Example

Step 1 - Go to granite parameters page

In the main Isolation Tool page click the button "Enter Granite Parameter"

Step 2 - Load Granite Parameters

In the granite parameter page click the buttons: 1. "Example" 2. "Calculate" and then 3. "Return"

This will load the model with the calculated mass and inertia of the granite base and will return to the main model page.

Step 3 - Go to Isolator and positioning stages parameter page

In the main Isolation Tool page click the button "Enter Isolator and Stage Parameters"

Step 4 - Load Isolator and Positioning stages parameters

In the Isolator and stages parameter page click the buttons: 1. "Example"  2. "Auto Load parameters" and then 3. "Return"

This will load the model with the isolator, X  stage and Y stage parameters and will return to the main model page.

Step 5 - Load Motion Profile parameters of the Positioning stages and Run the Analysis

In the main tool page click 1. "Example" to load stage motion profile parameters and then click 2.. "Calculate" to run the analysis.

Step 6 - View System Variable Dynamics

1. Select 1st, 2nd and 3rd variables to plot from the lookup list of system variables

Then click 2. "Plot"

The results will show in the chart area.

Step 7 - Observe System Performance

7.1. Stage Motion Profile

7.2. Granite linear acceleration

7.4 Granite Linear Position

7.5 Granite Angular Acceleration

7.6 Granite Angular Position ( Pitch, Roll, Yaw )

7.7 Isolator XYZ forces

Step 8 -  Conduct sensitivity analysis

Suppose that in the above example we like to decrease Y and Z oscillation of granite c.g from +/- 6 mm as shown below to +/- 1mm

We may first conduct sensitivity analysis to investigate the effect of various design parameters on the granite displacement. For example we may increase isolator horizontal and vertical stiffness.  To try it we click the button "Enter Isolator and Stage Parameters" on the main page change the isolator stiffness, load the new parameters and re run the analysis. The results of increasing isolator stiffness by a factor of 10 are shown below. Note that the natural frequency increases as well. Increasing stiffness also increases the transmissibility and reduces the isolator effectiveness in reducing ground vibrations.

Another way to reduce the granite oscillation without increasing it stiffness is to reduce the moving weight.. The example below shows the effect of reducing the moving mass in X and Y direction  by a factor of 5

Step 9 -  Modify design parameters to optimize system performance

Based on the results of the sensitivity analysis we may iterate on the optimized system performance. In the above example lets try increasing the isolator stiffness by a factor of 3 and decreasing the mass by a factor of 2.

Step 10  Run the Analysis in various conditions to understand dynamic characteristics

For example,  increase the travel of X stage to 1 m as shown below and analyze the granite motion and the isolator forces..

As shown the Y position of the granite c.g. settles to zero but the Z position maintains a steady state position after its move. The explanation is that passive isolators, as assumed in this example, do not regulate their elevation and therefore they assume a steady state height based on the unbalanced forces they need to support. This height change as result of moving weight position change, also changes the 3D orientation of the granite.

To validate the above result we may check the pitch. As shown below there is, as expected, a close correlation between pitch and z motion. The model assumes that the machine is statically balanced when the moving masses have no moments about the granite c.g. Therefore, at the end of travel of both X and Y the weights cause pitch and roll as shown below until it is balanced with the new isolator forces.

The resulting isolator forces are shown below. As shown, F1 and F3 are equal and opposite and F2 and F4 are equal and opposite to each. The pair F1 and F2 are acting in positive direction with F3 and F4 being negative  to balance the moment of Y moving mass about the c.g. Similarly The Pait F1 and F4 are acting with F2 and F3 to balance the moment of X moving mass.