Look-up Tables

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Look-up tables are indispensable for the dynamic simulation of fluid systems. A look-up table is mathematically a set of data points of a sampled function F with N variables, which can also be empirical. The look-up table maps input values onto the output value by search and interpolation.

The wide range of application for look-up tables is reaching from nonlinear component behavior, such as the flow area of valve metering edges or the stroke dependent working diameter of an air spring, to the representation of measured component behavior, such as cylinder friction, valve flow or the flow of a constant pump.

In practical applications the output value of a look-up table very often depends on more than one input value. While it is possible to describe a valve’s flow area or the stroke dependent working diameter through a simple x-y relation, for the representation of measured valve flow already two input values (valve opening and pressure difference) are required and for a fixed displacement pump flow the number of required input values increases to three (speed, system pressure, fluid temperature). In the case of a variable displacement pump the tilt angle would add a fourth input value.

The DSHplus look-up table editor is the administration module for making and modifying the look-up tables of the DSHplus components. 1-D look-up tables are described as an x-y set of points. Within the range of the look-up table intermediate values are derived from linear interpolation. An extrapolation outside of the table’s range is not carried out, the respective final value of the table is kept constant.

Higher dimensional look-up tables may be based on Cartesian coordinates or line-based look-up tables.

In a Cartesian table all data points form a grid structure with an output value assigned to each input value on either axis. This type of look-up table is suited for numerically derived data where all output values can be exactly calculated. In case of measurement values the Cartesian form poses to be problematic because data for the exact grid points is hard to obtain and requires complex postprocessing of the raw data.
Line-based tables are ideally suited for measurement data, a 2D-look-up table e.g. is constituted of several 1D-tables, which may all have different data point spacing. An example would be a set of measurements of flow vs. pressure drop of a valve for different valve openings.

3D-look-up tables are made by combining 2D-tables, there is no limitation in number or type, line-based and Cartesian tables can be mixed.

To create look-up tables DSHplus offers two modules. Using the Look-up Table Generator data curves e.g. from a manufacturer data sheet are digitalized into a 1D-look-up table. The DSHplus Data Interpolator can create 2D-tables from an arbitrary amount of unsorted x-y-z data points.