A Theoretical Analysis of the Response of a Loaded Hydraulic Relay

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Abstract
This paper is divided into four sections dealing with the response (both velocity and displacement) of a loaded hydraulic relay to Part I step function, Part II ramp function, Part III sinusoidal input, and Part IV general input. In Part IV equations of motion are developed for any variation of the input valve and these include a viscous-damping term and first-order contributions due to oil compressibility and leakage past the ram. The relay with feedback linkage is treated and parameter limits are established for normal (cavitation-free) motion. The remaining sections analyse the system in turn for the various inputs by solution of the equations of motion, but with increasing restrictions. In Part II methods are given for extending the case to linear closing of the valve and a delta function input. Valve overlap is briefly introduced in Part III. Cavitation criteria in terms of general non-dimensional parameters are developed in all sections. Many results are presented graphically or in tabular form, the mathematics being reserved for appendices whenever possible.

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