*2.3. Cross-Wedge Rolling*

Cross-wedge rolling is an efficient way to distribute masses on work pieces as a preform operation prior to forging or milling [31]. During the CWR process, material is axially shifted by wedge geometries on the tool surface (see Figure 9). Depending on the wedge geometry, reductions in diameters up to 90% can be achieved with high reproducibility [31]. CWR is one of the forming processes investigated within the tailored forming process chain, next to die forging and impact extrusion. The forming parameters of the CWR process have impact on the quality of the hybrid parts produced within the process chain, especially with regard to machining. Depending on the forming temperature and heating strategy, the forming velocities and tool spacing can have an influence on the quality of the rolled part [32,33]. Figure 9 shows the typical process of cross-wedge rolling, which is being investigated experimentally and via simulation.

**Figure 9.** Process overview of cross-wedge rolling of hybrid work pieces.

In this paper, the influence of the CWR process on the forming behavior of differently welded semi-finished workpieces is investigated with regard to its predictability via simulations and its potential influence on the service lifetime of hybrid parts. For this, differently shaped work pieces were welded, as shown in Section 2.1 and Figure 6. Out of the various types of workpieces, several were formed by CWR. At least three of the work pieces were cut in half after CWR, so that the material distribution of the cladding material could be examined. The CWR process was the same as that shown in Figure 9. The other halves of the formed work pieces then continued along the process chain until the final step of the research was reached: service life investigations.

#### 2.3.1. Cross-Wedge Rolling Simulation

Before any experimental investigations of cross-wedge rolling were conducted, the process was first simulated, to save resources and time. As mentioned before, finite element analysis (FEA) can accurately depict the CWR process [33,34]. The simulations were calculated within the commercial FEA software Forge NxT 3.0, developed by TRANSVALOR S.A. (CS 40237 Biot, 06904 Sophia Antipolis cedex, France). No custom subroutines were used. The simulations were set up within the graphical user interface of the software. No modifications to the software were made.

The tool geometries within the simulation are based on the Computer Aided Design (CAD) files of the tools that are used for the experimental trials. The advantage of the symmetry of parts in the area of the bearing seat was used to reduce calculation time (Figure 10).

**Figure 10.** CAD model of hybrid work piece and lower cross-wedge rolling tool as FEA input.

Only the first 1.5 s of the 11-s forming process were investigated, because that is when the bearing seat geometry is formed. After that, the rest of the part is formed. Figure 11 shows the final simulation step used to investigate the cladding distribution after forming the bearing seat region. Figure 12 shows the process at di fferent stages during simulation. The kinematics are analogous to the forming of the area in the experimental trials.

**Figure 11.** Simulation result of hybrid work piece cross-wedge rolling tool after 1.5 s process time.

**Figure 12.** Cross-wedge rolling process at di fferent time steps, where the base cylinder is in blue and the cladding in red.

To further improve calculation duration, di fferent mesh sizes of tetrahedral elements were used within each billet. The mesh sizes were analytically investigated within a mesh sensitivity analysis in previous work. Nonlinear shape with coupled thermal-mechanical functions were used. Especially for hybrid parts, choosing the optimal mesh sizes improves calculation times drastically while still giving significant results. In Forge NxT, contact is considered using a velocity field penalization method, which allows for a slight penetration of the part into the die. This is the only method/algorithm available by default [35].

*Metals* **2020**, *10*, 1336

The quality of a volume mesh generated in Forge NxT is measured using the surface and the volume shape factor. "The surface shape factor is the simplest criteria and should be investigated first. It indicates whether the element is close to (=1) or far away from (<< 1) the ideal equiangular triangle shape. It can also detect degenerate (<0), flat (=0), or quasi-flat ( →0) elements." [35]

The volume shape factor "determines whether the elements are close to (=1) or far away from (<< 1) the ideal equiangular tetrahedron shape. It can also detect degenerate (<0), zero volume (=0), or quasi-flat ( →0) elements." [35]

The remeshing algorithm is triggered if the quality is below 0.4. The quality is computed as a ratio between the surface and the square perimeter of an element [35]. The volume and surface shape factor were above 0.75 (0.4 is considered the recommended minimum [35]).

The distortion value was calculated as approximately 0.82. In order to measure element distortion while eliminating the scale factor between parent and actual element referential, a "normalized" value of the Jacobian, defined as the product of the original Jacobian and a correction term K, was computed. This is automatically done by Forge and can be displayed to the user [35].

The bearing seat area was meshed with a mesh size of 1 mm, and the rest of the work piece was discretized with a mesh size of 3 mm. For the initial material distribution, the multi-material-set feature of Forge NxT 3.0 was used. Early simulations within subproject B1 (before Forge NxT 3.0 was released) were realized by modeling the base cylinder and the cladding material as separate objects within the simulation, which were then linked by bilateral sticking. The heat transfer between cladding and base cylinder was not satisfactory [32]. As a result of close communication with Transvalor with regard to the needs of simulation for hybrid work pieces, the multi-material-set feature was improved in Forge NxT 3.0. Therefore, it is now possible to load one geometry as work piece and define the segments of the work piece that are supposed to be made of a di fferent material. This results in one mesh in which certain elements can be of a di fferent material from the others. This approach also improves the accuracy of remeshing, which is indispensable, due to the high degrees of deformation. The flow curves for the material C22.8 were created using a Gleeble 3800-GTC (Dynamic Systems Inc., Poestenkill, New York, USA) and a DIL 805A/D+T dilatometer (TA Instruments, New Castle, USA). The cladding material was taken from the Forge NxT Database and was fitted for the Hensel and Spittel approach. This model describes the forming behavior of the material in dependence of the temperature T, the effective strain, the flow behavior by parameter ε, and the strain rate dε/dt. Within Forge NxT, the Hensel and Spittel equation is simplified [35,36], resulting in a viscoplastic material model. The flow curves and parameters of several materials were input in Forge NxT. The initial work piece temperature was set to 1250 ◦C and the tool surface temperature to 250 ◦C. The tool velocity for rolling was set to 250 mm/s for each tool. The translational movement of the tools was generated by the hydraulic press preset. Before rolling, the work piece is slightly upset with vertical force. This is realized by the upper tool moving towards the lower tool for 1 s, reducing the spacing of the tools from 32 to 28 mm. The heat transfer between tools and work piece was set to the preset "steel hot medium", resulting in an alpha value of 10<sup>4</sup> <sup>W</sup>/m2K. The thermal e ffusivity of the tools was set to 11.76 kJ/m2·K·<sup>s</sup>0.5. The ambient air temperature was set to a constant temperature of 50 ◦C. The chosen preset "steel hot medium" and the heat-exchange algorithm within Forge NxT take conduction, convection and radiation between the tools, work piece, and ambient air into account. The friction between work piece and tools were set to the preset "very high Tresca", resulting in a value m = 0.8, which proved to be a good approximation of friction for hybrid CWR processes [32]. As default, thermal expansion calculation is not enabled for material flow simulations in Forge NxT. Additionally, as default, rigid dies are used to simulate a CWR process. To assure the accuracy of the simulation model used, simulations comparing these influences were conducted and the cladding thickness for each set of parameters was measured within Forge NxT (see Figure 13).

**Figure 13.** Measurement of the cladding thickness in the center of the bearing seat.

For this purpose, three different simulations setups (Table 4) were calculated up to the point where the cross-section of the bearing seat is nearly completely shaped. The results were compared. As Table 5 shows, the deviations between the results of the different FEA setups is small (deviation of < 2.5 % = 0.058 mm for the avg. cladding thickness), keeping in mind that the average mesh size in this cross-section area is approximately 1 mm. Therefore, the accuracy with the default settings is sufficient to predict the material flow behavior under justifiable expenditure of calculation time (Table 4). For setup #3, the calculation took more than 160 h, which is too long when simulating an array of variations.


**Table 4.** Comparison matrix for FEA calculation time of cross-wedge rolling of work piece.




Due to the little impact of the thermal expansion and tool elasticity, the simulations were set up with rigid dies and no thermal expansion calculation. The parameters used within the simulation are shown in Table 6.

**Table 6.** Simulation parameters used within the model of the hybrid cross-wedge rolling process.


Besides the work piece geometry, all simulation parameters remained the same for all investigations. Four types of cladding geometries were used for the material X45CrSi9-3 and combined with two di fferent base cylinder diameters (27 and 29 mm), which results in eight work piece variants. For 100Cr6, three cladding geometries were used and a 27 mm diameter due to limited availability of base cylinders in the chosen dimensions. After the hybrid semi-finished work pieces were welded, they were cooled down at ambient air conditions. The cooled-down work pieces were cut in half, and the di fferent cladding thicknesses were measured (Figure 6). The geometry of all 100Cr6 parts was created by milling similar welded work pieces (Figures 7 and 14) to three di fferent geometries: 10, 15, and 20 mm seam width and 2.5 mm seam height (Figure 14). This was done due to the less accurate layer application of PTA welding compared to the hot-wire deposition welding. This was the most reproducible way to immediately ge<sup>t</sup> similar cladding geometries.

**Figure 14.** Work piece 100Cr6/C22.8 milled to 27 mm diameter and 10 mm cladding material seam.

The average thickness of each cladding layer and its width were measured and input for the simplified geometry of the simulation. The various adapted geometries are shown in Figures 15 and 16.

**Figure 15.** CAD model of di fferent cladding (red) distributions on base cylinder (blue) forX45CrSi9-3, (**a**) 1 layer at 15 mm seam width (**b**) 1 layer at 8 mm seam width (**c**) 2 layers at 15 mm seam width (**d**) 2 layers at 8 mm seam width.

**Figure 16.** CAD model of different cladding (red) distributions on base cylinder (blue) for 100Cr6, (**a**) 10 mm seam width (**b**) 15 mm seam width (**c**) 20 mm seam width.

After the simulations were calculated, the material distribution was analyzed. The results of the simulation will be discussed in Section 3.

## 2.3.2. Cross-Wedge Rolling Experiment

For experimental investigations, the CWR module (a self-built test stand) of the Institut für Integrierte Produktion Hannover gGmbH (IPH) was used (see Figure 17). The module consists of a machine frame in which two sleds can glide by translatory motion. The sleds have mounting holes for the CWR tools. The translational (horizontal) movement of the sleds is created by hydraulic cylinders, providing each sled with up to 125 kN of force. The vertical force, which is necessary to ensure constant spacing between the tools, regardless of the forming forces, is generated by the hydraulic press into which the module is mounted. The 6,300 kN press (manufactured by NEFF) is set to 50 kN of closing force. The minimum spacing is ensured by spacing discs with standardized heights that function as a vertical end-stop.

**Figure 17.** Cross-wedge rolling test stand at the Institut für Integrierte Produktion Hannover.

Prior to CWR, the parts need to be heated. This can be done using either the furnace or the IPH induction heating unit (manufactured by EMA-TEC GmbH). The advantage of the furnace is the close to perfectly homogenous heating of the part, whereas induction heating creates slight gradients of temperature within the work piece. Nevertheless, the short amount of heating time (60 s) used compared to the furnace (at least 40 min) results in less scale on, and less surface decarburization in the surface of, the work piece. With extensive heating, too little carbon may remain to harden the surface of the bearing seat after rolling and milling. Therefore, the work pieces were heated by induction heating for this research. The work pieces were heated for 60 s, resulting in approx. 0.4 kWh of energy induction into the work piece, which led to a peak temperature of 1300 ◦C, before the 20 s for transport into the CWR module. After transport, the work piece retained a temperature around 1250 ◦C. The tools were heated by heating cartridges to a temperature of 200 ◦C. The bottom of each tool was isolated with a polymer plate made of AS600M to reduce temperature leakage. Figure 18a shows a variety of hybrid work pieces with different amounts of the cladding material shown in Figure 6.

**Figure 18.** (**a**) Work pieces with different amounts of cladding; (**b**) (cold) work piece in starting position.

The work pieces were placed with their center aligned to the center of the bearing seat forming wedges. A mechanical end-stop ensured correct positioning (Figure 18b). After positioning, the upper tool was lowered onto the end-stops with 50 kN of force, resulting in a defined rolling gap of 28 mm. As soon as the desired gap width was reached, the hydraulic cylinders of the tool sleds were moved to start the rolling process, which took about 9 s. After rolling, the work pieces were taken out of the CWR module and placed onto a steel tray to slowly cool in air with free convection to prevent hardening and distortion. When cooled down, the work pieces were cut in half to examine the material distribution and to check for defects, as shown in Figure 9.
