316 J. Eur. Opt. Society-Rapid Publ. 21, 30( 2025)
Fig
. 6. Imaging of the programming.
Fig. 7. Different simulations of the lever arm machine.
TwinCAT Vision is fundamentally different, so this is a good place to check each other. The center distance of the measurement artifacts was 521.33 Px( Pixels) in the PLC and 521.44 Px in the offline Python programming, which means a deviation of 0.02 %. There is no established threshold for acceptable deviation at this point.
4.2 Simulation: material removal
In Figure 7 the coordinate system lies in the center of the polishing / lapping tool. The y-axis is 0 ° and x-axis 270 °. Verifying the source code for material removal with real data appears too complex, so selected situations were simulated that are also easy to calculate manually. In the upper image, the two coordinate systems of the work piece and tool are superimposed, and the work piece has no velocity. The rotation velocity at the zero point and at the outermost edge can be calculated manually with the values in Table 1. In the upper right image, the work piece zero point has been shifted 40 mm to the right; the workpiece and polishing bowl also have a rotational speed. The radial displacement of 40 mm and the relative speeds are clearly visible. These speeds can also be reproduced by manual calculation. The lower left differs from the upper right only by a further shift in the y-direction. The minimum velocity is shifted to the lower right of the image. The image below right is a special case. The tool is larger than the work piece and the speeds are opposite. Neither of these occurs in the practice of lever-arm machines and occurs in sub-aperture computercontrolled polishing( CCP). The images shows that the material removal calculation works in a proper way. The shown calculated velocity is just the rotational velocity and not the lateral velocity. The calculation is very errorsensitive: even the smallest errors in the calculation lead to obviously incorrect outputs.
4.3
Camera angle in-situ measurement
The first and simplest evaluation is to consider the orientation angle of the work piece. If the angle is plotted( see Fig. 8) for a polishing step, it may only be in the range between 0 ° and 360 °. In the Matplotlib representation,