阅读说明：本技术 一种双侧同时搅拌摩擦焊工艺参数优化方法 (Method for optimizing technological parameters of bilateral simultaneous friction stir welding ) 是由 刘海涛 孟少飞 倪雁冰 肖聚亮 黄田 岳巍 于 2021-08-26 设计创作，主要内容包括：本发明公开了一种双侧同时搅拌摩擦焊工艺参数优化方法,基于搅拌摩擦焊接过程产热机理、傅里叶传热定律和能量守恒定律,建立双侧同时搅拌摩擦焊的产热模型,确定待优化工艺参数,以焊接单位长度输入能量最小为目标函数,根据焊接工艺设置约束条件,建立优化模型；采用序列二次规划算法求解优化模型,得到最优工艺参数值。本发明基于焊接过程的产热机理,与SQP优化算法相耦合,得到了全局最优的输入能量和最佳的工艺参数组合,优化后的参数提高了焊接的效率和改善了焊接接头的质量。(The invention discloses a method for optimizing technological parameters of bilateral simultaneous friction stir welding, which is characterized by establishing a heat production model of bilateral simultaneous friction stir welding based on a heat production mechanism, a Fourier heat transfer law and an energy conservation law in the friction stir welding process, determining technological parameters to be optimized, setting a constraint condition according to a welding process by taking minimum input energy of a welding unit length as a target function, and establishing an optimization model; and solving the optimization model by adopting a sequential quadratic programming algorithm to obtain the optimal process parameter value. The invention is based on the heat production mechanism of the welding process, and is coupled with the SQP optimization algorithm to obtain the globally optimal input energy and the optimal process parameter combination, and the optimized parameters improve the welding efficiency and the quality of the welding joint.)

1. A method for optimizing technological parameters of bilateral simultaneous friction stir welding is characterized in that a heat generation model of bilateral simultaneous friction stir welding is established based on a heat generation mechanism, a Fourier heat transfer law and an energy conservation law in the friction stir welding process, technological parameters to be optimized are determined, the minimum input energy of a welding unit length is taken as a target function, constraint conditions are set according to a welding process, and an optimization model is established; and solving the optimization model by adopting a sequential quadratic programming algorithm to obtain the optimal process parameter value.

2. The method for optimizing process parameters for double-sided simultaneous friction stir welding according to claim 1, wherein the process parameters to be optimized comprise: the rotating speed of the stirring head, the feeding welding speed of the stirring head and the distance between the end faces of the stirring needles on the two sides.

3. The method for optimizing parameters of a double-sided simultaneous friction stir welding process according to claim 1, wherein the method for establishing a heat generation model of double-sided simultaneous friction stir welding comprises:

because the stirring heads on the two sides are geometrically symmetric about the thickness direction of the workpiece and the welding process parameters of the stirring heads on the two sides are the same, the heat production models of the stirring heads on the two sides are the same, and only the heat production model of the stirring head on one side is established;

according to different contact surfaces of a stirring head and a workpiece, the thermal power generated in the stirring friction welding process is divided into the following four types: respectively the thermal power Q generated by the friction between the shaft shoulder end surface of the stirring head and the workpiece_sbThe thermal power Q generated by the friction between the side surface of the shaft shoulder of the stirring head and the workpiece_ssThe thermal power Q generated by the friction between the end surface of the stirring pin and the workpiece_pbThe thermal power Q generated by the friction between the side surface of the stirring pin and the workpiece_ps：

Setting: r₂Is the radius of the shaft shoulder of the mixing head, R₁Is the radius of the end of the stirring pin, h_pThe length of the stirring pin, h is the pressing amount of the shaft shoulder, and h_gIs the distance between the end faces of the stirring pins at two sides, H is the thickness of the workpiece, omega is the rotating speed of the stirring head, sigma_yieldQ is calculated for the yield stress of the workpiece material based on the heat generation mechanism in the friction stir welding process according to the following formula_sb、Q_ss、Q_pb、Q_ps：

A heat flux index is adopted to represent a heat production model, and the heat flux comprises a surface heat flux and a body heat flux;

the heat energy generated by friction between the stirring pin and the workpiece is uniformly applied in the volume range of the stirring pin and is Q_pb、Q_psTo obtain the body heat flux q_volumeComprises the following steps:

in the formula, V_pinIs the volume of the stirring pin and is,

let the heat energy generated by friction between the shoulder of the stirring head and the workpiece be linearly applied to the workpiece surface by the heat flux, let R be the distance from a point on the workpiece surface to the axis of the stirring head, and R₁≤r≤R₂(ii) a From H, h and h_gA relation of (a), and Q_sb、Q_ssTo obtain the heat flux q of the surface_surface(r) and is simplified as follows:

4. the method for optimizing process parameters of double-sided simultaneous friction stir welding according to claim 3, wherein x is set as a set of process parameters to be optimized, and the constraint conditions include:

1) setting the constraint condition of the heat affected zone of the surface of the workpiece as g₁(x)，In the formula (I), the compound is shown in the specification,andthe widths of the heat affected zones on the surface of the workpiece in the current iteration step i and the next iteration step i +1 are respectively;

2) setting the maximum temperature constraint condition of the contact area of the workpiece and the shaft shoulder edge of the stirring head as g₂(x)，g₂(x)＝T_max(x)-T_mLess than or equal to 0; in the formula, T_max(x) The highest temperature of the contact area of the workpiece and the shaft shoulder edge of the stirring pin is obtained; t is_mIs the melting point of the workpiece material;

3) setting the maximum temperature constraint condition of the middle thickness of the workpiece as g₃(x)，g₃(x)＝T_md(x)-T_wNot less than 0; in the formula, T_md(x) The highest temperature of the middle thickness area of the workpiece; t is_wIs the soldering temperature.

5. The parameter optimization method for double-sided simultaneous friction stir welding process according to claim 4, wherein if v is the welding speed of the feeding of the stirring head, S is the contact area between the workpiece and the shaft shoulder of the stirring head, and f (x) is the input energy per unit length of the double-sided simultaneous friction stir welding, f (x) is expressed as follows:

6. the method for optimizing parameters of a double-sided simultaneous friction stir welding process according to claim 5, wherein the following optimization model is established by constraint conditions and an objective function:

min f(x)；

s.t.x_l≤x≤x_u；

g₂(x)＝T_max(x)-T_m≤0；

g₃(x)＝T_md(x)-T_w≥0；

wherein x is_lAnd x_uThe upper and lower bounds of the parameter x.

7. The method for optimizing parameters in a double-sided simultaneous friction stir welding process according to claim 6, wherein the method for solving the optimization model using a sequential quadratic programming algorithm comprises the steps of:

step 1, inputting an initial process parameter x₀Calculating the initial energy f₀(x) And let i equal to 0;

step 2, let i become i +1, adopt the quadratic programming algorithm of the sequence to confirm the parameter value x of the variable_i；

Step 3, calculating the surface heat flux q of the current iteration step_surface(r) and body Heat flux q_volume；

Step 4, calculating the temperature distribution of the workpiece in the process of simultaneous friction stir welding at two sides according to the Fourier heat transfer law and the energy conservation law;

step 5, judging whether constraint conditions are met or not according to the temperature distribution of the workpiece in the welding process; if the constraint condition is not satisfied, making i equal to i-1, returning to the step 2, and if the constraint condition is satisfied, performing a step 6;

step 6, calculating an objective function f_i(x)；

And 7, judging whether the iteration termination condition is met: i > i_maxOr Δ f ═ f_i+1(x)-f_i(x)＜10³(ii) a If yes, the iteration process is terminated, and the x of the current ith generation is output as the optimal process parameter; otherwise, go to step 2.

8. The method for optimizing parameters of a double-sided simultaneous friction stir welding process according to claim 7, wherein the step 4 comprises the following specific steps:

from the fourier heat transfer law and the energy conservation law, the following control equation is obtained:

wherein ρ (T), k (T) and c_p(T) workpiece material density, workpiece thermal conductivity, and workpiece specific heat capacity, respectively, related to temperature T; q (x, y, z, t) is a function of the amount of heat generated by the variable in a unit volume of the workpiece in relation to the coordinates (x, y, z) and time t;

let T₀Setting h as the ambient temperature_∞For the coefficient of thermal convection between the surface of the welded workpiece and the surrounding environmentThe coefficient of thermal convection between the tool clamp and the surrounding environment;

body heat flux q_volumeSurface heat flux q_surface(r) ambient temperature T₀Coefficient h_∞Sum coefficientAnd loading the boundary conditions serving as control equations into a finite element model, and solving the control equations by adopting a numerical method to obtain the temperature distribution of the workpieces in the process of welding the friction stir welding at the two sides simultaneously.

Technical Field

The invention relates to a friction stir welding process parameter optimization method, in particular to a bilateral simultaneous friction stir welding process parameter optimization method.

Background

At present, the bilateral simultaneous friction stir welding has the advantages of generating symmetrical welding seams and heat input, improving the production efficiency and reducing the counter torque on the clamp compared with the conventional friction stir welding. In friction stir welding, heat is a critical factor in determining the quality of the final weld, and generally provides two primary functions (i) making the metallic material soft enough for the stir head to stir to form a solid weld, and (ii) causing the microstructure to evolve, thereby affecting the joint performance. The technological parameters are main factors influencing heat production, the research of the technological parameter optimization method is developed, and the method is beneficial to improving the quality of the welding joint of the friction stir welding at the two sides and expanding the application scene of the welding method. To date, there is no report on the parameters of the double-side simultaneous friction stir welding process, but a great deal of research work has been conducted on methods for optimizing the process parameters of the conventional friction stir welding to increase the application of the conventional friction stir welding in the industry.

The conventional friction stir welding process parameter optimization method mainly comprises an experimental method and a numerical method. When the experimental method is adopted for optimizing the technological parameters of the friction stir welding, a large amount of experiments and error correction work are needed to obtain a satisfactory result, the method needs a large amount of effort, manpower and financial resources and lacks theoretical guidance of a friction stir welding mechanism, and the application of the method is limited to a certain extent. The numerical method gradually becomes a favorable tool for predicting the friction stir welding parameters due to the advantages of high calculation efficiency, strong intuition and repeatability, but a large amount of numerical simulation is required in the process of optimizing the process parameters, and the global optimal value cannot be obtained, so that a satisfactory result cannot be obtained. Therefore, how to effectively avoid the numerical method from falling into local optimization and apply the numerical method to the optimization of the technological parameters of the double-side simultaneous friction stir welding becomes a main problem.

Disclosure of Invention

The invention aims to solve the problems of insufficient theoretical support of an experimental method, complex process and local optimization of a numerical method aiming at the optimization of technological parameters of friction stir welding in the background art, and provides a method for optimizing the technological parameters of double-side simultaneous friction stir welding.

The technical scheme adopted by the invention for solving the technical problems in the prior art is as follows: a method for optimizing technological parameters of bilateral simultaneous friction stir welding is characterized in that based on a heat generation mechanism, a Fourier heat transfer law and an energy conservation law in the friction stir welding process, a heat generation model of bilateral simultaneous friction stir welding is established, technological parameters to be optimized are determined, a minimum input energy of a welding unit length is taken as a target function, constraint conditions are set according to a welding technology, and an optimization model is established; and solving the optimization model by adopting a sequential quadratic programming algorithm to obtain the optimal process parameter value.

Further, the process parameters to be optimized include: the rotating speed of the stirring head, the feeding welding speed of the stirring head and the distance between the end faces of the stirring needles on the two sides.

Further, the method for establishing the heat generation model of the double-side simultaneous friction stir welding comprises the following steps:

because the stirring heads on the two sides are geometrically symmetric about the thickness direction of the workpiece and the welding process parameters of the stirring heads on the two sides are the same, the heat production models of the stirring heads on the two sides are the same, and only the heat production model of the stirring head on one side is established;

according to different contact surfaces of a stirring head and a workpiece, the thermal power generated in the stirring friction welding process is divided into the following four types: respectively the thermal power Q generated by the friction between the shaft shoulder end surface of the stirring head and the workpiece_sbThe thermal power Q generated by the friction between the side surface of the shaft shoulder of the stirring head and the workpiece_ssThe thermal power Q generated by the friction between the end surface of the stirring pin and the workpiece_pbThe thermal power Q generated by the friction between the side surface of the stirring pin and the workpiece_ps：

Setting: r₂Is the radius of the shaft shoulder of the mixing head, R₁Is the radius of the end of the stirring pin, h_pThe length of the stirring pin, h is the pressing amount of the shaft shoulder, and h_gIs the distance between the end faces of the stirring pins at two sides, H is the thickness of the workpiece, omega is the rotating speed of the stirring head, sigma_yieldQ is calculated for the yield stress of the workpiece material based on the heat generation mechanism in the friction stir welding process according to the following formula_sb、Q_ss、Q_pb、Q_ps：

A heat flux index is adopted to represent a heat production model, and the heat flux comprises a surface heat flux and a body heat flux;

the heat energy generated by friction between the stirring pin and the workpiece is uniformly applied in the volume range of the stirring pin and is Q_pb、Q_psTo obtain the body heat flux q_volumeComprises the following steps:

in the formula, V_pinIs the volume of the stirring pin and is,

let the heat energy generated by friction between the shoulder of the stirring head and the workpiece be linearly applied to the workpiece surface by the heat flux, let R be the distance from a point on the workpiece surface to the axis of the stirring head, and R₁≤r≤R₂(ii) a From H, h and h_gA relation of (a), and Q_sb、Q_ssTo obtain the heat flux q of the surface_surface(r) and is simplified as follows:

further, let x be a set of process parameters to be optimized, and the constraint conditions include:

1) setting the constraint condition of the heat affected zone of the surface of the workpiece as g₁(x)，In the formula (I), the compound is shown in the specification,andthe widths of the heat affected zones on the surface of the workpiece in the current iteration step i and the next iteration step i +1 are respectively;

2) setting the maximum temperature constraint condition of the contact area of the workpiece and the shaft shoulder edge of the stirring head as g₂(x)，g₂(x)＝T_max(x)-T_mLess than or equal to 0; in the formula, T_max(x) The highest temperature of the contact area of the workpiece and the shaft shoulder edge of the stirring pin is obtained; t is_mIs the melting point of the workpiece material;

3) setting the maximum temperature constraint condition of the middle thickness of the workpiece as g₃(x)，g₃(x)＝T_md(x)-T_wNot less than 0; in the formula, T_md(x) The highest temperature of the middle thickness area of the workpiece; t is_wIs the soldering temperature.

Further, if v is the stir head feed welding speed, S is the contact area between the workpiece and the stir head shoulder, and f (x) is the input energy per unit length of the double-sided simultaneous friction stir welding, f (x) is expressed as follows:

further, the following optimization model is established by the constraint conditions and the objective function:

min f(x)；

s.t.x_l≤x≤x_u；

g₂(x)＝T_max(x)-T_m≤0；

g₃(x)＝T_md(x)-T_w≥0；

wherein x is_lAnd x_uThe upper and lower bounds of the parameter x.

Further, the method for solving the optimization model by adopting the sequential quadratic programming algorithm comprises the following steps of:

step 1, inputting an initial process parameter x₀Calculating the initial energy f₀(x) And let i equal to 0;

step 2, let i become i +1, adopt the quadratic programming algorithm of the sequence to confirm the parameter value x of the variable_i；

Step 3, calculating the surface heat flux q of the current iteration step_surface(r) and body Heat flux q_volume；

Step 4, calculating the temperature distribution of the workpiece in the process of simultaneous friction stir welding at two sides according to the Fourier heat transfer law and the energy conservation law;

step 5, judging whether constraint conditions are met or not according to the temperature distribution of the workpiece in the welding process; if the constraint condition is not satisfied, making i equal to i-1, returning to the step 2, and if the constraint condition is satisfied, performing a step 6;

step 6, calculating an objective function f_i(x)；

And 7, judging whether the iteration termination condition is met: i > i_maxOr Δ f ═ f_i+1(x)-f_i(x)＜10³(ii) a If yes, the iteration process is terminated, and the x of the current ith generation is output as the optimal process parameter; otherwise, go to step 2.

Further, the step 4 comprises the following specific steps:

from the fourier heat transfer law and the energy conservation law, the following control equation is obtained:

wherein ρ (T), k (T) and c_p(T) workpiece material density, workpiece thermal conductivity, and workpiece specific heat capacity, respectively, related to temperature T; q (x, y, z, t) is a function of the amount of heat generated by the variable in a unit volume of the workpiece in relation to the coordinates (x, y, z) and time t;

let T₀Setting h as the ambient temperature_∞For the coefficient of thermal convection between the surface of the welded workpiece and the surrounding environmentThe coefficient of thermal convection between the tool clamp and the surrounding environment;

body heat flux q_volumeSurface heat flux q_surface(r) ambient temperature T₀Coefficient h_∞Sum coefficientAnd loading the boundary conditions serving as control equations into a finite element model, and solving the control equations by adopting a numerical method to obtain the temperature distribution of the workpieces in the process of welding the friction stir welding at the two sides simultaneously.

The invention has the advantages and positive effects that: the semi-analytic heat generation model provided by the invention comprehensively considers heat generation factors in the welding process of the bilateral simultaneous friction stir welding, establishes a self-adaptive heat source model based on the heat generation process, and can accurately predict the temperature field in the welding process of the bilateral simultaneous friction stir welding.

The invention provides a bilateral simultaneous friction stir welding process parameter optimization method based on a semi-analytic heat production model, which is based on a heat production mechanism in a welding process and is coupled with an SQP optimization algorithm to obtain globally optimal input energy and optimal process parameter combination, and the optimized parameters improve the welding efficiency and the quality of a welding joint. The method has simple operation in the whole process, can conveniently and efficiently optimize the technological parameters of the double-side simultaneous friction stir welding aiming at workpieces of different materials and sizes, and provides theoretical guidance for further application of the double-side simultaneous friction stir welding in engineering.

Drawings

FIG. 1 is a schematic diagram of the operation principle of the double-side simultaneous friction stir welding.

FIG. 2 is a diagram showing the distribution of heat generated by the stir head during the double-sided simultaneous friction stir welding process.

FIG. 3 is a schematic width view of a heat affected zone on a surface of a workpiece according to the present invention.

FIG. 4 is a graph comparing thermal cycles calculated using the method of the present invention with thermal cycles measured using thermocouples in the experiment.

In the figure: 1. one of aluminum alloy sheets to be welded; 2. a second aluminum alloy plate to be welded; 3. a stirring head; 4. a tooling fixture; 5. welding seams; 6. a stir head shoulder; 7. a stirring pin; 8. a heat affected zone; 9. a thermomechanical influence zone and a nugget zone.

Q_sbThe thermal power Q generated by friction between the end surface of the shaft shoulder of the stirring head and the workpiece_ssThermal power, Q, generated by friction between the side of the shaft shoulder of the mixing head and the workpiece_pbThermal power, Q, generated by friction between the end face of the pin and the workpiece_psThermal power, R, generated by friction between the side surface of the pin and the workpiece₂Is the radius of the shaft shoulder of the mixing head, R₁Is the radius of the pin, h_pThe length of the stirring pin, h is the pressing amount of the shaft shoulder of the stirring head, and h_gIs the distance between the end faces of the stirring pins at two sides, H is the overall thickness of the workpiece, L is the overall length of the workpiece, W is the overall width of the workpiece, omega is the rotating speed of the stirring head, and sigma is_yieldIs the work piece material yield stress, tau_contactShear stress generated by the contact point of the stirring head and the workpiece; p₁(L/2,y_d0) reference point for experimental verification, P₂(x_i,R₁,0)、P₃(x_i,R₁-H/2), j 1,2,3 two reference points for the calculation of the constraint function for the optimization process, L_HAZThe width of the heat affected zone on the surface of the plate.

Detailed Description

For further understanding of the contents, features and effects of the present invention, the following embodiments are enumerated in conjunction with the accompanying drawings, and the following detailed description is given:

referring to fig. 1 to 4, a method for optimizing process parameters of double-sided simultaneous friction stir welding establishes a heat generation model of double-sided simultaneous friction stir welding based on a heat generation mechanism, a fourier heat transfer law and an energy conservation law in a friction stir welding process, determines process parameters to be optimized, sets a constraint condition according to a welding process by taking minimum input energy of a welding unit length as a target function, and establishes an optimization model; and solving the optimization model by adopting a sequential quadratic programming algorithm to obtain the optimal process parameter value.

Optimally, the process parameters to be optimized may include: the rotating speed of the stirring head 3, the feeding welding speed of the stirring head 3 and the distance between the end surfaces of the stirring pins 7 on two sides.

Optimally, the method of establishing a heat generation model for double-sided simultaneous friction stir welding may comprise:

because the stirring heads 3 on the two sides are geometrically symmetric about the thickness direction of the workpiece and the welding process parameters of the stirring heads 3 on the two sides are the same, the heat production models of the stirring heads 3 on the two sides are the same, and the heat production model of the stirring head 3 on one side can be established;

according to different contact surfaces of the stirring head 3 and the workpiece, the thermal power generated in the stirring friction welding process can be divided into the following four types: respectively the thermal power Q generated by the friction between the end surface of the shaft shoulder 6 of the stirring head and the workpiece_sbThe thermal power Q generated by the friction between the side surface of the shaft shoulder 6 of the stirring head and the workpiece_ssThe thermal power Q generated by the friction between the end surface of the stirring pin 7 and the workpiece_pbThe thermal power Q generated by the friction between the side surface of the stirring pin 7 and the workpiece_ps：

Can be provided with: r₂Is the radius of the shaft shoulder 6 of the stirring head, R₁Is the radius of the end of the stirring pin 7, h_pThe length of the stirring pin 7, h is the pressing amount of the shaft shoulder, h_gIs the distance between the end faces of the stirring pins 7 at two sides, H is the thickness of the workpiece, omega is the rotating speed of the stirring head 3, sigma_yieldBased on the heat generation mechanism in the friction stir welding process, Q can be calculated according to the following formula_sb、Q_ss、Q_pb、Q_ps：

A heat production model can be represented by a heat flux index, wherein the heat flux comprises a surface heat flux and a body heat flux;

the heat energy generated by friction between the stirring pin 7 and the workpiece can be uniformly applied to the volume range of the stirring pin 7, and is Q_pb、Q_psTo obtain the body heat flux q_volumeComprises the following steps:

in the formula, V_pinIs the volume of the stirring pin 7 and,

it can be assumed that the heat energy generated by friction between the shoulder 6 of the stirring head and the workpiece is linearly applied to the workpiece surface by the heat flux, R is the distance from a point on the workpiece surface to the axis of the stirring head 3, and R is₁≤r≤R₂(ii) a From H, h and h_gA relation of (a), and Q_sb、Q_ssTo obtain the heat flux q of the surface_surface(r) and is simplified as follows:

optimally, x can be set as a set of process parameters to be optimized, and the constraint conditions can include:

1) setting the constraint condition of a heat affected zone 8 of the surface of the workpiece as g₁(x)，In the formula (I), the compound is shown in the specification,andthe widths of the heat affected zone 8 on the surface of the workpiece in the current iteration step i and the next iteration step i +1 are respectively;

2) the constraint condition of the highest temperature of the contact area of the workpiece and the edge of the shaft shoulder 6 of the stirring head is set as g₂(x)，g₂(x)＝T_max(x)-T_mLess than or equal to 0; in the formula, T_max(x) The highest temperature of the contact area of the workpiece and the shaft shoulder edge of the stirring pin 7; t is_mIs the melting point of the workpiece material;

3) setting the maximum temperature constraint condition of the middle thickness of the workpiece as g₃(x)，g₃(x)＝T_md(x)-T_wNot less than 0; in the formula, T_md(x) The highest temperature of the middle thickness area of the workpiece; t is_wIs the soldering temperature.

Optimally, v can be set as the feed welding speed of the stirring head 3, S can be set as the contact area of the workpiece and the stirring head shaft shoulder 6, and f (x) can be set as the input energy per unit length of the double-side simultaneous friction stir welding, so that f (x) can be expressed as follows:

optimally, from the constraints and the objective function, the following optimization model can be established:

min f(x)；

s.t.x_l≤x≤x_u；

g₂(x)＝T_max(x)-T_m≤0；

g₃(x)＝T_md(x)-T_w≥0；

wherein x is_lAnd x_uThe upper and lower bounds of the parameter x.

Optimally, the method for solving the optimization model by adopting the sequential quadratic programming algorithm can comprise the following steps:

step 1, inputting an initial process parameter x₀Calculating the initial energy f₀(x) And let i equal to 0;

step 2, let i become i +1, adopt the quadratic programming algorithm of the sequence to confirm the parameter value x of the variable_i；

Step 3, calculating the surface heat flux q of the current iteration step_surface(r) and body Heat flux q_volume；

Step 4, calculating the temperature distribution of the workpiece in the process of simultaneous friction stir welding at two sides according to the Fourier heat transfer law and the energy conservation law;

step 5, judging whether constraint conditions are met or not according to the temperature distribution of the workpiece in the welding process; if the constraint condition is not satisfied, making i equal to i-1, returning to the step 2, and if the constraint condition is satisfied, performing a step 6;

step 6, calculating an objective function f_i(x)；

And 7, judging whether the iteration termination condition is met: i > i_maxOr Δ f ═ f_i+1(x)-f_i(x)＜10³(ii) a If yes, the iteration process is terminated, and the x of the current ith generation is output as the optimal process parameter; otherwise, go to step 2. i.e. i_maxIs the set maximum number of iterations.

Optimally, the step 4 may include the following specific steps:

from the fourier heat transfer law and the energy conservation law, the following control equation is obtained:

wherein ρ (T), k (T) and c_p(T) is the workpiece material density, the workpiece thermal conductivity and the workpiece specific heat capacity, respectively, related to the temperature T(ii) a q (x, y, z, t) is a function of the amount of heat generated by the variable in a unit volume of the workpiece in relation to the coordinates (x, y, z) and time t;

can be provided with T₀Setting h as the ambient temperature_∞For the coefficient of thermal convection between the surface of the welded workpiece and the surrounding environmentThe coefficient of thermal convection between the tool clamp 4 and the surrounding environment;

can reduce body heat flux q_volumeSurface heat flux q_surface(r) ambient temperature T₀Coefficient h_∞Sum coefficientAnd loading the boundary conditions serving as control equations into a finite element model, and solving the control equations by adopting a numerical method to obtain the temperature distribution of the workpieces in the process of welding the friction stir welding at the two sides simultaneously.

The working process and working principle of the present invention are further explained by a preferred embodiment of the present invention as follows:

a method for optimizing technological parameters of double-side simultaneous friction stir welding comprises the following steps:

step 1: establishing semi-analytic heat production model for bilateral simultaneous friction stir welding

Step 1.1: heat production model hypothesis

The research model adopts a double-side simultaneous friction stir welding mode, two aluminum alloy plates with the same material are welded by a double-side simultaneous friction stir welding process, as shown in figure 1, one aluminum alloy plate 1 to be welded and the other aluminum alloy plate 2 to be welded are spliced together, stirring heads 3 are adopted to weld two side surfaces of the aluminum alloy plates simultaneously, the size of the whole workpiece after welding is L multiplied by W multiplied by H, the two stirring heads 3 are oppositely arranged, and H is carried out_gThe rotation direction is opposite to the distance between the end surfaces of the stirring pins 7 at two sides, and the stirring pins move along the welding seam 5 line in the positive direction of the x axis at the same rotation speed omega and feed speed v. In order to reduce the complexity of solving the thermal model, some necessary assumptions are made; the whole is weldedThe thermal conduction behavior of the workpiece in the process is three-dimensional transient, the inclination angle of the stirring head 3 is not considered, only the quasi-steady state stage of the welding process is modeled, and the thermal radiation of the welding process is not considered.

Step 1.2: governing equations and boundary conditions

The basic equation for heat transfer from the fourier heat transfer law and the law of conservation of energy is:

where ρ (T), k (T) and c_p(T) is the density, thermal conductivity and specific heat capacity of the workpiece material in relation to the temperature T. q (x, y, z, t) is the amount of heat generated per unit volume (as a function of the coordinates (x, y, z) of the heat source in the workpiece and time t). In order to solve the control equation, boundary heat transfer conditions of the welding workpiece need to be given, the welding workpiece is geometrically symmetric about the welding seam 5, the materials of the two plates are the same, only one of the welding workpiece is modeled, and coefficients for generating heat convection on the surface of the welding workpiece, the tool clamp 4 and the surrounding environment are respectively h_∞Anddenotes that the ambient temperature is T₀The heat generation of the stirring tip 3 and the workpiece is expressed by a heat flux q, which is composed of a surface heat flux and a body heat flux.

Step 1.3: establishing analytic heat production model for double-side simultaneous friction stir welding

The heat distribution profile during welding is shown in FIG. 2, where R₂Is the radius of the shaft shoulder 6 of the stirring head, R₁And h_pThe radius and the length of the stirring pin 7 are shown, and h is the pressing amount of the shaft shoulder 6 of the stirring head. Because the stirring heads 3 on the two sides are geometrically symmetrical relative to the thickness direction of the workpiece, modeling is carried out by taking the heat generation of the stirring head 3 on one side as an example. According to the difference of the contact surface between the stirring head 3 and the workpiece, the heat generation is mainly divided into the following four types of heat sources: thermal power Q generated by contact of the end surface of the shaft shoulder 6 of the stirring head and a workpiece_sbThe thermal power Q generated by the contact of the side surface of the shaft shoulder 6 of the stirring head and the workpiece_ssThe end face of the stirring pin 7 andthermal power Q generated by workpiece contact_pbThe thermal power Q generated by the contact of the side surface of the stirring pin 7 and the workpiece_ps(only the advancing side is in contact with the workpiece during movement along the weld 5). Shear stress tau generated at the contact point of tool and workpiece during welding_contactComprises the following steps:

τ_contact＝(1-δ)τ_friction+δτ_yield

where δ is the contact state variable, τ_frictionIs the frictional shear stress, τ, of the material_yieldIs the yield shear stress of the material, according to the von Mises yield criterion, the yield shear stress tau of the material_yieldAnd yield stress sigma_yieldThe following relationships exist:

when the welding process is in a quasi-steady state, the frictional shear stress and the yield shear stress are a pair of equilibrium forces, i.e., τ_friction＝τ_yieldThus shear stress tau occurring at the contact point of tool and workpiece_contactThe simplification is as follows:

by shear stress tau to the contact surface of the stirring head 3 and the workpiece_contactAnd integrating the contact area to obtain an analytical expression of each heat source, and simplifying the analytical expression into:

the heat source for generating heat of the stirring pin 7 and the workpiece is uniformly applied in the volume range of the stirring pin 7, and the body heat flux q is obtained by the above heat generation equation_volumeComprises the following steps:

in the formula, V_pinIs the volume of the stirring pin 7 and,

the heat source generated by the contact surface of the shaft shoulder 6 of the stirring head and the workpiece is applied to the surface of the workpiece by linear heat flux according to the heat generation equation, the pressing amount h of the shaft shoulder and the distance h between the stirring pins 7_gThe relationship (H-H)_g-2h_p) (ii)/2, obtaining the surface heat flux q_surface(r) and is simplified as follows:

q_surface(r)＝kr (3)

where k is a proportionality coefficient, let R be the distance from a point on the workpiece surface to the axis of the stirring head 3, and R₁≤r≤R₂(ii) a S is the radius R of the end surface of the shaft shoulder 6 of the stirring head₁To a radius R₂The area of (a).

The body heat source q obtained above_volumeSurface heat source q_surface(r) ambient temperature T₀Convection edge h_∞Andand loading the boundary condition serving as a control equation (1) into a finite element model (the other side stirring head 3 can obtain a surface heat source and a body heat source applied to the workpiece by the side stirring head 3 by adopting the same method for establishing the heat source), and solving the control equation (1) by adopting a numerical method to obtain the temperature distribution of the workpiece in the welding process of the double-side simultaneous friction stir welding.

Step 2: establishing optimization process of bilateral simultaneous friction stir welding process parameters based on semi-analytic heat production model step 2.1 establishing optimization variables and targets

Dimension R of the pin 3 during the bilateral simultaneous friction stir welding₁、R₂、h_pAnd the size L multiplied by W multiplied by H of the workpiece is a constant value set in advance, and the rotating speed omega, the welding speed v and the distance H between the stirring heads on the two opposite sides_gAre adjustable variables and these variables are the main factors influencing the heat input during the welding process, the process parameters to be optimized are therefore ω, v and h_gExpressed as vector x:

x＝(ω,v,h_g)

the target requirement is defined as a function describing the energy consumption during the welding process, and the target function during the optimization is obtained by dividing the total heat generated during the welding process by the welding speed v:

step 2.2: establishing constraint conditions

The microhardness of the workpiece after friction stir welding is in a W shape on the whole, the workpiece is close to a heat engine affected zone and a nugget zone 9 and is a heat affected zone 8, the hardness of the heat affected zone 8 is the lowest, and the heat affected zone is most prone to fracture in the stretching process, so the heat affected zone 8 is a dangerous zone, and the optimization process should minimize the zone. According to the heat cycle solving result of the semi-analytic heat production model, in the iterative optimization process, the constraint condition of the region is defined as g₁(x) The expression is as follows:

in the formula (I), the compound is shown in the specification,andthe width of the heat affected zone 8 of the workpiece surface in the current iteration step i and the next iteration step i +1, respectively, is a function of the process parameters.

The highest temperature T of the contact area of the edge of the shaft shoulder 6 of the stirring head and the workpiece in the welding process_max(x) Must be below the melting point T of the material_mThe constraint defining the state is g₂(x) The expression is as follows:

g₂(x)＝T_max(x)-T_m≤0

in order to ensure that the pin 3 moves smoothly along the weld seam 5, the material in the region around the end of the pin 7 should be sufficiently pasty, the maximum temperature T at the location of the intermediate thickness of the workpiece_md(x) Must be higher than or equal to the welding temperature T_wThe constraint of the state is g₃(x) The expression is as follows:

g₃(x)＝T_md(x)-T_w≥0

therefore, according to the above constraints, the optimization problem to be solved is obtained as follows:

min f(x)

s.t.x_l≤x≤x_u

g₂(x)＝T_max(x)-T_m≤0

g₃(x)＝T_md(x)-T_w≥0

wherein x is_lAnd x_uThe upper and lower bounds of the parameter x.

Step 2.3: optimization algorithm flow

Based on the constraint conditions and the objective function established above, the optimal process parameter value in the bilateral simultaneous friction stir welding is solved by a coupled sequence quadratic programming algorithm (SQP), and when the iteration number i of the algorithm exceeds the maximum iteration number i_maxThe difference value delta f of the energy functions of 50 or two adjacent iteration steps is less than 10³The iterative process is terminated. The procedure for deriving the optimization algorithm is as follows:

inputting an initial technological parameter x₀Calculating the initial energy f₀(x) And let i equal to 0.

② changing i into i +1, adopting SQP algorithm to determine the parameter value of variable in current iteration step i as x_i。

Calculating the surface heat flux q in the current iteration step i by adopting equations (2) and (3)_surface(r) and body Heat flux q_volume。

The surface heat flux q of the stirring head 3 at the other side is obtained by the same modeling method_surface(r) and body Heat flux q_volume。

Fourthly, the surface heat flux q obtained in the third step_surface(r) and body Heat flux q_volumeAnd as a boundary condition in the control equation (1), loading the heat flux density of the double-side friction stir welding into a heat generation model to solve the control equation (1) through a DFLUX subprogram of finite element software ABAQUS to obtain the temperature distribution in the welding process.

Fifthly, calculating constraint function g according to the result obtained in the step IV₁(x)、g₂(x)、g₃(x) And an objective function f_i(x)。

Sixthly, judging whether the iteration termination condition is met: i > i_maxOr Δ f ═ f_i+1(x)-f_i(x)＜10³. If yes, the iteration process is terminated, and the variable x of the current iteration step i is output as the optimal process parameter. Otherwise, go to step two.

And step 3: method for optimizing parameters of bilateral simultaneous friction stir welding process based on semi-analytic heat production model

Step 3.1: verifying correctness of semi-analytic heat production model by adopting experimental method

The overall geometric dimensions of the workpiece to be welded are 250mm x 150mm x 4mm, the dimensions of the stirring head 3 being; radius R of the pin shoulder 6 of the pin₂6.5mm, the radius R of the stirring pin 7₁2.5mm, the length h of the stirring pin 7_p1.8mm, aluminum alloy Al2024, convection boundary h_∞＝10W.m^-2.K^-1、The parameters of the initial welding are as follows; the rotational speed ω of the stirring head 3 was 1100rpm, the feeding speed v was 21mm/min, and the gap between the stirring heads 3 on both sides was h_g0 mm. In the experiment, a thermocouple is adopted to measure the temperature cycle result of the workpiece, and the position of the thermocouple is P₁(125,20,0)。

To facilitate the analysis of the results of the optimization process, three reference points P are provided₁(L/2,y_d,0)、P₂(x_i,R₁0) and P₃(x_i,R₁-H/2), j ═ 1,2, 3. As shown in FIG. 3, P₁The points represent the positions of thermocouples of the welding workpieces in the experiment, and the results obtained in the experiment are compared with the thermal cycle results of the semi-analytic heat production model for analysis. P₂Point sum P₃The points represent the positions of the end of the shoulder 6 of the pin and the middle thickness of the workpiece, respectively, in order to facilitate the calculation of the constraint g in the optimization problem₁(x)、g₂(x)、g₃(x) Wherein x is₁＝L/4，x₂＝L/2，x₃＝3L/4。

Step 3.2: on the basis of establishing a semi-analytic heat production model, the optimal process parameters of the double-side simultaneous friction stir welding can be obtained by coupling with a sequence quadratic programming algorithm (SQP) and adopting the process parameter optimization flow of the step 2.3.

The optimal process parameters of the double-side friction stir welding, the temperature result measured by the thermocouple and the thermal cycle result of the semi-analytic heat generation model are optimized by the optimization method of the invention, and the temperature cycle result of the semi-analytic heat generation model is shown in figure 4The peak temperature of the experiment result is close to the peak temperature of the thermocouple, and the temperature rise and the temperature fall have better consistency, so that the correctness of the semi-analytic heat generation model is verified, and the method can be accurately used for predicting the temperature distribution and the cooling rate. The results of the process parameter optimization are shown in Table 1 below, where it is seen that the weld heat input energy after optimization is lower than the initial input energy, T_P1Represents the peak temperature, L^HAZThe length of the heat affected zone 8 is shown, the length of the heat affected zone 8 is smaller than the length of the heat affected zone 8 corresponding to the initial parameters, and the optimized welding speed is greatly improved relative to the initial speed.

TABLE 1 optimization results

The above-mentioned embodiments are only for illustrating the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and to carry out the same, and the present invention shall not be limited to the embodiments, i.e. the equivalent changes or modifications made within the spirit of the present invention shall fall within the scope of the present invention.