Engine Gasket

Chapter 10: Engine Gasket

10

Engine Gasket



Summary



Introduction



Requested Solutions



Model Details

137



FEM Solution

138



Modeling Tip



Input File(s)



Video

144

136 137

143 144

137

136 MD Demonstration Problems CHAPTER 10

Summary Title

Chapter 10: Engine Gasket

Features

Glued contact, MPC’s for bolt modeling, Gasket material

Geometry

gasket ring gasket body

Cylinder diameter: 24 mm . Engine block width, breadth and height: 93.1 mm , 70 mm and 15 mm . Cylinder head thickness: 3 mm . Bolt diameter: 8 mm . Bolt head diameter: 14 mm . Gasket ring thickness: 1 mm ; gasket body thickness: 0.9091 mm Material properties

Linear elastic material for the engine block, cylinder head and bolts, 5

E engine = E head = E bolt = 2.1 10 MPa  engine =  head =  bolt = 0.3

Isotropic in-plane behavior of the gasket: E body = 120 MPa , E ring = 100 MPa ,  body =  ring = 0 . Transverse shear moduli of the gasket: G body = 40 MPa , G ring = 35 MPa . Out-of-plane elastic-plastic behavior of the gasket defined by loading and unloading curves. Analysis type

Quasi-static analysis

Boundary conditions

Symmetry conditions in ZX-plane: u y = 0 . Bottom of engine block fully clamped: u x = u y = u z = 0 . Glued contact between gasket and cylinder head, gasket and engine block, and bolts and cylinder head.

Applied loads

Prescribed shortening of the bolts l = 0.175 mm .

Element type

3-D 8-node hexahedral and 3-D 6-node pentahedral solid elements

Contact properties

Glued contact with extended tangential contact tolerance at sharp corners

FE results

Bolt forces and stresses in the gasket

CHAPTER 10 137 Engine Gasket

Introduction A gasket is assembled between an engine block and a cylinder head. The loading of the assembled structure consists of pre-tensioning the bolts connecting the cylinder head and the engine block. Striking features in this analysis are the MPCs used to load the bolts, the geometry and material description of the gasket, and the use of the contact algorithm to establish contact constraints between the grids of the gasket and the cylinder head and the engine block and between the grids of the bolts and the cylinder head.

Requested Solutions A numerical analysis will be performed to find the forces in the bolts and the response of the gasket in terms of gasket closure versus gasket pressure.

Model Details The gasket actually consists of two parts: the so-called gasket ring and the gasket body. These parts have different material properties and thicknesses. Assigning different material properties is straightforward, but modeling different thicknesses would require different finite element meshes for the ring and the body. Since this is inefficient from a modeling perspective, it is allowed to include both parts in one connected set of finite elements and to define the thickness difference as an initial gap. In the numerical analysis, this implies that as long as the thickness reduction of gasket element integration points is smaller than the initial gap, there will be no stress in the thickness direction. In Figure 10-1, a detailed view of the actual versus the modeled gasket geometry is shown.

initial gap magnitude

Figure 10-1

True Gasket Geometry (left) and Modeled Geometry (right)

The material behavior of a gasket is generally rather complex to characterize using conventional material models. Instead, a special gasket material model is adopted, which de-couples the in-plane and thickness behavior. The in-plane behavior is assumed to be linear and defined by Young’s modulus and Poisson’s ratio. The behavior in thickness direction is nonlinear and defined by experimentally determined loading and unloading curves, where the gasket pressure is measured as a function of the gasket closure. This gasket closure is given by the change in distance between the top and the bottom face of the gasket. The loading and unloading curves for the gasket ring and the gasket body are shown in Figure 10-2.

138 MD Demonstration Problems CHAPTER 10

Figure 10-2

Material Behavior in Thickness Direction for the Gasket Body and Ring

In order to apply pre-tensioning on the bolts, they are piece wise modeled by two parts, one upper and one lower part, obtained by a fictitious cut. The grids of the lower and the upper part of this cross section are connected using MPC’s to a so-called control grid. Calling the displacement of a grid in the lower part u lower , the displacement of a grid in the upper part u up per and the displacement of the control grid u control , then the MPC reads: u control = u lower – u upper

By assigning all the grids in the lower and upper part of the section of a bolt to the same control grid, one can easily define the shortening of a bolt by prescribing u control . As a result, the total bolt force is found as the reaction force on the control grid.

FEM Solution The numerical solution has been obtained with MD Nastran’s SOL 400 for the element mesh shown in Figure 10-3 using 3-D 8-node hexahedral and 6-node pentahedral elements. Based on symmetry, only half of the structure is modeled.

bolt cross section

bolt cross section

Figure 10-3

Element Mesh applied in the MD Nastran Simulation

CHAPTER 10 139 Engine Gasket

In total, four deformable contact bodies are used. The first deformable body consists of all elements of the gasket including the gasket body and ring. The cylinder head defines the second deformable body. The third deformable body contains the elements of the engine block. Finally, the fourth deformable body consists of the upper and lower parts of the bolts. The deformable contact bodies are identified as 3-D bodies referring to the BSURF IDs 1, 2, 3 and 4: BCBODY BSURF ... ... BCBODY BSURF ... ... BCBODY BSURF ... ... BCBODY BSURF

1 1 292

3D 285 293

DEFORM 286 294

1 287 295

288 296

289 297

290 298

291 299

2 2 8

3D 1 9

DEFORM 2 10

2 3 11

4 12

5 13

6 14

7 15

3 3 677

3D 670 678

DEFORM 671 679

3 672 680

673 681

674 682

675 683

676 684

4 4 974

3D 967 975

DEFORM 968 976

4 969 977

970 978

971 979

972 980

973 981

... ...

In addition to the BCBODY option to define the deformable contact bodies, the BCTABLE option will be used to indicate: • which grids are to be treated as slave grids and which as master grids in the multipoint constraints for deformable-deformable contact; • glued contact between the gasket and the cylinder head; • glued contact between the gasket and the engine block; • glued contact between the bolts and the cylinder head. Compared to the cylinder head and the engine block, the gasket has the finest mesh and is also relatively soft. In general, it is recommended to use the grids of the contact body with the finest mesh as the slave grids in the MPCs used to solve the contact problem. If the mesh density in the contact area is comparable, then the grids of the softest body should be chosen as the slave grids. In the current simulation, grids of the gasket and the bolts are selected as slave grids, which is done using the BCTABLE option. This option is also used to activate glued contact conditions, so that both relative normal and tangential displacements in the contact areas are prohibited: BCTABLE

1 SLAVE

1 1 MASTERS 2 SLAVE 1 1 MASTERS 3 SLAVE 4 1 MASTERS 2

0. 2

3 0. 0

0. 0 0. 0

0.

0.

1

0.

0. 0

0.

0.

1

0.

0. 0

0.

0.

1

0.

140 MD Demonstration Problems CHAPTER 10

Besides indicating the slave nodes and glued conditions, the first SLAVE MASTER combination also activates the extended tangential contact tolerance. The reason to use this is motivated by the coarse mesh of the cylinder head (see Figure 10-4) compared to the gasket. By activating the extended tangential contact tolerance, all grids at the top of the gasket are found to be in contact with the cylinder head.

grid outside contact surface

Figure 10-4

Detail of the FE mesh to illustrate the delayed slide off option

In order to activate the full nonlinear formulation of the 3-D isotropic elements (cylinder head, engine block and bolts), the nonlinear property extension of the PSOLID entry is used: PSOLID PSLDN1 + MAT1

3 3 C8 5

5 0 5 1 SOLI L 210000.

+ .3

1.

1.5-5

Where the isotropic material definition is straightforward, the gasket behavior needs more attention. Here, the MATG entry is used. For the gasket body, the definition is: PSOLID PSLDN1 + MAT1 MATG

1 1 C8 2 1

35. TABLES1 1 0. .108 TABLES1 2 .1 .16

2 1 SLCOMP 120. 2

0 1 L 60. 0

NO 1

+ 1. 2

5.-5 52.

72.

.090909 0. 33.28

.027 .135

2.08 52.

.054 .175

8.32 56.

.081 ENDT

18.72

0. 35.84

.1225 .1675

5.04 45.36

.1375 .175

14. 56.

.1525 ENDT

27.44

The PSLDN1 entry refers to the PSOLID with ID number 1 and activates the solid continuum composite element formulation via the SLCOMP option. The material ID number 2 of the MATG entry refers to MAT1 ID number 2 to define the in-plane (membrane) behavior of the gasket material. The loading curve is defined by the table with ID number 1, while the unloading curve is defined by the table with ID number 2. In general, up to ten unloading curves can be referred to, but in this example only one unloading curve is used. The onset of irreversible behavior of the gasket material is defined by a yield pressure of 52 MPa (see also Figure 10-2). As soon as the corresponding gasket closure

CHAPTER 10 141 Engine Gasket

has been exceeded, the unloading behavior will be interpolated between the loading and the unloading curve. The tensile modulus (in case the gasket would be loaded in tension) is set to 72 MPa and the transverse shear modulus to 35 MPa. The initial thickness difference between the gasket ring and gasket body is reflected by the initial gap of 0.090909 mm. The control grids for the bolt pre-tensioning, 4083 and 4095, are defined by: GRID

4083

-36.04921.31545 20.515 5

GRID

4095

36.0492 1.31545 20.515 6

CORD2R 5

-36.04921.31545 20.515 -36.0492-40.183220.515

5.44948 1.31545 20.515 CORD2R 6

36.0492 1.31545 20.515 36.0492 -40.183220.515

77.5479 1.31545 20.515

Using these control grids, the MPC entries are: MPC MPC MPC ... ... MPC MPC MPC

22 4083 22 4083 22 4083

4084 1 4085 1 4086 1

1 -1. 1 -1. 1 -1.

1.

3924

1

-1.

1.

3930

1

-1.

1.

3936

1

-1.

22 4095 22 4095 22 4095

4104 3 4105 3 4106 3

3 -1. 3 -1. 3 -1.

1.

1966

3

-1.

1.

1972

3

-1.

1.

1978

3

-1.

Alternatively, as of version MD 2010, the BOLT option can be used. Although the kinematic constraints involved are the same, the BOLT option has the following advantages: • the input format is more concise; • the option is easier to use in a contact analysis. When the MPC entries are used, the user defined MPC's may easily be conflicting with MPC's introduced by the contact algorithm, thus causing the contact constraints to be skipped. On the other hand, when the elements at both sides of the cross section are included in the same contact body, then the BOLT option causes the contact algorithm to treat this cross section in a special way, Consequently, grid points at the boundary of the cross section can touch another contact body, while grid points touching the body with the cross section can slide along this body, even when the cross section has to be passed. Using the same control grids as mentioned above, the input of the BOLT entries is: BOLT

1 TOP BOTTOM

BOLT

2 TOP BOTTOM

4083 3924 3966 4084 4091 4095 1918 1960 4096 4103

3930 3972 4085 4092

3936 3978 4086 4093

3942 3984 4087 4094

3948

3954

3960

4088

4089

4090

1924 1966 4097 4104

1930 1972 4098 4105

1936 1978 4099 4106

1942

1948

1954

4100

4101

4102

142 MD Demonstration Problems CHAPTER 10

The SPCDs defining the shortening of the bolts are: SPCD

1

4083

2

.175

SPCD

1

4095

2

.175

The nonlinear procedure used is defined via the NLPARM entry: NLPARM

1

10

FNT 10

1

25

UPW

YES

Here the FNT option is selected to update the stiffness matrix during every recycle using the full Newton-Raphson iteration strategy. Convergence checking is performed based on displacements, forces, and work. For all criteria, the default error tolerance is used. In order to avoid bi-sections, the field MAXDIV is set to 10. Figure 10-5 shows a plot of the displacement magnitudes in the structure corresponding to the maximum pretensioning of the bolts. The expected symmetry in the solution is clearly present.

Figure 10-5

Displacement Contours at Maximum Bolt Pre-tensioning

The values of the bolt force as a function of the bolt shortening are depicted in Figure 10-6 and clearly show a nonlinear response. The bolt force is found as the reaction force on grid 4083.

CHAPTER 10 143 Engine Gasket

5000

Bolt Force (N)

4000 3000 2000 1000 Bolt Shortening (mm)

0 0.00

0.05

Figure 10-6

0.10

0.15

0.20

Bolt Force as a Function of the Bolt Shortening

Finally, Figure 10-7 displays the gasket pressure as a function of the gasket closure, both for the gasket ring and the gasket body. As explained before, the gasket body has an initial gap which explains that the gasket pressure remains zero until this gap is closed. The fact that the gasket pressure seems to already be nonzero for a gasket closer smaller than the initial gap value (0.090909 mm) is due to the finite number of steps (10). Neither the gasket ring nor the gasket body is loaded yet beyond the yield stress.

Figure 10-7

Gasket Pressure as a Function of the Gasket Closure

Modeling Tip Contact Body Definition Since the mesh of the engine block and the lower part of the bolts is a continuous mesh, the automated contact algorithm will not be able to find a unique boundary description at the interface of the engine block and the bolts. This is reflected by messages like: warning: node

1407 belongs to bodies 3 4. for the contact algorithm it will belong to body

3 only.

144 MD Demonstration Problems CHAPTER 10

Although, in the current example, this will not affect the results (there will be no contact detection between the engine block and the bolts), it is generally not recommended. Instead, one should either make sure that the lower part of the bolts are separated from the engine block or include only the upper part of the bolts in the contact body definition.

Input File(s) File

Description

nug_10.dat

Engine Gasket with MPC option

nug_10_bolt.dat

Engine Gasket with BOLT option

Video Click on the image or caption below to view a streaming video of this problem; it lasts approximately 47 minutes and explains how the steps are performed.

bolt cross section

bolt cross section

Figure 10-8

Video of the Above Steps