Rope Drum

Power transmission system with tightly wound rope around cylindrical drum

Libraries:
Simscape / Driveline / Couplings & Drives

Description

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.

When rope ends A and B point in the same direction, they translate in opposite directions. When rope ends A and B point in opposite directions, they translate in the same direction.

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

$T = F_{B} \cdot R \cdot δ - F_{A} \cdot R + μ \cdot ω,$

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.

Variables associated with the Rope Drum demonstrated in the cross rope configuration and open rope configuration.

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

$\begin{matrix} V_{A} = - ω \cdot R \\ V_{B} = + ω \cdot R \end{matrix}$

where:

V_A is the translational velocity of rope end A.
V_B is the translational velocity of rope end B.

Assumptions and Limitations

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

Examples

Power Window System

A motor-driven power window system. A DC motor drives the power window mechanism via a self-locking worm gear with the ratio 1 : 50. The power window mechanism consists of a cable drum and four pulleys all connected by a cable. The window is attached to the cable at two points by the lift plate. This ensures both sides of the window move at the same speed and in the same direction, keeping the window level. The model also includes viscous friction in the guide rails.

Open Model

Ports

Conserving

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S — Drum shaft
mechanical rotational

Mechanical rotational conserving port associated with the drum shaft.

A — Rope end A
mechanical translational

Mechanical translational conserving port associated with rope end A.

B — Rope end B
mechanical translational

Mechanical translational conserving port associated with rope end B.

Parameters

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Rope Winding

Drum radius — Size of drum
`0.10` `m` (default) | positive scalar

Distance between the drum center and its periphery. The drum periphery coincides with the contact surface between the drum and the rope.

Rope windup type — Direction of B rope end with respect to A rope end
`Ends move in same direction` (default) | `Ends move in opposite direction`

Relative direction of the translation motion of the two rope ends, A and B, where B is the following end.

Tension warning — Optional lost tension warning
`Do not check tension` (default) | `Warn if either end loses tension`

Option to generate a warning when a rope end becomes slack. A rope end becomes slack when the net tensile forces responsible for keeping it taut fall below zero. Because slack cables do not transmit force, the simulation results may not be accurate when the rope loses tension.

Drum Dynamics

Bearing viscous friction coefficient — Viscous friction for drum rotation
`0.001` `N*m/(rad/s)` (default) | nonnegative scalar

Linear damping coefficient in effect at the drum bearing. This coefficient determines the power losses due to viscous friction at a given drum angular velocity.

Inertia — Resistance to angular acceleration
`No inertia` (default) | `Specify inertia and initial velocity`

Option to account for drum inertia.

No inertia — Select this setting if drum inertia has a negligible impact on driveline dynamics. This setting sets drum inertia to zero.
Specify inertia and initial velocity — Select this setting if drum inertia has a significant impact on driveline dynamics.

Drum inertia — Drum tendency to remain in motion
`0.01` `kg*m^2` (default) | positive scalar

Moment of inertia of the drum about its rotation axis. In the simple case of a solid cylindrical drum, the moment of inertia is

$I = \frac{1}{2} M R^{2},$

where M is the drum mass and R is the drum radius.

Dependencies

To enable this parameter, set Inertia to Specify inertia and initial velocity.

Drum initial velocity — Initial drum state
`0` `rad/s` (default) | scalar

Angular velocity of the drum at the start of the simulation.

Dependencies

To enable this parameter, set Inertia to Specify inertia and initial velocity.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2012a

Rope Drum