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Finite Element Simulation of a Technological Process of Welding

 Alexey I. Borovkov

 Alexander A. Michailov

Victor S. Modestov

Computational Mechanics Laboratory,

St.Petersburg State Polytechnical University, Russia

Abstract

Welding is often applied for jointing structural components with each other, and for increasing joint strength a

multilayer weld is to be performed. For example, this technology is used in the turbo-machine engineering for 

structural component fitting to a shaft. The structural component composed from two parts is fitted to a shaftwithout a gap, then both parts are coupled with each other, and the multilayer weld is made. In the process of 

welding, the high temperature differences result in large temperature strains, which affect the distribution of the

contact pressure between a structural component and a shaft after cooling of the weld, as a result of which therecould occur skewing, and a component would be attached to a shaft improperly. The results of the research of 

contact interaction between a structural component and a shaft during a manufacturing process of welding and a

consequent cooling are presented in the paper. On the basis of the developed mathematical models for a solution of adecoupled quasistatic termo-elasto-plastic problem with account of the contact interaction, the problem was solved

in two stages.

1.The first stage included a solution of the transient nonlinear 3D thermal problem, in which model of the welding process is the driving heat source of the appropriate power. The thermal properties of the materials are functions of 

the temperature. After laying the first joint weld, at the next stage of a solution the members modeling the second

 joint weld were taken into account. The obtained earlier solution is transferred to a new model and the all processrepeats. As a result, the variation of temperature fields during welding is obtained, and the time of the joint weld

cooling up to an ambient temperature was found.

2.The second stage included the solution of a series of the quasistatic nonlinear problems of the plasticity theorywith account of thermal fields obtained at the previous stage. For simplification of a problem the transferring of 

metal in to a fluid phase during welding was not considered. For accounting plastic strains, the bilinear model of 

kinematical hardening was chosen. As a result, the plastic strain localization areas were found out, and it was stated

that the contact pressure field is characterized by asymmetrical distribution on the contact surface and stabilizes withtime.

Introduction

Welding is often applied for jointing structural components with each other, and for increasing joint strength a mul-

tilayer weld is to be performed. For example, this technology is used in the turbo-machine engineering for structural

component fitting to a shaft. The structural component composed from two parts is fitted to a shaft without a gap,

then both parts are coupled with each other, and the multilayer weld is made. In the process of welding, the high

temperature differences result in large temperature strains, which affect the distribution of the contact pressure be-tween a structural component and a shaft after cooling of the weld, as a result of which there could occur skewing,

and a component would be attached to a shaft improperly.

The purpose of the research is analyzing contact interaction between a structural component and a shaft to developrecommendations on prevention of a skew. Because the problem is nonlinear, i.e. the result depends on loading his-

tory, at carrying out of the analysis it was required to simulate all process of a welding.

Describing of the Model

The construction consists of a shaft in diameter D and a structural element representing the cylinder with internal

 bore, composed from two symmetrical parts (Figure 1). Technology of connection of a structural element with shaftfollowing: the structural component is fitted to a shaft without a gap and then both parts are coupled with each other.

Initial contact pressure is absent. After that the multilayer weld is made.

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Figure 1. Technology of connection of a structural element with shaft

The multilayer weld is lying by pieces with width 1 cm and groove is filled along axis of shaft. So, the joint weld

composed from 9 pieces based on geometrical size of groove (Figure 2).

Figure 2. A model of the multilayer weld

Geometrical characteristics of the model (Figure 3):

D= intd ; intd =700 mm; extd = 900 mm; L= 2600 mm; h= 300 mm; rabh = 70 mm; b= 20 mm.

Owing to the symmetry of the problem, a quarter of the model is being considered.

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 Figure 3. Geometrical characteristics of construction

FE Model and Analysis Procedure

Some parameters of FEM for full model with all joints weld:

- Applied finite element: solid 20-node element SOLID90- for solution of the transient thermal problem;

contact 8-node element CONTA174 - for solution of the transient thermal problem andelastoplasticity problem,

solid 20-node element SOLID95 - for solution of the elastoplasticity problem.

- Number of elements: 49921 and 520 contact elements

- Number of nodes: 213643

- Number of degrees of freedom: 213643- for solution of the transient thermal problem; 640929 - for solu-

tion of the elastoplasticity problem.

- Thermal contact conduction between two contacting surfaces is used with contact conductance coefficient

(TCC-coefficient) exceeding properties of the materials on two orders.

- Main contact properties are used default for solution of the elastoplasticity problem.

The problem of thermoelastoplasticity is solved in the semi-coupled statement, i.e. at first, the transient thermal

 problem is solved, and then, after obtaining transient temperature distribution fields, the stress tensor componentdistribution and the plastic strain field are determined (successive analysis).

Transient Thermal Analysis

The goal of this analysis stage was obtained variation of temperature fields during welding and definition of the time

of the joint weld cooling up to ambient temperature.

Material of construction is carbon steel. Thermal properties of the material are functions of the temperature. Thermal

 properties are presented in the table below.

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Table 1

T, Co

 k,

Cm

Wo⋅

  c,Ckg

Jo⋅

   ρ  ,3

m

kg 

20 54 473 7800

700 33 - -

The welding process was simulated by the driving heat source appropriate to heat flow the power 3000 W. Thermal

flow heats up a surface the area 12

cm within 1 minute. After that heat source is moving and heats up the next

surface the area 12

cm within 1 min (simultaneously on previous surface a convection is occurred). This loop was

repeated again until the joint weld has been laid. Then joint weld was cooled up within 5 min and the process was

repeated again for new joint weld. Algorithm of welding process is shown in Figure 4 through 5. The axis of ab-

scesses axis is presented the total time, where wt  = 6 min - time of laying a joint weld, N=9 - number of joint welds.

Figure 4. Algorithm of welding process

Figure 5. Algorithm of welding process (the driving heat source)

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On other surface G convection boundary conditions were applied:

)TT(αn

Tk 

G

G

∞−=∂

∂− ,

where α  = 6.82

m

W- film coefficient,  ∞T   = 20 C

o- bulk temperature.

At initial time temperature was constant all over the model and was equaled 20 Co

.

The obtained earlier solution for model with i numbers of joint welds is being an initial distribution of temperature

for model with i+1 numbers of joint welds. For that Submodeling procedure was used. Theth

)1i( + joint weld had

initial temperature same as ambient temperature.

The time of simulation was chosen so that the joint weld was cooled up close to ambient temperature. If a joint weldtemperature was larger than ambient temperature then simulation time was increased and calculations were contin-

ued for new simulation time. In that way simulation time 150 min was chosen. It corresponds with time of the joint

weld cooling up within 50 min.

Results

The temperature fields for different number of joint welds at various moments of time are shown in Figure 6 through

9. The diagram temperature vs. time for different number of joint welds in control points is presented below. Based

on these plots we can conclude that at time t=150 min the average temperature on shaft surface didn't exceed 50

Co

. So, this moment of time we can assume as simulation time.

Figure 6. Temperature fields at laying the 1st joint weld

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Figure 7. Temperature fields at laying the 2nd joint weld

Figure 8. Temperature fields at laying the Nth joint weld

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Figure 9. Temperature fields at the joint weld cooling up process

Nonlinear thermoelastoplasticity analysis

The goal of this analysis stage was obtained variation of stress-strain state during welding and definition of a contact

force between shaft and structural element and also was revealed of a skew in attaching a structural element to ashaft as a result of welding process. For simplification of a problem the transferring of metal in to a fluid phase dur-

ing welding was not considered. For accounting plastic strains, the bilinear model of kinematical hardening was cho-

sen see Figure 10.

Figure 10. Stress-strain curve

Physical properties of the material are presented in the table below.

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Table 2

T, Co

 E,

2m

 N   µ    α  ,C

1o

 

20 11101.2 ⋅   0.3 5

10−

 

700 - - -

The contact interaction with friction by Coulomb's law was considered. Friction coefficient equaled 0.1.

At it was mentioned above, the obtained earlier solution for model with i numbers of joint welds is being an initialdistribution of displacements for model with i+1 numbers of joint welds. For that Submodeling procedure was used.

As a result of interpolation errors in stress tensor components evaluation can originate. The reason for this is that at

the time moment when the next joint weld is brought into the model, nodes lying on the joint weld interface have

non-zero displacement. Consequently, elements attached to theth

)1i( + joint weld have non-zero deformation.

Let's consider it by the example of a plane problem of the elasticity theory (Figure 11 - Displacement vector in joint 

weld interface elements). Let the elements e1 and e2 belong to theth

i joint weld (blue color) and elements e3, e4 

 belong to theth

)1i( + joint weld (red color). Let at the previous solution step the elements e1 and e2 have received

non-zero deformation to which there corresponds a displacement vector ( yx u,u ) in nodes 1 through 6. At the sub-

sequent solution step the elements belong to theth)1i( + joint weld is brought into the model. After Submodeling, 

the displacement in nodes will be distribution in the following way, see Figure 11. So, element e3 has a prestressed

state and stress level is able to exceed yield stress. It doesn't correspond to physics of a problem. Further we shall

show, that the given error can be neglected.

Figure 11. Displacement vector in joint weld interface elements

Results

From distribution of plastic strain intensity on a shaft surface and on a groove surface of structural element (see Fig-

ure 12) we can conclude that plastic strain intensity achieves the maximum value at joint weld interface. This plastic

strain intensity is localized and quickly decreased in time (Figure 12). On a shaft surface plastic strain intensity

achieves the greatest value in point 2 (Figure 13) and increases till the moment time 99 min. It is time of the th N  

 joint weld lying. Results show, that the error caused by the given algorithm is neglected, and does not influence an

arrangement of a structural element and distribution of contact pressure. Let's consider the contact pressure distribu-tion in contact zone (Figure 14). Let's note, that during technological process of welding the area of contact pressure

is small and increases at the moments of time corresponding to cooling up of joint welds (Figure 15 ). Let's estimate

force that will hold a structural element on to a shaft after performing of welding. For this we consider an average

contact pressure >< contP , acting after performing of welding (t=150 min):

∫=><contScont

cont dS pS

1P  

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By results of research >< contP =3.43 MPa, that compare favorably to experimental data. Uniform distribution of 

contact pressure zones on a surface of a structural element allows to conclude on absence of a skew in an arrange-

ment of a structural element on the shaft.

Figure 12. Distribution of plastic strain intensity (left - on the shaft, right - on the structural ele-ment). Location of the control points

Figure 13. Plastic strain intensity vs. time

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Figure 14. Distribution of contact pressure on structural element. Location of the control points

Figure 15. Contact pressure vs. time

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Conclusion

The mathematical model of a technological process of multilayer welding has been presented in the paper. The time

of the joint weld cooling up to an ambient temperature has been found. The plastic strain intensity localization areashave been found out, and it has been stated that the contact pressure field stabilizes with time. It has been shown,

that the error of the received plastic strain intensity quickly decreases in time and doesn't influence an analysis re-

sult. Also the force, that will hold a structural element on to a shaft after performing of welding, has been defined.

Reference

1. Ansys theory reference. Eleventh edition. SAS IP, Inc.

2. Lurie A.I., Elasticity theory. M.: Nauka, 1970., 939 pp. (in Russian)

3. Talypov G. B. Welding stresses and strains. L.: Mashinostroenye, 1973, 269 p.p. (in Russian)