Static and Dynamic Analysis of Machining Fixtures

8/11/2019 Static and Dynamic Analysis of Machining Fixtures

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Static and Dynamic Analysis ofStatic and Dynamic Analysis ofMachining FixturesMachining Fixtures

Bo Li , Graduate Research Assistant

Shreyes N. Melkote , Assistant Professor

The George W. Woodruff School of Mechanical Engineering

Georgia Institute of Technology

Sponsors: Ford Motor Company, MTAMRI


2/15

IntroductionIntroduction

Fixtures are devices used to locate and hold a

workpiece accurately during machining process.

3-2-1 Fixturing Scheme

L1 - L6 Workpiece-fixture locator

C1 - C2 Workpiece-fixture clamp

MX

-MY-M

ZMachining forces

Xg-Yg-Zg Inertial coordinate system

C1

L3

workpiece

Zg

OYg

Xg

L2

L1

OC2

L4

L6

L5

MX

MY

MZ


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Introduction (Introduction (contcont.).)

Typically, the workpiece rotates and translates in

machining fixture due to localized deformation ateach workpiece-fixture contact. This impacts the

part quality.

Xg

Zg

Yg

O

workpiece

w

y

w

x

w

z

w

Y

wX

wZ

Desired Position

Actual Position Workpiece Translation and RotationWork

piece Translation and Rotation


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Overall ObjectiveOverall Objective

Predict contact forces in the normal and tangentialdirections due to clamping and machining loads;

Investigate the workpiece rigid body motion in the

machining fixture and its impact on final partquality.

Predict the onset of undesired slip and loss ofcontact at workpiece-fixture interface duringmachining.


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Static indeterminacy in rigid body analysis can be

resolved by including the workpiece-fixturecontact compliance.

At each contact patch, normal force andtangential force are

discretized into

small components.

Undeformed Workpiece/ Fixture ElementContact

Static ModelStatic Model

x

Z

Fixture Element

Workpiece

1

i

2

i

k-th point

P

Initial Separation

P


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Static Model (Static Model (contcont.).)

Min WS.t. (1) Static equilibrium (2) Coulombs friction law (3) Non-negative normal force

The elastic deformation in the normal and

tangential directions is a linear summation of theinfluence of all forces components acting on thispatch.

The minimum total complementary energyprinciple is used to solve the contact problem.

W=0


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Experiment WorkExperiment Work

Static model verification: Normal force at each

fixture-workpiece contact is measured using apressure sensitive film (Fuji prescale film).

L4 L5

L6 L7

L1

L2

L3

C1

C2

Zg

Xg

Yg

5.03N

544.43N 7.80N

631.53N

631.53N 11.92N7.71N

357.02N

238.77N

Transducer

Locator

Workpiece

Locators

Clamp #1

Clamp #2Baseplate

63.5

P i

Qyi

Qxi

Xg

Yg

Normal force and actual contact area mapNormal force and actual contact areamapExperimental setup (top view)Experimental setup (top view)


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Experiment Work (Experiment Work (contcont.).)

Normal force:The maximum relative error for theside locators ranges from 2%to 10%for threedifferent sets of clamping forces. The absolute errorfor the bottom locators ranges from 0.12 Nto 1.29

N. Tangential force: The maximum absolute prediction

errors are 5.93Nfor X component and 0.57 N for Ycomponent at locator L3.

It is apparent from the above comparisons that themodel performs well under different clampingforces.


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Dynamic ModelDynamic Model

Lumped linear stiffness model.

Inertial effects are considered.

Kyi

Kxi

Kzi

workpiece

locator/clamp

xi

zi

yi

o

xi-y

i-z

i Local Coordinate at the i-thContact

Lumped stiffness is a function of: (1) workpiece-fixture material properties.

(2) workpiece-fixture contact geometry.

(3) clamping and machining loads.


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Dynamic Model (Dynamic Model (contcont.).)

Newton-Euler equations of motion

Machining

forces M(t)

P

T

Stick/slip

(Coulomb friction)

P

P

h

Complementary

contact

(P 0, h 0, hP=0)

Workpiece rigid body motion q(t)


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Dynamic Model SimulationDynamic Model Simulation

Intermittent contact andstick/slip transition at clamp C1

25.4mm wide slot machining condition:(1) spindle speed = 660rpm; (2) axial

depth of cut = 6.35mm, (3) feed rate = 7.6mm/sec. (4) clamping force c1=

266.88N, c2= 889.60N.

Contact break region Slip region Stick region

0

5

10

15

20

25

30

35

40

45

50

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5friction force normal force ratio

Sampling #

Friction

&n

ormalforce(

Friction

&n

ormalforce(N)

N

)

Ratiobetw

eenfriction&n

ormalforce

Ratiobetw

eenfriction&n

ormalforce


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14/15

ConclusionConclusion

The static model can accurately predict the

magnitude of the inwardly directed normal forces,and the magnitude and direction of the tangentialforce at each contact patch.

Localized deformation at each contact and the

workpiece rigid body motion due to the staticloading can be determined.

The dynamic model can predict the workpiece rigid

body motion in the fixture due to dynamic loadingwhile explicitly accounting for contact/no contactand stick/slip conditions.


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Ongoing/Future WorkOngoing/Future Work

Incorporate the impact of frictional damping andother energy dissipation mechanisms into themodel.

Eliminate the workpiece-fixture system vibrationdue to the dynamic loading through proper frictiondamping.

Develop an efficient fixture design strategy to yieldthe optimum fixture layout and correspondingoptimum clamping force(s) based on dynamic

model.

Static and Dynamic Analysis of Machining Fixtures

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