Bushing
Applies translational and rotational stiffness and damping in three directions between two frames
Description
Connections
Nonlinear Options
Parameters
See Also
The equations for the Bushing component are given below.
Reaction Forces:
F = −Ks⋅r−r0 − Kd⋅v
where
F=fx,fy,fz, is the reaction force vector,
r=rb−ra=xb−xa,yb−ya,zb−za, 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 = −Kθ⋅θ−θ0−Kω⋅ω
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,
Kω=dax000day000daz, is the diagonal angular damping coefficient matrix.
Name
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
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
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.
4
input
The coefficients are defined via Real input signal ports.
Modeling Parameters
Symbol
Default
Units
Rotation Sequence
[1,2,3]
Euler angles rotation sequence
RotSeq
sensor: r
(false)
Enables relative displacement sensor output
sensor_T
sensor: v
Enables relative velocity sensor output
sensor_Tv
sensor: θ
Enables relative angular displacement sensor output (expressed using the Euler angles selected by Rotation Sequence)
sensor_R
sensor: ω
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)
θ0
[rad]
Undeformed rotation of frame_b with respect to frame_a (expressed using the Euler angles selected by Rotation Sequence)
theta0
Translational Stiffness
Condition
Nonlinear
When checked, activates options to define variable coefficients.
nonlinear_TS
Data Source
Nonlinear = true
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
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
Data Source = inline or attachment or file
0
Number of rows that are skipped from the top of the data table.
sr_TS
Smoothness
Linearly interpolate table points
Determines whether the data points will be interpolated linearly or with a cubic spline.
sm_TS
Translational Damping
nonlinear_TD
DCM_TD
Kd
[1e4,1e4,1e4]
[N.s/m]
Damping constants: dx, dy, and dz
TD
[0,1e4,1e4,1e4]
TD_table
TD_data
TD_fileName
sr_TD
sm_TD
Rotational Stiffness
nonlinear_RS
DCM_RS
Kθ
[2.6e3,2.6e3,1e2]
[N.m/rad]
Rotational spring constants: kax, kay, and kaz
RS
[0,2.6e3,2.6e3,1e2]
RS_table
RS_data
RS_fileName
sr_RS
sm_RS
Rotational Damping
nonlinear_RD
GUI
DCM_RD
Kω
[26,26,5]
[N.m.s/rad]
Rotational damping constants: dax, day, and daz
RD
Nonlinear = true Data Source = GUI
[0,26,26,5]
RD_table
RD_data
RD_fileName
Data Source = GUI or attachment or file
sr_RD
sm_RD
Initial Conditions
ICr,v
Ignore
Indicates whether MapleSim ignores, tries to enforce, or strictly enforces the translational initial conditions
MechTranTree
s&conjugate0;0
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
[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
Indicates whether MapleSim ignores, tries to enforce, or strictly enforces the rotational initial conditions
MechRotTree
θ&conjugate0;0
Initial rotation of the center of mass frame at the start of the simulation, based on the Typeθ parameter values
InitAng
ω&conjugate0;0
[rad/s]
Initial angular 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
Forces and Moments
Multibody Overview
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