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Dynamics of a Cylindrical Roller Bearing
Introduction
Bearings are used in machines to reduce the friction between moving parts and thereby smoothen their relative motion. Rolling element bearing is one of the widely used bearings, where rolling elements or rollers are used to support the load. These rollers can be of different shapes- for instance- spherical, cylindrical, or tapered cylindrical.
This model simulates the dynamics of a cylindrical roller bearing. Here, multiple cylindrical rollers are inserted between the outer and inner race, and held in place with the help of the cage. The inner race is connected to a rotating shaft and the outer race to a fixed foundation. All components of the bearing are assumed rigid. Frictional contact is modeled between rollers and races using rigid body contact with friction. The connection between rollers and the cage is simplified using hinge joints. An external load is applied on the inner race and a transient study is performed to analyze the lateral dynamics of inner race, dynamics of rollers and cage, contact and friction forces, and energy dissipation due to friction.
Model Definition
The model geometry consists of twelve identical cylindrical rollers of radius 6 mm, inserted between two concentric cylindrical races of thickness 4.875 mm each.
Figure 1: Model geometry of the cylindrical roller bearing.
The inner radius of outer race is 45.125 mm and the outer radius of inner race is 32.875 mm. As shown in Figure 1, a slotted cylindrical ring called cage is used to hold the rollers in place and keep them separated. All components of the bearing are assumed rigid and use the material data for structural steel.
The connection between rollers and cage is modeled through hinge joints, having only one rotational degree of freedom about their axes (y-axis). The outer race is assumed to be connected to a fixed foundation without any translational or rotational motion. The inner race is connected to a shaft rotating with an angular speed of 5000 rpm. Additionally, a bearing load of 100 N is acting on inner race along -z direction.
For each rigid roller, a line of contact exists with both inner and outer races. Using the rigid body contact with friction functionality, the interaction between each roller and races are modeled as frictional contacts. The coefficient of friction between the rollers and races is assumed as 0.1.
A time dependent study is performed for 0.06 s, which corresponds to five cycles of rotation of shaft or inner race, to analyze the dynamics of inner race, cage and rollers. The contact and frictional forces between races and rollers are also studied.
Results and Discussion
Figure 2 shows the displacement in the inner race, rollers, and cage. As rollers are in contact with inner race, the rotation of inner race also leads to the rotation of rollers and cage. Figure 3 shows the velocity of rollers and cage. The contact force between rollers and inner race is also plotted here.
As rollers are free to rotate about their own axes, they exhibit an additional spinning motion about their axes. This can be visualized by plotting the relative velocity of rollers with respect to cage as shown in Figure 4.
Figure 2: Displacement of different components in cylindrical roller bearing at t = 0.06 s.
Figure 3: Velocity of rollers and cage at t = 0.06 s. Arrow plot shows the contact force between the rollers and inner race.
Figure 4: Relative velocity of rollers with respect to cage at t = 0.06 s.
The dynamics of the system is controlled by the inner race moving with a constant angular speed of 5000 rpm. This motion is transmitted to the contacting rollers and cage. Figure 5 shows the angular speed of inner race and cage.
Due to the contact with the rotating inner race, the direction of spin of rollers would be opposite to that of inner race. Angular speed of three sample rollers is shown in Figure 6. Contact and friction forces between the inner race and one of these sample rollers are shown in Figure 7. Frictional energy dissipation rate due to the contact between the three sample rollers and inner race is shown in Figure 8. Orbital motion of inner race is shown in Figure 9.
Figure 5: Angular speed of inner race and cage, as a function of time.
Figure 6: Angular speed of three sample rollers, as a function of time.
Figure 7: Contact and friction forces between a sample roller and inner race, as a function of time.
Figure 8: Frictional energy dissipation rate between three sample rollers and inner race, as a function of time.
Figure 9: Orbital motion of inner race.
Notes About the COMSOL Implementation
•
In this model, all components 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 rollers and cage 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.
Application Library path: Multibody_Dynamics_Module/Tutorials/roller_bearing_dynamics
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 roller_bearing_dynamics_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 roller_bearing_dynamics.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 roller_bearing_dynamics.mphbin.
6
Click Import.
Cage
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Cage in the Label text field.
3
On the object imp1(2), select Domain 1 only.
4
Locate the Color section. From the Color list, choose Color 18.
5
Click  Build Selected.
Races
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Races in the Label text field.
3
On the object imp1(1), select Domain 1 only.
4
On the object imp1(15), select Domains 1–4 only.
5
Locate the Color section. 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 128, 128, and 128, respectively.
9
Click Add to custom colors.
10
Click Show color palette only or OK on the cross-platform desktop.
11
Click  Build Selected.
Rollers
1
In the Geometry toolbar, click  Selections and choose Complement Selection.
2
In the Settings window for Complement Selection, type Rollers in the Label text field.
3
Locate the Input Entities section. Click  Add.
4
In the Add dialog box, in the Selections to invert list, choose Cage and Races.
5
Click OK.
6
In the Settings window for Complement Selection, locate the Color section.
7
From the Color list, choose Color 3.
8
Click  Build Selected.
Cage & Rollers
1
In the Geometry toolbar, click  Selections and choose Union Selection.
2
In the Settings window for Union Selection, type Cage & Rollers in the Label text field.
3
Locate the Input Entities section. Click  Add.
4
In the Add dialog box, in the Selections to add list, choose Cage and Rollers.
5
Click OK.
6
In the Settings window for Union Selection, click  Build Selected.
Cage & Rollers Boundaries
1
In the Geometry toolbar, click  Selections and choose Adjacent Selection.
2
In the Settings window for Adjacent Selection, type Cage & Rollers Boundaries in the Label text field.
3
Locate the Input Entities section. Click  Add.
4
In the Add dialog box, select Cage & Rollers in the Input selections list.
5
Click OK.
6
In the Settings window for Adjacent Selection, click  Build Selected.
Outer Race
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Outer Race in the Label text field.
3
On the object imp1(15), select Domains 1–4 only.
4
Click  Build Selected.
Outer Race Boundaries
1
In the Geometry toolbar, click  Selections and choose Adjacent Selection.
2
In the Settings window for Adjacent Selection, type Outer Race Boundaries in the Label text field.
3
Locate the Input Entities section. Click  Add.
4
In the Add dialog box, select Outer Race in the Input selections list.
5
Click OK.
6
In the Settings window for Adjacent Selection, locate the Output Entities section.
7
Select the Interior boundaries check box.
8
Click  Build Selected.
Boundaries without Outer Race
1
In the Geometry toolbar, click  Selections and choose Complement Selection.
2
In the Settings window for Complement Selection, type Boundaries without Outer Race 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 Outer Race Boundaries in the Selections to invert list.
6
Click OK.
7
In the Settings window for Complement Selection, click  Build Selected.
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
Click  Build Selected.
For better visualization, you can hide the top part of the outer race.
5
Click the  Click and Hide button in the Graphics toolbar.
6
Click the  Select Domains button in the Graphics toolbar.
7
On the object fin, select Domain 1 only.
Definitions
Variables 1
1
In the Model Builder window, under Component 1 (comp1) right-click Definitions and choose Variables.
2
In the Settings window for Variables, locate the Variables section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file roller_bearing_dynamics_variables.txt.
Ramp 1 (rm1)
1
In the Home toolbar, click  Functions and choose Local>Ramp.
2
In the Settings window for Ramp, locate the Parameters section.
3
In the Slope text field, type 1000.
4
Select the Cutoff check box.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Structural steel.
4
Click Add to Component in the window toolbar.
5
In the Home toolbar, click  Add Material to close the Add Material window.
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, click Physics Node Generation in the upper-right corner of the Automated Model Setup section. From the menu, choose Create Rigid Domains.
Rigid Domain 1: Outer Race
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 1: Outer Race in the Label text field.
Fixed Constraint 1
In the Physics toolbar, click  Attributes and choose Fixed Constraint.
Rigid Domain 3: Cage
1
In the Model Builder window, click Rigid Domain 3.
2
In the Settings window for Rigid Domain, type Rigid Domain 3: Cage in the Label text field.
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
Locate the Prescribed Rotation section. From the By list, choose Constrained rotation.
5
Select the Constrain rotation around x-axis check box.
6
Select the Constrain rotation around z-axis check box.
Rigid Domain 6: Inner Race
1
In the Model Builder window, click Rigid Domain 6.
2
In the Settings window for Rigid Domain, type Rigid Domain 6: Inner Race in the Label text field.
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
Locate the Prescribed Rotation section. From the By list, choose Prescribed rotation.
5
Specify the Ω vector as
0
x
1
y
0
z
6
In the φ0 text field, type omega*t.
Rigid Domain 6: Inner Race
In the Model Builder window, click Rigid Domain 6: Inner Race.
Applied Force 1
1
In the Physics toolbar, click  Attributes and choose Applied Force.
2
In the Settings window for Applied Force, locate the Applied Force section.
3
Specify the F vector as
0
x
0
y
-load*rm1(t[1/s])
z
Do as follows to generate Hinge Joint nodes between rollers and cage.
4
In the Model Builder window, click Multibody Dynamics (mbd).
5
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.
Rigid Body Contact 1
1
In the Physics toolbar, click  Global and choose Rigid Body Contact.
2
In the Settings window for Rigid Body Contact, locate the Source section.
3
From the Source list, choose Rigid Domain 2.
4
In the rs text field, type rr.
5
Locate the Destination section. From the Destination list, choose Rigid Domain 1: Outer Race.
6
In the rd text field, type ro.
7
Select the Use inside boundaries for contact check box.
8
Locate the Contact Settings section. In the fp text field, type fp.
9
In the τn text field, type 1[ms]*10.
Friction 1
1
In the Physics toolbar, click  Attributes and choose Friction.
2
In the Settings window for Friction, locate the Friction section.
3
In the μ text field, type mu.
4
In the v0 text field, type mbd.diag*1e-3[1/s]*10.
Roller-Outer Race Contact
Similarly create eleven more Rigid Body Contact nodes between rollers and outer race by duplicating Rigid Body Contact 1 and resetting the inputs using the information given in the table below.
Name
Source
Destination
Rigid Body Contact 2
Rigid Domain 4
Rigid Domain 1: Outer Race
Rigid Body Contact 3
Rigid Domain 5
Rigid Domain 1: Outer Race
Rigid Body Contact 4
Rigid Domain 7
Rigid Domain 1: Outer Race
Rigid Body Contact 5
Rigid Domain 8
Rigid Domain 1: Outer Race
Rigid Body Contact 6
Rigid Domain 9
Rigid Domain 1: Outer Race
Rigid Body Contact 7
Rigid Domain 10
Rigid Domain 1: Outer Race
Rigid Body Contact 8
Rigid Domain 11
Rigid Domain 1: Outer Race
Rigid Body Contact 9
Rigid Domain 12
Rigid Domain 1: Outer Race
Rigid Body Contact 10
Rigid Domain 13
Rigid Domain 1: Outer Race
Rigid Body Contact 11
Rigid Domain 14
Rigid Domain 1: Outer Race
Rigid Body Contact 12
Rigid Domain 15
Rigid Domain 1: Outer Race
Rigid Body Contact 1, Rigid Body Contact 10, Rigid Body Contact 11, Rigid Body Contact 12, Rigid Body Contact 2, Rigid Body Contact 3, Rigid Body Contact 4, Rigid Body Contact 5, Rigid Body Contact 6, Rigid Body Contact 7, Rigid Body Contact 8, Rigid Body Contact 9
1
In the Model Builder window, under Component 1 (comp1)>Multibody Dynamics (mbd), Ctrl-click to select Rigid Body Contact 1, Rigid Body Contact 2, Rigid Body Contact 3, Rigid Body Contact 4, Rigid Body Contact 5, Rigid Body Contact 6, Rigid Body Contact 7, Rigid Body Contact 8, Rigid Body Contact 9, Rigid Body Contact 10, Rigid Body Contact 11, and Rigid Body Contact 12.
2
Right-click and choose Group.
Roller-Outer Race Contact
In the Settings window for Group, type Roller-Outer Race Contact in the Label text field.
Add Rigid Body Contact nodes between rollers and inner race by duplicating Roller-Outer Race Contact and resetting the input values.
Roller-Inner Race Contact
1
Right-click Roller-Outer Race Contact and choose Duplicate.
2
In the Settings window for Group, type Roller-Inner Race Contact in the Label text field.
Rigid Body Contact 13
1
In the Model Builder window, expand the Roller-Inner Race Contact node, then click Rigid Body Contact 13.
2
In the Settings window for Rigid Body Contact, locate the Destination section.
3
From the Destination list, choose Rigid Domain 6: Inner Race.
4
Clear the Use inside boundaries for contact check box.
5
In the rd text field, type ri.
Roller-Inner Race Contact
1
Similar to the changes done for Rigid Body Contact 13, reset the inputs of other eleven Rigid Body Contact nodes using the information given in the table below.
Name
Source
Destination
Rigid Body Contact 14
Rigid Domain 4
Rigid Domain 6: Inner Race
Rigid Body Contact 15
Rigid Domain 5
Rigid Domain 6: Inner Race
Rigid Body Contact 16
Rigid Domain 7
Rigid Domain 6: Inner Race
Rigid Body Contact 17
Rigid Domain 8
Rigid Domain 6: Inner Race
Rigid Body Contact 18
Rigid Domain 9
Rigid Domain 6: Inner Race
Rigid Body Contact 19
Rigid Domain 10
Rigid Domain 6: Inner Race
Rigid Body Contact 20
Rigid Domain 11
Rigid Domain 6: Inner Race
Rigid Body Contact 21
Rigid Domain 12
Rigid Domain 6: Inner Race
Rigid Body Contact 22
Rigid Domain 13
Rigid Domain 6: Inner Race
Rigid Body Contact 23
Rigid Domain 14
Rigid Domain 6: Inner Race
Rigid Body Contact 24
Rigid Domain 15
Rigid Domain 6: Inner Race
In order to visualize the motion of the system with respect to the cage frame, you can use the option of defining a reference frame available in the Multibody Dynamics interface and plot the postprocessing variables for velocity with respect to the reference frame.
2
In the Model Builder window, click Multibody Dynamics (mbd).
3
In the Settings window for Multibody Dynamics, click to expand the Results section.
4
From the Body defining reference frame list, choose Rigid Domain 3: Cage.
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 Finer.
4
Click  Build All.
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,T/500,5*T).
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, then click Fully Coupled 1.
4
In the Settings window for Fully Coupled, click to expand the Method and Termination section.
5
In the Maximum number of iterations text field, type 15.
6
In the Model Builder window, click Time-Dependent Solver 1.
7
In the Settings window for Time-Dependent Solver, click to expand the Time Stepping section.
8
From the Steps taken by solver list, choose Intermediate.
9
In the Study toolbar, click  Compute.
Results
Click the  Show Grid button in the Graphics toolbar.
Follow the instructions below to plot system displacement as shown in Figure 2.
Displacement (mbd)
1
In the Model Builder window, under Results click Displacement (mbd).
2
In the Settings window for 3D Plot Group, locate the Plot Settings section.
3
Select the Propagate hiding to lower dimensions check box.
4
In the Model Builder window, expand the Displacement (mbd) node.
Selection 1
1
In the Model Builder window, expand the Results>Displacement (mbd)>Surface node.
2
Right-click Surface and choose Selection.
3
In the Settings window for Selection, locate the Selection section.
4
From the Selection list, choose Boundaries without Outer Race.
Surface 2
1
In the Model Builder window, right-click Surface and choose Duplicate.
2
In the Settings window for Surface, click to expand the Title section.
3
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 Gray.
Transparency 1
Right-click Surface 2 and choose Transparency.
Selection 1
1
In the Settings window for Selection, locate the Selection section.
2
Select the  Activate Selection toggle button.
3
From the Selection list, choose Outer Race Boundaries.
4
In the Displacement (mbd) toolbar, click  Plot.
Follow the instructions below to plot contact force and velocity. The resulting plot should match the one shown in Figure 3.
Contact Force & Velocity
1
In the Model Builder window, under Results click Velocity (mbd).
2
In the Settings window for 3D Plot Group, type Contact Force & Velocity in the Label text field.
3
Click to expand the Selection section. Locate the Plot Settings section. From the View list, choose New view.
Arrow Line
1
In the Model Builder window, expand the Contact Force & Velocity node.
2
Right-click Arrow Line and choose Delete.
Volume
1
In the Model Builder window, click Volume.
2
In the Settings window for Volume, locate the Coloring and Style section.
3
From the Coloring list, choose Uniform.
4
From the Color list, choose Gray.
5
Click to expand the Title section. From the Title type list, choose None.
Transparency 1
Right-click Volume and choose Transparency.
Selection 1
1
Right-click Volume and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Races.
4
In the list, choose 2 and 3.
5
Click  Remove from Selection.
6
Select Domains 1, 4, and 9 only.
Surface 1
1
In the Model Builder window, right-click Contact Force & Velocity and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type mbd.vel.
4
Locate the Coloring and Style section. From the Color table list, choose HeatCameraLight.
Deformation 1
1
Right-click Surface 1 and choose Deformation.
2
In the Settings window for Deformation, locate the Scale section.
3
Select the Scale factor check box.
4
In the associated text field, type 1.
Selection 1
1
In the Model Builder window, right-click Surface 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Cage & Rollers Boundaries.
Arrow Surface 1
1
In the Model Builder window, right-click Contact Force & Velocity and choose Arrow Surface.
2
In the Settings window for Arrow Surface, locate the Expression section.
3
In the X component text field, type Fnx.
4
In the Y component text field, type Fny.
5
In the Z component text field, type Fnz.
6
Select the Description check box.
7
In the associated text field, type Contact force (N).
8
Locate the Coloring and Style section. Select the Scale factor check box.
9
In the associated text field, type 5e-4.
10
From the Color list, choose Green.
Deformation 1
1
Right-click Arrow Surface 1 and choose Deformation.
2
In the Settings window for Deformation, locate the Scale section.
3
Select the Scale factor check box.
4
In the associated text field, type 1.
Selection 1
1
In the Model Builder window, right-click Arrow Surface 1 and choose Selection.
2
In the Settings window for Selection, locate the Selection section.
3
From the Selection list, choose Cage & Rollers Boundaries.
4
In the Contact Force & Velocity toolbar, click  Plot.
Follow the instructions below to plot the velocity with respect to cage frame. The resulting plot should match the one shown in Figure 4.
Velocity [Cage Frame]
1
In the Model Builder window, right-click Contact Force & Velocity and choose Duplicate.
2
In the Settings window for 3D Plot Group, type Velocity [Cage Frame] in the Label text field.
Surface 1
1
In the Model Builder window, expand the Velocity [Cage Frame] node, then click Surface 1.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type mbd.vel_ref.
Arrow Surface 1
In the Model Builder window, right-click Arrow Surface 1 and choose Delete.
Velocity [Cage Frame]
Follow the instructions below to plot angular speed of inner race and cage. The resulting plot should match the one shown in Figure 5.
Angular Speed [Inner Race & Cage]
1
In the Home toolbar, click  Add Plot Group and choose 1D Plot Group.
2
In the Settings window for 1D Plot Group, type Angular Speed [Inner Race & Cage] in the Label text field.
3
Click to expand the Title section. From the Title type list, choose Label.
Global 1
1
Right-click Angular Speed [Inner Race & Cage] and choose Global.
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.rd6.th_ty
rad/s
Rigid body angular velocity, y component
mbd.rd3.th_ty
rad/s
Rigid body angular velocity, y component
4
Click to expand the Legends section. From the Legends list, choose Manual.
5
In the table, enter the following settings:
Legends
Inner race
Cage
6
In the Angular Speed [Inner Race & Cage] toolbar, click  Plot.
Follow the instructions below to plot angular speed of rollers. The resulting plot should match the one shown in Figure 6.
Angular Speed [Rollers]
1
In the Model Builder window, right-click Angular Speed [Inner Race & Cage] and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Angular Speed [Rollers] in the Label text field.
Global 1
1
In the Model Builder window, expand the Angular Speed [Rollers] 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.rd11.th_ty
rad/s
Rigid body angular velocity, y component
mbd.rd15.th_ty
rad/s
Rigid body angular velocity, y component
mbd.rd10.th_ty
rad/s
Rigid body angular velocity, y component
4
In the Angular Speed [Rollers] toolbar, click  Plot.
5
Locate the Legends section. In the table, enter the following settings:
Legends
A
B
C
6
In the Angular Speed [Rollers] toolbar, click  Plot.
Follow the instructions below to plot contact and friction force between roller and inner race. The resulting plot should match the one shown in Figure 7.
Contact & Friction Force [Roller-Inner Race]
1
In the Model Builder window, right-click Angular Speed [Rollers] and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Contact & Friction Force [Roller-Inner Race] in the Label text field.
Global 1
1
In the Model Builder window, expand the Contact & Friction Force [Roller-Inner Race] node, then click Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
Click  Clear Table.
4
In the table, enter the following settings:
Expression
Unit
Description
mbd.rbc20.Fn
N
Contact force
mbd.rbc20.Ff
N
Friction force
5
Locate the Legends section. From the Legends list, choose Automatic.
Contact & Friction Force [Roller-Inner Race]
1
In the Model Builder window, click Contact & Friction Force [Roller-Inner Race].
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 Contact & Friction Force [Roller-Inner Race] toolbar, click  Plot.
Follow the instructions below to plot frictional energy dissipation rate between rollers and inner race. The resulting plot should match the one shown in Figure 8.
Frictional Energy Dissipation Rate [Roller-Inner Race]
1
Right-click Contact & Friction Force [Roller-Inner Race] and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Frictional Energy Dissipation Rate [Roller-Inner Race] in the Label text field.
Global 1
1
In the Model Builder window, expand the Frictional Energy Dissipation Rate [Roller-Inner Race] node, then click Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
Click  Clear Table.
4
In the table, enter the following settings:
Expression
Unit
Description
mbd.rbc20.Qf
W
Frictional energy dissipation rate
mbd.rbc24.Qf
W
Frictional energy dissipation rate
mbd.rbc19.Qf
W
Frictional energy dissipation rate
5
Locate the Legends section. From the Legends list, choose Manual.
6
In the table, enter the following settings:
Legends
A
B
C
Frictional Energy Dissipation Rate [Roller-Inner Race]
1
In the Model Builder window, click Frictional Energy Dissipation Rate [Roller-Inner Race].
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Clear the y-axis label check box.
4
In the Frictional Energy Dissipation Rate [Roller-Inner Race] toolbar, click  Plot.
Follow the instructions below to plot inner race orbit. The resulting plot should match the one shown in Figure 9.
Inner Race Orbit
1
Right-click Frictional Energy Dissipation Rate [Roller-Inner Race] and choose Duplicate.
2
In the Settings window for 1D Plot Group, type Inner Race Orbit in the Label text field.
Global 1
1
In the Model Builder window, expand the Inner Race Orbit node, then click Global 1.
2
In the Settings window for Global, locate the y-Axis Data section.
3
Click  Clear Table.
4
In the table, enter the following settings:
Expression
Unit
Description
mbd.rd6.w
mm
Rigid body displacement, z component
5
Locate the Legends section. Clear the Show legends check box.
6
Locate the x-Axis Data section. From the Parameter list, choose Expression.
7
In the Expression text field, type mbd.rd6.u.
8
From the Unit list, choose mm.
Inner Race Orbit
1
In the Model Builder window, click Inner Race Orbit.
2
In the Inner Race Orbit toolbar, click  Plot.
Displacement (mbd)
1
In the Results toolbar, click  Animation and choose Player.
2
In the Settings window for Animation, type Displacement (mbd) in the Label text field.
3
Locate the Frames section. In the Number of frames text field, type 100.
Contact Force & Velocity
1
Right-click Displacement (mbd) and choose Duplicate.
2
In the Settings window for Animation, type Contact Force & Velocity in the Label text field.
3
Locate the Scene section. From the Subject list, choose Contact Force & Velocity.
Velocity [Cage Frame]
1
Right-click Contact Force & Velocity and choose Duplicate.
2
In the Settings window for Animation, type Velocity [Cage Frame] in the Label text field.
3
Locate the Scene section. From the Subject list, choose Velocity [Cage Frame].