Rod

R2026b

Axially flexible bar or cable

• 

Rod block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

Libraries:
Simscape / Driveline / Couplings & Drives

Description

The Rod block represents an axially flexible bar or cable in tension or compression.

To represent the bar or cable, the block uses a lumped parameter model, where N is the value of the Number of flexible elements parameter. The block uses N spring and damper sets to connect N+1 lumped masses in series. The spring represents elasticity. The damper represents material damping. The figure demonstrates an equivalent network to the Rod block with the Number of flexible elements parameter set to 3.

When you set Parameterization to By stiffness and inertia or By material and geometry, the block evenly distributes the total mass of the rod over the mass blocks. The stiffness of the spring in each spring and damper circuit is equal to N times the stiffness of the rod material.

When you set Parameterization to By segment stiffness and inertia or By material and segment geometry, you define each segment by its individual properties. The block distributes the N flexible elements uniformly along the total rod length and interpolates the segment properties across the elements. The length of the vector parameters determines the number of segments.

Equations

The defining equations for the model are

$$\eta =2\zeta \sqrt{\frac{K\cdot m}{2}}$$

$$A=\frac{\pi (D^2-d^2)}{4}$$

$$K=\frac{E\cdot A}{L}$$

$$m=A\cdot L\cdot \rho$$

where:

• η is the damping of the rod.

• ς is the damping ratio of the rod material.

• K is the stiffness of the rod.

• A is the cross-sectional area of the rod.

• D is the outer diameter of the rod.

• d is the inner diameter of the rod, where

  • d = 0 for a solid rod.

  • d > 0 for an annular, or hollow, rod.

• E is the Young's modulus, or the modulus of elasticity, of the rod material.

• L is the length of the rod.

• m is the mass of the rod.

• ρ is the density of the rod material.

When you set Parameterization to By segment stiffness and inertia or By material and segment geometry, the block defines the mass, stiffness, and damping coefficient for each flexible element. x_j is the location of the j^th node, where j ∈ [1, 2, 3, … N+1]. The block distributes the nodes uniformly along the rod length, and assigns the mass to each flexible element, such that

$$M_i={\displaystyle {\int }_{x_i}^{x_{i+1}}\rho (x)A(x)dx,}$$

where, i ∈ [1, 2, 3, … N]. The block assigns the stiffness of the spring in each flexible element, such that

$$k_i={\left({\displaystyle {\int }_{x_i}^{x_{i+1}}\frac{1}{E(x)A(x)}}dx\right)}^{-1}.$$

The damping coefficient in each flexible element is

$${\eta }_i=2\zeta \sqrt{\frac{k_i{M}_i}{2}}.$$

In each segment, the block treats ρ(x), E(x), and A(x) as uniform and interpolates the segment properties across elements by using the tablelookup function.

The mass assigned to each nodal point is

$$m_j=\frac{1}{2}(M_{j-1}+M_j)\text{for }j\in [2,3,\dots ,N].$$

For the nodes at the two ends of the rod,

$$\begin{array}{l}{m}_1=\frac{1}{2}{M}_1\\ m_{N+1}=\frac{1}{2}{M}_N\end{array}$$

Assumptions and Limitations

• Cables do not go slack.

• Bars do not buckle.

• When you set Parameterization to By segment stiffness and inertia or By material and segment geometry, the block treats the material properties and cross-sectional geometry in each segment as uniform.

• The block does not support combinations of varying material properties and varying segment geometry.

Ports

Conserving

B — Base

translational mechanical

Translational conserving port associated with the rod or cable base.

Programmatic Use

Port: B

F — Follower

translational mechanical

Translational conserving port associated with the rod or cable follower.

Programmatic Use

Port: F

Parameters

Rod

Parameterization — Parameterization method

By stiffness and inertia (default) | By material and geometry | By segment stiffness and inertia | By material and segment geometry

Parameterization method for the rod. Select from these options:

• By stiffness and inertia — Specify uniform stiffness and mass for the entire rod.

• By material and geometry — Specify material properties and uniform geometry. The block computes the stiffness and mass from the geometry.

• By segment stiffness and inertia — Specify stiffness and mass for each segment individually as vectors.

• By material and segment geometry — Specify material properties and geometry for each segment. The block computes the stiffness and mass for each segment from the geometry.

Programmatic Use

Parameter:	parameterization
Values:	"sdl.enum.rodParameterization.stiffnessInertia" | "sdl.enum.rodParameterization.materialProperties" | "sdl.enum.rodParameterization.StiffnessInertiaVaried" | "sdl.enum.rodParameterization.MaterialPropertiesVaried"

Stiffness — Material stiffness

5e8 N/m (default) | nonnegative scalar

Stiffness of the bar of cable material.

Dependencies

To enable this parameter, set Parameterization to By stiffness and inertia.

Programmatic Use

Parameter: stiffness

Mass — Rod mass

20 kg (default) | positive scalar

Mass of the bar or cable.

Dependencies

To enable this parameter, set Parameterization to By stiffness and inertia.

Programmatic Use

Parameter: mass

Geometry — Rod cross-section

Solid (default) | Annular

Cross-sectional geometry of the bar or cable.

Dependencies

To enable this parameter, set Parameterization to By material and geometry or By material and segment geometry.

Programmatic Use

Parameter:	geometry
Values:	"sdl.enum.shaftConstruction.solid" | "sdl.enum.shaftConstruction.annular"

Length — Rod length

1 m (default) | positive scalar

Length of the bar or cable.

Dependencies

To enable this parameter, set Parameterization to By material and geometry.

Programmatic Use

Parameter: length

Outer diameter — Rod outer diameter

0.075 m (default) | positive scalar

Outer diameter of the bar or cable.

Dependencies

To enable this parameter, set Parameterization to By material and geometry.

Programmatic Use

Parameter: diameter_outer

Inner diameter — Rod inner diameter

0.050 m (default) | positive scalar

Rod inner diameter.

Dependencies

To enable this parameter, set Parameterization to By material and geometry and set Geometry to Annular.

Programmatic Use

Parameter: diameter_inner

Density — Material density

7.8e3 kg/m^3 (default) | positive scalar

Density of the bar or cable material.

Dependencies

To enable this parameter, set Parameterization to By material and geometry or By material and segment geometry.

Programmatic Use

Parameter: density

Young's modulus — Young's modulus

200e9 Pa (default) | positive scalar

Young's modulus of the bar or cable material.

Dependencies

To enable this parameter, set Parameterization to By material and geometry or By material and segment geometry.

Programmatic Use

Parameter: Youngs_modulus

Damping ratio — Material damping ratio

0.01 (default) | positive scalar

Bar or cable material damping ratio.

Programmatic Use

Parameter: damping_ratio

Number of flexible elements — Number of flexible elements

1 (default) | positive integer scalar

Number of flexible elements, N, that the block uses to approximate the bar or cable. A larger value of N increases the accuracy of the model but reduces simulation speed. A single-element model, where N = 1, approximates only the first eigenfrequency of the rod.

For higher-mode accuracy, increase N. For example, a 16-element model represents the four lowest eigenfrequencies with an accuracy of 0.1, 1.9, 1.6, and 5.3 percent.

When you set Parameterization to By segment stiffness and inertia or By material and segment geometry, the value of this parameter controls discretization accuracy.

Programmatic Use

Parameter: n_elements

Segment stiffness [B,...,F] — Segment stiffnesses

[400000, 200000, 100000] N/m (default) | vector of positive elements

Stiffness of each segment. Specify the parameter as a vector of positive elements, with the elements in order from the base to the follower.

Dependencies

To enable this parameter, set Parameterization to By segment stiffness and inertia.

Programmatic Use

Parameter: stiffnesses

Segment mass [B,...,F] — Segment masses

[10, 20, 30] kg (default) | vector of positive elements

Mass of each segment. Specify the parameter as a vector of positive elements, with the elements in order from the base to the follower.

Dependencies

To enable this parameter, set Parameterization to By segment stiffness and inertia.

Programmatic Use

Parameter: masses

Segment lengths [B,...,F] — Segment lengths

[1, 0.5, 0.25] m (default) | vector of positive elements

Length of each segment. Specify the parameter as a vector of positive elements, with the elements in order from the base to the follower.

Dependencies

To enable this parameter, set Parameterization to By material and segment geometry.

Programmatic Use

Parameter: lengths

Segment outer diameters [B,...,F] — Segment outer diameters

[0.085, 0.075, 0.065] m (default) | vector of positive elements

Outer diameter of each segment. Specify the parameter as a vector of positive elements, with the elements in order from the base to the follower.

Dependencies

To enable this parameter, set Parameterization to By material and segment geometry.

Programmatic Use

Parameter: diameter_outers

Segment inner diameters [B,...,F] — Segment inner diameters

[0.055, 0.050, 0.045] m (default) | vector of positive elements

Inner diameter of each segment. Specify the parameter as a vector of positive elements, with the elements in order from the base to the follower.

Dependencies

To enable this parameter, set Parameterization to By material and segment geometry and set Geometry to Annular.

Programmatic Use

Parameter: diameter_inners

Viscous Losses

Viscous friction coefficients at base (B) and follower (F) — Viscous friction coefficients

[0, 0] N/(m/s) (default) | nonnegative vector

Viscous friction coefficients at the base port, B, and the follower port, F.

Programmatic Use

Parameter: mu_visc

Extended Capabilities

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

Version History

Introduced in R2018b

R2026b: Model a shaft or rod of varying diameter

You can parameterize the block by individual segments. When you set Parameterization to:

• By segment stiffness and inertia, the block uses stiffness and inertia values to determine the behavior of each segment.

• By material and segment geometry, the block uses material and geometry to determine the behavior of each segment.