**2. High-Rate Laser Processing Technology**

The high-rate laser technology was developed at the Laserinstitut Hochschule Mittweida [16–18] with the goal to speed up the achievable processing speeds and throughputs in laser micro machining. In fact, high-rate machining combines powerful laser systems supplying hundreds to thousands Watts average laser powers and ultrafast beam deflection methods. Therewith, the ultrafast laser beam movement is essential for the efficient upscaling of the processing rates when using such unprecedented high laser powers. This is due to the fact that only a few micro joules optical energy at low fluence is needed for most-efficient material removal [19–21]. In consequence, the optimum method for upscaling the processing rate will be increasing the pulse repetition frequency instead of using higher pulse energies. In this case, the laser beam should be deflected at ultrafast speeds thus to avoid strong pulse-overlap effects, for example, laser beam shielding and heat accumulation that will detrimentally affect the machining process [18,22–24]. Therefore, the conventional (galvanometer mirror based) scan systems cannot reach the necessary fast scan speeds of hundreds of meters per second and above. Alternatively, in the last decade rotating cylinders, electro- and acousto-optical deflectors, resonant scanners or fast rotating polygons have been successfully tested for high-speed laser micro machining [25–28]. However, the multi-facet (polygon) mirror based biaxial scan technique seems to be the most promising approach for ultrafast and flexible two-dimensional (2-D) laser beam raster scanning.

Figure 3a depicts a schematic view of the unique polygon scanner architecture engineered at the Laserinstitut Hochschule Mittweida [18,29]. The fast rotating double-reflecting polygon mirror is used to achieve the ultrafast laser beam moving speed along the fast axis. For raster scanning, the laser beam is shifted along the slow axis by the galvanometer scanner when the beam flips from one facet to the other. The moving laser beam can be focused by standard f-theta lenses by what focus spot sizes in the range between 30 μm and 100 μm will be reached that depends on the focal length of the adapted objective. The maximum achievable laser beam moving speed is also determined by the optical scanner configuration, for example, up to 1000 m/s for the 420 mm lens. Therefore, representative laser textures produced on stainless steel metal sheets at ultrafast 950 m/s scan speed can be seen in Figure 3b,c.

**Figure 3.** Schematic view of the (**a**) polygon scanner architecture and (**d**) multi-beam high-speed scan technology, *pd* and *ld* represent the spatial pulse distance and line distance of a raster-scan pattern; nano-featured surface textures produced on stainless steel by applying a single pass raster-scan over the substrate at 950 m/s laser beam moving speed and (**b**) 20 μm or (**c**) 10 μm line distance; SEM micrograph (**e**) and optical microscope image (**f**) of a ripple textured stainless steel surface; the effective area processing rate for the given 40 <sup>×</sup> 50 mm<sup>2</sup> surface texture was 0.13 m2/min.

The nano-featured surface textures in Figure 3b were made by a single pass raster-scan over the substrate surface. Therefore, the picosecond laser pulses were placed one after another in fast axis direction by irradiating 263 W average laser power. The pulse distance *pd* was set of about the focus spot diameter and with little overlap in orthogonal direction (slow axis) as the line distance *ld* between the raster scanned lines was half of the spot diameter. In initial studies, such kind of weak surface roughness is considered as inter-pulse feedback mechanism for the self-organizing formation of regular surface patterns as induced upon multi-pulse laser irradiations [30–32]. This material response is also confirmed by the SEM micrograph presented in Figure 3c, showing more prominent surface features originating from the higher accumulated irradiation dose that was due to higher pulse overlap at smaller line distance.

A further technical development is schematically illustrated in Figure 3d, combining the polygon scanner and a four-spot diffractive optical element (DOE) for ultrafast and parallel surface texturing. The feasibility of this groundbreaking technology is exemplified in Figure 3f by the homogeneous ripple texture produced on a stainless steel metal sheet using a femtosecond laser beam of 416 W average power at 560 m/s scan speed. The laser beam was scanned three times over the sample in order to achieve a well-shaped ripple texture, as can be seen in Figure 3e.

The overall processing rate that will be achieved applying high-rate laser technologies in surface texturing can easily be estimated by the following calculations. In theory, the maximum area processing rate *APR*max for a complete single pass raster-scan pattern over the substrate surface results from the product of the applied scan speed *v*<sup>S</sup> and the chosen line distance *ld* according to Equation (1):

$$APR\_{\text{max}} = \upsilon\_{\text{S}} \cdot ld \tag{1}$$

$$APR\_{\rm eff} = \upsilon\_{\rm S} \cdot ld \cdot \eta \tag{2}$$

From practical point of view, the utilization rate η of the polygon scan system must seriously be taken into consideration to calculate the effective area processing rate *APR*eff on the substrate. This is described in Equation (2), where the utilization rate is the ratio between the theoretical and effective processible scan length on each polygon mirror facet. Hence, the utilization rate is restricted by the technical polygon scanner architecture and the implemented optical components ranging of 49% or rather 40% for the applied scanner configurations. Table 1 provides an overview of the area processing rates that can be reached for producing the laser textures shown in Figure 3. A maximum area processing rate of 1.14 m2/min or 3.76 m2/min could theoretically be achieved with the applied 263 W picosecond or 416 W femtosecond average laser power. The given effective area processing rates will only be reached when the full length of the accessible scan field is used. This was effectively 0.56 m2/min for the picosecond single spot and 1.51 m2/min for the femtosecond multi spot laser procedure. A further decrease of the area processing rate can be seen for the laser made ripple texture of Figure 3e. The shown highly uniform ripples were produced by three repeated overscans applied on the stainless steel substrate while the effective *APR* reduced to be 0.50 m2/min. Moreover, as the length of the rippled surface texture in Figure 3f was almost 1/4 of the accessible length of the scanning field the duty cycle decreased to 10%. Thus, the effective *APR* was as low as 0.13 m2/min for this specific machining example.


**Table 1.** Maximum and effective area processing rates *APR* estimated for different processing conditions and by considering a single pass raster-scan procedure applied on the substrate surface at maximal accessible scan length.

*APR*eff for 1) 40% facet utilization rate, 2) 3 scan passes and 3) 40 mm field length.

## **3. Static Friction Analysis Method**

A standard analysis procedure developed by the IKAT institute at Chemnitz University of Technology [33,34] was applied for the evaluation of the tribological behavior of the laser textured surfaces. Therewith, both the static coefficient of friction (COF) and the type of frictional performance could be assessed from the recorded slipping curves. The functional principle of this analysis method is shown in Figure 4, displaying the implemented friction test bench assembly (left) and the cylindrical test specimen with a specially defined geometry (top right). The inner and the outer diameter of the ring-shaped contact surface area on top of the cylinder were *D*in = 15 mm and *D*out = 30 mm, respectively, and the cylinder height was 65 mm. Two identical cylinders were clamped in the test bench and coaxially fastened with the normal force *F*<sup>N</sup> to achieve a nominal surface pressure of 100 MPa that is a typical contact pressure in tribological systems. Based on Equation (3), the effective friction diameter *D*<sup>F</sup> of the contact area was determined to be 23.3 mm. By rotating the cylinders against each other, friction shear stresses develop in the joint resulting from the frictional torque *T*<sup>F</sup> on the contact area. The frictional torque was measured by the strain gauges as a function of the torsion angle ϕ*,* which is indicated in Figure 4.

**Figure 4.** Test bench assembly and standard procedure developed at IKAT (Chemnitz University of Technology) to analyze the performance of frictional contacts [33,34].

The recorded slipping curves are schematically shown in Figure 5 by plotting the torque measurements as function of the relative displacement *s*<sup>F</sup> of the contact areas. In this depiction, the relative displacement *s*<sup>F</sup> calculates according to Equation (4) and by taking into account the torsion angle and the effective friction diameter of the ring-shaped contact surface. As further can be seen in the schematic (bottom, left), three different types of characteristic friction performance could be recognized for the tribological contacts. These different types are distinguished depending on their typical slipping curve progression [35–37] that is briefly described in Figure 5 (right).

$$D\_{\rm F} = \frac{2}{3} \cdot \frac{D\_{\rm out}^3 - D\_{\rm in}^3}{D\_{\rm out}^2 - D\_{\rm in}^2} \tag{3}$$

$$s\_{\text{F}} = q \cdot \frac{D\_{\text{F}}}{2} \tag{4}$$

$$
\mu = \frac{2 \cdot T\_{\text{F}}}{F\_{\text{N}} \cdot D\_{\text{F}}} \tag{5}
$$

In Coulomb´s law of friction, the static coefficient of friction μ is defined as the constant of proportionality for the frictional contact of two bodies under the action of normal and sheer forces. The static COF states the transition point from sticking/adhesion to sliding and can be understood as the maximum boundary value of the load capacity of a contact which does not yet trigger a relative displacement of the two active partners towards each other. For the specified friction characteristic of Type A, this boundary value is well defined by the first local maximum of the slipping curve. Though, the boundary value is less clear for the friction Types B and C that can be seen by the corresponding slipping curves presented in the schematic of Figure 5 (bottom, left).

**Figure 5.** Exemplary illustration of the evaluation methods applied to determine the static COF. In the example (top, left), the stiffness lines are indicated by dashed lines to determine the respective COF´s μ2, μ<sup>20</sup> etc. Three types of friction can be distinguished depending on the torque progression curve schematically shown bottom, left. A detailed description of the different friction types is provided in the table on the right.

Following the analysis procedure, stiffness lines are included in the plot of the torque vs. relative displacement measurements where their intersection points support the determination of the torque at a specific position along the slipping path. The advantage of this method is to eliminate deformations of the entire tribological system that will affect the nominal value of the torsion angle, such as elastic deformation of the test bench or rather micro-movements in the joint resulting from surface asperities during specimen alignments. In the example of Figure 5 (top, left), the stiffness lines are indicated by the dashed lines. By considering the slope of the slipping curve, the stiffness line is shifted parallel along the abscissa (displacement axis) until its intersection at a desired lateral displacement position, e.g., 2 μm or 20 μm relative displacement between the test specimen contact areas. Then, by taking into account the torque value at the respective intersection of the stiffness line with the slipping curve, the corresponding COFs μ2, μ20, etc. can be calculated according to Equation (5).

In the following, in order to consider static instead of dynamic friction performance of the laser textured surfaces, the static COFs μ<sup>2</sup> and μ<sup>20</sup> will be discussed. The static COFs were calculated on the basis of the maximum torque values determined for the torsion angles 0.01◦ and 0.1◦ that is equivalent to 2 μm and 20 μm lateral displacements in the frictional contact area. In addition, the maximum value of the COF μmax that could be obtained within the tested range (ϕ ≤ 3◦, sF ≤ 600 μm) will be presented. It should be mentioned for the static COF Type A, most commonly the maximum value will be obtained within 20 μm lateral displacement, while for COF Types B and C, the maximum COF value is steadily increasing with increasing relative displacement. In the latter case, where the highest values were obtained at comparably large lateral displacements, the maximum COF´s represent dynamic rather than static frictional performances.
