Your formulae need only the perpendicular component of vector B.  Exactly this component can be measured with Hall probe thin enough for insertion into the slot under investigation.

Connect the Hall probe to the head of a screw gauge or vernier calliper, then align it along the direction you want to measure the magnetic field, move it in the steps of distance you desire. Least count of screw gauge/vernier calliper and size of the hall probe determines the accuracy and precision of the magnetic field distribution.

Marek > what about the H_t, the tangential component of the field? If it would be B_t I wouldn't mind either since I am in the air.

Thank you both for your answers. I am aware that I can use Hall probes but do you have examples of such measurements already done Inside the air gap of an electric machine?

For accurate measurements Hall probe should be relatively small and its connection wires should have electrostatic and magnetic shielding (electrostatic interferences and parasitic electromagnetic induction may be induced in the wires).

As to space magnetic fields, their distribution, in principle, can be obtained using observations with enough high spatial resolution. The problem here is that even on the Sun the smallest magnetic structures are spatially unresolved, i.e. ‘sub-telescopic’. In fact, the highest spatial separation of solar observations is at present at level of about 70 km. In other hand, the smallest magnetic fluxtubes on the Sun have diameter about 15-20 km (see, e.g. Botygina O.O. et al., Estimation of the fluxtube diameters outside sunspots using Hinode observations. Preliminary results, Advances in Astronomy and Space Physics, 2016, v.6, p. 20-23). The classic method for local magnetic field measurements in spatially unresolved structures is the line ratio method (Stenflo J.O. 1973, Sol. Phys., 32, №1, 41). To measure the local magnetic fields in the solar flares other methods can be used (see, e.g., Lozitsky V.G. et al., Solar Physics, 2000, Vol. 191, No.1, pp. 171-183; Lozitsky V.G. Advances in Space Research, 2015, 55, 958).

Dear Guillaume,

There are papers where measurement obtained with the aid of a scanning Hall probe microscope (SHPM) were compared to simulations (see the link below). The main difficulty in your case, as you have pointed out, is that you need to measure the field distribution in a gap. The typical SHPM is just not designed for this purpose. Another difficulty in your case, as I understand, is that the surface of interest is not flat. Your measurement system will need to be custom-built to meet these requirements. It would help to see the specs you are aiming for to estimate the feasibility of building such a system. This also gives you the associated limitations.

What is the width of the air gap that you want to measure the field in? What is the curvature of the surface (if not flat)?

What is the required spatial resolution? What is the required size of the scanned image (i.e. what is the desired scan range)? What is the required magnetic field threshold sensitivity (i.e. what is the smallest field value that you want to measure)? How important it is to keep a constant distance between the Hall probe and the measured surface? How small should be this distance?

Regarding the tranverse component of the field, the paper by Vellekoop at al (see the other link bolow) can be useful.

Article Magnetic characterization of micropatterned Nd–Fe–B hard mag...

Article On the determination of the internal magnetic structure by m...

Mikhail,

Many thanks for your answer, this is what I am looking for! I never heard about SHPM before. I appreciate that you worked with the G2ELab and Institut Néel on that subject since I am using Flux FEA software from Cedrat.

My aim with that question is also to know if we can directly measure the magnetic force exerted on the stator by the rotor. Did you also work on that? The choise of using the Maxwell stress tensor or the virtual work principle to calculate the magnetic force is still unclear from the electrical engineer side, and measurements methods would be of great help. Some articles, such as  http://ieeexplore.ieee.org/document/4137761/ , do not show any measurements even though they work on computational problems and they only compare methods between them without a reference one. I emphasize the fact that I am looking for the local distribution and not the global distribution, in which measurements have been done and validate methods.

I will answer your questions. With what I am showing, can you tell me how realistic it is to only use FEA and if a measurement set-up would be of interest? Also did G2Elab tried to make it work on an actual machine?

• What is the width of the air gap that you want to measure the field in?

Air gaps of my motors range from 0.5 mm to 2.5 mm, so we can take the upper value to make it easier.

• What is the curvature of the surface (if not flat)?

From radii of 20 mm to 80 mm, so curvatures of 12 to 50.

• What is the required spatial resolution?

More than 50, the more the merrier but 180 would be very good for 360° around the machine

• What is the required size of the scanned image (i.e. what is the desired scan range)?

It can be a quarter of the machine or an eight depending on what we are working on. So it can be 15 points on 90° of a curvature of 20 m-1 to sum it up.

• What is the required magnetic field threshold sensitivity (i.e. what is the smallest field value that you want to measure)?

The field has huge variations between -1.5 T to 1.5 T so the threshold can be as high as 0.1 or 0.2 T.

• How important it is to keep a constant distance between the Hall probe and the measured surface?

Not so important as it is for comparison with finite elements. If I know how far I am, I will put the same distance in my model. I will not have the measurement apparatus while running a motor (the dynamic eccentricity will be problematic to keep the distance constant)

• How small should be this distance?

The air gap length so 0.5 to 2.5 mm.

Thanks a lot for your help!

Cheers,

Guillaume

Oops, somehow missed Ht.   Indeed, in air Bt is proportional to Ht, or even more generally full vector B is strictly proportional to vector H.  Deep inside the slot the tangential components of both fields can be safely assumed as being equal to zero.  The problem arises near the boundaries of a ferromagnetic parts, their sharp edges.  Here, as a rough approximation we may assume that |B| (or |H|, if you prefer) is conserved, thus Ht may be estimated as Ht2 = |H|2 - Hn2.  This approximation should work well near one edge but far the the next one.  Disregarding fully the situation outside slots will certainly introduce some errors.  But perhaps such an (in)accuracy is acceptable?  Besides, The Hall sensors indicates the values of B, not H.  Sometimes it may be important to distinguish the two.

Hi Guillaume,

The SHPM system in Institut Néel has been used for characterisation of magnetic films and magnetic micro/mesascopic systems.

I have worked on problems related to the force acting on a magnetised object in a magnetic field but your problem is more difficult, as the rotor is not a trivial object.

I think that designing a measurement system for evaluation of the magnetic field distribution inside a stator can be of interest. Let me think about it a bit more. I will send you a message later today or tomorrow.

Cheers,

Mikhail

Here is preliminary and crude answer. If You need, I will send a more detailed description with some links in a few days. To visualize and mapping of the magnetic field distribution, you can use transparent magnetic films of magnetic garnets, in which the stray field of the studied objects create the patterns of the magnetic flux lines . Another way is to scan the studied area using magnetoimpedance sensors of magnetic field with ferromagnetic microwires (some articles about this subject You can look in my profile).