is 0.618) and n m (n is 0.38)2) Setting a correction factor alpha T The method comprises the steps of carrying out a first treatment on the surface of the Correction factor alpha T The method consists of golden section coefficients m or n x m and the difference value between the current calculated temperature field and the current predicted temperature field, and is specifically expressed as follows:
α T ＝(T currently calculated temperature field -T Current predicted temperature field )*β
Each time correction is performed, the correction factor alpha T Directly adding to the predicted temperature field, correction factor alpha T To adjust the prediction direction when correcting the factor alpha T In order to be positive, the calculated temperature field is larger than the predicted temperature field, the predicted temperature field does not exceed the calculated temperature field, forward regulation is needed to be continued, and when the correction factor alpha is corrected T When the calculated temperature field is negative, the calculated temperature field is smaller than the predicted temperature field, and negative adjustment is needed when the predicted temperature field exceeds the calculated temperature field, and under normal conditions, the same correction factor alpha is still adopted T The correction is continued, the phenomenon that the position oscillation of the predicted temperature field and the calculated temperature field is repeated is generated, and the position oscillation of the predicted temperature field and the calculated temperature field is repeated and mutually surpassed, so that a large amount of prediction steps and calculation time are wasted, an error standard value is set before the oscillation repetition phenomenon is predicted to reduce the calculation time, the oscillation phenomenon is avoided, when the error standard value is larger than a preset error standard value, the golden section coefficient m is used for correction, and when the error standard value is smaller than or equal to the preset error standard value, the golden section coefficient n is used for correction. The selection basis of the error standard value is expressed as the mathematical expression of the contrast decreasing amplitude of the current predicted step temperature field and the previous predicted step temperature field: t (T) Current predicted temperature field /T The previous step predicts the temperature field The relative value of the amplitude is 0.75, and is related to the golden section coefficient, when the current predicted temperature field drop amplitude is larger than the relative value of 0.75, the golden section coefficient n is used for correction, otherwise, the golden section coefficient m is used for correction.
S6: taking the corresponding calculated temperature field of the current time step as the actual temperature field of the current time step;
s7: judging whether the current time step is smaller than the total forming time or not; if yes, repeating the steps S2-S6; otherwise, the actual temperature field for each time step is obtained as the temperature during the metal forming process.
Example 3
This embodiment provides a transient temperature field computing system for a metal forming process for implementing the methods described in embodiments 1 and 2, as shown in fig. 2, the system comprising:
the data acquisition module acquires material parameters of the metal blank and an initial temperature field of a forming process;
the prediction temperature field calculation module is used for setting the total forming time and the time step interval and judging whether the current time step is a first time step or not; if yes, calculating a first time step predicted temperature field according to the material parameters of the metal blank and the initial temperature field, and taking the first time step predicted temperature field as a current time step predicted temperature field; otherwise, calculating a current time step predicted temperature field by using a hybrid interpolation method according to the previous time step actual temperature field;
the calculation temperature field calculation module calculates a current time step calculation temperature field according to the current time step prediction temperature field and the material parameters of the metal blank;
the error judging module is used for calculating an error reference of the current time step predicted temperature field and the current time step calculated temperature field and comparing the error reference with a preset error threshold; if the error reference is larger than the preset error threshold, the method goes to a correction feedback module; otherwise, turning to an actual temperature field updating module;
the correction feedback module corrects the current time step predicted temperature field to obtain a corrected current time step predicted temperature field, and the corrected current time step predicted temperature field is used as a new current time step predicted temperature field and returns to the calculation temperature field calculation module;
the actual temperature field updating module is used for calculating a temperature field corresponding to the current time step as an actual temperature field of the current time step;
judging and executing a module in a time step, wherein whether the current time step is smaller than the total forming time or not; if yes, returning to a predicted temperature field calculation module; otherwise, the actual temperature field for each time step is obtained as the temperature during the metal forming process.
The same or similar reference numerals correspond to the same or similar components;
the terms describing the positional relationship in the drawings are merely illustrative, and are not to be construed as limiting the present patent;
it is to be understood that the above examples of the present invention are provided by way of illustration only and not by way of limitation of the embodiments of the present invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.
Claims (10)
1. A method of calculating a transient temperature field of a metal forming process, the method comprising:
s1: acquiring material parameters of a metal blank and an initial temperature field of a forming process;
s2: setting total forming time and time step intervals, and judging whether the current time step is a first time step or not; if yes, calculating a first time step predicted temperature field according to the material parameters of the metal blank and the initial temperature field, and taking the first time step predicted temperature field as a current time step predicted temperature field; otherwise, calculating a current time step predicted temperature field by using a hybrid interpolation method according to the previous time step actual temperature field;
s3: calculating a current time step calculation temperature field according to the current time step prediction temperature field and the material parameters of the metal blank;
s4: calculating an error reference of the current time step predicted temperature field and the current time step calculated temperature field, and comparing the error reference with a preset error threshold; if the error reference is greater than the preset error threshold, executing step S5; otherwise, executing step S6;
s5: correcting the current time step predicted temperature field to obtain a corrected current time step predicted temperature field serving as a new current time step predicted temperature field, and returning to the step S3;
s6: taking the corresponding calculated temperature field of the current time step as the actual temperature field of the current time step;
s7: judging whether the current time step is smaller than the total forming time or not; if yes, repeating the steps S2-S6; otherwise, the actual temperature field for each time step is obtained as the temperature during the metal forming process.
2. The method of calculating a transient temperature field for a metal forming process according to claim 1, wherein in S2, the initial temperature field includes an initial temperature of a metal blank and an initial temperature of a die;
the first time step predicted temperature field is:
T 1 ＝T blank material -(Δt*(T Blank material -T Mould )*0.1)
Wherein T is 1 Predicting a temperature field for a first time step; t (T) Blank material Is the initial temperature of the metal blank; Δt is the set time step interval; t (T) Mould Is the initial temperature of the mold.
3. The method for calculating a transient temperature field of a metal forming process according to claim 1, wherein in S2, a current time-step predicted temperature field is calculated from a previous time-step actual temperature field by using a hybrid interpolation method, the method comprising a linear interpolation method and a parabolic interpolation method;
the formula of the linear interpolation method is as follows:
wherein n is a sample point in a linear interpolation method; k is the number of time steps; x is x k Sample points for the current time step; x is x k-1 Sample points for a previous time step; x is x k+1 Sample points for the next time step; t (T) k-1 A predicted temperature field for a previous time step; t (T) k A predicted temperature field for the current time step; t (T) k+1 Predicting a temperature field for the next time step;
the formula of the parabolic interpolation method is as follows:
T k-2 ＝T k-1 *L k-1 (x)+T k *L k (x)+T k+1 *L k+1 (x)
wherein x is a sample point in a parabolic interpolation method; x is x k-2 Sample points for the first two time steps; t (T) k-2 Predicted temperature fields for the first two time steps; l (L) k+1 (x) Interpolation basis functions for the next time step; l (L) k (x) Interpolation basis functions for the current time step; l (L) k-1 (x) The interpolation basis function for the previous time step.
4. A transient temperature field calculation method for a metal forming process according to claim 2 or 3, wherein in S3, the heat flux density and the heat convection coefficient of the predicted temperature field are calculated before the calculated temperature field of the current time step is calculated according to the predicted temperature field of the current time step and the material parameters of the metal blank; the material parameters of the metal blank comprise the heat flux density of the metal blank, the height of the metal blank, the heat conductivity coefficient of the metal blank, the density of the metal blank and the specific heat capacity of the metal blank;
and calculating the heat flux density of the predicted temperature field, wherein the calculation formula is as follows:
wherein q s The heat flux density of the metal blank; lZ is the height of the metal blank; ks is the heat conductivity coefficient of the metal blank; t (T) Blank material Is the initial temperature of the metal blank; t (T) Mould Is the initial temperature of the mold;
and calculating the heat convection coefficient of the predicted temperature field, wherein the calculation formula is as follows:
pr is the Plandter number, and represents the relative thickness of the fluid thermal boundary layer and the flow boundary layer; c Air-conditioner Is the specific heat capacity of air; μ is aerodynamic viscosity; ks (ks) Air-conditioner Is the heat conductivity coefficient of air; c is a first constant; LT is a characteristic length; g is gravity acceleration; alpha is the bulk expansion coefficient; v is the air kinematic viscosity; n is a second constant.
5. The method for calculating a transient temperature field of a metal forming process according to claim 4, wherein the specific method of S3 is as follows:
s31: calculating a current time step predicted temperature field by using a numerical manifold method to obtain a plurality of unit shape functions;
s32: calculating a shape function matrix based on the obtained cell shape function;
s33: calculating a shape function matrix according to the heat flux density and the convective heat transfer coefficient of the current time step prediction temperature field to obtain a B matrix, a heat load array matrix and a heat capacity matrix;
s34: calculating a cell stiffness matrix based on the obtained B matrix;
s35: and (3) bringing the unit stiffness matrix, the unit heat load array matrix and the unit heat capacity matrix obtained by all the unit shape functions into a recursive formula to obtain a current time step calculation temperature field.
6. The method according to claim 5, wherein in S35, the calculation formula of the cell stiffness matrix is:
the calculation formula of the unit heat capacity matrix is as follows:
C＝∫ Ω T Ω T T Ω ρcdΩ
the calculation formula of the unit thermal load array matrix is as follows:
wherein T is A An air temperature that is in contact with the calculation region;a transpose of the shape function matrix for the second boundary condition cell; t (T) S3 T A transpose of the shape function matrix for the third boundary condition cell; t (T) Ω T A transpose of the shape function matrix for all cells; b (B) x T The transposed matrix of the bias derivative of the strain rate B matrix of all the units to x is calculated; b (B) y T A transposed matrix of the bias derivative of the strain rate B matrix of all the units on y is obtained; k is the heat conductivity coefficient of the metal blank; q is an internal heat source value; q is the heat flux density of the metal blank; h is the convective heat transfer coefficient of the metal blank; ρ is the density of the metal blank; c is the specific heat capacity of the metal blank.
7. The method of calculating a transient temperature field of a metal forming process according to claim 6, wherein in S35, the recursive formula is:
wherein T is Calculation of Calculating a temperature field for the current time step; t (T) Prediction A predicted temperature field for the current time step; Δt is a set time interval; c is a unit heat capacity matrix; k is a unit stiffness matrix; f is a unit thermal load array matrix; k is the number of steps in the current time; θ is a weighting coefficient.
8. The method of calculating a transient temperature field for a metal forming process according to claim 1, wherein in S4, the error reference is a two-norm difference between a calculated temperature field and a predicted temperature field.
9. The method for calculating a transient temperature field of a metal forming process according to claim 8, wherein in S5, the specific method for correcting the current time-step predicted temperature field is as follows:
setting golden section coefficients m and n; when the error reference is greater than a preset error standard value, the golden section coefficient m is used for correction, and when the error reference is less than or equal to the preset error standard value, the golden section coefficient n is used for correction.
10. A transient temperature field computing system for a metal forming process for implementing the method of claims 1-9, the system comprising:
the data acquisition module acquires material parameters of the metal blank and an initial temperature field of a forming process;
the prediction temperature field calculation module is used for setting the total forming time and the time step interval and judging whether the current time step is a first time step or not; if yes, calculating a first time step predicted temperature field according to the material parameters of the metal blank and the initial temperature field, and taking the first time step predicted temperature field as a current time step predicted temperature field; otherwise, calculating a current time step predicted temperature field by using a hybrid interpolation method according to the previous time step actual temperature field;
the calculation temperature field calculation module calculates a current time step calculation temperature field according to the current time step prediction temperature field and the material parameters of the metal blank;
the error judging module is used for calculating an error reference of the current time step predicted temperature field and the current time step calculated temperature field and comparing the error reference with a preset error threshold; if the error reference is larger than the preset error threshold, the method goes to a correction feedback module; otherwise, turning to an actual temperature field updating module;
the correction feedback module corrects the current time step predicted temperature field to obtain a corrected current time step predicted temperature field, and the corrected current time step predicted temperature field is used as a new current time step predicted temperature field and returns to the calculation temperature field calculation module;
the actual temperature field updating module is used for calculating a temperature field corresponding to the current time step as an actual temperature field of the current time step;
judging and executing a module in a time step, wherein whether the current time step is smaller than the total forming time or not; if yes, returning to a predicted temperature field calculation module; otherwise, the actual temperature field for each time step is obtained as the temperature during the metal forming process.
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