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Double-sided translational hard stop

Mechanical Translational Elements

The Translational Hard Stop block represents a double-sided mechanical translational hard stop that restricts motion of a body between upper and lower bounds. Both ports of the block are of mechanical translational type. The impact interaction between the slider and the stops is assumed to be elastic. This means that the stop is represented as a spring that comes into contact with the slider as the gap is cleared and opposes slider penetration into the stop with the force linearly proportional to this penetration. To account for energy dissipation and nonelastic effects, the damping is introduced as the block's parameter, thus making it possible to account for energy loss. The following schematic shows the idealization of the mechanical translational hard stop adopted in the block:

The hard stop is described with the following equations:

$$F=\{\begin{array}{ll}{K}_{p}\xb7\delta +{D}_{p}\left({v}_{R}-{v}_{C}\right)\hfill & \text{for}\delta ={g}_{p}\hfill \\ 0\hfill & \text{for}{g}_{n}\delta {g}_{p}\hfill \\ {K}_{n}\xb7\delta +{D}_{n}\left({v}_{R}-{v}_{C}\right)\hfill & \text{for}\delta ={g}_{n}\hfill \end{array}$$

$$\delta ={x}_{R}-{x}_{C}$$

$${v}_{R}=\frac{d{x}_{R}}{dt}$$

$${v}_{C}=\frac{d{x}_{C}}{dt}$$

where

`F` | Interaction force between the slider and the case |

δ | Relative displacement between the slider and the case |

`g` | Gap between the slider and the case in positive direction |

`g` | Gap between the slider and the case in negative direction |

`v` | Absolute velocities of terminals R and C, respectively |

`x` | Absolute displacements of terminals R and C, respectively |

`K` | Contact stiffness at positive restriction |

`K` | Contact stiffness at negative restriction |

`D` | Damping coefficient at positive restriction |

`D` | Damping coefficient at negative restriction |

`t` | Time |

The equations are derived with respect to the local coordinate system whose axis is directed from port R to port C. The terms "positive" and "negative" in the variable descriptions refer to this coordinate system, and the gap in negative direction must be specified with negative value. If the local coordinate system is not aligned with the globally assigned positive direction, the gaps interchange their values with respective sign adjustment.

The block is oriented from R to C. This means that the block transmits force from port R to port C when the gap in positive direction is cleared up.

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

**Upper bound**Gap between the slider and the upper bound. The direction is specified with respect to the local coordinate system, with the slider located in the origin. A positive value of the parameter specifies the gap between the slider and the upper bound. A negative value sets the slider as penetrating into the upper bound. The default value is

`0.1`

m.**Lower bound**Gap between the slider and the lower bound. The direction is specified with respect to the local coordinate system, with the slider located in the origin. A negative value of the parameter specifies the gap between the slider and the lower bound. A positive value sets the slider as penetrating into the lower bound. The default value is

`-0.1`

m.**Contact stiffness at upper bound**The parameter specifies the elastic property of colliding bodies when the slider hits the upper bound. The greater the value of the parameter, the less the bodies penetrate into each other, the more rigid the impact becomes. Lesser value of the parameter makes contact softer, but generally improves convergence and computational efficiency. The default value is

`1e6`

N/m.**Contact stiffness at lower bound**The parameter specifies the elastic property of colliding bodies when the slider hits the lower bound. The greater the value of the parameter, the less the bodies penetrate into each other, the more rigid the impact becomes. Lesser value of the parameter makes contact softer, but generally improves convergence and computational efficiency. The default value is

`1e6`

N/m.**Contact damping at upper bound**The parameter specifies dissipating property of colliding bodies when the slider hits the upper bound. At zero damping, the impact is close to an absolutely elastic one. The greater the value of the parameter, the more energy dissipates during an interaction. Keep in mind that damping affects slider motion as long as the slider is in contact with the stop, including the period when slider is pulled back from the contact. For computational efficiency and convergence reasons, MathWorks recommends that you assign a nonzero value to this parameter. The default value is 150 N*s/m.

**Contact damping at lower bound**The parameter specifies dissipating property of colliding bodies when the slider hits the lower bound. At zero damping, the impact is close to an absolutely elastic one. The greater the value of the parameter, the more energy dissipates during an interaction. Keep in mind that damping affects slider motion as long as the slider is in contact with the stop, including the period when slider is pulled back from the contact. For computational efficiency and convergence reasons, MathWorks recommends that you assign a nonzero value to this parameter. The default value is 150 N*s/m.

The block has the following ports:

`R`

Mechanical translational conserving port associated with the slider that travels between stops installed on the case.

`C`

Mechanical translational conserving port associated with the case.

The Mechanical System with Translational Hard Stop example illustrates the use of the Translational Hard Stop block in mechanical systems. Two masses are interacting through a hard stop. The mass on the left is driven by an ideal velocity source. Plotting the displacement of the second mass against the displacement of the first mass produces a typical hysteresis curve.

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