Target wheel eddy current modelling

1. Target wheel eddy current modelling James Rochford On behalf of the Helical collaboration STFC Technology

2. Introduction • Introduction • From previous modelling • Good confidence in VF Electra solutions • Now have agreement with Carmen models • Now evident simple electra wheel rim models behave quite differently to the real wheel. • Presence of the spokes makes a considerable difference to the predicted torque • Have only run model at slow speed 100rpm • Have done preliminary scaling the results • Here will present a summary of the latest results • Outline next steps

3. Previous models • Introduction • From previous modelling • LLB disk experiment results • Electra models • Good agreement with data Eddy currents A/mm2 @2000rpm

4. VF electra solutions • VF electra solutions • Have confidence in Electra solutions • Here look at inclusion of coils &iron • Model 1:Simple ring, coils only • Model 2:Simple ring , coil and iron • Field distribution different • Model constructed to have same Model 2 & 3 Model 1

5. VF electra solutions • VF electra results • Simple spread sheet estimate Good agreement

6. VF electra solutions • VF Electra results • All models agree well • Predict same torque and power dissipation • Both these models agree with • simple spread sheet estimates • For a speed of 100rpm • Electra prediction model 3 • Retarding torque of 7000 N.mm • Power dissipation of ~0.07kW.

7. VF electra solutions • Eddy distribution from Electra models • Both models give consistent current distrobutions Models 2&3: Gradient steeper dB circulation paths compressed and greater peak current. Model 1: Gradient not so steep and dB lower - circulation path elongated and lower peak currents.

8. Carmen spoke model • Description • Having under stood the Electra solutions and gained some confidence in the solution a Carmen model was constructed which includes the spokes • The CARMEN solver, has the capability to solve the full dynamic problem i.e the motion coupled to the electromagnetic solution and does not need any rotational symmetry in the problem. • A sacrificial mesh layer , “the gap” around the rotating region is re-meshed for all points in the solution • Meshing needs to be adequate to model current distribution and robust enough to allow the gap to be re-meshed at all points in the solution whilst giving consistent solutions Mesh distribution in wheel

9. Carmen spoke model • Model results; part revolution 0o-60 o • Run a number of Carmen solutions to look at the effect of step time on the problem solution • The effect of time not so critical can see step 2deg starts to deviate from 1deg solution- problem computationally very expensive. • In these solutions we see the force increases by a factor of 7 @ 100rpm w.r.t the Electra simple wheel rim prediction. • Is this real is it caused by the spokes? • Retarding torque predicted by CARMEN for 100rpm for a part revolution

10. Carmen spoke model • Model results; full revolution • Here a full rotation is run But the solution step is every 2 deg but the mesh is slightly cruder • So solution not quite as accurate as part solutions • But you can clearly see 5 equally spaced peaks in the torque • Rem; wheel has 5 spokes • Between peaks Torque drops to a value comparable with the Electra solution. • Retarding torque predicted by CARMEN for 100rpm for a full revolution

11. Carmen spoke model • Model results; full revolution • Here we see the torque peaks correspond to each point a spoke crosses the –ve X axis i.e. when a spoke passes through the coil centres 90o 162o 18o rotation 234o 18o 162o 234o 306o 90o 306o • Retarding torque predicted by CARMEN for 100rpm for a full revolution Alignment at t=0

12. Carmen spoke model • Why does the torque increase? • The reason becomes evident once one looks at the eddy current distributions • What happens is the spokes rotate they create additional current paths, all the paths meet in the center and return via the central spoke it passes the coil centre. • This current gives rise to large Ix (~600A) along the spoke coupled to the BZ field generates a large Fy giving rise to a larger retarding torque. • In between the spoke transit the current distribution reverts to one similar that seen in the Electra models. In this case the currents down the spokes are ~80 amps and the torque generated by each spoke should cancel. I-1 I-2 I-0 I-3 I-4 I-0=I-1+1-2+I-3+I-4=590A I-1=I-4=265A 1-2=I-3=30A

13. Carmen spoke model • Movie showing eddy currents a wheel rotates • Note the increase of currents in the R.H.S of the wheel as the spoke passes the coil centerline

14. Carmen spoke model • Off axis torques Tx • By symmetry there should be no torque about the X axis. • This is what the models show

15. Carmen spoke model • Off axis torques Ty • There may be a torque about Y causing the wheel to “jitter”. This could be generated by a nett Fz in the interaction region. • The models indicate there may be a significant Ty, • However the full revolution model (purple curve) seems to be too crude to resolve this, but the more accurate part revolution models seem to show something • It looks like we generate ~+(2-3)N.m as the spoke approaches the coil centre and switching to –(2-3)N.m as it recede from the coil centre • This is small @ 100rpm, and should scale with the speed, I would expect ~+/-(40-60)N.m @2000 rpm . • This is not huge, I may cause the wheel to jitter? • Additionally over time it may cause significant wear in wheel bearings, particularly at higher speeds?

16. Carmen spoke model • Power dissipation • Whilst Electra predicts a power of 0.07kW to continually drive the wheel rim through the field @ 100rpm. • Carmen predicts additional power of 0.32kW is needed by the spokes as they pass through, creating peaks of .39kW. • This increases the average power to something like 0.2kW • i.e. more than double the Electra prediction

17. What happens at higher speeds? • Extrapolating the results • Higher speeds • The torque is directly proportional to the rotational speed • At 100rpm we see torque peaks of ~40N.m • So at 2000rpm one would expect torque peaks of ~800N.m This is large (Rem Electra value was ~110N.m from the rim) • The power dissipation goes as the square of the rotational speed • Whilst Electra predicts a power of 0.07kW to continually drive the wheel rim through the field @ 100rpm. • Carmen predicts mean power of 0.2kW is needed by the spokes as they pass through. Peaking at 0.4kW • So @2000rpm from simple scaling we get mean power of 80kW, this seems rather large ?? i. • I will need to run some high speed models to investigate this • Greater immersion depths • In this model just the rim is immersed in the field • Things will get worse with greater immersion depths. • This needs investigation

18. Potential fix • Is there a way around the problem? • The spokes seem to have a big effect. • To eliminate these problems it is suggested that insulating breaks are inserted in the spokes, if possible. • Schematic below outlines suggestion • Is this feasible in the current scheme? axis Insulator Wheel rim Outer spoke Inner spoke

19. summary • Conclusions • The spokes have a considerable effect at 100rpm • The simplistic extrapolation to higher speeds is pessimistic and needs to be confirmed. • It seems that although the spikes in the torque are short lived they are quite significant and at high speeds could be problematic. • Next steps to run model at higher speeds to confirm simple extrapolations. • Run 1 model to investigate immersion depth • To eliminate these problems it is suggested that insulating breaks are inserted in the spokes, if possible.