1. Spinning Wheel Data Analysis Duncan Scott Magnetics and Radiation Sources group ASTeC STFC Daresbury Laboratory

2. Duncan Scott: Spinning Wheel April 2009 In this data the wheel is being moved in relation to the magnet poles Displacement refers to wheel edge and pole edge Changing Displacement Data March 27 th 2009 Magnet PoleWheel Displacement

3. Duncan Scott: Spinning Wheel April 2009 Changing Displacement Data March 27 th 2009 Wheel spun at 8.3 Hz for 120 seconds Wheel moved in and out of poles Example torque transducer reading 40mm displacement zero field (2.4Khz) Mean Torque

4. Duncan Scott: Spinning Wheel April 2009 Mean Torque Vs Displacement (27/3/09) Find means for each data set Colours define direction wheel is moved Looks like a systematic error – backlash in the wheel movement device (although only one way) Can’t move the wheel completely out of the field Edge of Wheel at edge of pole Wheel Inside pole Wheel outside pole

5. Duncan Scott: Spinning Wheel April 2009 Mean Torque Vs Displacement (27/3/09) Error bars are large for standard deviation …

6. Duncan Scott: Spinning Wheel April 2009 Mean Torque Vs Displacement (27/3/09) … or small for standard error (σ/√N)

7. Duncan Scott: Spinning Wheel April 2009 Line fit Displacement Data When compared to 1 line fit 2 line fit (separated at edge of wheel at edge of poles) looks better Correcting for systematic errors due to wheel direction could improve fit

8. Duncan Scott: Spinning Wheel April 2009 Fourier Transform of Torque Displacement Data We can also take the Fourier Transform of the torque data, e.g. 40mm displacement data from before

9. Duncan Scott: Spinning Wheel April 2009 Fourier Transform Displacement Data Close up and do some peak finding

10. Duncan Scott: Spinning Wheel April 2009 Fourier Transform Displacement Data However 1 large unexplained peak at ~135 Hz Wheel Harmonics, etc

11. Duncan Scott: Spinning Wheel April 2009 Fourier Transform Displacement Data Can look at the intensity of each peak as the wheel moves in and out of the field. E,g for peak at ~50Hz Colours similar to before to indicate direction of wheel

12. Duncan Scott: Spinning Wheel April 2009 Fourier Transform Displacement Data Plot Intensity of each peak Doesn’t look like much of a pattern

13. Duncan Scott: Spinning Wheel April 2009 Fourier Transform Displacement Data No real pattern for peaks due to the wheel freq, 8.3 Hz

14. Duncan Scott: Spinning Wheel April 2009 Fourier Transform Displacement Data Or spoke frequency, 5 x 8.3 Hz

15. Duncan Scott: Spinning Wheel April 2009 Acceleration Data Also looked at accelerating the wheel to 500 rpm This is measured directly in the.280 data (800Hz)…

16. Duncan Scott: Spinning Wheel April 2009 … or can be calculated from the angle data in the.180 files (2.4 kHz) I.e. look for complete revolutions Acceleration Data Initial Angle 1 Turn

17. Duncan Scott: Spinning Wheel April 2009 Acceleration Data Time Taken for one revolution Overlaps.280 data

18. Duncan Scott: Spinning Wheel April 2009 MI Calculation MI = Torque \ Angular acceleration Angular Acceleration = Δω\ΔT We’ve already calculated the time for each revolution

19. Duncan Scott: Spinning Wheel April 2009 MI calculation Torque is more tricky Try mean torque over revolution period (?) MI =2.2, σ=0.51 =2.5, σ=0.48 =3.5, σ=0.44 There must be other ways to calculate this…

20. Duncan Scott: Spinning Wheel April 2009