Rotational Hard Stop

Double-sided rotational hard stop

• Library:

• Simscape / Foundation Library / Mechanical / Rotational Elements

• 

Description

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 torque 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 basic hard stop model, Full stiffness and damping applied at bounds, damped rebound, is described with the following equations:

$$T=\{\begin{array}{ll}{K}_p\cdot \left(\phi -g_p\right)+D_p\cdot \omega \hfill & \text{for }\phi \ge g_p\hfill \\ 0\hfill & \text{for }{g}_n<\phi <g_p\hfill \\ K_n\cdot \left(\phi -g_n\right)+D_n\cdot \omega \hfill & \text{for }\phi \le g_n\hfill \end{array}$$

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

where

• T is interaction torque between the slider and the case.

• g_p is the initial gap between the slider and upper bound.

• g_n is the initial gap between the slider and lower bound.

• φ is the slider angular position.

• K_p is contact stiffness at upper bound.

• K_n is contact stiffness at lower bound.

• D_p is damping coefficient at upper bound.

• D_n is damping coefficient at lower bound.

• ω is the slider angular velocity.

• t is time.

In the Full stiffness and damping applied at bounds, undamped rebound hard stop model, equations contain additional terms, ge(ω,0) and le(ω,0). These terms ensure that damping is not applied on the rebound.

$$T=\{\begin{array}{ll}{K}_p\cdot \left(\phi -g_p\right)+D_p\cdot \omega \cdot ge\left(\omega ,0\right)\hfill & \text{for }\phi \ge g_p\hfill \\ 0\hfill & \text{for }{g}_n<\phi <g_p\hfill \\ K_n\cdot \left(\phi -g_n\right)+D_n\cdot \omega \cdot le\left(\omega ,0\right)\hfill & \text{for }\phi \le g_n\hfill \end{array}$$

Relational functions ge (greater or equal) and le (less or equal) do not generate zero crossings when angular velocity changes sign. For more information, see Enabling and Disabling Zero-Crossing Conditions in Simscape Language. However, the solver treats ge and le functions as nonlinear. Therefore, if simscape.findNonlinearBlocks indicates that the rest of your network is linear or switched linear, use the Full stiffness and damping applied at bounds, damped rebound model to improve performance.

The default hard stop model, Stiffness and damping applied smoothly through transition region, damped rebound, adds two transitional regions to the equations, one at each bound. While the slider travels through a transition region, the block smoothly ramps up the torque from zero to the full value. At the end of the transition region, the full stiffness and damping are applied. On the rebound, both stiffness and damping torques are smoothly decreased back to zero. These equations also use the ge and le relational functions, which do not produce zero crossings.

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

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.

Ports

Conserving

R — Rod (slider)

mechanical rotational

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

C — Case

mechanical rotational

Mechanical rotational conserving port associated with the case.

Parameters

Upper bound — Gap between slider and upper bound

0.1 rad (default)

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.

Lower bound — Gap between slider and lower bound

-0.1 rad (default)

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.

Contact stiffness at upper bound — Elasticity of collision at upper bound

1e6 N*m/rad (default)

This 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.

Contact stiffness at lower bound — Elasticity of collision at lower bound

1e6 N*m/rad (default)

This 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.

Contact damping at upper bound — Dissipating property at upper bound

0.01 N*m/(rad/s) (default)

This parameter specifies dissipating property of colliding bodies when the slider hits the upper bound. The greater the value of the parameter, the more energy dissipates during an interaction.

Contact damping at lower bound — Dissipating property at lower bound

0.01 N*m/(rad/s) (default)

This parameter specifies dissipating property of colliding bodies when the slider hits the lower bound. The greater the value of the parameter, the more energy dissipates during an interaction.

Hard stop model — Select the hard stop model

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

Select the hard stop model:

• Stiffness and damping applied smoothly through transition region, damped rebound — Specify a transition region, in which the torque is scaled from zero. At the end of the transition region, the full stiffness and damping are applied. This model has damping applied on the rebound, but it is limited to the value of the stiffness torque. In this sense, damping can reduce or eliminate the torque provided by the stiffness, but never exceed it. All equations are smooth and produce no zero crossings.

• Full stiffness and damping applied at bounds, undamped rebound — This model has full stiffness and damping applied with impact at upper and lower bounds, with no damping on the rebound. Equations produce no zero crossings when velocity changes sign, but there is a position-based zero crossing at the bounds. Having no damping on rebound helps to push the slider past this position quickly. This model has nonlinear equations.

• Full stiffness and damping applied at bounds, damped rebound — This model has full stiffness and damping applied with impact at upper and lower bounds, with damping applied on the rebound as well. Equations are switched linear, but produce position-based zero crossings. Use this hard stop model if simscape.findNonlinearBlocks indicates that this is the block that prevents the whole network from being switched linear.

Transition region — Region where torque is ramped up

0.001 rad (default)

Region where the torque is ramped up from zero to the full value. At the end of the transition region, the full stiffness and damping are applied.

Dependencies

Enabled when the Hard stop model parameter is set to Stiffness and damping applied smoothly through transition region, damped rebound.

Extended Capabilities

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

Version History

Introduced in R2007a