prediction of steel plate deformation in laser heating ... · estimation should be given for the...

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:01 111

174901-6262-IJMME-IJENS © February 2017 IJENS I J E N S

Prediction of Steel Plate Deformation in Laser

Heating Process via Simulation and Experiment Cheng

Zhang

1, a, Ming Lv

1, b, Guoxing

Liang

1, c, Yang Han

1, d * and Tao Liu

1, e

1Mechanical Engineering College, Taiyuan University of Technology, Shanxi Province, China

[email protected],

[email protected],

[email protected],

[email protected],

[email protected]

Abstract-- As a kind of clean production method, the

application of laser processing is more and more common in the

process of heat coating and heat treating. However, the laser

heating processing may result in reduced precision of workpiece

due to the residual thermal deformation. In order to ensure the

precision of the workpiece after laser heating process, accurate

estimation should be given for the control of the thermal

deformation. In this study, a three-dimensional model of plate

deformation under the action of pulse laser was constructed, and

the deformation of Q345 steel plates of different thickness were

simulated in the SYSWELD software, and then the deformation

field distribution, mathematical model of plates’ warping angle

under different laser parameters were obtained. The thermal

deformation of the plate wrapping angle was estimated with the

mathematical model, which provided a reference for plate

deformation control during laser heating process.

Index Term-- Laser heating process; Finite element analysis;

Deformation estimation; Warping angle

INTRODUCTION

Laser technic has many properties, such as high directivity,

high brightness, high purity and power density. Because of

this, there has been an extensive application of it in the

industrial production. During the course of laser heating

processing, its beam focusing on workpiece surface can

generate instantaneous high-temperature to melt materials,

which is very suitable for cutting materials and welding

workpiece. It has the powerful and potential capability in the

field of equipment manufacturing, automobile industry,

aviation and navigation industry etc. [1]

. On the other hand, the

deformation existing in the machined workpieces somehow

decreases the precision after laser heating process because of

residual stress caused by thermal gradient effect. To control

the deformation and ensure the highest quality of the

final-products, estimating the deformation of the workpiece

became critically important before laser processing so that a

good decision can be made for the effective methods to be

employed. So, If the deformation mechanism can be explored

for laser heating in sheet-forming field, its service would have

a good application in the materials forming technology.

Many studies of thermal deformation in laser processing have

recently focused on welding joints and phase transformation in

the microstructure, and a few discussions about the plate

thermal deformation are presented in papers [2-3]

. In the field of

metal sheet forming process, some scientific researches

have been conducted to explore the rules of plate forming with

laser. For example, the one done by Li Shaohai and his

colleagues in Xijing University, the relationship between laser

welding stress and strain distribution has been established

depending on their experiments and simulations when they

changed the parameters of time and laser energy input [4]

.

Another research on metal plate bending with laser and other

influencing factors in the area have also been done by foreign

scholars [5]

. But there has not been yet a more accurate method

for estimating thermal deformation of the plate in the laser

forming process. This paper aimed on finding change

regulation of wrapping angle in different experimental and

simulant parameters.

In experiment, the plates are made from Q345 with different

thickness, and it is a kind of mild alloy steel which is used in

the field of bridge building industry, automobile industry and

shipbuilding industry.

Simulation and experiment

In the software of SYSWELD, some models of steel plate with

different thickness need to be established. First, model and

mesh the geometry of the plate in VISUAL-ENVIRONMENT

software, determine the welding path critically avoiding

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generating the deviation in the simulation, and employ the

welding line as the center axis in the facula area of the welding

path. Secondly, precisely construct the relationship between

the welding line and the element node on the reference line. At

last, the excellent unit connection between heating input

region and a peripheral region were expected to be established.

Additionally, in order to improve the calculation accuracy and

efficiency, some sparse meshes were applied to meshing the

model surrounding the welding line. The boundary conditions

in simulations are filled in the Table 1 below.

Table I

The Simulation Condition

Items Value

convection heat transfer coefficient ha W/(mm2·℃) 15×10

-6

environmental temperature Ta ℃ 20

thermal emissivity Coefficient ε 0.8

Stefan-Boltzmann constant σ W/(m2·K

4) 5.67×10

-8

The density of materials ρ kg/m3 7.85×10

3

specific heat capacity C J/(kg·℃) 0.46×103

thermal conductivity λ W/(m·K) 1.047×103

Experimental study for deformation of plate in laser

processing: The KJG-1YAG-400A laser welding machine

was employed in the experiment, in which the stimulated

crystal is Nd: YAG. The laser wavelength is about 1064nm.

The facula of the single pulse energy is up to 90J, with its

instability tolerance of 5 percent, and it has a pulse width field

ranging from 0.1 to 20ms. Its optical frequency ranges from

0.1 to 150Hz, and the beam divergence angle is no more than

15 radians, and the minimum facula diameter is 0.2 millimeter.

The plate size parameters from the experiment and simulating

process are shown in Table 2, and the schematic diagram in

the laser heating process is shown in Fig. 1.

Table II

the simulation condition

Serial number length b width a

mm

thickness c

mm

1 100 50 2

2 100 50 6

3 100 50 10

Fig. 1. The schematic diagram in laser heating process

The steel plate in a certain position was fixed on the clamping

apparatus during the experiment, and in order to improve the

absorptivity to the laser energy, the black pigment was coated

on the plate in the motion path along the scanning path of the

laser facula. The process of pulse laser heating the Q345 plate

is shown in Figure 2. There is no splash phenomenon on the

plate around the laser facula area, and no molten pool

generated in the region of the surface on the plate, which

indicates a relatively stable laser processing. Choosing some

test points at 12.5 millimeter intervals shown in Figure 1, 27

test points in total served as the benchmark. Then the

coordinate of each point has been measured with

DAISY8106HA three-coordinate measuring equipment before

laser processing. After all experiments were finished, the

displacements of each test point on the plate in XOZ plane



were measured in the z direction. The deformations marked

No.a, No.b and No.c in the Z coordinate were measured.

Fig. 2. The experimental photo in laser processing

RESULTS AND DISCUSSION

Simulant and experimental deformation results of steel

plate with different thickness: In the same thermal source

conditions, the integral deformation contour of the plate after

1800 seconds is shown in figure 3.

In the same thermal source conditions, some simulations have

been done on the plates of the same length and width size, but

of different thickness, 2 millimeter, 6 millimeter, and 10

millimeter. Finally, after the temperature was cooled to the

room temperature of about 1800s, the plate’s integral

deformation contours are shown in Figs. 4, 5 and 6. The

experimental deformation result is shown in Fig. 7.

Fig. 3. The plate’s integral deformation contour

Fig. 4. The integral deformation contour of plate with 2mm thickness



Fig.7. The experiment result of the plant with different thickness

In order to analyze the relationship between warping angle and

various thickness of the plate, date acquisition for deformation



results have been done at the 27 test points on the plate in the

Z coordinate, and the results of the simulation and the

experiment are shown in Figs. 8, 9 and 10. The data

processing method in accordance with Equ(1) is shown below:

1, 2 ...... 93

i i i

i

a z b z c zD z i

(1)

Figs. 8, 9 and 10 show the bending deformation in Z direction

along the Y axis exiting both in stimulant and experimental

results. And the deformations have an increase tendency

forward along the Y axis, which presents a linear warping. The

deformations were generated near the welding line. It can be

seen from the simulation and experiment that the deformation

displacements in the Z direction along the Y axis were divided

into two parts by laser scanning path. The warping in the Z

direction was generated after the center of Y axis coordinate,

and the warping before the center is very small. Comparing

the three figures in Fig. 8, 9, 10. all plates generated the

warping deformations in the Z direction, but the deformations

decreased as the plate thickness grows. Because the

temperature had a sudden change close to the region of laser

input when the laser facula scans along the welding path, an

instantaneous expansion and plastic deformation of the plate

were performed as the temperature increases. With the

deformation zone expanding, the warping deformation along

the Y axis becomes clearer. When the thickness of the plate

grows, the extending deformation in the Y direction is

increasing, the plate tends to elongate along the positive Y

direction, and the displacement in the center of plate had a

small opposite deformation in the Z direction.

It can also be seen in the Fig.8, for 2 millimeter thin plate, the

simulation results and the test results have a very high

consistency. The plate indicated a deformation in the Z

positive direction, and a larger warping direction appeared at

the free end. The deformation is small, basically, and it

seemed to be a straight horizontal line from 0 to 50

millimeters along the Y direction in the XOY plane. The plate

deformation increased and reached its maximum at the end of

the plate along the Y positive direction. There were a little

deviation between the simulating results and the experiment

results in the laser processing. Supposing the deviation is

Δh(mm), and the plate thickness is h(mm), the deviation could

be described as follow:

Δh=n

1∑(ztest-zsim)

2 (2)

The deviations of thin steel plate of different thickness can be

obtained by solving the Equ(10). When the thickness is 2

millimeter, the deviation Δ2 is corresponding to 0.0004. When

the thickness is 6 millimeter, the deviation Δ6 is corresponding

to 0.0027. And when the thickness is 10 millimeter, the

deviation Δ10 is corresponding to 0.0152. From the calculation

results of deviation, it can be found that the simulation results

and the test results have a high consistency for the plate with 2

millimeter thickness. The deformation of the plate could be

accurately obtained in the simulation results, even if the

experiments with laser processing had not been done. But,

there is a little deviation exists between the simulation results

and the measured results for the thicker steel plate. Despite

this, the deformation tendency appears a preferable

consistency between the simulations and the experiments in

the laser heating processing.



Fig. 8. The simulation and test results of plate with 2mm thickness





The simulation and prediction about the thermal

deformation of thin steel plate and research of the

regularity under deformation

The Prediction of the relationship between the plate

thermal deformation and the facula moving speed: As

shown in Figs. 11, 12 and 13, the maximum deformation of

each point in the Z direction is not identical in different laser

scanning speed, but the trend of deformation is consistent.

Simultaneously, the deformation displacement of the plate

became smaller as the laser scanning speed increases. This is

because of the beam retaining in the same region on the plate

corresponding to reduction in time with the increment of laser

scanning speed, which leads to the heat input decreased, and

the total deformation decreased due to the change in

temperature. Define the angle between the connections from

midpoint of Y axis to the largest deformation point in the Z

direction at the end of Y axis, with the Y axis as θ, which is

the deformation warping angle. And the warp angle θ can be

obtained in the different scanning speed. It can be found that

the cubed fitting function had the minimize sum of squared

residuals, and the complex correlation coefficient close to 1,

and the fitting quality standards were the best in the range of

3mm/s≤v≤7mm/s. The function relationship between the warp

angle θ and laser scanning speed of v is as follow:

3 20.00716

0.1061

0.3713 0.5835 3, 7

v

v v v

v (3)

In the Equ (11) , when the confidence level is 0.95, the

confidence interval in fitting coefficient of the 0.007161 is the

range of (-0.08225, 0.09657), the -0.1061 is the range of

(-1.45，1.238) , the 0.3713 is the range of (-6.095，6.838), and

the 0.5835 is the range of (-9.311，10.48). The sum of square

error is 0.000713, and the mean-square root error is 0.0267.

The Prediction of the relationship between the plate

thermal deformation and the facula diameter: As the

matter of fact, the laser energy was dispersed with the

increase of the laser facula diameter, and the plate maximum

deformation decreased correspondingly. The warp angle with

the different facula diameter can be obtained by calculating

the existed data. It can be found that the Gaussian function

had the minimum sum of squared residuals, and the complex

correlation coefficient tends to the value of 1, and the fitting

quality standards are the best in the range of 3mm≤d≤7mm.

The relationship function between the warp angle θ and laser

facula diameter d is as follow:

24.78

0.9449exp 3.787

3, 7

dd

d

(4)

In the Equ (12), when the confidence level is 0.95, the

confidence interval of fitting coefficient of the 0.9449 is the

range of (0.7316, 1.158), the 4.78 is the range of (2.512,

7.047), and the 3.787 is the range of (1.468, 6.106). The sum

of square error is 0.003218, the multiple correlation

coefficient is 0.9895, the multiple correlation coefficient after

adjust the degree of freedom is 0.979, and the

root-mean-square error is 0.0267.

The Prediction of the relationship between thermal

deformation and laser power: The maximum deformation of

plate increased with the increase of the power input after the

heat was transformed to power. The warp angle in the

different laser power input can be obtained by calculating the

existed data. It can be found that the sine function had the

minimum sum of squared residuals, and the complex

correlation coefficient tends to 1, and the fitting quality

standards are the best in the interval of 200W≤p≤300W. The

function relationship between the warp angle θ and laser

power p is as follow:

0.9514sin 0.01064 4.517

200, 300

p p

p (5)

In the Equ (13), when the confidence level is 0.95, the

confidence interval of fitting coefficient of the 0.9514 is the

range of (0.7886, 1.114), of the 0.01064 is the range of

(0.005142, 0.01613), and of the 4.517 is the range of (3.405,

5.63). The sum of square error is 0.001154, the multiple

correlation coefficient is 0.9952, the multiple correlation

coefficient after adjusting the degree of freedom is 0.9905,

and the root-mean-square error is 0.02402.



Fig. 11. The simulation results under the condition of different laser speed

Fig. 12. The simulation results under the condition of different laser facula diameter

Fig. 13. The simulation results under the condition of different laser power



CONCLUSIONS

Under laser heating processing, the free end of the plate would

generate deformation bending to the laser input side. For thin

plate with thickness of about 2 millimeter, the simulation

results and test results have a high consistency, so the

simulation results can be developed for estimating thermal

deformation of thin plate under the action of laser.

Given the laser scanning speed v, the laser power input p, the

thickness of the plate and the laser facula diameter d ,

deformation of warping angle θ could be easily carried out

according to the function mentioned above. Obeying the

deformation law getting from the simulations and experiments,

the thermal deformation of steel plate in the different

parameters could be predicted.

In the results of finite element simulations and experiments,

the deformation of Q345 thin plate with the thickness of 2

millimeter can be accurately described and precisely predicted

through finite element simulations. But the thermal

deformation prediction has a little accuracy for medium and

heavy plate.

For reducing error and increasing the accuracy of the

simulation and prediction, some steps in further study should

be explored for medium and heavy plate.

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