Double-sided rotational hard stop

Mechanical Rotational Elements

The Rotational Hard Stop block represents a double-sided mechanical rotational hard stop that restricts motion of a body between upper and lower bounds. Both ports of the block are of mechanical rotational type. The impact interaction between the slider and the stops is assumed to be elastic. The stop is implemented as a spring that comes into contact with the slider as the gap is cleared. The spring 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 a block parameter, thus making it possible to account for energy loss.

The hard stop is described with the following equations:

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

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

$${\omega}_{R}=\frac{d{\phi}_{R}}{dt}$$

$${\omega}_{C}=\frac{d{\phi}_{C}}{dt}$$

where

`T` | Interaction torque between the slider and the case |

`δ` | Relative angular 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 |

ω_{R}, ω_{C} | Absolute angular velocities of terminals R and C, respectively |

φ_{R}, φ_{C} | Absolute angular 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 clockwise 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 torque from port R to port C when the gap in positive direction is cleared up.

**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`

rad.**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`

rad.**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/rad.**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/rad.**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 0.01 N*m*s/rad.

**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 0.01 N*m*s/rad.

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.

The block has the following ports:

`R`

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

`C`

Mechanical rotational conserving port associated with the case.

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