Exercise $7$ Positioning Process

There are three drives that are arranged at right angles to each other. You have

the following data

$x-$axis: $h_{sp}=5mm$;$n_{\text{m}\text{a}\text{x}}=2500$min$-1$

$y-$axis: $h_{sP}=5mm$;$n_{\text{m}\text{a}\text{x}}=2500$min$-1$

$z-$axis: $h_{SP}=5mm$;$n_{\text{m}\text{a}\text{x}}=2500$min$-1$

The axes are designed to perform a straight$-$line positioning process from the point $(10mm,$

$10mm,10mm)$ to the position $(x=210mm,y=310mm,z=110mm),$ where the target velocity

is $300m\frac{m}{s}.$

a$)$ How long does the positioning process take if the acceleration and braking times are

neglected?

b$)$ At what speed do the individual axes move?

c$)$ Determine the revolution speeds of each axis that are required for the positioning

process.

d$)$ Determine the maximum speed for the positioning process.

Exercise $8$ Position Error

An optical encoder is connected to a motor, which has a line count of $1000$ increments per

revolution and outputs square wave signals. The motor drives a preloaded steel threaded

spindle with a pitch of $5mm(h_{SP}=5(mm)).$ Determine the absolute and relative positioning

error when the spindle temperature increases by $T=50K({}_{\text{S}\text{t}\text{e}\text{e}\text{l}}=12*{10}^{-6}[\frac{1}{K}]).$

The drive travels a distance of $5\mathrm{.}5mm$ when the spindle is cold.

a$)$ How many optical encoder counts are recorded by the evaluation circuit?

b$)$ How does this value change when the same positioning process is performed with a

warm spindle?

c$)$ What problems do you recognize and how can they be eliminated?