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Lumped Model of a Vehicle Suspension System
Introduction
In this example, a lumped model of a vehicle suspension system having eleven degrees of freedom is analyzed. The Mass, Spring, and Damper nodes of the Lumped Mechanical System interface are used to model the wheels, including suspension system, as well as the seats with a passenger. The vehicle body, having three degrees of freedom, is modeled as a rigid body in the Multibody Dynamics interface. The External Source node of the Lumped Mechanical System interface and the Lumped-Structure Connection multiphysics coupling are used to connect the MBD model of the vehicle body to the lumped model of the rest of the system.
A transient analysis is performed to compute the vehicle motion and the seat vibration levels for a given road profile. The data for this model is taken from Ref. 1.
Model Definition
Figure 1: The lumped model of a vehicle suspension system including wheels, body, and seats. The eleven degrees of freedom of the system as well as the node numbers of the systems are also shown.
The lumped model of the vehicle suspension system is shown in Figure 1. This model has three main components:
•
Wheels (4 dofs)
•
Seats (4 dofs)
•
Body (3 dofs)
Wheel and Seat modeling
Each wheel and seat has only one degree of freedom in the form of vertical displacement and is modeled in the Lumped Mechanical System interface. In total, there are 4 wheels and 4 seats in the full vehicle model. Both components are defined as a subsystem as shown in Figure 2.
Figure 2: The lumped model of a wheel and seat of a vehicle.
The lumped model of a wheel includes the following:
•
Mass and stiffness of a wheel
•
Stiffness and damping of a vehicle suspension
The lumped model of a seat includes the following:
•
Stiffness and damping of a seat
•
Mass of a passenger
Vehicle body Modeling
The vehicle body has three degrees of freedom:
•
Roll
•
Pitch
•
Heave
As the body has rotational degrees of freedom, it is modeled using a Rigid Domain node in the Multibody Dynamics interface in 3D.
Wheel-Body and body-Seat Connection
The vehicle wheels and seats are modeled in the Lumped Mechanical System interface whereas the vehicle body is modeled in the Multibody Dynamics interface. In order to connect wheel-body and body-seat, Lumped-Structure Connection multiphysics coupling is used. The body is modeled as an External Source element in the lumped system model. Through the Lumped-Structure Connection multiphysics coupling, the displacement obtained from the MBD vehicle body model at the connection points are used in the lumped model. Similarly, the wheel and seat reaction forces obtained from the lumped model are applied in the MBD vehicle body model.
road Profile
The road profile is modeled as a rectangular wave function by assuming a series of bumps on the road. The bump height and width is assumed to be 4 cm and 7.5 cm, respectively. Also, the vehicle is assumed to be moving with a constant speed of 40 km/h.
The road excitation is prescribed to the bottom end of the wheels. In this model, only the left wheels of the vehicle are assumed to be moving on the uneven road.
Model parameters
The parameters used in the model are given in the table below:
Table 1: Model parameters
Description
name
Expression
Mass of vehicle body
m_body
670 kg
Inertia around roll
I_roll
800 kg·m2
Inertia around pitch
I_pitch
1100 kg·m2
Mass of wheels
m_wh
30 kg
Mass of passengers
m_p
120 kg
Stiffness of wheels
k_wh
175500 N/m
Stiffness of suspension springs
k_sus
17500 N/m
Stiffness of seat springs
k_seat
1750 N/m
Viscosity of suspension dampers
c_sus
1460 Ns/m
Viscosity of seat dampers
c_seat
700 Ns/m
Wheel base
r_wb
1.9975 m
Track width
r_tw
0.8025 m
Results and Discussion
Figure 3 shows the road excitation for the front-left and rear-left wheel of the vehicle. The phase difference between the front and rear wheel excitation can be seen.
Figure 3: Road excitation for the left wheels of the vehicle.
Figure 4 shows the time history of the vehicle roll, pitch, and heave motions at the center of gravity due to the road excitation under the left wheels of the vehicle. It can be seen that the roll rotation is much larger that the pitch rotation for the given road excitation. The corresponding velocities for the roll, pitch, and heave motions can be seen in Figure 5. Two different frequencies, low and high, corresponding to the natural frequencies for the components of the system can be seen in the velocity plot.
Figure 4: Vehicle roll, pitch, and heave motions at the center of gravity.
Figure 5: Vehicle velocities corresponding to the roll, pitch, and heave motions at the center of gravity.
Figure 6 and Figure 7 show the time history of displacement and acceleration at all four seat locations.
Figure 6: Time history of seat displacements.
Figure 7: Time history of seat accelerations.
Figure 8 and Figure 9 show the forces in springs and damper of the front-left wheel and seat respectively. It can be seen that the force magnitude in the spring and damper of the wheel is much larger than that of a seat. The reason for this is the fact that large amount of force is absorbed by inertia of wheels and the vehicle body so that only a fraction of the force is transmitted from the wheel to the seat.
It can also be noticed that the forces in the wheel has a frequency of vibration which is the same as the excitation frequency, whereas the forces in the seat has a much lower frequency of vibration.
Figure 8: Forces in the springs and damper of the front-left wheel.
Figure 9: Forces in the spring and damper of the front-left seat.
Notes About the COMSOL Implementation
•
Fixed Node is the default node of the Lumped Mechanical System interface. It can however be disabled if none of the nodes of the system is fixed.
•
To re-use the lumped model definition of a wheel and seat of a vehicle, use a Subsystem Definition node to define the component once. Then, use Subsystem Instance nodes multiple times to create more than one instance of the wheels and seats.
•
The Lumped-Structure Connection multiphysics coupling and External Source node can be used to connect a distributed model of a component to the lumped model of the system.
•
To restrict the number of degrees of freedom of the vehicle body to be only three, the Prescribed Displacement/Rotation subnode of Rigid Domain node is used.
•
To enter the lumped mass and inertia values of a vehicle body, the Mass and Moment of Inertia subnode of Rigid Domain node is used.
Reference
1. S.H. Zareh and M. Abbasi, “Semi-active vibration control of an eleven degrees of freedom suspension system using neuro inverse model of magnetorheological dampers,” Journal of Mechanical Science and Technology, vol. 26, no. 8, pp. 2459–2467, 2012.
Application Library path: Multibody_Dynamics_Module/Automotive_and_Aerospace/lumped_vehicle_suspension_system
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  3D.
2
In the Select Physics tree, select Structural Mechanics>Lumped Mechanical System (lms).
3
Click Add.
4
In the Select Physics tree, select Structural Mechanics>Multibody Dynamics (mbd).
5
Click Add.
6
Click  Study.
7
In the Select Study tree, select General Studies>Time Dependent.
8
Click  Done.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file lumped_vehicle_suspension_system_parameters.txt.
Use a Waveform function to define the road profile.
Waveform 1 (wv1)
1
In the Home toolbar, click  Functions and choose Global>Waveform.
2
In the Settings window for Waveform, locate the Parameters section.
3
From the Type list, choose Square.
4
In the Size of transition zone text field, type tb/10.
5
In the Duty cycle text field, type 0.25.
6
In the Angular frequency text field, type 2*pi/tb.
7
In the Amplitude text field, type hb/2.
Waveform 2 (wv2)
1
Right-click Waveform 1 (wv1) and choose Duplicate.
2
In the Settings window for Waveform, locate the Parameters section.
3
In the Phase text field, type -2*pi/tb*td.
Create the geometry of the vehicle body and define its connection points for the wheels and seats.
Geometry 1
Block 1 (blk1)
1
In the Geometry toolbar, click  Block.
2
In the Settings window for Block, locate the Size and Shape section.
3
In the Width text field, type 2*r_wb.
4
In the Depth text field, type 2*r_tw.
5
In the Height text field, type r_wb/20.
6
Locate the Position section. From the Base list, choose Center.
7
Click  Build All Objects.
Lumped Mechanical System (lms)
Fixed Node 1 (fix1)
In the Model Builder window, under Component 1 (comp1)>Lumped Mechanical System (lms) right-click Fixed Node 1 (fix1) and choose Disable.
Define the lumped model of a wheel and seat using Subsystem Definition node.
Subsystem Definition: Wheel
1
In the Model Builder window, right-click Lumped Mechanical System (lms) and choose Subsystem Definition.
2
In the Settings window for Subsystem Definition, type Subsystem Definition: Wheel in the Label text field.
Spring 1 (K1)
1
In the Physics toolbar, click  Global and choose Spring.
2
In the Settings window for Spring, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p1
a
p2
1
4
Locate the Component Parameters section. In the k text field, type k_wh.
Mass 1 (M1)
1
In the Physics toolbar, click  Global and choose Mass.
2
In the Settings window for Mass, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p1
1
4
Locate the Component Parameters section. In the m text field, type m_wh.
Spring 2 (K2)
1
In the Physics toolbar, click  Global and choose Spring.
2
In the Settings window for Spring, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p1
2
p2
b
4
Locate the Component Parameters section. In the k text field, type k_sus.
Damper 1 (C1)
1
In the Physics toolbar, click  Global and choose Damper.
2
In the Settings window for Damper, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p1
2
p2
b
4
Locate the Component Parameters section. In the c text field, type c_sus.
Subsystem Definition: Seat
1
In the Physics toolbar, click  Global and choose Subsystem Definition.
2
In the Settings window for Subsystem Definition, type Subsystem Definition: Seat in the Label text field.
Delete the second row of the table.
Spring 1 (K1)
1
In the Physics toolbar, click  Global and choose Spring.
2
In the Settings window for Spring, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p1
a
p2
1
4
Locate the Component Parameters section. In the k text field, type k_seat.
Damper 1 (C1)
1
In the Physics toolbar, click  Global and choose Damper.
2
In the Settings window for Damper, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p1
a
p2
1
4
Locate the Component Parameters section. In the c text field, type c_seat.
Mass 1 (M1)
1
In the Physics toolbar, click  Global and choose Mass.
2
In the Settings window for Mass, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node names
p1
1
4
Locate the Component Parameters section. In the m text field, type m_p.
Free Node 1 (fr1)
1
In the Physics toolbar, click  Global and choose Free Node.
2
In the Settings window for Free Node, locate the Node Connections section.
3
In the table, enter the following settings:
Label
Node name
p1
2
Now define the road excitation for all four wheels of the vehicle.
Displacement Node: Front-Left
1
In the Physics toolbar, click  Global and choose Displacement Node.
2
In the Settings window for Displacement Node, type Displacement Node: Front-Left in the Label text field.
3
Locate the Terminal Parameters section. In the up10 text field, type hb/2+wv1(t[1/s]).
Displacement Node: Front-Right
1
In the Physics toolbar, click  Global and choose Displacement Node.
2
In the Settings window for Displacement Node, type Displacement Node: Front-Right in the Label text field.
3
Locate the Terminal Parameters section. In the up10 text field, type 0[mm].
Displacement Node: Rear-Left
1
In the Physics toolbar, click  Global and choose Displacement Node.
2
In the Settings window for Displacement Node, type Displacement Node: Rear-Left in the Label text field.
3
Locate the Terminal Parameters section. In the up10 text field, type hb/2+wv2(t[1/s]).
Displacement Node: Rear-Right
1
In the Physics toolbar, click  Global and choose Displacement Node.
2
In the Settings window for Displacement Node, type Displacement Node: Rear-Right in the Label text field.
3
Locate the Terminal Parameters section. In the up10 text field, type 0[mm].
Subsystem Instance X1: Front-Left Wheel
1
In the Physics toolbar, click  Global and choose Subsystem Instance.
2
In the Settings window for Subsystem Instance, type Subsystem Instance X1: Front-Left Wheel in the Label text field.
3
Locate the Node Connections section. From the Name of subsystem link list, choose Subsystem Definition: Wheel (sub1).
4
In the table, enter the following settings:
Local node names
Node names
a
1
b
5
Subsystem Instances
Duplicate the node above and create more wheels using the information given in the table below:
Label
a
b
Subsystem Instance X2: Front-Right Wheel
2
6
Subsystem Instance X3: Rear-Left Wheel
3
7
Subsystem Instance X4: Rear-Right Wheel
4
8
Having defined the wheels, now define the vehicle body using an External Source node. The vehicle body has three degrees of freedom and is therefore defined in the Multibody Dynamics interface.
External Source E1: Front-Left
1
In the Physics toolbar, click  Global and choose External Source.
2
In the Settings window for External Source, type External Source E1: Front-Left in the Label text field.
3
Locate the Node Connections section. In the table, enter the following settings:
Label
Node names
p1
5
p2
9
4
Locate the Component Parameters section. From the Input displacement list, choose From multiphysics coupling.
5
Locate the Results section. Find the Add the following to default results subsection. Clear the Force check box.
6
Clear the Displacement check box.
External Sources
Duplicate the node above and create more external sources using the information given in the table below:
Label
p1
p2
External Source E2: Front-Right
6
10
External Source E3: Rear-Left
7
11
External Source E4: Rear-Right
8
12
Next, define the seats mounted on the body.
Subsystem Instance X5: Front-Left Seat
1
In the Physics toolbar, click  Global and choose Subsystem Instance.
2
In the Settings window for Subsystem Instance, type Subsystem Instance X5: Front-Left Seat in the Label text field.
3
Locate the Node Connections section. From the Name of subsystem link list, choose Subsystem Definition: Seat (sub2).
4
In the table, enter the following settings:
Local node names
Node names
a
9
Subsystem Instances
Duplicate the node above and create more seats using the information given in the table below:
Label
a
Subsystem Instance X6: Front-Right Seat
10
Subsystem Instance X7: Rear-Left Seat
11
Subsystem Instance X8: Rear-Right Seat
12
Now define the vehicle body using a Rigid Domain node and apply wheel and seat reaction forces.
Multibody Dynamics (mbd)
In the Model Builder window, under Component 1 (comp1) click Multibody Dynamics (mbd).
Rigid Domain 1
1
In the Physics toolbar, click  Domains and choose Rigid Domain.
2
Select Domain 1 only.
3
In the Settings window for Rigid Domain, locate the Density section.
4
From the ρ list, choose User defined. Locate the Center of Rotation section. From the list, choose User defined.
Mass and Moment of Inertia 1
1
In the Physics toolbar, click  Attributes and choose Mass and Moment of Inertia.
2
In the Settings window for Mass and Moment of Inertia, locate the Mass and Moment of Inertia section.
3
In the m text field, type m_body.
4
From the list, choose Diagonal.
5
In the I table, enter the following settings:
I_roll
0
0
0
I_pitch
0
0
0
0
Rigid Domain 1
In the Model Builder window, click Rigid Domain 1.
Prescribed Displacement/Rotation 1
1
In the Physics toolbar, click  Attributes and choose Prescribed Displacement/Rotation.
2
In the Settings window for Prescribed Displacement/Rotation, locate the Prescribed Displacement at Center of Rotation section.
3
Select the Prescribed in x direction check box.
4
Select the Prescribed in y direction check box.
5
Locate the Prescribed Rotation section. From the By list, choose Constrained rotation.
6
Select the Constrain rotation around z-axis check box.
Multiphysics
Lumped-Structure Connection: Front-Left
1
In the Physics toolbar, click  Multiphysics Couplings and choose Global>Lumped-Structure Connection.
2
In the Settings window for Lumped-Structure Connection, type Lumped-Structure Connection: Front-Left in the Label text field.
3
Select Point 7 only.
4
Locate the Point Selection, Port-2 section. Select the  Activate Selection toggle button.
5
Select Point 8 only.
Lumped-Structure Connection: Front-Right
1
In the Physics toolbar, click  Multiphysics Couplings and choose Global>Lumped-Structure Connection.
2
In the Settings window for Lumped-Structure Connection, type Lumped-Structure Connection: Front-Right in the Label text field.
3
Select Point 5 only.
4
Locate the Point Selection, Port-2 section. Select the  Activate Selection toggle button.
5
Select Point 6 only.
6
Locate the Connection Settings section. From the list, choose External Source E2: Front-Right.
Lumped-Structure Connection: Rear-Left
1
In the Physics toolbar, click  Multiphysics Couplings and choose Global>Lumped-Structure Connection.
2
In the Settings window for Lumped-Structure Connection, type Lumped-Structure Connection: Rear-Left in the Label text field.
3
Select Point 3 only.
4
Locate the Point Selection, Port-2 section. Select the  Activate Selection toggle button.
5
Select Point 4 only.
6
Locate the Connection Settings section. From the list, choose External Source E3: Rear-Left.
Lumped-Structure Connection: Rear-Right
1
In the Physics toolbar, click  Multiphysics Couplings and choose Global>Lumped-Structure Connection.
2
In the Settings window for Lumped-Structure Connection, type Lumped-Structure Connection: Rear-Right in the Label text field.
3
Select Point 1 only.
4
Locate the Point Selection, Port-2 section. Select the  Activate Selection toggle button.
5
Select Point 2 only.
6
Locate the Connection Settings section. From the list, choose External Source E4: Rear-Right.
Study 1
Step 1: Time Dependent
1
In the Model Builder window, under Study 1 click Step 1: Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
In the Output times text field, type range(0,0.0002,2).
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
3
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1)>Time-Dependent Solver 1 node.
4
Right-click Time-Dependent Solver 1 and choose Fully Coupled.
5
In the Settings window for Fully Coupled, click to expand the Method and Termination section.
6
From the Jacobian update list, choose On every iteration.
7
In the Maximum number of iterations text field, type 15.
8
In the Study toolbar, click  Compute.
Follow the instructions to plot the road excitation as shown in Figure 3.
Results
Road Excitation (Left Wheels)
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Road Excitation (Left Wheels) in the Label text field.
3
Click to expand the Title section. From the Title type list, choose Label.
4
Locate the Data section. From the Time selection list, choose Interpolated.
5
In the Times (s) text field, type range(0,0.0002,0.1).
Global 1
1
Right-click Road Excitation (Left Wheels) and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Node displacements>lms.u_1 - Displacement at node 1 - m.
3
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Node displacements>lms.u_3 - Displacement at node 3 - m.
4
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
lms.u_1
m
Front-Left
lms.u_3
m
Rear-Left
Road Excitation (Left Wheels)
1
In the Model Builder window, click Road Excitation (Left Wheels).
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the y-axis label check box.
4
In the associated text field, type Displacement (m).
5
In the Road Excitation (Left Wheels) toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.
Follow the instructions below to plot the vehicle motion and velocity as shown in Figure 4 and Figure 5 respectively.
Vehicle Motion (CG)
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Vehicle Motion (CG) in the Label text field.
3
Locate the Title section. From the Title type list, choose Label.
4
Locate the Plot Settings section. Select the Two y-axes check box.
Global 1
1
Right-click Vehicle Motion (CG) and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Multibody Dynamics>Rigid domains>Rigid Domain 1>Rigid body rotation (spatial frame) - rad>mbd.rd1.thx - Rigid body rotation, x component.
3
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Multibody Dynamics>Rigid domains>Rigid Domain 1>Rigid body rotation (spatial frame) - rad>mbd.rd1.thy - Rigid body rotation, y component.
4
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
mbd.rd1.thx
deg
Roll
mbd.rd1.thy
deg
Pitch
Global 2
1
In the Model Builder window, right-click Vehicle Motion (CG) and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Multibody Dynamics>Rigid domains>Rigid Domain 1>Rigid body displacement (spatial frame) - m>mbd.rd1.w - Rigid body displacement, z component.
3
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
mbd.rd1.w
m
Heave
4
Locate the y-Axis section. Select the Plot on secondary y-axis check box.
Vehicle Motion (CG)
1
In the Model Builder window, click Vehicle Motion (CG).
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the y-axis label check box.
4
In the associated text field, type Rotation (deg).
5
Select the Secondary y-axis label check box.
6
In the associated text field, type Displacement (m).
7
In the Vehicle Motion (CG) toolbar, click  Plot.
8
Click the  Zoom Extents button in the Graphics toolbar.
Vehicle Velocity (CG)
1
Right-click Vehicle Motion (CG) and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Vehicle Velocity (CG) in the Label text field.
3
Locate the Plot Settings section. In the y-axis label text field, type Angular velocity (rad/s).
4
In the Secondary y-axis label text field, type Velocity (m/s).
Global 1
1
In the Model Builder window, expand the Vehicle Velocity (CG) node, then click Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
mbd.rd1.th_tx
rad/s
Roll
mbd.rd1.th_ty
rad/s
Pitch
Global 2
1
In the Model Builder window, click Global 2.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
mbd.rd1.wt
m/s
Heave
Vehicle Velocity (CG)
1
In the Model Builder window, click Vehicle Velocity (CG).
2
In the Vehicle Velocity (CG) toolbar, click  Plot.
3
Click the  Zoom Extents button in the Graphics toolbar.
Follow the instructions below to plot the seat displacement and acceleration as shown in Figure 6 and Figure 7 respectively.
Seat Displacement
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Seat Displacement in the Label text field.
3
Locate the Title section. From the Title type list, choose Label.
Global 1
1
Right-click Seat Displacement and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Subsystem X5>Two port components>M1>lms.X5_M1_u - Displacement (M1) - m.
3
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Subsystem X6>Two port components>M1>lms.X6_M1_u - Displacement (M1) - m.
4
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Subsystem X7>Two port components>M1>lms.X7_M1_u - Displacement (M1) - m.
5
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Subsystem X8>Two port components>M1>lms.X8_M1_u - Displacement (M1) - m.
6
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
lms.X5_M1_u
m
Front-Left
lms.X6_M1_u
m
Front-Right
lms.X7_M1_u
m
Rear-Left
lms.X8_M1_u
m
Rear-Right
Seat Displacement
1
In the Model Builder window, click Seat Displacement.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the y-axis label check box.
4
In the associated text field, type Displacement (m).
5
In the Seat Displacement toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.
Seat Acceleration
1
Right-click Seat Displacement and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Seat Acceleration in the Label text field.
3
Locate the Plot Settings section. In the y-axis label text field, type Acceleration (m/s^2).
Global 1
1
In the Model Builder window, expand the Seat Acceleration node, then click Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
d(lms.X5_M1_dudt,t)
1/s
Front-Left
d(lms.X6_M1_dudt,t)
1/s
Front-Right
d(lms.X7_M1_dudt,t)
1/s
Rear-Left
d(lms.X8_M1_dudt,t)
1/s
Rear-Right
Seat Acceleration
1
In the Model Builder window, click Seat Acceleration.
2
In the Seat Acceleration toolbar, click  Plot.
3
Click the  Zoom Extents button in the Graphics toolbar.
Follow the instructions below to plot the forces in the front-left wheel and the seat as shown in Figure 8 and Figure 9 respectively.
Forces (Front-Left Wheel)
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Forces (Front-Left Wheel) in the Label text field.
3
Locate the Title section. From the Title type list, choose Label.
Global 1
1
Right-click Forces (Front-Left Wheel) and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Subsystem X1>Two port components>K1>lms.X1_K1_f - Spring force (K1) - N.
3
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Subsystem X1>Two port components>K2>lms.X1_K2_f - Spring force (K2) - N.
4
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Subsystem X1>Two port components>C1>lms.X1_C1_f - Damping force (C1) - N.
Forces (Front-Left Wheel)
1
In the Model Builder window, click Forces (Front-Left Wheel).
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the y-axis label check box.
4
In the associated text field, type Force (N).
5
In the Forces (Front-Left Wheel) toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.
Forces (Front-Left Seat)
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Forces (Front-Left Seat) in the Label text field.
3
Locate the Title section. From the Title type list, choose Label.
Global 1
1
Right-click Forces (Front-Left Seat) and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Subsystem X5>Two port components>K1>lms.X5_K1_f - Spring force (K1) - N.
3
Click Add Expression in the upper-right corner of the y-Axis Data section. From the menu, choose Component 1 (comp1)>Lumped Mechanical System>Subsystem X5>Two port components>C1>lms.X5_C1_f - Damping force (C1) - N.
Forces (Front-Left Seat)
1
In the Model Builder window, click Forces (Front-Left Seat).
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the y-axis label check box.
4
In the associated text field, type Force (N).
5
In the Forces (Front-Left Seat) toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.