COMSOL 6.4 - Dynamics of a Roller Chain Sprocket Assembly

Dynamics of a Roller Chain Sprocket Assembly

Chain drives are used for transmitting power from one shaft to another, located at some distance. This example simulates the dynamics of a chain sprocket assembly in 2D. The geometry consists of a roller chain wrapped around two sprockets. Both chain links and sprockets are assumed to be rigid. An angular velocity is prescribed at the driver sprocket.

The geometry of the chain sprocket assembly is created using built-in geometry parts. The node in the Multibody Dynamics interface is used for setting up the entire model. Using a transient study, the dynamics of the system is analyzed for two cases: when the driven sprocket is unloaded, and when it is loaded by a counteracting external torque. In the latter case, the driven sprocket is also assigned an additional moment of inertia. The results show comparisons of chain link motion, contact forces, and other results.

Model Definition

The model geometry consists of a chain wrapped around two sprockets in 2D, as shown in Figure 1.

Figure 1: Geometry of a roller chain sprocket assembly.

The chain is assumed to be of roller type, and composed of a number of link plates. A typical roller chain has two different types of link plates: roller plates and pin plates. Elastic bushings are used to reduce vibrations in the system. These plates are connected in such a way that the relative rotation between them is unrestricted. Figure 2 shows an enlarged view of a chain link.

Figure 2: Enlarged view of a chain link. A chain is formed by assembling roller plates and pin plates alternately.

Chain And Sprocket parameters

The distance between two adjacent links is called pitch. In this example, the pitch is 0.25 in. Remaining geometric dimensions of the link plates are taken as standard, and parameterized as a function of the pitch. Table 1 lists the chain parameters.

The two sprockets have 30 and 15 teeth, respectively. They are located at a distance of 3 in. Each sprocket has a bore at its center, which enables mounting of the sprocket on other mechanical components such as shafts. Table 2 lists the sprocket parameters.

Table 1: Chain parameters
Parameter	name	value
Pitch	p	0.25 in
Roller diameter to pitch ratio	Dr	0.52
Pin diameter to pitch ratio	Dp	0.362
Bushing diameter to pitch ratio	Db	0.45
Minimum link plate width to roller diameter ratio	Wl	0.6

Table 2: Sprocket parameters
Parameter	name	value
Pitch	p	0.25 in
Number of teeth, first sprocket	n1	30
Number of teeth, second sprocket	n2	15
Sprockets center distance	cd	3 in
Bore diameter to pitch diameter ratio for both sprockets	Dbr	0.2

materials

Both chain and sprockets are made of structural steel. They are modeled as rigid, and only the mass density of the steel is of relevance.

Chain drive

The assembly of the chain and sprockets is modeled using the node. For a selected geometry part, this node automatically creates rigid domains, attachments and hinge joints which can be used to analyze the roller chain assembly.

Selection settings

For automatic generation of physics nodes, you need to select a geometry of the chain sprocket assembly from the of COMSOL Multiphysics. You can also create your own geometry, however the geometry requires domain and boundary selections to be used as inputs for automatic creation of other physics nodes. In this example, the following selections are used to create physics nodes using the node.

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Links: This is a domain selection containing all chain link domains. The selection is used for creating a node for each of the link plates.

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Sprockets: This is a domain selection containing both sprocket domains. The selection is used for creating a node for each of the sprockets.

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Pin Inner Boundaries: This is a boundary selection containing the inner boundaries of all pin plates. The selection is used for creating an node for each of the pin plates.

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Roller Inner Boundaries: This is a boundary selection containing the inner boundaries of the roller plates. The selection is used for creating an node for each of the roller plates, and it is located at same geometrical position as the Pin Inner Boundaries (Figure 4). Attachments created for the pin and roller plates are used as and in nodes.

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Roller Outer Boundaries: This boundary selection contains the outer surfaces of all roller plates. The selection is used for modeling contact between links and sprockets, as shown in Figure 5.

Figure 3: Links and Sprockets selections for creating rigid domains.

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Sprocket Outer Boundaries: This boundary selection contains the outer surfaces of the sprockets. As shown in Figure 5, these are the boundaries which come in contact with chain rollers.

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Sprocket Inner Boundaries: This boundary selection contains the inner surfaces of the sprockets, as shown in Figure 6. It is used for creating attachments and hinge joints for mounting the sprockets onto shafts.

Figure 4: The Pin Inner Boundaries selection for creating attachments.

Figure 5: The Roller Outer Boundaries and Sprocket Outer Boundaries selections, used for rigid contact modeling.

Figure 6: The Sprocket Inner Boundaries selection for creating attachments and hinge joints to mount the sprockets onto shafts.

Additional details about the functionality can be found in the Multibody Dynamics Module User’s Guide.

Triangular mesh created on sprockets as well as chain links as shown in Figure 7

Figure 7: Finite element mesh created on sprockets and links.

Boundary conditions

An angular velocity of 10 rad/s is prescribed on the left sprocket, which acts as the driver for the mechanism. The system is analyzed for two conditions of driven sprocket. In the first case, the driven sprocket is unloaded. In the second case, an external, counteracting torque of 0.01 Nm is applied, and an external moment of inertia of 10-5 kgm2 is assigned to the driven sprocket.

Study

A Time Dependent study is used to analyze the chain drive. The analysis is performed for a duration of 0.3 s. The load path, contact forces, joint forces, and other results, are analyzed.

Results and Discussion

Figure 8 shows the displacement in the chain sprocket assembly, when the driven sprocket is unloaded.

Figure 8: Displacement of chain links and sprockets at t = 0.3 s.

In Figure 9, velocity arrows show the direction and magnitude of the link motion for the unloaded and loaded cases.

Figure 9: The motion of the chain links, illustrated by velocity arrows for the unloaded (top) and loaded (bottom) cases.

Structural contact between the rigid sprockets and the chain is modeled using a penalty based formulation. Figure 10 shows the contact forces on the chain links.

Figure 10: Contact forces for (a) unloaded and (b) loaded conditions.

The rotation of a sample link joint is plotted in Figure 11. In Figure 12, the variation of joint force with time is shown for the same link.

The dynamics of the system is controlled by the angular velocity prescribed on the driver sprocket. The chain transmits the motion to the second (driven) sprocket by a continuous engage-and-disengage mechanism. The rotation, angular velocity, and angular acceleration of the driven and driver sprockets are plotted in Figure 13, Figure 14 and Figure 15 respectively. Results from both the unloaded and loaded cases are shown.

Figure 11: Rotation of a sample link joint, as a function of time.

Figure 12: Variation of force with time, in a sample link joint.

Figure 13: Sprocket rotation as a function of time.

Figure 14: Driver and driven sprocket angular velocity, for the unloaded and loaded cases.

Figure 15: Driver and driven sprocket angular acceleration, for the unloaded and loaded cases.

Figure 16: Frequency response of driver and driven sprocket angular acceleration for unloaded and loaded conditions.

Notes About the COMSOL Implementation

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To build a chain drive system geometry, you can import a roller chain sprocket assembly part from the ,and customize it by changing its input parameters.

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node operates on the geometry in the assembly state.

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node creates new physics nodes from selections available in geometry. If you are using part imported from the ,select the checkbox in to keep noncontributing selections. If you are building a geometry of a roller chain and sprocket assembly, you also need to create appropriate selections for the node to operate.

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When one or more selection inputs of node change, the selections of the physics nodes created by the node also change. Hence these nodes have to be deleted and recreated. This is indicated by a warning node appearing under the node. In that case, you need to press the button. This will automatically create new groups of physics nodes in accordance with the changed selection inputs.

Multibody_Dynamics_Module/Tutorials,_Transmission/roller_chain_dynamics

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
omega	10[rad/s]	10 rad/s	Angular velocity of drive shaft
T_ext	0.01[N*m]	0.01 N·m	External torque
I_ext	1e-5[kg*m^2]	1E-5 kg·m²	External moment of inertia
kb	1e5[N/m]	1E5 N/m	Spring constant, bushing
cb	1e5[N*s/m]	1E5 N·s/m	Damping coefficient, bushing
para	0	0	Load parameter