# Motorcycle Chain

Implement motorcycle chain

• Library:
• Powertrain Blockset / Drivetrain / Couplings

Vehicle Dynamics Blockset / Powertrain / Drivetrain / Couplings

## Description

The Motorcycle Chain block implements the dynamic effects of a motorcycle chain on the Motorcycle Body Longitudinal In-Plane block, including dynamic tension and moment drive coupling.

This figure shows how the chain relates geometrically to the motorcycle frame, rear arm, and rear wheel.

FrameVariable in FigureDescription

Motorcycle main frame

• xm – Forward along vector pointing to front fork

• zm – Downward

• ym – Orthogonal to motorcycle plane

Om

Main frame origin

## Ports

### Input

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Drive shaft moment on front sprocket about ym, in N·m.

Longitudinal and vertical forces at rear wheel contact patch OCpR, along iCpR and kCpR, in N. Signal vector dimensions are `[1x2]` or `[2x1]`.

Main frame pitch angle, ϴfrm, in rad.

Rear arm pitch angle, ϴra, in rad.

Brake moment at the rear wheel GWhlRr, about jWhlRr, in N·m.

Rear wheel angular acceleration, in rad/s2.

### Output

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Bus signal containing these block calculations.

SignalDescriptionUnits
`FChn`

Chain force applied to rear arm

N
`AngVSprtR`

Angular velocity of rear sprocket

`MDrvSprtR`

Wheel damper moment applied to rear sprocket

N·m
`WhlDmpAng`

Angle between rear sprocket and rear wheel

Wheel damper moment applied to rear sprocket, in N·m.

Drive chain moment at rear arm OArmRr, about jArmRr, in N·m.

Drive chain moment at the frame OFrm, about jFrm, in N·m.

## Parameters

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This figure shows how the chain relates geometrically to the motorcycle frame, rear arm, and rear wheel.

Front Sprocket

Position of front sprocket, SprktFrPxz, along xm zm, respectively, in m.

Front sprocket mass moment of inertia, SprktFrIyy, in kg·m2.

Front sprocket radius, SprktFrR, in m.

Rear Sprocket

Rear sprocket mass moment of inertia, SprktRrIyy, in kg·m2.

Rear sprocket radius, SprktRrR, in m.

Rear Wheel

Rear wheel mass moment of inertia, WhlRrIyy, in kg·m2.

Rear wheel radius, WhlRrR, in m.

Swing Arm

Arm length, ArmRrLen, in m.

Wheel Damper

Wheel damper stiffness, WhlDmpK, in N/rad.

Wheel damper damping, WhlDmpC, in N·s/rad.

Initial Conditions

Rear sprocket angular velocity, SprktRrAngV0, in rad/s.

Rear wheel angular velocity, WhlRrAngV0, in rad/s.

## References

[1] Giner, David Moreno. “Symbolic-Numeric Tools for the Analysis of Motorcycle Dynamics. Development of a Virtual Rider for Motorcycles Based on Model Predictive Control.” PhD diss., Universidad Miguel Hernández de Elche, 2016.