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Pump and Motor Characteristic Curves

What Are Characteristic Curves?

A characteristic curve is a component-specific plot that shows how a change in one dynamic variable might affect others. Such curves capture the performance of a component over a range of operating conditions and are commonly used in component selection, sizing, and analysis. To aid in these tasks, Simscape™ Fluids™ software enables you to plot the characteristic curves of select components.

Supported Blocks and Block Variants

You can plot the characteristic curves of the following blocks from the Hydraulics (Isothermal) library:

These components have variants that you can select from. Only one variant enables you to plot characteristic curves—the default Analytical or tabulated data. To check or change the block variant, right-click the block to open its context-sensitive menu and select Simscape > Block Choices. Selecting the Analytical or tabulated data variant adds a Fluids > Plot characteristic option to the context-sensitive menu.

Performance, Efficiency, and Loss Curves

The types of characteristic curves that you can visualize depend on the block parameterization that you select. Three performance curves are always shown—one of the volumetric flow rate, one of the mechanical power, and one of the mechanical-hydraulic power ratio. The pressure difference and output shaft speed serve as the independent variables in each case. The pressure difference is shown on the horizontal axis. The shaft speed is shown through a series of curves, one for each value of the shaft speed.

Characteristic Curves of a Fixed-Displacement Motor in the Default Configuration

If the Leakage and friction parameterization parameter is set to a Tabulated data option, two additional curves are shown. These curves are of the volumetric and mechanical efficiencies for the Tabulated data — volumetric and mechanical efficiencies parameterization and of the volumetric and mechanical losses for the Tabulated data — volumetric and mechanical losses parameterization.

Here, too, the shaft speed and pressure difference serve as the independent variables. However, the shaft speed is now the variable on the horizontal axis. The pressure difference is now shown through a series of curves, one for each value of the pressure difference. The values plotted are those specified directly in the block dialog boxes. The purpose of these curves is to provide a means to visually check your tabulated data inputs for inadvertent errors.

Efficiency Curves of a Fixed-Displacement Motor in the Default Configuration

The table summarizes the types of curves that Simscape Fluids generates for the different block parameterizations. Notice that this table applies only to the Fixed-Displacement Motor and Fixed-Displacement Pump blocks in the Hydraulics > Pumps and Motors library.

How Characteristic Curves Are Generated

Simscape Fluids generates the characteristic curves of a component from a test harness for that component. The test harness comprises a simple model with blocks representing the component of interest, the hydraulic operating conditions, the mechanical operating conditions, and the fluid properties. You open the test harness from the block context-sensitive menu. Right-click the block and select Fluids > Plot Characteristic.

The model simulates under a variety of operating conditions—at different shaft speeds and pressure differences—with the simulation results providing the data need to plot the performance curves. You can change the fluid properties and block parameters in the source model or in the test harness before simulation. If you change block parameters in the source model, you must regenerate the test harness by right-clicking the block and selecting Fluids > Plot characteristic again.

Changes that you make to the block parameters do not carry over to the source model, even after you close the test harness. If you intend to keep any changes to the test block, consider making those changes in the source model directly.

Example 1: Plot Performance Curves

As an example, plot the performance curves of a fixed-displacement motor in a hydrostatic transmission model. You can use these curves to analyze the performance of the motor under different operating conditions.

  1. At the MATLAB® command prompt, enter sh_hydrostatic_trans. A Simscape Fluids model of a hydrostatic transmission system opens. The model contains a Fixed-Displacement Motor block, named Motor, with the Leakage and friction parameterization parameter set to Analytical.

  2. Right-click the Motor block and select Fluids > Plot Characteristic. A test harness opens with a list of steps needed to generate the characteristic curves. Step 2, Define range of pressure and angular velocity, provides the range of operating conditions under which to simulate the motor.

  3. Click step 4, Generate plots. Simscape Fluids simulates the motor component at various shaft speeds and pressure differences and uses the simulation results to generate the characteristic curves. The shaft speeds and pressure differences are the defaults specified in step 2, Define range of pressure and angular velocity.

Notice that the characteristic curves generated in the Analytical parameterization do not include efficiency or loss curves. The purpose of such curves is to visually check any input efficiency or loss data, and this data is reduced to a constant in the Analytical parameterization.

Example 2: Plot Efficiency Curves

Specify the motor efficiency in tabulated form and visually check the specified data for errors by plotting the efficiency curves. This example is based on the same sh_hydrostatic_trans model used to plot the characteristic curves of a fixed-displacement motor in the Analytical parameterization.

  1. In the dialog box of the Fixed-Displacement Motor block named Motor, set the Leakage and friction parameterization parameter to Tabulated data — volumetric and mechanical efficiencies. The data ranges of the Pressure drop vector for efficiencies, dp and Shaft angular velocity vector for efficiencies, w parameters replace those entered in step 2 of the motor test harness for the Analytical parameterization.

  2. In the field for the Volumetric efficiency table, e_v(dp,w) parameter, enter the matrix shown below. This matrix is similar to the default efficiency matrix but contains an intentional numerical error.

    [0.816, 0.908, 0.954, 0.977, 0.981, 0.984;...
     0.325, 0.663, 0.831, 0.916, 0.925, 0.0946;...
     0.137, 0.568, 0.78, 0.892, 0.893, 0.91]

  3. In the block diagram, right-click the Motor block and select Fluids > Plot Characteristic. A new test harness opens for the motor component.

  4. Click step 4, Generate plots. Simscape Fluids simulates the motor component and generates two sets of curves—the performance curves, similar to those obtained in Example 1: Plot Performance Curves, and the efficiency curves showing the efficiency tabular data.

    The figure shows the volumetric efficiency curves. The curve corresponding to a pressure difference of 1,000,000 Pa reveals that the data point corresponding to a shaft speed of 400 rad/s is a likely numerical error and should be fixed before simulation.

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