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# Chain Drive

Roller chain wrapped around two sprockets

## Library

Couplings & Drives

## Description

The block represents a drive built of two sprockets that are connected by a roller chain. The model accounts for chain slack and can be backdriven. The chain has damping relative to its linear velocity and stiffness that counteracts stretching when the chain is taut.

When one end of the chain is taut, the chain drive behaves as shown.

The damping effect in the chain always acts on the relative tangential velocity of the sprockets. The stiffness effect in the chain acts only when either the upper or lower leg of the chain is taut.

These equations describe the chain drive.

• x is the chain linear displacement.

• RA is the radius of sprocket A.

• RB is the radius of sprocket B.

• ωA is the angular velocity of sprocket A.

• ωB is the angular velocity of sprocket B.

• F is the chain tensile force.

• S is the chain slack length.

• k is the chain stiffness.

• μ is the chain damping.

• TA is the torque acting on sprocket A.

• TB is the torque acting on sprocket B.

You can add bearing viscous friction to either sprocket.

If you specify a maximum chain tension, then the simulation ends with an error when this value exceeds that maximum during runtime.

Connections A and B are conserving rotational ports that are associated with sprockets A and B, respectively.

### Assumptions and Limitations

• The sprocket tooth ratio is equal to the sprocket pitch radius ratio.

• Chain inertia is negligible.

## Dialog Box and Parameters

Use the Geometry pane to specify sprocket characteristics such as the pitch radius and chain slack length.

### Sprocket A pitch radius

The pitch radius of sprocket A. Default is 80 mm.

### Sprocket B pitch radius

The pitch radius of sprocket B. Default is 40 mm.

### Chain slack length

The slack length of the chain is the length that the chain can move before becoming taut. If one sprocket is held in place while the chain is taut, then the slack length is the tangential distance that the other sprocket must rotate before the other chain end is taut. Default is 50 mm.

### Chain initial displacement

The initial displacement of the chain. A value of 0 indicates that the chain can displace by half the slack length in either direction before it is taut. Default is 0 mm.

Select the Dynamics tab to specify stiffness, damping, and viscous coefficients.

### Chain stiffness

The longitudinal stiffness of the chain. This force is required to stretch the taut end of the chain. Default is 1e+5 N/m.

### Chain damping

The longitudinal damping of the chain. Default is 5 N/(m/s).

### Viscous friction coefficient of sprocket A

Viscous friction associated with the bearings that hold sprocket A. Default is 0.001 N*m/(rad/s).

### Viscous friction coefficient of sprocket B

Viscous friction associated with the bearings that hold sprocket B. Default is 0.001 N*m/(rad/s).

Select the Maximum tension tab to specify the maximum tension.

### Maximum tension

Specifies whether the block throws an assertion when the chain tension is too large.

• No maximum tension — (Default) Does not throw an assertion.

• Specify maximum tension — Throws an assertion when the chain tension meets or exceeds the value of the Chain maximum tension parameter.

### Chain maximum tension

Maximum allowable tension for the chain. If the chain tension meets or exceeds this value, the simulation ends with an error. Default is 1e+6 N.

The Chain maximum tension parameter is visible only when the Maximum tension is Specify maximum tension.

## Ports

PortDescription

A

Conserving rotational port associated with sprocket A

B

Conserving rotational port associated with sprocket B

## Example

The sdl_sheet_metal_feedersdl_sheet_metal_feeder SimDriveline™ example model shows the use of the Chain Drive block.

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