page 387

60. ELECTRON BEAM MACHINING

•The basic physics is an electron beam is directed towards a work piece, the electron heat and vaporize the metal.

•Typical applications are,

-annealing

-welding

-metal removal

•electrons accelerated with voltages of approx. 150,000V to create velocities over 200,000 km/ sec.

•beam can be focused to 10 to 200 micro m and a density of 6500 GW/mm2

•good for narrow holes and slots.

e.g. a hole in a sheet 1.25 mm thick up to 125 micro m diameter can be cut almost instantly with a taper of 2 to 4 degrees

•the electron beam is aimed using magnets to deflect the stream of electrons

•a vacuum is used to minimize electron collision with air molecules.

•beam is focussed using an electromagnetic lens.

ASIDE: Power density available from different processes power density (W/mm2)

108	electric discharge
106	laser beam
			electron beam
104
			welding arc
102				gas flame
1				feature size ( m)
10	102	103	104	105

page 388

• The process looks like,

	cathode	hot tungsten
-		emits electrons
+	anode
		electromagnetic lens
		electron beam
vacuum chamber
(10-5 mmHg)		beam deflector
	workpiece

• Some examples of cutting performance are given below,
	EBM DRILLING EXAMPLES
	material		workpiece		Hole		Drilling		Accelerating		Beam
			thickness		diameter		time		Voltage		Current
			(mm)		(micro m)		(sec)		(KV)		(micro A)
	tungsten		0.25		25		<1		140		50
	stainless steel		2.5		125		10		140		100
	stainless steel		1.0		125		<1		140		100
	aluminum		2.5		125		10		140		100
	alumina (Al2O3)		0.75		300		30		125		60
	Quartz		3.0		25		<1		140		10

page 389

	EBM SLOT CUTTING EXAMPLES
	Material			Workpiece Slot				Cutting		Accelerating	Average
				thickness			Width	Speed		Voltage	Beam
				(mm)			(micro m)	(mm/min)		(KV)	Current
											(micro A)
	Stainless steel			0.175			100	50		130	50
	tungsten			0.05			25	125		150	30
	brass			0.25			100	50		130	50
	alumina			0.75			100	600		150	200
• typical energy requirements for cutting are,
		Material					C (W/mm3/min)
		Tungsten					12
		Fe					7
		Ti					6
		Al					4

•e.g. to cut a 150 micro m wide slot in a 1mm thick tungsten sheet, using a 5KW power source, determine the cutting speed.

-assume speed is v mm/min

-Q = 150/1000 * 1 * v mm3/min

-beam power P = CQ = 12 ( 150/1000) v = 5000 therefore, v = 46 mm/sec

•Basic mechanics,

page 390

Me = 9.109×					10–31kg		electron properties
C = 1.602× 10–19 coulombs
	1			2	2
E =	--M	e	( u		– u ) e V		potential field accelerated through
	2				o

electron charge

final velocity

initial velocity

electron with energy E

vacuum

	material	transparent layer

total range

δ

the electron travels through the vacuum until it strikes the material. They generally penetrate the top layer, then become trapped in some layer beneath the surface.

δ = 2.6× 10		–17 V2
		-----
		ρ ( mm)
V =	Accelerating potential (V)
ρ =	material density (kg/mm3)

• e.g.

page 391

When drilling steel with EBM an accelerating voltage of 150KV is used. What is the electron range?

ρ	= 76× 10	–7		kg
				----------
				mm3

δ× –17 150× 103 2 µ

=2.6 10 -------------------- mm = 77 m

76× 10–7

•the heat rise can be estimated using a one dimensional heat flow equation

∂θ( z, t)	=	α∂ 2θ ( z, t)	1
∂t		∂z2	+ Cp H( z, t)
-----------------		------------------------	-----

θ= temperature of metal

α= thermal diffusivity

z	= distance from surface
t	= time
Cp = specific heat of metal
ρ	= metal density
H( z, t)			= heat source intensity
H( z)		= Ae–bz
		A =		constant
		b =		constant of energy absorption by the metal
	∂θ( z, t)		=	α∂ 2θ ( z, t)	+	A	e	–bz
	-----------------∂t			------------------------∂z2		ρ---------Cp

page 392

now assume,

1.the metal body is semi-infinite

2.the surface of the metal is insulated, except for the hot spot

3.the heat H(z) remains constant over time

longer pulses lead to the
hot spot near the surface
theta
			τ 3 large
			pulse durations
			τ 2 medium
			τ 1 short
Z3	Z2	Z1	z
• We can estimate the melting temperature with,

		P
Z = 0.1	------------------------------
	θ	m kdvρ Cp

• e.g.