# Presentation: 126403

## TF Joint Operations ReviewSimplified Modeling &Protection

- C Neumeyer
- 2/10/05

- IP and OOP Load Modeling
- Linear Model of IP and OOP pressure at Joint
- FEMLAB thermal/electrical simulation
- Other limiting factors
- Spreadsheet assessment of test shots
- Hardware and Software Protection

## EM Influence Matrix 

- Sub-domains were created to represent regions of the TF coil so J_tf x B_r and J_tf x B_z forces on TF bundle and flags could be calculated per kA in each OH/PF coil

- EM Influence Matrix

## EM Influence Matrix

-  z/zmax term is applied to the bundle moment calculation to approximate the amount of torsional load taken out at the hub end of the bundle as if it was a fixed boundary
-  Note relative importance of OH on bundle torque and PF2/PF3 on flag lateral load and moment

- TF Influence Coefficients (forces: lbf/kA2, moments: lbf-in/kA2, radii: inches)
*Note: Moments taken about NSTX machine axis*

## Out-Of-Plane Moment

-  Net moment on joint is estimated as follows...
- Assume equal bundle torque taken out per each of the 36 flags
- Flag torque at joint based on lateral force and equivalent radius
- Net moment at joint is sum of applied torques times coefficient reflecting       	load sharing with structure
- Structural coefficient C_s_oop  derived from NASTRAN FEA,
-     	one per PF current (OH, PF1a ~ 25%, others ~ 10%)

## In-Plane Moment

-  Prior calculations show that moment generated on flag and flex link w.r.t.
-    joint is 70653 in-lbf @ 6kG
- Field and moment proportional to BT2
- Net moment at joint is sum is applied moment times coefficient reflecting load sharing with structure
- Structural coefficient Cs_ip  ~ 30% derived from NASTRAN FEA

## Linear Pressure Model w/o Liftoff

- P

- h

- P=P0+kh

- Pmax

- H

- Pa

- P0

- Moment taken about H/2,
- Stud moments cancel out

- H/2

- H/2

- H

## Linear Pressure Model w/Liftoff

- P

- h

- P=klo(h-(H-Hlo))

- Pmax_lo

- P0_lo= 0

- Hlo

- Pa_lo

- Hlo

## Combined IP and OOP

- Equations developed for IP apply to OOP with H and W reversed
- Assume superposition IP and OOP effects
-  Question: how to estimate peak pressure considering effects of inserts, etc.

- IP Only

- OOP Only

- IP & OOP Combined

## Pressure Peaking Factor

-  6kG moments ~ ANSYS case with M_ip = 20klbf-in  and M_oop=3905

- Red areas ~ 30ksi
- Grey areas > 30ksi

- Note: estimated worst case M_ip
- During last run ~ 27klbf-in!!

## Pressure Peaking Factor

-  Linear model under same conditions as ANSYS run results in 30.5ksi based on gross average pressure
-  How to handle non-uniformity in simplified model?
-  Ignore peaking factor in model
-  Set allowable for simple model based on knowledge of actual situation
-  Judgement to be applied in setting allowable
-  Peaking at corner is to some extent an artifice of the calculation
-  Plastic deformation at corner is to some extent tolerable
-  Bundle conductor is C107 copper specified with yield strength 30 ksi min/36ksi max
-  Flag conductor is C101 copper
- Tested Rockwell Hardness B = 45
- H04 tensile yield ~ 40ksi per CDA specs

## FEMLAB Modeling

- Linear pressure model
- In-plane moment set proportional to Itf2
- Out-of-plane moment set proportional to Itf at OHSS value (conservative)
- Contact electrical resistivity based on curve fit to measurements on prototype assembly
- Contact thermal conductivity varied along with electrical conductivity
- Water cooling ignored

- Fit:  = max(KA+KB*P, KC*P)^KD)

## FEMLAB Meshing

-  Contact region simulated using thin (0.125”) layer
- 	viable for FEA meshing
- 	presents correct impedance and power dissipation
- 	small thermal capacity
- 	stable temperatures
- 	temperatures in layer are an artifice of the calculation and are ignored
-  Noted that primary effect of contact resistance is to steer the current flow, and that    power dissipation is a secondary factor

- 8490 elements

## FEMLAB Simulation - Front Face of Conductor

-  Simulation (6kG shown) predicts Tmax ~ 155C in conductor in thin region near insert

## FEMLAB Simulation - Front Face of Flag

## FEMLAB Simulation - Back Side of Conductor

## FEMLAB Simulations - 6kG - Pressure (psi)

- ~ 30ksi

## FEMLAB Simulations - 6kG - J (A/m2)

## FEMLAB Simulations - 6kG - T (OC)

## FEMLAB Simulations - 6kG - T (OC)

- Should be ~ worst case, since J and heating is aligned with insert

## FEMLAB Simulations - Summary

-  Copper mechanical properties do not degrade until ~ 200C (flag) and 300C (conductor)
-  TF bundle insulation (near hot spot) pre-cured 2hrs at 177C and post-cured 7hrs at 200C
- Heat distortion temperature should be close to  200C
-  Set temperature limit to 150C, corresponding to ~ 0.5s flat top @ 6kG worst case
- Water cooling region will remain below well below 100C
-  Conclusion: I2T protection presently in place is adequate for thermal protection

- Yield strength of cold
- worked Cu vs. Temp with
- various silver contents

- CDA107 (conductor)

- CDA101 (flag)

## Other Limiting Factors - Box Friction

- In-Plane

- Out-Of-Plane

## Box Friction - Out Of Plane

-  Simplified model treats flag/box assembly as a simple rigid body statics problem, and friction response of the interface as point responses at the radii of the box studs
- Flateral from EM influence matrix
- Fbundle from influence matrix w/structural coefficient C_s (82%) from NASTRAN FEA
-  Load response of flex links is ignored

## Box Friction - Out Of Plane

- Individual Fx assumed equally divided between the two friction surfaces
- Total lateral load ∑F = F1 + F2 + F3 loads has to be transmitted by outer surface
- Inner layer boxes have to transmit∑F loads generated on outer layer boxes

## Box Friction - In Plane

-  Moment generated on flag and flex link w.r.t. joint is 70653 in-lbf @ 6kG
- Field proportional to Bt^2 at lower fields
-  Net friction shear at interface based on applied moment, moment arm, 2 interfaces, 3 studs per interface, and coefficient Cs reflecting load sharing with structure
- Structural coefficient C_s_ip  (28%) derived from NASTRAN FEA

## Box Friction - Net

-  Net friction shear load for each stud taken as vector sum of IP and OOP loads
-  COF = 0.47 based on full scale tests on friction coated samples
-  Stud loads taken to be 5500lbf based on average of torque vs. load tests
-  Safety factor calculated for each of 3 studs on inner and outer flags, surfaces
-  furthest away from midplane
-  SF = 1 corresponds to a load of 0.47*5500=2585 lbf per stud

## Joint Friction - Out of Plane

-  Torque generated in TF bundle has to be reacted in frictional shear at joints
-  Total bundle torque estimated using EM influence matrix with structural
-  coefficient from NASTRAN FEA
-  Total of 36 joints at 20klbf with COF = 0.2 for Ag plated copper (min R&D value)
-  Safety factor based on total friction capability divided by total bundle torque
-  (assumes equal load per turn)

## Spreadsheet Assessment of Test Shots

-  Test shots designed to simulate plasma ops envelope in terms of current magnitudes, polarities, and time dependence, used during commissioning and daily start up
-  Magnitudes selected will support upcoming run based on input from physics ops
-  Loss of control could theoretically result in all currents aligned to the max
-   magnitude in either direction, as limited by software and hardware protection

- Test Shot Spec

- Limit Spec

## Spreadsheet Assessment - 4.5kG

-   All factors are OK with limits at “Req’d”
-   Pressure > 30ksi and Box Stud SF ~1 are possible with limits set to “Rated”

## Spreadsheet Assessment - 6.0kG

-  Pressures >> 30ksi are possible in “Req’d” and “Rated” cases
-  Box stud friction SF < 1 in “Rated”
-  Flag OOP friction SF OK in all cases

## Spreadsheet Assessment - Comparison w/NASTRAN

-  OOP Combined field cases add up pretty well at 4.5kG and 6kG
-  IP is overestimated at 6kG, particulary for combined field
-  Modeled P_max would be reduced to 20ksi from 28ksi if M_ip was 10340 at 6kG

- Combined field

## Spreadsheet Assessment - Conclusions

- At 4.5kG
*According to modeling results *overcurrent limits set per present *requirements* are adequate, and exposure to problems will be minimal
- At 6kG
*According to modeling results* nominal waveforms are feasible, with liftoff and local yielding.
- Moments at the joint will be less than were experienced by worst case joints during prior run at 4.5kG
- Real time protection against P_max overloads is necessary even if currents are limited in magnitude to *required* values

## Spreadsheet Assessment - Conclusions

-  Simplified linear modeling provides results which are reasonably close to detailed analysis and are suitable for real time protection accounting for PF current combinations
-  Real time protection is required to prevent P_max and box friction overloads *if/when PF operating levels are increased over present requirements, and/or when Bt is operated above 4.5kG*
-  Protection of box friction based on the most inboard stud will blanket worst case conditions
-  OOP joint friction retains adequate margins in all cases

## Hardware and Software Protection

-  Overcurrent Protection
- - Analog Coil Protection (ACP) and Rochester Instrument System (RIS) and Power Supply Real Time Control (PSRTC) protection will continue to be set based on *required* currents, less than or equal to *rated* currents
-  PSRTC at 1% overcurrent
-  ACP at 2% overcurrent
-  RIS at 5% overcurrent

## Hardware and Software Protection

-  I2T Protection
- Prior PSRTC and RIS settings were based on 1 second flat top at 4.5kG, would allow ~ 250mS at 6kG
- - Settings will have to be increased to allow 0.5 sec at 6kG

- Range of prior run
- And initial range of
- Upcoming run

## Hardware and Software Protection

-  Protection for TF joint (pressure, box stud load) will be implemented in PSRTC prior to operation beyond 4.5kG
-  Although a “software” system, PSRTC software is segregated from and is more stable than the Plasma Control System (PCS)
-  PSRTC will prevent any misoperations due to operator error or PCS malfunction