_{1}

The purpose of this research is to develop a
SolidWorks
^{?} model for transient temperature field of laser welding of PMMA/SS 304 materials for application in fabrication of the ultrasonic back-plate, with a view of optimizing the experimental conditions. The study is carried out on these materials because of the increasing application of both metals and non-metals. The work focuses specifically on these materials because they have been experimentally studied previously and as such, this study can be accepted as an assessment into feasibility of using
SolidWorks
^{?} model to study the temperature field of the laser welding processes of metals and non-metals. The results of the
SolidWorks
^{?} transient thermal model show that there is a concentration of high temperatures at the point of contact. It also shows that temperature decreases as we move in (between laser and the top face) to the thickness of the part. Additionally the maximum temperature occurs at the last point of the welding; this may be due to the accumulation of the temperature before arriving at the end. These findings are comparable to the previous simulated and experimental results on temperature field during laser welding of PMMA/SS 304 materials. However,
SolidWorks
^{?} is shown to present a challenge in modeling a moving source of laser power.

Laser welding is a complex and nonlinear process, which involves very high thermal conditions [

The thermal profile and shape of the welding bead for Nd:YAG laser welding operation of AISI 304 steel lap joint has been studied [

Usually, the laser beam is assumed to have a conical shape and travels at a constant velocity in the X-axis and according to Conical Gaussian distribution. Study [_{keyhole}) while 16% gets absorbed into the surfaces of the parts being welded (denoted as Q_{surf}). The distribution of heat flux (Q_{xy}) for the heat source according to Gaussian and as modeled by studies [

The radius of the heat source, R, is usually determined as shown in Equation (2).

where M is the constant, which depicts the characteristic of the laser beam, _{z})

exhibits a Gaussian distribution as depicted in the Equation (3) below.

These parameters are illustrated and defined in literature [

Using MARC finite element software Kim et al. [

where:

_{0} is the radial distance perpendicular to the x-axis of the distribution. The values of _{0} are functions of the shape of the heat source and therefore depends on the shape of the heat source. They can be determined from the heat source’s shape constants.

In a different study [

where:

Q is the thermal energy absorbed by the weld specimen, r is the radius of the beam of the laser and

From this discussion, most of the simulations from previous researchers on laser welding have used 3D conical shaped sources of heat models. It can also be noted that the Gaussian heat distribution for a moving heat source has been used widely to model the source of heat in finite element analysis of laser welding. The keyhole mode of welding, reported by [

Using SYSWELD software, study [

The effect of the laser power on the geometry of the bead of the laser weld has been also reported [

A similar study [

One-dimensional numerical model for investigation of the depth of penetration of laser during laser welding has been developed based on conduction of heat theory and energy balance equations [

In this equation, p represents the laser’s peak power, t is the pulse duration, r refers to the radius of the beam of the laser and T_{m} is the maximum temperature, which the welding specimens can achieve. R is the reflectivity of the material and T_{0} is the temperature at the extreme edge (opposite edge to that where the welding starts).

L_{m} represents the latent heat of fusion of the materials and

The effect of scanning speed on the geometry of the laser welding for AISI 304 steel has been reported [

The results by study [

According to this equation, the power density exhibits an indirect relationship with the square of the radius of the laser beam. As such, the power density decreases with increase in the radius of the laser beam. As such, for very high spot weld radius, the power density will be very low. Similar relationship has been attributed to low depth of penetration in other studies [

Mathematical models are effective in studying the interaction among several laser-welding parameters. Hussein et al. [

Keyhole laser welding is the most used mode and therefore the equations represented here apply to keyhole welding. The keyhole can be assumed a circular cylinder. In most models, the line source of heat has been used to simulate laser keyholes [

Joint type | P_{P} (KW) | PRR (Hz) | Pulse Shape | F_{b} (N) | b (mm) | v (mm/s) | |
---|---|---|---|---|---|---|---|

LTJ | 5 | 3 | 30 | RC | 935 | 8 | 4 |

CJ | 5 | 3 | 30 | RC | 495 | 8 | 4 |

The heat energy from the keyhole is transferred to the work piece through heat conduction. Therefore, the general 3D-dimensional heat conduction equation applies [

where:

T is the temperature of the specimen.

t is the time of heat exposure.

u, v, w refer to velocities in x, y, and z directions.

In this model, the following assumptions usually apply:

1) Properties of the material such as density, specific heat and conductivity are constant.

2) The set-up is in steady state.

3) The material moves with a unidirectional velocity, U.

4) The effect of the latent heat of fusion is insignificant.

Based on these assumptions, the heat conduction equation reduces to the following form

where:

k represents the thermal diffusivity of the work piece

The solution to the heat conduction equation gives the temperature distribution within the material due to the laser energy. These solutions depend on the approach employed. The most inclusive solution assumes a point source of power on the surface and inside the work piece and line source power.

The temperature distribution (solution to the heat equation) has been developed as follows [

The quantities P (power intensity supplied by the laser source) and Q (thermal energy) are functions of power absorption by the material and are well described in literature [

The temperature distribution within the keyhole has been used to determine the radius of the keyhole using the line source model. This is achieved by assuming that the mean temperature of the circular keyhole of with radius, a (perpendicular distance from the center of the laser source), is the temperature of the boiling (T_{B}) of the molten material. The following equations govern this relationship [

This has been simplified as

where:

From Equation (10), the relationship between a’ and

cally to determine a. It gives the relationship between power absorbed and the radius of the keyhole.

This is the most basic solution to the heat equation. However, there are formulations that are more complicated such as Davis-Noller solution to the heat equations, which give close approximation. Davis-Noller solution to the heat equation is written as [

where:

Modeling of the keyhole has proven difficult. However, the simplest equation used to model various keyhole parameters can be illustrated as follows [

This model can be used to approximate the depth of penetration and other keyhole parameters.

From the review, it can be deduced that FEA in laser welding uses heat conduction equation to solve for the temperature distribution due to laser heat power. However, different FE Software use different approaches and therefore have different accuracies. It is clearly seen that most of the finite element models published in literature have used the advanced software. As such, the present research uses SolidWorks® (a simple tool) to optimize laser-welding parameters for Nd:YAG Laser welding of PMMA/SS 304 materials.

SolidWorks® software undertakes the thermal modeling for laser welding by solving the heat (governing) equation shown in Equation (7) by using the finite element method. The heat equation is solved for each node. This means that system of simultaneous equations are generated based on the number of nodes used. Temperature, T, is the unknown in each equation. These equations form a matrix, which takes the following general format.

In this case, K is the thermal stiffness of the material and is a function of conductivity, length and area and P is the heat power supplied by the laser beam. The finite element method solves these systems of linear equations iteratively until a convergence is achieved [

As stated in the introduction section, the purpose of this work is to study the laser welding of PET and Aluminum sheets. To evaluate the applicability of the SolidWorks® in studying laser welding, a preliminary simulation was undertaken on PMMA and stainless steel sheets. This study is an attempt to simulate the thermal behavior of two thin hybrid materials plates of polymer (PMMA) and Stainless steel that are being joined by an Nd:YAG laser. The study is the application of the SolidWorks® Software and particularly the Transient Thermal Model. Hussein et al. [

The following physical assumptions were considered during the SolidWorks® modeling of PMMA and Stainless steel sheets:

1) The laser was considered as a moving source of power

2) SolidWorks® transient thermal analysis was used for the analysis

3) Although SolidWorks® does not offer a way to model the moving thermal power, the available SolidWorks® tools were used to simulate the case

4) The simulation did not consider the cooling of the material due to the laser heat power on a zone. The cooling was ignored for the present simulation since it requires advanced studies with flow or convection simulation

The reliability of the numerical results depends on the thermal and optical characteristics of the materials. The most critical properties for heat flow studies include conductivity, specific heat and density of the materials of the components being studied [

The model of the PMMA/SS 304 steel joint was created using the SolidWorks® drafting tools. The

The moving heat power was then applied as illustrated in

To model the moving power source, we used the following technique: we modeled the surfaces of the weld region as multiple rectangles that are similar and ordered such that the laser hits these positions at different times. Since the laser will irradiate these rectangles at different times, it means that the laser power is changing its position with time. The region was divided into 10 sub regions and considering that the laser passes throughout the entire surface for 1 second, each region will have the beam acting on it for 0.1 second. In other terms, the power activity between 0 and 0.1 sec will only act on the first region, 0.1 and 0.2 will only act on the second region and so on.

The parts were then meshed using the curved elements with sizes of 1.8653 mm. A total number of elements used were 18,636 with 35,014 nodes as shown in

Material | Volumetric properties | Density | Specific Heat | Conductivity |
---|---|---|---|---|

PMMA | Mass: 0.00714 kg | 1190 kg/m^{3} | 1250 J/(Kg∙K) | 0.21 W/(m∙K) |

Volume: 6 × 10^{−6} m^{3} | ||||

Weight: 0.069972 N | ||||

SS 304 | Mass: 0.0234 kg Volume: 3 × 10^{−}^{6} m^{3 } Weight: 0.22932 N | 7800 kg/m^{3} | 460 J/(Kg∙K) | 18 W/(m∙K) |

The initial conditions,

The heat power of 200 Watts was applied to the 10 points with a time step of 0.1 seconds. As the study is linear, we could eventually use a multiplier to approach a closer power. In this way, the laser beam power acted on the first point from 0 to 0.1 seconds and the last at 0.9 - 1 second. Therefore, for each time step (0.1 seconds) a solution was provided for each node.

These results show a concentration of high temperatures at the point of contact in line with the expectations and temperature decreasing as we move in (between laser and the top face) to the thickness of the part. It is also clear that the variation of the temperature/with time as the application of the power source is only partial on a certain region at a certain time. These observations are similar and comparable to those reported by Hussein et al. [

This work illustrates that SolidWorks® software can be used to model temperature field during laser welding of metallic and nonmetallic materials. However, it is challenging to model a moving source of power with this software. Furthermore, non-linearity behavior of materials cannot be modeled using this software. As such, SolidWorks® models can be used as a preliminary study into the temperature field during laser welding of different materials.

Mwema, F.M. (2017) Transient Thermal Modeling in Laser Welding of Metallic/Nonmetallic Joints Using SolidWorks® Software. International Journal of Nonferrous Metallurgy, 6, 1-16. https://doi.org/10.4236/ijnm.2017.61001