Transcript Linear Magnetic Bearing/Actuators and Prototype for

PRECISION
MECHATRONICS
LABORATORY
A new method for characterizing
spindle radial error motion
a two-dimensional point of view
Xiaodong Lu
Special presentation at noon of Aug 25, 2009
Organized by James Bryan
BACKGROUND
PRECISION
MECHATRONICS
LABORATORY
• J. Tlusty, “System and Methods of Testing Machine Tools”,
Microtecnic, 13(4):162-178, 1959.
• J. Bryan, R. Clouser, and E. Holland. “Spindle Accuracy”, American
Machinist, 111(25):149-164, 1967
• R. Donaldson, A Simple Method for Separating Spindle Error from
Test Ball Roundness Error, CIRP Annals, Vol. 21/1, 1972
• J. Peters, P. Vanherck, An Axis of Rotation Analyser, Proc. Of 14th
International MTDR Conference, 1973.
• ANSI/ASME B89.3.4M – 1985, Axes of Rotation: Methods for
specifying and testing, 1985.
• ISO 230-7:2006, Test code for machine tools—Part 7: Geometric
accuracy of axes of rotation, 2006
• J. B. Bryan, The History of Axes of Rotation and my Recollections,
Proceedings of ASPE Summer Topical Meeting on Precision Bearings
and Spindles, 2007.
• E. R. Marsh, Precision Spindle Metrology, DEStech Publications, 2008.
SOMETHING IS WRONG!
PRECISION
MECHATRONICS
LABORATORY
• Darcy Montgomery of Kodak Graphics (Vancouver) sent
Email to Prof. Yusuf Altintas (UBC), questioning about
ASNI B89.3.4, what if the amplitudes of once-perrevolution components in X and Y are not equal to each
other? The removal of once-per-revolution component
is questionable.
• Darcy’s question motivated me and my students (UBC) to
develop a new method for a more rigorous treatment of
the spindle radial error motion.
MOTIVATION: AXIS-ASYMMETRIC TURNING
Y
PRECISION
MECHATRONICS
LABORATORY
FACE TURNING AS WELL
PRECISION
MECHATRONICS
LABORATORY
SPINDLE MOTION ANALYSIS FRAMEWORK
PRECISION
MECHATRONICS
LABORATORY
Layer 1: Test Point Motion
Layer 2: Spindle Motion
Layer 3: Predict Application Error:
effect of spindle radial error motion on a specific application
1: TEST POINT MOTION: POINT TAGGING
Test point motion:
vP ( )  xP ( )  jyP ( )
PRECISION
MECHATRONICS
LABORATORY
M
1

v (  2 i )
v p ( ) 

i 1 p
M


v p ( )  v p ( )  v p ( )
PRECISION
MECHATRONICS
LABORATORY
1: TEST POINT VECTOR MOTION
Test point 2D motion: vP ( ) 
k 
V[-2]
jk
V
(
k
)
e
 P
V[2]
k 
1
where Fouriercoefficient VP (k ) 
2
2
2ω
 jk
v
(

)
e
d
 P
V[-1]
0
ω
ω
V[1]
V[0]
V[0]
V[1]
V[-1]
V[2]
V[-2]
Error Motion
2ω
PRECISION
MECHATRONICS
LABORATORY
1: TEST POINT VECTOR MOTION
Test point 2D motion: vP ( ) 
k 
jk
V
(
k
)
e
 P
2ω
k 
2ω
ω
ω
1: TEST POINT VECTOR MOTION
Test point 2D motion: vP ( ) 
PRECISION
MECHATRONICS
LABORATORY
k 
jk
V
(
k
)
e
 P
k 
k  0 : VP (0), the spindle rotation average point drift.
Spindle rotation average point: the intersection between the spindle axis
average line and the radial plane at the specified axial location
k  1: VP (1),drift between the test point and the rotation center
Spindle rotation center: the intersection between the spindle axis of
rotation and the radial plane at the specified axial location
k  0,1: VP ( k ) is independent of test point seleciton
such as VP ( 1), VP (2), VP ( 2), VP (3), VP ( 3),
VP (4), VP ( 4),......
2: SPINDLE ERROR MOTION
Spindle 2D motion:  ( ) 
PRECISION
MECHATRONICS
LABORATORY
k 
jk
V
(
k
)
e
 P
k 
k 0,1
Spindle motion along a particular radial direction of interest:
 k 

 j
j ( k  ) 



 ( )  Re  ( )e  = Re  VP ( k )e
 k 

 k 0,1

PRECISION
MECHATRONICS
LABORATORY
3: SPINDLE ERROR MOTION EFFECT ON APPLICATIONS
Applications with two sensitive directions:
ae( )   ( ) 

jk
V
(
k
)
e
 p
k 
k 0,1
Applications with single fixed sensitive direction:
ae( )   ( )  Re[V p ( 1)e
 j  0 
]
 

j k 
 Re   V p ( k )e  0  
 k 

 k 0,1,1

Applications with single rotating sensitive direction:
ae( )   ( )  Re[V p (2)e
j  0 
]
 

j ( k 1) 0  
 Re   V p (k )e 
 k 

 k 0,1,2

ONCE-PER-REVOLUTION RADIAL MOTION
Y
PRECISION
MECHATRONICS
LABORATORY
Y
X
The perfect spindle
xc ( )  0; yc ( )  0
X
A spindle with once-pre-revolution
radial error motion
xc ( )  cos ; yc ( )   sin 
ONCE-PER-REVOLUTION RADIAL MOTION
Y
PRECISION
MECHATRONICS
LABORATORY
Y
X
The perfect spindle
xc ( )  0; yc ( )  0
X
A spindle with once-pre-revolution
radial error motion
xc ( )  cos ; yc ( )   sin 
E-BEAM ROTARY WRITING MACHINE
A spindle with once-pre-revolution
radial error motion
xc ( )  cos ; yc ( )   sin 
PRECISION
MECHATRONICS
LABORATORY
E-BEAM ROTARY WRITING MACHINE
A spindle with once-pre-revolution
radial error motion
xc ( )  cos ; yc ( )   sin 
PRECISION
MECHATRONICS
LABORATORY
E-BEAM ROTARY WRITING MACHINE
A spindle with once-pre-revolution
radial error motion
xc ( )  cos ; yc ( )   sin 
PRECISION
MECHATRONICS
LABORATORY
E-BEAM ROTARY WRITING MACHINE
A spindle with once-pre-revolution
radial error motion
xc ( )  cos ; yc ( )   sin 
PRECISION
MECHATRONICS
LABORATORY
PRECISION
MECHATRONICS
LABORATORY
E-BEAM MACHINE WITH MULTI-TOOLS
A spindle with once-pre-revolution
radial error motion
Produced pattern on
xc ( )  cos ; yc ( )   sin 
a once-per-rev error spindle
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10
-10
-10
-5
-5
0
55
10
10
PRECISION
MECHATRONICS
LABORATORY
MUTLI-TOOL BORING WITH K=2 ERROR
A spindle with K=2 radial error motion:
 xc ( )  x0  cos(2 )
, by R. Donaldson, 1972

 yc ( )  y0  sin(2 )
Produced holes
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10
-5
0
5
10
PRECISION
MECHATRONICS
LABORATORY
MUTLI-TOOL BORING WITH K=2 ERROR
A spindle with K=2 radial error motion:
 xc ( )  x0  cos(2 )
, by R. Donaldson, 1972

 yc ( )  y0  sin(2 )
Produced holes
10
8
6
4
2
0
-2
-4
-6
-8
-10
-10
-5
0
5
10
PRECISION
MECHATRONICS
LABORATORY
ANOTHER EXAMPLE
Spindle Error Motion:
 xc ( )  x0  cos( )  cos(2 )  cos(3 )

 yc ( )  y0  sin( )  sin(2 )  sin(3 )
 ( )  e
 j
e
 j 2
e
j 3
ANSI/ASME B89.3.4M
Fixed X direction:  X , ANSI ( )  cos(2 )  cos(3 )
Fixed Y direction: Y , ANSI ( )  sin(2 )  sin(3 )
Rotating direction:  ROTATING , ANSI ( )  0
APPLICATIONS WITH 2 SENSITIVE DIRECTIONS
PRECISION
MECHATRONICS
LABORATORY
• Machining/measuring axis-asymmetric patterns
• Machining/measuring axis symmetric pattern with
multiple tools installed at different radial directions
EXPERIMENT 1
PRECISION
MECHATRONICS
LABORATORY
BALL MOTION MEASUREMENT,
4000 RPM
PRECISION
MECHATRONICS
LABORATORY
ERROR MOTION ACROSS SPEEDS
PRECISION
MECHATRONICS
LABORATORY
STRUCTURE STIFFNESS
PRECISION
MECHATRONICS
LABORATORY
EXPERIMENT 2
PRECISION
MECHATRONICS
LABORATORY
BALL MOTION MEASUREMENT AT 500 RPM
PRECISION
MECHATRONICS
LABORATORY
ERROR MOTION ALONG X AT 500 RPM
PRECISION
MECHATRONICS
LABORATORY
V(-1) ERROR MOTION ACROSS SPEEDS
PRECISION
MECHATRONICS
LABORATORY
PRECISION
MECHATRONICS
LABORATORY
Application errors
Error motion
CONCLUSIONS
Purpose
ANSI/ISO specifications
2D method
along single fixed direction
Application with single fixed
sensitive direction








Application with single rotating
sensitive direction


Application with two sensitive
directions


along single rotating direction
In two dimensions