\section*{Task 2 - 011022}

For cuboid workpieces with dimensions \(a=120 \mathrm{~mm}, b=60 \mathrm{~mm}\), and \(c=17 \mathrm{~mm}\), the thickness \(c\) is to be reduced from \(17 \mathrm{~mm}\) to \(15 \mathrm{~mm}\). This is to be done using a short planing machine. The following settings are possible:

(1) 46 strokes per minute, stroke length up to \(180 \mathrm{~mm}\),

(2) 108 strokes per minute, stroke length up to \(77 \mathrm{~mm}\).

a) How should the workpiece be clamped and which setting should be chosen to perform the work as quickly as possible?

b) What result is obtained for a workpiece with dimensions \(a=150 \mathrm{~mm}, b=50 \mathrm{~mm}\), \(c=17 \mathrm{~mm}\)?

Note: The feed rate should be \(1.5 \mathrm{~mm}\).
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a) At setting 1, one will set up such that \(a\)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-1177.jpg?height=192&width=625&top_left_y=1703&top_left_x=333)
is in the lifting direction. For an area, \(\frac{60}{1.5}=40\) lifts are needed, so \(\frac{40}{46}=\frac{20}{23} \mathrm{~min}\) of pure working time. At setting 2, one sets up such that \(b\) is in the lifting direction. Then 80 lifts are needed, so a working time of \(\frac{20}{27}\) min.

Thus, setting 2 is more rational.

b) At setting 1, one chooses the setup as described above; 34 lifts are needed, so \(\frac{17}{23}\) min. At setting 2, one also chooses the setup as described above and needs 100 lifts, so a working time of \(\frac{25}{27} \mathrm{~min}\).

Here, setting 1 is more rational.