1. PS Internal Dump - actuation system
G. Gobbi
30/06/2017

2. Outline Introduction to the PS Internal Dump actuation system
Calculations:
Initial analytical estimation
Rigid dynamics simulations (Multibody)
Transient structural simulations (Fem)
Conclusions
30/06/2017
G. Gobbi

3. PS Internal Dump - actuation system
EN-STI-TCD: two PS Internal Dumps to be installed in the PS accelerator during LS2
Design by Yannick Coutron and Didier Steyaert
+12˚ 0˚
-12˚
6 springs in parallel
Magnet
-12˚ Parking position
0˚ Neutral position
+12˚ In beam position
Dump mass: 20 kg
F vacuum = 1100 N Fv
Requirement
Dump movement go and return from -12° to +12° in less than 400ms (300ms)
30/06/2017
G. Gobbi

4. Job objectives
EN-MME: Engineering design of the actuation system of PS internal dump
design of dynamic response
spring dimensioning
magnet force
bearing load
fatigue assessment
30/06/2017
G. Gobbi

5. k equivalent 6 springs in parallel
Analytical approach
𝛼 0 =29.5°
Aim: preliminary estimation of dynamic response and dimensioning of springs, bearings and magnet
1 DOF system
Equation of motion:
𝜃 𝐼+𝑐 𝜃 − 𝑀 𝑚 𝑔 𝐿 𝑚 sin 𝛼 0 +𝜃 + 𝑀 𝑑 𝑔 𝐿 𝑑 cos 𝜃 +𝐾 𝐿 𝑠 2 sin 𝜃 cos 𝜃 +𝐾 𝑥 0 𝐿 𝑠 cos 𝜃 =0
𝐹 𝑠
Where:
is the total inertia of the system 𝐼
𝑐=𝜁∙ 𝑐 𝑐𝑟
is the damping coefficient with a 𝜁 equal to 2.5%
𝜃 𝐼+𝑐 𝜃 − 𝑀 𝑚 𝑔 𝐿 𝑚 sin 𝛼 0 +𝜃 + 𝑀 𝑑 𝑔 𝐿 𝑑 cos 𝜃 +𝐾 𝐿 𝑠 2 sin 𝜃 cos 𝜃 +𝐾 𝑥 0 𝐿 𝑠 cos 𝜃 =0
𝑀 𝑚 g 𝐿 𝑚 sin (𝛼 0 +𝜃) − 𝑀 𝑑 𝑔 𝐿 𝑑 𝑐𝑜𝑠𝜃−𝐾 𝑥 0 𝐿 𝑠 𝑐𝑜𝑠𝜃−𝐾 𝐿 𝑠 2 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃=0
𝑇= 2𝜋 𝜔 𝑑
𝐾=30780𝑁/𝑚
k equivalent 6 springs in parallel
300ms
30/06/2017
G. Gobbi

6. Analytical approach 𝑥 0 =14 𝑚𝑚 From equation of equilibrium:
𝑀 𝑚 g 𝐿 𝑚 sin (𝛼 0 +𝜃) − 𝑀 𝑑 𝑔 𝐿 𝑑 𝑐𝑜𝑠𝜃−𝐾 𝑥 0 𝐿 𝑠 𝑐𝑜𝑠𝜃−𝐾 𝐿 𝑠 2 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃=0
𝑥 0 =14 𝑚𝑚
displacement of the equilibrium position
Natural equilibrium of the system = -3˚
Imposed equilibrium at 1˚ with spring preload
30/06/2017
G. Gobbi

7. Analytical approach Equation of equilibrium in parking position:Fs Ls Ld Lm
Md g
Mm g
𝛼 0 Fm 𝛽
𝛼 0 =17.5°
β=−12°
𝑀 𝑚 𝑔 𝐿 𝑚 sin 𝛼 0 − 𝐹 𝑚 𝐿 𝑚 cos 𝛼 0 −𝐾 𝐿 𝑠 2 𝑠𝑖𝑛𝛽 cos 𝛽 −𝐾 𝑥 0 𝐿 𝑠 cos 𝛽 − 𝑀 𝑑 𝑔 𝐿 𝑑 cos 𝛽 =0
𝐹 𝑚 =2240 𝑁
Minimum force needed to hold the magnet attached to the socket
30/06/2017
G. Gobbi

8. Rigid dynamics simulation
Aim: validation of the analytical calculations
RIGID BODY
Dump in parking position
One spring body to ground equivalent to 6 springs in parallel:
K = N/m
Preload = N
Cylindrical joint in correspondence to the bearings with a damping ratio of 2.5%
Dump and magnet masses taken into account (standard earth gravity applied)
Vacuum force FV = 1100 N
Transient analysis: end time t=1s (few periods)
30/06/2017
G. Gobbi

9. Rigid Dynamics Simulation - Results
Rotation
Angular velocity
30/06/2017
G. Gobbi

10. Transient structural FEA
Aim: evaluation of the stress state of components under dynamic conditions
FLEXIBLE BODY
Dump in parking position
One spring body to ground equivalent to 6 springs in parallel:
K = N/m
Preload = N
Cylindrical joint in correspondence to the bearing with a damping ratio of 2.5%
Dump and magnet masses taken into account (standard earth gravity applied)
Vacuum force FV = 1100 N
Transient analysis: end time t=0.3s (1 period)
30/06/2017
G. Gobbi

11. Transient structural FEA - Rotation
30/06/2017
G. Gobbi

12. Transient structural FEA - Rotation
30/06/2017
G. Gobbi

13. Transient structural FEA – Bearings
Fb = 3643 N for each bearing
30/06/2017
G. Gobbi

14. Transient structural FEA – Stress field
Al AW6082 T6
MPa
MPa
304L Stainless Steel (Inox)
σ y =240MPa
σ y =175MPa
MPa
316LN (Inox)
σ y =300MPa
316LN (Inox)
σ y =300MPa
30/06/2017
G. Gobbi

15. Fatigue assessment Normal stress – X Axis
MPa
σmax =70 MPa
Lifetime requested: /y flips per 20 years  4E+06 cycles
For safety: infinite life
σmin = MPa
30/06/2017
G. Gobbi

16. Fatigue assessment σ a = σ max − σ min 2 =48 MPa
σ m = σ max + σ min 2 =21.75 MPa
R= σ min σ max =−0.38
Eurocode 3 recommends to use a safety coefficient of 1.25.
In that case σ a =48MPa∗1.25=𝟔𝟎 𝐌𝐏𝐚
infinite life
σ e =240MPa from literature
30/06/2017
G. Gobbi

17. Fatigue assessment Equivalent Alternating Stress
MPa
304L Stainless Steel (Inox)
σ e =175MPa
MPa
σ a =99MPa∗1.25=𝟏𝟐𝟒 𝐌𝐏𝐚
316LN (Inox)
σ y =240MPa
σ a =134MPa∗1.25=𝟏𝟔𝟖 𝐌𝐏𝐚
30/06/2017
G. Gobbi

18. Conclusions
Engineering evaluation of the actuation system of PS Internal Dump  optimization of the dynamic response
A preliminary analytical approach complemented with rigid dynamics and transient structural simulations
Few iterations on the design before meeting the requirements  i.e. spacer
30/06/2017
G. Gobbi

19. Thanks for your attention

20. 𝑐 𝑐𝑟 =2𝐼∙ 𝐾 𝐿 𝑠 2 − 𝑀 𝑚 𝑔 𝐿 𝑚 cos 𝛼 0 𝐼
𝐼= 𝑀 𝑚 𝐿 𝑚 2 + 𝑀 𝑑 𝐿 𝑑 2 + 𝑀 𝐴𝑑 𝐿 𝑑 𝐼 1
𝑐 𝑐𝑟 =2𝐼∙ 𝐾 𝐿 𝑠 2 − 𝑀 𝑚 𝑔 𝐿 𝑚 cos 𝛼 0 𝐼
𝑐=𝜁∙ 𝑐 𝑐𝑟
𝜃 𝐼+𝑐 𝜃 − 𝑀 𝑚 𝑔 𝐿 𝑚 sin 𝛼 0 −𝑀 𝑚 𝑔 𝐿 𝑚 θ cos 𝛼 0 + 𝑀 𝑑 𝑔 𝐿 𝑑 +𝐾 𝐿 𝑠 2 θ+𝐾 𝑥 0 𝐿 𝑠 =0
𝑀 𝑚 g 𝐿 𝑚 sin 𝛼 0 − 𝑀 𝑑 𝑔 𝐿 𝑑 −𝐾 𝑥 0 𝐿 𝑠 =0
30/06/2017
G. Gobbi