TEAM Workshop Problem No. 24
Nonlinear Time-Transient Rotational Test Rig

N. Allen and D. Rodger
School of Electrical Engineering, University of Bath, Bath, BA2 7AY, U.K.

Abstract

A test rig for validating 3D nonlinear time-transient codes is presented. The rig, of configuration similar to that of a switched reluctance machine, is made of solid medium-carbon steel and mounted in a nonmagnetic cage which can rotate about a stainless shaft. The steel magnetization curve and conductivity have been measured. Various measured output quantities are presented for comparison with computer simulations.


General Description of the Test Rig

The test rig consists of a rotor mounted on a nonmagnetic stainless steel shaft and a stator fixed inside a swinging nonmagnetic cage which can move relative to the shaft. The dimensions of the solid steel rotor and stator are shown in Fig. 1. The axial length is chosen to be 25.4 mm, which should be small enough compared with radial dimensions to produce non-negligible 3D end effects.
The stator poles are fitted with 350-turn coils, of dimensions as detailed in Fig. 2. The rotor is loked at 22° with respect to the stator, providing only a small overlap between the poles. A step voltage of 23.1 V is applied to the coils which are connected in series and have a combined resistance of 3.09 Ohms. The resulting torque rise which would tend to align the stator and the rotor poles is measured using a piezoelectric force transducer restraining the movement of the stator cage. The magnetic fields are high enough to significantly saturate the iron in the overlapping pole corners. Preliminary results under conditions similar to those described here are presented in [1].
The test rig is not design-specific for only this experiment but can potentially be of use for other types of experiments. The rotor can be set to any angle and different levels of saturations can be easily studied.

Fig. 1 - Dimensions of stator and rotor



Fig. 2 - Coils dimensions



Fig. 4 - Hall probe location in air gap


Material Parameters

The conductivity of the EN9 steel used for the rotor and stator is measured on a sample of regular cross-section and found to be approximately 4.54E+6 S/m. The B-H initial magnetization curve of the material is also measured.
A Magnet-Physik Remagraph RE3 BH tester is used for measurements up to approximately 2T. Lucas A.V.S.D. provided measured values for the range 2T º 2.5T. The combined B-H curve is shown in Fig. 3. A set of points taken from the curve is presented in Table I. It is worth noting that prior to these material measurements, the samples, rotor, and stator pieces are annealed after machining in order to homogenize the magnetic characteristics.

Measurement System and Results

The test rig design offers a range of measurement quantities which can be compared with those obtained through computer simulations. A Kistler piezoelectric force link restraining the swinging stator cage measures the force rise when the step voltage is applied, and is easily converted to a torque curve. The force link is calibrated in situ using a range of weights. A current shunt connected in series with the set of coils measures the rise in current. The coil current is considered as an unknown variable in the computer modelling. Only the coil voltage and resistance are known initial parameters. A search coil wrapped around a rotor pole at 8.7 mm from the corner, as shown in Fig. 1, enables the measurement of the total magnetic flux. Lastly, a Hall probe is secured at a known position, shown in Fig. 4, in the air gap between the overlap of the stator and rotor poles. The reference point shown is the stator pole corner. The Hall probe measures a single component of the magnetic flux density (By in Figs. 1 and 4). It also serves as a check when a variable amplitude A.C. signal is used to demagnetize the rig before applying the step voltage. Figs. 5 through 9 show the measured step voltage, coil current, torque, search coil flux, and Hall probe flux density, respectively. As may be observed from Fig. 5, the experimental step voltage is not perfect. There is an initial overshoot of approximately 0.5 V, which is disregarded in the author's computer model. However, others may wish to use the actual measured voltage versus time. Sampled points of the voltage curve are showwn in Table II.


Suggested Computations and Discutions

Current, torque, rotor pole flux, and air gap point flux density measurements should all be compared with computer predictions. Since the size of the experimental curves included in this problem description may not be sufficiently detailed for accurate reading, Tables III to IV contain sampled points. These points are obtained from smoothed versions of the raw data. The actual raw data is readily availabe on request.
Although the proposed problem has a relatively short axial length and would be better suited to 3D eddy current modelling, a 2D representation could be used to initially explore a few aspects of the problem. The choice of the time step and option to have a variable time-stepping scheme for computational efficiently is an obvious point of discussion. The size and order of the element in the skin of the iron may be of interest. The detail of the air gap mesh required for accurate force computations can also be discussed. The periodicity property of the problem can be exploited to reduce the size of the model. Finally, for codes which do not incorporate external circuit connection, the current curve can be directly used as the input.
A complete set of all actual measured quantities can be supplied on request by email (eepna@ee.bath.ac.uk, D.Rodger@bath.ac.uk). It is hoped eventually to have the entire description available on a WWW TEAM page.


Acknowledgment

Thanks go to Lucas Advanced Vehicle Systems Development, Solihull, U.K., for their B-H measurements.


Table I - Sampled points from B-H curve

Table II - Sampled points from voltage curve

Table III - Sampled points from current curve

Table IV - Sampled points from torque curve

Table V - Sampled points from rotor pole flux curve

Table VI - Sampled points from magnetic flux density curve

References

  1. D. Rodger, N. Allen, H.C. Lai, and P.J. Leonard, "Calculation of transient 3D eddy currents in non linear media - Verification using a rotational test rig", IEEE Transactions on Magnetics, 30(5):2988-2991, September 1994.