Linear Mathematical Models are used to Conduct Pre-Development Feasibility Studies Regarding the Doubly-Compensated Hydrostatic Transmission
Linear, steady-state mathematical models are used to investigate the performance and tuning of the doubly-compensated hydrostatic transmission (HST). Adoubly-compensated hydrostatic transmission is one in which both the pump and the motor are outfitted with pressure compensation controls, both sequentially active and simultaneously active. The approach consists of development of a methodology to converge on the compensator settings that will achieve a targeted final performance. The synthesized compensator settings become the input into the performance models. The models then simulate the expected performance characteristics, including speed-torque characteristics, overall efficiency, insights into the actions inside the transmission along with input and output power. The techniques discussed in this paper are useful for doing pre-development feasibility investigations. It is a theoretical study. The linear models are based upon performance data for the pump and motor and do not rely upon internal mechanical dimensions, so they are practical when planning for specific applications, not for pump and motor design. The models apply to all types of positive displacement pumps and motors and with simple extensions, the models can be adapted to dynamic simulations as well, however, this paper explores only the steady-state models and methods. Graphs of the simulated performance data and all key equations are given.
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Predicting the Dominant Resonant Frequency in Hydromechanical Systems Containing Fluid Compressibility, Fixture Compliance and Unequal Area Cylinders
Many fluid power application engineers have little or no access to advanced computational methods, such as simulation and mathematical modelling. And yet, they are called upon time and again, to design and commission complex industrial machines. Many of these machines are one-of-a-kind, therefore neither funding nor time is available to conduct extensive mathematical verification, eg, simulation, before or after committing to hardware. Unlike mass produced machines of the large OEMs, who are wise to conduct extensive mathematical modelling, the designers of limited production machinery are required to rely upon less mathematically intense methodologies and rules of thumb. At the same time, clients expect complete success. The heart of many modern hydraulic machines is the electrohydraulic positional servomechanism, which lends itself admirably to computerized motion control technology. Fortunately, the design of such machines has been reduced to a series of formulas that yield the key quantities that designers need to increase the likelihood of application success. It is well-known that the hydromechanical resonant frequency can have a profound effect on servo system performance, limiting closed loop bandwidth and ultimately, positional accuracy among other things. Just knowing the dominant resonant frequency allows the designer to use simple design tools to predict the suitability of a given design to an application. There is a very well-known formula for calculating the resonant frequency of a system that is based on the load mass and fluid compressibility. However, experienced machine designers know that mechanical deflection of the housing and fixturing works to lower the resonant frequency, adding to the difficulty in achieving system control and smoothness in a routine way. This paper outlines a semi-empirical method by which a very simple algebraic formula has been derived that allows calculation of the dominant hydromechanical resonance in the presence of both fluid compressibility and mounting fixture compliance with the commonly used single rod.
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