Design Of Experiments

First, we need to look at the inputs that are under our control. We do this with the Design of Experiments (DOE) tool.

First we consider the passive suspension. We want to estimate the effect of the damper rate on both outputs.

Step1: Define a Full Factorial DOE for the passive suspension

Procedure

1. Click the New button.

2. Change the study name to PS_DOE.

Note Do not use spaces in studies names. If you do insert spaces, they will be replaced with "_" characters.

3. In the Type drop-down list, select DOE.

You can also click the down arrow next to the New button and directly select DOE in the drop-down list that appears. To rename the study, double-click its name on the left hand side list. Warning The new name will only be saved if you click OK in the Study Manager.

4. Full factorial Under Study settings, select Full factorial for the DOE technique.

With this technique, if there are N controls each with a high and low value, every combination of parameters is run. This gives 2N runs. Here N=1 gives two runs.

5. Go to Study parameter definition and select the PS_DamperRate check box in the Inputs/Controls list. This declares it as used as a control in the study. The other two parameters will not be used as controls in this study.

Note You can hide unused controls by selecting the Hide unused checkbox. This is for display purposes only, the controls are not removed from the available inputs list.

6. Click on the Low level cell to edit it and change the value to 500.

7. Click on the High level cell to edit it and change the value to 1500.

Figure 7: Definition a Full Factorial DOE

8. Select the Outputs/Responses tab.

9. Select the check boxes for PS_max_BodyAcceleration and PS_min_TireCompression to declare them as used as responses.

Step 2: Run PS_DOE and display the main effects

Procedure

1. Click on the Start Run button and wait until the end of the process.

The Run details pane expands. Two runs are done corresponding to the two extreme values of the control parameter.

2. Click the Add plot button at the top, or right-click the PS_DOE study in the list and select Add Plot in the menu.

The Design Exploration Plots dialog box appears.

3. Select Main Effect Diagram in the Plot type drop-down list.

4. Select PS_DamperRate in the Factor drop-down list. In this case there is only one item in the list.

5. Select PS_max_BodyAcceleration in the Response drop-down list.

6. Click OK.

A plot window appears with the selected main effect plot. (See figure: Figure 8)

7. Do the same for PS_min_TireCompression (see figure: Figure 9).

Results

Figure 8: Main effect plot of the PS body acceleration

Figure 9: Main effect plot of the PS tire compression

The Figure 8 figure shows that when the damper rate increases, the maximum value of the body acceleration increases too. So we have to decrease the damper rate. To get the maximum acceleration below 9.81 m/s/s we need a damper rate lower than about 1050 N/(m/s).

On the other hand, the Figure 9 figure shows that when the damper rate increases, the minimum value of the tire compression increases too. With the lowest damper rate value the acceleration is significantly low but the spring compression is negative and the wheel has left the ground. To ensure the wheel does not leave the road, we require a damper rate of at least 770 N/(m/s).

In conclusion we can say that we can achieve our objectives with the passive suspension with a damper rate between 770 and 1100 N/(m/s). Since there is only one control parameter, it would be very easy to experiment with values between these extremes.

Step 3: Define parameters for the active suspension

Procedure

1. Add the parameters of the active suspension: AS_Main_Damper, AS_Sky_Hook_Damper and AS_Tire. Drag and drop them:

into the Input parameters table of the Parameters tab, or,

directly into the Inputs/Controls table of the Studies tab.

Figure 10: Updated Input parameters

2. Drag and drop the AS_Body_Acceleration, AS_Body_Velocity, AS_Body_Displacement, and AS_Tire_Compression variables:

into the Simple outputs table of the Parameters tab, or,

directly into the Outputs/Responses table of the Studies tab.

Figure 11: Updated Simple output parameters

3. In the Parameters tab, define the Compound output parameters. FinalDisp will represent the gap between the actual final position of the body and the expected final position: 0.1 m.

Figure 12: Updated Compound output parameters

4. Go to the Studies tab.

Step 4: Define a Full Factorial DOE for the active suspension

In the same way as in the previous steps, create a new DOE study and name it AS_DOE.

There are two factors involved:

Figure 13: Factors

• MainDamp: change the low level to 500, and the high level to 1500.

• SkyHookDamp: change the default value to 700, the low level to 200, and the high level to 1200.

The other factor is not involved. The responses involved are:

• MaxBodyAcc

• MinTireComp

Step 5: Examine the design matrix

Procedure

1. Expand the Study settings again and click the Show design matrix button.

2. Tick the Show values check box to display the values that will be used for the four runs. (With N=2, 2N =4.)

Figure 14: The Design matrix dialog box

3. Click Close.

Step 6: Run AS_DOE and display the effect table

Procedure

1. Select the AS_DOE study in the list.

2. Click on the Start Run button and wait until the end of the process.

The Run details pane expands. Four runs are performed.

3. Effect Table Click the Effect Table button at the top, or right-click the AS_DOE study in the list and select Effect Table in the menu.

Figure 15: Effect table

Results

The table shows linear regression coefficients linear regression coefficients. The positive value 2.02993 indicates that body acceleration increases as the main damper rate increases whereas the value of -0.197151 indicates the acceleration decreases as the skyhook damper rate increases. We hope to control acceleration with a high skyhook damping rate.

The value -0.00146984 indicates that the skyhook damper rate has very little influence on tire compression whereas 0.0126438 indicates the main damper rate is more important for the tire compression. We can ignore the skyhook damper rate and keep the tire compression positive by a sufficiently large main damper rate.

With two parameters it is not easy to manually optimize the values but we have an automatic way of doing it.