Appunti completi del corso "Advanced Manufacturing Processes"

Manufacturing Processes

Tornitura = TurningAlesatura = BoringForatura = DrillingFresatura = MillingRettifica = Grinding= Planing= ShapingBrocciatura = BroachingFinitura ~ Polishing/BuffingImbutitura = Deep DrawingPiegatura = BendingPunzonatura = PunchingTrafilatura = wire drawingTranciatura = Blanking

GENERAL ISSUES

• Classification of unconventional manufacturing processes
• General modeling of processes and systems

THERMAL PROCESSES

• Thermal modeling
• Laser beam processing
• Electro discharge machining
• Plasma arc processing
• Additive manufacturing processes

MECHANICAL PROCESSES

• Waterjet processing
• Hydroforming
• Ultrasonic processing
• Micromachining

USM

Abrasion (MA)

Abrasives

Slurry

Workpiece

WJM

Cutting (C)

Jet

Fluid

Workpiece

EDM

Discharges

Plasma

Dielectric

Workpiece

PAC

Plasma beam

Plasma

Gas

Workpiece

LBM

Laser beam

Photons

Air

Workpiece

EBM

Electron beam

Electrons

Vacuum

Workpiece

IBM

Ion beam

Ions

Vacuum

Workpiece

Conservation of Energy

I Thermodynamics Law:

• Inflow and Outflow Energy: Ė_in and Ė_out are surface phenomena
• Generated Energy: Ė_g is a volumetric phenomenon, it comes from conversion of other energy forms (chemical, nuclear, electrical ...)
• Stored Energy: ΔĖ_st = ΔŪ + ΔXE_potential + ΔXE_kinetic

ΔŪ = ΔŪ_sen + ΔX_ε

ΔŪ_sen = ρc_p ^∂T/_∂t dxdydz

ΔU_sen = sensible thermal component (energy required to heat up this infinitesimal volume)ΔU_t = latent component

Heat Diffusion Equation

Energy conservation into a medium:

• homogeneous medium
• no mass movements
• no heat sources
• no phase change

ΔT → heat flow at control area

Ė_in - Ė_out = Ė_st

erf(x) = ²/_√π ∫₀^x e^-x2/2σ2dx

• Complementary Error function:

erfc(x) = 1 - erf(x)

• Integral of the Complementary Error function:

ierfc(x) = ∫_-x^x erfc(x) dx

ierfc(x) = - erfc(x) x + e^-x2 / √π

• ierfc(0) = ¹/_√π = 0.56
• ierfc(∞) = -∞₀ + e^-σ2 / √π = 0

We consider only the positive values, because x indicates depth.

This form of the equation is the multiplier of the space component.

Example: Laser turned off after 1 μs:

As we go deeper inside the material, the heating effect is blunt, and there is a lag in the temperature.

The temperature then will go towards the initial value in each case.

Cooling Rate:

The "resonator" is the rear and front mirrors.

The mirrors are gently curved, in order to concentrate the light always in the middle.

Properties of Lasers

Monochromaticity

(same wavelength)

Coherence

(same phase)

Useful for measurement applications.

Moving from long to short pulses, the average power will be smaller, because the duty cycle will be lower, the energy will be smaller, but the peak power will be higher.

So we have different laser architecture:

• Long:
  • Free running: t=10³-10^-4 s   f_p=0.01-100.000 Hz
  • Fast switching of the laser source. The properties of the resonator are not changed.
  • It's just switched on and off
• Short:
  • Q-switch: t=10^-9 s   f_p=100 kHz
  • The active medium is saturated prior to the stimulated emission
  • rotating mirror method,
  • electro-optic Q-switching,
  • acousto-optic Q-switching
  • passive Q-switching.
  • There is a block, while the active medium is still being pumped, so it's full of excited electrons
• Ultrashort:
  • Mode locking: t=10^-12-10^-15 s   f_p=1-1000 MHz
  • Occurs due to interaction between the longitudinal modes and results in oscillatory behavior of the laser output. This makes the longitudinal modes maintain fixed phase relationship resulting in mode locking.
  • The different modes cancel out each other

Frequency Multiplication

The wavelength of the laser is determined by the active medium, but it can be changed through the "frequency multiplication".

A non-linear crystal can convert the initial wavelength into its harmonic wavelengths.

Frequency multiplying is a technique used to produce a wavelength that is one half (or one third or one quarter) of the fundamental wavelength of a laser.

Beam Delivery System

• Reflective Mirrors:
  • Advantages:
    • it's easy
  • Disadvantages:
    • it has open beam paths
• Transmission Fiber:
  • Advantages:
    • it has a high flexibility
  • Disadvantages:
    • only some wavelengths are suitable

Reflective Mirrors

They are:

• simple
• suitable for all lasers (CW, PW)
• it generates a straight path of the beam
• cooled by convection or water cooling

They need cooling because a portion of light will always be absorbed, and if it heats up, it'll expand and become curved.

Mirrors can be moved by:

• translation
• rotation

Step index fiber:

Graded index fiber:

This gives the laser a distribution similar to a gaussian one, but we can't call this a Gaussian beam, because it has a M² > 1

There are also single mode fibers:

• Multi mode (M>2)
• Single mode (M²=1)

Single mode fibers have a better beam quality, but are more expensive to produce, and also since all the power is concentrated in a smaller beam, there is the problem of irradiance. So the multimodes laser can withstand more power.

I = P/A

Now we need to focus the beam. We can do this with:

• Reflective optics: mirrors
• Transmissive optics: lenses

Not suitable for CO₂ lasers

There are two slabs, between which there is the CO2 gas. It is pumped by electrical inputs, with alternate current and radio frequencies.

Vibration Modes:

• equilibrium
• Symmetric stretching 1^st mode (e₂): 1,41*10^-20 J
• Bending 2^nd mode (e₃): 3,08*10^-20 J
• Asymmetric stretching 3^rd mode (e₄): 4,96*10^-20 J

The photonic release happens between the third and second mode:

Gas mixture composition (vol%)

• He: 45% (good heat conduction)
• N₂: 45% (coupling effect)
• CO₂: 10%

The problem is that it's difficult to take the electron to the third level, and to get rid of all the collision's heat due to the rapid decay after the second level.

So we work with a mixture, with helium for good heat conduction and nitrogen for coupling effect, and only a 10% of CO2.

The idea is this: it's easier to excite nitrogen with the electrical energy, and when it decays it couples energy to CO2, and then the helium is used to dissipate the heat because it has a much higher convection behaviour.

It's not very efficient.

Let's calculate the wavelength of the laser:

c = ν = λ * f (source at low pressure)

λ_{CO 2} = c/f₄₃

e₄ = e₃ + hf₄₃ → f₄₃ = (e₄ - e₃)/h

Frequency of the photons

λ_{CO 2} = c/f₄₃ = ch/(e₄ - e₃) = (3 * 10⁸)(6.63 * 10^-34)/(4.96 - 3.08) * 10^-20 = 10.6 * 10^-6 m ≈ 10 μm (IR)

The energetic efficiency is:

η ~ 10%

Beam distribution:

TEM₀₀ d = 30 mm, TEM₂₀ d = 50 mm, TEM₁₁ d = 50 μm