Engee documentation

Translational Hard Stop

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Two-way translational rigid limiter.

blockType: AcausalFoundation.Mechanical.Translational.Elements.HardStop

translational hard stop

Path in the library:

/Physical Modeling/Fundamental/Mechanical/Translational/Elements/Translational Hard Stop

Description

Block Translational Hard Stop It represents a two-sided mechanical translational rigid limiter that restricts the movement of the body between the upper and lower boundaries.

translational hard stop 1 en

The stem corresponds to port R, and the body corresponds to port C. The unit transmits force from port R to port C when the gap is closed in the positive direction.

The block calculates the position of the rod based on the speed of the rod .

If the stem length is , and the position of the rod on the negative side Then . The block assumes that the rod length is 0 and the length is and they are not modeled, but in the diagram these symbols are used to explain the basic design of the rigid limiter.

Meaning — the initial clearance on the positive side, measured from :

  • In order for the positive gap to be open, the value it should be positive.

  • Negative value this means that the rod penetrates beyond the upper limit.

  • The gap is closed if .

Meaning — the initial gap on the negative side, measured from :

  • In order for the negative gap to be open, the value it should be negative.

  • Positive value this means that the rod penetrates beyond the lower boundary.

  • The gap is closed if .

The block provides several modeling options.:

  • Three options based on stiffness and damping. These models use similar basic equations and differ in how stiffness and damping are applied at the boundaries.

  • A simulation option based on the coefficient of elastic recovery upon impact. This model differs from the other three in that it uses a mode diagram to represent the behavior of a hard stop.

Models based on stiffness and damping

It is assumed that the impact interaction of the rod and the limiters is elastic. The limiter is presented in the form of a spring that comes into contact with the rod when the gap is eliminated. The spring counteracts the movement of the rod inside the limiter with a force linearly proportional to the magnitude of this movement. To account for energy dissipation and inelastic effects, damping is introduced as a block parameter, which allows energy losses to be taken into account.

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

,

where

  • — the force of interaction between the rod and the body;

  • — the initial gap between the rod and the upper limit;

  • — the initial gap between the rod and the lower boundary;

  • — stem position;

  • — stiffness of the contact at the upper boundary;

  • — stiffness of the contact at the lower boundary;

  • — the damping coefficient at the upper limit;

  • — the damping coefficient at the lower limit;

  • — the speed of the rod;

  • — the time.

In the hard stop model Full stiffness and damping applied at bounds, undamped rebound The equations contain additional terms and . These conditions ensure that no damping is applied during rebound.

The default hard stop model Stiffness and damping applied smoothly through transition region, damped rebound adds two transition regions to the equations, one at each boundary. As the rod passes through the transition area, the block smoothly increases the force from zero to full value. At the end of the transition area, full rigidity and damping are applied. Upon rebound, both stiffness and damping forces gradually decrease to zero. These equations also use comparison functions. ge and le.

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

A model based on the coefficient of elastic recovery upon impact

Unlike models based on rigidity and damping, this model does not allow the rod to penetrate into the rigid limiters. The behavior of the hard limiter is presented as a mode diagram with three regular and three instant modes.:

  • FREE — there is no force transfer between the rod and the housing.

  • CONTACT_UPPER — the positive gap is closed.

  • CONTACT_LOWER — the negative gap is closed.

  • RELEASE_UPPER — Instant mode required to switch from CONTACT_UPPER to FREE.

  • RELEASE_LOWER — Instant mode required to switch from CONTACT_LOWER to FREE.

  • IMPACT — Instant mode used when the rod is bouncing.

If the rod hits the housing slowly, at a speed less than the threshold speed of static contact, the rod and the housing remain in contact. Otherwise, the rod bounces off. Upon rebound, the rod loses speed due to the elastic recovery coefficient. In any of the contact modes, the rod speed is . To switch from contact mode to free mode, a force exceeding the threshold value of the static contact opening force must be applied to the rod, and the transition must pass through the instantaneous opening mode to set the initial velocity.

This simulation option improves simulation performance because static contact mode does not require the unit to calculate a hard stopping force when the unit is in contact mode.

Ports

Conserving

# R — stock
translational mechanics

Details

A mechanical translational port corresponding to the rod, which moves between the limiters mounted on the housing.

Program usage name

rod_flange

# C — housing
translational mechanics

Details

Mechanical translational port corresponding to the body.

Program usage name

case_flange

Parameters

Parameters

# Upper bound — the gap between the rod and the upper boundary
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The gap between the stem and the upper border. The direction is set in the local coordinate system, with the rod located at the origin. The positive value of the parameter determines the gap between the rod and the upper limit. A negative value sets the rod as penetrating the upper boundary.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.1 m
Program usage name

upper_bound
Evaluatable

Yes

# Lower bound — the gap between the rod and the lower boundary
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The gap between the rod and the lower border. The direction is set in the local coordinate system, with the rod located at the origin. The negative value of the parameter determines the gap between the rod and the lower boundary. A positive value sets the rod as penetrating the lower boundary.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

-0.1 m
Program usage name

lower_bound
Evaluatable

Yes

# Hard stop model — choosing a hard stop model
Stiffness and damping applied smoothly through transition region, damped rebound | Full stiffness and damping applied at bounds, undamped rebound | Full stiffness and damping applied at bounds, damped rebound | Based on coefficient of restitution

Details

Select a set of assumptions when the block is running:

  • Stiffness and damping applied smoothly through transition region, damped rebound — a transition region is set in which the resistance force increases from zero. At the end of the transition area, full rigidity and damping are applied. This model uses rebound damping, but it is limited by the value of the moment of stiffness. In this sense, damping can reduce or eliminate the torque provided by stiffness, but never exceed it. All equations are smooth.

  • Full stiffness and damping applied at bounds, undamped rebound — This model has full rigidity and damping applied on impact at the upper and lower boundaries, without damping on rebound. The equations do not result in a zero crossing when the velocity changes sign, but there is a zero crossing at the boundaries based on position. The absence of damping during rebound helps to quickly remove the rod from this position. This model has nonlinear equations.

  • Full stiffness and damping applied at bounds, damped rebound — This model has full rigidity and damping applied on impact at the upper and lower boundaries, with damping applied on rebound too. The equations switch linearly, but result in a zero crossing based on position.

  • Based on coefficient of restitution — This model uses a mode diagram with regular and instantaneous modes to represent the behavior of a hard stop. All equations are smooth and have no zero crossings. This simulation option improves simulation performance.

Values

Stiffness and damping applied smoothly through transition region, damped rebound | Full stiffness and damping applied at bounds, undamped rebound | Full stiffness and damping applied at bounds, damped rebound | Based on coefficient of restitution
Default value

Stiffness and damping applied smoothly through transition region, damped rebound
Program usage name

model
Evaluatable

No

# Contact stiffness at upper bound — the coefficient of collision elasticity at the upper boundary
N/m | mN/m | kN/m | MN/m | GN/m | kgf/m | lbf/ft | lbf/in

Details

This parameter determines the collision elasticity property when the rod reaches the upper limit. The higher the value of the parameter, the less the bodies penetrate into each other, the more rigid the limiter becomes. A lower parameter value makes contact softer, but overall improves convergence and computational efficiency.

Dependencies

To use this parameter, set for the parameter Hard stop model one of the values is:

  • Stiffness and damping applied smoothly through transition region, damped rebound;

  • Full stiffness and damping applied at bounds, undamped rebound;

  • Full stiffness and damping applied at bounds, damped rebound.

Units

N/m | mN/m | kN/m | MN/m | GN/m | kgf/m | lbf/ft | lbf/in
Default value

1e6 N/m
Program usage name

k_upper_bound
Evaluatable

Yes

# Contact stiffness at lower bound — coefficient of elasticity at the lower boundary
N/m | mN/m | kN/m | MN/m | GN/m | kgf/m | lbf/ft | lbf/in

Details

This parameter determines the collision elasticity property when the rod reaches the lower limit. The higher the value of the parameter, the less the bodies penetrate into each other, the more rigid the limiter becomes. A lower parameter value makes contact softer, but overall improves convergence and computational efficiency.

Dependencies

To use this parameter, set for the parameter Hard stop model one of the values is:

  • Stiffness and damping applied smoothly through transition region, damped rebound;

  • Full stiffness and damping applied at bounds, undamped rebound;

  • Full stiffness and damping applied at bounds, damped rebound.

Units

N/m | mN/m | kN/m | MN/m | GN/m | kgf/m | lbf/ft | lbf/in
Default value

1e6 N/m
Program usage name

k_lower_bound
Evaluatable

Yes

# Contact damping at upper bound — damping coefficient at the upper limit
N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in

Details

This parameter determines the collision damping when the rod reaches the upper limit. The higher the value of the parameter, the more energy is dissipated during the interaction.

Dependencies

To use this parameter, set for the parameter Hard stop model one of the values is:

  • Stiffness and damping applied smoothly through transition region, damped rebound;

  • Full stiffness and damping applied at bounds, undamped rebound;

  • Full stiffness and damping applied at bounds, damped rebound.

Units

N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in
Default value

150.0 N*s/m
Program usage name

C_upper_bound
Evaluatable

Yes

# Contact damping at lower bound — damping coefficient at the lower limit
N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in

Details

This parameter determines the collision damping when the rod reaches the lower limit. The higher the value of the parameter, the more energy is dissipated during the interaction.

Dependencies

To use this parameter, set for the parameter Hard stop model one of the values is:

  • Stiffness and damping applied smoothly through transition region, damped rebound;

  • Full stiffness and damping applied at bounds, undamped rebound;

  • Full stiffness and damping applied at bounds, damped rebound.

Units

N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in
Default value

150.0 N*s/m
Program usage name

C_lower_bound
Evaluatable

Yes

# Transition region — the area where the power increases
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The area where the force increases from zero to its full value. At the end of the transition area, full rigidity and damping are applied.

Dependencies

To use this parameter, set for the parameter Hard stop model meaning Stiffness and damping applied smoothly through transition region, damped rebound.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.1 mm
Program usage name

transition_region
Evaluatable

Yes

# Coefficient of restitution — the ratio of the final and initial relative velocity between the rod and the limiter after a collision

Details

The ratio of the final and initial relative velocity between the rod and the limiter after the rod rebounds.

Dependencies

To use this parameter, set for the parameter Hard stop model meaning Based on coefficient of restitution.

Default value

0.7
Program usage name

restitution_coefficient
Evaluatable

Yes

# Static contact speed threshold — the threshold value of the relative velocity between the rod and the limiter before the collision
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

The threshold value of the relative velocity between the rod and the limiter before the collision. If the rod hits the housing at a speed lower than the value of this parameter, they remain in contact. Otherwise, the rod bounces off. To avoid simulating static contact between the rod and the housing, set this parameter to 0.

Dependencies

To use this parameter, set for the parameter Hard stop model meaning Based on coefficient of restitution.

Units

m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn
Default value

0.001 m/s
Program usage name

v_static_contact_threshold
Evaluatable

Yes

# Static contact release force threshold — the threshold value of the force required to transition from the contact state to the free state
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

Details

The minimum force required to remove the rod from the static contact state.

Dependencies

To use this parameter, set for the parameter Hard stop model meaning Based on coefficient of restitution.

Units

N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf
Default value

0.001 N
Program usage name

F_static_contact_release_threshold
Evaluatable

Yes

Examples