Landing Gear

Chapter 38: Landing Gear

38

Landing Gear



Summary



Introduction



Solution Requirements



FEM Solution



Results



Modeling Tips



Input File(s)



Video

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567

574

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566 MD Demonstration Problems CHAPTER 38

Summary Title

Chapter 38: Landing Gear

Contact features

• Frictionless Deformable-Deformable Contact • Glued Contact for non-matching meshes

Geometry DRAG STRUT

UPPER CYLINDER

GAS SPRING

SIDE STRUT

SIDE STRUT PIVOT DRAG STRUT PIVOT

UPPER LINK SPACER

UPPER LINK PIVOT

UPPER TORQUE LINK

AXLE

APEX SPACER

TORSION LINK APEX PIVOT LOWER TORQUE LINK INNER CYLINDER LOWER LINK SPACER

Material properties

Young’s Modulus = 3.0x107 Psi, Poisson’s ratio = 0.3

Boundary conditions

Pinned Connections with/without Glued Contact SOL 400 )

P I N NE D C O N NE C T I O N S

Element types

HEXA, TETRA, BAR

FE results

Verify the contact conditions (GLUE and nonGLUE)

CHAPTER 38 567 Landing Gear

Introduction This test case demonstrates contact analysis using MD Nastran. Two types of contact conditions between components are considered: • glue contact • nonglue contact In the first one, the contact is maintained for all the analysis after it occurs. In other words, nodes in contact are not allowed to separate whereas, in the second one, separation can change depending on the loading conditions. Large displacement/rotation and nonlinear materials are not taken into account in this example.

Solution Requirements The numerical analysis is performed to demonstrate the behaviors of the 3-D surface contact solution into MD Nastran. In particular, the simultaneous presence of glue, nonglue surface contact is considered. The deformed structure, the satisfaction of the relative motion between components, and the stresses in the contact regions are considered as result of the analysis.

FEM Solution FEM solutions have been obtained with MD Nastran’s solution sequence 400. The details of finite element models, contact simulations, material, load, boundary conditions, and solution procedure are discussed.

Finite Element Models The structure consists of different components that have been modeled independently taking into account that matching meshes are not needed in the contact regions. Due to geometrical behaviors: • The pins and the spacers have been modeled by 8-node HEXA elements • 4-node TETRA elements have been used to model the remaining components. Note that fine meshes have been used for these components in order to avoid the rigidity of such kind of element associated with this type of element. For the axle, two BAR elements have been used. In this way the proper load has been applied in the middle grid point. No LGDISP parameter has been defined and therefore no geometrical nonlinearity is considered.

568 MD Demonstration Problems CHAPTER 38

Contact Models In defining the contact regions for the structure, the components are modeled as deformable bodies. In particular, 15 contact bodies have been defined by specific BCBODY and BCSURF entries (each couple of options has been defined using the same identifier). Note that each of them has been defined considering all the elements belonging to the specific components. Table 38-1

Contact Body General Information

BCBODY/BSU 1

Component Name Drag Strut

Elements 217804 - 237802

2

Drag Strut Pivot

159301 - 160572

3

Gas Spring

160575 - 161534

4

Inner Cylinder

200218 - 217803

5

Lower Link Pivot

157797 - 158596

6

Lower Torque Link

277629 - 297917

7

Side Strut

237803 - 257846

8

Side Strut Pivot

159717 - 160332

9

Torsion Link Ape Pivot

158597 - 159300

10

Upper Cylinder

161663 - 200217

11

Upper Link Pivot

156997 - 157796

12

Upper Torque Link

257847 - 277628

13

Lower Link Spacer

161551 - 161582

14

Upper Link Spacer

161599 - 161630

15

Apex Spacer

161647 - 161662

Each contact body has been defined in the same way so, as an example, one set of options is used to define one of them that has been listed: $ Deform Body Contact LBC set: lower_link_spacer BCBODY 13 3D DEFORM 13 0 BSURF 13 161551 161552 161553 161554 161558 161559 161560 161561 161562 161566 161567 161568 161569 161570 161574 161575 161576 161577 161578 161582

161555 161563 161571 161579

-1 161556 161564 161572 161580

161557 161565 161573 161581

In the above BCBODY option, the 3-D (third field) elements mentioned in the BSURF which identifier is 13 (look at the fifth field) define the contact body number 13. Furthermore: • The fourth field defines the general behavior of the contact body. In this case, it is a deformable contact body • The null value in the sixth field means that symmetric penetration or double side contact check is considered. The contact is verified symmetrically and both the contact surfaces are checked for penetration and, also, if we need to define a MASTER and a SLAVE in any case.

CHAPTER 38 569 Landing Gear

• The empty seventh field forces a null friction coefficient. It means that no tangential forces are generated when the contact condition occurs, unless these bodies are glued together. • The negative value in the eighth field allows activating the analytic option for a deformable body. It is used in this case because the part of each component involved in the contact process is cylindrical and therefore is simple to represent it analytically. In this way, the contact is represented in the best way. After the definition of the contact bodies, each couple of bodies that could be in contact must be defined in the BCTABLE option. In this entry, one of the contact bodies is defined as the MASTER while the other one is the SLAVE.

The contact behaviors are completely defined. An example of the option format used in this case is listed below: BCTABLE

1 SLAVE MASTERS SLAVE MASTERS SLAVE MASTERS SLAVE

1 0 FBSH 2 2 0 FBSH 10 3 0 FBSH 4 3 0 FBSH 10

MASTERS ... ... SLAVE 12 0 FBSH MASTERS 14 SLAVE 12 0 FBSH MASTERS 15

4.-2 0 1.+20

19 0. 0 0.

4.-2 0 1.+20

0. 0 0.

0.

4.-2 0 1.+20

0. 0 0.

0.

4.-2 0 1.+20

0. 0 0.

0.

4.-2 0 1.+20

0. 0 0.

0.

4.-2 0 1.+20

0. 0 0.

0.

0.

0.

1

0.

1

0.

0

0.

1

0.

1

0.

0

0.

0.

0.

0.

0.

0.

It can be checked how the nineteen contact regions (look at the fifth field of the above BCTABLE option) are defined in the same. The only difference is in the eighth field of the option where the SLAVE option is defined. In fact, we can see a unit or null value. If a unit value is defined, the two contact surfaces must be glued. It means that the glue option is activated and all the degrees of freedom of the nodes are tied in case of deformable-deformable contact once the node comes in contact. In general, if the unit value is defined, all degrees of freedom are MPCd in the deformabledeformable contact once the grids have come in contact. To turn on the general SOL 400 contact algorithm the entry: BCPARA, 0, NLGLUE,1 is used. It should be taken into account that if, in SOL 400 on the BCTABLE, there are multiple GLUE and nonGLUE entries associated with different SLAVE entries, then, the above option must be used. It is the case in this example. A null value activates the standard contact conditions. It means that a SLAVE node can move only over the MASTER contact surface when it comes in contact (except if glued). In this case, if the general load condition leads to the separation of the contact bodies, the slave node start again to move without constraints. Note that in this entry different

570 MD Demonstration Problems CHAPTER 38

contact parameters (the distance below which the node is considered in contact, friction coefficient, separation force, stress friction limit, contact tolerance bias, etc…) can be defined for each contact region. The BCTABLE entry is activated by BCONTACT option in the Case Control section. Note that in this case, a BCONTACT = 0, defined above the subcase level activates the corresponding BCPARA,0 and BCTABLE,0 entries defined in the Bulk Data Section. It allows to initially identify contacting bodies. Note that in SOL 400, a BCONTACT = 0 is allowed above all subcases but is not required. Any of the contact Bulk Data entries that allow a 0 and have a 0 value ID field are automatically sensed by SOL 400 with or without a BCONTACT = 0 command. The contact regions are summarized in the table below. Table 38-2 Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Contact Body General Information (ID in Parenthesis) SLAVE Component (BCBODY ID) Drag Strut (1) Drag Strut Pivot (2) Gas Spring (3) Gas Spring (3) Inner Cylinder (4) Inner Cylinder (4) Inner Cylinder (4) Lower Link Pivot (5) Lower Torque Link (6) Lower Torque Link (6) Lower Torque Link (6) Side Strut (7) Side Strut Pivot (8) Torsion Link Apex Pivot Upper Cylinder (10) Upper Cylinder (10) Upper Link Pivot (11) Upper Torque Link (12) Upper Torque Link (12)

MASTER Component (BCBODY ID) Drag Strut Pivot (2) Upper Cylinder (10) Inner Cylinder (4) Upper Cylinder (10) Lower Link Pivot (5) Upper Cylinder (10) Lower Link Spacer (13) Lower Torque Link (6) Torsion Link Apex Pivot Lower Link Spacer (13) Apex Spacer (15) Side Strut Pivot (8) Upper Cylinder (10) Upper Torque Link (12) Upper Link Pivot (11) Upper Link Spacer (14) Upper Torque Link (12) Upper Link Spacer (14) Apex Spacer (15)

GLUE YES YES YES YES YES YES YES YES YES YES YES -

CHAPTER 38 571 Landing Gear

b

a

DRAG STRUT DRAG STRUT PIVOT

c

DRAG STRUT PIVOT UPPER CYLINDER

e

d

LOWER LINK PIVOT LOWER TORQUE LINK

Figure 38-1

GAS SPRING UPPER CYLINDER

f

LOWER TORQUE LINK TORSION LINK APEX PIVOT

LOWER TORQUE LINK LINK LOWER SPACER

Glued Contact Regions Panels a-e, Nonglued Contact Panel f

Looking at the behaviors of the defined contact regions, it can be checked that: • The gas spring is attached in its upper end to an internal surface of the UPPER cylinder. This system can move along their common axis according to the non-glued contact regions defined between them and the INNER cylinder. • The torsion link apex pivot is rigidly connected to the LOWER torque link while a nonglued contact region is defined between the first body contact and the UPPER torque link. Also, the APEX SPACER is in the same contact condition. Considering the null friction coefficient, this modeling solution allows to avoid any singularity maintaining the relative rotational motion between the two links. • The rigid link pivot is rigidly connected to the LOWER torque link but it is connected by nonglued contact region with the INNER CYLINDER. It is the same modeling solution than the above one. • The two struts are rigidly connected to the UPPER cylinder. • The two torque links (UPPER and LOWER) can rotate around the axes of the two pivots that connect each of them respectively with the UPPER and the INNER cylinders.

572 MD Demonstration Problems CHAPTER 38

Figure 38-2

Possible Relative Motion Between the Different Components

Material The isotropic elastic material properties of the steel used for all the components have been defined by the following MAT1. MAT1

1

3.+7

.3

7.3-4

Nonlinear behaviors of the material are not considered.

Loading and Boundary Conditions The set of boundary conditions (SPC = 2) defined in the model simulates hinges between some components and the ground. In particular, they are positioned in the upper ends of the: Drag Strut Side Strut Upper Cylinder The following options are used to define this boundary condition: SPCADD ... SPC1

2

1

1

123

108520

108521

313468

313469

313470

313471

The braking load condition is considered. It consists of: • Concentrated forces and moments applied to the middle point of the axle. They define three different loads acting on this component:

CHAPTER 38 573 Landing Gear

Brake drag FORCE MOMENT

1 3

314410 314410

0 0

60000. 0.

-1. .57735

0. .57735

0. .57735

314410 314410

0 0

0. .57735 1.335+6 0.

.57735 1.

.57735 0.

314410 314410

0 0

140000. 0. 0. .57735

0. .57735

1. .57735

Brake side moment FORCE MOMENT

4 5

Brake vertical FORCE MOMENT

Z

6 7

FX X

Y

Z

MY X

Y

Figure 38-3

Z

FZ X

Y

Pressure Load Applied to the Axle

• Breaking Pressure in the inner part of the Upper Cylinder (Load sets from 8 to 11) PLOAD4 PLOAD4 PLOAD4 ... PLOAD4 PLOAD4

Figure 38-4

11 11 11

164669 1190.4 164864 1190.4 166091 1190.4

33161 33236 55196

7479 7156 49965

10 10

199542 1190.4 199546 1190.4

54157 105944

106392 106130

Pressure Load Applied to the Axle

574 MD Demonstration Problems CHAPTER 38

All these loads are combined by LOAD Bulk data entry to define the applied static load condition LOAD

2 1. 1.

1. 5 9

1. 1. 1.

1 6 10

1. 1. 1.

3 7 11

1. 1.

4 8

Solution Procedure In the present analysis, contact is the only nonlinearity. It means that the provided load condition generates small displacements and only the stresses are in the linear elastic part of the stress-strain curve of the material. As consequence, no geometrical and material nonlinearity are taken in account. Furthermore, looking at the geometries, the contact conditions seems to be not so complicated, It simplifies the approach to be used in the analysis. First of all no STEP is defined under the SUBCASE level. BCONTACT = 0 SUBCASE 1 TITLE=This is a default subcase. BCONTACT = 1 SPC = 2 LOAD = 2 DISPLACEMENT(plot)=ALL $ SPCFORCES(SORT1,REAL)=ALL STRESS(plot)=ALL BOUTPUT(SORT1,REAL)=ALL NLPARM = 1 The nonlinear procedure is defined through the following NLPARM entry with ID 1. NLPARM

1

1

FNT

PV

YES

Here: • Only one increment is considered. • FNT represents the Full Newton-Raphson Technique wherein the stiffness is reformed at every iteration. • PV indicates that convergence will be checked on vector component (V) of the residuals (P). In this V method, convergence checking is performed on the maximum vector component of all components in the model. • YES indicates that intermediate output is produced after every increment.

Results No results to compare are available for this test case so what has been obtained by the calculation will be checked from a qualitative viewpoint. The maximum total displacement occurs in the bottom part of the inner cylinder, close to the axle (where the concentrated loads are applied).

CHAPTER 38 575 Landing Gear

Figure 38-5

Undeformed and Scaled Deformed Structure

To check how the contact is working it is possible to take advantage of a procedure that in MD R2 Nastran allows storing all the contact results into the database. In fact it is not possible to obtain these data into XDB (PARAM,POST,0) or OUTPUT2 (PARAM,POST,-1) postprocessing files while adding the keyword: scr = post in the Nastran command line, all the results, including the contact ones, are stored into the database. They are retrieved into MD Patran selecting: Action

 Access Results

Object

 Attach Entities

Method

 Result Entities or Both

in the Results Window. The following results can be displayed for contact regions Contact Status Friction contact force, Magnitude Normal contact force, Magnitude Contact force, Friction Contact force, Normal Contact stress, Friction 1 Contact stress, Friction 2 Contact stress, Normal It is possible to understand which components are in contact displaying the Contact Status output. As first example some of the contact regions belonging to the lower and upper torque links will be considered. Looking at the Contact Status Contours in Figure 38-7 and taking into account the contact regions behaviors (as summarized in Figure 38-6) we can say that: • Both the contact bodies regions (MASTER and SLAVES) are highlighted.

576 MD Demonstration Problems CHAPTER 38

• The contact status in the UPPER TORQUE LINK-TORSION LINK APEX PIVOT nonglued contact region put in evidence how the deformation of the structure determines the contact only in a limited part of the bodies. • A good contact modeling is recognized by a congruent representation of the Contact Status output in the MASTER and SLAVE contact bodies. In particular in case of glued contact a continuous contact status contour should be displayed. A different representation could highlights problems in the geometries of the contact bodies. UPPER LINK PIVOT - SLAVE in contact region with UPPER TORQUE LINK (GLUED) - MASTER in contact region with UPPER CYLINDER

833(572548(/,1. $3(;63$&(5 0$67(5LQERWKWKH*/8('FRQWDFWUHJLRQV

/2:(572548(/,1. 7256,21/,1.$3(;3,927 6/$9(LQFRQWDFWUHJLRQZLWK833(572548(/,1. 0$67(5LQFRQWDFWUHJLRQZLWK/2:(572548(/,1.*/8(' 

Figure 38-6

Upper and Lower Torque Links Connections

$3(;63$&(5 121*/8(' 

7256,21/,1.$3(;3,927

0$67(56/$9(

/2:(572548(/,1. 0$67(56/$9( 833(572548(/,1.

Figure 38-7

*/8(' 

First Contact Status Contour Plot Example

A nonclear situation is displayed for the nonglued contact between UPPER TORQUE LINK and TORSION APEX PIVOT. In fact, the contact status is differently represented in the corresponding contact regions of the two components. Probably, the combined effects of the deformation and the different element types in the two components determine it.

CHAPTER 38 577 Landing Gear

Differently, in case of nonglued contact regions defined in the UPPER CYLINDER-UPPER LINK PIVOT connection the contact status seems to be represented correctly (see Figure 38-8). In fact, there is a complete congruency between the two regions that are in contact. 833(5&
833(5/,1.3,927

Figure 38-8

Second Contact Status Contour Plot Example

Modeling Tips Important behaviors of this example are the definition of glued and nonglued contact regions and the effects of contact geometries to obtain good results. Contact is only verified in a qualitative viewpoint by the analysis of the Contact Status output. The following are some guidelines and tips for modeling this benchmark: • The geometry of a contact surface should be defined property in order to avoid problems when it touches another surface contact. • The density of the mesh affects the results in the contact region in particular in case of contact surfaces with nonplanar shape and in which different types of elements are used. • Use the Contact Status output to check if the contact is working properly (use scr=post in the Nastran command line to obtain this kind of output).

Input File(s) File nug_38.dat

Description MD Nastran SOL 400 input for the landing gear model

578 MD Demonstration Problems CHAPTER 38

Video Click on the image or caption below to view a streaming video of this problem; it lasts approximately 40 minutes and explains how the steps are performed.

Figure 38-9

Video of the Above Steps