Study on Welding Parameter Model of Resistance Spot Welding of Body-in-white Al Alloy Plate

In this paper, the welding parameter model of resistance spot welding (RSW) of body-in-white(BIW) Al alloy plate was studied in details, and the key welding parameters that influence the RSW quality are analysed in-depth. Based on the concept of equivalent plate thickness (SV ), simplification of nugget volume and thermodynamic theories, combined with the properties of Al alloy, the mathematical models of welding current, pressure, time were established through production data and test verification. These models reflect the relationship between key welding parameters and equivalent plate thickness. The welding current and pressure are linear with SV , and the expressions are different when SV is greater than 2. For welding pressure, there exist two critical curves according to the different yield strength of welding materials. The yield of the material lies in between and pressure can be chosen between two critical curves. The welding time is directly linear to the actual thickness of the plate. Actual welding parameters can be obtained by the models and least test, which is very important for decision of welding parameters rapidly.


Introduction
During RSW process, resistance heat and deformation pressure is employed to make the metallic atoms on the two separated surfaces close to the lattice distance and to form common grains on the bonding surface.RSW is a welding method with stable welding quality, high production efficiency and easy-realizing automation.It plays an important role in the production of automobile body.
Welding current, welding pressure and welding time are three important welding parameters of RSW.Reasonable selection and combination of welding parameters is of great significance to improve welding quality and to save energy [1][2].
At present, there is no systematic selection standard for parameters of RSW of Al plate for automobile materials.Due to lack of general guiding principles, the Al alloy RSW is limited and restricted in application of automotive products.With respect to the selection of new product RSW process parameters, there is also a lack of essential knowledge basis, which is high required in the process, manufacturing and design of automobile products.Therefore, it is of great significance to study the general rules of welding parameter selection for RSW and to establish a scientific mathematical model in order to choose welding parameters rapidly and save time and cost [3][4].
This paper explores abundant welding parameters data of Al alloy RSW in Volkswagen production.Based on big data analysis, mathematical models associated with welding current, pressure and time are established.It provides theoretical guidance for the selection of welding parameters thickness, but also closely related to properties of welded plate.In this case, some special methods are employed in the study and modelling of RSW parameters, e.g. the principle of plate thickness equivalence, simplification for nugget shape, compound resistance and nugget heat conduction, etc.The purpose is to minimize the negative effect of some non-main control factors, and to provide a physical and mathematical basis for the establishment of effective model [5][6][7][8].
The model of welding parameters calculated in this paper is based on the production big data, and is combined with experimental welding test, with the combination of one or more different materials, plate thickness, coatings and adhesives.
In general, the models established in this paper are suitable for varying types of Al materials commonly used in automotive body, including plate, profile and die casting material.
Plate thickness, composition and material properties all have pronounced influence on the performance of RSW joints.Moreover, the influence of plate thickness is more prominent as compared with composition and material properties.In the case of welding process of automobile products, In general, the condition of two-and/or three-layer plate is involved.In special case, welding could be carried out under the condition of four-layer plate.
Plate thickness is an important factor exerting influence on the welding parameters, which plays a pivotal role in controlling the size of resistance and rigidity, welding current and pressure.
In the case of parameters of RSW of automobile body, relatively stable values are obtained in the small range of plate thickness.The absolute thickness of plates in calculating welding parameters cannot lead to the establishment of mathematical models.Therefore, the concept of equivalent plate thickness is proposed to provide a more scientific way for the establishment of welding parameter model.
For multilayer plate assembly, the equivalent plate thickness can be defined as follows: Where   is a constant,   is the thickness of a certain plate,   is equivalent thickness of plates.
In general, combination of two or three layers of plate is regared as regular cases for welding process of automobile body.In order to restrict inappropriate welding conditions such as more than four layers, individual process test is usually employed to evaluate the selection of welding parameters above four layers.
For three-layer plate welding, with respect to equivalent thickness, the influence of the thinnest layer can be ignored, so the above formula is simplified as follows: Further, rewrite the above formula as: Where,  1 and  2 are the weight factor, and their values should meet the following requirements: The definition of equivalent thickness is the basis of theoretical calculation of welding parameter model.The definition should consider not only the thickness of the plate, but also the physical and chemical properties of the Al alloy plate, resistance composition near the welding spot, influence of plate thickness on the resistance.So selection of coefficient  1 ,  2 should reflect the characteristics of resistance combination, and moreover consider the comprehensive effects on welding procedure calculation.
The composition of sheet resistance of RSW is shown in figure 1 The main heat source of forming nugget derives from the heat generated by contact resistance between two plates, plate resistance and contact resistance between the electrode cap and the plate.In welding process, different heat sources have respective rules: the contact resistance of plate increases with the increase of temperature, which is conducive to the increase of contact area, and on the other hand, the resistance decreases gradually to stable value.
In order to undermine the influence of plate thickness, with respect to  1 + 2 =1 and based on experiment,  1 and  2 are taken as 0.2 and 0.8, respectively.Therefore, formula (1) can be written as: Combined with the limited requirements of plate thickness, the above formula can be written as: Therefore, combination comparison between the absolute and equivalent plate thickness is shown in figure 2. As shown in figures 2a & b, adoption of equivalent concept undermines significantly the influence resulting from plate thickness.
In the case of the actual combination of plate thickness, the minimum plate thickness should be greater than 0.5 mm, the maximum plate thickness should be less than 4.0 mm, and the maximum plate thickness accumulation should be less than 7.0mm.The ratio of equivalent thickness to absolute thickness is approximately 1/2, and the thickness ratio between plates should address the following requirements:

Model of Welding Current
The RSW process is to the resistance heat and energy of plastic deformation to form metallic bond between individual plates.Welding current is a leading parameter in the formation of welding joint.The energy required for the formation of molten nugget is mainly from resistance heat.It should be noted that welding pressure also provides part of the energy, which, however, is mainly used to reduce the welding spot contact area, cracks and pores [9-10].
Only part of the heat generated by RSW is used to form welding joint.The other part is lost due to conduction or radiation to the neighboring material around nugget.The heat loss mainly includes heat transmitted through electrode cap and workpiece, and heat radiated to surrounding atmosphere.
Plate thickness with 0.5+0.5 mm is the minimum design accumulation.In actual welding process, welding current varies with plate thickness and has a linear characteristic, indicating that it is related to material properties of plate.Therefore, it is of great significance to explore the welding current of minimum plate thickness accumulation.
For easy calculation, the simplified welding joint and neighboring area model is shown in figure 3. The volume of nugget area is: The weight of nugget area is: ρ is the density of Al alloy plate, and its value is 2.75kg/m 3 in this experiment.
Under the effect of resistance heat, the base metal in nugget area has undergone a twophase transition process, namely solid-solid phase transition and solid-liquid phase transformation, respectively.It indicates that energy loss caused by heat conduction should be considered with respect to the two-phase transition.
According to Fourier's law, in the mode of one-dimensional heat conduction, there is the following relationship [11][12][13]: Where   ,, is the heat flux, namely the heat transfer rate in the x direction on a unit area perpendicular to the transmission direction, T is the temperature, and k is the heat conduction coefficient.
Under the assumption of isotropy, uniform and constant thermal conductivity, the heat lost by conduction can be expressed as follows: Where   is conduction heat, S is the interface area of heat conduction, ∆T is the temperature difference, L is the conduction length and  ′ is the conduction time.The HAZ width is assumed 3 mm.
Temperature is a physical parameter changing with time and space, and is associated with heat generation or consumption.Here, heat conduction is three-dimensionally motivated and non-stationary.In view of the complex physical environment around nugget, heat conduction and dissipation condition were treated isotopically in order to simplify the model, that is, the same heat conduction and dissipation is flowed to surrounding environment in all directions, while ignoring the effect of latent heat of crystallization.It is assumed that heat conduction is uniform and stable in the direction of heat dissipation.Heat conductivity of Al alloy in the test at room temperature is 228 W/(m• K).
S can be calculated by the following formula: Therefore, energy generated by resistance heat and welding pressure should be equal to the total value of melting heat and energy lost by heat conduction near nugget.The influence of welding pressure is not considered here.
The specific heat capacity of Al alloy plate is 880 (J/kg.℃).According to the standard, the minimum diameter of welding spot for 0.5+0.5mmplate is 5×√t , that is, 3.5mm.The resistivity is 2.85 × 10 -8 S/m, and the melting point is 660℃.
Combining (4), ( 5) and ( 6) and using relevant data mentioned above, the theoretical value of welding current of the minimum plate accumulation can be obtained as 29154 A, which is close to the actual welding value.
In actual welding process, heat dissipation condition of nugget is very complicated.The environmental parameters of Al alloy plate are employed in this calculation model, together with isotropic principle, which is different from the actual environment.For instance, the heat dissipation conditions of upper and lower ends of welding joint will vary due to different heat conductivity coefficient of copper electrodes, and change with its erosion degree in welding process.Therefore, establishment of this model has certain limitation, which is based on simplification of many conditions [14][15].
Based on the theoretical current of minimum thickness accumulation, the model of Equation ( 7) is established by exploring physical characteristics of welding spot and longterm study on spot welding process parameters of Volkswagen Group.Formula ( 7) is the mathematical model of current and equivalent thickness under the conditions of   ≤2.0 mm and   >2.0 mm.Effective contact diameter of electrode cap is 6 mm.
= 13.33 + 24 (  ≤ 2.0) The relation curve between current and equivalent thickness is shown in figure 4. It indicates that the current model is divided into two stages.The slope of second stage is lower than that of first one, indicating that the increase of current increases slightly with the increase of equivalent thickness.The increase of current can reduce effectively the deformation resistance of welding joint.

Model of Welding Pressure
Welding pressure has an important effect on spot welding quality.It can change the contact area of welded joint in welding process.With the increase of welding pressure, effective contact area will be reduced until the welding resistance of contact point is stable, which enables nugget formation.
The physical characteristics and thickness of Al plate have an important influence on welding pressure.Furthermore, the yield strength of Al plate has even a great influence on it, which is related with the rigidity of Al plate, that is, the reverse deformation ability of Al plate.
In order to deform the spot area, welding gun should provide the press that can at least cause plastic deformation.According to theoretical calculation, the press should be approximately comparable to the product of yield strength of Al plate and the boundary area where welding joint is located.Thus the following condition is met:  Thus: Where F is the deformation pressure,  0.2 is the yield strength of plate,   is the thickness of plate, and  ′ is the diameter of the nugget, including the heat affected zone (HAZ).
The effective contact radius between electrode cap and plate is 3 mm.The thinnest plate accumulation is 0.5 mm+0.5 mm, and the minimum yield strength of materials is 100 MPa.So the welding pressure value of above formula is calculated as follows: As a result, the minimum welding pressure should not be less than 1.884 KN.With respect to the requirements of some joint diameter, it can be adjusted accordingly, and the proper value of step size is ~0.25KN.The round value is 2.0 KN.
In order to analyze the influence of yield strength on welding pressure, the concept of average yield strength is adopted, and quantity degradation is carried out to make it one of the weight factors.
According to experimental result, sit indicates that there is a linear relationship between welding pressure and equivalent thickness within a certain yield strength range.Since it is affected by temperature with ease, there are certain fluctuations in the welding process.
According to definition of equivalent thickness, establishment of the welding pressure is divided into two sections.
Combining equations ( 2) and ( 8), the mathematical model between welding pressure, equivalent thickness and yield strength is established as follows.In this model, the yield strength of multilayer plates is averaged, and then further degraded so that its value is between 0 and 1.With respect to the effect of equivalent plate thickness and rigidity, together with the empirical data, different constants are eventually employed for balance compensation.
When   ≤2mm, the following relation can be expressed: When   >2mm, there is the following relation: Where,  1p0.2 is the yield strength of a plate, and    is the welding pressure.The yield strength of Al alloy plate of car body is between 110 ~ 500 MPa.When plate material and accumulation are determined, the yield strength is also determined.Under the condition of welding three-layer plate, the two values are 3×100 MPa and 3×500 MPa respectively.
Consequently, the relationship curves between welding pressure and equivalent thickness are shown in figures.5 and 6.
The shaded area is the window reflecting the relationship between welding pressure and equivalent thickness under two ultimate yield strengths.
In addition, selection of welding pressure also is influenced by the size of matching gap, refinement of nugget grain, crack, porosity and size of joint indentation.It can be adjusted within a certain range, depending on application scenario and product joint design requirements.

Model of Welding Time
Welding current and welding time are also two important parameters.The joint can be obtained not only with large current and short time, but also with small current for a long time.Welding time and welding current can complement each other within a certain range.Related selection depends on the properties of materials, thickness and power of welder.When varying properties and thickness are involved, there is an upper and lower range.It is necessary to consider the impact of spatter, HAZ performance changes and other factors, so it is a comprehensive selection.
The heat source of RSW is mainly from resistance heat, which has the following relationship: Where, Q is the resistance heat, I is the welding current,  1 is the plate contact resistance,  2 is the base metal resistance,  3 is the contact resistance between electrode cap and plate, and  w is the welding time.
Considering that  3 is significantly lower than  1 and  2 , the above equation can be approximately abbreviated as: There is: c is defined as a constant, which is a conclusion obtained without considering the effect of temperature on resistivity and under the condition that the resistivity heat required for the formation of molten nugget is approximately constant.So  2 is inversely related to  w .The selection of welding time, based on the optimization of welding current, try to obtain the small splash, small heat affected zone and nugget diameter and other factors.The physical and chemical properties and strength requirements of the joint should also be considered.
After the selection of welding current and welding pressure, welding time depends directly on the requirements of nugget diameter and forming coefficient, and is also directly related to the thickness of plate accumulation.
While ignoring other minor factors, the mathematical expressions of welding time and plate thickness can be expressed as follows: is the actual thickness of Al plates, and  0 is the adjustment constant.100 ms is an ordinary value for the two-layer accumulation of Al plates with the thickness of 1.0 mm.According to the simplification and linear relationship, in the case of the three-layer accumulation of Al plates,  0 =1.4 mm is employed in Equation ( 12).Therefore, the relation curve between welding time and thickness of three layers of plates is shown in figure 7. The thickness of plate accumulation should change in the range 1.0 mm and 7.0 mm.In the meanwhile, the minimum thickness of three-layer plate accumulation is 1.5 mm.

Conclusions
In this paper, the concept of equivalent thickness was proposed and its definition was described in detail.The RSW parameter models of Al alloy plate were studied.The design principle of the models for welding parameters was analyzed in depth, and mathematical model was established.The model of parameters of RSW for Al alloy plates has a significant role in parameter selection of body-in-white RSW.
(1) The definition of equivalent plate thickness is proposed, which provides a necessary fundamental for the establishment of welding parameter models, and can help to simplify the complicated affecting factors and make it possible to establishment of welding parameter model.
(2) For the RSW of Al plate, by exploring the characteristics of RSW, the physical and chemical properties, and long-term welding parameter study on RSW, the mathematical models of welding current, welding pressure and welding time are established, which provides necessary theoretical guidance for welding parameter selection.
(3) Welding current model shows that welding current has a linear relationship with the equivalent plate thickness   and increases with it.The inflection point occurs when   equals to 2. Welding voltage is not only related to   , but also closely related to material yield strength  10.2 .For welding pressure in between, welding pressure can be choose between the two curves based on the highest and lowest yield strengths.Welding time has a linear (4) Due to the high thermal conductivity of Al alloy, welding becomes more difficult with the increase of plate thickness.The mathematical model of Al alloy RSW in this paper is only applicable to the combination of plate thickness that is no higher than 7 mm.

Figure 1 .
Figure 1.Resistance composition of resistance spot welding

Figure 4 .
Figure 4. Relationship between welding current and equivalent thickness   (mm)

Figure 6 .Figure 5 .
Figure 6.Relationship between welding pressure and equivalent thickness S  (mm)

Figure 7 .
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