Vacuum: Rules of thumb

Engineering Fundamentals

Introduction

This sheet will give some basics about a vacuum chamber itself and about mechanical setups that are placed in it.

ClassificationLevel [mbar]PumpsSensorsExamples
LVLow103 … 100Dry/wetMechanicalFood seals, domestic vacuum cleaner
MVMedium100 … 10-3Dry/wetMechanicalLight bulb
HVHigh10-3 … 10-6+TurboElectronicThermos bottle insulation
VHVVery high10-6 … 10-9+TurboElectronicVacuum vessel LHC CERN (particle accelerator)
UHVUltra high10-9 … 10-12+TurboElectronicAtomic physics research (e.g. gravity wave)
EHVExtreme high< 10-12(Space)ElectronicSpace

Pressure conversion

$1MPa\ =1\frac{N}{mm^2}=145psi=10bar $
$1mbar={10}^{-4}MPa=0.0145psi=100\frac{N}{m^2}$

Gas law

$pV=nRT$ with $R=8.314JK^{-1}mol^{-1}$

Estimates for wall thickness ($p=1$ bar)

$\tau_{0.2}\approx0.4\cdot\sigma_{0.2}$ (JPE Estimate for metals), $t=$ thickness,
$\delta=$ deformation

Welded flanges
Vacuum: Rules of thumb$$t=\sqrt{\frac{{3d}^2p}{2\sigma_{max}}}$$$$\delta=\frac{d^4p}{32{\rm Et}^3}$$
$$t=\sqrt{\frac{{3pL}^2}{\sigma_{max}}}$$$$\delta=\frac{{\rm pL}^4}{16{\rm Et}^3}$$
O-ring-sealed flanges
Vacuum: Rules of thumb$$t=\frac{dp}{2\tau_{max}}$$$$\delta=\frac{d^4p}{8{\rm Et}^3}$$
$$t=\frac{pL}{\tau_{max}}$$$$\delta=\frac{{\rm pL}^4}{4{\rm Et}^3}$$
Thin walled tubes ($r>20t$)
Vacuum: Rules of thumb$$t=\frac{pr}{2\sigma_{max}}$$$$\delta=\frac{2\pi{\rm pr}^2}{Et}$$

Types of leakage

  • Real leakage (holes, porous materials)
  • Virtual leakage (pocket sealed with bolt)
  • Desorption / outgassing (solvents)
  • Diffusion (e.g. H-atoms from steel)
  • Permeability (O-rings)
  • Evaporation (finger prints, lubricants)
  • Backflow pump (dry > wet > turbo)

Paschen’s law

This law states that the breakdown potential (necessary to start a discharge between 2 electrodes) is pressure dependent. JPE Rule: vacuum must be below ${10}^{-1}mbar$

In-vacuum-design rules of thumb

  • Prevent virtual leakage: drill holes in bolts etc.
  • Do not use lubricants
  • Check outgassing spec’s from synthetic materials
  • Be aware of high friction (dry environment)
  • Use hybrid bearings
  • Heat must be conducted through material (no convection)

Pumps (mbar)

  • Dry: Diaphragm ${(10}^0)$, Screw $({10}^{-2})$
  • Wet: Roots ${(10}^{-2})$, Rotary vane $({10}^{-4})$
  • +Turbo: Molecular pump $({10}^{-10})$
  • Ionization $({10}^{-11})$

Sensors (mbar)

  • Mechanical:
    • Bourdon ${(10}^1)$
    • Diaphragm ${(10}^0)$
  • Electronic:
    • Piezo based ${(10}^0)$
    • Capacitive ${(10}^{-3})$
    • Thermal conductivity (Pirani) ${(10}^{-4})$
    • Ionization
      • cold: Penning ${(10}^{-8})$
      • hot: Inverted magnetron ${(10}^{-12})$

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