**3. Results**

The cladding distribution and thickness in the simulation can be compared to experimental results for every parameter combination. From now on, the parameter combinations will be given as a string based on the diameter of the base cylinder, the cladding width and number of layers (e.g., 27\_15\_1). The simulation pictures for X45CrSi9-3 were taken at 1.25 s of process time. The pictures of the experiment were taken after completion of the CWR process and subsequent splitting in half.

As shown in Figures 19–26, the results of the simulations are similar to the experimental findings. Especially for the parameter combinations with 27 mm base cylinder diameter and one cladding layer, the shape and the measurements are very similar (Figures 19–21; Figure 25). The deviations are within the margin of error. The parameter combination 27\_15\_1 (Figure 19) shows a deviation of 0.45% in cladding width and 3.47% in cladding height, resulting in only 0.04 mm difference in cladding height between simulation and experiment, which is almost indistinguishable.


**Figure 19.** Comparison experiment/simulation; 27 mm base cylinder, 15 mm cladding width, 1 layer.




**Figure 22.** Comparison experiment/simulation; 29 mm base cylinder, 15 mm cladding width, 1 layer.

**Figure 23.** Comparison: experiment/simulation; 29 mm base cylinder, 15 mm cladding width, 2 layers.

**Figure 24.** Comparison experiment/simulation; 29 mm base cylinder, 8 mm cladding width, 2 layers.

**Figure 25.** Comparison experiment/simulation; 27 mm base cylinder, 8 mm cladding width, 2 layers.


**Figure 26.** Comparison experiment/simulation; 27 mm base cylinder, 15 mm cladding width, 2 layers.

For the 100Cr6 work pieces (Figures 27–29, simulation picture taken at 2.0 s process time), the deviations between simulation and experiment decrease with increasing amount of cladding material. The overall shape of the cladding after rolling is comparable to the results of the simulation and, in the best case (Figure 29), below 3% deviation. Comparing the 15 and 20 mm cladding widths, it can be shown that the increase in cladding height is marginal. The additional cladding material just flows out of the bearing seat area without any use in future application. Which height will be sufficient for 100Cr6 hybrid shafts will be investigated in future research.

**Figure 27.** Comparison experiment/simulation 100Cr6, 27 mm base cylinder, 10 mm cladding width.


**Figure 28.** Comparison experiment/simulation 100Cr6, 27 mm base cylinder, 15 mm cladding width.


**Figure 29.** Comparison experiment/simulation 100Cr6, 27 mm base cylinder, 20 mm cladding width.

The parameter combinations with 29 mm base cylinder bear more cladding after welding, since the diameter is increased, while the same initial layer height is kept. Therefore, more cladding material is spread, resulting in too much cladding material flowing over the edges of the bearing seat, when two layers of cladding combined with 15 mm cladding width are used (Figure 26). When comparing simulation and experimental results for this parameter combination, the deviation in geometry is visually apparent. As for the experimental results, the cladding material gushed over the edge of the bearing seat, forming a curvilinear tail (Figure 26). In the corresponding simulation, the cladding material remains completely within the borders of the bearing seat. No significant amount of cladding material is distributed over to the next shaft segment.

Even though this amount of cladding material would not be considered for future investigations due to its wastefulness, the accuracy of the simulation models needed to be confirmed. Therefore, simulations with even more cladding material were calculated to see at which point the simulation diverges from the experimental findings. For this, additional hybrid work pieces were welded. This time, the diameter of the base cylinder was set to 29 mm and the cladding width to 20 mm. The simulation was again analyzed at 1.25 s of process time.

The cladding material distribution is similar between simulation and experiment (Figure 30) for 29\_20\_3S work pieces at 1.25 s process time. To investigate this, more simulations were calculated, varying only the cladding material width in 1 mm steps between 15 and 20 mm. The base cylinder diameter was set to 27 mm (Figure 31).

**Figure 30.** Comparison experiment/simulation; 29 mm base cylinder, 20 mm cladding width, 3 layers.

**Figure 31.** Di fferent amount of cladding material resulting in di fferently shaped bearing seat material distribution at 1.25 s process time.

To further investigate possible reasons for the simulation model not fitting experimental results for certain amounts of cladding material, the cladding distribution was analyzed for di fferent time steps of the simulation to ensure the simulation had been calculated to a su fficient process duration. Figure 32 shows the cladding material distribution for a 29\_15\_2S work piece over time as simulation output. It can be shown that the cladding material changes its shape over time during the CWR process. Whereas the cladding material of work pieces with small amounts of cladding material, e.g., 27\_8\_1S, remains within the bearing seat and is fully formed after 1.25 s of process time, the large cladding material amounts of the 29\_15\_2S work piece continue to change shape with further work piece rotations (Figure 32).

**Figure 32.** Analysis of cladding material distribution during cross-wedge rolling over time—cladding material X45CrSi9-3 (red) on C22.8 (blue).

The reason for this behavior becomes clear when inspecting the cross-section of the bearing seat segmen<sup>t</sup> of the shaft during forming at different process time steps within the simulation (Figure 33).

**Figure 33.** Over time analysis of the cladding material distribution within the cross-section of the work piece during cross-wedge rolling—cladding material X45CrSi9-3 (red) on C22.8 (blue).

At the beginning of the forming process, right after the closing of the tools, the work piece is deformed from a cylindrical shape to an ellipsoid shape (~0.25 s, Figure 33). This is intended to increase the degree of deformation to improve the material properties of the cladding material after the forming process. For small amounts of cladding material, mainly the cladding itself is deformed and the base cylinder remains a cylindrical shape. Due to the large amount (≥15 mm width) of cladding material, the whole bearing seat segmen<sup>t</sup> becomes deformed. For work pieces with 8 mm cladding width, 1.25 s process time was sufficient to return the work piece to a cylindrical shape in the area of the bearing seat after the initial upsetting. This results in more work piece rotations necessary to completely shape the bearing seat cladding. Therefore, when calculated to a further process time, the simulation model is sufficient again (Figure 32). Additionally, incorrect insertion of work pieces in the CWR module can result in unsymmetrical cladding distribution. If the influence of the work piece positioning is to be investigated, a non-symmetric simulation setup will be required. Then, even incorrectly inserted work pieces could be simulated with high accuracy, as Figure 34 qualitatively shows.

**Figure 34.** Unsymmetrical cladding distribution (experiment left, simulation right) due to positioning error.

When comparing the deviations between the di fferent cladding geometries, especially the height, several influences can be identified. As shown in Figure 19 to Figure 29, the overall shape of the cladding material distribution is comparable, although the cladding height deviates more than 30% in some cases (e.g., 100Cr6). To analyze the e ffects of the initial work piece geometry on the cladding height deviation, the standardized and main e ffects were determined (Figure 35). It can be seen that the diameter of the work piece's base cylinder has a significant e ffect on the deviation between simulation and experiment with regard to the cladding height (Figure 35a). The combination of seam height and seam width (total cladding volume) has less but still significant e ffect. The seam width alone has barely any e ffect, and the seam height by itself is not significant at all. Figure 35b shows that with increasing base cylinder diameter, the deviation also increases. The deviation also increases for the higher seam widths. This can be explained by more material spreading out from the bearing seat area of the work piece. The more that material is kneaded and spread out from the center part of the work piece, the larger the deviation between simulation and experiment becomes. This is analog to the previous findings, where a larger amount of cladding material resulted in larger geometry deviations (Figure 32).

**Figure 35.** Influence of the cladding material amount on the accuracy of the simulation (X45CrSi9-3); (**a**) Pareto chart of standardized e ffects, (**b**) Main e ffect plot for simulation and experiment deviation

Since only the width of the seam was varied for the 100Cr6 work pieces, the approach to deviation comparison is di fferent. Figure 27 to Figure 29 show that for 10 mm of cladding material width, the cladding height deviates more between simulation and experiment than it does in the case of larger cladding widths and therefore cladding volume.

Figure 36 shows the influence of the cladding material volume on the deviation between simulation and experiment. When the cladding material geometries of the 100Cr6 and the X45CrSi9-three work pieces are compared, it is obvious that the 100Cr6 has experienced less forming, and the cladding is not spread as wide as on the X45CrSi9-3. This can be explained by the higher flow curves of the 100Cr6 welding material compared to the database material stored in Forge NxT. Due to this, simulations

with flow curves of the actual welding material should be considered in the future to improve FEA prediction accuracy.

**Figure 36.** Influence of the cladding material amount on the accuracy of the simulation (100Cr6).

#### **4. Discussion and Conclusions**

When comparing experiments with simulation results of the cross-wedge rolling process of hybrid material work pieces, it is not sufficient to analyze only the first seconds of the forming process. Even though the axial material shifting by the wedges is technically over after the first rotation, there is still axial material flow due to excess volume remaining within the bearing seat area when using work pieces with too much cladding material. The takeaway from this would be that the time of the process simulated should be adapted to the cylindrical shape of the work piece. Only when the bearing seat is cylindrical within the simulation have the calculations progressed far enough to make a statement about the cladding distribution. When the whole process was computed, which takes almost 10 times longer than the first 1.25 s of the process, an accurate prediction of the cladding material distribution could be made. Since such a large amount cladding material would not be used for this application, such long calculation times are not something to consider. For smaller amounts of X45CrSi9-3 cladding material, the simulation model is sufficient and the method of cladding material thickness prediction is valid. For 100Cr6, more detailed simulations with more variations should be carried out. Considering that these were the first investigations with this not conventionally weldable material, the results are reasonably good.

It could be shown that the simulation results of cross-wedge rolling with coaxially arranged hybrid work pieces are in good agreemen<sup>t</sup> with the experimental results. In previous work, the basic suitability of the simulations for serially arranged work pieces [32] or work pieces with constant cladding thickness [37] but varied process parameters were investigated. Building on these findings, the research in this work concludes the investigations with regard to "if" and "how accurately" these multi-material simulations can predict the material flow during cross-wedge rolling. These numerical predictions of material flow can be used to weld work pieces with exact amounts of cladding materials to save material and ensure optimal layer thickness within the functional area of the part.

Too much cladding results in wasted material after machining. The goal would be to use as little cladding material as possible but enough to ensure optimal service life of the part. Which amount of cladding material will result in optimal service life of the part will be investigated in further research.

Further simulations will be carried out with flow curves taken from actual welded cladding material. Currently, specimens are being prepared in order to carry out material characterization for every material used within the research project. This will help to improve the simulation model's accuracy even more.

**Author Contributions:** Conceptualization, J.K. and A.B.; formal analysis, J.K., L.B., M.Y.F., and A.B.; investigation, J.K., L.B., and M.Y.F.; methodology, J.K., M.M., L.B., T.C., and M.Y.F.; project administration, M.S., T.H., and F.P.; software, J.K.; supervision, M.S., T.H., L.O., and G.P.; validation, J.K., M.M., L.B., and M.Y.F.; visualization, J.K., L.B., T.C., and M.Y.F.; writing—original draft, J.K., L.B., T.C., and M.Y.F.; writing—review and editing, M.M., M.S., T.H., F.P., M.L., J.H., S.K., L.O., and G.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—CRC 1153, subproject B1, A4, C3, T1—252662854.

**Conflicts of Interest:** The authors declare no conflict of interest.
