Cable

Cable connection that enables tension transfer

Since R2021a

• 

Libraries:
Simscape / Driveline / Couplings & Drives

Description

The Cable block represents an element that transfers tension between two contact points. You can treat the block as an arbitrary tension transfer device to simulate a variety of situations, including pulley networks, cable drives, and serpentine belts. You can choose whether the cable exhibits slack upon loss of tension. The block has a base port, B, and a follower port, F. The cable stretches in tension when the base port leads the follower port.

The block considers only the longitudinal translational motion and force exerted at the cable ends. The first figure shows a Translational Spring and Translational Damper block in parallel, which is functionally equivalent to the Cable block with zero mass. The second figure shows the same spring and damper blocks but with an additional Mass block on either side, which is functionally equivalent to the Cable block with a nonzero mass.

These figures only apply when the cable is in tension.

Tip

Confirm that your model operates as expected before you select the Model slack and Model mass parameters. Verify that the B and F ports are oriented properly by viewing the tension plots of each cable in the Simscape Results Viewer and looking for unexpected negative values.

The Cable block can act as a rope, belt, cable, or any other device that has tensile strength and transmits tension between two contact points. A contact point can be a pulley, a drum, or an ideal source. You can use the Stretch parameterization parameter to control whether the block acts as a constant or tabulated connection.

You can use this block to model stationary or travelling pulley networks. You can drive the Cable block with sources like the Ideal Translational Velocity Source block, or a Rope Drum block attached to an Ideal Force Source block.

For greater fidelity or numerical stability, you can choose to model the effect of mass on the system. When you select Model mass, the block distributes half of the total mass to either end of the cable. Adding a small amount of mass can improve the initialization of your model. You can also specify the initial conditions of the cable. If you choose to simulate slack, the block does not apply stiffness and damping when the cable is in slack. Selecting Model slack or Model mass enables the Model gravity parameter. Including the effect of gravity improves accuracy for heavy cable segments.

For cable segments with variable rest length, use the Model variable rest length parameter to improve results for travelling pulley applications. The block supports these examples of variable rest length scenarios:

• One end of the cable is stationary, and the other end connects to a travelling pulley.

• A cable is connected to a travelling pulley at each end.

You must use the correct orientation for the block when you select Model variable rest length. To learn more, see Best Practices for Modeling Pulley Networks.

Equations

The block equations refer to these quantities:

• F is the tension force, where $$F=F_B=-F_F.$$

• x_s is the deformation due to stretching, which you specify by using the Stretch variable. Simscape Results Explorer displays this quantity as s.

• K is the spring stiffness coefficient. $$K(x_s)=0$$ when you select Model slack and $$x_s<0$$.

• D is the damping coefficient.

• m is the total mass, which you specify by using the Mass parameter. The block distributes half of the total mass to each end.

• x_B is the position of the base node.

• x_F is the position of the follower node.

• ẋ_s is the stretch velocity.

• L_Rest is the rest length of the cable segment.

• L_min is the Minimum rest length parameter.

• μ is the Linear density parameter.

The Cable block responds to external load at the port B as

$$F_B(x_s(t),t)=\frac{m}{2}{\ddot{x}}_B(t)+D{\dot{x}}_s(t)+K{x}_s(t),$$

and port F as,

$$F_F(x_s(t),t)=\frac{m}{2}{\ddot{x}}_F(t)-D{\dot{x}}_s(t)-K{x}_s(t),$$

where $$x_s(t)=x_B(t)-x_F(t)$$. The definitions of D and V depend on the parameterization.

• D and K are constant when you set Stretch parameterization to Constant stiffness and damping and clear Model variable rest length.

• D is constant and K = EA/L_Rest when you set Stretch parameterization to Constant stiffness and damping and select Model variable rest length, where EA is the value of the Rigidity parameter.

• D = TLU(x_s) and K = TLU(x_s) when you set Stretch parameterization to Tabulated stiffness and damping and clear Model variable rest length.

• D = TLU(x_s, x_s/L_Rest) and K = TLU(L_Rest, x_s/L_Rest) when you set Stretch parameterization to Tabulated stiffness and damping and select Model variable rest length.

The block overrides the value of K to 0 when you select Model slack and x_s < 0.

The forces vary as functions of time and the stretch deformation, x_s. K and B are functions of x_s, such that $$K(x_s)=K$$ when there is no slack or you are not simulating slack. Otherwise, $$K(x_s)=0$$ when slack occurs at $$x_s<0$$. The same logic applies for B. The terms that involve mass only apply when you select the Model mass parameter.

When you select Model variable rest length, takes the length as an input at port L. To input the rest length, use a Translational Motion Sensor block to determine the motion of the cable segment. The block saturates the rest length such that

$$L_{rest}=max(L-x_s,L_{min})$$

When you select Model variable rest length and Model mass, the block uses the value of the Linear density parameter to determine the mass of the cable segment such that

$$\begin{array}{l}m= \mu L_{Rest}\\ f_{Mass,B}=\frac{m}{2}{\dot{v}}_B\\ f_{Mass,F}=\frac{m}{2}{\dot{v}}_F\end{array}$$

When you select Model variable rest length, Model mass, and Model gravity, the block applies gravity to each end of the cable segment, such that

$$\begin{array}{l}{f}_{Gravity}=mgcos(\theta )\\ f_{Gravity,B}=\frac{f_{Gravity}}{2}\\ f_{Gravity,F}=\frac{f_{Gravity}}{2}\end{array}$$

Positive cable velocity acts from port B to port F. Positive gravity acts downward according to the cable orientation.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Limitations

When you select the Model mass and Model variable rest length parameters, the block uses a quasi-static model to calculate force due to mass. The block does not account for the rate of change in the cable segment mass. You can use a Variable Mass block to include the effect of the varying mass on the tension due to mass.

Examples

Compound Pulley

A block and tackle system that is represented by the Belt Pulley and Cable blocks from the Simscape™ Driveline™ library. This compound pulley is rigged as a threefold purchase with two triple blocks. The system has a mechanical advantage of 6.

• Open Model

Elevator

Models an elevator system comprising a car with passengers, a counterweight, a hoist cable, and a compensating cable. The motor drives a top pulley. A PID controller senses the car's velocity and adjusts the motor torque to achieve the velocity command. In this scenario, the elevator starts at rest, moves upward at 1 m/s, stops, then moves downward at -1 m/s, and stops again. Sensors measure the car's height, velocity, and acceleration, as well as the motor's torque, power, and energy.

• Open Model

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

Hydromechanical Hoist

A hydromechanical hoist lifting a payload. An ideal hydraulic motor is driven by the pressure commanded by a controller. The controller estimates the current height of the payload by reading the angular velocity from the motor's flexible shaft. The rope is represented as a spring and damper, and the payload is modeled as a mass with gravitational force.

• Open Model

Ports

Input

L — Length

physical signal

Physical signal input port associated with the length between the instantaneous contact points at either end of the cable segment.

Dependencies

To enable this port, select Model variable rest length.

Conserving

B — Base contact location of cable

mechanical translational

Mechanical translational conserving port associated with the base instantaneous contact location of the cable segment.

F — Follower contact location of cable

mechanical translational

Mechanical translational conserving port associated with the follower instantaneous contact location of the cable segment.

Parameters

Model variable rest length — Variable rest length option

off (default) | on

Whether to model variable rest length. Variable length affects stiffness and damping. When you select Model mass, variable length affects the mass of the cable. When you select Model gravity, variable length affects the force acting on the cable due to gravity.

Minimum rest length — Minimum rest length

0.01 m (default) | positive scalar

Minimum rest length of the cable. The value of the Minimum rest length parameter represents the lower-bound of the cable length when simulating variable rest length. The block smoothly transitions to and from this value and saturates inputs below this value.

Dependencies

To enable this parameter, select Model variable rest length.

Stretch parameterization — Constant or tabulated parameterization

Constant stiffness and damping (default) | Tabulated stiffness and damping

Whether to parameterize the cable using constants or tabulated stiffness and damping values.

Rigidity — Cable rigidity

1000 N (default) | positive scalar

Effective rigidity of the cable segment. The value of this parameter is equivalent to the axial stiffness when the cable stretch motion is purely longitudinal.

Dependencies

To enable this parameter, select Model variable rest length and set Stretch parameterization to Constant stiffness and damping.

Stiffness — Resistance to deformation

1000 N/m (default) | positive scalar

Effective translational spring stiffness of the cable segment.

Dependencies

To enable this parameter, clear Model variable rest length and set Stretch parameterization to Constant stiffness and damping.

Damping — Tendency to dissipate energy

100 N/(m/s) (default) | positive scalar

Effective translational damping of the cable segment. When you select the Model slack parameter and $$x_s<0$$, the block ignores damping.

Dependencies

To enable this parameter, set Stretch parameterization to Constant stiffness and damping.

Stretch vector — Stretch displacement

[.1, .2, .5, 1] m (default) | vector

Stretch displacement of a given point along the cable. The vector must have a minimum length of two and must be strictly increasing. The block determines the displacement as a function of the cable velocity.

Dependencies

To enable this parameter, clear Model variable rest length and set Stretch parameterization to Tabulated stiffness and damping.

Stiffness vector — Tabular energy dissipation

[500, 520, 540, 540] N/m (default) | vector of nonnegative values

Cable stiffness for a given stretch displacement. The elements in this parameter correspond one-to-one with the Stretch vector parameter.

Dependencies

To enable this parameter, clear Model variable rest length and set Stretch parameterization to Tabulated stiffness and damping.

Damping vector — Tabular damping

[50, 60, 80, 80] N*s/m (default) | vector of nonnegative values

Cable damping for a given stretch displacement. The elements in this parameter correspond one-to-one with the Stretch vector parameter.

Dependencies

To enable this parameter, clear Model variable rest length and set Stretch parameterization to Tabulated stiffness and damping.

Rest length vector, Lr — Tabulated rest length

[.25, .5, 1] m (default) | vector of length M

Vector of rest length values, L_Rest.

Dependencies

To enable this parameter, select Model variable rest length and set Stretch parameterization to Tabulated stiffness and damping.

Stretch per rest length vector, s/Lr — Tabulated stretch per rest length

[.01, .02, .1, .25] (default) | vector of length N

Vector of stretch values for a given rest length, s/L_Rest. The elements correspond one-to-one with the Rest length vector, Lr parameter.

Dependencies

To enable this parameter, select Model variable rest length and set Stretch parameterization to Tabulated stiffness and damping.

Stiffness table (Lr, s/Lr) — Tabulated stiffness

[500, 600, 600, 500; 250, 300, 300, 250; 125, 150, 150, 125] N/m (default) | MxN matrix

Table of stiffness values for a given rest length, L_Rest, and stretch, s/L_Rest.

Dependencies

To enable this parameter, select Model variable rest length and set Stretch parameterization to Tabulated stiffness and damping.

Damping table (Lr, s/Lr) — Tabulated damping

[50, 60, 60, 50; 50, 60, 60, 50; 50, 60, 60, 50] N*s/m (default) | MxN matrix

Table of damping values for a given rest length, L_Rest, and stretch, s/L_Rest.

Dependencies

To enable this parameter, select Model variable rest length and set Stretch parameterization to Tabulated stiffness and damping.

Model slack — Slack parameterization option

off (default) | on

Whether to model slack. The block does not transfer spring force when the cable is not in tension. When you select this parameter, the Cable block is equivalent to a Translational Hard Stop block with Upper bound set to 0 and Lower bound set to -inf. For more information, see Translational Hard Stop.

Slack model — Slack transition behavior

Stiffness and damping applied smoothly through transition region, damped rebound (default) | Full stiffness and damping applied at bounds, undamped rebound | ...

Stiffness and rebound options for the slack model. The slack model is equivalent to a Translational Hard Stop block. You can choose from these options:

• Stiffness and damping applied smoothly through transition region, damped rebound

• Full stiffness and damping applied at bounds, undamped rebound

• Full stiffness and damping applied at bounds, damped rebound

Dependencies

To enable this parameter, select Model slack.

Linear density — Linear density

0.2 kg/m (default) | positive scalar

Linear density of the cable segment, μ.

Dependencies

To enable this parameter, select Model variable rest length and select either Model mass or Model slack.

Transition region — Region of partial slack effects

0.1 mm (default) | positive scalar

Distance from full compression or full extension where the effects of stiffness and damping are partially applied. When you set Slack model to Stiffness and damping applied smoothly through transition region, damped rebound, the block smoothly transitions the onset of stiffness and damping as the spring approaches full extension or full compression.

Dependencies

To enable this parameter, select Model variable rest length or clear Model variable rest length and select Model slack and set Slack model to Stiffness and damping applied smoothly through transition region.

Model mass — Mass parameterization option

Off (default) | On

Whether to model mass. When you select Model mass, the block considers the mass of the cable segment that it represents. Including mass can help initialize some models but can also be more computationally costly.

Dependencies

To enable this parameter, clear the Model slack parameter.

Mass — Cable segment mass

1 kg (default) | positive scalar

Mass of the cable segment that the block represents. The block distributes half of the total mass to each end of the cable.

Dependencies

To enable this parameter, clear Model variable rest lengthselect Model mass or Model slack.

Model gravity — Gravity option

off (default) | on

Whether to model gravity.

Dependencies

To enable this parameter, select Model mass or Model slack.

Gravitational acceleration, g — Gravitational acceleration

9.81 m/s^2 (default) | positive scalar

Acceleration due to gravity. You can specify the direction of positive acceleration with the Angle of gravity relative to positive direction, θ parameter.

Dependencies

To enable this parameter, select Model mass or Model slack and Model gravity.

Angle of gravity relative to positive direction, θ — Positive gravity angle

0 deg (default) | scalar

Angle at which the value of the Gravitational acceleration, g parameter is positive, θ. A value of 0 represents downward acceleration.

Dependencies

To enable this parameter, select Model mass or Model slack and Model gravity.

Warn if cable loses tension — Lost tension warning option

off (default) | on

Whether to generate a warning when the cable segment is no longer in tension. Use this parameter to identify if your system experiences instances of slack.

Error if cable exceeds maximum tension — Maximum tension error option

off (default) | on

Whether to generate an error when the cable segment exceeds the value of the Cable maximum tension parameter.

Cable maximum tension — Maximum allowable tension force in cable segment

1e5 N (default) | positive scalar

Tension value error target. When the tension in the cable segment exceeds this parameter, the block generates an error.

Dependencies

To enable this parameter, select Error if cable exceeds maximum tension.

Extended Capabilities

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

Version History

Introduced in R2021a

R2024b: Variable rest length

Represent a connection with variable rest length. When you select Model variable rest length, the block generates results with higher accuracy for travelling pulley applications.

Additionally, you can now include the force of gravity. To enable the Model gravity parameter, select the Model mass parameter.

R2023b: Tabular stiffness and damping

You can set the new Stretch parameterization parameter to Tabulated to specify tabulated data for the cable behavior. The associated Stretch vector, Stiffness vector, and Damping vector parameters are also new. These parameters have been updated to support block enhancements:

Old Parameter	New Parameter
Rope model	Model slack
Maximum tension	Specify maximum tension
Tension warning	Warn if cable loses tension

R2023b: Name change

The Rope block was renamed to the Cable block.