© Altair Engineering 2009 17-1

Composite Optimisation of a Formula One Front Wing David Mylett, Lewis Butler, Dr. Simon Gardner Force India Formula One Team Ltd Dadford Road, Silverstone, Northamptonshire, NN12 8TJ, UK dave.mylett@forceindiaf1.com lewis.butler@forceindiaf1.com simon.gardner@forceindif1.com

Abstract This paper will show the application of a 3-stage approach to designing the optimum composite structure for a front wing on a Formula One car using Altair OptiStruct 9.0 Continual development of aerodynamic components is normal practice in the world of Formula One and the time taken to respond is paramount if a team is to be competitive. The design must: • Be completed in a highly compressed time frame • Meet stiffness targets set by the regulations • Withstand the aerodynamic loads • Be as light as possible • Be easy to manufacture The objective is to minimise mass whilst adhering to all constraints. This is achieved through the use of Opitstruct 9.0 and follows this procedure: • Identification of efficient ply boundaries / fibre orientation / material. • Number of each ply • Optimise stacking sequence to minimise peak composite failure indices / ensure

efficient ply distribution. The result of this optimisation should yield a minimum mass design, whilst meeting all criteria in a significantly reduced timeframe relative to traditional methods. Keywords: Composite Optimisation, Discrete, Free Size, OptiStruct, Shuffle 1.0 Introduction Formula One is one of the fastest industries in the world, not only in terms of speed on the track but also behind the scenes in the design offices and manufacturing facilities. Throughout a season a Formula One car is constantly being developed and can typically improve in speed by as much as 1-2 secs/lap. As a result, designs are constantly evolving with new designs implemented. For a team to be competitive it must be able to react and produce components which are not only lightweight & robust but also designed in a highly compressed timeframe. Carbon composites are widely used on a Formula One car, and traditionally the process of defining a robust yet lightweight composite component is a very complex, time consuming and generally difficult task. Not only must you consider many variables such as material, ply angles, ply sequence, number of plies etc., but you must also restrict many of these variables to discrete values.

Within Force India Formula One Team CAE tools are widely used during the design & development process and Optimisation software such as OptiStruct can be a useful tool to assist in reducing the number of design iterations and time taken to design a lightweight robust component. This paper provides an overview of a 3-stage approach used for composite optimisation of a front wing using OptiStruct, ensuring all strength & stiffness targets are met, with the objective of minimising mass. 2.0 Background The primary role of a front wing assembly on a Formula One car is to generate front axle downforce (balancing the downforce generated at the rear of the car). Typically around 30% total downforce is generated over the front wing assembly and can be in excess of 6kN total force. The front wing stiffness plays a significant role in maintaining the aerodynamic profile and as such the bending and torsional stiffness can be tailored to meet specific aerodynamic requirements. This means that the design of the front wing must be able to withstand large aerodynamic forces generated by airflow at high speed, whilst ensuring deflections are managed. Coupled to the aerodynamic constraints, the front wing assembly must pass stringent regulatory deflection tests, (FIA Formula One Technical Regulations, 3.17.1, excerpt below)[1]; while at the same time ensuring the mass of the assembly is at a minimum. FIA Technical Regulation 3.17.1 (2008) Bodywork may deflect no more than 5mm vertically when a 500N load is applied vertically to it 700mm forward of the front wheel centre line and 625mm from the car centre line. The load will be applied in a downward direction using a 50mm diameter ram and an adapter 300mm long and 150mm wide. In order to achieve these requirements the front wing is generally constructed from carbon composite, and comprises a wide selection of construction materials and methods. Typically multiple layers of uni-directional and woven fibres, and lightweight core materials are used. 3.0 Baseline Assessment The objective of this study was to design a new front wing for the 2008 VJM1 Formula One car which exceeded the structural performance of its predecessor. As the aerodynamic shape of the wings change from season to season, it is necessary to assess the geometric differences between the wings. This is done as a preliminary analysis and simplified isotropic models are built which represent the shapes of the 2007 and proposed 2008 wing being considered.

Figure 1: 2007 vs. 2008 Geometry Super-imposed To assess the geometric stiffness of the two wings it is necessary to find the position of the neutral axis at the end of the wings and apply loads at this location. In order to discover the © Altair Engineering 2009 Composite Optimisation of a Formula One Front Wing 17-2

geometric stiffness of interest (vertical bending and rotational twisting) both wings are subjected to two load cases

1. A point load is applied in a vertical direction (-Z) – Vertical stiffness 2. A torque is applied in Y (across car) – Torsional stiffness.

The results of this preliminary analysis can be seen in Figure 2, and show that the proposed 2008 wing is significantly less stiff in bending (-48%) whilst torsion is not significantly affected.

Bending

Rotation

Figure 2: 2007 vs. 2008 Geometric Stiffness Results

Once the geometric differences were known, it was apparent that the vertical bending would be the limiting factor to ensure the 2008 geometry out-performed the 2007 wing. As a further comparison, a more detailed model of the 2008 wing was built, which contained all elements from the front wing assembly, an up-to-date mapped pressure profile and a representative composite lay-up (Laminate Stack) was applied, based on the 2007 wing. This model was subsequently analysed considering an aerodynamic load case and FIA regulatory load case and again compared to the 2007 baseline model. As expected the 2008 wing performed significantly worse compared to the baseline, however the total deficit was not as severe with a maximum difference of ~26% seen, and a considerable increase in composite failure index was observed around the centre transition section. © Altair Engineering 2009 Composite Optimisation of a Formula One Front Wing 17-3

4.0 Optimisation Process The traditional method of defining a laminate stack can be generally split into three discrete stages:

• Define Ply Boundary (including ply orientations & differing materials) • Vary numbers of individual plies • Organise the stack to ensure structural integrity is achieved

Even with this simplified process, the number of design variables and required manual iterations would be significant and very time consuming to perform. Particularly at the first stage where for each individual ply, different materials and orientations must also be considered. The use of OptiStruct can simplify this process, and uses the same 3-stage approach 4.1 Free Sizing In order to yield the best results for composite lay-up optimisation it is necessary to first define the individual ply boundaries. Free sizing is used to size each ply of each individual element allowing the designer to see the best distribution of material, thus aiding in the definition of the ply boundaries. A global laminate is defined using a variety of materials and orientations with various thicknesses’ ranging from 0 to tmax. The free size optimisation can aid in screening out in-efficient materials and orientations. 4.2 Discrete Sizing Once the ply boundaries have been defined (by the previous step), the number of each individual ply is optimised. Move limits (TMANUF) can be set according to individual manufacturable ply thicknesses and force the optimiser to reach discrete values for thickness, highlighting the total number of plies required.

4.3 Stacking The position of each individual ply in the stack sequence is optimised to ensure all design and manufacturing requirements are met and in some cases exceeded.

This process using Altair products can be summarised in the flow chart below in Figure 3.

Figure 3: Process Flow Chart for Composite Optimisation Using Altair Products

© Altair Engineering 2009 Composite Optimisation of a Formula One Front Wing 17-4

5.0 Stage 1: Free Size – Definition & Results As previously mentioned the first stage to a composite optimisation problem is the Free Size stage. With the results from the geometric study showing the significant requirement for extra stiffness, the study was limited to the use of one material as this would significantly decrease the problem size and yield a result in a much shorter timeframe. Therefore the composite stack was modelled with two cloths at 45o (orientation set from previous experience) covering uni-directional material set at 4 different orientations; 0o,15o,30o and 45o. Each ply orientation was also given a maximum total thickness which results in 1,317,184 design variables (equivalent to the number of free size elements multiplied by number of composite layers). Manufacturing constraints can also be set at this stage, so to avoid small patches and aid final manufacture, a minimum member size was utilised. It is also pertinent to note that SMEAR was used in order to remove any effect of stacking sequence, as this first stage is used to define efficient ply boundaries. The use of new laminate cards within OptiStruct [2] were also tested as opposed to the traditional PCOMP/PCOMPG. With these new cards the complete process can be automated to provide an easy transition from each optimisation stage. See Figure 4.

ID MID T [THETA] [SOUT] [TMANUF] [DRAPE_ID]PLY 101 5 2.8 45 YES 0.2

ESID1

PID Z0 NSM SB FT TREF GEPCOMPP 101 0 200 STRN

ID LAM PLYID(1) PLYID(2) PLYID(3) PLYID(4) PLYID(5) PLYID(6)

STACK 1000 SMEAR 101 102 103 104 105 106PLYID(7) PLYID(8) PLYID(9) PLYID(10) PLYID(11) PLYID(12) PLYID(13) PLYID(14)

201 202 203 204 205 206 300 301

Figure 4: Ply & Stack Card Used for Free Size Optimisation OptiStruct now has the ability to automatically generate ply boundaries based on the results from stage 1, and the OUTPUT card FSTOSZ was utilised. This is an output request that automatically writes out an input deck for use in stage 2, which comprises PCOMPP(replaces traditional PCOMPG), STACK, PLY and Element Set cards which describe the resulting optimised ply-based composite model, and define efficient ply boundaries. For the front wing, two load cases were considered and Optimisation responses defined such that displacements due to the FIA load and aerodynamic loads were constrained, with the objective to minimise mass.

• The analysis converged in 14

iterations (see Figure 5) • Analysis time: 22mins on a

standard windows desktop. • Memory used 1.4Gb(in core) • Mass reduced by 57% compared

to 2007 wing • all Displacement constraints were

met

Figure 5: Normalised Convergence Curves

A sample of the optimised thicknesses for each of the orientations can be seen below: © Altair Engineering 2009 Composite Optimisation of a Formula One Front Wing 17-5

Cloth @ 45o

UD @ 0o

UD @ 15o

UD @ 30o

UD @ 45o

Cloth @ 45o

Figure 6: Element Thickness Results from Free Size Optimisation

The free sizing results show that the cloth at 45o, UD at 0o and 15o are working hardest. This is not surprising as these orientations are directed along the load path and would help prevent bending for the FIA load case and resist twisting due to the aerodynamic loads. As expected the UD at 30o and 45o are not being worked and as such require very little in the way of thickness. This result is also present on the lower wing surfaces. 6.0 Stage 2: Discrete Ply Thickness – Definition & Results With the inclusion of the output card FSTOSZ, an input deck for stage 2 is automatically generated by OptiStruct and contains a base set-up for stage 2. All of the previous manufacturing and optimisation constraints are automatically preserved and transferred into the stage 2 deck. At this point it is also possible to introduce additional performance constraints and for this analysis composite failure index was included. The first stage in setting up the discrete ply optimisation deck was to interrogate the automatically generated boundaries, and modify them into rationalised easy to manufacture domains. Below is a selection of automatically generated plies showing the element sets for 3 separate plies.

Discrete Ply boundary - No Material

Figure 7: Automatically Generated Element Sets Showing Ply Boundaries As can be seen above the automatically generated ply boundaries would require some rationalisation, and so the element sets are simply edited to reflect rationalised manufacturable plies (see Figure 8)

Discrete Ply boundary - No Material

Figure 8: Updated Element Sets Showing Rationalised Ply Boundaries

© Altair Engineering 2009 Composite Optimisation of a Formula One Front Wing 17-6

With the ply boundaries updated & defined it was necessary to update the design variables for the discrete plies ensuring the TMANUF flag, reflected the discrete values for ply thickness and updated the total number of allowable plies through modifying the lower and upper bound thicknesses on the DESVAR card. Additional manufacturing constraints were also added via the DCOMP card and the output card SZTOSH was implemented to automatically generate an input deck for stage 3. Interpretation and visualisation of results for discrete ply optimisation can sometimes be complicated and as such an easy way to review the results is to produce a chart illustrating the number of required individual plies [Figure 9].

PLY

ID

Number of Discrete Plies 0 1 2 3 4 5 6 7 8 9

2060400MP_LWR_TW@452060300MP_LWR_TW@452060200MP_LWR_TW@452060100MP_LWR_TW@452040400MP_LWR_UD@302040300MP_LWR_UD@302040200MP_LWR_UD@302040100MP_LWR_UD@302030400MP_LWR_UD@152030300MP_LWR_UD@152030200MP_LWR_UD@152030100MP_LWR_UD@15

2020400MP_LWR_UD@02020300MP_LWR_UD@02020200MP_LWR_UD@02020100MP_LWR_UD@0

2010400MP_LWR_TW@452010300MP_LWR_TW@452010200MP_LWR_TW@452010100MP_LWR_TW@451060300MP_UPR_TW@451060200MP_UPR_TW@451060100MP_UPR_TW@451040300MP_UPR_UD@301040200MP_UPR_UD@301040100MP_UPR_UD@301030300MP_UPR_UD@151030200MP_UPR_UD@151030100MP_UPR_UD@15

1020300MP_UPR_UD@01020200MP_UPR_UD@01020100MP_UPR_UD@0

1010300MP_UPR_TW@451010200MP_UPR_TW@451010100MP_UPR_TW@45

10

Figure 9: Graphical representation of number of discrete plies required

As can be seen from the above chart, the most influential plies are the 0o & 15o Uni-directional plies, which is not surprising as these directions lie on the load path, and will provide the majority of the support for vertical bending and torsion. • The analysis converged in 18

iterations (see Figure 10) • Analysis time : 40mins • Memory used 1.4Gb(in core) • Mass reduced by 1%

compared to 2007 wing • Composite Failure Index and

all Displacement constraints were met.

Figure 10: Normalised Convergence Curves

7.0 Stage 3: Stacking Sequence – Definition & Results At this stage, a basic lay-up has been defined, which comprises all the optimum ply boundaries, and optimum number of discrete plies. However it is now possible to further optimise the laminate by re-ordering the stacking sequence of the lay-up whilst considering manufacturing details, to further improve the structural performance of the wing. © Altair Engineering 2009 Composite Optimisation of a Formula One Front Wing 17-7

As the output card SZTOSH was requested during the last stage of optimisation, OptiStruct automatically generates an input deck for the shuffle stage of optimisation. Manufacturing constraints are set by using the DSHUFFLE card [Figure 11] and for this analysis no more than 3 successive plies of uni-directional materials of the same orientation were allowed. It was also possible to define closing plies and so a single cloth ply at 45 was selected.

© Altair Engineering 2009 Composite Optimisation of a Formula One Front Wing 17-8

Figure 11: DSHUFFLE Card Used for the Shuffle Optimisation

Due to the process of element free size and discrete optimisation, by definition the laminate stack must already satisfy all constraints previously set in the earlier stages of optimisation. As such the shuffle only applies desired manufacturing constraints, and should improve on the previous stages. Therefore optimisation responses and objectives for the final optimisation stage were altered slightly such that the minimum mass which had already been achieved during stage 2 was no longer required. Instead, it was decided to constrain the composite failure indices only and the objective was altered to minimise a weighted compliance. The optimisation converged in 2 iterations taking 18mins using 1.5Gb to run in core. The images below show the displacement results for the fully optimised shuffled lay-up vs. the baseline 2007 model for both the aerodynamic and FIA loading regimes. As can be seen from the displacement results, the optimisation process has produced a fully finished wing structure which meets and exceeds all design criteria set at the start of the analysis. The composite failure indices were not violated, and the largest improvement was achieved for the FIA loading showing a reduction in displacement of 47%. The aerodynamic results also showed a marked improvement and exhibited deflections ~30% lower than the 2007 baseline. Despite the mass reduction being less than originally anticipated, the significant increase in stiffness compared to the baseline 2007 model justifies the optimisation given the large geometric differences between the two wings.

AERODYNAMIC LOADING

ID ETYPE EID1 EID2 EID3 EID4 EID5 EID6DSHUFFLE 1000 STACK 1000

MAXSUCC MANGLE MSUCC VSUCC+ MAXSUCC 0 3 1+ MAXSUCC 15 3 1+ MAXSUCC 30 3 1

COVER VREP VANG1

+ COVER 1 45

FIA LOADING

Figure 12: 2007 vs. Optimised 2008 Wing Displacements

The images in Figure 13 illustrate how the optimiser treats each stage of the optimisation process. Far-left shows the laminate stack used for the element free size stage showing the simple laminate with each orientation defined (symmetric about mid ply). The middle image shows the optimised stack where the number of each individual ply has been altered, but its position within the laminate stack has not. The final image shows the result from the shuffled stage, which now satisfies all manufacturing and design constraints.

Figure 13: Stacking Sequence During the 3-Stages of Optimisation

8.0 Discussion of Results The original objective of this optimisation study was to produce a lightweight wing structure which performed as well if not better than the baseline 2007 wing. However even before any optimisation was started the pre-optimisation geometry studies showed that the structural differences between the two wings were large and the ability to generate a lighter stiffer solution for the 2008 wing was likely to be a difficult task. Stage 1 was able to demonstrate the effectiveness of free size optimisation in order to screen out inefficient plies and orientations, whilst automatically identifying efficient ply boundaries, all within a minimal time frame compared to traditional analysis methods. Stage 2 demonstrated the ability of OptiStruct to vary the number of discrete plies whilst ensuring deign constraints were met. It is worthy of note that this stage significantly increased the mass of the model compared to stage 1, as SMEAR was removed in order to consider composite failure indices within the design domain. The large difference in geometric stiffness compared to the baseline would mean larger displacements of the wing and hence larger strains in the laminate skins. As a result the composite failure index became the significant factor in this optimisation stage. Therefore in order to ensure the failure index constraints were not violated, additional material would be added and displacements reduced as a direct consequence. Stage 3 further improved the laminate stack, by ensuring the stack would be easy to manufacture, complied with manufacturing constraints and also improved the stiffness of the model further. © Altair Engineering 2009 Composite Optimisation of a Formula One Front Wing 17-9

© Altair Engineering 2009 Composite Optimisation of a Formula One Front Wing 17-10

9.0 Conclusions This paper has shown the successful use of OptiStruct for the design and optimisation of a composite front wing using a 3-stage approach, whilst ensuring all strength & stiffness targets are met and with an objective to minimise mass. The final design was able to meet both internal and FIA regulation displacement limits, improve min safety reserve factors (minimise composite failure index), meet manufacturing demands and minimise mass, whilst all being achieved in a significantly reduced time frame. 10.0 References [1] FIA Formula One Technical Regulations (2008) [2] Altair OptiStruct 9.0