Jackson M.J. Micro and Nanomanufacturing

Подождите немного. Документ загружается.

Meso-micromachining 181

Fig. 4.26.

[15]

A specimen with uniform distribution of points of stress concentration

In this strain gradient theory two types of dislocations are pro-

posed: geometrically necessary dislocations (pg) that are responsible

for work hardening and statistically stored dislocations (ps) that are

affected by a strain gradient. When pg»ps conventional plasticity

pertains (strain rate unimportant) but when pg«ps a constitutive

equation including strain rate should be included.

The impression one obtains in reading Dinesh et al [39] is that

the strain gradient approach is uniquely responsible for the size ef-

fect in cutting. In their concluding remarks it is suggested that it

should be possible to verify the validity of the strain rate formulation

by experiments designed to test predictions of this approach. This

has not yet been done and until it is it will not be possible to deter-

mine whether the influence of strain rate is significant in the chip

formation application. In any case, it is believed the explanation pre-

sented here based on the influence of defects and normal stress on

the shear plane is sufficiently well supported by the experiments de-

scribed that it should not be considered insignificant.

182 Micro- and Nanomanufacturing

4.6 Meso-Micromachining Processes

There is already a growing trend to develop microcutting proc-

esses whose effectiveness may be curtailed because of the size ef-

fect. At present, these processes are in an embryonic phase of devel-

opment. These processes offer the ability to machine engineering

materials other than silicon for use in MEMS components. The

overall development of these miniature machine tools will clearly be

affected by the nature of machining at the microscale and the size ef-

fect. The physical processes that are of secondary importance at the

conventional scale dominate at the microscale. Examples include

the size of the cutting tool being smaller than the individual grains in

the material being machined, the resulting large cutting tool edge ra-

dius producing very large plowing forces, and the reduced stiffness

of the tool rendering very pronounced dynamic effects at the micro-

scale. These effects will result in the development of: (a) mechanis-

tic models for multi-phase materials; (b) molecular dynamic models

of chip formation in milling; and (c) micro drilling dynamic models.

4.6.1 Mechanistic IVIodel Development for IVIulti-Phase

IVIaterials

A mechanistic force model for the micro milling of multi-phase

materials has been developed [40]. The model considers the various

phases in a material, for instance, ductile iron is composed of ferrite,

graphite, and pearlite. Secondary and tertiary phases are modeled as

spheres in determining the magnitude and size of cutting force (Fig.

4.27). These spheres are randomly generated and are located near to

grid points in the model matrix.

The grid point spacing and the radii of the spheres are chosen

to approximate the volumetric composition of the workpiece being

machined. Through simulations it was shown that frequency of the

variation in machining is attributed to the spacing of the second

phase. The second phase clearly has an impact at the microscale and

at the mesoscale. The model was validated by constructing work-

pieces made from the constituents of ductile iron. It was found that

up to 35% of the energy consumed was due to cutting.

Meso-micromachining 183

:1_

'N-

y'-:.„^;^;jv«y

ItHttlM^'hl

(a)

(U)

(c)

Fig. 4.27. Microstructure of ductile iron: (a) ferrite; (b) pearlite; and (c) pearlitic-

ferritic ductile iron

184 Micro- and Nanomanufacturing

Fig. 4.28. Machined ferrite workpiece

Slots were machined in ferrite and are shown in Figure 4.28. Ini-

tial experiments on aluminum created burrs and the edge condition

of the tool confirmed the generation of burrs. Peak cutting forces

ranged from 300 mN to 3N when the tool rotated at 120,000 rpm

with a feedrate of

microns per tooth and a depth of cut of 50 to 100

microns. The measured waviness had a wavelength of 20 microns

with feed marks with a period of 4 microns.

4.6.2 Molecular Dynamics Models for Micromilling

Numerical simulations have been carried out that determine the

mechanisms of chip formation when the uncut chip thickness is

much smaller than the edge radius of the cutting tool [41]. When

cutting aluminum, material is removed when the depth of cut is

about one half of the radius of the cutting edge (Figure 4.29). The

size of the cutting tool and the geometry is shown in Figure 4.30.

Meso-micromachining 185

The surface roughness shown on the surface of aluminum is shown

in Figure 4.31.

(1) T,R =0.125

\ (2)T,.'VO-25

(4)

T.'R_.=0.5

Fig. 4.29. Molecular dynamic simulations of chip formation in meso-

micromachining

L :

Fig. 4.30. Scanning electron micrograph of micromilling tools

186 Micro-and Nanomanufacturing

Fig. 4.31. Micrographs of the milled slot in aluminum

4.6.3 Micro Drilling Dynamic Model

A mechanistic force model for micro drilling has been developed

that considers the influence of tool grinding errors [42], errors in

torque, and the dynamic characteristic of cutting force components.

The model considers the skidding or wandering of the tool with re-

spect to the center of

the

cut at the initial contact. The ability to pre-

dict this behavior is critical in assuring the ability to machine holes

at the microscale. A comprehensive set of experiments has been

conducted that verify the accuracy of the models [42]. A set of ex-

perimental values of the predicted bahavior is shown in Figure 4.32.

Meso-micromachining 187

C loo!

Kporimo

.1..0...

datii

^ uu

-4xp«r.mn

-.- =

•ntitnlnti

.l„lrt«M

:.r„„

/'"^

•^v-r

y..y-~

y—vr

c^"'^^

>v..Vj

0,1 0.2 0.3 O.* 0.5 0.6 O O.I 0.2 0,3 0.« 0.5 O.C

Tifn.

{«)

Tim*

(s)

(a) Drilling torque and thrust force

^ aKpsrtm«ntn] dun

- itfnLiifliBil

'Mi;

IIV

Bin

ejmulntotllclaLn

^aill

iff

ill

vy'

4^1

0.1 0,2 0.3 0.4 0.5 O.e 'O 0.1 0.2 0.3 0.4 O.S 0.

Tirrm

{*>

Tlin«

(s)

<b) Drilling radial forces Fj< and f^v

i/ir^^

^^vx VV**^'^

J -0 2

0.4 0.6 O.H -0.2 0 1 0 0,1 0 2 0,3

^'A

f'l/i

„

% 0

0.2

D3 D.4 0.3 O.O 0.7 -0.2 -D.I O

0 1 0 2

Timo

fs)

Transvar»a <l*t(»cUon

DX (mm>

(d) Simulatod drill tip wandoring and its orbit

5 -1

1 '2

^('(

^<r^-

'(^'

^v::z

-^-

zir^^^

^ilSS^

Fig. 4.32. Comparison of predicted and measured micro-drilling process variables

in the presence of initial drill contact errors

188 Micro-and Nanomanufacturing

4„7 Problems

What are size effects in micromachining processes?

Explain the variation in specific energy required to grind

small chips of material.

What is the shear stress required to micromill SAE 1112

steel at a depth of cut of 0.001 inches?

Explain the mechanism of slip in polycrystalline metals.

Explain the mechanism of slip in single crystal metals.

6. Calculate how shear plane angles can be predicted.

Does a shear plane zone occur in micromilling?

8. Describe Langford's and Cohen's model of plastic behavior

at large strains.

9. Explain saw-tooth chip formation in hard turning.

10.

What effect does CCI4 lubricant have on chip formation?

11.

Describe Eugene's experimental apparatus to describe fluid-

like flow in metal cutting.

12.

Describe the mechanism of large plastic flow and how it may

affect burr formation at the microscale.

13.

What is inhomogeneous strain?

14.

Briefly describe the origins of

the

size effect.

15.

What special problems does the size effect have on mi-

cromilling?

References

Backer WR, Marshall ER, and Shaw MC, 1952, Trans. ASME, 74,

p.61

Taniguchi N, 1994, Precision Engineering, 16, 5-24.

Shaw

MC,

1952, J. Franklin Inst., 254,2,109.

Heidenreich RO, Shockley W, 1948, Report on Strength of Solids,

Phys.

Soc. of London, 57.

Emst HJ, Merchant ME,

1941,

Trans. Am. Soc. for Metals, 29, 299.

6. Merchant ME, 1945, J. Appl. Phys., 16, 267-275.

Piispanen V, 1937, Teknillinen Aikakaushehti (Finland), 27, 315.

8. Merchant ME, 1950, Machining Theory and Practice, Am Soc. for

Metals, 5-44.

Meso-micromachining U

9. Merchant ME, 1945, J. Appl. Phys, 16, 318-324.

10.

Barrett CS, 1943, Structure of

Metals,

McGraw Hill Co., NY, 295.

U.Bridgman PW, 1952, Studies in Large Plastic Flow and Fracture,

McGraw Hill Co., NY.

12.

Langford G, Cohen M, 1969, Trans. ASM, 62, 623.

13.

V. Piispanen, 1948, J. Appl. Phys., 19, p.876.

14.

Blazynski TZ, Cole J M, 1960, Proc. Instn. of Mech. Engrs., 1, 74,

757.

15.

Shaw MC, 1950, J. Appl. Phys., 21, 599.

16.

Walker TJ, 1967, PhD Dissertation, Carnegie-Mellon University, PA.

17.

Walker TJ, Shaw M C, 1969, Advances in Machine Tool Design and

Research, Pergamon Press, 241-252.

18.

Usui E, Gujral A, Shaw MC 1960, Int. J. Mach Tools and Res., 1, 187-

197.

19.

Vyas A, Shaw MC, 1999, Trans. ASME-J. Mech. Sc, 21, 1, 63-72.

20.

Eugene F, 1952, Annals of

CIRP,

52,11,

13-17.

21.

Shaw MC, 1980, Int. Jour. Mech. Sc, 22, 673-686.

22.

Kwon KB, Cho DW, Lee SJ, Chu CN, 1999, Annals of CIRP, 47/1,

43-46.

23.

Eyring H, Ree T, and Harai N, 1958, Proc. Nat. Acad. Scs., 44, 683.

24.

Eyring H, Ree T, 1961, Proc. Nat. Acad. Scs., 47, 526-537.

25.

Eyring H, Jhon MS, 1969, Significant Theory of Liquids, J. Wiley and

Sons,

NY.

26.

Kececioglu D, 1958, Trans. ASME, 80, 149-168.

27.

Kececioglu D, 1958, Trans. ASME, 80, 541-546.

28.

Kececioglu D, 1960, Trans. ASME-J. Eng for Industry, 82, 79-86.

29.

Anderson TL, 1991, Fracture Mechanics, CRC Press, Florida.

30.

Zhang B, Bagchi A, 1994, Trans. ASME- J. of Eng for Industry, 116,

289.

31.

Argon AS, Im J, Safoglu R, 1975, Metallurgical Transactions, 6A, 825.

32.

Komanduri R, Brown RH, 1967, Metals and Materials, 95, 308.

33.

Drucker DC, 1949, J. Appl. Phys., 20, 1.

34.

Fleck NA, Muller GM, Ashby M F, Hutchinson J M, 1994, Acta Met-

allurgica et Materialia, 41, 10, 2855.

35.

Stelmashenko NA, Walls M G, Brown L M, Milman Y V, 1993, Acta.

Metallurgica et Materialia, 41, 10:, 2855.

36.

Ma Q, Clarke D R, 1995, J. Materials Research, 46, 3, 477.

37.

Nix WD, Gao H, 1998, J. Mech. and Physics of Solids, 1,4, 853.

38.

Gao H, Huang Y, Nix W D, Hutchinson J W, 1999, Jour, of Mechanics

and Physics of Solids, 47, 1239.

39.

Dinesh D, Swaminathan S, Chandrasekar S, and Farris T N, 2001, Proc

ASME-IMECE,NY: 1-8.

190 Micro-and Nanomanufacturing

40.

Vogler M, DeVor R, Kapoor SG, 2001, Symposium on Modeling,

Sensing and Controlling Micro Machining Processes, IMECE

2001,

New York, USA.

41.

Kim, CJ, 2001, Cutting Mechanics and Surface Generation in Micro

Milling Processes, Ph. D. Thesis, University of Michigan.

42.

Gong Y and Ehmann K, Symposium on Modeling, Sensing and Con-

trolling Micro Machining Processes, IMECE 2001, New York,

USA.