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Power transmission system with tightly wound rope around cylindrical drum
This block represents a power transmission system with two key components:
Rope
Drum
The rope is tightly wound around the cylindrical drum, at a sufficient tension level to prevent slipping between the two components. The rope can be wound such that its ends point in equal or opposite directions. Depending on the rope configuration, the two rope ends can move in equal or opposite directions. These are the rope windup types that you specify in the block dialog box:
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.
During normal operation, a driving torque causes the cylindrical drum to rotate about its symmetry axis. The rotating drum transmits a tensile force to the rope ends, which translate with respect to the drum center line. The relative direction of translation between the two rope ends depends on the rope windup type. However, a positive drum rotation always corresponds to a positive translation at rope end A.
The rope drum model assumes that each rope end remains taut during simulation. This assumption is important since slack rope ends do not transmit force. An optional tension warning indicates if this assumption fails. The warning, which appears at the MATLAB^{®} command prompt, should prompt careful analysis of the simulation results.
Optional effects in the rope drum model include:
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 table below.
Rope Windup Type | δ |
Ends move in the same direction | -1 |
Ends move in opposite directions | +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.
Slip does not occur at the rope-drum contact surface.
Rope compliance is ignored.
Distance between the drum center and its periphery. The drum periphery coincides with the contact surface between the drum and the rope. The default value is 0.1 m.
Relative direction of the translation motion of the two rope ends, A and B. Options include:
The ends move in the same direction
The ends move in opposite direction
Optional warning at the MATLAB command line indicating that at least one rope end has become slack. A rope end becomes slack when the net tensile forces responsible for keeping it taut fall below zero. Since slack cables do not transmit force, you must interpret simulation results carefully if a tension warning appears at the MATLAB command line. Warning options include:
Do not check rope tension
Warn if either rope end loses tension
Linear damping coefficient in effect at the drum bearing. At a given drum angular velocity, this coefficient determines the power losses due to viscous friction. The default value is 0.001 (N*m)/(rad/s).
Optional parameter accounting for drum inertia, its resistance to angular acceleration. Options include:
No inertia — Default mode. Keep this mode if drum inertia has a negligible impact on driveline dynamics. Selecting this mode sets drum inertia to zero.
Specify drum inertia and initial velocity — Select this mode if drum inertia has a significant impact on driveline dynamics. Selecting this mode exposes additional parameters enabling you to specify the drum inertia and initial angular velocity.
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.
The default value of the drum inertia is 0.01 kg*m^2.
Angular velocity of the drum at simulation time zero. The default value is 0 rad/s.
Port | Description |
---|---|
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 |
Featured example sdl_power_windowsdl_power_window shows an application of the Rope Drum block.