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Is topological optimisation really optimal?

Light-weight, efficient product design is one of the key drivers behind the increasing adoption of additive manufacturing (AM) for series production. AM supports a range of light-weighting approaches including generative design techniques such as topological optimisation. These iterative methods explore many possible design solutions and result in components with organic forms that mimic efficient natural structures.

AM's flexibility enables the manufacture of complex forms, making it the ideal means to realise such designs. However, it is a mistake to think that designs that have been optimised for load bearing can simply be printed at the touch of a button. Whilst it is possible to make just about any shape that a optimisation tool can produce, the resulting build can be very inefficient to print and finish.

  • Spider bracket

It is a mistake to think that designs that have been optimised for load bearing can simply be printed at the touch of a button

As pointed out in recent article Can you build AM parts without support?, best practice in 'design for AM' requires us to think about how a part will be built so that we minimise unnecessary support structures. This process inevitably results in some modifications to our design so that we either eliminate supports, or integrate supporting structures into the product itself.

This post looks at a 'real world' approach to integrating topological optimisation into an AM design process. We will use a case study to explore how modern weight reduction techniques can be combined with conventional engineering design approaches to develop a practical solution. The emphasis is on speed and on getting the job right first time.

Case study: suspension bell-crank

Our illustrative example is a pivoting bell crank from the suspension system for a racing car, modelled with the spring at full-travel.

In this case, most of the design work would ordinarily focus on the kinematics of a suspension design: motion ratios, wheel rates etc. These determine the points in space where the interfaces need to be. All the other elements that must be packaged beside the bell-crank component determine the overall envelope that we have to play with. When it finally comes to designing the “meat” of the part, we are aiming for something that's light and not going to break.

In this case, most of the design work would ordinarily focus on the kinematics of a suspension design: motion ratios, wheel rates etc. These determine the points in space where the interfaces need to be. All the other elements that must be packaged beside the bell-crank component determine the overall envelope that we have to play with. When it finally comes to designing the “meat” of the part, we are aiming for something that's light and not going to break.

Conventional design approach

Before we look at generative design solutions, let's consider a conventional approach to give us a baseline. Taking account of the fixed points defined in the design space, we can quickly arrive at a sensible and reasonably light-weight design. It's a simple solution to a simple problem - to reduce the weight of a member in bending you make it into an I-beam section. After about 30 minutes work, we have a workable solution:

Finite element analysis (FEA) is a critical tool in AM part design, enabling us to evaluate the strength of alternative structures, no matter how complex they may be. The part volume is divided up into thousands of discrete regions and FEA is used to calculate stresses and strains in each element, comparing each to its neighbours in an iterative process. Once the solver has got to the point where there is relatively little variation between each iteration, the solution is said to have “converged”. Note that the quality of this analysis depends on the quality of the defined initial conditions - if assumptions or simplifications are made, then the analysis may be flawed.

When we run our conventional bell-crank design through FEA we see no large stress raisers and the peak loads are where we would expect them to be:

The safety factor is overly generous (8.5), indicating that we could shave some more weight off the part. But this is a good, pragmatic starting point. It's mass in Ti6Al4V is 338g.

Topological optimisation basics

Topological optimisation is a technique used to reduce the weight of a component by removing material that is not required to bear the anticipated loads. First we create an allowable design envelope within which the component can be generated. Next we create regions within or attached to this envelop through which loads are transferred into the bulk volume. 

Image right - allowable design space for our bell-crank case study, starting with the conventional design shown earlier. We have simplified the geometry by getting rid of chamfers, fillets and machined features. We nominate “non-design” space (green) by creating separate bodies within the model - these are assumed to be rigidly connected to the main body.

Next an FEA analysis is performed on this design space under the same load conditions as before. The topological optimisation step involves determining how much each element contributes to the structure. The constraint here could be stress, strain energy, or resonant frequency. Each element is given a weighting and we can eliminate the low-scoring elements from the structure to achieve our performance goals. What we are trying to do here is get something that indicates where the load paths run through the part and to form a representation of a single, contiguous body with material only where we need it.

We now have a reduced-volume component comprised of the higher-scoring elements. This is generally rather irregular, and so a clean up stage is needed to form these elemental shapes into smoother structures. We do this by constructing geometry around the mesh using polyNURB technology. The representative geometry can then be exported as a parasolid file that can be imported into CAD software for further modification and analysis.

Image above - topological optimisation of the bell-crank, eliminating unnecessary elements to leave a reduced-volume part. The resulting structure is subsequently encased in polyNURB surfaces to result in a smooth, organic component. We have performed this in Altair's solidThinking Inspire software.

Common sense tells us that removing material from the part will also reduce both its strength and its stiffness. It makes sense, therefore, to run this new design through an independent FEA analysis to check that it still meets the design criteria with an appropriate safety factor.

Image left - FEA analysis of the topologically optimised design, using ANSYS structural analysis software. The safety factor is reduced to 5 and rigidity also falls, while peak stresses increase, but all of this is expected and within acceptable limits.

All of this has taken us a little longer than in the baseline case - perhaps 3 or 4 hours of design effort. But the result is a 46% reduction in mass to 181g.

Sub-optimal optimisation

So, we have an efficient part design, but this does not necessarily mean that the results are optimal from the point of view of building a successful component. The problem is that we have designed for function, but not for manufacture.

Topological part build support design

In our case study, the resulting design needs lots of supports to make it buildable, even in the most suitable orientation. If we give little or no thought to how the part is to be orientated during the design stage, then this is where we can end up. 

And the pain doesn't stop there. Each time we make changes to the design, even small modifications that do not invalidate the stress analysis, we enter a loop of exporting a new STL model and supporting it afresh - at least an hour of work each time in this case.

If we give little or no thought to how the part is to be orientated during the design stage, then we will need lots of supports to build it

Supports are also bad news in other ways. They require extra time and material to produce. As I pointed out in Can you build parts without supports?, the regions where supports and the part intersect may exhibit different local properties due to re-melting. Subsequent support removal and clean-up is time-consuming and has the potential to affect the component integrity.

Residual stress and heat dissipation are other potential bear-traps. With insufficient design for manufacture thinking up front, we may produce builds that exhibit unacceptable accumulations of heat and stress which, combined with a reliance on supports, may lead to build failures.

Intelligent design optimisation

If we plan to use AM to manufacture our efficient part designs, we must think about build ability much earlier in the process. We need to combine design for AM (DfAM) and topological optimisation intelligently.

Intelligent design optimisation starts with a design space that is in self-supporting

This starts at the design space definition. With a little more thought, we can determine the direction in which we want the part to build and generate a starting point for the optimisation process that is buildable without supports (we will deal with the lateral holes later). In the case of our bell-crank, this means defining a tapered base to attach it to the build plate, plus extra fixed regions that connect the load-bearing regions together. 

DfAM-refined design space for the bell-crank












Image above - DfAM-refined design space for the bell-crank. The part will be attached to the base plate by the tapered point shown in green on the right. The green regions connecting the lateral holes, including along the spine of the part, ensure that the shape now self-supports before any topological optimisation is performed.

Topological design from DfAM












Image above - topological optimisation starting from the DfAM-refined design space, with polyNURB surfaces added. Most of the design is buildable as it is, but the highlighted strut, which will exhibit a significant overhang, is problematic.

By taking care over the detail design of the struts, we can eliminate overhangs to make the component self-supporting. The problematic overhanging strut (highlighted below) has been incorporated into some central webbing to make it buildable (See image to the right)

Of course, we need to validate this new design. The FEA shows some slightly higher peak stresses than in the previous design, but the factor of safety is still an acceptable 3.2:

Happily, the component mass has been further reduced to 164g. Note also that the build volume will be much lower due to the self-supporting nature of the design. The total design time in this case is about the same as the previous optimisation process, but now we are not facing multiple build preparation / redesign cycles thanks to the up-front DfAM thinking.

Topological finalised build

Image right - finalised build, in which we have designed in the build orientation, and replaced all the lateral holes with self-supporting diamonds. The struts have been carefully considered, with fillet radii added to reduce stress raisers. An allowance has been made for wire EDM removal from the build plate. Finally, finish machining operations have been thought about and catered for.

Comparison of design solutions

The table below compares key metrics for the three designs - the conventional original, topological optimisation alone, and an intelligent combination of DfAM and topological optimisation. We can see clear progress in terms of the efficiency of the design, both in functional performance and in terms of manufacturing efficiency. We also see a predictable trade-off between mass and strength / rigidity.

VersionPart mass (g)Build volume (cm3)Build wastePeak VM stress (MPa)Peak Max Principle stress (MPa)Min FOSPeak Max Shear (MPa)Peak deflection (mm)
Original 338N/A77.3%11168.68.5859.20.107
Top Opt18172.040.7%19021751030.254
DfAM16443.716.6%2942023.2388.00.349

The benefit of combining DfAM with topology optimisation is perhaps best summarised by this image:

Summary

Although AM is incredibly flexible in terms of what we can build, we still need to be aware of the characteristics of the process when we design components for printing.  If we optimise solely for function, we compromise our build efficiency, quality and design intent.

By combining up front DfAM thinking with powerful topology optimisation tools, we can create efficient, light-weight designs that are also easy to manufacture in series production.