ELECTRON BEAM MACHINING EBM 1 Electron Beam Machining

ELECTRON BEAM MACHINING EBM 1

Electron Beam Machining (EBM) • Thermal process • A stream of high speed electron – Can be obtained by enough voltage 1. 5 x 105 V can produce electron velocity of 2. 28 x 105, km/sec • Heat generated • Material • – Melt – vaporize Focus diameter – • Power density – • 10 μm to 200 μm Go up to 6. 5 x 109 W/mm 2 Precisely controlled – Hole drilled precisely • – 25 μm - 125 μm Almost instantaneous in sheet of thickness • 25 μm 2

Cont. . . • Can be deflected – Magnetic deflection coils – Complex contours can be machined – Collision of electron can be avoided • In vacuum – ≈10 -5 mm Hg – Not suitable for large workpiece 3

Basic arrangement of EBM • Electrons emitted from cathode – A hot tungsten filament • Shaped by grid cup • Accelerated due to large potential difference between cathode and anode • Focussed with the help of magnetic lenses • Controlled by using deflecting coils 4

Figure. Schematic view of electric beam machine 5

Table. Performance characteristics of electron beam machining 6

Table. Slot cutting capability of electron beam for some materials 7

Power consumption (P) • Approximately power requirement (P) is proportional to metal removal rate (ṁ) i. e. P≈Cṁ C is the constant of proportionality depends upon the work material. The equation provides a very rough estimation 8

Table. Specific power consumption in EBM for various metals 9

Drilling a hole by EBM • Hole diameter, Dh depends upon – Beam diameter, Db – Energy density • When Dh > Db – The beam is deflected in a circular path • Small crater on the incident side of work • Taper – 2 o to 4 o – When sheet thickness > 0. 1 mm – Taper of 1 o to 2 o while cutting slot • Material splat on incident side 10

Mechanics of electron beam machining • Mass of electron – 9. 11 x 10 -31 kg • Negative charge – 1. 602 x 10 -19 coulomb • Kinetic energy due to potential difference – ½me(v 2 -u 2) e. V • Where – me is the mass of electron – v/u is the final/ initial velocity – e is the charge of electron – Hence v ≈ 600 √V 11

Figure. Movement of electron below surface 12

Cont. . . • Electron impinges the metal surface • Collides with molecules and stopped • Layers penetrated undisturbed – • • Transparent layer While colliding – Heat is generated – But below the transparent layer (skin) Range of penetration (δ) depends upon – Kinetic energy – Accelerating voltage • δ (in mm) =2. 6 x 10 -17 (V 2/ρ) • Where ρ is the density of material in kg/mm 3 13

Estimation of temperature rise • Can be estimated • By solving one dimensional heat conduction equation • For heat source placed inside the metal Where θ = temperature α = thermal diffusivity of metal z = distance from surface t = time c = specific heat of metal ρ = metal density H(z, t) = heat source intensity, i. e. heat generated/time/volume 14

Cont. . • At steady state, the heat source intensity depends upon z • H(z) = Ae-bz • Where A = a constant b = coefficient describing energy absorption characteristics of the metal • The above equation becomes 15

Assumptions • The metal body is semi-infinite • Surface of metal is insulated except the hot spot • Rate of heat input is uniform with time during the pulse duration • By solving the equation, • The nature of temperature variation for different pulse duration, τ is shown as: 16

T 3 T 2 θ T 1 z We see, The pulse duration increases, the peak temperature shifts towards the surface 17

Estimation of functional characteristics • Dimensional analysis is quite satisfactory • The quantities: P = beam power = beam current x accelerating voltage d = beam diameter v = beam velocity with respect to work k = thermal conductivity of metal ρc = specific heat of metal θm = melting point of metal z = depth of penetration of melting temperature Hence z = z(P, v, d, k, ρc, θm ) 18

Selected basic dimensions (m) • • • M (mass) L (length) T (time) θ (temperature) m=4 19

Number of parameters (n) • • P = ML 2 T-3 v = LT-1 d=L k = MLT-3 θ-1 ρc = ML-1 T-2 θ-1 θm = θ z=L n=7 20

Buckingham's π theorem • According to Buckingham's π theorem • Number of dimensionless groups can be formed =n-m=7 -4=3 • z, d and θm as the quantities which goes directly in the groups, we have: 21

Cont. . • Substituting the dimensions of each quantity and equating to zero as they are dimensionless. We get: 22

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Cont. . 24

Cont. . . • Ultimate relationship can be assumed as πi = f(πj, πk) Let i=1, j=2 & k=3 Then π1 = f(π2, π3) Or 25

Cont. . • It has been experimentally found the z is directly proportional to P. Thus • It has been experimentally observed that the dependence is of the form of 26

Cont. . • It has been experimentally observed that the dependence is of the form of Any consistent system of units for the quantities should be used 27

Effects of EBM on work materials • Machining without raising the temperature of the surrounding (except a very thin layer) • The work material 25 50 μm away from the spot remains at room temperature • Hence no effect on work material • The machining is in vacuum, chance of contamination is less 28

Thanks 29