Permanent magnet linear actuator: non-linear causal modelling

Abstract:
In order to better understand the causes of vibration in a two-actuator permanent-magnet compressor between 50 and 500 Hz, a precise model is necessary. Vibrations in this type of compressor are mostly due to asymmetries, while their harmonic content is dictated by non-linearities. In this paper, measured magnetic properties of magnet assemblies are used in a finite element model in order to obtain behaviour laws for each actuator. In order to obtain a causal model, force and current are represented as a function of the piston position and magnetic flux through the actuator. The model is validated using inductance measurements as well as force measurements at fixed rest position. This allows to model the actuators non-linear behaviour and to give an estimate of the vibration forces order of magnitude at different frequencies induced by the magnetic asymmetries. Causal behaviour laws generated by the proposed model can be easily integrated into a global compressor model to predict vibrations, power consumption or electrical harmonics. The global model could also be used to test vibration reduction algorithms.