Package Modelica.​Mechanics.​MultiBody.​Forces
Components that exert forces and/or torques between frames

Information

This package contains components that exert forces and torques between two frame connectors, e.g., between two parts.

Content

Model	Description
WorldForce	External force acting at the frame to which this component is connected and defined by 3 input signals, that are interpreted as one vector resolved in frame world, frame_b or frame_resolve.
WorldTorque	External torque acting at the frame to which this component is connected and defined by 3 input signals, that are interpreted as one vector resolved in frame world, frame_b or frame_resolve.
WorldForceAndTorque	External force and external torque acting at the frame to which this component is connected and defined by 3+3 input signals, that are interpreted as a force and as a torque vector resolved in frame world, frame_b or frame_resolve.
Force	Force acting between two frames defined by 3 input signals resolved in frame world, frame_a, frame_b or in frame_resolve.
Torque	Torque acting between two frames defined by 3 input signals resolved in frame world, frame_a, frame_b or in frame_resolve.
ForceAndTorque	Force and torque acting between two frames defined by 3+3 input signals resolved in frame world, frame_a, frame_b or in frame_resolve.
LineForceWithMass	General line force component with an optional point mass on the connection line. The force law can be defined by a component of Modelica.Mechanics.Translational
LineForceWithTwoMasses	General line force component with two optional point masses on the connection line. The force law can be defined by a component of Modelica.Mechanics.Translational
Spring	Linear translational spring with optional mass
Damper	Linear (velocity dependent) damper
SpringDamperParallel	Linear spring and damper in parallel connection
SpringDamperSeries	Linear spring and damper in series connection

Extends from Modelica.​Icons.​SourcesPackage (Icon for packages containing sources).

Package Contents

Model Modelica.​Mechanics.​MultiBody.​Forces.​WorldForce
External force acting at frame_b, defined by 3 input signals and resolved in frame world, frame_b or frame_resolve

Information

The 3 signals of the force connector are interpreted as the x-, y- and z-coordinates of a force acting at the frame connector to which frame_b of this component is attached. Via parameter resolveInFrame it is defined, in which frame these coordinates shall be resolved:

If resolveInFrame = Types.ResolveInFrameB.frame_resolve, the force coordinates are with respect to the frame, that is connected to frame_resolve.

If force={100,0,0}, and for all parameters the default setting is used, then the interpretation is that a force of 100 N is acting along the positive x-axis of frame_b.

Note, the cut-torque in frame_b (frame_b.t) is always set to zero. Conceptually, a force and torque acts on the world frame in such a way that the force and torque balance between world.frame_b and frame_b is fulfilled. For efficiency reasons, this reaction torque is, however, not computed.

This force component is by default visualized as an arrow acting at the connector to which it is connected. The diameter and color of the arrow can be defined via variables diameter and color. The arrow points in the direction defined by the force signal. The length of the arrow is proportional to the length of the force vector using parameter N_to_m as scaling factor. For example, if N_to_m = 100 N/m, then a force of 350 N is displayed as an arrow of length 3.5 m.

An example how to use this model is given in the following figure:

This leads to the following animation

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialOneFrame_b (Base model for components providing one frame_b connector + outer world + assert to guarantee that the component is connected).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​WorldTorque
External torque acting at frame_b, defined by 3 input signals and resolved in frame world, frame_b or frame_resolve

Information

The 3 signals of the torque connector are interpreted as the x-, y- and z-coordinates of a torque acting at the frame connector to which frame_b of this component is attached. Via parameter resolveInFrame it is defined, in which frame these coordinates shall be resolved:

If resolveInFrame = Types.ResolveInFrameB.frame_resolve, the torque coordinates are with respect to the frame, that is connected to frame_resolve.

If torque={100,0,0}, and for all parameters the default setting is used, then the interpretation is that a torque of 100 N is acting along the positive x-axis of frame_b.

Note, the cut-force in frame_b (frame_b.f) is always set to zero. Conceptually, a force and torque acts on the world frame in such a way that the force and torque balance between world.frame_b and frame_b is fulfilled. For efficiency reasons, this reaction torque is, however, not computed.

This torque component is by default visualized as a double arrow acting at the connector to which it is connected. The diameter and color of the arrow can be defined via variables diameter and color. The double arrow points in the direction defined by the torque vector. The length of the double arrow is proportional to the length of the torque vector using parameter Nm_to_m as scaling factor. For example, if Nm_to_m = 100 Nm/m, then a torque of 350 Nm is displayed as an arrow of length 3.5 m.

An example how to use this model is given in the following figure:

This leads to the following animation

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialOneFrame_b (Base model for components providing one frame_b connector + outer world + assert to guarantee that the component is connected).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​WorldForceAndTorque
External force and torque acting at frame_b, defined by 3+3 input signals and resolved in frame world, frame_b or in frame_resolve

Information

The 3 signals of the force and torque connector are interpreted as the x-, y- and z-coordinates of a force and torque acting at the frame connector to which frame_b of this component is attached. Via parameter resolveInFrame it is defined, in which frame these coordinates shall be resolved:

If resolveInFrame = Types.ResolveInFrameB.frame_resolve, the force and torque coordinates are with respect to the frame, that is connected to frame_resolve.

If force={100,0,0}, and for all parameters the default setting is used, then the interpretation is that a force of 100 N is acting along the positive x-axis of frame_b.

Conceptually, a force and torque acts on the world frame in such a way that the force and torque balance between world.frame_b and frame_b is fulfilled. For efficiency reasons, this reaction torque is, however, not computed.

The force and torque are by default visualized as an arrow (force) and as a double arrow (torque) acting at the connector to which they are connected. The diameters and colors of the arrows can be defined via variables forceDiameter, torqueDiameter, forceColor and torqueColor. The arrows point in the directions defined by the force and torque vectors. The lengths of the arrows are proportional to the length of the force and torque vectors, respectively, using parameters N_to_m and Nm_to_m as scaling factors. For example, if N_to_m = 100 N/m, then a force of 350 N is displayed as an arrow of length 3.5 m.

An example how to use this model is given in the following figure:

This leads to the following animation

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialOneFrame_b (Base model for components providing one frame_b connector + outer world + assert to guarantee that the component is connected).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​Force
Force acting between two frames, defined by 3 input signals and resolved in frame world, frame_a, frame_b or frame_resolve

Information

The 3 signals of the force connector are interpreted as the x-, y- and z-coordinates of a force acting at the frame connector to which frame_b of this component is attached. Via parameter resolveInFrame it is defined, in which frame these coordinates shall be resolved:

If resolveInFrame = ResolveInFrameAB.frame_resolve, the force coordinates are with respect to the frame, that is connected to frame_resolve.

If force={100,0,0}, and for all parameters the default setting is used, then the interpretation is that a force of 100 N is acting along the positive x-axis of frame_b.

Note, the cut-torque in frame_b (frame_b.t) is always set to zero. Additionally, a force and torque acts on frame_a in such a way that the force and torque balance between frame_a and frame_b is fulfilled.

An example how to use this model is given in the following figure:

This leads to the following animation (the yellow cylinder characterizes the line between frame_a and frame_b of the Force component, i.e., the force acts with negative sign also on the opposite side of this cylinder, but for clarity this is not shown in the animation):

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialTwoFrames (Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​Torque
Torque acting between two frames, defined by 3 input signals and resolved in frame world, frame_a, frame_b or frame_resolve

Information

The 3 signals of the torque connector are interpreted as the x-, y- and z-coordinates of a torque acting at the frame connector to which frame_b of this component is attached. Via parameter resolveInFrame it is defined, in which frame these coordinates shall be resolved:

If resolveInFrame = ResolveInFrameAB.frame_resolve, the torque coordinates are with respect to the frame, that is connected to frame_resolve.

If torque={100,0,0}, and for all parameters the default setting is used, then the interpretation is that a torque of 100 N.m is acting along the positive x-axis of frame_b.

Note, the cut-forces in frame_a and frame_b (frame_a.f, frame_b.f) are always set to zero and the cut-torque at frame_a (frame_a.t) is the same as the cut-torque at frame_b (frame_b.t) but with opposite sign.

An example how to use this model is given in the following figure:

This leads to the following animation (the yellow cylinder characterizes the line between frame_a and frame_b of the Torque component, i.e., the torque acts with negative sign also on the opposite side of this cylinder, but for clarity this is not shown in the animation):

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialTwoFrames (Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​ForceAndTorque
Force and torque acting between two frames, defined by 3+3 input signals and resolved in frame world, frame_a, frame_b or frame_resolve

Information

The 3 signals of the force connector and the 3 signals of the torque connector are interpreted as the x-, y- and z-coordinates of a force and of a torque acting at the frame connector to which frame_b of this component is attached. Via parameter resolveInFrame it is defined, in which frame these coordinates shall be resolved:

If resolveInFrame = ResolveInFrameAB.frame_resolve, the force and torque coordinates are with respect to the frame, that is connected to frame_resolve.

If force={100,0,0}, and for all parameters the default setting is used, then the interpretation is that a force of 100 N is acting along the positive x-axis of frame_b.

Note, a force and torque acts on frame_a in such a way that the force and torque balance between frame_a and frame_b is fulfilled.

An example how to use this model is given in the following figure:

This leads to the following animation (the yellow cylinder characterizes the line between frame_a and frame_b of the ForceAndTorque component, i.e., the force and torque acts with negative sign also on the opposite side of this cylinder, but for clarity this is not shown in the animation):

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialTwoFrames (Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​LineForceWithMass
General line force component with an optional point mass on the connection line

Information

This component is used to exert a line force between the origin of frame_a and the origin of frame_b by attaching components of the 1-dimensional translational mechanical library of Modelica (Modelica.Mechanics.Translational) between the two flange connectors flange_a and flange_b. Optionally, there is a point mass on the line connecting the origin of frame_a and the origin of frame_b. This point mass approximates the mass of the force element. The distance of the point mass from frame_a as a fraction of the distance between frame_a and frame_b is defined via parameter lengthFraction (default is 0.5, i.e., the point mass is in the middle of the line).

In the translational library there is the implicit assumption that forces of components that have only one flange connector act with opposite sign on the bearings of the component. This assumption is also used in the LineForceWithMass component: If a connection is present to only one of the flange connectors, then the force in this flange connector acts implicitly with opposite sign also in the other flange connector.

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​LineForceBase (Base model for line force elements).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​LineForceWithTwoMasses
General line force component with two optional point masses on the connection line

Information

This component is used to exert a line force between the origin of frame_a and the origin of frame_b by attaching components of the 1-dimensional translational mechanical library of Modelica (Modelica.Mechanics.Translational) between the two flange connectors flange_a and flange_b. Optionally, there are two point masses on the line connecting the origin of frame_a and the origin of frame_b. These point masses approximate the masses of the force element. The locations of the two point masses are defined by their (fixed) distances of L_a relative to frame_a and of L_b relative to frame_b, respectively.

In example MultiBody.Examples.Elementary.LineForceWithTwoMasses the usage of this line force element is shown and is compared with an alternative implementation using a MultiBody.Joints.Assemblies.JointUPS component. The composition diagram of this example is displayed in the figure below.

The animation view at time = 0 is shown in the next figure. The system on the left side in the front is the animation with the LineForceWithTwoMasses component whereas the system on the right side in the back is the animation with the JointUPS component. Both implementations yield the same result. However, the implementation with the LineForceWithTwoMasses component is simpler.

In the translational library there is the implicit assumption that forces of components that have only one flange connector act with opposite sign on the bearings of the component. This assumption is also used in the LineForceWithTwoMasses component: If a connection is present to only one of the flange connectors, then the force in this flange connector acts implicitly with opposite sign also in the other flange connector.

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​LineForceBase (Base model for line force elements).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​Spring
Linear translational spring with optional mass

Information

Linear spring acting as line force between frame_a and frame_b. A force f is exerted on the origin of frame_b and with opposite sign on the origin of frame_a along the line from the origin of frame_a to the origin of frame_b according to the equation:

   f = c*(s - s_unstretched);

where "c" and "s_unstretched" are parameters and "s" is the distance between the origin of frame_a and the origin of frame_b.

Optionally, the mass of the spring is taken into account by a point mass located on the line between frame_a and frame_b (default: middle of the line). If the spring mass is zero, the additional equations to handle the mass are removed.

In the following figure a typical animation of the spring is shown. The blue sphere in the middle of the spring characterizes the location of the point mass.

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialTwoFrames (Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​Damper
Linear (velocity dependent) damper

Information

Linear damper acting as line force between frame_a and frame_b. A force f is exerted on the origin of frame_b and with opposite sign on the origin of frame_a along the line from the origin of frame_a to the origin of frame_b according to the equation:

   f = d*der(s);

where "d" is a parameter, "s" is the distance between the origin of frame_a and the origin of frame_b and der(s) is the time derivative of "s".

In the following figure a typical animation is shown where a mass is hanging on a damper.

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialLineForce (Base model for massless line force elements) and Modelica.​Thermal.​HeatTransfer.​Interfaces.​PartialElementaryConditionalHeatPort (Partial model to include a conditional HeatPort in order to dissipate losses, used for textual modeling, i.e., for elementary models).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​SpringDamperParallel
Linear spring and linear damper in parallel

Information

Linear spring and linear damper in parallel acting as line force between frame_a and frame_b. A force f is exerted on the origin of frame_b and with opposite sign on the origin of frame_a along the line from the origin of frame_a to the origin of frame_b according to the equation:

   f = c*(s - s_unstretched) + d*der(s);

where "c", "s_unstretched" and "d" are parameters, "s" is the distance between the origin of frame_a and the origin of frame_b and der(s) is the time derivative of s.

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialLineForce (Base model for massless line force elements) and Modelica.​Thermal.​HeatTransfer.​Interfaces.​PartialElementaryConditionalHeatPort (Partial model to include a conditional HeatPort in order to dissipate losses, used for textual modeling, i.e., for elementary models).

Parameters

Inputs

Connectors

Model Modelica.​Mechanics.​MultiBody.​Forces.​SpringDamperSeries
Linear spring and linear damper in series connection

Information

Linear spring and linear damper in series connection acting as line force between frame_a and frame_b:

  frame_a --> damper ----> spring --> frame_b
          |              |
          |-- s_damper --|  (s_damper is the state variable of this system)

A force f is exerted on the origin of frame_b and with opposite sign on the origin of frame_a along the line from the origin of frame_a to the origin of frame_b according to the equations:

   f = c*(s - s_unstretched - s_damper);
   f = d*der(s_damper);

where "c", "s_unstretched" and "d" are parameters, "s" is the distance between the origin of frame_a and the origin of frame_b. "s_damper" is the length of the damper (= an internal state of this force element) and der(s_damper) is the time derivative of s_damper.

Extends from Modelica.​Mechanics.​MultiBody.​Interfaces.​PartialLineForce (Base model for massless line force elements) and Modelica.​Thermal.​HeatTransfer.​Interfaces.​PartialElementaryConditionalHeatPort (Partial model to include a conditional HeatPort in order to dissipate losses, used for textual modeling, i.e., for elementary models).

Parameters

Inputs

Connectors