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Slider Crank Mechanism with Joint Clearance
Introduction
Joints between two components of a mechanical system are not always perfectly fitting. For the ease of assembly and to allow relative movement between the components, a small gap called clearance is provided between the joining components. The presence of clearance on joints can sometimes adversely affect the performance of the system by generating impact forces thus giving rise to noise and vibrations.
This model compares the performance of a slider crank mechanism with and without a joint clearance. All components of the mechanism are assumed rigid. Hinge Joint node is used when there is no clearance on a joint whereas Clearance Joint node is used to include clearance on a joint. A transient analysis is performed to analyze the effect of joint clearance on slider velocity, slider acceleration, and crank moment. In addition to this, the dynamics of journal within the bearing and the reaction force in the clearance joint are also analyzed.
Model Definition
As shown in Figure 1, the model geometry consists of four rigid components: support, crank, connecting rod, and slider.
Figure 1: Model geometry of a slider crank mechanism.
One end of the crank is connected to the fixed support and other end to the connecting rod. Connecting rod, in turn, is connected to the center of the slider, which can slide freely along x-direction.
The connection between the support and crank is modeled as a hinge joint with one rotational degree of freedom about y-axis. A similar hinge joint is used to model the connection between crank and connecting rod also. To model the connection between connecting rod journal and slider, two different cases are considered:
•
In the first case, a perfect hinge joint without any clearance is assumed between journal and the slider.
•
In the second case, a clearance of 0.5 mm is provided between journal and the slider. A clearance joint is used to model this connection, which allows the connected members to move within the provided clearance distance.
The mechanism is driven by the crank which rotates with an angular velocity of 5000 rpm. A time dependent study is performed for 0.025 s to analyze the effect of joint clearance on slider velocity, slider acceleration, and crank moment.
Results and Discussion
Figure 2 shows the displacement of components in the slider crank mechanism for hinge joint and clearance joint cases. To visualize the motion of connecting rod with respect to the slider, the relative displacement of connecting rod is plotted in Figure 3. For hinge joint case, the relative motion is purely rotational without any translation, however for clearance joint case, connecting rod journal exhibits both translational and rotational motion within the slider hole. This trajectory of the journal within the slider hole is plotted in Figure 7.
The time variation of slider velocity is plotted in Figure 4. It is observed that the velocity profile in hinge joint case is smoother compared to the clearance joint case. Unlike the continuous contact in hinge joint, the translation and the consequent impact of journal with the slider generate a step like velocity profile in clearance joint case. As shown in Figure 5 and Figure 6, the impact between journal and slider also causes sudden variations in slider acceleration and reaction moment in the crank.
Figure 8 shows the variation in clearance joint force as a function of time. The zero value of force at times denotes the intermittent contact within the clearance joint. The variation of gap distance with crank rotation is shown in Figure 9. When gap distance is negative (inside magenta circle), journal and slider are in contact and penalty force acts on the bodies to maintain the relative movement of journal within the specified clearance.
Figure 2: Displacement of slider crank mechanism for hinge joint and clearance joint cases respectively at t = 0.025 s.
Figure 3: Relative displacement of connecting rod journal with respect to the slider for hinge joint and clearance joint cases respectively at t = 0.025 s.
Figure 4: Variation of slider velocity, as a function of time.
Figure 5: Variation of slider acceleration, as a function of time.
Figure 6: Variation of crank reaction moment, as a function of time.
Figure 7: Journal trajectory within the slider hole for clearance joint case. Here blue color denotes the initial position and red color denotes the final position.
Figure 8: Variation of clearance joint force, as a function of time.
Figure 9: Variation of gap distance, as a function of crank rotation. Here blue color denotes the initial position, red color denotes the final position, and magenta dotted circle corresponds to the zero gap distance.
Notes About the COMSOL Implementation
•
In this model, linkages are modeled as rigid elements using the Rigid Domain nodes which can be created automatically using the Create Rigid Domains button in the Automated Model Setup section at the physics interface.
•
Joint nodes between two respective components can also be created automatically using the Create Joints button in the Automated Model Setup section at the physics interface. The automatic joint creation requires the geometry to be in assembly mode and Identity Boundary Pair nodes to be available in the Definitions. In case geometry doesn’t create an identity pair automatically because of a geometric clearance between the two sets of boundaries, then the identity pair can be created manually in order to create a joint between those two components.
Reference
P. Flores and J. Ambrosio, “Revolute Joints with Clearance in Multibody Systems”, Computers and Structures, vol. 82, pp. 1359–1369, 2004.
Application Library path: Multibody_Dynamics_Module/Tutorials/slider_crank_mechanism_with_clearance
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>Multibody Dynamics (mbd).
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies>Time Dependent.
6
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 slider_crank_mechanism_with_clearance_parameters.txt.
If you do not want to import the geometry and create selections, you can load the geometry sequence from the stored model. In the Model Builder window, under Component 1 (comp1) right-click Geometry 1 and choose Insert Sequence. Browse to the model’s Application Libraries folder and double-click the file slider_crank_mechanism_with_clearance.mph. You can then continue to the Definitions section below.
To import the geometry and create selections from scratch, continue here.
Geometry 1
Import 1 (imp1)
1
In the Model Builder window, expand the Component 1 (comp1)>Geometry 1 node.
2
Right-click Geometry 1 and choose Import.
3
In the Settings window for Import, locate the Import section.
4
Click  Browse.
5
Browse to the model’s Application Libraries folder and double-click the file slider_crank_mechanism_with_clearance.mphbin.
6
Click  Import.
Form Union (fin)
1
In the Model Builder window, under Component 1 (comp1)>Geometry 1 click Form Union (fin).
2
In the Settings window for Form Union/Assembly, locate the Form Union/Assembly section.
3
From the Action list, choose Form an assembly.
4
In the Home toolbar, click  Build All.
Support
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Support in the Label text field.
3
On the object fin, select Domain 1 only.
4
Locate the Color section. From the Color list, choose None or — if you are running the cross-platform desktop —Custom. On the cross-platform desktop, click the Color button.
5
Click Define custom colors.
6
Set the RGB values to 128, 128, and 128, respectively.
7
Click Add to custom colors.
8
Click Show color palette only or OK on the cross-platform desktop.
9
Click  Build Selected.
Crank
1
Right-click Support and choose Duplicate.
2
In the Settings window for Explicit Selection, type Crank in the Label text field.
3
Locate the Entities to Select section. Click  Clear Selection.
4
On the object fin, select Domain 2 only.
5
Locate the Color section. Click Define custom colors.
6
Set the RGB values to 209, 255, and 28, respectively.
7
Click Add to custom colors.
8
Click Show color palette only or OK on the cross-platform desktop.
9
Click  Build Selected.
Connecting Rod
1
Right-click Crank and choose Duplicate.
2
In the Settings window for Explicit Selection, type Connecting Rod in the Label text field.
3
Locate the Entities to Select section. Click  Clear Selection.
4
On the object fin, select Domain 3 only.
5
Locate the Color section. Click Define custom colors.
6
Set the RGB values to 255, 128, and 128, respectively.
7
Click Add to custom colors.
8
Click Show color palette only or OK on the cross-platform desktop.
9
Click  Build Selected.
Slider
1
Right-click Connecting Rod and choose Duplicate.
2
In the Settings window for Explicit Selection, type Slider in the Label text field.
3
Locate the Entities to Select section. Click  Clear Selection.
4
On the object fin, select Domain 4 only.
5
Locate the Color section. Click Define custom colors.
6
Set the RGB values to 0, 255, and 255, respectively.
7
Click Add to custom colors.
8
Click Show color palette only or OK on the cross-platform desktop.
9
Click  Build Selected.
Connecting Rod Boundaries
1
In the Geometry toolbar, click  Selections and choose Adjacent Selection.
2
In the Settings window for Adjacent Selection, type Connecting Rod Boundaries in the Label text field.
3
Locate the Input Entities section. Click  Add.
4
In the Add dialog box, select Connecting Rod in the Input selections list.
5
Click OK.
Journal Boundaries
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Journal Boundaries in the Label text field.
3
Locate the Entities to Select section. From the Geometric entity level list, choose Boundary.
4
On the object fin, select Boundaries 33 and 37 only.
5
Select the Group by continuous tangent check box.
Connecting Rod without Journal
1
In the Geometry toolbar, click  Selections and choose Difference Selection.
2
In the Settings window for Difference Selection, type Connecting Rod without Journal in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Input Entities section. Click  Add.
5
In the Add dialog box, select Connecting Rod Boundaries in the Selections to add list.
6
Click OK.
7
In the Settings window for Difference Selection, locate the Input Entities section.
8
Click  Add.
9
In the Add dialog box, select Journal Boundaries in the Selections to subtract list.
10
Click OK.
The identity pair between connecting rod and slider is not added automatically because of the geometric clearance. Add it manually to allow automatic joint creation functionality to create a hinge joint between the two components.
Definitions
Identity Boundary Pair 3 (p3)
1
In the Model Builder window, expand the Component 1 (comp1)>Definitions node.
2
Right-click Definitions and choose Pairs>Identity Boundary Pair.
3
Select Boundaries 31, 32, 37, and 38 only.
4
In the Settings window for Pair, locate the Destination Boundaries section.
5
Click to select the  Activate Selection toggle button.
6
Select Boundaries 42 and 43 only.
Multibody Dynamics (mbd)
Do as follows to generate Rigid Domain nodes for all components.
1
In the Model Builder window, under Component 1 (comp1) click Multibody Dynamics (mbd).
2
In the Settings window for Multibody Dynamics, locate the Automated Model Setup section.
3
Select the Include mass and moment of inertia node check box. This automatically sets the density of all rigid domains to zero and adds a Mass and Moment of Inertia subnode to each Rigid Domain node.
4
Click Physics Node Generation in the upper-right corner of the Automated Model Setup section. From the menu, choose Create Rigid Domains.
Rigid Domain: Support
1
In the Model Builder window, expand the Rigid Domains (All) node, then click Rigid Domain 1.
2
In the Settings window for Rigid Domain, type Rigid Domain: Support in the Label text field.
Fixed Constraint 1
In the Physics toolbar, click  Attributes and choose Fixed Constraint.
Rigid Domain: Crank
1
In the Model Builder window, expand the Component 1 (comp1)>Multibody Dynamics (mbd)>Rigid Domains (All)>Rigid Domain 2 node, then click Rigid Domain 2.
2
In the Settings window for Rigid Domain, type Rigid Domain: Crank in the Label text field.
Mass and Moment of Inertia 1
1
In the Model Builder window, click Mass and Moment of Inertia 1.
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 m1.
4
In the I text field, type I1.
Rigid Domain: Connecting Rod
1
In the Model Builder window, expand the Component 1 (comp1)>Multibody Dynamics (mbd)>Rigid Domains (All)>Rigid Domain 3 node, then click Rigid Domain 3.
2
In the Settings window for Rigid Domain, type Rigid Domain: Connecting Rod in the Label text field.
Mass and Moment of Inertia 1
1
In the Model Builder window, click Mass and Moment of Inertia 1.
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 m2.
4
In the I text field, type I2.
Rigid Domain: Slider
1
In the Model Builder window, expand the Component 1 (comp1)>Multibody Dynamics (mbd)>Rigid Domains (All)>Rigid Domain 4 node, then click Rigid Domain 4.
2
In the Settings window for Rigid Domain, type Rigid Domain: Slider in the Label text field.
Mass and Moment of Inertia 1
1
In the Model Builder window, click Mass and Moment of Inertia 1.
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 m3.
Rigid Domain: Slider
In the Model Builder window, click Rigid Domain: Slider.
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 y direction check box.
4
Select the Prescribed in z direction check box.
5
Locate the Prescribed Rotation section. From the By list, choose Constrained rotation.
6
Select the Constrain rotation around x-axis check box.
7
Select the Constrain rotation around y-axis check box.
8
Select the Constrain rotation around z-axis check box.
Do as follows to generate Hinge Joint nodes between components.
9
In the Model Builder window, click Multibody Dynamics (mbd).
10
In the Settings window for Multibody Dynamics, click Physics Node Generation in the upper-right corner of the Automated Model Setup section. From the menu, choose Create Joints.
Hinge Joint 1
In the Model Builder window, expand the Hinge Joints node, then click Hinge Joint 1.
Prescribed Motion 1
1
In the Physics toolbar, click  Attributes and choose Prescribed Motion.
2
In the Settings window for Prescribed Motion, locate the Prescribed Rotational Motion section.
3
From the Prescribed motion through list, choose Angular velocity.
4
In the ωp text field, type omega.
5
Click to expand the Reaction Force Settings section. Select the Evaluate reaction forces check box.
In order to visualize the motion of the system with respect to the slider, you can use the option of defining a reference frame available in the Multibody Dynamics interface and plot the postprocessing variables for displacement with respect to the reference frame.
6
In the Model Builder window, click Multibody Dynamics (mbd).
7
In the Settings window for Multibody Dynamics, click to expand the Results section.
8
From the Body defining reference frame list, choose Rigid Domain: Slider.
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
From the Element size list, choose Extra fine.
4
Click  Build All.
Study 1: Hinge Joint
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, type Study 1: Hinge Joint in the Label text field.
Step 1: Time Dependent
1
In the Model Builder window, under Study 1: Hinge Joint 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(0,0.00001,0.025).
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: Hinge Joint>Solver Configurations>Solution 1 (sol1)>Dependent Variables 1 node, then click Reaction moment (comp1.mbd.hgj1.pm1.RM).
4
In the Settings window for State, locate the Scaling section.
5
In the Scale text field, type 1e8*(0.1*0.22463859864235272)^3*500.
6
In the Study toolbar, click  Compute.
Results
Click the  Show Grid button in the Graphics toolbar.
Displacement: Hinge Joint
1
In the Model Builder window, under Results click Displacement (mbd).
2
In the Settings window for 3D Plot Group, type Displacement: Hinge Joint in the Label text field.
Velocity: Hinge Joint
1
In the Model Builder window, under Results click Velocity (mbd).
2
In the Settings window for 3D Plot Group, type Velocity: Hinge Joint in the Label text field.
Follow the instructions below to plot relative displacement in hinge joint case. The resulting plot should match the one shown in Figure 3.
Relative Displacement: Hinge Joint
1
In the Model Builder window, right-click Displacement: Hinge Joint and choose Duplicate.
2
In the Settings window for 3D Plot Group, type Relative Displacement: Hinge Joint in the Label text field.
3
Locate the Plot Settings section. From the View list, choose New view.
4
From the Frame list, choose Material  (X, Y, Z).
Surface
1
In the Model Builder window, expand the Relative Displacement: Hinge Joint node, then click Surface.
2
In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Multibody Dynamics>Displacement>mbd.disp_ref - Displacement magnitude, reference frame - m.
3
Locate the Coloring and Style section. From the Color table list, choose Spectrum.
Selection 1
Right-click Surface and choose Selection.
Deformation
In the Settings window for Deformation, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Multibody Dynamics>Displacement>u_ref,...,w_ref - Displacement field, reference frame (spatial frame).
Selection 1
1
In the Model Builder window, click Selection 1.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Journal Boundaries.
Contour 1
1
In the Model Builder window, right-click Relative Displacement: Hinge Joint and choose Contour.
2
In the Settings window for Contour, locate the Expression section.
3
In the Expression text field, type mbd.disp_ref.
4
Click to expand the Title section. From the Title type list, choose None.
5
Locate the Coloring and Style section. From the Color table list, choose Spectrum.
6
Clear the Color legend check box.
Deformation 1
1
Right-click Contour 1 and choose Deformation.
2
In the Settings window for Deformation, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Multibody Dynamics>Displacement>u_ref,...,w_ref - Displacement field, reference frame (spatial frame).
3
Locate the Scale section. Select the Scale factor check box.
4
In the associated text field, type 1.
Selection 1
1
In the Model Builder window, right-click Contour 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Journal Boundaries.
Surface 2
1
In the Model Builder window, right-click Surface and choose Duplicate.
2
In the Settings window for Surface, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Geometry>dom - Entity index.
3
Click to expand the Title section. From the Title type list, choose None.
4
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
5
From the Color list, choose Custom.
6
On Windows, click the colored bar underneath, or — if you are running the cross-platform desktop — the Color button.
7
Click Define custom colors.
8
Set the RGB values to 255, 128, and 128, respectively.
9
Click Add to custom colors.
10
Click Show color palette only or OK on the cross-platform desktop.
Selection 1
1
In the Model Builder window, expand the Surface 2 node, then click Selection 1.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Connecting Rod without Journal.
Volume 1
1
In the Model Builder window, right-click Relative Displacement: Hinge Joint and choose Volume.
2
In the Settings window for Volume, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Geometry>dom - Entity index.
3
Click to expand the Title section. From the Title type list, choose None.
4
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
5
From the Color list, choose Cyan.
Selection 1
1
Right-click Volume 1 and choose Selection.
2
Select Domain 4 only.
Transparency 1
1
In the Model Builder window, right-click Volume 1 and choose Transparency.
2
In the Settings window for Transparency, locate the Transparency section.
3
Set the Transparency value to 0.75.
Deformation 1
1
Right-click Volume 1 and choose Deformation.
2
In the Settings window for Deformation, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Component 1 (comp1)>Multibody Dynamics>Displacement>u_ref,...,w_ref - Displacement field, reference frame (spatial frame).
3
Locate the Scale section. Select the Scale factor check box.
4
In the associated text field, type 1.
Volume 2
1
Right-click Volume 1 and choose Duplicate.
2
In the Settings window for Volume, locate the Coloring and Style section.
3
From the Coloring list, choose Color table.
4
From the Color table list, choose TrafficLight.
5
Clear the Color legend check box.
Selection 1
1
In the Model Builder window, expand the Volume 2 node, then click Selection 1.
2
In the Settings window for Selection, locate the Selection section.
3
Click  Clear Selection.
4
Select Domains 1 and 2 only.
Transparency 1
In the Model Builder window, under Results>Relative Displacement: Hinge Joint>Volume 2 right-click Transparency 1 and choose Delete.
Relative Displacement: Hinge Joint
1
In the Model Builder window, under Results click Relative Displacement: Hinge Joint.
2
In the Relative Displacement: Hinge Joint toolbar, click  Plot.
Multibody Dynamics (mbd)
Clearance Joint 1
1
In the Physics toolbar, click  Global and choose Clearance Joint.
2
In the Settings window for Clearance Joint, locate the Attachment Selection section.
3
From the Source list, choose Rigid Domain: Connecting Rod.
4
From the Connection point list, choose Centroid of selected entities.
Source Point: Boundary 1
1
In the Model Builder window, click Source Point: Boundary 1.
2
In the Settings window for Source Point: Boundary, locate the Boundary Selection section.
3
From the Selection list, choose Journal Boundaries.
4
In the list, select 33.
5
Click  Remove from Selection.
6
Select Boundaries 31, 32, 37, and 38 only.
Clearance Joint 1
1
In the Model Builder window, click Clearance Joint 1.
2
In the Settings window for Clearance Joint, locate the Attachment Selection section.
3
From the Destination list, choose Rigid Domain: Slider.
4
Locate the Clearance Settings section. In the C text field, type C.
5
In the pj text field, type mbd.crj1.Eequ*(0.1*mbd.diag)/100.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select General Studies>Time Dependent.
4
Click Add Study in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2: Clearance Joint
1
In the Model Builder window, click Study 2.
2
In the Settings window for Study, type Study 2: Clearance Joint in the Label text field.
Step 1: Time Dependent
1
In the Model Builder window, under Study 2: Clearance Joint 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(0,0.00001,0.025).
4
Locate the Physics and Variables Selection section. Select the Modify model configuration for study step check box.
5
In the tree, select Component 1 (Comp1)>Multibody Dynamics (Mbd)>Hinge Joints>Hinge Joint 3.
6
Right-click and choose Disable.
Solution 2 (sol2)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 2 (sol2) node.
3
In the Model Builder window, expand the Study 2: Clearance Joint>Solver Configurations>Solution 2 (sol2)>Dependent Variables 1 node, then click Reaction moment (comp1.mbd.hgj1.pm1.RM).
4
In the Settings window for State, locate the Scaling section.
5
In the Scale text field, type 1e8*(0.1*0.22463859864235272)^3*500.
6
In the Study toolbar, click  Compute.
Results
Displacement: Clearance Joint
In the Settings window for 3D Plot Group, type Displacement: Clearance Joint in the Label text field.
Velocity: Clearance Joint
1
In the Model Builder window, under Results click Velocity (mbd).
2
In the Settings window for 3D Plot Group, type Velocity: Clearance Joint in the Label text field.
Follow the instructions below to plot relative displacement in clearance joint case. The resulting plot should match the one shown in Figure 3.
Relative Displacement: Clearance Joint
1
In the Model Builder window, right-click Relative Displacement: Hinge Joint and choose Duplicate.
2
In the Settings window for 3D Plot Group, type Relative Displacement: Clearance Joint in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 2: Clearance Joint/Solution 2 (sol2).
4
In the Relative Displacement: Clearance Joint toolbar, click  Plot.
Follow the instructions below to plot slider velocity. The resulting plot should match the one shown in Figure 4.
Slider Velocity
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Slider Velocity in the Label text field.
3
Click to expand the Title section. From the Title type list, choose Label.
4
Locate the Legend section. From the Position list, choose Upper left.
Global 1
1
Right-click Slider Velocity 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: Slider>Rigid body velocity (spatial frame) - m/s>mbd.rd4.u_tx - Rigid body velocity, x component.
3
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
mbd.rd4.u_tx
m/s
Hinge joint
Global 2
1
Right-click Global 1 and choose Duplicate.
2
In the Settings window for Global, locate the Data section.
3
From the Dataset list, choose Study 2: Clearance Joint/Solution 2 (sol2).
4
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
mbd.rd4.u_tx
m/s
Clearance joint
Slider Velocity
1
In the Model Builder window, click Slider Velocity.
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 Rigid body velocity (m/s).
5
In the Slider Velocity toolbar, click  Plot.
Follow the instructions below to plot slider acceleration. The resulting plot should match the one shown in Figure 5.
Slider Acceleration
1
Right-click Slider Velocity and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Slider Acceleration in the Label text field.
3
Locate the Plot Settings section. In the y-axis label text field, type Rigid body acceleration (m/s<sup>2</sup>).
4
Locate the Legend section. From the Position list, choose Upper right.
Global 1
1
In the Model Builder window, expand the Slider 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
mbd.rd4.u_ttx
m/s^2
Hinge joint
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.rd4.u_ttx
m/s^2
Clearance joint
Follow the instructions below to plot crank reaction moment. The resulting plot should match the one shown in Figure 6.
Reaction Moment
1
In the Model Builder window, right-click Slider Acceleration and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Reaction Moment in the Label text field.
3
Locate the Plot Settings section. In the y-axis label text field, type Reaction moment (N*m).
Global 1
1
In the Model Builder window, expand the Reaction Moment 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.hgj1.pm1.RM
N*m
Hinge joint
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.hgj1.pm1.RM
N*m
Clearance joint
4
In the Reaction Moment toolbar, click  Plot.
Follow the instructions below to plot journal trajectory for clearance joint case. The resulting plot should match the one shown in Figure 7.
Journal Trajectory: Clearance Joint
1
In the Home toolbar, click  Add Plot Group and choose 3D Plot Group.
2
In the Settings window for 3D Plot Group, type Journal Trajectory: Clearance Joint in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 2: Clearance Joint/Solution 2 (sol2).
4
Click to expand the Title section. From the Title type list, choose Label.
5
Locate the Plot Settings section. From the View list, choose New view.
6
Clear the Plot dataset edges check box.
Point Trajectories 1
1
In the Journal Trajectory: Clearance Joint toolbar, click  More Plots and choose Point Trajectories.
2
In the Settings window for Point Trajectories, locate the Trajectory Data section.
3
From the Plot data list, choose Global.
4
Click Replace Expression in the upper-right corner of the Trajectory Data section. From the menu, choose Component 1 (comp1)>Multibody Dynamics>Clearance joints>Clearance Joint 1>mbd.crj1.dx,...,mbd.crj1.dz - Instantaneous distance.
5
Locate the Coloring and Style section. Find the Line style subsection. From the Type list, choose Tube.
6
In the Tube radius expression text field, type 1e-8.
7
Select the Radius scale factor check box.
8
In the associated text field, type 500.
Color Expression 1
1
Right-click Point Trajectories 1 and choose Color Expression.
2
In the Settings window for Color Expression, locate the Expression section.
3
In the Expression text field, type t.
4
Locate the Coloring and Style section. From the Color table list, choose RainbowLight.
5
Clear the Color legend check box.
Parameterized Curve 3D 1
1
In the Results toolbar, click  More Datasets and choose Parameterized Curve 3D.
2
In the Settings window for Parameterized Curve 3D, locate the Data section.
3
From the Dataset list, choose Study 2: Clearance Joint/Solution 2 (sol2).
4
Locate the Parameter section. In the Maximum text field, type 2*pi.
5
Locate the Expressions section. In the x text field, type C*sin(s).
6
In the z text field, type C*cos(s).
Line 1
1
In the Model Builder window, right-click Journal Trajectory: Clearance Joint and choose Line.
2
In the Settings window for Line, locate the Data section.
3
From the Dataset list, choose Parameterized Curve 3D 1.
4
Locate the Expression section. In the Expression text field, type 1.
5
Locate the Coloring and Style section. From the Line type list, choose Tube.
6
In the Tube radius expression text field, type 1e-8.
7
Select the Radius scale factor check box.
8
In the associated text field, type 500.
9
From the Coloring list, choose Uniform.
10
From the Color list, choose Magenta.
11
In the Journal Trajectory: Clearance Joint toolbar, click  Plot.
12
Click the  Zoom Extents button in the Graphics toolbar.
Follow the instructions below to plot force in clearance joint. The resulting plot should match the one shown in Figure 8.
Joint Force: Clearance Joint
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Joint Force: Clearance Joint in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 2: Clearance Joint/Solution 2 (sol2).
4
Locate the Title section. From the Title type list, choose Label.
5
Locate the Legend section. Clear the Show legends check box.
Global 1
1
Right-click Joint Force: Clearance Joint 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>Clearance joints>Clearance Joint 1>mbd.crj1.Fj - Joint force magnitude - N.
3
In the Joint Force: Clearance Joint toolbar, click  Plot.
Follow the instructions below to plot gap distance in clearance joint. The resulting plot should match the one shown in Figure 9.
Gap Distance: Clearance Joint
1
In the Home toolbar, click  Add Plot Group and choose Polar Plot Group.
2
In the Settings window for Polar Plot Group, type Gap Distance: Clearance Joint in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 2: Clearance Joint/Solution 2 (sol2).
4
Click to expand the Title section. From the Title type list, choose Label.
5
Locate the Grid section. Clear the Show grid check box.
6
Locate the Legend section. Clear the Show legends check box.
Global 1
1
Right-click Gap Distance: Clearance Joint and choose Global.
2
In the Settings window for Global, click Replace Expression in the upper-right corner of the r-Axis Data section. From the menu, choose Component 1 (comp1)>Multibody Dynamics>Clearance joints>Clearance Joint 1>mbd.crj1.gap - Gap distance - m.
3
Locate the θ Angle Data section. From the Parameter list, choose Expression.
4
In the Expression text field, type mbd.hgj1.th.
5
Click to expand the Coloring and Style section. In the Width text field, type 2.
Global 2
1
Right-click Global 1 and choose Duplicate.
2
In the Settings window for Global, locate the r-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
0
1
 
4
Locate the Coloring and Style section. Find the Line style subsection. From the Line list, choose Dotted.
5
From the Color list, choose Magenta.
Color Expression 1
1
In the Model Builder window, right-click Global 1 and choose Color Expression.
2
In the Settings window for Color Expression, locate the Expression section.
3
In the Expression text field, type t.
4
Locate the Coloring and Style section. From the Color table list, choose RainbowLight.
5
In the Gap Distance: Clearance Joint toolbar, click  Plot.
Displacement: Hinge Joint
1
In the Results toolbar, click  Animation and choose Player.
2
In the Settings window for Animation, type Displacement: Hinge Joint in the Label text field.
3
Locate the Frames section. In the Number of frames text field, type 50.
Displacement: Clearance Joint
1
Right-click Displacement: Hinge Joint and choose Duplicate.
2
In the Settings window for Animation, type Displacement: Clearance Joint in the Label text field.
3
Locate the Scene section. From the Subject list, choose Displacement: Clearance Joint.
Relative Displacement: Hinge Joint
1
In the Model Builder window, right-click Displacement: Hinge Joint and choose Duplicate.
2
In the Settings window for Animation, type Relative Displacement: Hinge Joint in the Label text field.
3
Locate the Scene section. From the Subject list, choose Relative Displacement: Hinge Joint.
Relative Displacement: Clearance Joint
1
Right-click Relative Displacement: Hinge Joint and choose Duplicate.
2
In the Settings window for Animation, type Relative Displacement: Clearance Joint in the Label text field.
3
Locate the Scene section. From the Subject list, choose Relative Displacement: Clearance Joint.
Journal Trajectory: Clearance Joint
1
Right-click Relative Displacement: Clearance Joint and choose Duplicate.
2
In the Settings window for Animation, type Journal Trajectory: Clearance Joint in the Label text field.
3
Locate the Scene section. From the Subject list, choose Journal Trajectory: Clearance Joint.