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Power transmission system with tightly wound rope around cylindrical drum

**Library:**Simscape / Driveline / Couplings & Drives

The Rope Drum block represents a power transmission system
where a rope is tightly wound around a cylindrical drum at a sufficient tension level to
prevent slipping. You can configure the rope so that the ends point in the same or
opposite directions. You can set the direction that the ends move with the
**Rope windup type** parameter:

If the rope ends point in the same direction, they translate in opposite directions.

If the rope ends point in opposite directions, they translate in the same direction.

The equations refer to rope ends A and B, as illustrated by the figure.

During normal operation, a driving torque causes the cylindrical drum to rotate about its
axis of symmetry. The rotating drum transmits tensile force to the rope ends, which
translate with respect to the drum centerline. The relative direction of translation
between the two rope ends depends on the setting of the **Rope windup
type** parameter. However, a positive drum rotation always corresponds to a
positive translation at port **A**.

The block assumes that each rope end remains taut during simulation because slack rope ends do not transmit force. You can set the block to warn you if the rope loses tension.

You can optionally set parameters for:

Drum inertia

Viscous friction at the drum bearing

The net torque acting on the cylinder satisfies the force balance equation

$$T={F}_{B}\xb7R\xb7\delta -{F}_{A}\xb7R+\mu \xb7\omega ,$$

where:

*T*is the net torque acting on the drum.*F*_{A}and*F*_{B}are the external forces pulling on rope ends A and B.*R*is the drum radius.*μ*is the viscous friction coefficient at the drum bearings.*ω*is the drum angular velocity.*δ*is the rope windup type according to the parameter settings:When you set

**Rope windup type**to`Ends move in the same direction`

,*δ = -1*.When you set

**Rope windup type**to`Ends move in the opposite directions`

,*δ = +1*.

The figure shows the equation variables.

The translational velocities of the two rope ends are functions of the drum radius and angular velocity. Each translational velocity is equal to the tangential velocity of a point at the drum periphery according to the expressions

$$\begin{array}{c}{V}_{A}=-\omega \text{\hspace{0.17em}}\xb7R\\ {V}_{B}=+\omega \text{\hspace{0.17em}}\xb7R\end{array}$$

where:

*V*_{A}is the translational velocity of rope end A.*V*_{B}is the translational velocity of rope end B.

The block ignores slip at the rope-drum contact surface.

The block ignores rope compliance.