Defining Load Curves


The information on this page applies to the following analysis types except where indicated:

Mechanical Event Simulation (MES)

Static Stress with Nonlinear Material Models

 

In a mechanical event simulation analysis and a static stress with nonlinear material analysis, a majority of the loads follow load curves. The load curves are defined in the "Load Curves" tab of the "Analysis Parameters" dialog. Any shape of curve can be entered here.

 

Select the "Add next load curve..." or "Add load curve..." button to add another load curve. This allows you to have different loads follow different loading curves. For example, gravity may be constant throughout the analysis, so it is assigned to one load curve. A force may vary sinusoidally to simulate a rotating imbalance, so it is assigned to a different load curve.

 

The load curve is defined in the "Data for Selected Load Curve" section by a set of points that idealizes the real curve by a series of straight line segments. The first column is either time or a result (see details below), and the remaining columns adjust the loads assigned to the load curve, typically by multiplying the load. (Actuator elements and prescribed displacements use the load curve "multiplier" as the change in length or rotation, not as a multiplying factor.) The load curve is linearly interpolated as necessary to determine the multiplier at the corresponding time or result.

 

Use the "Add Row" button as necessary to define more points on the load curve, or the "Delete Row" button to remove the current row. The load curve data points need to be entered in ascending order by the time or result; use the "Sort" button if the data is not entered as such.

 

You can also import a load curve using the "Import load curve..." button. First, create a text file in a "Comma Separated File (.csv)" format where each line of the text file corresponds to a row of the load curve, and a comma separates each value on the line for each column of the load curve. (The load curve's "Index" column is not included in the text file.)

 

Tip

The destination load curve should have the same number of columns as the CSV file. For example, if using a CSV file with 4 columns for a results-based load curve, use the "Add load curve..." and "Add Column" buttons as needed to create a blank load curve table with 4 columns.

Tip

The values in the comma separated file are imported using the active Display Units. Change the Display Units if necessary before importing the data. For example, a value of "3.14" is imported as 3.14 second if the Display Units are set seconds, and 3.14 minutes if the Display Units are minutes.

Time-Based Load Curves:

When the load varies as a function of time, choose "Time" in the "Data for Selected Load Curve" section. The load curve then has two columns: "Time" and "Multiplier 1". Enter the data points for the load curve directly into the "Load Curve" spreadsheet, or import the load curve (see above).

 

Note that the "Time" column of the load curve is converted based on the active Display Units.

 

Tip

When approximating a higher order curve with a series of straight line segments, the spacing of the points in the load curve should be smaller than the smallest time step that will be encountered in the analysis. For example, imagine a runway crane that accelerates at a known rate. This is simulated by applying a prescribed displacement at the location of the wheels, where the displacement versus time is d = 0.5*a*t^2. If the load curve is calculated and entered at time steps t based on the capture rate, then the curve is followed precisely as long as the time steps are never reduced in the analysis. As soon as the time step is automatically reduced in order to converge on the solution, the load curve is interpolated. When this occurs, the prescribe displacement is not following the precise acceleration equation. See Figure 1.

 

Load Curve Multiplier

 

Load Curve:

theoretical

approximation

 

Time

Figure 1: Section of a Load Curve
Time steps #15, #16, and #17 follow the theoretical curve. If step #18 were able to converge, the load would still be on the theoretical curve (#18). But when the time step is reduced, steps #18 and #19 are interpolated, so this results in a slightly different load. In many cases, the difference is negligible (especially considering the approximations made by FEA in general).

 

Result-Based Load Curves:

Imagine magnetic contacts in a switch assembly. The force due to magnetic attraction is not a known function of time because the displacement of the contact (due to other loads in the analysis) versus time is unknown. The magnetic force varies depending on the separation between the parts. In this situation, define a load curve as a function of a result, and the analysis will vary the load appropriately throughout time.

 

Before accessing the "Analysis Parameters" dialog in order to define a result-based load curve, add probes to the model. The probes are the locations in the model whose results are used in the load curve. To add a probe, select a vertex or multiple vertices ("Selection: Select: Vertices"), right-click, and choose "Add: Nodal Probe...". A dialog appears in which a description can be entered for the nodal probe objects. (See the page "Loads and Constraints: Probes".)

 

To set the load curve to be based on a result, choose "Lookup Value" in the "Data for Selected Load Curve". The load curve then starts with two columns: "Lookup" and "Multiplier 1". (Addition columns can be added as described below.) The Lookup Value is defined with the "Define/Edit Lookup Values..." button. Once defined, the lookup value can be set with the "Lookup Value" pull-down. The name of the lookup value will become the heading of the first column of the load curve spreadsheet.

 

Note

Prescribed displacements and actuator elements cannot use a results-based load curve.

Note

The first column of the lookup load curve – which contains the results of the lookup value equation is not converted based on the active Display Units. The units for the lookup value and first column are based on the Model Units.

 

Defining and Editing Lookup Values:

 

Clicking the "Define/Edit  Lookup Value..." button will display the "Define Lookup Value" dialog which is where the lookup values are defined based on results at given locations. The functions on the "Define Lookup Value" dialog are as follows, listed in the order in which they are normally used.

 

Condition Statements and Multiple Load Curve Multipliers:

 

As described thus far, the lookup value selected for the load curve becomes the single value that is used to determine the multiplier for the load – just like time is the single value in a time-based load curve that is used to determine the load multiplier. There are situations in which multiple results or multiple lookup values are affecting the magnitude of the load. In these situations, the "Condition" text box is used in conjunction with multiple columns in the spreadsheet to determine which multiplier column is interpolated based on the selected lookup value.

 

For example, imagine a 2-cycle engine, shown schematically in Figure 2. Note that the piston's position is the same in figure 2a as in figure 2b. However, the pressure in figure 2a is based on the supply pressure and the motion of the piston since the exhaust port became closed (compressing the gas), and the pressure in figure 2b is based on the combustion pressure and the motion of the piston since combustion (expanding the gas). Thus, the load curve cannot be based on the piston's position, but it can be based on the piston's position and velocity. This type of control is obtained by using the "Condition" text box. The format is as follows:

IF("Lookup Value" "test" "comparison"; "multiplier column if true"; "multiplier column if false")

where

Note that the semi-colon character (;) is used to separate the three parts of the IF condition.

 

(a) The supply gases are compressed.

 

(b) The combustion gases are expanding.

Figure 2: Two-Cycle Piston
Although the position of the piston is the same in these two positions, the pressure P is different.

 

Based on the result of the conditional test, the appropriate column of the load curve spreadsheet will be interpolated. Use the "Add Column" and "Delete Column" buttons to add or remove multiplier columns from the spreadsheet. If no condition statement is used (the "Condition" text box is blank), then only "Multiplier 1" column will be used regardless of how many columns are entered into the spreadsheet.

 

Tip

The condition equation can be nested so that "and" type operations can be included. For example, let's break down the statement "IF(sep1<10;3;IF(vel>0;1;2))". If the result defined by the variable "sep1" is less than 10, then use multiplier column 3 (true condition). If sep1 is not less than 10 (the false condition), then the multiplier column for the false condition is another test which needs evaluated — if the result defined by the variable "vel" is greater than 0, then use the multiplier in multiplier column 1; if the "vel" is not greater than 0, use multiplier column 2. To summarize,

  1. use multiplier column 3 if "sep1" is less than 10.

  2. use multiplier column 1 if "sep1" is greater than or equal to 10 and if "vel" is greater than 0.

  3. use multiplier column 2 if "sep1" is greater than or equal to 10 and if "vel" is less than or equal to 0.

 

Example 1: Magnetic Force

 

For the magnetic force example shown in Figure 3, imagine the following parameters:

Figure 3: Magnetic Attraction Example

 

The steps specific to the setup the magnetic forces are as follows:

  1. Select the top node "A" ("Selection: Select: Vertices") and apply a nodal force (right-click, "Add: Nodal Force..."). Set the magnitude of the force to -1 and the direction to the Z direction. By using a unit force, the load curve multiplier will be the total magnetic force. Click the "OK" button to apply the force.

  2. With the node still selected, add a probe (right-click, "Add: Nodal Probe..."). Enter a description of Top Node and click the "OK" button.

  3. Select the bottom node "B" ("Selection: Select: Vertices") and apply a nodal force (right-click, "Add: Nodal Force..."). Set the magnitude of the force to +1 and the direction to the Z direction. Click the "OK" button to apply the force.

  4. With the node still selected, add a probe (right-click, "Add: Nodal Probe..."). Enter a description of Bottom Node and click the "OK" button.

  5. Access the Analysis Parameters dialog ("Analysis: Parameters") and choose the radio button to set the load curve type to "Lookup Value". The first column of the load curve spreadsheet changes from "Time" to "Lookup Value".

  6. Define a new variable that represent the calculated separation between the two magnets. Click the "Define/Edit Lookup Values..." button. This opens a new dialog. Click the "Add..." button and enter the new variable name Separation. Click the "OK" button to complete the entry of the lookup value name and return to the "Define Lookup Value" dialog.

  7. The separation is an equation based on the displacement of two nodes, so click the "Add Row" button once to add a second variable, V2, to the spreadsheet.

  8. For the variable V1, select the probe "Top Node" and result of "Z Displacement".

  9. For the variable V2, select the probe "Bottom Node" and result of "Z Displacement".

  10. The equation for the calculated separation is then entered in the "Equation" text box. Type 0.5+V1–V2. Note that a positive displacement of the top node will increase the separation; hence V1 is added to the initial separation of 0.5. A positive displacement of the bottom node will decrease the separation; hence V2 is subtracted from the initial separation of 0.5.

  11. Click the "OK" button to close the "Define Lookup Value" dialog.

  12. Back on the main "Analysis Parameters" dialog, use the "Lookup Value" pull-down and choose "Separation" as the lookup value. The first column of the load curve spreadsheet changes from "Lookup Value" to "Separation".

  13. Finally, evaluate the multiplier (the magnetic force in this setup) at various separations and enter them into the load curve spreadsheet. Although the force is infinite in theory when the separation is 0, the following load curve is more practical from an FEA perspective (where contact is required to prevent the parts from passing through each other, so the separation should not reach a magnitude of 0). Note the additional entries for separation greater than 0.5 (the initial separation). You want the load curve to cover all possible ranges of separation should the items vibrate or other loads cause them to be further apart than the initial separation.
     

    Index

    Separation

    Multiplier 1

    1

    0

    100

    2

    0.1

    31.25

    3

    0.2

    7.81

    4

    0.3

    3.47

    5

    0.4

    1.95

    6

    0.5

    1.25

    7

    0.6

    0.868

    8

    0.7

    0.638

    9

    0.8

    0.488

  14. Click the "View Plot..." button to confirm the shape is hyperbolic as expected. It looks as if more data points are needed between 0 and 0.2 in order to produce a smoother curve.

Example 2: Two-Cycle Piston

 

For the 2-Cycle piston shown in Figures 2 and 4, imagine the following (fictitious) parameters:

Figure 4: 2-Cycle Piston Example

The piston is shown in three positions. X=0 is the position the model is drawn, X0=0 is when the exhaust port becomes blocked, so the trapped gases have a volume of V0 and pressure P, and X0=–1.5 is the forward position of the piston.

 

Naturally, the pressures applied in the load curve can be more sophisticated than the ideal gas law in order to take compressibility and heat losses into account. Also, this write-up only includes the pressure on the cylinder head and blind side of the piston. Additional work is required to include the pressure on the sides of the cylinder walls and on the rod end of the piston; these pressures follow a different result-based load curve.

  1. Select the surfaces ("Selection: Select: Surfaces") on the blind end of the piston and cylinder head and apply a unit pressure of 1 psi (right-click and "Add: Surface Pressure/Traction..."). Check the box "Follows Displacement" and click the "OK" button to apply the pressure.

  2. Ignoring the deflection of the cylinder head, the volume of the trapped air can be calculated solely from the position of the piston. Select a node on the piston ("Selection: Select: Vertices"), right-click, and choose "Add: Nodal Probe...". Enter a description of Piston and click "OK" to add the probe.

  3. Access the Analysis Parameters dialog ("Analysis: Parameters") and choose the radio button to set the load curve type to "Lookup Value". The first column of the load curve spreadsheet changes from "Time" to "Lookup Value".

  4. Define a new variable that represent the position of the piston relative to the exhaust port, or the position X0 in Figure 4. Click the "Define/Edit Lookup Values..." button. This opens a new dialog. Click the "Add..." button and enter the new variable name X0. Click the "OK" button to complete the entry of the lookup value name and return to the "Define Lookup Value" dialog.

  5. For the variable V1, select the probe "Piston" and result of "X Displacement".

  6. The equation for the piston position relative to the exhaust port X0 is then entered in the "Equation" text box. Type V1+1.25.

  7. Define a new variable that represent the velocity of the piston. Click the "Add..." button and enter the new variable name Velocity. Click the "OK" button to complete the entry of the lookup value name and return to the "Define Lookup Value" dialog.

  8. For the variable V1, select the probe "Piston" and result of "X Velocity". Note how the same probe is used for multiple lookup values. Also, the variable V1 in the lookup value X0 is completely independent of the variable V1 in the lookup variable Velocity.

  9. The equation for the piston velocity is simply the variable V1. Type V1 in the "Equation" text box and click the "OK" button to close the "Define Lookup Value" dialog.

  10. Back on the main "Analysis Parameters" dialog, use the "Lookup Value" pull-down and choose "X0" as the lookup value. The first column of the load curve spreadsheet changes from "Lookup Value" to "X0".

  11. A condition based on velocity is required in this analysis, as described previously. Enter the text IF(Velocity>0;1;2) in the "Condition" text box. When the velocity is positive (piston moving to the right), the combustion gases are expanding, and multiplier column 1 will be used. When the velocity is negative (piston moving to the left), the supply gases are being compressed, and multiplier column 2 will be used.

  12. Click the "Add Column" button to add a second multiplier column to the load curve spreadsheet.

  13. Finally, evaluate the multipliers (the pressure in this setup) at various positions of the piston and enter them into the load curve. Using the Ideal Gas Law, the pressure Pc for the compression stroke (–1.5<=X0<=0) can be calculated from the initial pressure Psupply and volume Vinitial as follows:

Pinitial*Vinitial = P*V

Psupply*V0 = P*(V0+X0*(pi/4)*Bore^2)

(10 psig + 14.7 psi)*(14.2 inch^3) = (Pc+14.7 psi)*(14.2 inch^3+7.0686*X0)

Pc = 350.74/(14.2+7.0686*X0) – 14.7

 

and for the expansion stroke, the gage pressure Pe can be calculated from

 

Pinitial*Vinitial = P*V

Pcombustion*(V0 – (stroke)*(pi/4)*Bore^2) = P*(V0+X0*(pi/4)*Bore^2)

(1000 psig + 14.7 psi)*(14.2 inch^3–10.60 inch^3) = (Pe+14.7 psi)*(14.2 inch^3+7.0686*X0)

Pe = 3652.92/(14.2+7.0686*X0) – 14.7

 

Index

X0

Multiplier 1

(gases expanding, Pe)

Multiplier 2

(gases compressing, Pc)

1

-1.75

1981

177

2

-1.5

1000

82.8

3

-1.25

666

50.7

4

-1.0

498

34.5

5

-0.5

328

18.2

6

0

243

10

7

0.1

10

10

8

10

10

10

 

Note the "gradual" change in pressure as the exhaust port is opened (0<X0<0.1). Also, the piston theoretically never displaces to positions –1.5<X0, but some lead way is necessary for round off and deflections of the system. Thus, the load curve is calculated for a stroke of –1.75.