Optimization of a Cessna 150/172 wing model
Reducing the weight of a plane and its wings can be achieved by various means: material innovation (optimised materials, composites), aerodynamic improvements (refining the shape of the wings, features like winglets), systems integration (going from mechanical to electrical or hydraulic system) or structural optimization.
With help from CAD and structural optimization tools, it’s possible to optimize the design of the airframe’s components. That ensures material is only used where it’s most needed.
A simplified yet optimized wing model will be set up, based on the Cessna 150 and the 172. In order to do this, we’ll start by generating a CA TIA model of the left wing using the Generative Surface Design (GSD) workbench, then we will use an optimisation tool to minimise the weight of the wing by increasing the radius of the wholes at the ribs and by reducing the thickness of the surface, the spars, the stringers and the ribs of the wing. After that, based in our optimised model, we will generate a 3D volumic part of the wing, to make a 3D FEA model analysis of it and compare it with the results of the 2D.
With help from CAD and structural optimization tools, it’s possible to optimize the design of the airframe’s components. That ensures material is only used where it’s most needed.
A simplified yet optimized wing model will be set up, based on the Cessna 150 and the 172. In order to do this, we’ll start by generating a CA TIA model of the left wing using the Generative Surface Design (GSD) workbench, then we will use an optimisation tool to minimise the weight of the wing by increasing the radius of the wholes at the ribs and by reducing the thickness of the surface, the spars, the stringers and the ribs of the wing. After that, based in our optimised model, we will generate a 3D volumic part of the wing, to make a 3D FEA model analysis of it and compare it with the results of the 2D.
Geometrical informations
Our left wing will follows the dimensions related to those plans :
The model should have as internal structure : 2 spars, 12 ribs, and 6 stringers (3 attached to the upper wing surface, and 3 attached to the lower wing surface). The stringers should be equidistantly placed between the spars. The spars should have an I profile and a Z-profile for the stringers. The dimensions of the Z-profile and the I profile weren’t fully knowned so the unknown values has been selected in function of the aesthetic coherence’s of lengths. The final dimension of the profile of the stringers and spars are :
The ribs will follow the airfoil pattern of the NACA2412 :
Material
The chosen material is the Aluminium 2024-T3, here are it isotropic values :
Name | Value | Units |
Young modulus | 73.1 | GPa |
Density | 2780 | Kg/m3 |
Elastic limit | 324 | MPa |
Poisson ratio | 0.33 | / |
Plastic limit | 469 | MPa |
Fatigue limit | 138 | MPa |
This material has been selected compared to the Aluminium 7075 because of its lighter weight and the non necessity to have a material as resistant than the 7075.
Pressure field computation
The maximum absolute pressure is the load that will be applied to all of our simulations. This value will be extracted from a Fluent simulation in which the wing surface will be subjected to an indicated airspeed of 158 knots which is 81.28 m/s at mean sea level condi-
tions. The means sea level conditions means that the indicated airspeed can be considered as the real airspeed of the wind. If we weren’t at those conditions, we should have adjusted our value.
The first step is the preparation of the space claim file, from the wing surface. The output of this step is to have an enclosure of the wing, ready to be meshed and named selection of the different enclosure side and the wing :
tions. The means sea level conditions means that the indicated airspeed can be considered as the real airspeed of the wind. If we weren’t at those conditions, we should have adjusted our value.
The first step is the preparation of the space claim file, from the wing surface. The output of this step is to have an enclosure of the wing, ready to be meshed and named selection of the different enclosure side and the wing :
The fluent meshing consists of a basic mesh configuration, locally sized on the enclosure limits and the wings with poly-hexcore cells. Fluent compute an average skewness of 0.06 and an average orthogonality of 0.92, which testimony the high quality of that mesh, and thus, its results.
The analysis consisted of a pressure based (because of the low-speed, incompressible case), K-omega SST (because of his good adaptability to the boundary conditions and the separation of the flows) turbulence model, an velocity of 82m/s in x axis in the inlet, COUPLED, with the global time step and air as material.
As final , we have obtained this contour and this value :
From now, we will use 0.1049 MPa as maximum absolute pressure.
The analysis consisted of a pressure based (because of the low-speed, incompressible case), K-omega SST (because of his good adaptability to the boundary conditions and the separation of the flows) turbulence model, an velocity of 82m/s in x axis in the inlet, COUPLED, with the global time step and air as material.
As final , we have obtained this contour and this value :
From now, we will use 0.1049 MPa as maximum absolute pressure.
The 2D model
The 2D model has been generated following an integral philosophy, it is composed of 4 joints, each of them uniting a different component of the wing :
- The initial thickness values for the surface; stringers, ribs and spar is 10mm.
- As an integral model, all its line connections have been declared as welded.
- The initial radius values for all the six wholes is 20mm.
- Then we used those analysis configurations to simulate the first 2D analysis with 10mm as initial thickness for the surface, stringers, ribs and spars
- The root rib and the face of the stringers and spars are clamped.
- As computed with Fluent, a maximum absolute pressure of 0.1049MPa is applied to the upper part par the surface.
We can have the initial mass of the wing thank to the inertia tool :
With this initial configuration, we’ve got those results :
According to those contours, with the initial configuration of 10mm of thickness and 20mm of diameter of the wholes the maximum displacement would be 341mm whereas the pressure max would be 1890MPa locally but less than 189 overall. Those high pressure local points are located near the welding spot connection. As the welding connection haven’t been initialised all over the ribs but only at the beginning and the end, the pressure has not been distributed right and those welded points are taking the most part of its. The "realistic" answer is therefore more close of the 189 than the 1890MPa.
The optimization tool present on CATIA permit to minimize global sensor such as mass here in order to gain efficiency. With this configuration, the optimization process selected values that are, according to it the best ratio mass/1.5 ultimate load limit.
The optimization tool present on CATIA permit to minimize global sensor such as mass here in order to gain efficiency. With this configuration, the optimization process selected values that are, according to it the best ratio mass/1.5 ultimate load limit.
The optimum values are : 
In this situation, the mass decreased from 167kg to 44kg just by modifying the thicknesses and the radius. In order to check if the constraints of not over passing 1.5 times the load limit, a new optimised 2D static simulation is conducted :
As we can see, the optimised model is going out of limits, we can observe those "waves" on the mesh deformation that indicate that the upper surface collapses on the lower one. The max translation went from 341mm to 5,2m. The first hint of this reaction would be a wrong optimization, but we’ll see later that some other option will appear.
As we can see, the optimised model is going out of limits, we can observe those "waves" on the mesh deformation that indicate that the upper surface collapses on the lower one. The max translation went from 341mm to 5,2m. The first hint of this reaction would be a wrong optimization, but we’ll see later that some other option will appear.
The 3D model
Contrary to the 2D, the 3D model is generated following the differential philosophy. That means that there results of this model are supposed to be more precise, closer to the reality :
Knowing that the surface area of the wing is 14.8 m2, and that the material reference weight limit's 68.6kg/m2. That means that the wing is theoretically able to support 1015.28kg per wing or 9959,89N. As Pascal are newton per meter2, we can calculate the theorical maximum pressure that a wing can handle by dividing 9959.89N by 14,8. According to this reference data, a wing could only support 672.9N.m2 or 672.9 Pa. This is 155 892 time lower than the pressure extruded from Fluent.
Using the 3D model with the calculates pressure load leads us to those results :
Even thought there’s a stringer not well connected and that generate a translational displacement of 40mm, the tip of the wing have a translation of 26mm whereas it is supposed to be the maximum. Those values makes more sense than the initial 3D modellisation and give credit the optimization process.
Conclusion
He have started the assignment by generating a 2D model using integral approach, then we have configured the line and surface connections as the welding spot connection. We have created a new material, the Aluminium 2024 T3 and applied it in all our component. We imported the surface of the wing into Space Claim to build an enclosure around it, simulate on fluent an indicated airspeed of 158 knots and extract the maximum absolute pressure of 0.1049MPa into our CATIA FE analysis. The root rib and the coincident faces has been clamped to ensure to not have any singularities. The first simulation gave us a maximum displacement of 341 mmm and a maximum Von Mises value of 1890MPa. We noticed that this maximum is very localised around the welding points connection declared before and the rest of the structure Von Mises is around 189MPa which is more realistic.
The second part of the assignment was the optimization of our model. We used the optimization tool of CATIA by declaring that we wanted to minimize the total mass, without having the maximum Von Mises below 1.5 time the ultimate load. We have selected the thickness of ribs, stringers, surface and spars as well as the radius of the whole inside the ribs as parameters. After some time, the optimization tool reduced the mass from 167kg to 44kg.
Finally, using the optimized values and the surfacic model, we have generated a 3D model and applied a differential philosophy in order to construct the wing. We have created fastened and contact connections instead of welding spot, applied the absolute pressure, the clamps and then we launch the simulation. We noticed that the pressure, translational and mesh deformation values were incoherent.
We discuss of the non coherency of the computed absolute value of 104MPa and calculate a theorical absolute pressure limit with the given reference data. This simulation was more coherent and the optimum values of the optimisation process were gaving us realistic values.
In the end , the optimised wing of 45kg could support the theorical pressure but not the computed one. Additional research would be necessary to understand why the computed value is so high. One of the clues could be an inaccurate extracted data due to errors on Fluent. The second idea i had was that the mesh wasn’t fine enought because of the use of the OCTREE tetrahedron mesher sometimes. It would also be insteresting to calculate the autonomy gained going from a wing at 167kg to 45 and compare it to the real Cessna plane autonomy. To do that, it would be necessary to know the specific consumption of our plane per hour or per kilometer and then calculate the difference with and without the optimization.
The second part of the assignment was the optimization of our model. We used the optimization tool of CATIA by declaring that we wanted to minimize the total mass, without having the maximum Von Mises below 1.5 time the ultimate load. We have selected the thickness of ribs, stringers, surface and spars as well as the radius of the whole inside the ribs as parameters. After some time, the optimization tool reduced the mass from 167kg to 44kg.
Finally, using the optimized values and the surfacic model, we have generated a 3D model and applied a differential philosophy in order to construct the wing. We have created fastened and contact connections instead of welding spot, applied the absolute pressure, the clamps and then we launch the simulation. We noticed that the pressure, translational and mesh deformation values were incoherent.
We discuss of the non coherency of the computed absolute value of 104MPa and calculate a theorical absolute pressure limit with the given reference data. This simulation was more coherent and the optimum values of the optimisation process were gaving us realistic values.
In the end , the optimised wing of 45kg could support the theorical pressure but not the computed one. Additional research would be necessary to understand why the computed value is so high. One of the clues could be an inaccurate extracted data due to errors on Fluent. The second idea i had was that the mesh wasn’t fine enought because of the use of the OCTREE tetrahedron mesher sometimes. It would also be insteresting to calculate the autonomy gained going from a wing at 167kg to 45 and compare it to the real Cessna plane autonomy. To do that, it would be necessary to know the specific consumption of our plane per hour or per kilometer and then calculate the difference with and without the optimization.