Spindle Error and Thermal Effects Analysis - ZAOiOS

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Prof. Krzysztof Jemielniak
Spindle Error
and Thermal
Effects
Analysis
Outline
• rotary motion axis errors, sensitive
directions
• spindle error definitions
• calculation of spindle errors accordingly to
B5.54
• Spindle Error & Thermal Effects Analyzer
• other solutions
École Polytechnique Montréal, Politechnika Warszawska
1
Subject of the Presentation
•
Heart of any CNC machine is the spindle.
•
Problems resulting from bad or damaged bearings, improperly match
gear trains and thermal conditions will seriously effect the
performance of any CNC machine.
•
The ASME B5.54 standard ("Methods for Performance Evaluation of CNC
Machining Centers") provides methods for performance testing of
spindle radial error motion and rotating sensitivity.
•
École Polytechnique Lab is equipped with Spindle Error Analyzer
System of Lion Precision, with SEA 7 and SETEA software
Rotary Motion Axis Errors
Every rotary motion axis has one large degree
of freedom... and five small error motions:
Reference axis ZR
Axis of rotation Zn
ΘZ(t)
Yn
δZ
δY
δX
εY
Two other sensors senso
X2
rY
sor
2
allow to measure tilt
sen
XR
Rotating body
(spindle)
εX
so
sen
rX
YR
Xn
Radial displacements sen
sor
Y
are made parallel to
XR and YR axis
sensor Z
2
Target and sensors
Sensitive direction
3
Rotating Sensitive Direction
sensitive
direction
Xn
YR
non-sensitive
direction
Θ
XR
Yn
Calculation of Radial Error Motion
YR
n
REM(Θ) = ∆X(Θ) cos(Θ)
+∆Y(Θ) sin(Θ)
∆Y
Er
r
or
M
ot
io
Xn
Yn
Ra
Θ
∆X
l
dia
or
Err
Mo
n
tio
•
both X and Y
displacements can be
positive and negative
•
obtained plot would
be tangled,
unreadable
XR •
we need Error Motion
Polar Plot
4
Creation of Error Motion Polar Plot
YR
r (Θ) = r0+ ∆X(Θ) cos(Θ) +∆Y(Θ) sin(Θ)
r0
1
4
Θ
XR
2
3
Creation of Error Motion Polar Plot
YR
r (Θ) = r0+ ∆X(Θ) cos(Θ) +∆Y(Θ) sin(Θ)
r0
Θ
XR
5
Error Motion Polar Plot
Test data from rotating measurements is displayed
with a polar plot showing target position at successive
angular locations on successive rotations, projected on
sensitive direction (radii) and is evaluated, in a manner
similar to the roundness plot of a machined part.
Error Motion Acquisition
1.
Find the spindle rotational speed in
rev/sec (rps): acquire 100kS with
fs=100kHz, then find frequency of
the dominant component
2.
Acquire 10kS with fs=200*rps (Hz),
meaning 50 revolutions, 200
samples at each.
3
Check the spindle rotational speed
again. If the difference is bigger
then 1%, go to point 1.
4
Find number of full revolutions,
actual real number of points per
revolution T…
and beginning of the first revolution
i0
#rev
i0
i0
i0
i1
i2
T=pt/rev and i0 can be evaluated statistically by means of least squares method from array
[in, n] as a slope and an intersection of the line in=i0+nT
6
Error Motion Calculations
5
Find a circle best fitted to all data acquired
(Least Square Circle) and move the data to
the center of the XY polar plot
6
For each of ~200 angular location project the
actual spindle position on sensitive direction
so instead “curly” plot (gray in the background)
all measurements are neatly ordered along
radii (red)
Radial Error Motion Plot –
Least Squares Circle
The calculation of rotational error motions is based upon the radii of circles
that define the ideal and actual motion of a rotating spindle.
LSC
LSC
Least squares fitting generates a
perfect circle (Least Squares Circle LSC) that best describes the data
represented.
The radius of the LSC in radial measurements
is generated by the intentional eccentricity of
the target, and its actual value is not related to
error motion.
The LSC radius can be increased or decreased
manually to adjust the appearance of the plot.
In the calculation of some error motions, other circles are drawn
relative to the LSC and it is the relationship of their radii that
describes the error motion value. Therefore LSC can be called
“the reference circle”.
7
Total Error Motion
Total error motion is the total combination of all the error motions of the
spindle. This value provides a worst case number giving a preliminary
indication of the capability of the machine tool to produce parts.
Physically LSC center represents the center of the rotating spindle.
Two red circles are drawn with the same center location as the LSC
The first circle is drawn in the blank area inside
the plotted data with the largest possible radius
without encroaching on the data (maximum
inscribed circle).
The second circle is drawn in the blank area
outside the plotted data with the smallest
possible radius without encroaching on the
data (minimum circumscribed circle).
The difference between the radii
of these two circles is defined as
the total error motion value.
Asynchronous Error Motion
Asynchronous Error Motions are not related
to the rotational frequency of the spindle.
While their source may be well defined and
repetitive, they are not synchronous to the spindle
rotation, i.e. they repeat at a frequency that is not a
multiple of the rotational frequency.
The figure shows a radial error motion plot for fifty
revolutions. The “fuzziness”of the plot indicates that
at any particular angular location, the location of the
target varied significantly on each successive
revolution.
Once the data has been taken, the range of
data (maximum - minimum) is determined at
each angular location.
The largest range (worst case)
is defined as the asynchronous
error value.
8
Synchronous (Average) Error Motion
Error motions that are related to the rotational frequency of the spindle
are called synchronous or average error motions.
If the error motion were completely
synchronous, the plot of data would draw a
pattern with the same value at each angular
location on each successive rotation.
Because there is always some amount of
asynchronous error present, the synchronous error
must be extracted from the asynchronous data.
First the values at each angular location are
averaged (plotted in green.)
Like total error, maximum inscribed circle and
minimum circumscribed circle that just contain the
averaged data are drawn.
The synchronous error motion
value is defined as the difference
in radii of these two circles
Spindle Error & Thermal Effects Analyzer –
System Overview
thermocouples
target
probes
thermocouples
Probe drivers
SETEA
or SEA 7
PCI eXtensions for
Instrumentation
(PXI)
target
probes
Signal Conditioning eXtensions
for Instrumentation (SCXI)
connector block
9
Master Target
The master ball fixture consists of a precision ball mounted on a fixture that allows
you to adjust the eccentricity (run-out) of the ball when mounted onto a spindle.
Adjustable dual 1in.
diameter master ball
fixture (X,Y,Z,X2,Y2)
Adjustable single 1in.
diameter master ball
fixture (X,Y,Z)
6K rpm
30K rpm
Adjustable single
0.5in. diameter
master ball fixture
(X,Y,Z)
50K rpm
High speed
carbide target
(X,Y,X2,Y2)
80K rpm
In general, the higher the speed, the smaller the ball and fixture.
Capacitance Probes and Probe Drivers
Capacitance probes measure the air gap between the probe and the target by
detecting a change in capacitance as the air gap changes.
Capacitance is an electrical property of a gap between two conductors. The capacitance is dependent on
three things:
1. The distance between probe and target
2. The material that fills the gap
3. Shape of the target
The measuring range of a probe is affected by two factors:
• The area of the sensing tip
• The sensitivity of the calibration
range: 250 µm = ±10V
12.5 µm/V
10
Probe Calibration
Since the probes are calibrated to a flat target,
measuring a target with a curved surface will cause
errors
In cases where a non-flat target must be
measured, the system can be factory
calibrated to the final target shape.
11.6 µm/V
9.625 µm/V
11.75 µm/V
Probe Holders
11
Configuration of the SETEA
12
Probe adjustment
0
Range (distance from target, µm)
125 190
310 375
Results displayed by SETEA
13
Review of Detailed Results
Results Obtained with SEA7 and SETEA
Lion Precision SEA 7
SETEA
14
Error Motions Measurements During Machining
Process
Center for Precision Metrology, The University of North Carolina at Charlotte
BT-40Tool
toolHolder
holder with
target disk mounted on it
Target disk mounted on the tool
holder with rectangular and
cylindrical capacitance gauges
targeting at it
Process
M-270 machine spindle
15
Process
Connector plate
Process
Mounts for the R1-A
capacitance gauges
16
Process
Target disk and
tool holder
Process
Mounts for the C1-B
Capacitance gauges
17
Stand for High Speed Spindle Testing in AVIA,
Warsaw, Poland
Program for Data Acquisition and Analysis
18
Program for Data Acquisition and Analysis
Raport
19
Stand for Thermal Effects Analysis in CBKO, Poland
20

Spindle Error and Thermal Effects Analysis - ZAOiOS

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