DETAILED DOCUMENT ABOUT Electron Beam Machining

1. 19
Chapter 3
ELECTRON BEAM MACHINING (EBM)
3.1 INTRODUCTION
Electron beams are now used in many industrial types of equipment. They have many
special characteristics which make them most suited for specific applications. The most important
of These characteristics is the high resolution and the long depth of field that is obtained because
of the short wavelength of high energy electrons. Other features of the beams include their extra
ordinary energy (e.g. power densities of 106
kw/cm2
have been achieved) ability to catalyze many
chemical reactions, controllability, and compatibility with high vacuum. Electron beam
machining (EBM) can be classified into two types. In one, which can be termed ‘thermal type’,
the beam is used to heat the material up to the point where it is selectively vaporized. The other,
called ‘non-thermal type’ utilizes the beam to cause a chemical reaction. The ability of electron
beams to cause drastic thermal effects has been known since a long time. In the late 1930s it was
used for drilling the apertures of electron microscopes. In 1950, Steigerwald and his colleagues at
Carl Zeiss A.G. (Germany) developed an electron beam milling machine. E.B. Bas, in 1960,
made fine holes in ruby crystals. In attempting to drill holes in diamond, Steigerwald found that
the electron beam could raise the temperature of diamond to as much as 3000o
C even though
diamond tends to disintegrate into graphite at 2000o
C. by introducing oxygen into the vacuum
system, CO or CO2 could be formed at 300o
C, thus burning away the material which was not
possible to vaporize. The ability of low energy electrons to bring about a surface chemical
reaction was first observed and studied by P.H. Carr. Significant research in both thermal and
non-thermal EBM has since then been done by many researches.
As a metals-processing tool, the electron beam is used mainly for welding, to some extent
for surface hardening, and occasionally for cutting (mainly drilling). Electron beam
machining (EBM) is a thermal process that uses a beam of high-energy electrons focused
on the workpiece to melt and vaporize metal. This process shown in Figure 28-26 is
performed in a vacuum chamber (10-5 torr), The electron beam is produced in the

2. 20
electron gun (also under vaccum) by thermionic emission. In its simplest form, a filament
(tungsten) is heated to temperatures in excess of2ooo°C where a stream (beam) of
electrons (more than 1 billion per second) is emitted from the tip of the filament.
Electrostatic optics are used to focus and direct the beam. The desired beam path can be
programmed with a computer to produce any desired pattern in the workpiece. The
diameter of the beam is on the order of 0.012 to 0.025 mm, and holes or narrow slits with
depth-to-width ratios of 100:1 can be "machined" with great precision in any material.
The interaction of the beam with the surface produces dangerous X-rays; therefore,
electromagnetic shielding of the process is necessary. The layer of recast material and the
depth of the heat damage are very small. For micromachining applications, MRRs can
exceed that of EDM or ECM, Typical tolerances are about 10% of the hole diameter or
slot width. These machines require high voltages (50 to 200 kV) to accelerate the
electrons to speeds of 0,5 to 0.8 the speed of light and should be operated by fully trained
personnel.
A typical electron beam installation for drilling is shown in fig. 1. It consists of five basic units:
1) electron gun which generates and directs a controlled beam of electrons of high energy density
on the work material to change it chemically and physically,
2) Vacuum chamber and a high vacuum pump system,
3) Movable table with in the chamber for mounting the work piece,
4) An electronic system which controls the size and movement of beam and
5) A monitoring instrument.
3.2 GENERATION AND CONTROL OF ELECTRON BEAM
The electron beam is a stream of negatively charged particles which are generated,
accelerated, and to some extent, focused inside a device called an ‘electron gun’. The essential
constituents of an electron gun are:
a) A cathode, which serves as the source of electrons. It may be a current carrying, self
heating filament, or a solid block indirectly heated by radiation from a filament.
b) A grid cup, which is negatively biased with respect to filament.

3. 21
c) An anode which is kept at ground potential, and through which the high velocity
electrons pass.
The beam of electrons is emitted from the tip of the hot cathode. It is accelerated towards the
anode by the high potential applied between the anode and cathode. It passes through the anode at
a speed up to two-third of the velocity of light. The flow of electrons is controlled by the negative
bias applied to the grid cup.
A magnetic deflection coil fitted below the electron gun is used to make the electron beam
circular in cross-section and deflect it anywhere. The beam is generated in a high vacuum for two
reasons:
1) The emitter would rapidly oxidize when incandescent, at anything like atmospheric pressure,
and
2) The electrons would lose energy by collision with air molecules. The electron emitter with its
focusing coils is used at a vacuum of 10-4
or 10-5
torr.
A power density of as high a magnitude as a billion Watts/square cm can be attained in the
beam. This is sufficient to immediately fuse and vaporize any material n which it falls. Thus, in a
thermal type EBM, cutting is, in fact, a precisely controlled vaporization process.
The rate R at which the material is vaporized can be calculated by
R == η P/W (3.1)
Where η is the cutting efficiency, P is the power (J/s), and W is the specific energy required to
vaporize the material (J/cm3
) given as
W == Cp (Tm - 20) + Cp (Tb - Tm) + Hf + Hv
== Cp (Tb - 20) + Hf + Hv (3.2)
in which Cp is the specific heat, Tm is the melting temperature, Tb is the boiling temperature, Hf is
the heat of fusion and Hv is the heat of vaporization. The values of these terms for some metals
are given in table. The cutting efficiency is normally very low (2-20 per cent) and depends on the
cross-sectional area of the cut made.

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3.3 PHYSICAL AND THERMAL PROPERTIES OF METALS
Property
Metal
Melting
Temp.
Tm
o
C
Boiling
Temp.
Tb
o
C
Specific
Heat
C
cal/g/ o
C
Heat of
Fusion
Ht
cal/g
Heat of
Vaporization
Hv
cal/g
Specific
energy of
vaporization
W/ cm3
Iron 1536 3000 0.11 65 1514.8 06.3 * 104
Molybdenum 2610 5560 0.061 70 1340 07.5 * 104
Tungsten 3410 5930 0.032 44 1006 10.0 * 104
Titanium 1668 3260 0.126 36.7 222.3 05.0 * 104
3.4 THEORY OF ELECTRON BEAM MACHINING
3.4.1Thermal Type
The theory of thermal type of EBM has not yet been completely developed due to many
reasons. First, since the process has shown many practical results, no pressure has been put on the
researchers in the field to develop extensive theories or to make difficult analyses. Second,
although the individual physical processes involved are simple, their number, non-linearity and
complicated geometry, all combine to make a theoretical analysis of the process difficult. Third
the small dimensions, short time intervals, and lack of thermodynamic equilibrium make it
difficult to get the required experimental data for correlation with any theory.
3.4.1.1Forces in Machining
Since the temperature in the vicinity of the electron beam cause the material to be in
molten state, the material is acted upon by forces of surface tension, gravity, electron beam
pressure and the reaction force of the departing vaporized material. In machining non-conducting
materials, electrostatic forces may also be present. A study of these forces (Fig. 2) will be made
and the relationships established to find their magnitudes.

5. 23
(a) Electron Pressure: The pressure due to electron bombardment can be estimated from the
momentum loss suffered by the electron beam as it impinges upon the work surface.
fe= meve i/e
Where fe is the electron pressure (N/m2
), me the electronic mass, Ve the velocity (m/s),i is the
current density (amp/m2
) and e the electron charge. The velocity Ve can be calculated from the
accelerating voltage U as
Ve= (2 e U/me) ½
(3.3)
Thus fe= (2 me U/e)½
i (3.4)
The total force due to electron bombardment is
fe = Л r2
fe
= Л r2
(2 me U/e) ½
i
= (2 me U I2
/e)½
Where r is the radius of the hole and I is the total current.
(b) Back Pressure of Evaporating Atoms: The effect of momentum of the thermally
evaporating material can be studied by considering the conservation of momentum.
pa == mo va (3.5)
Where pa is the back pressure of evaporating atoms, mo the mass of material removed per unit area
of surface per unit time, va the atomic velocity given as
va == (2 k T/mp M)½
(3.6)
Because the average energy of particles evaporating from a surface is 2 kT, of which kT will be
in the direction normal to the surface. In the above equation, k is Boltzmann constant, T the
temperature, mp the proton mass and M the atomic weight. The total force exerted by the back
pressure is

6. 24
Fbp == m1 va (3.7)
Where m1 is the mass of material removed per unit time, provided the surface over which mo is
integrated to get m1 is plane.
(a) Surface Tension: The total force of surface tension, tending to close the cavity formed,
equals tension force (N/m length) times the circumference of the cavity, that is
Fs == fs .2 Л r (3.8)
Where r is the radius of the cavity of the hole produced. A force equal in magnitude will at the
same time resist the formation of a liquid lip at the top of the hole.
Surface tension has not been studied till now for liquid metals at such high temperatures as are
involved in EBM. However, the values are available for many metals near their melting points.
For gold, silver, copper etc, the values are in the range of 500-2000 dynes/cm.
(b) Hydrostatic Pressure of Molten Metal :The hydrostatic pressure due to the molten
surface on the side of the cavity being generated is
Fh == ρ g h (3.9)
and the total force exerted on the bottom of the hole towards the top is
Fh == ρ g h Л r2
(3.10)
Where ρ is the density of the molten metal (kg/m3
) g the acceleration due to gravity, h the depth
of the cavity, and r the radius of the cavity formed.
In the calculation with actual data, the hydrostatic force is normally very small and can be
neglected. The electron pressure force is the largest of all these forces but the other two forces are
also significant. If the surface tension force is larger than the atomic reaction force, molten metal
would tend to flow from the walls into the bottom of the wall, where it would be evaporated by
the beam; otherwise, if the reaction force is larger than the surface tension force (in case of big
holes), molten material would be pushed out of the hole.

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3.4.2 Non-thermal Type
` Christly, who has made an excellent study in this field, has put forward a phenomenological
theory which predicts the rate of film growth for the polymerization of organic films by electron
bombardment. His theory is summarized here.
Consider a surface on which a film is being deposited as a result of the polymerization of the
molecules arriving at the rate no per unit area per unit time by the action of electrons arriving at
rate ne per unit area per unit time. Further, let a denote the cross-section for reaction, τ the mean
time of stay of an interacted molecule on the surface. It can be assumed that a reacted molecule
remains on the surface permanently. Also, it is assumed that the initial surface is made up of
already polymerized molecules so that no anomalous surface effect takes place for the first layer,
then
dN1/dt == a no No (3.11)
and
dNo/dt == no - No/ τ – dN1/dt (3.12)
By solving these equations for No
No == no/(a ne+ 1/ τ){1 – K [exp – (a no + 1/ τ) t ]} (3.13)
Where K is a dimensionless constant and depends upon the initial surface coverage. K = 0
corresponds to the steady state solution; K≤0 or K>0 to an initial concentration greater or less,
respectively than the steady state condition. The following cases arise.
Case 1: This case corresponds to the condition when surface density of unrelated molecules No is
less than that of one monolayer. This mans that No<1/ao, where ao is the surface area of one
molecule. Thus,
no < (a/ao) ne + 1/ao τ (3.14)
Also from Eqs. 1.12 & 1.14
dN1/dt == no/ (1+1/aneτ) {1 – K [exp – (a no + 1/ τ) t ]} (3.15)
And on integration

8. 26
N1 == no/ (1+1/aneτ) [t + K/ (a ne+ 1/ τ) exp – (a ne + 1/ τ) t] (3.16)
It is assumed that N1 = 0 at t = 0. For K=1 corresponding to the initial coverage and
t < (a ne + 1/ τ), dN1/dt is proportional to t, and N1 is proportional to t2
. In steady state conditions,
the rate of film growth can be written as
Rt == dN1/dt. Vm
Where Vm is the volume of one molecule. Thus
RT == no Vm/ (1+1/ aneτ) (3.17)
Case 2: This is the case when the arrival rate of molecules is sufficient to maintain a monolayer
on the surface at all times. The case is restricted to the situation No = 1/ao, that is, more than one
monolayer is not possible because of a significant lowering of the binding energy of molecules in
the second layer. The condition can be visualized by considering that T approaches zero for the
second layer, thus
no ≥ (a/ao) ne + 1/ aoτ
No == 1/ao
And
Rt == (a/ao ) ne.Vm
Case 3: This case corresponds to the condition when all the arriving molecules stick to the
surface regardless of the surface conditions, that is, τ approaches infinity and a thick film of
unreacted material is formed. Equations (1.14), (1.15), and (1.17) transform to
No = no/a ne + K’ exp (-a ne t)
dN1/dt = no + a ne K’ exp (-a ne t)
N1 =no t – K’ [exp (-a ne t) -1]

9. 27
Where K’ is another dimensionless constant and it has been assumed that the probability of a
given molecule reacting is not dependent upon its depth below the surface. This means that the
total film is quite thin and is transparent to the bombarding electrons. The rate of deposition of
reacted molecules under steady state conditions is given by
Rt == no Vm
Case 4: This case refers to the situation when the unreacted film is completely deposited before
the electron bombardment. In this case we will have x = 0 and
No == K’ exp (-a ne t)
dN1/dt == a ne K’ exp (-a ne t)
N1 == K’ [1- exp (-a ne t)]
The deposition rate calculation in this case has no meaning. It can be seen, however, that to form
a film K’ thick, containing less than 1 percent of unreacted molecules, bombardment is required
for a time of 5/a ne because e-5
== 1/150
Christly has also experimentally studied the formation of polymerized organic films. He has
shown that the product a ne depends exponentially upon the reciprocal temperature dependence of
τ. Ennos also studied this phenomenon. He observed that reaction cross-section remains almost
constant in the electron energy range of 2-74 k eV.
3.5 PROCESS CAPABILITIES AND LIMITATIONS
The main uses of this process today include the cutting and welding of materials. The chief
advantage of cutting from the engineer’s point of view is that the process is not dependent on the
work material properties. The materials which can be cut include aluminum, beryllium, cemented
carbides, ceramics, copper alloys, glass, alloy steels, tantalum, titanium, tungsten, and zirconium.
The process works as effectively on extremely hard and tough alloys as on soft nonferrous metals.
Though the process does not possess the advantage of high material removal rates, it is claimed
that it can be use to cut very accurate slots and shapes in all kind of materials. The electron beam
machining has a promising future in the cutting of delicate and consistent shapes which are

10. 28
needed in certain electronic assemblies. In such applications, it can be a formidable competitor of
ultrasonic and chemical machining processes which are currently used for this type of work.
3.6 COMPARISION OF THERMAL AND NON-THERMAL PROCESSES
The two processes are not as much in competition as the initially may appear to be. For
drilling holes and making slots or other deep constructions, the thermal processes are better
because the high energy density required necessities working on a small area only. Due to the fact
that electrons give up most of their energy at approximately 5 to 15 microns below the surface,
the work surface can not be vaporized without melting the material in this region, and therefore,
the use of this process for machining the top layer of a thick laminar structure is not
recommended. The thermal has reached the technical stage where it can mind immediate
industrial use but the non-thermal process has not. The non-thermal process is particularly useful
for machining large areas of thin films. Greater depth can not be attained due to very low reaction
rates but resolution is comparatively much superior. The material removal rate per unit area in
this process is only 10-20 per cent of that achievable in the thermal process.
SUMMERY OF EBM CHARACTERSTICS
Mechanics of material removal Melting, vaporization Medium Vacuum Tool Beam of
electrons moving at very high velocity
Maximum material removal rate 10 mm3
/min
Specific power consumption 450 W/mm3
-min
(typical)
Critical parameters accelerating voltage, beam current, beam diameter, work speed,
melting temperature
Materials application All materials
Shape application Drilling fine holes, cutting contours in sheets, cutting narrow
slots
Limitations Very high specific energy consumption, necessity of vacuum,
expensive machine