1. (FEA) Analysis P J Smith University of Sheffield 27 th November 2008

2. Purpose There is a need to do some FEA analysis of the target mechanism to further understand the source of the driving forces and to see how critical the alignment of the components are in terms of producing non-axial forces on the target shaft. Many parameters to explore…will not list all of them here. Preliminary analysis is based upon the stator body only. Secondary analysis will introduce the shaft and the magnets and look at the interaction of these with the stator.

3. Purpose An initial simple model of the stator has been built. This model assumes complete axisymmetric driving coils and does not introduce any other material. This model is to be compared to a field map that was produced using the R78 demonstrator stator. (Where excessive wear was observed on the target shaft after 340K actuations.) It’s a very simple model but as will be shown the overall agreement with the data is fairly good. The model will be improved to see if the agreement can be improved.

4. Modelling Software The modelling is done using a software package called ‘Opera’ produced by a company called ‘Vector Fields’. GUI based application but it can be controlled through the use of COMI scripts. This is a scripting language that allows a model to be built in code. Its taken some time to build the necessary scripts to build the stator and to produce the data. However it is now very easy to change parameters and obtain significant amounts of data from the model. Will certainly prove to be worth the effort!

5. States These represent the six states that the stator can be in. Note that the symmetry dictates two sets of data is required at a minimum. Taken AB and AC (States 1 & 2)

6. Data Taking The stator was set up in a rig that allowed the stator’s radial field to be measured. Thanks to Craig McWaters for persevering with the set up and obtaining the data!

7. Data Taking The stator was set up in a rig that allowed the stator’s radial field to be measured.

8. Data Taking The stator was set up in a rig that allowed the stator’s radial field to be measured.

9. Data The stator was set up on a rotating stage so that the it could be freely rotated around a given point by a full 360 deg. The hall sensor was at the end of a long probe. The probe could be moved up and down and the hall probe reading recorded through computer control. (The probe motion corresponds to axial motion through the stator) The probe was placed on the inner edge of the vacuum tube that passes through the centre stack of coils and drawn out axially. This process was repeated at 30 deg increments around the inner edge of the stator by rotating the stator on the stage. This process was repeated twice with a DC current of 7.2 Amps, once through phases AB and once through phases AC (States 1 & 2)

10. Data Analysis B Field measured for every 0.2mm axially over a distance of 120mm. Repeated at 30 deg increments.

11. Data Analysis B Field measured for every 0.2mm axially over a distance of 120mm. Repeated at 30 deg increments.

12. Data Analysis B Field measured for every 0.2mm axially over a distance of 120mm. Repeated at 30 deg increments. For perfect axis-symmetry then the data should overlap perfectly, so taking the standard deviation on the spread of the data for each set of points at a given axial depth gives some indication of either field asymmetry or misalignment/error of the measuring rig. There clearly is an offset in the data

13. Data Analysis Show that there are several peaks in the data that are at different heights. Will justify that this is an expected feature later. But there are a couple of other interesting features in the data that I wish to show before matching this to the model. If you take the value at each peak in each set of data (different sets correspond to different rotation angles) you will expect to see a spread of points as each peak is at a different amplitude. If you take the average of these peaks for each set of data and see how this average evolves as you move through the sets of data then any trend indicates a deviation from axisymmetry. Difficult to estimate the error on the reading as there is only one data reading for every geometric position. (Any suggestions welcome)

14. Graphs for AC phase (State 2)

16. Graphs for AB Phase

18. Data Analysis AB - > Almost certainly a measurement misalignment at some point during data taking. AC -> Not clear whether this is statistical fluctuation, measurement uncertainty or a real field asymmetry.

19. Modelling Simple axisymmetric model using only coils. FEA not used for this simple case because OPERA can use a field calculator where only coils and air exist.

20. Modelling Plots of axial field as a function of radial distance from the centre-line of the stator….

21. Modelling Plot of axial field as a function of radial distance from the centre-line of the stator.

22. Modelling Plot of axial field as a function of radial distance from the centre-line of the stator.

23. Modelling

25. Matching the Data to the Model Does the matching distance make sense? Yes! - Considering the geometry of the vacuum tube and the hall probe. One assumption made wrt orientation of probe within the stator – waiting for confirmation.

26. Matching the Data to the Model So how quickly is the field changing as a function of distance? Take a radial plot at the point where the axial field is at a maximum. Numerically Differentiate

27. Matching the Data to the Model So how quickly is the field changing as a function of distance? Take a radial plot at the point where the axial field is at a maximum. Numerically Differentiate

28. Matching the Data to the Model Summary… PhaseHall Position  Ave  Max dB/dR  (mm) Ave  (mm) MAX AB7mm0.0003430.0007530.00382 0.0900.197 AC7mm0.0005390.0011680.003899 0.1380.300

29. Conclusion The data appears to fit the model quite well although further refinements may be possible. Matching the data to the model suggest that there is a field asymmetry on phase AB of 200um and on phase AC of 300um. It is not possible to tell with the current data whether this field asymmetry is real or whether it is an artefact of the measurement apparatus. But it has put an upper limit on the error. Next job is to – Improve the stator model. Can we get a better match – end effects? – Introduce the shaft and magnets and have a look at the predicted force profiles in the case of perfect symmetry. Does this match what is observed?