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

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

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

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

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

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

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

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 = 31000 N/m Preload = -1708 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

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

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 = 31000 N/m Preload = -1708 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

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

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

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

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

Fatigue assessment Normal stress – X Axis MPa σmax =70 MPa Lifetime requested: 200000/y flips per 20 years  4E+06 cycles For safety: infinite life σmin = -26.5 MPa 30/06/2017 G. Gobbi

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

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

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

Thanks for your attention

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 2 3 + 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