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This paper addresses the upset prediction problem of friction welded joints. Based on finite element simulations of inertia friction welding (IFW), a radial basis function (RBF) neural network was developed initially to predict the final upset for a number of welding parameters. The predicted joint upset by the RBF neural network was compared to validated finite element simulations, producing an error of less than 8.16% which is reasonable. Furthermore, the effects of initial rotational speed and axial pressure on the upset were investigated in relation to energy conversion with the RBF neural network. The developed RBF neural network was also applied to linear friction welding (LFW) and continuous drive friction welding (CDFW). The correlation coefficients of RBF prediction for LFW and CDFW were 0.963 and 0.998, respectively, which further suggest that an RBF neural network is an effective method for upset prediction of friction welded joints.

Friction welding (FW) is a solid-state joining process where heat is generated directly by mechanical friction between a rotating or oscillating workpiece and a stationary component under pressure. After some time, movement is terminated and softened thermal-plastic material is extruded to form the joint. Due to the advantage of no melting during the FW process, various defects (e.g., hot cracking, porosity, and segregation) inherent in conventional fusion welding processes can be avoided or minimized. FW is now being used with metals and thermoplastics in a wide variety of aviation and automotive applications, and various aspects of research have been done on a large scale, which were reviewed in detail by Maalekian [

Although both experimental and FE methods are powerful approaches for the investigation of FW, the ability to perform experiments is seriously limited due to high cost and time required. In addition to these restrictions, it is impossible to experiment with continuously varying processing parameters. Therefore, using the available experimental and simulated results, further predictions can be made of practical significance for engineering applications.

The Artificial neural network (ANN) is an excellent tool for solving complex engineering problems due to its powerful nonlinear and adaptive nature and self-learning capacity [

The BP algorithm has been used extensively, while the radial basis function (RBF) algorithm has been rarely used in welding and not all for FW. Therefore, it is necessary to select and compare the appropriate mathematical models which will be used to predict the effects of welding parameters on FW. Inertia friction welding (IFW), continuous drive friction welding (CDFW), and linear friction welding (LFW) are typical FW processes where two components stand against each other with relative motion under a pressure. It follows the subsequent local frictional heat generation and plastic deformation. When the softened thermal-plastic material yields to the welding pressure, a subsequent upset (i.e., axial shortening) of components happens. The original component surfaces will be broken up and extruded out to realize self-cleaning, and then the fresh metal organizes the new atomic contact to form a weld. Therefore, the upset is an important geometric feature for the precise friction welding. In this study, the RBF algorithm model of upset for each FW process has been developed using results of FE simulations of the process.

A two-dimensional (2D) axisymmetric model was built, as shown in Figure

The geometry of IFW specimens (a) and meshed 2D axisymmetric model (b).

The available energy for heating is equal to the flywheel kinetic energy

The thermal conduction problem within the joint was solved using the 2D axisymmetric Fourier’s heat conduction equation. In addition, heat dissipation through convection was also considered and a constant heat transfer coefficient of 30 W·m^{−2}·K^{−1} was adopted to prescribe the boundary condition between joint surfaces and the environment [

The temperature dependent material properties of the GH4169 superalloy were used in the finite element simulations. GH4169 according to the Chinese classifications, the same as Inconel 718, is a nickel-based superalloy with the following chemical composition by weight, 0.04% C, 0.13% Si, 0.10% Mn, 52.61% Ni, 18.95% Cr, 3.03% Mo, 5.14% Nb, 0.46% Al, 0.98% Ti, and balance Fe. The thermal and mechanical properties of GH4169 were drawn from literature [

Properties of GH4169 superalloy used in simulations [

Temperature (°C) | 20–1300 |
---|---|

Young’s modulus (GPa) | 205–20 |

Thermal conductivity (W·m^{−1}·K^{−1}) |
13.4–32.55 |

Specific heat capacity (J·kg^{−1}·K^{−1}) |
430–720 |

The IFW processing parameters studied.

Parameter | Value |
---|---|

Moment of inertia (kg·m^{2}) |
1.178 |

Axial pressure (MPa) | 250, 300, 350, 375, 400, 450, 475, 500 |

Initial rotational speed (rad/s) | 122.8, 132.8, 142.8, 152.8, 162.8 |

Temperature and strain rate dependent flow stress adopted in simulations.

The simulation was conducted using the reported parameters of IFW of GH4169 superalloy tube by Yang et al. [^{2}, 400 MPa, and 152.8 rad/s, respectively.

The change of flywheel rotational speed is shown in Figure

Variations of maximum interface temperature, rotational speed, and upset with welding time.

Figure

Temperature contours and upset variation at different welding times.

When the welding time reaches about 4 s, the flash shape remains unchanged and the joint temperature begins to fall as shown in Figure

The RBF neural network is commonly used in functional approximation, spline interpolation, and mixed models [

Structure of RBF neural network model.

In fact, the upset prediction can be viewed as an interpolation problem, which can be stated as follows.

Given a set of

For a strict interpolation, the interpolating surface (function

The RBF technique consists of choosing a function

According to the interpolation conditions, a set of simultaneous linear equations for the unknown coefficients (weights) of the expansion

Normally, training and testing points (

30 sets of final upsets under different IFW processing parameters are shown in Table

The final upsets under different IFW processing parameters.

No. | Parameters | Upset (mm) | |
---|---|---|---|

Axial pressure (MPa) | Initial rotational speed (rad/s) | ||

1 | 350 | 122.8 | 0.13 |

2 | 375 | 122.8 | 0.73 |

3 | 400 | 122.8 | 1.36 |

4 | 350 | 132.8 | 1.40 |

5 | 375 | 132.8 | 2.15 |

6 | 400 | 132.8 | 2.85 |

7 | 250 | 142.8 | 0.01 |

8 | 300 | 142.8 | 1.18 |

9 | 350 | 142.8 | 2.99 |

10 | 375 | 142.8 | 3.78 |

11 | 400 | 142.8 | 4.53 |

12 | 450 | 142.8 | 5.76 |

13 | 475 | 142.8 | 6.31 |

14 | 500 | 142.8 | 6.86 |

15 | 250 | 152.8 | 0.51 |

16 | 300 | 152.8 | 2.80 |

17 | 350 | 152.8 | 4.73 |

18 | 375 | 152.8 | 5.51 |

19 | 400 | 152.8 | 6.20 |

20 | 450 | 152.8 | 7.47 |

21 | 475 | 152.8 | 8.06 |

22 | 500 | 152.8 | 8.56 |

23 | 250 | 162.8 | 2.12 |

24 | 300 | 162.8 | 4.70 |

25 | 350 | 162.8 | 6.46 |

26 | 375 | 162.8 | 7.24 |

27 | 400 | 162.8 | 7.99 |

28 | 450 | 162.8 | 9.18 |

29 | 475 | 162.8 | 9.86 |

30 | 500 | 162.8 | 11.50 |

Mean squared error of the network to predict upset of IFW.

Surface plot of prediction results by RBF network.

To explore the feasibility of using such a network and the precision of its predictions, another 9 sets of FE simulated data, not used in the initial neural network training, were produced. The comparison between FE simulated upsets and RBF predicted ones and the relative error is shown in Table

Comparison between FE simulated upsets and RBF predicted ones.

No. | Condition | Upset (mm) | Absolute error (mm) | Relative error (%) | |
---|---|---|---|---|---|

FE simulated | RBF predicted | ||||

1 | 300 MPa—147.8 rad/s | 1.96 | 2.12 | 0.16 | 8.16 |

2 | 300 MPa—157.8 rad/s | 3.72 | 3.64 | 0.08 | 2.15 |

3 | 300 MPa—167.8 rad/s | 5.53 | 5.23 | 0.30 | 5.42 |

4 | 400 MPa—147.8 rad/s | 5.38 | 5.35 | 0.03 | 0.56 |

5 | 400 MPa—157.8 rad/s | 7.09 | 7.06 | 0.03 | 0.42 |

6 | 400 MPa—167.8 rad/s | 8.75 | 8.83 | 0.08 | 0.91 |

7 | 500 MPa—147.8 rad/s | 7.72 | 7.64 | 0.08 | 1.04 |

8 | 500 MPa—157.8 rad/s | 9.43 | 9.54 | 0.11 | 1.17 |

9 | 500 MPa—167.8 rad/s | 11.63 | 11.5 | 0.13 | 1.12 |

From the surface plot of prediction results as shown in Figure

Effect of square of initial rotational speed on upset predicted by RBF network.

However, it should also be noted that there is almost no upset under 300 MPa and when the square of initial rotational speed is smaller than 17689 (rad/s)^{2} (i.e., speed of 133 rad/s), suggesting that insufficient deformation develops at the interface. In a similar fashion, when axial pressure increases, there is also a low threshold of acceptable initial rotational speed necessary to produce the upset for a given axial pressure.

The effect of axial pressure on the upset was investigated and the results predicted by the RBF network are shown in Figure

Effect of axial pressure on upset predicted by RBF network.

For example at the initial rotational speed of 142.8 rad/s, there is almost no upset under an axial pressure smaller than 265 MPa, while the upset reaches 5 mm under 420 MPa. According to the principle of IFW, the rotated flywheel is the sole mechanical energy source for welding, and the total energy for welding is up to its initial rotational speed. Thus the most appropriate expression for the upset change could be that the axial pressure affects significantly the efficiency of the conversion of mechanical energy to effective heat. Although the available flywheel kinetic energy is sufficient, it is difficult to heat rapidly (i.e., effective heat) at the interface and yield locally the workpiece under a relative low axial pressure. Therefore, in a similar fashion to critical initial rotational speed, there is a critical axial pressure for each initial rotational speed whose finding is necessary for process parameter selection.

In fact, insufficient deformation (small upset) during IFW is generally considered as the reason for lacking of bonding, weak self-cleaning, and severe oxidation. According to Ates et al. [

Moreover, according to the results above, the RBF network predicts the critical welding parameters. To further develop the capability of the RBF network, the parameter prediction window was established based on the upset as shown in Figure

Parameter window based on the predicted upset by RBF network.

In published works [

In literature [

Scatter diagram of RBF prediction versus actual upset of LFW.

In addition, the FE simulation of the CDFW process has also been developed using a 2D axisymmetric thermal-mechanically coupled model, of a mild steel bar with a length of 150 mm and diameter of 20 mm. Furthermore, experimental and calculated upsets show an error of only 2.5%. Based on simulations using parameters provided in literature [

Scatter diagram of RBF prediction versus actual upset of CDFW.

According to the analysis in this paper, the following conclusions can be drawn.

The finite element modeling of IFW: a superalloy can well reveal the friction and upsetting processes. Based on these simulations, an RBF neural network was applied initially to establish a welding parameter prediction window based on the upset.

The developed RBF network model shows that there is a critical axial pressure for acceptable upset for each initial rotational speed. Similarly, there is also a critical initial rotational speed, that is, critical flywheel kinetic energy, for each axial pressure.

Depending on the energy conversion, the analysis of effects of IFW parameters on the upset indicates that the initial rotational speed determines the heat source and that axial pressure will significantly affect the heat accumulation at the weld interface.

Applications of the RBF network on LFW and CDFW were also developed, with correlation coefficients for LFW and CDFW being 0.963 and 0.998, respectively, suggesting that RBF is an effective prediction method for friction welding.

The authors declare that they do not have a direct relation with any commercial identities that might lead to a conflict of interests for any of them.

The authors would like to thank for financial support the National Natural Science Foundation of China (51005180 and 61065009) and the 111 Project (B08040).