Papers

Displacement and Flow Modeling of a Non-Linear Gear Pump With Multi- Viscosity Testing Using Exhaustive Regressor Search – A Case Study

Published 2024

Abstract:

A precision, iterative algorithm called Exhaustive Regressor Search (XRS) has been developed for optimizing hydraulic fluid power pump models based on empirical data. XRS starts with user-defined regressors derived from established physical properties and performs regressions on all possible combinations of regressors iteratively, progressively increasing complexity until convergence. The ultimate goal is to identify the optimal model and displacement.

The number of potential models can be extensive, reaching hundreds or thousands depending on the regressor count. Following regression, analysis algorithms identify the optimal model and two displacements: theoretical and regression-based. These align when the constant regression coefficient is precisely 0.0, a condition virtually impossible due to measurement error. The practical aim is to converge on the model with the least difference between theoretical and regression-based outcomes.

XRS employs a unique binary truth table with 1’s and 0’s to govern regressor combinations. Each regressor corresponds to a specific truth table bit column, ensuring all combinations are considered exhaustively. This contrasts with manual regressor selection/deselection, which could consume weeks or months if using commercial regression programs which require manual trial- and-error searches for the optimal combination of regressors.

The primary aim of the paper is to provide sufficient instruction on the principles of XRS Analyses, supported by the results of a case study involving a hydraulic pump, with detail sufficient to guide computer programmers to develop a public domain program for conducting XRS Analyses. The secondary aim is to develop the best methods for analyzing the results

This paper provides comprehensive insights for readers interested in implementing XRS Analysis. It combines convergence analysis with iterative model creation, accommodating nonlinear models and multiple test viscosities using ISO standard data. XRS Analysis converges on optimal pump models and displacements, even in the presence of non-linearities, offering advantages over linear Operational Regression Functions (ORF) that expose systematic non-linearities but yield sub-optimal models.

It is a narrative on how XRS Analyses will converge on an optimal model of the pump and the optimal value of its displacement in the presence of measurable non-linearities. It also shows how a linear Operational Regression Function (ORF) will lead to a sub-optimal model, but will expose the systematic non-linearities.

Predicting the Dominant Resonant Frequency in Hydromechanical Systems Containing Fluid Compressibility, Fixture Compliance and Unequal Area Cylinders

Published 2005

Abstract:

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.