CN104942113A - Method for rapidly predicting welding seam movement in deep-drawing forming process of laser tailor-welded blank - Google Patents

Abstract

The invention discloses a method for rapidly predicting welding seam movement in a deep-drawing forming process of a laser tailor-welded blank. The method comprises steps as follows: 1), a workpiece is dispersed to form triangle elements, formed part grids are obtained, and a virtual work equation is established for final configuration of a plate material; 2), a finite element equation of a one-step simulation method is established; 3), an iterative equation is established by adopting a Newton-Laplace method with convergence factors; 4), the iterative equation is solved; a non-linear equation set is obtained, and a second iterative equation is established by adopting the Newton-Laplace method with convergence factors; the second iterative equation is solved to obtain an initial displacement field; the process is transferred to the step 3), and tailor-welded blank grids obtained through back calculation can be output after Newton-Laplace iterative convergence; 5), two space curves 11 and 12 are obtained by connecting nodes of the elements in welding seams of the formed part grids and the tailor-welded blank grids obtained through back calculation; 6), the two space curves 11 and 12 are projected to the X-Y plane respectively so as to obtain two plane curves 1'1 and 1'2; the welding seam offset is calculated.

Description

Laser assembly solder plate drawing process weld movement method for quick predicting

Technical field

The present invention relates to a kind of weld movement Forecasting Methodology, especially a kind of laser assembly solder plate drawing process weld movement method for quick predicting.

Background technology

In order to reduce tare, improve the assembly precision of vehicle body, increase the rigidity of vehicle body, reduce punching press in body of a motor car manufacture process and assembly cost, its integration is very important by the number reducing bodywork parts simultaneously.Thus, a kind of production form simultaneously overcoming traditional separating shaped method and integral forming method shortcoming--tailor welded is stamping to have grown up.Tailor welded refers to the cold-rolled steel sheet of similar and different thickness, intensity, material, is cut into suitable size and dimension, and then Laser Welding is connected into a desirable entirety.The commercial this tailor welded of automobile making strikes out specific Assembly of the parts automobile, with the multiple demand meeting oneself and consumer improves vehicle product quality, reduces production cost, alleviates car weight, reduces the aspect such as oil consumption, protection of the environment.

Although the use of tailor welded brings many benefits, but also there is a lot of technical insoluble problem simultaneously, wherein topmost problem be that the forming property that caused by weld metal zone tissue change declines and weld movement causes cannot accurately by problems such as certain material location: intensity higher side sheet metal deformation is less, and intensity lower side sheet metal deformation is comparatively large, weld seam both sides are made to form inhomogeneous deformation.In addition, mechanical process and the shaping influence factor of laser assembly solder plate shaping are very complicated, it is a strong nonlinearity problem integrating geometrical non-linearity, material nonlinearity, boundary nonlinear, especially for comparatively complicated automobile panel, calculating expends time in tens hours at least, more than one week at most.If adopt traditional method of addition simulation softward, need repeatedly to call execution in optimization design, the time that optimization consumes, often because exceeded the limit that can bear, is thus optimized and loses meaning.Particularly at the beginning of stamping products design, the quantity of parameters such as mould and technique information is undetermined, if adopt this strategy to need to consume a large amount of manpowers and time, feasibility is lower.

Inverse analog algorithm is a kind of blank Optimization Design founded about the nineties in 20th century, but not yet finding that there is Patents for the prediction of laser assembly solder plate forming process weld movement declares.

Summary of the invention

The object of the invention is for overcoming above-mentioned the deficiencies in the prior art, a kind of laser assembly solder plate drawing process weld movement method for quick predicting is provided.

For achieving the above object, the present invention adopts following technical proposals:

A kind of laser assembly solder plate drawing process weld movement method for quick predicting, comprises the following steps:

1). by discrete for workpiece be triangular element, obtain formation of parts grid, following virtual work equation set up to the final configuration of the plate of workpiece

$W=\mathrm{\Σ}{\∫}_{V_e}{{\mathrm{\δ}}_{\mathrm{\ϵ}}}^T\mathrm{\σ}dV-{\∫}_{A_e}{{\mathrm{\δ}}_u}^{T}FdA=0---\left(1\right)$

δ ε in formula---in unit, the sham of arbitrfary point is moved;

δ u---the virtual strain of arbitrfary point in unit;

σ---cauchy stress;

F---outer force vector;

V _e---volumetric spaces;

A _e---surf zone;

T---represent transposed matrix;

2). set up the finite element equation of One-step simulation

k(u)u＝p(u) (2)

K (u) in formula---stiffness matrix;

P (u)---external force load vector;

U---displacement;

3). because formula (1) and formula (2) they are all the functions of displacement components u, therefore formula (2) is a Nonlinear System of Equations, adopt newton-Laplce's method of band convergence factor, suppose that the difference of external force and internal force is R (u), its iterative equation is

$\left\{\begin{array}{c}{k}_T\left(u^i\right){\mathrm{\Δu}}^i=R\left(u^i\right)\\ u^{i+1}=u^i+{\mathrm{\ω\Δu}}^i\end{array}\right.---\left(3\right)$

ω in formula---iteration relaxation factor, Δ u ⁱ---the displacement increment of the i-th step, R (u ⁱ)---the external force internal force of the i-th step is poor, u ⁱ⁺¹---the displacement increment of the i-th+1 step, u ⁱ---the displacement increment of the i-th step, k _t---tangent stiffness matrix;

4). in order to solve formula (3), need to provide the displacement field that is initial, i.e. the initial value of displacement components u; The quality of initial value determines the efficiency that formula (3) solves; Suppose that external force load is zero, namely

k(u)u＝0 (4)

K (u) in formula---stiffness matrix;

U---displacement;

Similar, obtain a Nonlinear System of Equations, adopt newton-Laplce's method of band convergence factor, suppose that the difference of external force and internal force is R (u), its iterative equation is

$\left\{\begin{array}{c}{k}_T\left(u^i\right){\mathrm{\Δu}}^i=F_{in}\left(u^i\right)\\ u^{i+1}=u^i+{\mathrm{\ω\Δu}}^i\end{array}\right.---\left(5\right)$

ω in formula---iteration relaxation factor, Δ u ⁱ---the displacement increment of the i-th step, F _in(u ⁱ)---the internal force of the i-th step, u ⁱ⁺¹---the displacement increment of the i-th+1 step, u ⁱ---the displacement increment of the i-th step, k _t---tangent stiffness matrix;

Solve this equation group, can initial displacement field u be obtained ₀; Then (3) step is forwarded to, the tailor welded grid of i.e. exportable inverse acquisition after newton-Laplce's iteration convergence;

5). inside the tailor welded grid two nested grid system that formation of parts grid and inverse obtain, the node of each unit in attachment weld place can obtain two space curve l ₁and l ₂;

6). by two space curve l ₁and l ₂respectively to X-Y plane projection, obtain two plane curve l ' ₁with l ' ₂; According to formula $\mathrm{\Δ}l=\underset{i=1}{\overset{N-1}{\Σ}}\sqrt{{\left(x_1^i-x_2^i\right)}^2+{\left(y_1^i-y_2^i\right)}^2}$ Calculate the side-play amount of weld seam;

Δ l in formula---weld excursion amount;

N---curve l ' ₁with l ' ₂by the hop count on average divided;

---curve l ' ₁the abscissa of i-th point;

---curve l ' ₁the ordinate of i-th point;

---curve l ' ₂the abscissa of i-th point;

---curve l ' ₂the ordinate of i-th point.

Step 4) in for the simple part of some shape matching, such as non-straight wall class part, can project three-dimensional grid directly to X-Y plane, thus obtains the 3rd) initial displacement field u needed for step ₀, this type of part requirements does not overlap to the grid after X-Y plane projection.

The present invention only considers the shape of final workpiece, and known parameters is the profile of workpiece, the thickness of original blank, and unknown parameter has the shape of blank and the thickness of workpiece.These parameters can by minimizing plastic deformation work to try to achieve.In order to ignore the impact in different distortion path, made a series of hypothesis, two wherein main aspects are: load in proportion; Ignore the contact boundary condition of mould and plate, and use the friction boundary condition (shown in Fig. 1) of simplification instead.In order to ignore the impact in different distortion path, make a series of hypothesis:

1. Large Elastic-Plastic Deformation, material is completely incompressible.

2. deformation process is load on rate, namely based on plastic deformation theory.

3. material etc. are to strengthening or anisotropic strengthening.

4. the effect of mould shows as drift normal pressure heterogeneous, the frictional force under drift and blank holder.

The present invention only considers the end-state after being out of shape and initial plate blank, does not consider loading history, and the active force of mould adopts the external applied load of equivalence to replace.The frictional resistance that blank holder produces replaces with an equivalent load vector, and the active force of drift and mould replaces with a normal pressure and a tangential friction force.

The present invention proposes a kind of inverse analog method being applicable to laser assembly solder plate, and the method only has two frees degree due to each node, and analog rate quickly, carries out analysis and the optimization of technique at the beginning of being very suitable for product and Design of Dies.By the line of demarcation of bi-material in the blank of inverse analog method inverse, instead fast can push away various technique situation affected on weld movement in tailor welded part forming process, this is Forecast and control weld movement for how, what take into full account that the decline of the forming property that the existence of weld seam causes and the movement of weld seam cause accurately by problems such as certain material location, cannot have important reference value.And theoretical and experiment has all demonstrated inverse analog method calculating weld movement measurer satisfied Engineering Reliability.

By with Experimental comparison, although there is the difference of 36% when adopting the result of method inverse of the present invention and the value of actual measurement maximum, its prediction trend and actual conditions fit like a glove; Can reflected well compared to flange, rectangular-shaped piece bottom section has larger weld movement amount.The present invention can at the tailor welded blank forming Element Design initial stage, the situation of movement of this part of fast prediction weld seam in actual drawing process, the position of convenient design weld seam and other technological parameters, the decline of the performance caused with the movement reducing weld seam as far as possible, accurately orientation problem cannot provide a kind of new method for solving.

Accompanying drawing explanation

Fig. 1 is Method And Principle figure of the present invention;

Fig. 2 is the location drawing of the desirable weld seam of the embodiment of the present invention 1;

Fig. 3 is technical solution of the present invention step 3) calculate the initial displacement field u obtained ₀;

Fig. 4 is the blank and bonding wire figure that utilize the present invention to obtain in embodiment 1;

Fig. 5 is laser assembly solder plate schematic diagram in embodiment 2;

Fig. 6 is that in embodiment 2, thin side plate applies bead schematic diagram;

Fig. 7 is without bead effect schematic diagram in embodiment 2;

Fig. 8 is without bead effect (pressure-pad-force reduction) schematic diagram in embodiment 2;

Fig. 9 is that in embodiment 2, surrounding all applies bead schematic diagram.

Detailed description of the invention

Below in conjunction with drawings and Examples, the present invention is further described.

Embodiment 1: quick obtaining blank position of bonding wire

Fig. 2 display be part drawing after being shaped, transversal AB is the position (not skew) of the desirable weld seam of setting, and its terminal A is also measure the reference point of each point situation of movement on weld seam under each operating mode.Transversal CD is parallel with the length direction of part, namely vertical with setting bead direction, and be positioned at the center of part, this cross section, respectively across the welded seam area of the flange of thin thick plate side, sidewall and bottom surface, can reflect that the variation tendency of thickness and strain on this cross section and different schemes affect situation to it.

Start with from drawing and forming part, inverse analog calculating is carried out according to kind of the scheme of 4 shown in table 1, scheme one, two, four adopts the pressure-pad-force of 70KN, scheme three adopts the pressure-pad-force of 40KN, scheme one, four adopts the equivalent drawbead model of 0.14KN/mm, by the blank shape under the different operating mode of calculating acquisition and position while welding.Concrete steps are as follows:

According to technical solution of the present invention step 1) by discrete for workpiece be triangular element, obtain formation of parts grid, following virtual work equation set up to the final configuration of the plate of workpiece

$W=\mathrm{\Σ}{\∫}_{V_e}{{\mathrm{\δ}}_{\mathrm{\ϵ}}}^T\mathrm{\σ}dV-{\∫}_{A_e}{{\mathrm{\δ}}_u}^{T}FdA=0---\left(1\right)$

δ ε in formula---in unit, the sham of arbitrfary point is moved; δ u---the virtual strain of arbitrfary point in unit; σ---cauchy stress; F---outer force vector; V _e---volumetric spaces; A _e---surf zone; T---represent transposed matrix;

Obtain invention technical scheme steps 2 according to formula (1)) in the finite element equation of One-step simulation.

k(u)u＝p(u) (2)

K (u) in formula---stiffness matrix; P (u)---external force load vector; U---displacement;

Because formula (1) and formula (2) are all the functions of displacement components u, therefore formula (2) is a Nonlinear System of Equations, adopt newton-Laplce's method of band convergence factor, suppose that the difference of external force and internal force is R (u), its iterative equation is

$\left\{\begin{array}{c}{k}_T\left(u^i\right){\mathrm{\Δu}}^i=R\left(u^i\right)\\ u^{i+1}=u^i+{\mathrm{\ω\Δu}}^i\end{array}\right.---\left(3\right)$

ω in formula---iteration relaxation factor, Δ u ⁱ---the displacement increment of the i-th step, R (u ⁱ)---the external force internal force of the i-th step is poor, u ⁱ⁺¹---the displacement increment of the i-th+1 step, u ⁱ---the displacement increment of the i-th step, k _t---tangent stiffness matrix;

In order to solve invention technical scheme steps 3) equation group, need first to calculate invention technical scheme steps 4) Nonlinear System of Equations, namely in order to solve formula (3), need to provide the displacement field that initial, the i.e. initial value of displacement components u, the quality of initial value determines the efficiency that formula (3) solves; Suppose that external force load is zero, namely

k(u)u＝0 (4)

K (u) in formula---stiffness matrix; U---displacement;

Similar, obtain a Nonlinear System of Equations, adopt newton-Laplce's method of band convergence factor, in supposing, force value is F _in(u ⁱ), its iterative equation is

$\left\{\begin{array}{c}{k}_T\left(u^i\right){\mathrm{\Δu}}^i=F_{in}\left(u^i\right)\\ u^{i+1}=u^i+{\mathrm{\ω\Δu}}^i\end{array}\right.---\left(5\right)$

ω in formula---iteration relaxation factor, Δ u ⁱ---the displacement increment of the i-th step, F _in(u ⁱ)---the internal force of the i-th step, u ⁱ⁺¹---the displacement increment of the i-th+1 step, u ⁱ---the displacement increment of the i-th step, k _t---tangent stiffness matrix;

Solve this equation group (5), obtain initial displacement field u ₀, result of calculation as shown in Figure 3.

The grid of Fig. 3 submits to invention technical scheme steps 3 as initial solution) solve Nonlinear System of Equations, see formula (3).Be the tailor welded grid of exportable inverse after newton-Laplce's iteration convergence, final solving result as shown in Figure 4.

Assuming that be just to thin side to moving, on acquisition weld seam, each point is relative to the displacement of terminal A.

At the tailor welded grid that formation of parts grid and inverse obtain, the node of each unit in attachment weld place obtains two space curve l ₁and l ₂;

By two space curve l ₁and l ₂respectively to X-Y plane projection, obtain two plane curve l ' ₁with l ' ₂; According to formula $\mathrm{\Δ}l=\underset{i=1}{\overset{N-1}{\Σ}}\sqrt{{\left(x_1^i-x_2^i\right)}^2+{\left(y_1^i-y_2^i\right)}^2}$ Calculate the side-play amount of weld seam;

Δ l in formula---weld excursion amount; N---curve l ' ₁with l ' ₂by the hop count on average divided; ---curve l ' ₁the abscissa of i-th point; ---curve l ' ₁the ordinate of i-th point; ---curve l ' ₂the abscissa of i-th point; ---curve l ' ₂the ordinate of i-th point.

Table 1 experimental program

Scheme one	Thin plate side applies bead (cylinder pressure 0.35MPa)
		Scheme two	Without bead (cylinder pressure 0.35MPa)
Scheme three	Adopt less pressure-pad-force (cylinder pressure 0.20MPa)
		Scheme four	Surrounding applies bead (cylinder pressure 0.35MPa)

。

For the simple part of some shape matching, such as non-straight wall class part, can project three-dimensional grid directly to X-Y plane, thus the initial displacement field u needed for obtaining ₀, this type of part requirements does not overlap to the grid after X-Y plane projection.

Verify the reliability of embodiment 1 result of calculation below.

The tailor welded that experimental section adopts is respectively the rectangle plate (Fig. 5) of 0.8mm and 1.2mm by two block sizes identical (240 × 160mm), thickness, adopt CO2 laser weld to form, bonding power is 4KW, speed of welding 3m/min.Experiment material used is Baosteel GM6409M cold-rolled steel sheet.The material property parameter of cold-rolled steel is as shown in table 2.Because the drawing of tailor welded is different from the drawing of whole plate, the design of mould also needs the particularity considering this respect.The tailor welded that this experiment adopts is formed by the welding of two blocks of different-thickness plates, if punch, blank holder and die are all flat, thin plate side is wrinkling because of insufficient pressure.What this testing program was taked is arrange step on punch and blank holder, and die is constant, to ensure the requirement of part outer surface quality.In order to obtain the amount of movement of weld seam, three-coordinates measuring machine is adopted to measure.The present invention is not limited to the data that experiment adopts, and this experimental data is only illustratively.

Table 2 Baosteel GM6409M cold-rolled steel sheet performance parameter

The drawing experiment mould of comparative analysis reality and the complete laser assembly solder plate part of drawing.After drawing parts is fixing, choose measurement point and adopt three-coordinates measuring machine to measure the movement of weld seam.Respectively each scheme drawing experimental data and numerical simulation result are contrasted, obtain the correlation curve figure shown in Fig. 6 ~ 9.Due to the simplification of inverse analog method boundary condition, do not consider the impact of deformation history on forming process, and have ignored the effect of heat affected area around weld seam, the error produced when adding measurement, the maximum deviation that two kinds of curves are produced in each scheme is respectively 36%, 24.8%, 24.2%, 30.3%.Find in addition, the result of numerical simulation is generally all less than the result of actual measurement.But the trend of numerical simulation result and experimental data are consistent: flange weld seam is significantly less than the amount of movement of rectangular-shaped piece bottom section weld seam to rear side to the amount of movement of thin side, illustrate in order to obtain rational Strain Distribution need mainly be controlled the weld movement of box part bottom section.

Claims (2)

1. a laser assembly solder plate drawing process weld movement method for quick predicting, is characterized in that, comprise the following steps:

1). by discrete for workpiece be triangular element, formation of parts grid, sets up following virtual work equation to the final configuration of the plate of workpiece

δ ε in formula---in unit, the sham of arbitrfary point is moved; δ u---the virtual strain of arbitrfary point in unit; σ---cauchy stress; F---outer force vector; V _e---volumetric spaces; A _e---surf zone; T---represent transposed matrix;

2). set up the finite element equation of One-step simulation

k(u)u＝p(u) (2)

K (u) in formula---stiffness matrix; P (u)---external force load vector; U---displacement;

3). because formula (1) and formula (2) they are all the functions of displacement components u, therefore formula (2) is a Nonlinear System of Equations, adopt newton-Laplce's method of band convergence factor, suppose that the difference of external force and internal force is R (u), its iterative equation is

$\left\{\begin{array}{c}{k}_T\left(u^i\right){\mathrm{\Δu}}^i=R\left(u^i\right)\\ u^{i+1}=u^i+{\mathrm{\ω\Δu}}^i\end{array}\right.---\left(3\right)$

ω in formula---iteration relaxation factor, Δ u ⁱ---the displacement increment of the i-th step, R (u ⁱ)---the external force internal force of the i-th step is poor, u ⁱ⁺¹---the displacement increment of the i-th+1 step, u ⁱ---the displacement increment of the i-th step, k _t---tangent stiffness matrix;

4). in order to solve formula (3), need to provide the displacement field that is initial, i.e. the initial value of displacement components u, the quality of initial value determines the efficiency that formula (3) solves; Suppose that external force load is zero, namely

k(u)u＝0 (4)

K (u) in formula---stiffness matrix; U---displacement;

Similar, obtain a Nonlinear System of Equations, adopt newton-Laplce's method of band convergence factor, in supposing, force value is F _in(u ⁱ), its iterative equation is

$\left\{\begin{array}{c}{k}_T\left(u^i\right){\mathrm{\Δu}}^i=F_{in}\left(u^i\right)\\ u^{i+1}=u^i+{\mathrm{\ω\Δu}}^i\end{array}\right.---\left(5\right)$

ω in formula---iteration relaxation factor, Δ u ⁱ---the displacement increment of the i-th step, F _in(u ⁱ)---the internal force of the i-th step, u ⁱ⁺¹---the displacement increment of the i-th+1 step, u ⁱ---the displacement increment of the i-th step, k _t---tangent stiffness matrix;

Solve this equation group (5), obtain initial displacement field u ₀; Then the 3rd is forwarded to) step is the tailor welded grid of exportable inverse after newton-Laplce's iteration convergence;

5). at the tailor welded grid that formation of parts grid and inverse obtain, the node of each unit in attachment weld place obtains two space curve l ₁and l ₂;

6). by two space curve l ₁and l ₂respectively to X-Y plane projection, obtain two plane curve l ' ₁with l ' ₂; According to formula $\mathrm{\Δ}l=\underset{i=1}{\overset{N-1}{\Σ}}\sqrt{{\left(x_1^i-x_2^i\right)}^2+{\left(y_1^i-y_2^i\right)}^2}$ Calculate the side-play amount of weld seam;

Δ l in formula---weld excursion amount; N---curve l ' ₁with l ' ₂by the hop count on average divided; ---curve l ' ₁the abscissa of i-th point; ---curve l ' ₁the ordinate of i-th point; ---curve l ' ₂the abscissa of i-th point; ---curve l ' ₂the ordinate of i-th point.

2. laser assembly solder plate drawing process weld movement method for quick predicting as claimed in claim 1, it is characterized in that, described step 4) in for the simple part of some shape matching, formation of parts grid is projected directly to X-Y plane, thus obtains the 3rd) initial displacement field u needed for step ₀, this type of part requirements does not overlap to the grid after X-Y plane projection.