A new mathematical model of a four-way directional control valve is presented that relies only upon externally measurable performance data to quantify the model's operational parameters. It consists of the assembling of four individual variable lands, each with its own set of independent operational parameters, thus allowing for any desired degree of asymmetry, whether deliberate or merely the consequences of typical manufacturing tolerances. Each land is modeled as a two-segment function, with constant C_D, consisting of an arbitrary order hyperbola in the land's overlap regions and an arbitrary order parabola in the land's flowing (open) regions. The two segments are fused together by forcing both the functions' values and their slopes to be equal at the transition point, one to the other. This provides a single, smoothly continuous variation in the four variable flow coefficients that ranges from 100% overlap to 100% open. Methods are derived for evaluating the operational parameters from real valve performance characteristics. The four-land model is written into a simulation program to emulate a conventional servo or proportional valve and the entire gamut of steady-state tests in the manner prescribed by ISO 10770-1 is presented. Simulated tests are conducted regarding flow metering, pressure metering, leakage metering and valve flow coefficient variation for a variety of conditions, including symmetrical parameters and arbitrarily asymmetrical overlaps for subjective comparison to known valve performance data. The model also includes parasitic pressure losses and parasitic spool bypass leakages, which are many times important contributors to valve performance and control system damping. Methods for evaluating the parasitic operational parameters are presented. The simulations are confined to steady-state because it is the steady-sate source data that reveals the most subtleties in a real valve's performance, however, dynamic performance is easily added by those who are experienced in that science. A companion paper has been written for this same conference that applies the model to a commercial, non-linear, hjghly overlapped, real proportional valve with model and simulation data compared, Johnson.
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