A new method for characterizing spindle radial error motion a two-dimensional point of view

PRECISIONMECHATRONICSLABORATORY

A new method for characterizing spindle radial error motion

a two-dimensional point of view

Xiaodong Lu

Special presentation at noon of Aug 25, 2009Organized by James Bryan


• 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.

BACKGROUND


•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-per-revolution 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.

SOMETHING IS WRONG!


MOTIVATION: AXIS-ASYMMETRIC TURNING

X

Y

PRECISIONMECHATRONICSLABORATORYFACE TURNING AS WELL


SPINDLE MOTION ANALYSIS FRAMEWORK

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:

( ) ( ) ( )P P Pv x jy 1

1( ) ( 2 )

( ) ( ) ( )

M

p pi

p p p

v v iM

v v v

PRECISIONMECHATRONICSLABORATORY1: TEST POINT VECTOR MOTION

V[0]V[1]V[-1]V[2]V[-2]Error Motion

Test point 2D motion: ( ) ( )k

jkP P

k

v V k e

V[0]

ω

V[0]

V[1]ω

ω

V[0]

V[1]

V[-1]

ωω

2ω

V[0]

V[1]

V[-1]

V[2]

ωω

2ω

2ω

V[0]

V[1]

V[-1]

V[2]

V[-2]

2

0

1where Fouriercoefficient ( ) ( )

2jk

P PV k v e d


ωω

2ω

2ωTest point 2D motion: ( ) ( )k

jkP P

k

v V k e


Test point 2D motion: ( ) ( )k

jkP P

k

v V k e

1: (1),drift between the test point and the rotation center.Pk V

0 : (0), the spindle rotation average point drift.Pk V

0,1: ( ) is independent of test point seleciton

such as ( 1), (2), ( 2), (3), ( 3),

(4), ( 4),......

P

P P P P P

P P

k V k

V V V V V

V V

Spindle rotation average point: the intersection between the spindle axis average line and the radial plane at the specified axial location

Spindle rotation center: the intersection between the spindle axis of rotation and the radial plane at the specified axial location

PRECISIONMECHATRONICSLABORATORY2: SPINDLE ERROR MOTION

0,1

Spindle 2D motion: ( ) ( )k

jkP

kk

V k e

( )

0,1

Spindle motion along a particular radial direction of interest:

( ) Re ( ) = Re ( )k

j j kP

kk

e V k e


3: SPINDLE ERROR MOTION EFFECT ON APPLICATIONS

0,1

ae( ) ( ) ( ) jkp

kk

V k e

0

0( 1)

0,1,2

ae( ) ( ) Re[ (2) ]

Re ( )

jp

j kp

kk

V e

V k e

Applications with single rotating sensitive direction:

Applications with two sensitive directions:

0

0

0,1, 1

ae( ) ( ) Re[ ( 1) ]

Re ( )

jp

j kp

kk

V e

V k e

Applications with single fixed sensitive direction:


ONCE-PER-REVOLUTION RADIAL MOTION

The perfect spindle A spindle with once-pre-revolutionradial error motion

X

Y

( ) 0; ( ) 0c cx y ( ) cos ; ( ) sinc cx y

X

Y


E-BEAM ROTARY WRITING MACHINEA spindle with once-pre-revolution

radial error motion( ) cos ; ( ) sinc cx y


E-BEAM MACHINE WITH MULTI-TOOLS

Produced pattern on a once-per-rev error spindle

-10 -5 0 5 10-10

-8

-6

-4

-2

0

2

4

6

8

10

-10 -5 0 5 10-10

-8

-6

-4

-2

0

2

4

6

8

10

A spindle with once-pre-revolutionradial error motion

( ) cos ; ( ) sinc cx y


-10 -5 0 5 10-10

-8

-6

-4

-2

0

2

4

6

8

10

MUTLI-TOOL BORING WITH K=2 ERROR

A spindle with K=2 radial error motion:

0

0

( ) cos(2 ),by R. Donaldson, 1972

( ) sin(2 )c

c

x x

y y

Produced holes


MUTLI-TOOL BORING WITH K=2 ERROR

A spindle with K=2 radial error motion:

-10 -5 0 5 10-10

-8

-6

-4

-2

0

2

4

6

8

10

Produced holes

0

0

( ) cos(2 ),by R. Donaldson, 1972

( ) sin(2 )c

c

x x

y y

PRECISIONMECHATRONICSLABORATORYANOTHER EXAMPLE

0

0

( ) cos( ) cos(2 ) cos(3 )

( ) sin( ) sin(2 ) sin(3 )c

c

x x

y y

2 3( ) j j je e e

,

,

,

Fixed X direction: ( ) cos(2 ) cos(3 )

Fixed Y direction: ( ) sin(2 ) sin(3 )

Rotating direction: ( ) 0

X ANSI

Y ANSI

ROTATING ANSI

Spindle Error Motion:

ANSI/ASME B89.3.4M


APPLICATIONS WITH 2 SENSITIVE DIRECTIONS

•Machining/measuring axis-asymmetric patterns

•Machining/measuring axis symmetric pattern with multiple tools installed at different radial directions

PRECISIONMECHATRONICSLABORATORYEXPERIMENT 1


BALL MOTION MEASUREMENT, 4000 RPM

PRECISIONMECHATRONICSLABORATORYERROR MOTION ACROSS SPEEDS

PRECISIONMECHATRONICSLABORATORYSTRUCTURE STIFFNESS

PRECISIONMECHATRONICSLABORATORYEXPERIMENT 2


BALL MOTION MEASUREMENT AT 500 RPM


ERROR MOTION ALONG X AT 500 RPM


V(-1) ERROR MOTION ACROSS SPEEDS

PRECISIONMECHATRONICSLABORATORYCONCLUSIONS

Purpose ANSI/ISO specifications 2D method

Error motion

along single fixed direction along single rotating direction In two dimensions

Application errors

Application with single fixed sensitive direction Application with single rotating sensitive direction Application with two sensitive directions

A new method for characterizing spindle radial error motion a two-dimensional point of view

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