J. Eur. Opt. Society-Rapid Publ. 21, 12( 2025) 129
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Figure 6. Schematic illustration of surface formation:( A) theoretical surface formation( side view; feed direction perpendicular to the image plane) in ball tool grinding by combining descending grinding paths and( B) schematic comparison between an ideal spherical tool impression and a deformed( pressed wide) tool impression into the workpiece surface.
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Figure 7. Schematic visualization of Alvarez freeform grinding with a variation of grinding kinematics:( A) feed direction vertical to tool inclination angle a and( B) feed direction parallel to tool inclination angle a.
4.1.1 Fine grinding investigations on shape correction and mid-spatial form errors
In the experiments on the Alvarez geometry generation, the influence of kinematic settings was first analyzed. The influence of the fine grinding step( D30 metal bond) was found to be most influential on shape accuracy and introduction or removal of periodic mid-spatial defects. Because of this, the following investigations are carried out in the fine grinding regime. For this purpose, the direction of the feed movement in the x / y-direction was varied in relation to the inclination angle plane, as shown in Figure 7. On the one hand, feed direction and tool inclination angle a were oriented vertical to each other( Fig. 7( A)) and on the other hand, they were oriented parallel to each other( Fig. 7( B)). Grinding parameters regarding removal depth( a p = 60lm), feed rate( v f = 300 mm / min) and cutting velocity( v c = 7.9 m / s) were set at constant, experiencebased values. A ball tool diameter of 10 mm was used.
The resulting microtopography of the samples was measured using WLI. In order to make the medium and highfrequency surface defects recognizable, a form subtraction was applied to the measurement images using a third-order polynomial. The result shows that in contrast to the vertical
orientation, which leaves behind clearly recognizable grinding structures in Figure 8( A) with a period that exactly reproduces the chosen path distance of 100 lm, the parallel feed-to-tilt kinematics is highly advantageous, as this produces a relatively homogeneous surface( Fig. 8( B)) which was shown in these investigations for the first time.
The proposed explanation for this is that the contact behavior of the vertical feed-to-inclination setting can be approximately compared with lateral surface grinding on cylindrical tools, which also generally results in a scored surface. Here, all engaged grains are at the same distance from the tool center at a fixed position and thus all have the same cutting speed. The grains all have a minimally different grain protrusion, and each grain re-engages in the same area of the sample surface after each full tool rotation. More protruding grains are thus formed directly in the machined sample surface, shown in Figure 9( A). With a parallel feed rate to the inclination, however, the engagement behavior is comparable to face grinding, which can enable more homogeneous grinding results. Each grain covers a circular path on the sample surface, which is superimposed with the linear feed movement. Depending on the position of the grain on the tool face, the circular path size and cutting