Mechanical Engineering for Scientific Infrastructuresrvanderb/KES/zanoni/KES_lecture_Zanoni.pdfJ. Ekin “Experimental Techniques for Low-Temperature Measurements: Cryostat Design,

Mechanical Engineering for

Scientific Infrastructures

Carlo Zanoni

[email protected]

1. https://www.youtube.com/watch?v=FzCsDVfPQqk

2. https://videos.cern.ch/record/1753412

3. https://www.eso.org/public/videos/alma16-8mm-tafreshi/

4. https://www.ligo.caltech.edu/page/vibration-isolation

https://www.youtube.com/watch?v=FzCsDVfPQqk

https://videos.cern.ch/record/1753412

https://www.eso.org/public/videos/alma16-8mm-tafreshi/

https://www.ligo.caltech.edu/page/vibration-isolation

[K]

Carlo Zanoni, KES lecture

1. Role of Engineers

2. Basic Concepts

1. Elasticity and structures

2. Mechanisms

3. Vibrations

4. Heat Transfer

5. Manufacturing

3. Tools

4. Examples

Outline

3


Engineering

Engineering

Civil

Engineering

Mechanical

Engineering

Electrical

Engineering

Automotive

AerospaceStructures

….

Engineering is the use of scientific principles to design and build

machines, structures, and other things, including bridges, roads, vehicles,

and buildings.https://dictionary.cambridge.org/dictionary/english/ Cambridge Academic Content Dictionary © Cambridge University

4

Management


Mechanical Engineering

Engineering is the use of scientific principles to design and build

machines, structures, and other things, including bridges, roads, vehicles,

and buildings.https://dictionary.cambridge.org/dictionary/english/ Cambridge Academic Content Dictionary © Cambridge University

Mechanical Engineering is the study of objects and systems in motion.

The role of a Mechanical Engineer is to take a product from an idea to the

marketplace. To accomplish this, the Mechanical Engineer must be able

to determine the forces and thermal environment that a product will

encounter.https://me.columbia.edu/what-mechanical-engineering

5

DesignStructures, vibrations,

dynamics, heat transfer and thermodynamics,

electromagnetics, optics…

ManufacturingTesting AIV


❖Translate a scientific dream into a reality

Role of Engineers

1. Phase 0 Mission analysis and

identification

2. Phase A Feasibility

3. Phase B Preliminary Definition

4. Phase C Detailed Definition

5. Phase D Qualification and Production

6. Phase E Utilization

7. Phase F Disposal

[ESA mission lifetime cycle]

Scientific

requirements

Technical

requirements

Design

Manufacturing,

AIV,

Commissioning

7

Feasibility

check


ElasticityBasic

Concepts

𝐹 = 𝑘 ∆𝑥

𝐹 = 𝑘 ∆𝑥

𝜎 = 𝐸 𝜀

8


ElasticityBasic

Concepts

• 𝜎: stress [Pa]

• 𝜀: strain [-]

• 𝐸:Young’s modulus or Elastic modulus [Pa]

https://www.youtube.com/watch?v=4PbdRgyW0uI9

https://www.youtube.com/watch?v=4PbdRgyW0uI

• 𝜎: stress [Pa]

• 𝜀: strain [-]

• 𝐸:Young’s modulus or Elastic modulus [Pa]


ElasticityBasic

Concepts

Slope = E

End of elastic regime (yield)

Plastic regime (deformation

is permanent)

W.D.Callister “Material Science and

Engineering: an Introduction” 2013

10


ElasticityBasic

Concepts

Elastic regime: deformation is not permanent and is recovered once

the load is removed. It mostly follows a linear behavior

Plastic regime: deformation is permanent, when a load is removed

the shape is different from the original one

Brittle → limited

deformation possible

Ductile → large

deformation possibleGlass

Steel

11


ElasticityBasic

Concepts

Reality is a bit more complex…

Stress is not a scalar value

Infinitesimal volumes have 9 components of stress

➢ 3×3 matrix

➢ Symmetric → 3 normal stresses, 𝜎, and 3 shear stresses, 𝜏

12

Is there a way to estimate an equivalent value from the 3×3 matrix?

Yes. There are theories that derive an equivalent stress from a tri-axial stress

state.

Most used is Von Mises:


ElasticityBasic

Concepts

13

What is an acceptable level of equivalent stress (aka strength) for a part?

It depends on the material.

For most applications, the strength is the elastic limit. This also assures the

problems can be solved with linear equations.


ElasticityBasic

Concepts

Yield

@300 K

[MPa]

Rupture

@300 K

[MPa]

Steel, structural ASTM A36 steel 250 400–550

Steel S355 355 470-630

Steel, 2800 Maraging steel 2617 2693

Steel, high strength alloy ASTM A514 690 760

Polypropylene 4–369 9–80

Cast iron 4.5% C, ASTM A-48 130 200

Beryllium 99.9% Be 345 448

Aluminium alloy 2014-T6 414 483

Aluminium alloy 6061-T6 241 300

Copper 99.9% Cu 70 220

Brass 200 500

Tungsten 750 980

Titanium alloy, Ti-6Al-4V 880 900

J. Ekin “Experimental Techniques for Low -Temperature Measurements: Cryostat Design,

Material Properties and Superconductor Critical-Current Testing” 200614


Reality is even a bit more complex…

StructuresBasic

Concepts

Need of calculating everywhere in the

structure the stress due to various

loads:

• Gravity

• Earthquakes

• Wind

• Temperature

15


Idealization of structures, with ideal constraints blocking specific

degrees of freedom (dof):

StructuresBasic

Concepts

1 dof – y translation


– x translation


– rotation


– x translation

– rotation

16


Idealization of structures, with ideal constraints blocking specific degrees

of freedom (dof)

Equilibrium equations (σ𝐹 = 0 and σ𝑀 = 0) for the whole structure and

single beams allow the calculations of internal actions everywhere.• Solution of 3D complex structures relies on the use of computer codes.

Euler-Bernoulli equation relates local bending moment (𝑀) to

displacements (𝑤):

𝑑2𝑤

𝑑𝑥2= −

𝑀(𝑥)

𝐸𝐼

StructuresBasic

Concepts

17

Reality is even more complex than this…


MechanismsBasic

Concepts

For a mechanism, stress is not a

sufficient design quantity.

Need of calculating multiplication

of displacements/rotations and of

forces/moments.

This is done by means of properly

derived equations of motion, so

called kinematic chains, the

principle of virtual work and other

tools.

18

M2 Hexapod

➢ The Hexapod or Stewart platform is the mechanism supporting most of mirrors

that need rigid body motion


MechanismsExample

19

METIS chopper mechanism


MechanismsExample

20


▪ All mechanical systems vibrate (they are elastic and have mass) due to seismic

noise of the ground, wind, motion of mechanisms…

• Small vibrations → displacements and deformations, reduction of life of components• Displacement and deformations of mirrors is a killer for a telescope

• Large vibrations (e.g. earthquake) → rupture

▪ Vibrations are analyzed in the frequency domain

VibrationsBasic

Concepts

𝑚 ሷ𝑥 = 𝑘 𝑦 − 𝑥 + 𝑐( ሶ𝑦 − ሶ𝑥)𝑚 ሷ𝑥 + 𝑐 ሶ𝑥 + 𝑘𝑥 = 𝑐 ሶ𝑦 + 𝑘𝑦

⋮𝑋(𝜔)

𝑌(𝜔)=

𝑐 𝑖𝜔 + 𝑘

−𝑚 𝜔2 + 𝑐 𝑖𝜔 + 𝑘

=2𝜁𝜔𝑛 𝑖𝜔 + 𝜔𝑛

2

−𝜔2 + 2𝜁𝜔𝑛 𝑖𝜔 + 𝜔𝑛2

1. Make a model of the system 2. Write motion equations(for complex cases numerical models

are used)

3. Derive transfer function(for verification purposes: measure)

S.S. Rao “Mechanical Vibrations” 2010 21

Pre-focal Station (PFS)

➢ Distributes the optical beam to the

instruments

➢ Contains sky metrology used by the

active optics of the telescope


VibrationsExample

M6N

M6C22

The PFS is required to provide a focal

position with M6N and M6C with a stability

better than 1 μm in [1,100] Hz

Seismic noise, wind and mechanisms

motion shake the structure

Transfer Functions are optimized to

minimize resonance effects

➢ Use of isolators/dampers if needed


VibrationsExample

23


Heat TransferBasic

Concepts

Conductivity

𝑞 = −𝜆∇𝑇

𝜆 thermal conductivity [W m-1 K-1]

𝑞 heat flux [W m-2]

∇𝑇 temperature gradient [K m-1]

0

300

600

900

1200

1500

1800

0 50 100 150 200 250 300

λ [W

m-1

K-1

]

T [K]

Conductivity (Cu)

Convection

𝑞 = ℎ𝐴(𝑇𝑓 − 𝑇)

ℎ convection coefficient [W m-2 K-1]


A area [m2]

𝑇 local surface temperature [K]

𝑇𝑓 fluid temperature [K]

Estimation of the convection coefficient

is very hard as it depends strongly on

the specific problem.

ℎ~𝑁𝑢 𝜆

𝐿𝑁𝑢 = 0.023 𝑅𝑒0.8𝑃𝑟0.4

Where Re and Pr are a-dimensional

numbers (Reynolds, Prandtl)

Thermal Radiation

𝑞 = 𝜀 𝜎 𝐴(𝑇14 − 𝑇2

4)

𝜎 Boltzmann constant,

5.67038×10-8 [W m-2 K-4]

𝜀 emissivity


A area [m2]

𝑇1 temperature ambient [K]

𝑇2 temperature surface [K]

When heat is exchanged between two

surfaces, the above relationship

becomes more complex because of the

view factors between the surfaces.

Emissivity, 𝜀, is very dependent on the

surface quality of the material, which

makes it hard to estimate a priori.

24

Thermal Contact Resistance

[W/K]

Key for estimating temperature distribution and power needed to keep cool/warm


ManufacturingBasic

Concepts

Forging

27

https://www.youtube.com/watch?v=Lqf-vJKs-28

https://www.youtube.com/watch?v=Lqf-vJKs-28


ManufacturingBasic

Concepts

Turning

28

https://www.youtube.com/watch?v=MwgobIVj4fU

https://www.youtube.com/watch?v=MwgobIVj4fU


ManufacturingBasic

Concepts

Milling

29

https://www.youtube.com/watch?v=h74HO5ltd_o

https://www.youtube.com/watch?v=h74HO5ltd_o


ManufacturingBasic

Concepts

Each manufacturing process has a typical range of tolerances (i.e. dimensional and geometrical

deviations from nominal geometry). These tolerances are key aspects when drafting realistic

scientific and technical requirements.

forging→

30

http://www2.mae.ufl.edu/designlab/Lab%20Assignments/EML2322L-Tolerances.pdf

http://www2.mae.ufl.edu/designlab/Lab%20Assignments/EML2322L-Tolerances.pdf

Example

MESH:

Deformation:

(enhanced)

Stress:


Finite ElementsTools

31

Motivation & Principle

• Problems often complex due to their

uniqueness (e.g. geometry)

• Analytical techniques available only

for simple cases

• Numerical tools developed (and now

implemented in professional very

expensive software packages)

• The PDE of the elastic

theory/Fourier law/… are substituted

by a set of algebraic equations

elements nodes


StandardsTools

Loads and material properties have a statistical distribution

➢ Material could be weaker than expected

➢ Loads could be higher than planned

32

Failures can cause deaths, injuries and/or

economic losses (that includes a stop to an experiment)

The loads are multiplied by certain factors and

the material strength is divided. Margin

Factors

For common applications margin factors are

prescribed by National or International norms.

In some cases, norms have the status of laws

EN 13445-8:

Unfired pressure vessels - Part 8:Additional requirements for pressurevessels of aluminium and aluminium

alloys


RF Crab CavitiesExamples

33




RF Crab Cavities

34

RF equipment has very tight requirements (pressure,

magnetic fields, thermal losses, vibrations…)

On top of that, fabricating such a shape is very

challenging:

• tolerances requested are ~100 μm

• hard to access the inside volume

• Niobium (not a widely used material)

• maximum cleanliness

→ test program to be able to fabricate with the

required tolerance

Process called

deep drawing

Courtesy of A. Amorim Carvalho, CERN

Examples


RF Crab CavitiesExamples

35

Subjects touched:

• Elasticity and materials

• Structural mechanics

• Mechanisms

• Vibrations

• Heat Transfer

• Manufacturing

• Finite Elements

• Standards

Time for questions…!

Documents

Mechanical Engineering for Scientific Infrastructuresrvanderb/KES/zanoni/KES_lecture_Zanoni.pdfJ. Ekin “Experimental Techniques for Low-Temperature Measurements: Cryostat Design,