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On the dynamics of ultrasonic actuators, coupled to near-field acoustically levitated objects – Reduced order modelling and experiments
Last modified: 2017-05-20
Abstract
When an ultrasonic tool is subject to an external loading, its impedance may change, affecting its resonance frequencies, damping ratios, and amplification. The same effect occurs when an ultrasonic actuator is used to levitate planar objects by means of near-field acoustic levitation. Namely, different loadings or excitation conditions, change the thickness of the gas layer trapped between the levitated object and the actuator’s driving surface, altering the stiffness and the damping of the coupled system. Moreover, for sake of high efficiency, the actuator being used usually has a very low damping. Thus, even small variations in the different parameters of the system can reduce its performance, dramatically. Therefore, in order to be able to accurately and efficiently control the height of a near-field acoustically levitated object, a constant excitation frequency is impractical, so a resonance-tracking algorithm must be used.
To investigate the phenomenon discussed above, in this work a comprehensive model, coupling a piezoelectric actuator operating at ultrasonic frequencies, to a near-field acoustically levitated object, through a thin layer of compressible gas is developed, see Fig. 1 (Left). The latter is derived by introducing a simplified model of the nonlinear squeezed layer of gas, and a variational model of the solid structure and the piezoelectric elements. The resulted model couples a transfer function, representing the complex excitation amplitude of the driving surface assuming the steady-state height of the levitated object is given, to a transcendental equation, providing the additional relation between the height and the excitation amplitude. Since the last relation was already verified in the recent past, in order to validate the abovementioned model, an experimental setup, obviating the use of the transcendental equation was utilized. In this setup, the object is fixed to an XYZ stage, allowing to change the average thickness of the squeezed gas layer, manually.
Fig. 1 (Right) presents several experimental frequency responses of the actuator's driving surface, measured under different average clearances between the driving surface and the fixed object. From this figure, one can notice that the maximal gain, the natural frequency and the damping ratio of the designated mode, vary monotonically with the clearance. The monotonic increment of the maximal gain and the monotonic decrement of both the natural frequency and the damping ratio are all highly correlated with the developed model. Therefore, this model can serve as a basis for model based resonance-tracking algorithms, striving to provide the optimal excitation frequency, for sake of maximal efficiency.
To investigate the phenomenon discussed above, in this work a comprehensive model, coupling a piezoelectric actuator operating at ultrasonic frequencies, to a near-field acoustically levitated object, through a thin layer of compressible gas is developed, see Fig. 1 (Left). The latter is derived by introducing a simplified model of the nonlinear squeezed layer of gas, and a variational model of the solid structure and the piezoelectric elements. The resulted model couples a transfer function, representing the complex excitation amplitude of the driving surface assuming the steady-state height of the levitated object is given, to a transcendental equation, providing the additional relation between the height and the excitation amplitude. Since the last relation was already verified in the recent past, in order to validate the abovementioned model, an experimental setup, obviating the use of the transcendental equation was utilized. In this setup, the object is fixed to an XYZ stage, allowing to change the average thickness of the squeezed gas layer, manually.
Fig. 1 (Right) presents several experimental frequency responses of the actuator's driving surface, measured under different average clearances between the driving surface and the fixed object. From this figure, one can notice that the maximal gain, the natural frequency and the damping ratio of the designated mode, vary monotonically with the clearance. The monotonic increment of the maximal gain and the monotonic decrement of both the natural frequency and the damping ratio are all highly correlated with the developed model. Therefore, this model can serve as a basis for model based resonance-tracking algorithms, striving to provide the optimal excitation frequency, for sake of maximal efficiency.