Documentation

Chain Drive

Power transmission system with chain and two sprockets

• Library:
• Simscape / Driveline / Couplings & Drives Description

The Chain Drive block represents a power transmission system with a chain and two sprockets. The chain meshes with the sprockets, transmitting rotary motion between the two. Power transmission can occur in reverse, that is, from driven to driver sprocket, due to external loads. This condition is known as back-driving. The drive chain is compliant. It can stretch under tension or slacken if loose. The compliance model consists of a linear spring-damper set in a parallel arrangement. The spring resists tensile strain in the chain. The damper resists tensile motion between chain elements.

The spring and damper forces act directly on the sprockets that the chain connects. The spring force is present when one chain branch is taut. The damper force is present continuously. To represent and report a failure condition, the simulation stops and generates an error if the net tensile force in the chain exceeds the specified maximum tension value.

The block accounts for viscous friction at the sprocket joint bearings. During motion, viscous friction causes power transmission losses, reducing chain-drive efficiency. These losses compound due to chain damping. To eliminate power transmission losses in the chain drive, in the Dynamic settings, set the parameters for viscous friction and chain damping to zero.

The tensile strain rate in the chain is the difference between the sprocket tangential velocities, which are each the product of the angular velocity and pitch radii. Mathematically,

$\stackrel{˙}{x}={\omega }_{A}{R}_{A}-{\omega }_{B}{R}_{B},$

where:

• x is the tensile strain.

• ωA, ωB are the sprocket angular velocities.

• RA, RB are the sprocket pitch radii.

The figure shows the relevant variables. The chain tensile force is the net sum of the spring and damper forces. The spring force is the product of the tensile strain and the spring stiffness constant. This force is zero when the tensile strain is smaller than the chain slack. The damper force is the product of the tensile strain rate and the damping coefficient. Mathematically,

$F=\left\{\begin{array}{cc}-\left(x-\frac{S}{2}\right)k-\stackrel{˙}{x}b,& x>\frac{S}{2}\\ -\stackrel{˙}{x}b,& \frac{S}{2}\ge x\ge -\frac{S}{2}\\ -\left(x+\frac{S}{2}\right)k-\stackrel{˙}{x}b,& x<-\frac{S}{2}\end{array},$

where:

• S is the chain slack.

• k is the spring stiffness constant.

• b is the damper coefficient.

The chain exerts a torque on each sprocket equal to the product of the tensile force and the sprocket pitch radius. The two torques act in opposite directions according to the equations

${T}_{A}=-F·{R}_{A},$

and

${T}_{B}=F·{R}_{B},$

where:

• TA is the torque that the chain applies on sprocket A.

• TB is the torque that the chain applies on sprocket B.

Variables

Use the Variables tab to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables (Simscape).

Unlike block parameters, variables do not have conditional visibility. The Variables tab lists all the existing block variables. If a variable is not used in the set of equations corresponding to the selected block configuration, the values specified for this variable are ignored.

Assumptions and Limitations

• The sprocket tooth ratio equals the sprocket pitch radius ratio.

• Chain inertia is negligible.

Ports

Conserving

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Conserving rotational port associated with sprocket A.

Conserving rotational port associated with sprocket B.

Parameters

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Geometry

Radius of the pitch circle for sprocket A. The pitch circle is an imaginary circle passing through the contact point between a chain roller and a sprocket cog at full engagement.

Radius of the pitch circle for sprocket B. The pitch circle is an imaginary circle passing through the contact point between a chain roller and a sprocket cog at full engagement.

Maximum distance the loose branch of the drive chain can move before it is taut. This distance equals the length difference between actual and fully taut drive chains.

If one sprocket is held in place while the top chain branch is taut, then the slack length is the tangential distance that the second sprocket must rotate before the lower chain branch becomes taut.

Dynamics

Linear spring constant in the chain compliance model. This constant describes the chain resistance to strain. The spring element accounts for elastic energy storage in the chain due to deformation.

Linear damping coefficient in the chain compliance model. This coefficient describes the resistance to tensile motion between adjacent elements in the chain. The damper element accounts for power losses in the chain due to deformation.

Friction coefficient due to the rolling action of the joint bearing for sprocket A in the presence of a viscous lubricant.

Friction coefficient due to the rolling action of the joint bearing for sprocket B in the presence of a viscous lubricant.

Maximum Tension

Select whether to constrain the maximum tensile force in the drive chain.

• No maximum tension — Chain tension can be arbitrarily large during simulation.

• Specify maximum tension — Chain tension must remain lower than a maximum value. If the tension exceeds this value, the simulation generates an error and stops.

Dependencies

Selecting Specify maximum tension exposes the Chain maximum tension parameter.

Maximum allowed value of the tensile force acting in the chain.

Dependencies

Selecting Specify maximum tension for the Maximum tension parameter exposes this parameter.

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™. 