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57. ULTRA SONIC MACHINING (USM)

•First built 1950s.

•Originally used for finishing EDM surfaces.

•Best suited to poorly conducting materials, and brittle materials.

•The basic process is a ductile and tough tool is pushed against the work with a constant force. A constant stream of abrasive slurry passes between the tool and the work to provide abrasives and carry away fractured particles. The majority of the cutting action comes from an ultrasonic (cyclic) force applied in addition to the other force.

tool

			fx = 20 KHz
Ffeed
		x	Ax = 15-20 micro m

abrasive slurry

work

•The basic components to the cutting action are believed to be,

1.The direct hammering of the abrasive into the work by the tool (major factor)

2.The impact of the abrasive on the work

3.Cavitation induced erosion

4.Chemical erosion caused by slurry

•M.C. Shaw generated a model to estimate the cutting action.

Q	vZf
Q = volume of work material removal rate
v =	volume of material removed per particle imapct
Z =	number of particles impactingpercycle
f =	frequency (cycles per second)

• Consider the impact pictured below.

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grain impact

work
d/2	h	d/2	d/2-h
		D/2

				D
D 2	=	d 2	–	d	2
---		--		--	– h
2		2		2

D2 = 4dh – 4h2

assume the impact depth ‘h’ is small compared to d.

D ≈ 2dh

now assume

D3(volume) v(volume per impact)

	3	3
Q vZf D3Zf	--	--
	( dh) 2	( dh) 2 Zf

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Also assume the force is as shown below,
+	T/4
	approximate with triangle
	Fimax
	delta T
	Fstatic
-	T
	-ve force means no contact, and no force to abrasive

F =

1

T

--∫ Fi( t) dt

T

0

or F ≈

1

1

--F ∆

t--

2

imax

T

tool

A

tool at highest

point

B

tool at mid position

C

tool touches grain

D

tool pushes grain

to lowest point

work

When the tool has pushed the grain to the lowest point, the tool-grain-work interface looks like,

page 357

ht

D							hw

The total indent is therefore

h = ht + hw

If A is the amplitude of oscillation of the tool, the average velocity from B to D is,

vB → D ≈	A
	--------
	T
	--
	4

∆

t ≈

dist·

h

1

T

=

ht + hw

T

--------- =

--

--

----------------

--

vel

A

4

A

4

F ≈

Fimax ∆ t

Fimax

ht

+ hw

T 1

---------- ----

----------

----------------

----

2 T ≈

2

A

4 T

8FA

Fimax ≈ ----------------

ht + hw

This force is applied to 2 grains to give a force per grain

		=	Fi
F			max
	g		----------
			Z
The contact area per grain is
				D	2
Ag = π				---	= π dhw
				2

Therefore the maximum stress is

σ w	=	Fimax	=	Fg	=	8FA
		π----------------Zdhw		-----		π--------------------------------------Zdhw	( hw	+ ht)
				Ag

Assume that the depth of penetration is inversely proportional to the flow stresses (this is reasonable if the other forces and geometries remain constant)

	h	1
		--			tool/work indentation ratio
		σ	σ
	ht	=		w	λ
	-----		------ =
	hw		σ	t

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Flow stress sigma and Brinell hardness H are the same so,

hw2 =	-----------------------------------8FA
	π ZdHw( 1 + λ )

We can assume the number of grains per impact is,

			C
	Z = χ		----
			d	2
	C =	concentration of grains yurinlshet
	χ =	constant of proportionality
	thus hw		=		8FAd
					πχ------------------------------------HwC( 1 + λ )

further

Q		d8FAd
		π--------------------------------HwC( 1 + λ )

3

--

2χ

C

----f d2

3	1	3	1
--	--	--	--

Q	A4 d4 F4 C4
	-------------------------f
	3
	--
	Hw4

•Material is also removed by grains moving quickly and building up kinetic energy. When they strike the work surface, they transfer their energy quickly causing surface work. This effect is smaller than hammering.

•The grains are not actually perfectly spherical, and as a result smaller rounds actually lead to faster machining.

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actual

d4

d

d3

theoretical

d2

d1

we can approximate d1 = d*d and

use d1 in place of d for the calculations

(all units in mm)

The relationship has been experimentally determined to be more like,

	3	3	1
	-- -- --
Q	dF4 A4C4
	---------------------------f
	3		3
	--		--
	Hw4 ( 1 + λ ) 4			theory
mrr (Q)
				actual
				feed force (F)
mrr				mrr
				theory

fincreases

actual

f

A

• mmr decreases when static force F gets high enough to crush abrasive grains.

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mrr

A increases

F (feed force)

mrr

lambda = tool/work hardness

• f = 16.3 KHz, A = 12.5 micro m, grain = 100 mesh.

work material	relative mrr
glass	100.0
brass	6.6
tungsten	4.8
titanium	4.0
steel	3.9
chrome steel	1.4

• If d approaches A the grains start to crush.

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mrr		mrr
	theory
		B4C
	actual	SiC
	d	C (abrasive concentration %)
	1.0

relative mrr
	0.25
	0.2		0.8	viscosity (poise)
	100
			glass
average	75
surface
roughness
(micro m)	50
	25		tungsten carbide
	50	100	150

mean grain dia. (micro m)

• Example - Find the machining time for a hole 5mm in diameter in a tungsten carbide plate 1cm thick. The grains are .01mm in diameter, the feed force is 3N, and the amplitude of oscillation

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is 20 micro m at a frequency of 25KHz. The fracture hardness is approximately 6900N/mm2. The slurry is mixed in equal parts water and abrasive.

											volume = 1
							a				a
Therefore,
		d=.01 * 10-3 m			a
		F = 3N
		A = 20 * 10-6 m
		f = 25 KHz
		H = 6900 * 106			N/m2
		w						d
			3
	2		--				tool gap b = d
Q =		π ( dH )	2	Zf
	--						N cubes in contact area
	3	w

hw	≈	8FA		a	3	= N	4	π r	3
		-------------------------------------					--
		π Zd1Hw	( 1 + λ )				3
We still need Z, d1, lambda, therefore find with,
Z ≈	1 4a2		assumes a square hole
	-- --------
	2 π	d2

λHw

=------ = 5(assumed)

Ht

d1 = d2 (mm)

Therefore Z = ?????, hw = ?????????, Q = ?????????? mm3/sec considering the volume of the hole, the required time is,

	V		5mm	2	( 1cm)
		π	2
			-----------
t =	---	= ---------------------------------------			=
	Q		????

• Basic machine layout,

page 363

feed
mechanism
position indicator	manual drive
	machine body
acoustic head
tool	slurry pump
work
work table	slurry tank
ultrasonic drilling machine

•The acoustic head is the most complicated part of the machine. It must provide a static force, as well as the high frequency vibration

•The magnetostrictive head is quite popular,

page 364

	20KHz and up
	signal
	generator
cooling fluid	magnetic core with
	windings

Basic Idea - the coil induces a
vibration when the alternating
magnetic filed reverses	resonant concentrator
	tool

For magnetostrictive head,

λc 1 E

=- = -- --

f f ρ

•Magnetostrictive materials should have a good coupling of magnetic and mechanical energy,

Kr	Ew
	= ------
	Em

where,

Ew = mechanical energy Em = magnetic energy

material	coeff.magnetostrictive	coeff. of
	elongation 10**6 (Ems)	magnetomechanical
		elongation, Kr
Alfer (13% Al, 87% Fe)	40	0.28
Hypernik (50% Ni, 50% Fe)	25	0.20
Permalloy (40% Ni, 60% Fe)	25	0.17
Permendur (49% Co, 2% V, 49% Fe)	9	0.20

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•The vibrating head is supplied with a constant force using,

-counter weights

-springs

-pneumatics and hydraulics

-motors

counterweight

counterweight and pulley

counterweight with lever and fulcrum

fulcrum system

counterweight

electric solenoid control

core and solenoid coil

page 366

spring control

hydraulic (pneumatic) control

•If a tool is designed to increase flow, better cutting speeds will occur.

•Tools

-hard but ductile metal

-stainless steel and low carbon

-aluminum and brass tools wear near 5 to 10 times faster

•Abrasive Slurry

-common types of abrasive

-boron carbide (B4C) good in general, but expensive

-silicon carbide (SiC) glass, germanium, ceramics

-corundum (Al2O3)

-diamond (used for rubies, etc)

-boron silicarbide (10% more abrasive than B4C)

-liquid

-water most common

-benzene

-glycerol

-oils

-high viscosity decreases mrr

-typical grit size is 100 to 800

•Little production of heat and stress, but may chip at exit side of hole. Sometimes glass is used on the back side for brittle materials.

•Summary of USM characteristics

-mechanics of material removal - brittle fracture caused by impact of abrasive grains due to vibrating at high frequency

-medium - slurry

-abrasives: B4C; SiC; Al2O3; diamond; 100-800 grit size

-vibration freq. 15-30 KHz, amplitude 25-100 micro m