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Light Aircraft Main Landing Gear Design and Development

Amit Goyal M.S. Ramaiah, School of Advanced Studies, INDIA.

Abstract: The need for lightweight, high performance flying machine has today shifted the emphasis from the use of conventional advanced metallic materials to that of composites. High specific strength and stiffness characteristics coupled with techno economic feasibility are a password to the acceptability of any material in aircraft construction. This paper presents an approach for “Design; Analysis; of a Main Landing Gear of an Aircraft” made of advanced composites materials using advanced CAE tools and techniques.

In this paper, first of all, functional specification of the part has been specified. General principles of composite design were followed in arriving at suitable designs. In the design phase using the FEA tool ANSYS 5.7, starting form shape and wall construction, choosing a proper element type, loadings, constraints, materials and behavior modeling have been done. Various constants and lamination parameters were used to define the element.

In the development phase, a rigorous non-linear stress and buckling analysis was carried out for the part. The Finite Element Analysis software ANSYS was used for this purpose. Various experimentations were done using different combinations of loads and orientations. The most significant feature of the analysis was perhaps the thickness and orientation optimization with buckling, stress and different failure criteria. This optimization was the key to utilize the directional properties of the laminated composites. Tsai-Wu laminated failure criterion and Maximum Stress Failure Criterion had been specified. Results such as stresses in layer coordinate system, deflections, failure index had been determined. A true assessment of the critical regions in the part was made so as to predict the behavior of the gear at extreme landing conditions. It had been made sure that all stress values lie well within the limits. A margin of Safety was determined for each combination. Finally design was optimized and conclusions were drawn.

Introduction: The main landing gear is one of the most critical components of an aircraft, capable of reacting the largest local loads on the airplane. It is a primary source of shock attenuation at landing. It controls the rate of compression extension and prevents damage to the vehicle by controlling load application rates and peak values. Thus utmost care must be taken while designing a main landing gear.D.W.Young [1] discusses the technological developments in aircraft landing gears and explains some basic requirements in designing a main landing gear.

Problem Definition: When the aircraft lands at normal sink rate, maximum amount of energy has to be absorbed by the main landing gear, which undergoes large deformations and rotations. This necessitates a rigorous non-linear finite element analysis of the main landing gear to predict its behavior prior to manufacturing a prototype. Energy absorbed by the main landing gear is stored in the form of elastic strain energy and hence the material used for making the main landing gear should have high elastic strain energy storage capacity. The desired characteristics of a main landing gear are high strength, lightweight, medium stiffness and high elastic strain energy storage capacity. Dorothea C.Walden [2] discusses application of composites in

commercial airplanes and explains some technical aspects, which should be kept in mind while designing an aircraft part using composites.

Fiber reinforced plastics have an outstanding combination of high specific strengths and specific stiffness and this material ideally meets the desired characteristics of a main landing gear material. The anisotropic property of the composite material can be better utilized in main landing gear because the principal stress component in the landing gear is a normal stress component along the length of the gear. By orienting the fibers in the axial directions, thus, the composite material system can be effectively utilized in making a landing gear.

Objectives: The objective here is to suggest the design for the main landing gear of a light aircraft, which satisfies all the design specifications in making a landing gear. Main objectives of this project are

Geometric and material modeling •

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Non-linear finite element analysis to predict its behavior of the gear prior to manufacturing.

Determination of stresses and deflection for different load and orientations.

Computation of load-deflection curves.

Assessment of critical regions and to limit damage tolerance.

Weight Reduction

Design optimization.

Design Approach: Following are the design specifications for a main lading gear.

Part Name Main Landing Gear

Function To absorb the shock (kinetic energy of the vertical velocity on landing)

Sinking speed 2.5 to 3 m/sec

Landing ‘g’ permitted 2.5 g (3 g max.)

Max. Vertical Weight 560 Kg

Efficiency 0.5

Aesthetics rate Very high

Functional Properties High toughness, high strength, corrosion resistant.

Material

Which can store the greatest elastic potential energy per unit mass / volume without failing

Functional Requirements for design of a main landing gear of a light aircraft:

It should be able to take 90% of the weight of the aircraft while standing. •

• At minimum sinking speed of 3 m/sec it should be able to take 80% of the take off weight.

Main landing gear can be considered as a thin curved shell. Here we will consider the ‘Bending theory or general theory, which includes the effects of bending. Thus it permits the treatment of discontinuities in the stress distribution, taking place in a limited region in the vicinity of a load or structural discontinuity.

A line diagram showing the loading at the gear is shown in the figure (1).

Figure 1 - Line Diagram of the landing gear

The maximum bending stress at any point along the length of the landing gear can be given as

σb = 6 M / t2 N/mm2

Where, M = Bending moment, t = thickness of the wall

In order to get uniform strength gear with minimum weight, the stresses along the length should be kept constant. This method not only reduces the amount of material required for construction but also allows the bending stresses to be uniformly distributed along the length.

Most significant feature of the analysis is optimization of thickness and orientation with different stress, fatigue and failure criteria. This concept can be utilized for designing a main landing gear using advanced composite material system. In this investigation the design is analyzed with four different combinations of loads and orientations.

Procedure: Though the main landing gear behaves like a thin curved shell element, analysis of the landing gear is quite complex mainly because of the varying shape geometry of the landing gear, the complex loading conditions and the nature of supports provided. In a typical main landing gear construction, landing gear is provided with fixed supports at the point of attachments with rigid aircraft body. At both the ends, a rigid link is provided between the wheel and the landing gear wall. Vertical load is applied at the end of each link (as the aircraft lands, a vertical force tries to lift the gear in vertical direction). As landing gear undergoes large deformations and rotations at the time of landing of the aircraft, it becomes necessary to carry out a non-linear finite element analysis to predict its behavior. A suitable lamination theory has been selected which offers a systematic way to study the mechanical properties when combined with the theory of shells which forms the basis for composite structural analysis. J.N.Reddy and C.F.Liu [3] explain a higher order theory for analysis of composite laminates having geometric non-linearity. Failure criteria (maximum stress criterion and Tsai-wu criterion) have been selected to predict the onset of failure when a lamina is subjected to a multi axial state of stress. Using a finite element method of analysis (FEM), the stresses and deflections were determined for different load combinations, and different layer orientations. The critical regions are assessed, a suitable margin of safety is determined and the design is optimized.

Preprocessing: Finite element model has been created using SHELL 91 element type. It is a 3 D, 8 noded, non-linear layered structural shell element. The element has six degrees of freedom at each node: translations in the nodal x, y and z directions and rotations about the nodal x, y and z-axes. The element is defined by eight nodes, layer thickness, layer material direction angles, and orthotropic material properties.

Total numbers of layers have been specified. The part has been modeled using three layers of equal thickness of 8 mm. i.e. the total thickness of the landing gear has been considered as 24mm.Supports are considered to consist of three layers with each layer having a thickness of 12mm. Layer material direction angles are specified with respect to element co-ordinate system. The material properties of each layer may be orthotropic in the plane of the element. The material x direction corresponds to the local layer xi direction. The failure criterion selection is input in the data table. Maximum stress criteria and Tsai- Wu failure criteria have been chosen to predict the response.

Since axle is assumed to be very rigid, actual dimensions are irrelevant in this case and it has been modeled using 2 D elastic beam element.

Material properties for GFRP / EPOXY unidirectional lamina: E11 38610.88 N/mm2

E22 8273.76 N/mm2

E33 8273.76 N/mm2

V12 .26

V23 .26

V31 .26

G12 4136.88 N/mm2

G23 4136.88 N/mm

G31 4136.88 N/mm

ρ 25.438*10-7 Kg/mm3

Material properties for GFRP / EPOXY Bi-directional lamina: E11 20684.4 N/mm2

E22 20684.4 N/ mm2

E33 20684.4 N/ mm2

V12 .104

V23 .104

V31 .104

G12 4895.308

G23 4895.308

G31 4895.308

ρ 25.438*10-7 Kg/mm3

In the case of axle, carbon steel with high stiffness is used to model it. Properties assigned are shown below.

Material properties for C- Steel: Modulus of Elasticity 2.01x 105 N/mm2

Position’s Ratio 0.29

Geoff Ecold [4] has discussed different failure criterion used in predicting onset of failure when a lamina is subjected to multi axial state of stress. Based on this the data table as input for Structural-Non-Linear-Inelastic-Failure Criteria, referred from Ansys online documentation [6], is as shown below:

Failure Criteria Table: 1 2 3 4 5 6

CritKeys 0 1 1 0 0 0

Temps 0 0 0 0 0 0

XTenStrn 0 0 0 0 0 0

XComStrn 0 0 0 0 0 0

YtenStrn 0 0 0 0 0 0

YComStrn 0 0 0 0 0 0

ZTenStrn 0 0 0 0 0 0

ZComStrn 0 0 0 0 0 0

xyShStrn 0 0 0 0 0 0

yzShStrn 0 0 0 0 0 0

xzShStrn 0 0 0 0 0 0

xTenStrs 1681 0 0 0 0 0

xComStrs -1681 0 0 0 0 0

yTenStrs 1681 0 0 0 0 0

yComStrs -1681 0 0 0 0 0

zTenStrs 10000 0 0 0 0 0

zComStrs -10000 0 0 0 0 0

XyShStrs 840 0 0 0 0 0

YzShStrs 10000 0 0 0 0 0

XzShStrs 10000 0 0 0 0 0

Cplng-xy -1 0 0 0 0 0

Cplng-yz -1 0 0 0 0 0

Cplng-xz -1 0 0 0 0 0

Loads & Constraints: The main goal of a finite element analysis is to examine how a structure or component responds to certain loading conditions. Maximum vertical load of 5600 N has been applied at each end of the axle. A coupled degree of freedom is applied in Y direction at the line where axle attaches with the landing gear, so as to distribute the load to all the nodes in that line. All six degrees of freedom have been fixed at top of both the supports.

Analysis Construction of the Finite Element model began with a very detailed study of the part. The part was surveyed and key information was noted. The list of necessary dimensions and data was provided by “Aircraft Research & Design Center, HAL”.

First of all, the geometric model of the part was imported from PRO-E 2000i to ANSYS 5.7.The next step was to generate the elements. Each element requires four parameters before it can be defined, co-ordinate system, material table, element type and real constant table. Proceeding with these parameter specifications, the elements were defined based on node connectivity. Area quad mapped meshing was used to generate the elements. All six degree of freedom were restricted at the top of the supports and degree of freedom was coupled in y direction at main landing gear and axle attachment. Maximum vertical load was applied at each end of the rigid axle beam. For the simplicity of the problem, we considered only half of the model and applied symmetric boundary conditions in x direction. The finite element model with ESHAPE turned on is shown in figure (2) i and figure (2) ii shows the finite element model with all the constraints, loads. Robet.H.Mallett, A.M.ASCE and, Pedro V. Marcal [5] explains the finite element analysis of non-linear structures and explains the basic computational technology in analyzing non-linear analyses.

Figure 2 - Finite Element Model, i- with ESHAPE turned ON, ii- with all loads and constraints

As we are carrying out a non –linear static analysis, Total load has been applied in different sub-steps to apply the loads gradually so that an accurate solution can be obtained. The load applied is ramped so that its value increases gradually at each sub – step, with the full value occurring at the end of the load step. At the completion of each incremental solution, the program adjusts the stiffness matrix to reflect the nonlinear changes in structural stiffness before proceeding to the next load increment Before each solution, the Newton – Raphson method evaluates the out of – balance load vector, which is the difference between the restoring forces (the loads corresponding to the element stresses) and the applied loads. The program then performs a linear solution, using the out-of-balance loads and checks for convergence. If convergence criteria are not satisfied, the out-of balance load of vector is re-evaluated, the stiffness matrix is updated, and a new solution is obtained. This iterative procedure continues until the problem converges.

In setting additional solution option, sparse equation solver has been used to solve the equations. Stress stiffening option has been kept on to account for buckling, bifurcation. Then problem is solved and Results are reviewed in post 1 and Post 26 processor.

Results & Discussion: A rigorous non-linear finite element analysis of the composite main landing gear was carried out with different combinations of load cases, and orientations. The most significant feature of the analysis phase was perhaps the characterization of non-linear behavior and thickness and orientation optimization, with different stress and failure criteria.

In the analysis phase we experimented with four cases

Unidirectional fiber arrangement at 5600 N •

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Bi-directional fiber arrangement at 5600 N

Unidirectional fiber arrangement at 11200 N

Bi-directional fiber arrangement at 11200 N

In these four cases, we used two failure criteria to predict onset of failure when lamina is subjected to multi axial state of stress.

Maximum stress failure criteria •

• Tsai-wu failure criteria

Figures (3), (4), (5), (6) show the nodal deflection plots for the above four cases. It is clearly observed that with bi-directional fiber arrangement deflections are much larger than compared to unidirectional fiber arrangement and maximum deflection is occurring at both ends where it is attached to the axle.

Figure 3 - Nodal deflection plot at 5600N with unidirectional fiber arrangement

Figure 4 - Nodal deflection plot at 5600N with bi-directional fiber arrangement

Figure 5 - Nodal deflection plot at 11200N with unidirectional fiber arrangement

Figure 6 - Nodal deflection plot at 11200N with bi-directional fiber arrangement

An element table below shows the comparative study of the results obtained from different experiments.

Element Table Result Data:

Characteristic 5,600 N

(With unidirectional fiber arrangement)

5,600 N

(With bi-directional fiber arrangement)

11,200N

(With unidirectional fiber arrangement)

11,200N

(With bi-directional fiber arrangement)

Maximum Stress in x direction 260.98 N/mm2 283 N/mm2 592 N/mm2 663.9 N/mm2

Maximum Stress in y direction 24.2N/mm2 20.3 N/mm2 45.89 N/mm2 46.86 N/mm2

Maximum Shear Stress in xy plane 8.767N/mm2 69.4 N/mm2 21 N/mm2 109 N/mm2

Maximum Stress Failure Index

number 2 2 2 2

Index value for Maximum Stress Failure Criterion

0.77 .17 1.458 .394

Tsai-Wu Failure Criteria Index

number 3 3 3 3

Index value for Tsai-Wu Failure

Criteria 0.6 .03 2.16 .145

Maximum Failure Index value in

Layer 1 0.77 .17 2.16 .394

Maximum Failure Index value in

Layer 2 0.26 0.055 .49 .129

Maximum Failure Index value in

Layer 3 0.76 0.15 2.13 .36

Margin of Safety 1.3 5.9 < 1 >1

It was observed that at a maximum designed load of 5600 N (maximum take-off weight), design is quite safe with unidirectional fiber arrangement as well as with bi-directional fiber arrangement. Maximum stresses are occurring at the curved region where supports are attached to the landing gear. And it has been found that all stresses values are well with in the limits, quite lesser than allowable stresses values for the chosen material. Failure indexes are lower than one with maximum stress failure criteria as well as for Tsai-wu failure criteria. Thus with both the arrangement, it satisfies all the design requirements at the maximum design load of 5600 N. Further load deflection curves for each case have been computed and non-linear characteristics of the gear at different loadings and orientations have been studied. Figures (7), (8), (9), (10) show load deflection curves for all the four cases. It can be observed that at twice of the design load, landing gear is showing highly non-linear characteristics with both fiber arrangements. Failure criteria index is more than one using unidirectional fiber arrangement. Using bi-directional layer orientations, at a load level of 11200 N failure indexes are lower than one. Thus design is still safe at twice the load level using bi-directional fiber arrangement.

Figure 7 - Load deflection curve at 5600 N with unidirectional fiber arrangement

Figure 8 – Load deflection curve at 5600 N with bi-directional fiber arrangement

Figure 9 - Load deflection curve at 11200 N with unidirectional fiber arrangement.

Figure 10 - Load deflection curve at 11200 N with bi-directional fiber arrangement

As we are designing a main landing gear at a maximum design load of 5600 N, and it satisfies all the design requirements at this load level using both the fiber arrangement. But factor of safety is quite higher using bi-directional layer arrangement, and it shows a conventional approach of design. Thus we recommend designing a main landing gear using unidirectional fiber arrangement, which satisfies all the stresses and failure criteria and also meets all the design requirements. Margin of safety is 1.3 using this arrangement.

It justifies designing a main landing gear of an aircraft using unidirectional layer orientation at a maximum design load of 5600 N. Thus design is optimized with this arrangement at the specified design load level. These results were co-related with field results and it was found that there was a reasonable agreement between them.

Conclusion The findings from the above investigation are as follows.

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The development study has shown that composite main landing gear is as good as any advanced metallic landing gear, in their performance.

This development shows that application of GFRP / EPOXY material makes it possible to reduce the weight of the landing gear without any reduction in load carrying capacity and stiffness resulting in 13th times lesser weight than than the metallic landing gear.

Glass fiber reinforced plastics has the necessary combination of properties such as high strength, medium stiffness, corrosion resistance, fatigue strength etc. That makes the material quite suitable for landing gear construction.

The results from non-linear finite element analysis show that landing gear design with unidirectional fiber arrangements satisfies all the design requirements and failure criteria at a maximum design load level of 5600 N.

Hence it is proved that the design is quite safe.

References [1] D.W. Young, “Aircraft Landing Gears – Past Present and Future” Proceeding of IME, Vol. 200, No. D2 PP 75-92, 1986.

[2] Dorothea C. Walden, “Applications of composites in Commercial Airplanes” Structural composites Design & Processing Technologies, Proceedings of the sixth Annual ASM / ESP Advanced composite conference, Detroit, Michigan, USA, 8-11 Oct, pp 77-80, 1990.

[3] J.N. REDDY and C.F. Liu, “A Higher Order Theory for Geometrically Nonlinear Analysis of Composite Laminates, NASA CR-4056, March 1987.

[4] Geoff Ecold, “Design and Manufacture of Composite Structures”, Jaico Publishing House, Bombay, 1995, PP. 1 – 387.

[5] R.H. Mallett and P.V. Marcal, “Finite Element Analysis of Non-linear structures,” Jst Div, Vol. 94, No. ST9, 1968, PP. 2081 – 2105.

[6] Ansys online documentation.