Chapter 28: Model Airplane Analysis

28 Model Airplane Engine Analysis

Summary 475

Introduction 476

Required Solution 476

FEM Solution 476

Input File(s) 484

Video 485

475CHAPTER 28

Model Airplane Engine Analysis

SummaryTitle Chapter 28: Model Airplane Engine Analysis

Contact features • Deformable-deformable contact - glue contact; Segment - Segment Contact• Gasket material• Bolt modeling with BOLT entry

Geometry

Material properties • Linear elastic material (Steel) for the engine block, plug, and bolts:

, • Linear elastic material (aluminium) for the cylinder head:

, • Isotropic in-plane behavior or the gasket body:

,

• Isotropic in-plane behavior of the gasket body:

,

• Out-of-plane pressure-over closure curves are used for the gasket body and gasket ring using loading and unloading curves.

Analysis type Quasi-static analysis

Boundary conditions Some nodes on the outer boundaries on the engine block are constrained in all directions

Applied loads Step 1: Enforces displacement of 0.25 mm on the bolts using BOLT.Step 2: Pressure load of 16 MPa

Element type • 4-node tetrahedron elements• 8-node CHEXA to model the gasket

Contact properties • Glue contact, segment to segment contact• Extended tangential contact tolerance at sharp corners

FE results • Displacement of the engine model, Load history chart for bolt• Contact pressure and forces on the gasket

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Eq. Stress At Pressure

E 2.1 105 MPa= 0.3=

E 7.0 104 MPa= 0.3=

E 120MPa= G 60MPs=

E 100MPa= G 50MPa=

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IntroductionThe model airplane engine analysis consists of a cylinder head, a engine block, a gasket, bolts, and a plug. The gasket is assembled between the head and the block. The problems demonstrates how the solution sequence 400 of MD Nastran can be used for a typical analysis for engine involving the nonlinear pressure-over closure relationship of the gasket material and bolt pre-tension load. Glued contact is used to establish contact between the different parts of this engine model.

Required SolutionThe nonlinear analysis involving large displacement and gasket nonlinearity is carried for the model airplane engine to find the forces in the bolts and contact forces in the gasket.

FEM SolutionMD Nastran’s nonlinear solution sequence SOL 400 is used to analyze the engine model under the bolt and pressure loads in two steps. The details of finite element models, contact simulations, material, load, boundary conditions, and solution procedure are discussed in the following sections.

Finite Element ModelThe finite element model used for the 3-D solid approach is shown in Figure 28-1. The model consists of 88293 CTETRA element and 468 CHEXA elements. MD Nastran’s 4-node tetrahedral elements are used for block using the following PSOLID and PSLDN1 options. Head, bolts, and plug are also models with 4-node tetrahedral elements.

PSOLID 1 1 0PSLDN1 1 1

Figure 28-1 Finite Element Model for Model Airplane Engine

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Using the following PSOLID and PSLDN1 options, the gasket body is modeled using MD Nastran’s 8-node hexahedral gasket elements. Here, the gasket material is referred to by the material ID 5.

PSOLID 5 3 0PSLDN1 5 3 1 C8 SLCOMP L

The gasket ring is also modeled in a similar way using the different material ID 6.

PSOLID 5 6 0PSLDN1 5 6 1 C8 SLCOMP L

Contact ModelFor the contact definition, various parts of the model airplane engine are defined as deformable contact bodies. the following BCBODY and BSURF entries show the contact body definition for the gasket.

BCBODY 1 3D DEFORM 4 0 0 BSURF 4 70172 THRU 70639

The contact bodies for other parts of the model as also defined in a similar way. Figure 28-2 presents the details of different contact bodies defined for the model airplane engine.

Figure 28-2 Details of the Different Contact Bodies

The following BCTABLE entries identify how the contact bodies can touch each other. The BCTABLE with ID 1 is used to define contact conditions at the first step of the analysis. Since there is no difference in the contacts in Second Step the same BCTABLE with ID 1 is used to define the contact conditions for second step in the analysis, and it is flagged using the option BCONTACT = 2 in the case control section. Glued contact is used for all the six contact pairs defined

Zoomed view of contact partswithout head and block

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in the BCTABLE option. Delayed sliding is enabled for the contact pairs involving gasket by choosing the value 2 for the field ICOORD.

BCTABLE 1 6 SLAVE 1 0.0 0.0 0.0 1 1 2 0 MASTERS 4 SLAVE 1 0.0 0.0 0.0 1 1 2 0 MASTERS 5 SLAVE 2 0.0 0.0 0.0 1 1 0 0 MASTERS 4 SLAVE 2 0.0 0.0 0.0 1 1 0 0 MASTERS 5 SLAVE 3 0.0 0.0 0.0 1 1 0 0 MASTERS 4 SLAVE 4 0.0 0.0 0.0 1 1 0 0 MASTERS 5

MaterialThe linear isotropic elastic properties of the steel and aluminium materials are defined using the following MAT entries. Steel properties are used for block, bolts and plug and aluminium properties are used for cylinder head.

MAT1 1 210000. .3 7.86-6 1.-5MAT1 2 70000. .3 2.7-6 2.4-5

The in-plane membrane properties of gasket body (ID 3) and gasket ring (ID 4) materials are defined using the following MAT1 entries. The nonlinear pressure-over closure relation for the gasket body (ID 3) and gasket ring (ID 5) are defined using the following MATG entries.

MAT1 3 120. 60. 9.99E-7 5.E-5 MAT1 4 100. 50. 1.99E-6 0.0001 MATG 5 3 0 1 2 52. 72. 35. 0.05 MATG 6 4 0 3 4 42. 64. 35. 0.0

Figure 28-3 shows the pressure-over closure properties for the gasket materials. The following TABLES1 entries (referred in the MATG entries) are used to define these nonlinear gasket properties.

$ Displacement Dependent Table : body_loadingTABLES1 1 + + 0.0 0.0 0.027 2.08 0.054 8.32 0.081 18.72+ + 0.108 33.28 0.135 52. 0.175 56. ENDT$ Displacement Dependent Table : body_unloadingTABLES1 2 + + 0.1 0.0 0.1225 5.04 0.1375 14. 0.1525 27.44+ + 0.16 35.84 0.1675 45.36 0.175 56. ENDT$ Displacement Dependent Table : ring_loadingTABLES1 3 + + 0.0 0.0 0.026 1.68 0.052 6.72 0.078 15.12+ + 0.104 26.88 0.13 42. 0.18 48. ENDT$ Displacement Dependent Table : ring_unloadingTABLES1 4 + + 0.12 0.0 0.138 4.32 0.15 12. 0.162 23.52+ + 0.168 30.72 0.174 38.88 0.18 48. ENDT

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Figure 28-3 Pressure-over Closure Relations for Gasket Materials

Loading and Boundary ConditionsThe analysis for the model airplane engine is carried out in two steps. In the first step, a pre-tension load is applied on bolts. In the second step, a pressure load is applied in the part of head and gasket. Some nodes on the outer boundaries on the block are constrained in all directions. Figure 28-4 shows these boundary conditions applied in both Steps 1 and 2.

Figure 28-4 Constraints used in Steps 1 and 2

0.00 0.05 0.10 0.15 0.200

10

20

30

40

50

60

Unloading Curve Ring

Loading Curve Ring

Unloading Curve Body

Loading Curve Body

Ring

Body

Gasket Pressure (MPa)

Gasket Closure (mm)

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The following data in case control section of the input file defines the load and boundary conditions at the two different steps of the analysis. The bulk data entries SPCD, SPC1, and PLOAD4 are used to define the boundary condition and loads in these steps. Bolt pretension loading is simulated using BOLT.

In order to define Pre-Stress in Bolts, Bolt modeling is carried out using BOLT entry. BOLT consists of combination of two pairs, TOP and BOTTOM nodes set. The key idea is to split the element mesh of the bolt across the shaft in two disjoint parts, such that duplicate grid points appear at the cut, and to create an overlap or gap between the two parts via multi-point constraints. If the motion of these parts is somehow constrained in the direction in which the gap or overlap is created, then an overlap (shortening) will introduce a tensile (pre-) stress in each of the parts and a gap (elongation) will result in a compressive stress. This technique is more elaborated in Chapter 23: Bolted Plates.

However the internal MPC equations are generated between the TOP and BOTTOM nodes to a free node which is also called as Control node. The BOLT entry for Bolt_1 is defined as

follows:

BOLT 89847 38083 TOP 38271 38272 38273 38274 38275 38276 38277++ 38278 38279 38280 38281 38282 38283 38284++ 38285 38286 38287 38288 38289 38290 38291++ 38292 38293 38294 38295 38296 38297 38298++ 38299 38300 38301 38302 38303 38304 38305++ 38306 38307 BOTTOM 22467 22459 22466 22470 22481 22817 22460++ 22463 22461 22814 22813 22478 22474 22462++ 22341 22816 22480 22458 22477 22473 22464++ 22475 22465 22472 22471 22275 21642 22476++ 22482 21643 22469 22479 22468 21644 22815++ 21641 21640

Here 89847 indicates the BOLT ID; 38083 indicates the Control node ID; TOP indicates the set of node IDs and BOTTOM indicates the bottom node IDs. Similarly the remaining 3 bolts are defined as follows:

BOLT 89848 38007 TOP 38308 38309 38310 38311 38312 38313 38314++ 38315 38316 38317 38318 38319 38320 38321++ 38322 38323 38324 38325 38326 38327 38328++ 38329 38330 38331 38332 38333 38334 38335++ 38336 38337 38338 38339 38340 38341 38342++ 38343 38344 BOTTOM 20192 20191 20194 21827 20202 22544 20195++ 21825 21828 20184 20186 20187 20838 20207++ 21826 20185 20196 20188 20189 20183 21829++ 20205 19867 20199 20197 20201 19870 19869++ 20193 20190 19868 20203 20198 20200 20204++ 19871 20206

BOLT 89849 38084 TOP 38345 38346 38347 38348 38349 38350 38351++ 38352 38353 38354 38355 38356 38357 38358++ 38359 38360 38361 38362 38363 38364 38365++ 38366 38367 38368 38369 38370 38371 38372++ 38373 38374 38375 38376 38377 38378 38379++ 38380 38381 BOTTOM 20324 20318 20320 20321 20309 20310 20307++ 20322 19721 20311 20325 20304 22009 21808++ 20308 20305 20312 20313 20315 20316 20319++ 20327 20317 22008 20328 20326 20306 20323+

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+ 22451 19722 22007 19723 22006 22005 19720++ 20314 19719

BOLT 89850 38085 TOP 38382 38383 38384 38385 38386 38387 38388++ 38389 38390 38391 38392 38393 38394 38395++ 38396 38397 38398 38399 38400 38401 38402++ 38403 38404 38405 38406 38407 38408 38409++ 38410 38411 38412 38413 38414 38415 38416++ 38417 38418 BOTTOM 21071 21069 21068 21080 21078 21076 21077++ 21089 21074 21066 21073 21086 21401 21400++ 21065 21067 21398 21075 21087 22540 21088++ 22539 21070 22541 21072 21395 21082 21079++ 22542 21083 21399 21081 21085 21084 21326++ 22543 21397

The SPCD data is used for applying the imposed displacement of 0.25 mm in the vertical direction in Steps 1 and 2 at the controlled nodes for bolts. The lateral displacements at these four control nodes are constrained.

STEP 1$! Step name : Bolt_Preload SPC = 30 LOAD = 31 BCONTACT = 1 ANALYSIS = NLSTAT NLSTEP = 2STEP 2$! Step name : Static_Pressure SPC = 31 LOAD = 32 BCONTACT = 1 ANALYSIS = NLSTAT NLSTEP = 3...SPCD 31 38083 3 0.25SPC1 31 3 38083SPCD 31 38007 3 0.25SPC1 31 3 38007SPCD 31 38084 3 0.25SPC1 31 3 38084SPCD 31 38085 3 0.25SPC1 31 3 38085...SPC1 9 123 987SPC1 9 123 2453 THRU 2465...PLOAD4 1 85127 16. 24238 23579...PLOAD4 2 55616 16. 15870 15071...

Solution ProcedureThe nonlinear procedure for the Step 1 is defined through the following NLSTEP entry with ID 2.

NLSTEP specifies the convergence criteria, step size control between coupled loops and step/iteration control for each physics loop in MD Nastran SOL 400. NLSTEP entry is represented as follows:

NLSTEP 2 1. GENERAL 50 FIXED 10 1 MECH P 0.01 PFNT

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Here, 1. Indicate the total Time for the Load case; GENERAL indicates the keyword for parameters used for overall analysis; 50 indicates the maximum number of iterations per increment; FIXED indicates the fixed stepping is to be used; 10 indicate the number of increments for fixed stepping; 1 indicates interval for output. Every increment will be saved for output; MECH indicate the keyword for parameters for mechanical analysis; P indicates the load convergence criteria; 0.01 indicates convergence tolerance for load; PFNT indicates the Modified Full Newton Raphson Technique for updating stiffness matrix. The fields MAXQN, MAXLS, and MAXBIS are set to zero to disable the Quasi Newton, line search, and bisection techniques in the iterative process.

Similar NLSTEP option with ID 3 is used for Step 2.NLSTEP 3 1. GENERAL 50 FIXED 10 1 MECH P 0.01 PFNT

Segment to Segment Contact method is activated using BCPARA. Here METHOD indicates the Global Contact type; SEGSMALL indicates the Small Segment-to-Segment Contact. If, in BCTABLE, there are multiple GLUE with different “SLAVE” entries, then NLGLUE, 1 must be used.

BCPARA 0 METHOD SEGSMALL NLGLUE 1

ResultsThe variation of the bolt forces at grid points 38007,38083,38084 and 38085 as a function of the bolt shortening is shown in Figure 28-5. This clearly shows a nonlinear response. The normal contact forces in gasket are shown in Figure 28-6.

Figure 28-5 Bolt Force as a Function of Bolt Shortening

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Figure 28-6 Normal Contact Forces in Gasket

The displacement contours of the engine model in y-direction at Steps 1 and 2 are shown in Figure 28-7 and Figure 28-8.

The pressure-closure output for the gasket element 70582 is presented here from the f06 output file at the end of Step 2. It is observed that the pressure for this gasket element exceeded the yield pressure of 52 MPa and this result in a plastic closure of 0.12 mm.

ELEMENT ID PLY ID INT. PT. ID PRESSURE CLOSURE PLASTIC CLOSURE 70582 1 1 7.805712E+01 1.997745E-01 1.200000E-01 2 8.207688E+01 2.024191E-01 1.200000E-01 3 7.722001E+01 1.992237E-01 1.200000E-01 4 8.107123E+01 2.017574E-01 1.200000E-01

Figure 28-7 Displacement Contours in y-direction at Step 1

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Figure 28-8 Displacement Contours in y-direction at Step 2

Figure 28-9 Von Mises Stress Contours for Node-Segment and Seg-Seg method

Input File(s)File Description

nug_28m.bdf MD Nastran SOL 400 input for model airplane engine

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VideoClick on the image or caption below to view a streaming video of this problem; it lasts approximately 44 minutes and explains how the steps are performed.

Figure 28-10 Video of the Above Steps

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Eq. Stress At Pressure