Page 745 - Mechatronics with Experiments

PROGRAMMABLE MOTION CONTROL SYSTEMS 731
10.5.2 Electronic Gearing Coordinated Motion
In mechanically coordinated designs, one axis motion can be tied to the other axis through
a mechanical gear. The motion of axis one axis is directly proportional to the motion of
the other axis in position, velocity, and acceleration (neglecting transmission imperfections
due to backlash and tolerances). In mechanical designs, the relationship is fixed by the gear
ratio mechanically.
The drawback of mechanical gearing is that if a different gear ratio is needed for a
different product, the gear ratio between the shafts needs to be mechanically changed by
installing different gears for every different gear ratio. This will increase the setup time. It
may also be economically in feasible for applications involving many different gear ratios
to keep many different gears in stock. The functionality needed here is to provide a motion
to the second shaft which is proportional to the motion of the first shaft. The proportionality
constant may vary for different products.
If both shafts have their independent actuation source, the commanded motion to the
slave axis can be derived from the commanded or the actual motion of the master shaft. In
the process of calculating the commanded motion for the slave shaft, any desired gear ratio
can be used (Figure 10.11b). The gear ratio can be constant or variable. Furthermore, in
certain positions in the cycle additional forward or backward moves can be implemented
to change the phasing of the slave shaft with respect to the master shaft. This type of
motion profile generation is called electronic gearing or software gearing since it is done
electronically by software implementation as opposed to mechanical gears. The position
tracking accuracy should be at least very close to those accuracy that would be obtained if
the shafts were connected to each other through mechanical gears.
The gear ratio is set in software and easily changeable without any time consuming
mechanical disassembly and re-assembly. Electronic gearing is perhaps the most common
type of programmable motion control application encountered in industry today. Let us
consider two axes: each are driven by a separate motor. Axis 1 is the master. The axis 2
desired motion can be generated from the motion of axis 1 using a fixed (or changing)
ratio. As long as the servo loop delivers a good position tracking accuracy, the net result is
a two-axis motion system making geared motion. The commanded motion to axis 2 can be
generated from either the actual or the commanded motion of axis 1. The acceleration and
deceleration rate of the slave axis can be defined as a function of the master axis position
change instead of being defined as a function of time. In all electronic gearing applications,
the slave axis motion profile can be defined as a function of one of two independent
variables:
1. time, or
2. master axis position.
The accuracy of the electronic gear tracking is as good as the tracking accuracy of each
slave axis whatever method of control is used. Therefore, for the electronic gearing to be
successful, the servo loops should be properly tuned. Otherwise, the tracking errors may
deteriorate the performance to the point that it does not resemble the performance that
would be achieved had the shafts been connected to each other by mechanical gears.

Fixed Ratio Gearing This is the simplest form of electronic gearing. It exactly
emulates the relationship between two shafts connected to each other via a fixed gear ratio.
During the cycle, the slave axis (or axes) are commanded to move at a certain gear ratio
relative to the master axis motion. It is also very straightforward to use two or more fixed
gear ratios between two axes where the gear ratio is changed from one fixed value to another
at certain positions during a cycle. For instance, rotating knife applications where the web