A sensor-less coil current-inductance based spool displacement polynomial model was proposed and key coupling parameters were obtained from designed experiments in order to address the drawbacks of the affected dynamic characteristics of the valve core by the externally connected sensor. The coupled electromagnetic models of the on-off solenoid valve were developed, and the time-varying inductance-spool displacement model was derived. A solenoid valve optical experimental system was constructed, and the non-contact single beam laser measurement method was used to capture the valve spool displacement. An algorithm for inductance-displacement fitting was established. The results from the model and experiments were compared when the coil voltage was tested from 25 V to 29 V, and the spool was set in air or oil. Results showed that the average estimation error of the inductive method in air and oil environment was 7.0% and 9.2%, and the sensitivity to coil supply voltage variation was low. The model is suitable for valve spool displacement sensing.
Fig.1Structural diagram of SV08-25 solenoid-operated on-off valve
Fig.2Electromagnetic schematic diagram of valve’s driving coil
Fig.3Analysis of laser optical path in the oil environment
Fig.4Optical measurement system
S/mm
L/%
r/μm
w/nm
d/mm
f/kHz
100±35
±0.1
70
655
120
0.66
Tab.1Major parameters of laser displacement sensor
Fig.5Laser displacement sensor calibration curve
Fig.6Extraction of desired coil current and laser displacement sensor signal sections
s5/(mm· mH?5)
s4/(mm· mH?4)
s3/(mm· mH?3)
s2/(mm· mH?2)
s1/(mm· mH?1)
s0/ mm
4.70
?5.67
2.76
?6.74
8.37
?41.67
Tab.2Inductance-displacement polynomial model coefficients
Fig.75th order polynomial fitting of inductance and spool displacement
Fig.8Comparison of inductance model and laser displacement sensor measurement results
Fig.9Absolute error between inductance model and laser displacement measurement results
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