Precision Engineering Center

COMPENSATION OF TOOL FORCES INSMALL DIAMETER END MILLS

Thomas Dow, Edward Miller, Kenneth Garrard and Alexander Sohn

Precision Engineering Center,North Carolina State University

Thomas WrightEastman Kodak Co

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Miniature Milling Tools

• BACKGROUND– Tool Diameter less than 1 mm

– Length from 1- 12 mm

– Needed to create small features in hard steel

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SC+OPE

• DEVELOP TOOL FORCE MODEL

• DEVELOP TOOL DEFLECTION MODEL

• CREATE COMPENSATION TECHNIQUE

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CUTTING/THRUST FORCES

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TOOL FORCE MODEL

• DRESCHER/ARCONA MODEL

–Cutting and Thrust forces (friction)

–Function of tool rotation angle

–Function of tool geometry

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TOOL FORCE COMPONENTS

Width of wear land

Local chip thickness

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MEASURE TOOL FORCE

• HIGH SPEED MILL– 60,000 rpm

– Mounted on DTM

– Position resolutionless than 10 nm

• 3-AXIS LOAD CELL– X,Y, Z forces

– Average force overseveral rotations

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FORCE COMPARISON

r,θ,z x,y,z

Transformation

Compare

x,y,zdata

0

1

2

3

4

5

0 50 100 150 200 250 300 350 400

F_cuttingF_thrust

Forc

e, N

angle, deg

-3

-2

-1

0

1

2

3

4

5

0 50 100 150 200 250 300 3

FxFyFz

Forc

e, N

angle, deg

-3

-2

-1

0

1

2

3

4

5

0 50 100 150 200 250 300 3

FxFyFz

Forc

e, N

angle, deg

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TOOL FORCESUpfeed = 10 µm/fluteDepth = 25 µmSpeed = 40,000 rpm

-3

-2

-1

0

1

2

3

4

5

0 6 0 120 180 240 300 360

F xFyF z

Fx_expFy_expFz_exp

Fo

rce,

N

Tool rotation angle, degrees

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TOOL FORCESUpfeed = 25 µm/fluteDepth = 100 µmSpeed = 10,000 rpm

-20

-10

0

1 0

20

30

0 6 0 120 180 240 300 360

F xFyF z

Fx_expFy_expFz_exp

Fo

rce,

N

Tool rotation angle, degrees

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TOOL DEFLECTION

z

y x

Feed Directio

Tilt angle

Tool Rotation(Clockwise viewed from above)

• TOOL DEFLECTIONEXPERIMENTS

– Slot with increasingdepth

– Thrust force reducesdepth of cut

– Stiffness depends ontilt of tool

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50 deg tilt (no compensation)

0

10

20

30

40

50

60

70

80

0 5 10 15 20

Measured depth, µmModeled Depth, µmDesired Depth, µm

Dep

th o

f G

roov

e, µ

m

Distance,mm

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50 deg tilt (compensation)

0

10

20

30

40

50

60

70

80

0 5 10 15 20

Measured depth, µmModeled Depth, µmDesired Depth, µm

Mea

sure

d de

pth,

µm

Distance,mm

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COMPENSATION EXPERIMENT

• Cut 0.5 mm deepgroove with 1.5 mmradius ball end mill

• Remove 0.1 mm using0.4 mm radius ball mill (sweep angle ± 50 deg)

• Compensate for tooldeflection in y-z plane

+Z

+Y

+XThrustForce andToolDisplacement

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TOOL FORCE DIRECTIONS

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Groove with Short Tool

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

- 5 2 - 4 4 - 3 6 - 2 8 - 2 0 - 1 2 - 4 4 1 2 2 0 2 8 3 6 4 4 5 2Sweep Angle (deg)

Err

or

(mm

)

Measured Groove SA Measured Groove NCSUncompensated Deflection Model

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Groove with Long Tool

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

-52 -44 -36 -28 -20 -12 -4 4 12 20 28 36 44 52Sweep Angle (deg)

Err

or

(mm

)

Measured Groove A Uncompensated Deflection Model Measured Groove LA

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Groove - Extra Long Tool

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

-52 -44 -36 -28 -20 -12 -4 4 12 20 28 36 44 52Sweep Angle (deg)

Err

or

(mm

)

Measured Groove NCXL Uncompensated Deflection Model Measured Groove XLA

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Compensated GrooveExtra Long Tool

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

-52 -44 -36 -28 -20 -12 -4 4 12 20 28 36 44 52Sweep Angle (deg)

Err

or

(mm

)

Measured Groove NCXL Measured Groove XLA Compensated Data

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Best Fit Radii (1.6 mm)

- 0 . 1

-0 .08

-0.06

-0.04

-0.02

0

0.02

100000 200000 300000 400000

Uncompensated Error, mmCompensated Error, mm

Err

or in

the

bes

t-fit

rad

ius

to

the

mac

hine

d gr

oove

, mm

Tool Stiffness, N/mm

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CONCLUSIONS

• CUTTING FORCES ARE PREDICTABLEAND REPEATABLE

• TOOL DEFLECTIONS CAN BECALCULATED AND COMPENSATED

• OPEN-LOOP MODEL CAN BE USED TOIMPROVE THE SHAPE OF SMALLFEATURES

• LIMITATIONS INVOLVE TOOL SHAPE ANDTOOL WEAR