Installation manual
CNC 8055
CNC 8055i
CONCEPTS
7.
SOFT: V02.2X
·421·
Compensation of the elastic deformation in the coupling of an axis
Conclusions:
The elastic deformation on the axis of a machine is directly proportional to the acceleration and when
its dynamics is a circular path, it is also directly proportional to the square of the feedrate.
Therefore, the higher the relative feedrate between the tool tip and the table, the more significant
the elastic deformation will be.
Machining a part following a circular path at low feedrate considering the elastic deformation only
on one axis or on both implies practically getting the desired circular path because the path deviation
suffered on the axes will be very small. It will not be a perfect circle, but, in practice, it will not be
necessary to compensate for elastic deformation.
Machining a part following a circular path at high feedrate considering the elastic deformation only
on one axis or on both implies getting an elliptic path because the path deviation suffered on the
axes will be considerable. The other main radius of the ellipse will be the same as the radius of the
circular path when assuming that there was no elastic deformation on the other axis. Considering
elastic deformation on both axes will also result in an elliptic path where none of the two main radii
coincides with the radius of the programmed circular path.
To offset these deformations, set machine axis parameter DYNDEFRQ (P103) for each axis with
the value of the resonance frequency of its elastic coupling.
Remarks:
Before compensating the elastic deformation, the CNC will always display a circular path, not
elliptical as could be expected because there is elastic deformation.. The motor feedback is placed
before the elastic coupling and does not register the path deviation due to elastic deformation at all.
After compensating the elastic deformation, the CNC will always display an elliptical path, not
circular as could be expected after compensating the elastic deformation..
Resonance frequency of the elastic coupling
From the formula of the oscillation frequency of a simple harmonic movement (s.h.m.) it is possible
to obtain its relationship with acceleration and deformation through this equation:
For a circular path, the x deviation with respect to R may be obtained directly by measuring the
part that has been previously machined.
The acceleration of the system is calculated from the formula shown earlier:
With these values, now determined, the formula of the frequency provides the value for setting
machine axis parameter DYNDEFRQ (P103) to offset the elastic deformation caused on that axis.
f
1
2
------
k
m
----
1
2
------
a
x
------==
a
F 60
2
R
---------------------
=
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