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# Rope Drum

Rope wrapped around a drum

## Library

Couplings & Drives

## Description

The block represents a drum wrapped with a flexible rope so that no slip exists between the drum and the rope. The block accounts for viscous friction in the drum bearings. You can include drum inertia. The block simulates drums with two types of the rope windup.

In left-hand figure (a), the rope is wound around the drum in such a way that its ends move in the same direction. In the right-hand figure (b), the rope ends move in opposite direction.

Rope compliance is not modeled. The model is valid when both ends of the rope are in tension. An optional warning can display at the MATLAB® command line when either rope end loses tension. When assembling a model, ensure that tension is maintained throughout the simulation. Interpret the results with this in mind.

The branch A end moves in a positive direction, if the drum rotates in a positive direction.

The branch B end moves either in a positive or negative direction, depending on whether the Rope windup type parameter specifies that ends move in the opposite direction or in the same direction.

Positive translation for end A corresponds to positive rotation of the drum.

The three block equations are:

T = FB· R· orFA · R + μ· ω

VB = –ω· R· or

VA = ω· R

where

• R is the drum radius.

• T is the drum torque.

• FB is the force acting along branch B.

• FA is the force acting along branch A.

• ω is the drum angular velocity.

• VA is the linear velocity of branch A.

• VB is the linear velocity of branch B.

• or is the parameter that accounts for the rope windup type.

• If you set the Rope windup type parameter to Ends move in the same direction, then or is set to -1.

• If you set the Rope windup type parameter to Ends move in opposite direction, then or is set to 1.

Connection S is a conserving rotational port associated with the drum shaft. Connections A and B are the conserving mechanical translational ports associated with the rope ends.

### Assumptions and Limitations

• Both rope ends maintain adequate tension throughout the simulation.

• Rope compliance is not modeled.

• The drum does not translate.

## Dialog Box and Parameters

The Rope Drum dialog box includes two tabs. In the Rope winding pane, specify the drum radius and type of rope windup.

### Drum radius

The radius of the drum. Default is 0.1 m.

### Rope windup type

Specifies whether the ends of the rope travel in the same or opposite direction.

• The ends move in the same direction — (Default)

• The ends move in opposite direction

### Tension Warning

Specifies whether the block writes a warning at the MATLAB command line when the tension at either end of the rope falls below zero.

• Do not check rope tension — (Default)

• Warn if either rope end loses tension

Select the Drum dynamics tab to specify a bearing viscous friction coefficient and inertia.

### Bearing viscous friction coefficient

Viscous friction associated with the bearings that hold the axis of the rope drum. Default is 0.001 (N*m)/(rad/s).

### Inertia

Specifies whether the block models the rotational inertia of the drum.

• No inertia — (Default) Does not model rotational inertia.

• Specify drum inertia and initial velocity — Models rotational inertia. Exposes the Drum inertia and Initial rotational velocity parameters.

### Drum inertia

The rotational inertia of the drum. Default is 0.01 kg*m^2.

The Drum inertia parameter is visible only when the Inertia parameter is Specify drum inertia and initial velocity.

### Drum initial velocity

The initial rotational velocity of the drum. Default is 0 rad/s.

The Drum initial velocity parameter is visible only when the Inertia parameter is Specify drum inertia and initial velocity.

## Ports

PortDescription

S

Conserving rotational port associated with the drum shaft

A

Conserving translational port associated with rope end A

B

Conserving translational port associated with rope end B

## Example

Featured example sdl_power_windowsdl_power_window shows an application of the Rope Drum block.

## See Also

Wheel and Axle (in the Simscape™ documentation)

Basic Motion, Torque, and Force Modeling

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