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Bushing

Applies translational and rotational stiffness and damping in three directions between two frames

 

Description

Connections

Nonlinear Options

Parameters

See Also

Description

The equations for the Bushing component are given below.

Reaction Forces:

F = Ksrr0  Kdv

where

F=fx,fy,fz, is the reaction force vector,

r=rbra=xbxa,ybya,zbza, is the relative displacement vector,

r0, is the undeformation distance frame_b with respect to frame_a expressed along Inboard frame (frame_a), and

v=ddtr,

Ks=kx000ky000kz, is the diagonal stiffness coefficient matrix,

and,

Kd=dx000dy000dz, is the diagonal damping coefficient matrix.

 

Reaction Torques:

T = Kθθθ0Kωω

where

T=τx,τy,τz,is the reaction torque vector,

θ=θ1,θ2,θ3T, are the Euler angles - defined by Rotation Sequence parameter - calculated from the relative rotation matrix of frame_b with respect to frame_a (see Euler Angle Sensor),

θ0 designates the undeformed rotation of frame_b with respect to frame_a,

ω=ωx,ωy,ωz, is the relative angular velocity vector,

Kθ=ka1000ka2000ka3, is the diagonal angular stiffness coefficient matrix,

and,

Kω=dax000day000daz, is the diagonal angular damping coefficient matrix.

Connections

Name

Description

Modelica ID

framea

Inboard frame

frame_a

frameb

Outboard frame

frame_b

K

Real signal of dimension 3x1. Three elements of diagonal translational stiffness matrix kx,ky,kz.

K_in

D

Real signal of dimension 3x1. Three elements of diagonal translational damping matrix dx,dy,dz.

D_in

Ka

Real signal of dimension 3x1. Three elements of diagonal rotational stiffness matrix ka1,ka1,ka1.

Ka_in

Da

Real signal of dimension 3x1. Three elements of diagonal rotational damping matrix dax,day,daz.

Da_in

r

Real signal of dimension 3x1. Relative displacement vector of frame_b with respect to frame_a, expressed in the frame selected by the Resolved Frame parameter.

r_out

v

Real signal of dimension 3x1. Relative velocity vector of frame_b with respect to frame_a, expressed in the frame selected by the Resolved Frame parameter.

v_out

θ

Real signal of dimension 3x1. Relative Euler angles describing the rotation of frame_b with respect to frame_a. Rotation sequence is defined by Rotation Sequence parameter.

th_out

ω

Real signal of dimension 3x1. Relative angular velocity vector of frame_b with respect to frame_a, expressed in the frame selected by the Resolved Frame parameter.

w_out

Nonlinear Options

The translational and rotational spring and damping coefficients can be time varying. By selecting the nonlinear Boolean parameter (checked = true), the user is given four options to define variable coefficients:

 

Data Source option

Description

1

inline

The tri-axial coefficients are interpolated from an n by 4 table entered by user.

For Ks, the first column is displacement [m]. Columns 2, 3, and 4 correspond to kx, ky, and kz ([N/m]), respectively.

For Kd, the first column is velocity [m/s]. Columns 2, 3, and 4 correspond to dx, dy, and dz ([N.s/m]), respectively.

For Kθ, the first column is angular displacement [rad]. Columns 2, 3, and 4 correspond to ka1, ka2, and ka3 ([N.m/rad]), respectively.

For Kω, the first column is angular velocity [rad/s]. Columns 2, 3, and 4 correspond to dax, day, and daz ([N.m.s/rad]), respectively.

To change the dimensions of a table, right-click (Control-click for Mac) and select Edit Matrix Dimensions. You can then specify the number of rows and columns to include in the table.

2

attachment

The tri-axial coefficients are interpolated from a n by 4 attachment table. The data can be retrieved from an attached .csv, .xls, or .xlsx file. For more information, see Attaching a File to a Model.

Data columns in the attached file are assumed to have the same order and attributes as those described in the inline option.

3

file

The tri-axial coefficients are interpolated from a n by 4 table stored on disk. The data can be retrieved from an attached .csv, .xls, or .xlsx file.

Data columns in the attached file are assumed to have the same order and attributes as those described in the inline option.

4

input

The coefficients are defined via Real input signal ports.

Parameters

Modeling Parameters

Symbol

Default

Units

Description

Modelica ID

Rotation Sequence

[1,2,3]

Euler angles rotation sequence

RotSeq

sensor: r

(false)

Enables relative displacement sensor output

sensor_T

sensor: v

(false)

Enables relative velocity sensor output

sensor_Tv

sensor: θ

(false)

Enables relative angular displacement sensor output (expressed using the Euler angles selected by Rotation Sequence)

sensor_R

sensor: ω

(false)

Enables relative angular velocity sensor output

sensor_Rw

r0

[0,0,0]

[m]

Undeformed distance of frame_b with respect to frame_a (expressed in Inboard frame: frame_a)

r0

θ0

[0,0,0]

[rad]

Undeformed rotation of frame_b with respect to frame_a (expressed using the Euler angles selected by Rotation Sequence)

theta0

Translational Stiffness

Symbol

Condition

Default

Units

Description

Modelica ID

Nonlinear

-

(false)

When checked, activates options to define variable coefficients.

nonlinear_TS

Data Source

Nonlinear = true

inline

Enumeration defining the data source of variable coefficients. See Nonlinear Options section above.

DCM_TS

 

 

 

Ks

 

 

Nonlinear = false

[4.5e6,4.5e6,8.0e5]

[N/m]

Spring constants: kx, ky, and kz 

TS

Nonlinear = true Data Source = inline

[0,4.5e6,4.5e6,8.0e5]

-

Table for displacement-dependent coefficients. See Nonlinear Options section above.

TS_table

Nonlinear = true Data Source = attachment

-

-

MapleSim attachment where data for displacement-dependent coefficients is stored. See Nonlinear Options section above.

TS_data

Nonlinear = true Data Source = file

-

-

Path to a file where data for displacement-dependent coefficients is stored.  See Nonlinear Options section above.

TS_fileName

Skip Rows

Nonlinear = true

Data Source = inline or attachment or file

0

-

Number of rows that are skipped from the top of the data table.

sr_TS

Smoothness

Nonlinear = true

Data Source = inline or attachment or file

Linearly interpolate table points

-

Determines whether the data points will be interpolated linearly or with a cubic spline.

sm_TS

Translational Damping

Symbol

Condition

Default

Units

Description

Modelica ID

Nonlinear

-

(false)

When checked, activates options to define variable coefficients.

nonlinear_TD

Data Source

Nonlinear = true

inline

Enumeration defining the data source of variable coefficients. See Nonlinear Options section above.

DCM_TD

 

 

 

Kd

 

 

Nonlinear = false

[1e4,1e4,1e4]

[N.s/m]

Damping constants: dx, dy, and dz 

TD

Nonlinear = true Data Source = inline

[0,1e4,1e4,1e4]

-

Table for displacement-dependent coefficients. See Nonlinear Options section above.

TD_table

Nonlinear = true Data Source = attachment

-

-

MapleSim attachment where data for displacement-dependent coefficients is stored. See Nonlinear Options section above.

TD_data

Nonlinear = true Data Source = file

-

-

Path to a file where data for displacement-dependent coefficients is stored.  See Nonlinear Options section above.

TD_fileName

Skip Rows

Nonlinear = true

Data Source = inline or attachment or file

0

-

Number of rows that are skipped from the top of the data table.

sr_TD

Smoothness

Nonlinear = true

Data Source = inline or attachment or file

Linearly interpolate table points

-

Determines whether the data points will be interpolated linearly or with a cubic spline.

sm_TD

 

Rotational Stiffness

Symbol

Condition

Default

Units

Description

Modelica ID

Nonlinear

-

(false)

When checked, activates options to define variable coefficients.

nonlinear_RS

Data Source

Nonlinear = true

inline

Enumeration defining the data source of variable coefficients. See Nonlinear Options section above.

DCM_RS

 

 

 

Kθ

 

 

Nonlinear = false

[2.6e3,2.6e3,1e2]

[N.m/rad]

Rotational spring constants: kax, kay, and kaz 

RS

Nonlinear = true Data Source = inline

[0,2.6e3,2.6e3,1e2]

-

Table for displacement-dependent coefficients. See Nonlinear Options section above.

RS_table

Nonlinear = true Data Source = attachment

-

-

MapleSim attachment where data for displacement-dependent coefficients is stored. See Nonlinear Options section above.

RS_data

Nonlinear = true Data Source = file

-

-

Path to a file where data for displacement-dependent coefficients is stored.  See Nonlinear Options section above.

RS_fileName

Skip Rows

Nonlinear = true

Data Source = inline or attachment or file

0

-

Number of rows that are skipped from the top of the data table.

sr_RS

Smoothness

Nonlinear = true

Data Source = inline or attachment or file

Linearly interpolate table points

-

Determines whether the data points will be interpolated linearly or with a cubic spline.

sm_RS

 

Rotational Damping

Symbol

Condition

Default

Units

Description

Modelica ID

Nonlinear

-

(false)

When checked, activates options to define variable coefficients.

nonlinear_RD

Data Source

Nonlinear = true

GUI

Enumeration defining the data source of variable coefficients. See Nonlinear Options section above.

DCM_RD

 

 

 

Kω

 

 

Nonlinear = false

[26,26,5]

[N.m.s/rad]

Rotational damping constants: dax, day, and daz 

RD

Nonlinear = true Data Source = GUI

[0,26,26,5]

-

Table for displacement-dependent coefficients. See Nonlinear Options section above.

RD_table

Nonlinear = true Data Source = attachment

-

-

MapleSim attachment where data for displacement-dependent coefficients is stored. See Nonlinear Options section above.

RD_data

Nonlinear = true Data Source = file

-

-

Path to a file where data for displacement-dependent coefficients is stored.  See Nonlinear Options section above.

RD_fileName

Skip Rows

Nonlinear = true

Data Source = GUI or attachment or file

0

-

Number of rows that are skipped from the top of the data table.

sr_RD

Smoothness

Nonlinear = true

Data Source = GUI or attachment or file

Linearly interpolate table points

-

Determines whether the data points will be interpolated linearly or with a cubic spline.

sm_RD

 

Initial Conditions

Symbol

Default

Units

Description

Modelica ID

ICr,v

Ignore

-

Indicates whether MapleSim ignores, tries to enforce, or strictly enforces the translational initial conditions

MechTranTree

s&conjugate0;0

[0,0,0]

[m]

Initial displacement of the center of mass frame at the start of the simulation. These values are expressed along the x-, y- and z-axis of the inboard frame respectively

InitPos

v&conjugate0;0

[0,0,0]

[m/s]

Initial velocity of the center of mass frame at the start of the simulation. These values are expressed along the x-, y- and z-axis of the inboard frame respectively

InitVel

ICθ,ω

Ignore

-

Indicates whether MapleSim ignores, tries to enforce, or strictly enforces the rotational initial conditions

MechRotTree

θ&conjugate0;0

[0,0,0]

[rad]

Initial rotation of the center of mass frame at the start of the simulation, based on the Typeθ parameter values

InitAng

ω&conjugate0;0

[0,0,0]

[rad/s]

Initial velocity of the center of mass frame at the start of the simulation, based on the Typeω parameter values

InitAngVel

Typeω

Euler

-

Indicates whether the initial angular velocity is expressed in the inboard or outboard frame.  If Euler is selected, the initial angular velocities are assumed to be the direct derivatives of the Euler angles defined by Rotation Sequence.

AngVelType

See Also

Forces and Moments

Multibody Overview