Simulation of Timing Chain Drives

Timing chains (or toothed belts) transfer the rotation of the engine’s crankshaft to the camshaft which in turn actuates the valves, synchronized to the piston’s motion. The crankshaft must complete precisely two rotations to one camshaft rotation. The chain’s motion deviates from its ideal kinematic path especially at high engine speeds. Dynamic and inertial phenomena cause vibrations that increase noise levels and mechanical wear. The vibration also causes the accuracy of the motion coupling to deteriorate. Thus the camshaft’s rotational velocity is not constant but contains undesired high frequency components. This can induce rougher and less controlled valve operation which can also reduce fuel economy, engine performance, and degrade emission quality. This behavior can be simulated in software thus simulation tools are used extensively in the design of timing chain drives.

Simulation model

Strictly speaking, timing drives consist of the chain or belt, sprockets on the crankshaft and on the camshaft(s), and one or more fixed or spring-loaded guides. The basic approach is to model each chain link as a single rigid body connected by spring/damper units to neighboring chain links, and simulate the resulting multibody system based on the Newton-Euler laws. The crankshaft and the camshaft sprockets are modeled as generic mass elements with only one degree of freedom (DOF), the rotation around the x-axis, which coincides with their natural axis. Similarly, guides can rotate around thex-axis on their pivot point. The motion of the chain is computed only in they-zplane. The motion perpendicular to the plane can be ignored without

7.2. INTERACTIVE VISUAL ANALYSIS OF A TIMING CHAIN DRIVE 105

Figure 7.13: Contact forces between chain links and sprockets. The red region indicates the overlap area of the contact contours. Each chain link has smaller circular contours at both ends that model the bushing which comes into contact with the sprockets. The side-bar contour is the outer edge of the chain link that slides on guides.

influencing the validity of the simulation. Therefore, each chain link has three enabled DOFs:

translation inyandzdirections and rotation aroundx-axis.

In a simulation the objects are described using their contact contours. The contours of sprockets and guides reflect their actual shapes. The contours of chain links are a less intu-itive. The contour of a chain link consists of circles around the pins that interconnect the chain links. There are two circular contours at each pin of the chain link. The smaller circle is the surface that comes into contact with sprockets. The larger circle is the outer surface of the link that slides on guides. Simulation of toothed belt drives works in a very similar way. The belt is represented as a spring-connected sequence of rigid sections, typically one section per tooth.

The contour of each section is the cross-section of the respective part of the belt.

The simulation computes dynamic motion quantities of all chain links and forces between elements. There are two classes of forces: (a) contact forces between chain links and the sprock-ets/guides, and (b) connection forces between neighboring chain links. The contact forces act when a link comes into contact with a sprocket or guide. The algorithm for computing contact forces is based on evaluating the size of the overlap area between the contact contours of the two objects, the stiffness of materials, the relative velocities, and the damping properties of the materials. The connection forces act between neighboring chain links and are computed in a similar way. Figures 7.13 and 7.14 illustrate the corresponding connection and contact force models. For a more detailed explanation about the simulation of chain drives with rigid body dynamics please refer to the work of Sopouch et al. [241].

In this case study we use a model of a basic type chain drive system which consists of two

106 CHAPTER 7. DEMONSTRATION

Figure 7.14: A model of the connection forces in the chain drive simulation. Each chain link is connected to its neighbors via stiff spring and damper elements.

Parameter Values Unit

sprocket stiffness 1.0E+7, 4.0E+7, 7.0E+7, 1.0E+8 [N/m]

guide stiffness 5.0E+6, 2.0E+7, 3.5E+7, 5.0E+7 [N/m]

chain preload 100, 200, 300, 400 [N]

sprocket offset -0.5, 0.0, +0.5 [mm]

engine speed 1000, 2000, 3000, 4000, 5000, 6000 [rpm]

Table 7.2: Control parameters (independent variables) of the timing chain drive simulation.

sprockets, the camshaft sprocket (38 teeth) and the crankshaft sprocket (19 teeth). Two guides lead a bushing chain along the chain path to reduce lateral vibrations. The constant load is applied at the camshaft sprocket and a constant rotation is prescribed at the crankshaft sprocket.

Lash in the chain and friction in the contacts between the chain and sprockets are not considered.

A commercially available software package, EXCITE Timing Drive from AVL was used for the timing drive simulation. It is a multibody simulation software tool for the simulation of engine valve train components. The model is shown in Figure 7.15.

Simulation parameters

Several control parameters can be defined in the simulation software. In the scope of this case study we varied engine speed and four design parameters: stiffness of the sprocket material, stiffness of the guide material, chain preload and camshaft sprocket offset from the designed position in thezdirection (see Figure 7.15). A positive offset means that the camshaft sprocket is further away from the crankshaft than its kinematically ideal position; therefore the chain becomes relatively short. Table 7.2 shows the ranges of variation of the parameters. With respect to the data model in Section 3.2, the control parameters are the independent variables in the data set. There are 1,152 possible combinations of these parameters or, in other words, 1,152 different simulation runs. In each simulation run the simulation period is long enough for all chain links to complete a full revolution.

7.2. INTERACTIVE VISUAL ANALYSIS OF A TIMING CHAIN DRIVE 107

Figure 7.15: Left: 3D model of the chain. Right: the model simplified to simulation contact contours. Red boxes indicate the centers of gravity of chain links.

108 CHAPTER 7. DEMONSTRATION In the context of timing drive simulation, the simulation results are termed response pa-rameters. In the visual analysis data model, they are the dependent variables. Three response parameters were computed for each simulation run from the raw simulation output described in Section 6.2.1. All three are function graphs.

• Maximum contact forces [N] over the simulation time for each chain link.

• Maximum connection forces [N] over the simulation time for each chain link.

• Fourier transform of the camshaft sprocket’s rotational velocity [rad/s vs. orders].

The independent variabletin function graphs is often time. On the contrary, in the contact and connection force function graphstrather represents a chain link numbered from 1 to 100, thus 1 ≤ t ≤ 100, t ∈ N. The value of the function graph represents the maximum of the contact or connection forces that act on the given link during the entire simulation time span.

That implies that the function graphs are not continuous.

Engineers generally face four main tasks in the analysis of chain drive simulations:

• finding invalid parameter combinations

• parameter sensitivity analysis

• reducing chain noise

• keeping contact and connection forces within a range

In the following, we demonstrate many of the concepts introduced in the previous chapters, including iterative composite brushing, the segmented curve view, data aggregation, and the 3D visualization of rigid body systems are useful in the analysis of timing chain drive simulation data.