Translational Hard Stop

Double-sided translational hard stop

Library:
Simscape / Foundation Library / Mechanical / Translational Elements

Description

The Translational Hard Stop block represents a double-sided mechanical translational hard stop that restricts motion of a body between upper and lower bounds. 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, damping is introduced as the block’s parameter, thus making it possible to account for energy loss. The schematic shows the idealization of the mechanical translational hard stop adopted in the block.

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

$F = {\begin{array}{l} K_{p} \cdot (x - g_{p}) + D_{p} \cdot v & for x \geq g_{p} \\ 0 & for g_{n} < x < g_{p} \\ K_{n} \cdot (x - g_{n}) + D_{n} \cdot v & for x \leq g_{n} \end{array}$

$v = \frac{d x}{d t}$

where

F is interaction force 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.
x is the slider 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.
v is the slider velocity.
t is time.

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

$F = {\begin{array}{l} K_{p} \cdot (x - g_{p}) + D_{p} \cdot v \cdot g e (v, 0) & for x \geq g_{p} \\ 0 & for g_{n} < x < g_{p} \\ K_{n} \cdot (x - g_{n}) + D_{n} \cdot v \cdot l e (v, 0) & for x \leq g_{n} \end{array}$

Relational functions ge (greater or equal) and le (less or equal) do not generate zero crossings when 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 force 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 forces 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 force 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

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`R` — Rod (slider)
mechanical translational

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

`C` — Case
mechanical translational

Mechanical translational conserving port associated with the case.

Parameters

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`Upper bound` — Gap between slider and upper bound
`0.1 m` (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 m` (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` (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` (default)

`Contact damping at upper bound` — Dissipating property at upper bound
`150 N/(m/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
`150 N/(m/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 force 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 force. In this sense, damping can reduce or eliminate the force 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 force is ramped up
`0.1 mm` (default)

Region where the force 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.

Model Examples

Mechanical System with Translational Hard Stop

Two masses connected by a hard stop. Mass 1 is driven by an Ideal Velocity Source. As the velocity input changes direction, Mass 2 will stay at rest until Mass 1 reaches the other end of the backlash modeled by the Translational Hard Stop. Plotting the displacement of Mass 2 against the displacement of the Mass 1 produces a typical hysteresis curve.

Translational Hard Stop