J. Eur. Opt. Society-Rapid Publ. 21, 30( 2025) 317
Table 1. Parameters for the simulation.
Upper left
Upper right
Fig. 7
Lower left
Lower right
x wp [ mm ] |
0 |
0 |
80 |
0 |
y wp [ mm ] |
0 |
40 |
80 |
0 |
Ø wp [ mm ] |
400 |
400 |
400 |
500 |
Ø tool [ mm ] |
500 |
500 |
500 |
300 |
rpm wp [ min �1 ] |
50 |
50 |
50 |
50 |
rpm tool [ min �1 ] |
0 |
20 |
20 |
�20 |
addressed in case a reader wants to implement this in the future. It has therefore been omitted at this point. But it is probably not necessary to constantly record and evaluate the data: in most cases the surface of the work piece can be assumed to be rotationally symmetrical. After changing the polishing lever position, a rotationally symmetrical shape is polished anyway. This saves computing time and two recordings( camera, no other sensors) are necessary for the lever positions. All other positions can then be calculated from this.
At least the positions of the two rotary actuators( not the angular position) and the lengths of the individual links should be known. This allows the relative speeds and thus the removal to be calculated qualitatively with two known positions of the each joint points of the lever arm polisher. In principle, the amount of material removed could be calculated from two images. The information on the link lengths should be accurate to 0.1 mm in order to generate meaningful results.
5 Validation
5.1 Camera
The camera was able to collect 34 fps( frame per seconds). To reach a higher fps an FPGA( field programmable gate array) is necessary or the priorities on the PLC has to change. Image acquisition and image processing compete on the PLC. In order to optimize computing time, the images were not cached, but only evaluated and then deleted. However, if required, these can be saved and subsequently evaluated: for example, contamination of the polishing suspension can lead to a different friction behavior and this can be detected in the images.
Fig. 8. Data validation of the work piece.
the upper tick is displayed above the maximum value: the maximum value output is 360 ° and the minimum value is 1.6 °. The flanks are vertical. The artifacts at the maxima indicate either an error in the PLC programming or a tribological behavior when the work piece is rotated. Subsequent removal images show that the removal is not rotationally symmetrical.
As a second step, the x-andy-positions of the work piece are validated. The plot of those values should look like a sawtooth because the lever always swings from left to right and vice versa. It is clearly visible that the trigonometric function pattern of the wave is not perfectly periodic or regular: this prevents mid-spatial-frequency errors on the surface. Overall the data generated corresponds to the expected data situation.
4.4 Calculation of the lever arm machine
The inverse kinematic problem( calculation of linkages and angles from image recordings; Eqs.( 2)–( 5)) is analytically complex and closed-form solutions do not always exist. The calculation is not trivial. Nevertheless, it will be
5.2 Metadata With the data also several meta data can be filtered out. For example frequency analysis: In Figure 9 the specific frequency and amplitude values are not shown due to business secret. With that value conclusions can be drawn about the process. Using an FFT( fast Fourier transformation) of the orientation of the work piece, statements can be made about the motors of the polishing machine. The two unlabeled peaks are not multiples and could not yet be assigned to the process. They are probably pressure frequencies.
5.3 Material removal
In the test, polishing was only carried out for 5 min: Zerodur is a relatively soft material( compared to SiC, for example). Therefore, material removal can be measured after just a few minutes. The work piece was measured interferometrically before the test and then polished. The lever was set to concave by an experienced machine operator. After polishing, the surface was measured again interferometrically and then subtracted from the first measured surface. The difference image is shown in Figure 10, right, as relative material removal. The unit is nm. On the left side, the