Presentation Title: A Landing Gear FEM Analysis Using MSC.Patran/MSC.Nastran Authors: Sousa, Everton M.; W. Rodolfo and Tréz, Márcia P. Company Name: EMBRAER LIEBHERR Equipamentos do Brasil S.A. (ELEB). City: São José dos Campos Country: Brazil Phone: 55 12 39355263 Fax: 55 12 39355320 Email: esousa@eleb.net, rodolfo.wurzba@eleb.net, marcia.trez@eleb.net

ABSTRACT

A finite element static analysis of a Landing Gear part (Main Fitting) is presented. The Main Fitting is the larger part of the Landing Gear with the function of shock absorption during aircraft landing and also supports the aircraft in ground maneuvers. This part is subjected to various types of loads like internal pressure, bending, shear and torsion. The effect of the secondary moment is considered in the loads applied on the model with an amplification factor to take into account the variation of the load application point. This describes the way of transference of loads from the ground to the component showing the equilibrium equations. Boundary conditions to simulate the bearings and the contact point are described. In general, bad representation of boundary conditions can induce errors that are only discovered late during the static test phase. Detailed models of the attachment points are presented where contact elements are used in order to better represent the assembly. A nonlinear plastic analysis is also employed to improve the representation of the contact between gap and solid (tetra10) elements in the attachment locations. To validate the analysis and the element mesh used the finite element results are compared with the results of the static test to show how conservative or non conservative the analysis is. Although, in reality, the behavior of a real part of a landing gear is plastic and geometrically nonlinear with contact problems, it could be represented by a static linear analysis in the global model since the effect of secondary bending has been included in the loads and localized plastic models to better represent the contact effects.

1- Introduction EMBRAER LIEBHERR Equipamentos do Brasil S.A. (ELEB) is responsible for ERJ135/145 Main Landing Gear and ERJ170/190 Nose Landing Gear design, development and production. The design and integration process encompasses numerous engineering departments, e.g., structures, weights, runway design and economics; and has become extremely sophisticated in the last few years. Depending on the aircraft category, the Landing Gear Assembly, can range from 3 to 7% of aircraft total mass. Being an enormous challenge for the Engineering Department to achieve a reduced weight, easy maintenance, high levels of safety and low cost structure. The Landing Gear is composed by strut, shock absorber, extraction/retraction mechanism, breaks, wheels and tires; its function is energy absorption at landing, braking and taxi control. Energy absorption is performed by a hydraulic structure denominated Shock Strut. It is composed by a Piston and a Cylinder; the latter is called Main Fitting.

Figure 1: Nose Landing Gear location.

This important part is subjected to various types of loads like internal pressure, bending, shear and torsion. In this paper a Main Fitting analysis using MSC.Patran/Nastran is presented. In static analysis, large models were used to obtain stress results in the Main Fitting structure, being necessary dynamic memory allocation. But in cases where the contact area was the analysis focus, both parts were modeled and GAP elements were employed in a nonlinear analysis. The Landing Gear structural behavior is plastic and geometrically nonlinear with contact problems. Therefore, MSC.Patran/Nastran software was a powerful tool in contact and plastic analysis. The Nose Landing Gear referenced here includes all components and parts

required to perform the functions of gear extension, down-locking, up-locking, energy absorption and emergency system. 2- Problem definition During the Main Fitting base line definition the Engineering Department is responsible for projecting aeronautical structures that mind weight reduction, easy maintenance, high levels of safety and low cost. Landing, taxi and breaking are the dimensioning loads considered in the Landing Gear development practice. The Structural Engineering Department is responsible for dimensioning the Main Fitting structure with safety for limit and ultimate loads, reduced weight, no stress concentration, complying with the airworthiness requirements. In most cases, the Strength of Material Theory is not accuracy enough to evaluate stress result in complex parts as the Main Fitting structure. Therefore, MSC Patran/Nastran software is applied in order to obtain accurate results of displacement and stress and additional tools are applied to achieve convergence and reduce processing time. The FEM model size is one of the great limitations faced by the Structure Engineering Department in the Main Fitting MSC Patran/Nastran analysis, being necessary to use recourses of dynamic memory allocation. In the non-linear analysis using gap elements, material plastic properties or both, the most common problem faced by the Structural Engineering Department was no convergence and memory allocation.

Figure 2: Main Fitting boundary conditions.

The Nose Landing Gear is attached to the aircraft structure by four ball bearing points. The right socket pin has three translation directions fixed while the left one has two translation

direction fixed, in order to allow the “y” movement. The ball bearing is represented by MPC elements. In this kind of component is normal to have a lot of combined efforts as internal pressure, bending, shear and torsion. The transmissions of these loads are made between contact surfaces from the ground to the part and from the part to the aircraft. The idea is to represent in a better way the applications of these loads to get results more realistic as possible. In a complex structure the Strength of Materials Theory analysis is not sufficient accurate to evaluate stress distribution at the entire structure. Then, MSC.Patran/Nastran software is applied to simulate the Main Fitting behavior when submitted to combined loads as internal pressure, bending, shear and torsion. In practice, the loads transmission in the Main Fitting occurs by bearings, sockets and pressure at the inner surface. The pressure is applied straight at the solid element faces. To analyze the stress distribution at regions far from the contact point, a linear analysis is performed using TETRA10, ROD and BEAM elements. The justification for this solution is save processing time during the analysis. But in cases where the contact area was the analysis focus, both parts were modeled and GAP elements were employed in a non-linear analysis.

Figure 3: Contact Elements.

To evaluate displacement results at the Main Fitting structure, TETRA4 elements were employed, but to evaluate stress results, a more accuracy element TETRA 10 is used.

3- Analysis The Main Fitting analysis can be performed as a separate component or in one assembly. If the Nose Landing Gear assembly is modeled, it can bring some size complexities to the model, as the number of elements and nodes increase. But this requires lead to a nonlinear analysis with the increase the time processing and the size of memory allocation and the number of iteration to get the convergence of the nonlinear analysis. Therefore, the choose of analyze a separate part was employed to reduce the processing time and the numbers of gap elements and to permit the increase of the numbers of elements of the model once we did not have elements of others interface components. For the detailed models where the stiffness of the interface components is important, the modeling of these parts was considered. Loading During the aircraft landing and ground maneuvers (taxing, pivoting, turning, braking, engine run up and towing), some loads are transmitted from the ground to the Main Fitting that is attached to the aircraft through bearings. Internal pressure is generated from the shock absorber deflection simultaneously with contact loads transmitted from the internal parts. Geometric nonlinear model could also be considered to take in account direction of the load application or secondary moment. If is knowledge the stiffness of the assembly it is possible to simplify with a linear analysis where this effect of secondary moment is included into the loads. Model size and memory allocation In order to obtain more precise results, the mesh size must be adapted to all regions of the part mainly in proximity of the concentration points. For the model the Main Fitting with around of 420000 nodes is necessary to allocate the computer memory with the special cards. Boundary conditions It is requested a critic allocation of boundary conditions in order to simulate the real operational conditions. A not well representation of an attachment point can bring a delay in the development phase with the hazard of to damage the part. A complete analysis of the Main Fitting was done in three steps of analysis being the first one a linear analysis of the whole main fitting, the second step a geometric nonlinear analysis of local lower part and the step 3 geometric and material nonlinear analysis of this lower part. The nonlinear analysis was required to have a good stiffness representation of the others components of the gear. These components are responsible of the loads transmission from the ground to the main fitting. STEP 1: Linear stress analysis A stress analysis was performed for the Main Fitting hole structure. The load cases applied were chosen among the critical conditions of landing and ground maneuvering. It is usual to evaluate the attachment point pre dimensioning calculi, in order to get a faster convergence to the final design. This analyzes is done by simple Strength of Materials Theory, where are used

dedicated programs to calculate lug, socket submitted to bending, shear, torsion efforts. The finite element model used in the linear analysis is made of 415000 nodes and 265000 TETRA10 elements. The loads and the boundary conditions are applied to the model and the reactions are verified at the aircraft attachment points in order to obtain values smaller than the tolerance established. Figure 4 shows the von Mises stresses of a FEM analysis for a critical landing load case.

Figure 4: von Mises Stress.

As the linear stress analysis model do not represent the correct stiffness for some regions, detailed models must be performed in order to obtain more accurate stress results. One of these regions is the Sliding Tube Housing. The Main Fitting and the Sliding Tube parts are entirely modeled as described in steps 2 and 3. STEP 2: Geometrical nonlinear analysis In regions with stress concentration, it is important to detail the components interface, to better represent the contact between the parts. Due to the linear FEM size, the Main Fitting and the Sliding Tube interface were not very well represented. Therefore, a refined analysis is then performed using GAP and HEX 8 elements as presented in Figure 3. In this step is presented a geometrical nonlinear analysis, with gap elements. It is interesting to observe that the limit stress achieved at the FEM analysis is about the limit test stress value at the test.

Figure 5: Max. Principal Stress.

STEP 3: Material and Geometrical nonlinear analysis In the ultimate condition, the material is submitted up to its yield condition. Being necessary to input the plasticity material curve as presented in figure 7. In this step is presented a geometrical and material nonlinear analysis, with gap elements and material nonlinear curve. It is possible to show that the ultimate stress achieve is about the ultimate test stress value.

Figure 6 – Max. Principal Stress.

The Al7175-T74 tensile stress-strain curve is obtained from MIL - HDBK – 5H and it is presented in Figure 7.

Figure 7 – Al7175-T74 - Material strength curve.

Table 1 presents a comparison between the 3 models presented before.

Table 1 – Test correlation for the linear analysis. 1ST. STEP 2ND STEP 3RD. STEP N. ELEMETS 265000 5658 5658 N. NODES 415000 9222 9222 2D ELEMENT TYPE BAR GAP GAP 3D ELEMENT TYPE TETRA 10 HEX 8 HEX 8 SOLUTION TYPE LINEAR (SOL 101) NON LINEAR (SOL 106) NON LINEAR (SOL 106) PROCESSING TIME 9018.171 seconds 224.421 seconds 275.265 seconds HARDWARE CONFIGURATION Pentium4/1806 Pentium4/1806 Pentium4/1806

Table 2 – Test correlation for the linear analysis.

CHANNEL STRAIN

(1E-6)

TEST STRESS

(MPa)

NOMINAL STRESS

(MPa)

FEM STRESS

(MPa)

%

FEM/NOMINAL

E03101861 2617 172 185 209 13

R031062B61 3693.113 253 271 287 6

E03106861 3586.013 235 252 294 16

E03107561 -3280.658 -215 -231 -270 16

Table 3 – Test correlation for the nonlinear analysis.

CHANNEL STRAIN

(1E-6)

TEST STRESS

(MPa)

NOMINAL STRESS

(MPa)

FEM STRESS

(MPa)

%

FEM/NOMINAL

E031084-61 1424.513 100 93 110 18

E031086-61 4840.159 340 317 375 18

4- Discussions Considering that in aeronautical companies the structural weight is one of the principal Engineering challenges, the material and the analysis methodologies should be employed up to its limits. Then, the MSC Patran/Nastran was extensive applied in the Main Fitting analysis. Comparing the strain results evaluated by strain gages and the results obtained from the Main Fitting model using gap elements, is possible to observe that nonlinear analysis has become essential in the Main Fitting analysis. The gap parameters are extremely important in the analysis time processing, being the key for the model convergence and also the processing analysis time. 5-Conclusions This analysis is important to the Nose Landing Gear weight optimization, being on of the biggest challenge for the aircraft development nowadays. Based on this analysis, it is possible to preview strain test results reducing the time schedule of the Landing Gear development. It was fundamental to provide a database for fatigue analysis, once that the stress level in all parts of the component will be previewed. This analysis is utile to reduce the time of the product development. This kind of analysis shows for the users that is possible to do a FEM in almost all types of mechanical components as was done for this complex Main Fitting. 6- Acknowledgements The work presented in this congress could not have been possible without the guidance and support of many people. The group would like to thank ELEB, for support and giving us the opportunity of this presentation. And also to MSCsoftware for the invitation and technical support during the problem development. 7- References MSC software products MSC.Nastran User’s manual, Version 68, The MacNeal-Schwendler Corporation, Los Angeles, CA, November 1997. BOOKS

-BRUHN, E. F. - Analysis and Design of Flight Vehicle Structures. Ohio, USA, Tri-State Off-Set, 1973. AIRCRAFT DESIGN STANDARDS - Department of Transportation, Federal Aviation Administration – Federal Aviation Regulations Part 25 – “Airworthiness Standards: Transpot Categtory Airplane” – Change 13, Amendment 25-97, eff. June 26th, 1998 and Amendment 25-98, eff. March 10th, 1999. - 8- Figures and Plots Not applicable.