A core loss measurement system including a custom-made fixture, a signal generator, a power amplifier, and a power analyzer was developed and tested. The fixture was built with 16 copper wire turns wound in a closed loop geometry bundle. This arrangement also mechanically held in place the stator under test. A magnetic circuit was completed once the fixture was powered. The sinusoidal excitation signal was provided by an Agilent Signal 33220A generator (Agilent, Santa Clara, California) and swept from 0 to 50 kHz. The signal was amplified using a high-fidelity AE Techron 7224 (AE Techron, Elkhart, Indiana) power amplifier and the amplifier’s gain adjusted to maintain a constant amplitude of 2 V at the amplifier’s output terminals (VI(t) on Figure 3). A Yokogawa WT1600 digital power meter (Yokogawa, Newnan, Georgia) was used to capture electrical parameters at various circuit locations.
During individual test runs, the power amplifier drove the circuit using a reference sinusoidal waveform produced by the signal generator. The power analyzer measured a set of parameters including root mean square (RMS) voltages, RMS currents, and active and reactive powers. The complete core loss test included a comprehensive frequency sweep. The system was fully automated via LabVIEW (National Instruments, Austin, TX).
Fixture Modeling and Parameter Identification
Physically, the fixture was built using an inductor element coupled to a resistor. Based on this premise, the fixture modeling was developed as two different R-L configurations as shown in Figure 3. The resistive element (Rf) in the model represents the resistance of the wires, whereas the inductive element (Lf) represents the inductance resulting from the geometry of the wire bundle that constitutes the fixture. The power analyzer allowed for the measurement of active and reactive power components of the given load, facilitating the estimation and validation of the R-L model’s parameters. The measured power components without a stator in the fixture were used to estimate the parameters in both series and parallel R-L configurations. The fixture’s model parameters were identified from the acquired input-output data set using Matlab (The MathWorks, Natick, Massachusetts).
The first model of the fixture’s impedance (Zf) consisted of having a resistance (Rf) and inductance (Lf) in series; Zf was represented as
where ω is the angular frequency. The second model included the same two Rf and Lf parameters arranged in parallel, with Zf represented as
Stator Core Loss Characterization
Following the characterization study on the performance of the fixture, tests were conducted to investigate the core loss characteristics of the MVAD pump stator. A representative set of 30 stators was randomly obtained from stock. These stators had completed the RI process and were all approved to be conformant to the drawing’s specifications. The system was calibrated after instrumentation warm-up and before each run so that the voltage measured at the output of the amplifier (input to the fixture circuit), VI(t) in Figure 3, with the fixture in place but without a stator core, was 2 ± 0.001 V at 1 kHz. The calibration ensured consistent measurements throughout the test series and mitigated potential variability introduced by cabling or any other physical variables. Each stator was installed in the fixture and run over a frequency range spanning from 0 to 50 kHz at a resolution of 10 Hz. The system’s data set was automatically captured to file via LabVIEW and included frequency, input and output voltages, fixture current, and input and output powers.
A parameter estimation study was conducted on both series and parallel fixture models (Figure 3). The mean square error (MSE) figure of merit was used to rank the model’s fit to the experimental data. The MSE for the series R-L model was 1.461 × 10−6, whereas the MSE for the parallel R-L model was 0.508. Based on the MSE and similarity to the physical and electrical configuration of the fixture, the series R-L model of the circuit was selected as the best fit to the fixture’s behavior. For the series R-L model, the values of the estimated parameters Rf (resistance of the fixture) and Lf (inductance of the fixture) were 0.509 ± 0.01 Ω and 32.79 ± 0.001 μH, respectively. The parameters for the parallel configuration Rf and Lf were 1.015 ± 0.01 Ω and 94.22 ± 0.001 μH, respectively.
The impedance behavior of the fixture from 0 to 5 kHz compared with the theoretical model is presented in Figure 4. These results provided confirmation that the series R-L model is capable of adequately reproducing the behavior of the physical core loss fixture in the frequency range of interest.
The fixture was further characterized by analyzing the power transfer function (output-to-input power ratio) versus frequency. The frequency response of the power transfer function was flat from 10 Hz to 5 kHz. Analysis of the fixture’s response indicated that the fixture did not interfere with the stator core loss measurements.
The core loss fixture behaved as a high pass filter, as expected for a series R-L circuit model. As frequency increases, the voltage at the fixture’s terminals tends to follow the input voltage. However, current decreases because the inductor’s impedance increases with frequency. Thus, the fixture’s power also decreases with increasing frequency as shown in Figure 5 (trace B).
Performance of the stators was evaluated by comparing the total power used by the fixture when the stator was in place. Figure 5 (trace A) shows a snapshot of 10 representative stators and their respective average and standard deviation power performance from 0 to 50 kHz. The power variability across stators is depicted in Figure 5 (trace A). Figure 5 (trace C) shows the calculated stator power core losses. A characteristic response curve with a peak at around 2.5 kHz was further investigated. Figure 6 shows a close-up of the performance of four stators in a range of 2–3 kHz. The peak of the fixture power was used to differentiate the stators. Figure 6 depicts in detail the power used by four stators of the 30 tested during the study.
Results from a sample population of 30 stators demonstrated that the peak power consumption of all the stators under test occurred within a frequency range of 2.3–2.5 kHz. Stators 2 and 3 represented the maximum and minimum powers of the stator population, respectively. The measured power range between stators 2 and 3 was approximately 0.005 W corresponding to a span of approximately 1.5%.
As described earlier, detailed motor performance data in mechanical circulatory support devices have not been widely reported in the literature. In particular, for contactless devices such as the MVAD pump where the pump impeller also serves as the free floating motor rotor, core loss behavior remains an important, albeit complex, field of study. The study described in this article explored a combined modeling and experimental approach to develop a system capable of capturing the core losses of the MVAD pump stator including the small differences within a stator population caused by manufacturing variability. Results from the modeling study confirmed that a series R-L model was capable of reproducing the electrical characteristics of the core loss fixture. The model could be used to explore the expected performance system variations with different circuit topologies. Furthermore, the modeling results also provided the initial building blocks for a more comprehensive model where more complex behaviors, such as the ones produced with motor commutation signals, could be explored. Results from the stator core loss study presented an initial indication of manufacturing variability among the stator population. In addition, the observed small differences in core loss between stators not only revealed a tightly distributed stator population but also confirmed that the core loss measurement system had the capability to discern small manufacturing differences expressed in the peak of the fixture’s power measurement. The study was focused to evaluate a single electrical configuration topology and a single fixture design.
A core loss measurement system for the MVAD pump was developed and tested. The system was used to characterize the core losses in the stator and to investigate differences within a population of stators. Results from the study demonstrated that the system was capable of measuring differences between stators when using the peak power as an indication of core loss. The system could be further used to better characterize and model the stator’s core magnetic behavior, and it has the potential to be used for future motor evaluation and motor design optimization. Overall, the results from the study support the potential use of the core loss system as a tool to be implemented during manufacturing operations with the final goal of assuring consistent pump performance.
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MVAD; core loss; statorCopyright © 2015 by the American Society for Artificial Internal Organs