Prediction of the Evolution of the Surface Roughness in Dependence of the Lubrication System for Cold Forming Processes

Figure 2 depicts the process of specimen preparation for the SCT as well as the rod extrusion process. Two different lubrication systems were investigated; both consisted of a ZnP conversion coating. For lubrication, a MoS₂ coating and a salt–wax coating were chosen. All specimens consisted of 16MnCrS5 (1.7139).

The test specimens were blasted to ensure a comparable surface roughness as well as surface morphology. The surfaces of both the rod extrusion process and the sliding compression specimens were blasted with blasting abrasive F20/S390 from Ferrosad to adjust the initial surface roughness to Sq_rod = 7.8 ± 0.7 µm and Sq_SCT = 6.8 ± 0.4 µm. After blasting, specimens were coated with a ZnP conversion layer. Then, all specimens were coated with a 80 wt% solution of MoS₂ or salt–wax. From here onwards, the lubrication system ZnP + MoS₂ and ZnP + salt–wax are referred to as MoS₂ and salt–wax (if subscripted, s–w), respectively. After coating, the surface roughness of the specimens was measured at Sq_MoS2 = 3.4 ± 0.6 µm and Sq _s–w  = 3.8 ± 1.1 µm. Specimens with a diameter of d _SCT = 15 mm and a height of h _SCT = 15 mm were used to carry out the SCTs. Specimens with a diameter of d _RE = 14.5 mm and a height of h _RE = 50 mm were used to carry out the rod extrusion process. To obtain the material characteristics for the numerical simulation, flow curves were determined with a Zwick + Roell Z100 testing machine according to specifications by the German Cold Forging Group [16]. The specimens were obtained from the same material charge and turned to a diameter of d = 10 mm and a height of h = 12 mm. According to these guidelines, the height/diameter ratio can vary from 1.2 to 2.0. However, all specimens with a ratio above 1.2 were asymmetrical after upsetting. Therefore, the mentioned geometry (d = 10 mm, h = 12 mm) was chosen. To reduce friction to a minimum, the faces of the specimens were ground to a roughness Sq < 0.1 µm and a 50-µm-thick Teflon foil was used as lubrication at both faces during upsetting. Flow curves were obtained at room temperature for strain rates of 0.1–0.2 s⁻¹, see Fig. 3. The experiments were repeated three times each. Initial plastic flow was identified at 507 N/mm². Due to the force limitation of 100 kN of the testing machine, flow curves could only be determined up to a true strain of φ = 0.45. For the FEA, the flow stress curve was extrapolated up to a true strain of 1 with the help of the power law in the form of

with A = 819 and B = 0.1. The power law was fitted to the flow curve within the interval of true strain of 0.3 < φ < 0.45 with a mean square error of the residuals mse < 0.01.

The confocal white light microscope µSurf from NanoFocus was used to determine the surface topography. All measurements were performed with an objective lens from Olympus with 20× magnification. Measurements of specimens from the rod extrusion process were performed along the outline of the extruded specimen diameter, see Fig. 4a. Each measurement comprised a measuring field of 800 × 800 µm². For the determination of the resulting roughness of the sliding compression test, multiple measurements of the specimen surface were performed, see Fig. 4b. In total, four measurements were taken per specimen, with each measurement comprising a measuring field of 1460 × 1460 µm².

For analyzing the surface data, the software MountainsMap Expert from Digitalsurf was used to derive the surface roughness Sq _m . To compensate skewness of the measured field, the measured data were adjusted with a linear (for the face surface of the cylinder specimen) or a polynomial (for the curved surface of the cylinder specimens) fitting function.

The determination of the surface evolution during cold forming processes was conducted with the SCT. This tribological test stand was developed at the Institute for Production Engineering and Forming Machines (PtU) [17]. A dual acting hydraulic press is utilized to apply the necessary contact normal stresses of up to 3000 N/mm² and surface enlargements of up to 11 by compressing the specimen. For reproducing the acting relative velocities, which can amount to 500 mm/s during cold forging operations, the compression plate is slid in relative motion against the specimen while the compression force is maintained, see Fig. 5.

All experiments in this study were conducted with a number of three specimens per series. The specification for the SCT is given in Table 1.

The first stage of an industrial rod extrusion process for the production of bolts was used to verify the predictions of the FEA. The process specifications are given in Table 2. The specimen was prepared as depicted and described in Fig. 2. The forming process was carried out with a 250-t direct-driven servo motor press SWP 2500 from SynchroPress. Both experimental forming series were reproduced three times. After each series, the tool was cleaned.

For conducting the FEA, Simufact version 11 was utilized. The rod extrusion process was modeled axisymmetric with a four-node element type and four integration points. The mesh was discretized with an initial edge length of 0.1 mm. The tools were modeled as rigid bodies. The SCT was modeled with a four-node element type and initial edge length 0.4 mm with Coulomb’s law of friction with a constant friction coefficient of µ = 0.00, µ = 0.04 and µ = 0.08. These simulations were used to determine the loading cases for the parameterization of the friction model. The FEA of the SCT was compared to experimental results in order to ensure its viability, see Fig. 6.

For both simulations, an adaptive global remeshing criterion, dependent on element strain and work piece penetration, was used.

To describe the evolution of the surface, the three-dimensional root mean square Sq of the profile was used [18], see Eq. (2),with A constituting the measured field, x and y being the coordinates of the digitized surface and z representing the height of the measured surface.

According to [15], the evolution of the surface roughness can be described by its incremental changewith dSq being the incremental change of the surface roughness between two states and Sq _i − 1 being the surface roughness of the preceding increment. The incremental roughness change is in turn determined with Eq. (4):with dψ = dA ₁ /A ₀ describing the incremental change of the surface enlargement and d(σ _n /k _f ) describing the incremental change in the normalized contact normal pressure, p ₁ and p ₂ being dimensionless parameters that allow for an alignment of the surface evolution model to the forming environment, e.g., the employed tribological system, the material combination and surface morphology. Sq_tool denominates the roughness of the employed tools.

For application of the surface evolution model, parameters p ₁ and p ₂ are determined with the help of the sliding compression test. Test runs with different process loads are performed, and the change in roughness is determined with the help of confocal white light microscopy. Parameters p ₁ and p ₂ are then identified by a least squares fit, as depicted in Eq. (5) [15].

For implementation of the surface evolution model within FEA, subroutines were used. The implementation of the surface evolution model is described in the flowchart in Fig. 7.

In contrast to Stahlmann et al.’s implementation [15], the surface data were not stored in an additional background mesh, e.g., matrix. Within Simufact, it is possible to store user-defined data (up to 20 data sets) alongside other nodal data (such as coordinates or contact stress). These datasets were used to store the surface roughness Sq. This approach of using the available user variables has the advantage that the surface data are not mapped to the additional background mesh at every increment step since they are stored alongside the nodal data. This results in less of an information loss, since the surface data is only remeshed and mapped during global remeshings, while the data stored on a background mesh are mapped at every increment step. For further details, see [15].

However, a distortion of the surface data is observed during remeshing. This is due to the fact that during remeshing, the weighted average of nodal data from adjacent nodes is computed. This can lead to miscalculations in regard to the data stored in the user variables when nodes from the inner volume of the work piece are taken into account, since these contain no data relating to the surface. Therefore, if a remeshing has been detected in between increments, user variables are interpolated by means of a subroutine after the start of a new increment. For every node of the newly created mesh, two nodes with the lowest distance are identified with the help of a linear search algorithm. Then, surface values are computed based on an inverse distance weighted algorithm, see Eq. (6) and for explanation see Fig. 8.

\({\text{Sq}}_{{n_{l} }}^{h + 1}\) here stands for the interpolated value of the newly created node l at increment h + 1, d _i being the distance in between the nodes and w _i being the inverse distance weight. Since a linear interpolation was chosen, value p equals 1.

For example (see Eq. 7), if a remeshing is detected after increment h = 50, a matrix based on the latched (surface) data is created, which contains the distances of each new and old node. With the linear search algorithm, the two nearest nodes n₁ and n₂ regarding the newly created node n_l are detected. Then, it is possible to calculate, for example, the surface roughness \({\text{Sq}}_{{n_{l} }}^{50 + 1}\) as follows (with d ₁ = 0.10 mm, d ₂ = 0.15 mm, \({\text{Sq}}_{{n_{1} }}^{50} = 4.2\) and \({\text{Sq}}_{{n_{2} }}^{50} = 3.7\)):

In order to determine the model coefficients p ₁ and p ₂ , sliding compression tests were performed at different loading levels, see Table 3. The loading levels, characterized by the normalized contact normal stress and surface enlargement, were determined with the help of FEA.

Figure 9a shows the friction coefficient µ in dependence of the load case and the lubrication system, while Fig. 9b presents the dependence of the mean square roughness Sq.

The measured friction coefficients show a qualitatively equal dependence in regard to both lubrication systems with a steady decline of the friction force. However, the friction coefficient for specimens lubricated with MoS₂ is about 50 % higher than for specimens lubricated with salt–wax.

In contrast, the leveling of the surface is highly dependent on the used lubrication system. While specimens lubricated with MoS₂ show a gradual decline of surface roughness, specimens lubricated with salt–wax exhibit an increase in surface roughness for lower load cases. After this initial increase, the surface roughness for specimens lubricated with salt–wax also gradually declines for higher load cases (σ _n /k _f  > 1.11). In addition, the variance of the surface roughness across the contact area is greater for this lubrication system.

Figure 10 depicts the surface evolution of the sliding compression specimens for the studied lubrication systems which were used to determine the surface roughness. While for loading cases around 1, some marks from the blasting process are still visible when using MoS₂ as a lubricant, this cannot be observed in the case of salt–wax. With increasing loads, the surface morphology of specimens with salt–wax leads to the assumption that for low contact pressures the load is largely carried by the lubricant. For higher loads, an overall flattening of the surface asperities is observed, but still some rather large lubricant pockets remain. It can be assumed that under the given contact pressures, the salt–wax lubrication system exhibits fluid-like properties, while with a MoS₂ lubrication, the surface asperities are in direct contact, thus resulting in a more smooth surface.

The parameters p ₁ and p ₂ for each lubrication system, determined with the help of a least squares fit of Eq. (4), as well as the lubrication system investigated by Stahlmann et al., are shown in Table 4.

By comparison, the influence of the surface enlargement is significantly lower for both investigated lubrication systems than for the originally studied lubrication system. In addition, it is remarked that the surface enlargement has a negative sign. This would lead to the conclusion that surface enlargement leads to a roughening of the surface. More likely, since the absolute value of p ₁ is very small, another interpretation would be that the surface enlargement does not play a significant role toward calculating the surface roughness. This assumption is also supported by the fact that the absolute value of p ₁ is at least one magnitude lower than the value p ₂ .

The averaged force–displacement curves as well as the standard deviations of the rod extrusion process for both lubrication systems are shown in Fig. 11.

The maximum occurring load differs by about 9 %. In addition, it is also noticeable that the general trend of the force displacement curves differs. The force–displacement curve of the MoS₂ lubrication system follows a linear downward trend after reaching the maximum force level. In contrast, the salt–wax-lubricated specimens exhibit a sharper fall of force after reaching the maximum level after which a linear trend is apparent. This is mainly due to the varying sticking friction coefficient of the lubrication systems. Also, the difference of deviations in between the series becomes obvious. The source of the high deviations for specimens lubricated with MoS₂ lies in the difference in between the three test runs. These deviations could be a result of remaining lubricant within the die. Although the die was cleaned with acetone in between test runs, it proved difficult to clean all remaining lubricant.

The force–displacement curves were used to calibrate the FE-model of the rod extrusion process. The best fit for the MoS₂ lubrication system was found for a friction coefficient µ _MoS2 = 0.0475 and for the salt–wax lubrication system µ _s–w  = 0.0375, see Fig. 12.

Overall, the findings of the rod extrusion process are in agreement with the SCT when looking at the forming forces. The maximum registered forming forces for the rod extrusion process performed with MoS₂ lie above the maximum forming forces of the salt–wax lubrication system. This coincides with the experimentally determined friction coefficients in the SCT, where the friction is lower for the salt–wax lubrication system compared to the MoS₂ lubrication system for equal loads.

Figure 13b, c depicts the resulting work pieces of the rod extrusion process as well as the path along the outline of the specimen. The surfaces of specimens extruded with a lubrication system consisting of salt–wax appear dull, while the surfaces of specimens with MoS₂ have a shiny appearance. Measurements conducted with confocal white light microscopy, depicted in Fig. 13d, confirm that the surface of MoS₂-lubricated specimens has a lower roughness, i.e., more smooth.

The experimentally determined surface roughness and the numerically calculated surface roughness are compared in Fig. 14. The surface roughness is significantly reduced for specimens lubricated with both lubrication systems after the forming zone. While specimens with MoS₂ have an average roughness of Sq = 0.58 ± 0.17 µm after the forming zone, the roughness of specimens lubricated with salt–wax is higher with an average roughness Sq = 1.05 ± 0.28 µm.

While the numerical prediction for both lubrication systems is accurate for work piece surfaces which have been formed (zone 3: Z3, see Fig. 15), the numerically predicted work piece roughness for the surface above the forming zone (zone 1: Z1) differs to a great extend in relation to the measured roughness. Within Z1, the roughness is actually higher than the initially determined roughness of the lubricated specimen. It can be assumed that due to the low contact normal stress in zone 1, see Fig. 15, the surface asperities are not leveled. Excess lubricant, which adheres to the container, is transferred to the work piece during the forming process in Z1, resulting in a higher roughness. This theory is supported by Fig. 13a, where it can be seen that the initially lubricated surfaces exhibit only few elevations of more than 10 µm (color yellow), whereas the formed specimens in Z1, see Fig. 13d (1, 3), exhibit numerous elevations of 10 µm and higher which can be ascribed to the lubricant. Due to a possible more homogenous consistence of MoS₂, the increase in roughness is more evenly distributed compared to salt–wax. Crossing over into zone 2 (Z2), the contact normal stress σ _n increases significantly while the surface expansion ψ increases only slightly. Both causes result in the leveling of the surface asperities. The peak of roughness, seen in Fig. 14 for MoS₂, can be attributed to the incline of surface enlargement in combination with a loss of contact crossing over from Z1 into Z2, as observed in Fig. 15, which leads to a high localized roughness due to unbounded forming. The lower maximum roughness for lubrication with salt–wax in comparison with MoS₂ is most likely a result of the transferal of lubricant into the forming shoulder, thus averting an unbounded forming.

In conclusion, Fig. 14 depicts that the proposed model shows a good accordance with the experimentally obtained measurements. Both predictions lie within the error bars gathered by measurement.