A simple, theoretically based time domain model for the propagation of small, arbitrary signals in a finite, circular, fluid transmission line is developed. A recent simple theoretical solution for the step response at a downstream point in a semi-infinite fluid line is combined with a two-port representation of a finite line. The major feature of this finite line model is two “filters” which represent a convolution of their arbitrary inputs with the unit impulse response at the equivalent location in a semi-infinite line. Experimental tests are reported which further verify the simple semi-infinite line solution and verify the response of several example systems containing finite lines. The models developed herein show good agreement with experiment. The major anomaly noted was an amplitude dependence in the experimental response for signals larger than one percent of the bulk modulus of the fluid. Since the theory represents a linearized, small perturbation model, such disagreement might have been anticipated and is viewed as a limitation, rather than invalidation, of the model. Finally, quantitative comparisons are made between the proposed model and those in current use.
The amplitude frequency response (transfer gain curve) of 0.170-in-ID blocked pneumatic lines of the type used in fluidic systems was experimentally determined. Several lengths (20 ft and less) of tubing at several mean pressures (10 to 40 psig) were studied over the frequency range of 1-1000 cps. The electric-pneumatic analogy was used to develop theoretical predictions of the gain curves. Correlation with experiment showed that a frequency-dependent resistance and a frequency-dependent conductance were required in the analogy when the signal frequency was somewhat greater than a characteristic frequency of the line. A high-frequency model, based on the work of Nichols, was developed; it predicted the resonant gains within 2 db and the resonant frequencies within 10 percent.
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