If a CAD model is optimised using the parameters defining its features then the resulting model can easily be used for downstream design processes.
One roadblock to this approach is that often the parameters which define the model do not offer sufficient shape flexibility for successful optimisation.
Parametric effectiveness rates the quality of a parameterisation for the purpose of optimisation. It compares the change in performance achieved:
PE ≈1: the parameterisation enables the model to move in a way that is close to optimum, and optimisation should proceed using the current model parameters.
PE ≈0: the parameterisation should be improved before optimisation can occur.
Parametric effectiveness can be calculated for different sets of parameters in the model, allowing the set with the parametric effectiveness closest to 1 to be selected for optimisation.
Figure 1 shows contours of strain energy for a turbine disc component which is defined by 48 parameters.
Figure 2 compares the parametric effectiveness for sets of parameters comprised of the specified number of parameters with the highest performance sensitivity values. For this component the set containing all 48 parameters has a parametric effectiveness close to 1, allowing the shape to change in a way that is close to optimum.
A low Parametric effectiveness indicates that more features should be added to the CAD model before optimisation is attempted.
When a model is to be optimised, and its parametric effectiveness is low, new features should be added to the model. One example of feature addition is to add control points to the curves bounding the model, the positions of which can be used for optimisation. Techniques have been developed to determine the most appropriate position to add the control point. Figure 3 shows the change in shape and strain energy caused by adding control points to a simply loaded beam.
This work has also determined that for the four common feature types shown in Figure 4
the benefit (dJ) to be obtained by adding a feature is:
The benefit obtained is normalised with respect to a small amount of boundary movement dV. The optimum location to add a feature can also be identified.
The CAD feature providing the greatest benefit should be added to the model before optimisation is attempted. Once the new feature is added the model should be optimised before another new feature is added.
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Trevor T. Robinson, Cecil G. Armstrong, Hung Soon Chua; Determining the parametric effectiveness of a CAD model; Engineering with Computers; DOI: 10.1007/s00366-011-0248-4
Trevor T. Robinson, Cecil G. Armstrong, Hung Soon Chua; Strategies for adding features to CAD models in order to optimize performance; Structural and Multidisciplinary Optimization, Volume 46, Issue 3 , pp 415-424, DOI: 10.1007/s00158-012-0770-z
An assembly is where the sub-assemblies and parts which comprise a product come together. The intellectual arrangement of parts in an assembly is a difficult task. Modern CAD environments ontain tools which allow CAD part models to be brought together and problems such as clashes to be discovered. If these problems are not solved before manufacture the physical parts will not assemble ogether without expensive rework.A well-captured design intent for assembly models will enable the designer to design out manufacturing and assembly difficulties at an early design stage.
The aim is to introduce an automated CAD based process defining and capturing design intent in assemblies, and to eliminate clashes which present in a CAD model assembly.
Step 1: Calcukate initial clash in the CAD model assembly (if any).
Step 2: Perturb the parameters in the assmebly model by a small amount (ΔP) and recalculate the clash in the assembly.
Step 3: Calculate the sensitivity of each parameter as the change in clash with respect to the change in parametric value (ΔP).
Step 4: Generate a list of parameters with a sensitivity value along with the features which the parameter represent.
Step 5: Establish any relationships which may exist in the assembly by using the algorithm developed.
Step 6: Constrain the assembly using the identified relationships.
Fig. 1: Process work flow
The fig. 1 shows the method in which sensitivities are calculated for each parameter in the assembly as the change in clash volume due to a change in each component parameter value. These sensitivities are used to calculate the optimum combination of changes in each parameter to eliminate the clashes.
Relationship identified: Shaft diameter = Hole diameter in the housing component
Fig. 2: Bracket Assembly
|Clash Volume (mm3)|
|Initial Clash 1||6200|
|Initial Clash 2||852.16|
Table 1: Clash elimination
The aim of this research is to develop a tool to compute geometric CAD sensitivities called design velocities and link these with adjoint CFD simulation data to allow efficient aerodynamic optimisation of parametric CAD models.
Design velocity is a measure of geometric shape change in response to parameter change. It links parametric perturbation to boundary movement. More specifically, the normal component of design velocity (Vn) is the outward normal movement of a point on the model boundary due to a parametric perturbation.
Adjoint sensitivity maps can show the sensitivity of an objective function to boundary movement across a complete model boundary. The sensitivity map is computed from a single adjoint analysis, irrespective of the number of design parameters.
Linking these two concepts gives information on the relationship between CAD model parameters and model performance which can be used to optimise the model.
The diagram below illustrates the method used in this research. The process begins with a parametric CAD model with a certain number of parameters. The wing model shown is defined by more than 1000 parameters.
The method used to compute design velocities is based on a finite-difference approach using faceted approximations of the parametric CAD geometry.
Each appropriate CAD model parameter is automatically perturbed, and a faceted version of each perturbed geometry is exported. Each of these perturbed faceted geometries is then compared in turn to the original unperturbed geometry and a design velocity field computed for each parameter. The use of faceted models allows this data to be computed very efficiently, with each design velocity evaluation taking just a few seconds computation.
This design velocity field data is then combined with surface sensitivity data obtained from an adjoint CFD solver, allowing a sensitivity to be calculated for each model parameter. These sensitivities can then be used for gradient-based optimisation.
For complex aerodynamic models with many parameters, this method has the potential to significantly reduce the number of CFD computations required for optimisation compared to conventional finite-difference based methods of gradient evaluation.
A method has been developed to enable automated computation of design velocity fields for parametric CAD models and link the resulting data with adjoint sensitivity results to allow efficient computation of parametric sensitivities for CAD models.
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