Rotational Hard Stop
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Two-way rotary rigid limiter.
blockType: AcausalFoundation.Mechanical.Rotational.Elements.HardStop
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Description
Block Rotational Hard Stop It is a two-sided mechanical rigid stopper that restricts the rotation of the body between the upper and lower boundaries of the angular position. Both ports of the unit are of the mechanical rotary type. It is assumed that the impact interaction between the shaft and the limiters is elastic. The limiter is made in the form of a spring that comes into contact with the shaft when the gap is eliminated. The spring counteracts the movement of the shaft inside the limiter with a torque 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 shaft corresponds to port R, and the body corresponds to port C. The unit transmits the torque from port R to port C when the gap is closed in the positive direction.
Angular position of the shaft It is determined based on the angular velocity of the shaft .
If the angle of the shaft arc is , and the angular position of the shaft on the negative side Then . The block assumes that the arc angle of the shaft is 0 and the angles are 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 :
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To open the gap in the positive direction, the value it should be positive.
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Negative value this means that the rod penetrates beyond the upper limit.
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The gap is closed if .
Meaning — the initial gap on the negative side, measured from :
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To open the gap in the negative direction, the value it should be negative.
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Positive value this means that the rod penetrates beyond the lower boundary.
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The gap is closed if .
The block provides several modeling options:
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Three options based on stiffness and damping. These models use similar basic equations and differ in how stiffness and damping are modeled at the boundaries.
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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 between the shaft and the limiters is elastic. The limiter is made in the form of a spring that comes into contact with the shaft when the gap is eliminated. The spring counteracts the movement of the shaft inside the limiter with a torque 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, is described by the following equations:
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where
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— the torque between the shaft and the housing;
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— the initial angle between the shaft and the upper boundary of the angular position;
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— the initial angle between the shaft and the lower boundary of the angular position;
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— angular position of the shaft;
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— stiffness of the contact at the upper boundary;
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— stiffness of the contact at the lower boundary;
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— the damping coefficient at the upper limit;
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— the damping coefficient at the lower limit;
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— angular velocity of the shaft;
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— 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, add two transition regions to the equations, one at each boundary. As the shaft moves through the transition area, the unit smoothly increases the torque from zero to full value. At the end of the transition area, full rigidity and damping are applied. Upon rebound, both stiffness and damping moments smoothly decrease back 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 torque from port R to port C when the gap in the positive direction is closed.
A model based on the coefficient of elastic recovery upon impact
Unlike models based on rigidity and damping, this model does not allow shaft penetration into rigid limiters. The behavior of the hard limiter is presented as a mode diagram with three regular and three instant modes.:
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FREE— there is no torque transfer between the shaft and the housing. -
CONTACT_UPPER— the gap in the positive direction is closed. -
CONTACT_LOWER— the gap in the negative direction is closed. -
RELEASE_UPPER— Instant mode required to switch fromCONTACT_UPPERtoFREE. -
RELEASE_LOWER— Instant mode required to switch fromCONTACT_LOWERtoFREE. -
IMPACT— Instant mode used when the rod is bouncing.
If the shaft hits the housing slowly, at a speed less than the threshold speed of static contact, the shaft and the housing remain in contact. Otherwise, the shaft bounces off. Upon rebound, the shaft loses speed due to the elastic recovery coefficient. In any of the contact modes, the shaft speed is . To switch from contact mode to free mode, a torque exceeding the threshold value of the moment of static friction must be applied to the shaft, and the transition must pass through the instantaneous opening mode to set the initial speed.
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
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R
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shaft
rotational mechanics
Details
A mechanical rotary port corresponding to a shaft that rotates between limiters mounted on the housing.
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C
—
body
rotational mechanics
Details
A mechanical rotary port corresponding to the body.
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Parameters
Parameters
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Upper bound —
the initial angle between the shaft and the upper boundary
rad | deg | rev | mrad | arcsec | arcmin | gon
Details
The angle between the shaft and the upper boundary. The direction is set in the local coordinate system, with the shaft located at its starting point. The positive value of the parameter determines the initial angle between the shaft and the upper boundary. A negative value defines the shaft as penetrating the upper boundary.
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Yes |
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Lower bound —
the initial angle between the shaft and the lower boundary
rad | deg | rev | mrad | arcsec | arcmin | gon
Details
The angle between the shaft and the lower boundary. The direction is set in the local coordinate system, with the shaft located at its starting point. The negative value of the parameter determines the initial angle between the shaft and the upper boundary. A positive value defines the shaft as penetrating the upper boundary.
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Yes |
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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:
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Stiffness and damping applied smoothly through transition region, damped rebound— a transition region is set in which the resistance torque 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 shaft 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.
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No |
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Contact stiffness at upper bound —
coefficient of elasticity at the upper limit
N*m/rad | mN*m/rad | kN*m/rad | kgf*m/rad | lbf*ft/rad | N*m/deg | mN*m/deg | kN*m/deg | kgf*m/deg | lbf*ft/deg | W*s/rad | HP_DIN/rpm | HP_DIN*s/rad
Details
This parameter determines the degree of collision elasticity when the shaft reaches the upper limit. The higher the parameter value, the less the bodies penetrate each other, the harder the impact 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:
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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.
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
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Contact stiffness at lower bound —
coefficient of elasticity at the lower boundary
N*m/rad | mN*m/rad | kN*m/rad | kgf*m/rad | lbf*ft/rad | N*m/deg | mN*m/deg | kN*m/deg | kgf*m/deg | lbf*ft/deg | W*s/rad | HP_DIN/rpm | HP_DIN*s/rad
Details
This parameter determines the degree of collision elasticity when the shaft reaches the upper limit. The higher the parameter value, the less the bodies penetrate each other, the harder the impact 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.
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
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Contact damping at upper bound —
damping coefficient at the upper limit
N*m/(rad/s) | ft*lbf/(rad/s)
Details
This parameter determines the collision damping when the shaft reaches the upper limit. The higher the parameter value, 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:
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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 |
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
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Contact damping at lower bound —
damping coefficient at the lower limit
N*m/(rad/s) | ft*lbf/(rad/s)
Details
This parameter determines the collision damping when the shaft reaches the lower limit. The higher the parameter value, 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:
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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.
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |
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Transition region —
the area where the torque increases
rad | deg | rev | mrad | arcsec | arcmin | gon
Details
The area where the torque 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.
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| Evaluatable |
Yes |
# Coefficient of restitution — the ratio of the final and initial relative velocity between the shaft and the limiter after a collision
Details
The ratio of the final and initial relative velocity between the shaft and the limiter after the shaft rebounds.
Dependencies
To use this parameter, set for the parameter Hard stop model meaning Based on coefficient of restitution.
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| Evaluatable |
Yes |
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Static contact speed threshold —
the threshold value of the relative velocity between the shaft and the limiter before the collision
rad/s | deg/s | rad/min | deg/min | rpm | rps
Details
The threshold value of the relative velocity between the shaft and the limiter before the collision. If the shaft hits the housing at a speed lower than the value of this parameter, they remain in contact. Otherwise, the shaft bounces off. To avoid simulating static contact between the shaft 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.
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| Evaluatable |
Yes |
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Static contact release torque threshold —
the threshold value of the torque required for the transition from the contact state to the free state
N*m | uN*m | mN*m | kN*m | MN*m | GN*m | kgf*m | lbf*in | lbf*ft
Details
The minimum value of the torque required to bring the shaft out of static contact.
Dependencies
To use this parameter, set for the parameter Hard stop model meaning Based on coefficient of restitution.
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| Evaluatable |
Yes |