IEEE Robotics & Automation Magazine - September 2023 - 63

muffle or fully cover one or more peaks during an individual
update of the PSD plot, due to its high refresh rate. For example,
Figure 5(b) is a such a plot with different signal characteristics,
with several peaks around the first modal frequency that make it
difficult to identify correctly. This causes conventional filters to
be unreliable in their tracking. Therefore, an algorithm to track
the dominant frequency variation correctly and stably is required.
We propose a tracking algorithm that follows the flowchart
in Figure 5(c). In every loop in which the PSD frequency is
calculated, the first step is removing environment noise, usually
in the lower frequency range. In our environment, this
background noise has been estimated to reach up to 1,000 Hz
( ,).
f 1 000 Hz
en =
pi,
For the ith loop of the algorithm, we compute
the frequency of the peak with the highest amplitude
as
f . To judge whether f ,pi represents a spindle's mode or
noise, its value is compared with the peak frequency of the
previous loop
pi, 1f
. Since the spindle frequency value should
be continuous, the newly acquired f ,pi is kept as a valid frequency
only when its difference from f ,pi 1is
smaller than
a given interval Δ (here set to 250 Hz after an experimental
calibration). When this difference is higher than the threshold,
we discard the acquired f ,pi and keep using the value of
f .
pi, 1If
f ,pi is identified as one of the modes of the spindle
frequency, we check which mode it is and consequently obtain
the dominant frequency.
CALIBRATION OF MACHINING FORCE
AND SPINDLE FREQUENCY
To estimate the machining force from the spindle frequency,
the relationship between them should be mapped through an
experimental calibration. Here, we describe a calibration procedure
to map radial machining force and spindle frequency
when milling and grinding titanium and aluminum workpieces
with the robot.
As described before, the haptic joystick's position in its
own reference frame is mapped onto the robot tip's position
in Cartesian space. Thus, the pose of the end-effector tool
can be controlled by joystick movement. To execute accurate
repeated trials, the haptic joystick is driven by a linear motor
(Actuonix L12-50-100-12-P, dc) at a constant velocity of
1 mm/s along a slider, as in Figure 4. In each trial, the motor
drives the joystick from its initial position, where the tool is
not in contact with the workpiece, to the end position, where
the tool has stalled.
The real-time radial force between the milling tool and
the workpiece is measured by a load cell (LCMFD-10N). The
workpiece (100 × 30 × 1.35 mm) is made of titanium and fixed
on a slider (MISUMI SSE2BWLZ14G-160). When the milling
tool engages the edge of the workpiece, its opposite edge
pushes onto the load cell to guarantee that the force measured
by the load cell equals the radial milling force. The real-time
milling frequency is also acquired and recorded by the system.
The trial is repeated 25 times, and every trial is conducted on a
new (nonmachined) contact point.
To obtain the relationship between frequency and radial
force, the recorded frequency and radial force are synchroHAPTIC
FORCE FEEDBACK
The haptic force feedback is designed according to the
principle described in the " System Overview " section, with
two modes employed to ensure that
the user feels the
machining force while keeping the system both safe and
stable. When the robot tip is not in contact with the workpiece,
the
system works in motion control mode, as
described in the " System Overview " section, and a springlike
force is generated as
Fk PPH
I
=-$^h
I
H
E
H
I
where FH
I is the haptic feedback force, P RH
E
(6)
! 3 is the position
vector in the haptic device coordinate system calculated
from the current actuator position, P RH
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
-0.01
0.2 0.4 0.6 0.81 1.2 1.4 1.6 1.8
× 104
Frequency (Hz)
Deviation of Measured Value
Average Value
Fit Curve
FIGURE 6. The measured frequency and corresponding force.
Each black bar indicates the result deviation of all trials, each
black point indicates the average value at a given frequency, and
the red curve fits the average values.
SEPTEMBER 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE
63
I ! 3 is the commanded
nized and combined, and the correspondence between the
frequency and force values is identified for each frequency
sample. In the example trials on the titanium workpiece, the
sample frequency ranges from 3,500 to 16,000 Hz, with increments
of 2,500 Hz. After getting the data from all 25 trials, a
fitting curve generated from their average value is identified.
Figure 6 shows the deviation in the measured radial milling
force for each sample frequency among all the trials, the average
radial milling force value, and the fitting curve (in red),
generated by using a polynomial function from the average
radial force of all trials.
When the milling tool enters into contact with the titanium
workpiece, the spindle frequency is about 17,500 Hz, whereas
the detectable lower-limit frequency is 2,000 Hz. In the range
between 2,000 and 175,000 Hz, the radial milling force has a
near-linear relationship with the spindle frequency.
Radial Milling Force (N)
IEEE Robotics & Automation Magazine - September 2023

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