Simulation of Elastic Body Systems

Many components of internal combustion engines suffer significant deformations when the en-gine is running. Conrods bend under load during the combustion, crankshafts endure bending and torsional deformation, and the engine block itself vibrates as well. The amplitude of the de-formation is of course not very large, but the dede-formation reduces the durability and contributes to the emission of noise. The deformation can be computed using a simulation model based on the theory of elastic multibody systems. This concept is often used in engineering in fatigue and stress analysis [154] as well as in engine noise analysis [188]. The simulation model consists of two fundamentally different types of entities: linear elasticbodiesthat represent engine compo-nents (crankshaft, conrods, pistons, etc.); andjoints(bearings, dampers, etc.) that connect the bodies and often feature non-linear behavior.

Bodies are defined via finite element (FE) meshes that are built from 3D CAD models.

The FE mesh of an engine block, for example, may consist of several hundred thousands of elements. Each node has three translational and three rotational degrees of freedom. Running forced response analysis in the time domain on a structure with so many degrees of freedom

84 CHAPTER 6. INTERACTIVE 3D VISUALIZATION OF MULTIBODY DYNAMICS is not feasible on current hardware. Therefore, the meshes go through a condensation process before simulation.

Thecondensation process[229] creates a simplified, “condensed” mesh. It chooses a subset of the nodes (typically not more than a few hundred) of the mesh that represent the body in the simulation. The nodes are identified bynode IDs(numbers). The engineer can also manually mark degrees of freedom of specific nodes that are to be preserved in the condensed model.

These nodes are calledretained static degrees of freedom.Single point constraintscan be defined to disable one or more degrees of freedom of specific nodes.Multiple point constraintsestablish a relationship between degrees of freedom of a group of nodes. The condensation also creates mass, stiffness and damping matrices that describe the dynamic properties assigned to the nodes in the condensed mesh. The resulting reduced model and the matrices define the bodies in the simulator. The simulator output is directly available for the condensed mesh nodes only.

The data can berecoveredfor the entire FE mesh using the information from the condensation process. It is important to understand that the simulator works only with the condensed meshes, not with original FE meshes. The result is a much faster simulation which produces results that are still valid for the entire structure, provided the condensation was correct. FE modeling and condensation is performed in third party software (Abaqus², MSC.Nastran³, etc.).

Joints establish connections between bodies and restrict their motion. A joint connects groups of nodes in two bodies. The nodes are referenced by their node IDs, for example: “con-nect node 2 of the crankshaft with nodes 10,11,12,13 of the block”. Alternatively, namednode setscontaining several nodes can be defined and used in the specification of joints. For exam-ple, the nodes of the engine block that can come in contact with the crankshaft can be listed in sets called “MainBearing1”, “MainBearing2”, and so forth, for each main bearing, respectively.

There is a utility that can automatically identify the nodes that constitute main bearings.

After all bodies and joints are created, additional information about the crank train, external loads and boundary conditions, such as lubricant type are defined, and then the simulation is run.

The simulation is usually run for 3–4 engine cycles which equal 6–8 complete revolutions of the crankshaft to allow the initial transients to settle. Depending on model’s complexity and the length and the resolution of the simulated time interval this may take several hours for a single simulation case. The computed motion of the bodies consists of two components: (1) the global motion, and (2) the local displacement of nodes. About 10 additional attributes are computed for each node, including load and inertia forces, as well as shear rate and stress. The interaction of the crankshaft’s overall rotation with the vibration of its parts is taken into account. The resulting non-linear inertia forces like gyroscopic effects are also handled in the simulator.

6.3.2 3D Visualization of Elastic Multibody Systems

The visualization of elastic multibody systems involves displaying the meshes of the bodies enhanced with several different glyphs to indicate features like joints and constraints. Occlusion is generally a major issue in this visualization; hence we propose possible techniques to alleviate the problem.

2ABAQUS Inc.http://www.simulia.com

3MSC.Software Corp.http://www.mscsoftware.com

6.3. INTERACTIVE 3D VISUAL ANALYSIS OF ELASTIC BODY DYNAMICS 85 Bodies

Bodies are the structural components of the model. Each body has a local coordinate system which is also indicated by an axis triad. The axis of rotation is highlighted in a different color.

Each body can have two associated meshes: the FE mesh and the condensed one.

FE mesh This is the FE mesh that was used as input for the mesh condensation process. Sur-face and/or wireframe FE meshes can be shown. Occlusion is a major issue in this context, since virtually everything (crankshaft, conrods, etc.) that is of interest to the engineer is contained.

Furthermore, joints usually represent contacts between bodies thus these bodies almost always obscure them. We offer four means of reducing occlusion in FE meshes:

• The outermost layers of FE meshes can be removed one-by-one temporarily, much like peeling an onion. This allows investigation of the inner elements.

• An arbitrary clipping plane can be applied to each FE mesh. The elements (cells) in one half-space are removed. This can be used to remove half of the engine block, for instance, creating an exploded view of the engine. The plane can be freely rotated and dragged. Unlike typical clipping planes defined in OpenGL or other libraries, this plane clips complete elements of the FE mesh. An element (cell) is either completely visible or completely clipped, but never cut in half, thus the notion of elements in the mesh is better preserved.

• Similarly, an arbitrary intersection plane can also be used. Only elements that intersect the plane are shown. As with the clipping plane, complete elements are preserved.

• Arbitrary groups of FE elements called cell sets can exist. Those sets often represent semantic parts of the mesh; for instance, the left side of the engine block. They can be hidden or rendered in different colors. Cell sets in FE mesh files are read automatically.

In addition, there are several powerful ways to define and edit sets.

Transparency can be combined with any of the above tools. Figure 6.14 demonstrates these methods in order to provide a good view of the whole engine. Half of the block is clipped away and the crankshaft is drawn semi-transparently.

Special node constraints are represented by small wireframe glyphs attached to the nodes (see Figure 6.15). Retained static degrees of freedom are indicated by a small coordinate system icon. For each enabled translational degree of freedom, the corresponding axis of the coordinate system is shown. Rotational degrees of freedom are indicated by small arcs around the respective axes. Single point constraints are depicted by the triangular “constraint” icon commonly used in mechanical engineering software. Multiple point constraints are displayed by connecting the constrained nodes.

Condensed mesh As described in Section 6.3.1, this is a reduced mesh, consisting of nodes only. The visualization simply shows the nodes with optional node ID labels and line segments connecting the nodes. Figure 6.16 shows the reduced mesh of a crankshaft.

86 CHAPTER 6. INTERACTIVE 3D VISUALIZATION OF MULTIBODY DYNAMICS

Figure 6.14: 3D view of a 4 cylinder inline engine. Half of the engine block is clipped to make the inside visible.

Figure 6.15: Close-up views of an engine block with glyphs representing retained static degrees of freedom (left), single point constraints (middle), and multiple point constraints (right). Labels show node IDs.

6.3. INTERACTIVE 3D VISUAL ANALYSIS OF ELASTIC BODY DYNAMICS 87

Figure 6.16: Condensed mesh of the crankshaft used in the simulator. The transparent FE mesh is also shown as context.

Joints

It is worth mentioning that joints cannot be represented as easily as bodies because they differ fundamentally: there is no mesh associated with them. They merely describe the contacts be-tween nodes of meshes. There are over 20 different joint types in the elastic body dynamics simulator we used. In the 3D view they are represented by lines that connect the actual nodes of the bodies. We also show different icons for each joint type, the same small bitmaps that are used elsewhere in the simulator’s user interface to represent joints. For some specific types (bearings, piston liners, etc.) 3D glyphs have been incorporated. A main bearing is shown in Figure 6.17(a). In this image the ring is a glyph that indicates the diameter and the width of the bearing. In Figure 6.17(b), a piston-liner guidance is shown. The beams indicate how nodes of the engine block are connected to the piston pin for simulation. The yellow labels show IDs of the connected nodes.