|
We can take advantage of the fact that the governing equations for heat conduction and electrostatics are the same, and use the Thermal module of Pro/MECHANICA® very effectively to solve basic electrostatic di-electric problems. Using this method, as described in this article, is very simple and straightforward.
Heat conduction can be described by the following differential equation:
where:
 is the conductivity,
 is the Laplacian operator,
 is the temperature, and
 is the internal heat generated (source or sink).
For basic electrostatics we have the same governing equation, where:
is the relative permittivity,
is the field potential (voltage), and
 .
This differential equation can be solved by the finite element method and is implemented, for example, in the Pro/MECHANICA Thermal module.
We will demonstrate this method by using Pro/MECHANICA 2001 to analyse a hypothetical high voltage bushing, subjected to a voltage of 550 kV, in this case.
To start, we need to generate the geometry. Since this will be a 2D analysis, we need to somehow generate a 2D surface geometry. This can be defined directly using surfaces in Pro/ENGINEER, but mostly it is easier to define 3D geometry that has a 2D plane in the correct position. Since the geometry is axisymmetrical, we can create one quarter of the geometry and use one of the two radial planes.
We also want to end up with only the geometry of all the non-conducting materials, as this is where the static voltage distribution is. All contacting conducting (metal) parts will be at the same voltage and can therefore be represented as boundary conditions in the analysis.
Since this hypothetical bushing is made from 4 parts (the metal bottom flange; the metal top flange plus busbar; the composite tube; and the external silicone rubber layer with sheds) we need to create an assembly in Pro/ENGINEER.
Keep in mind that Pro/MECHANICA 2001 complains (or mostly does not work) if there are any assembly features like cuts present (even if suppressed) in the assembly that is analysed.
We therefore have to create any needed cuts (if we have the full 360° geometry available and need to cut three quarters away) in the separate parts and not in the assembly.
In our case we just create the 4 parts using a 90° solid revolution for each. We also need some kind of tank to mount the bushing onto. Lastly we need the gas volume in and around the bushing. This is just a simple quarter of a cylinder, in this case, extending far enough in the axial and radial directions.
In this case we set the units of the parts to millimeter, Newton, seconds and °C. Other consistent unit systems should also work, but this was not yet verified.
To help prevent any problems further down the line, be sure to set the absolute accuracy of the parts to 0,001mm.
Now we can assemble the bushing and the tank in an assembly. To simplify things, be sure to assemble the components such that the requited 2D plane is aligned with the FRONT datum plane and the axis of revolution of the geometry lines up with the y-axis of the default assembly co-ordinate system. For a 2D-Axisymmetric analysis in Pro/MECHANICA, all the geometry needs to be on the positive side of the x-axis and the y-axis will be the axis of revolution.
This is the physical geometry of the equipment as shown in figure 2.
Now we need to assemble the gas volume and then cut the above geometry from this gas volume, using <Component> <Adv Utils> <Cut Out>.
We end with the following:
Figure 3: Bushing assembled in and cut out from the gas volume
Now we take this assembly and create a simplified representation of only the non-conducting components.
Figure 4: Create a simplified representation with only the non-conducting parts
Now we are ready to enter Pro/MECHANICA.
Keep in mind that we are mainly interested in the voltage (temperature) gradient distribution, which is a derivative of the voltage (temperature) distribution. Therefore, to ensure a smooth and accurate distribution, it is very important to have a very good mesh in the important areas and that the analysis must converge properly.
So, before we enter the Thermal module of Pro/MECHANICA, we should set more desirable settings for AutoGEM by selecting <Settings> <AGEM Settings> on the MECHANICA menu.
Figure 5: Adjusting AutoGEM settings
For 2D analyses, it is possible to set very tight settings (shown in bold below), without having long meshing and solving times. Set the “Allowable Angles” to anything from 10° to 25° (Min) and 150° to 170° (Max). Set the “Max Allowable Edge Turn” to anything from 10° to 45°. Set the “Max Allowable Aspect Ratio” to anything between 2 and 10. Most combinations of these suggested values give excellent results, when the analysis has converged properly. For simple models, start with the tightest values and relax them as needed for more complicated models.
First we have to define the model type. In this case we want to define a 2D Axisymmetric model.
Figure 6 : Setting the Model Type
We select the geometry and the co-ordinate system. As already stated above, all the geometry must be on the positive side of the x-axis and the y-axis will be the axis of revolution.
Now we can assign the boundary conditions. Since all contacting metal parts have the same voltage, and temperature is equivalent to voltage, we need to apply a constant prescribed temperature boundary condition to all the edges of the non-conducting materials that are in contact with the metal parts. The numerical value of the temperature (filled into the "Temperature" box) should be that of the applied voltage and can be in any units [mV, V or kV] as long as you are consistent. In this case we apply 550kV to the live parts and 0kV to the grounded parts.
Figure 7: Setting the Boundary Conditions
Now we need to define and assign the materials to the surfaces. The easiest way is to define a new di-electric material for each non-conducting material in the model, starting with the gas. Since the relative permittivity is equivalent to the thermal conductivity, we only need to fill this value into the "Thermal conductivity" box on the "Thermal" tab. For example, for gases and vacuum, this is 1; and in this case, for fiberglass it is around 5 and for silicone rubber it is around 3. Leave the units of the conductivity as [N/(sec) C].
Pro/MECHANICA also requires numerical values in the "Density" box and in the "Young's Modulus" box (on the "Structure" tab). We just set them both to 1, since it makes no difference.
Figure 8: Define new di-electric materials
After the materials are defined, we assign them to the required surfaces of the model.
Figure 9: Assign the materials to the required surfaces
To get the voltage (temperature) and voltage (temperature) gradient distribution, we need to run a steady thermal analysis. To ensure that the analysis converges properly, we set it up as follows.
We set the "Method" to Multi-Pass Adaptive, with the "Minimum Polynomial Order" to 3 and the "Maximum" to 9. We can set the "Percentage Convergence" to anything from 0,25% to 5% (depending on the model and our requirements).
Figure 10: Analysis definition settings
We make it converge on "Measures". As measures, we choose: "energy_norm", "max_grad_mag", "max_grad_x", "max_grad_y" and "max_grad_z".
Figure 11: Measures to converge on
Figure 12: Start the analysis
Figure 13: Confirm these prompts
The analysis should now run. Most 2D analyses should complete in less than a minute.
The first thing we need to check is the convergence in the Summary file. We should confirm that it converged properly. If not, there are probably errors in the boundary condition assignments or in the model in general (like sharp corners, where it should be rounded).
Figure 14: Check convergence in the Summary file
Since this is OK, we insert a new results window.
Figure 15: Insert a new result window
We choose a fringe plot and set the "Feature Angle" to zero. This way we can easily see the geometry and also confirm that the mesh generation was good.
Figure 16: Define temperature (voltage) distribution result window
The first thing we look at is the temperature (voltage) distribution. If there were errors in the boundary condition assignment, we should see it here.
Figure 17: Temperature (voltage) distribution
Next we define the result window for the temperature (voltage) gradient. This is one of the most important results.
First we make sure that the "Average" option is unchecked and look at the continuity of the results in the important areas of interest. If it is bad, then the results will not be accurate and we might need a finer mesh. Since, in this case, it looks good, we redefine the window with the "Average" option checked. It was found that in this way the results are closer to reality, since small local (unrealistic) peaks and steps between elements are smoothed.
Figure 18: Define temperature (voltage) gradient distribution result window
We have to look for small localised hot spots. This normally indicates that either the boundary conditions are discontinuous or that we need to round a sharp corner. Since there are no hot spots, the distribution is good from a calculation point of view.
The units of the gradient is in kV/mm, since the unit of length of the model is millimeter and we set °C equivalent to kV.
Figure 19: Temperature (voltage) gradient distribution
The second important result to look at is the tangential distribution along boundaries. To do this we need a co-ordinate system with an axis along the required direction. This must be defined before the analysis is run. For arcs, we need a cylindrical co-ordinate system at the center point and can then look at the T-component.
We can look at the tangential distribution along a chosen vertical boundary, by defining the result window as follows.
Figure 20: Define the tangential temperature (voltage) gradient distribution result window
We need to select the required edge. Unfortunately in Pro/MECHANICA 2001 it is not possible to plot the tangential gradient along a compound curve, and it needs to be done one segment at a time.
Figure 21: Choose the required edge
Below we can see the tangential gradient along the chosen segment. This could be exported to a file. If this is done for all the required segments, we can import it into some other software to get a complete graph along the total boundary.
Figure 22: Tangential temperature (voltage) gradient
It is also possible to model a metal component in a di-electric assembly with a non-fixed (floating) voltage (because it is surrounded by non-conducting material) that is dependent on its position. The way to do this is to include the geometry of this metal part in the model and assign it a thermal conductivity (relative permittivity) that is very high (say 106).
Another possibility is to do 3D analyses of components or assemblies that cannot be modeled in 2D. This is a special case that needs some special care, but it is not (normally) more complicated. This will be covered in a future article. 
Johannes Tredoux is an analysis engineer with ABB Trasmissione & Distribuzione S.p.A. in Lodi, Italy. He can be reached via e-mail at Johannes.Tredoux@it.abb.com.
|
Building the geometry in Pro/ENGINEER
Assemble in an assembly