basic-knuckle joint pinchasek/me 501/ansys... · knuckle joint pin problem: a pin in a knuckle...

Knuckle Joint Pin

Problem:

A pin in a knuckle joint carrying a tensile load F deflects somewhat because of theloading resulting in the distribution of reaction and load shown in part b of the figure.The usual designer’s assumption of loading is shown in part c; others sometimeschoose the loading shown in part d. If a = 0.5 in, b = 0.75 in, d = 0.5 in, andF = 1000 lb, estimate the maximum bending stress using the loading assumption shownin part c.

Joseph Shigley and Charles Mischke. Mechanical Engineering Design5th ed. New York: McGraw Hill, May 2002.

Knuckle Joint PinOverview

Outcomes1) Learn how to start ANSYS 8.0 2) Gain familiarity with the graphical user interface (GUI)3) Learn how to create and mesh a simple geometry4) Learn how to apply boundary constraints and solve problems

Tutorial OverviewThis tutorial is divided into six parts:

1) Tutorial Basics2) Starting Ansys3) Preprocessing4) Solution5) Post-Processing6) Hand Calculations

Anticipated time to complete this tutorial: 1 hour

AudienceThis tutorial assumes minimal knowledge of ANSYS 8.0; therefore, it goes into moderatedetail to explain each step. More advanced ANSYS 8.0 users should be able to completethis tutorial fairly quickly.

Prerequisites1) ANSYS 8.0 in house “Structural Tutorial”

Objectives1) Model the pin in ANSYS 8.02) Analyze the pin for maximum bending stress using ANSYS 8.0

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Knuckle Joint PinTutorial Basics

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In this tutorial:Instructions appear on the left.

Visual aids corresponding to the textappear on the right.

All commands on the toolbars arelabeled. However, only operationsapplicable to the tutorial are explained.

The instructions should be used as follows:

Bold > Text in bold are buttons, options, or selections that the user needs to click on

Example: > Preprocessor > Element Type > Add/Edit/DeleteFile would mean to follow the options as shown to the right to get you to the Element Types window

Italics Text in italics are hints and notes

MB1 Click on the left mouse buttonMB2 Click on the middle mouse

buttonMB3 Click on the right mouse

button

Some basic ANSYS functions are:

To rotate the models use Ctrl and MB3.

To zoom use Ctrl and MB2 and move themouse up and down.

To translate the models use Ctrl and MB1.

Knuckle Joint PinStarting Ansys

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For this tutorial the windows version ofANSYS 8.0 will be demonstrated. The pathbelow is one example of how to accessANSYS; however, this path will not be thesame on all computers.

For Windows XP start ANSYS by eitherusing:

> Start > All Programs > ANSYS 8.0> ANSYSor the desktop icon (right) if present.

Note: The path to start ANSYS 8.0 may be different foreach computer. Check with your local network manager tofind out how to start ANSYS 8.0.


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Once ANSYS 8.0 is loaded, two separatewindows appear: the main ANSYSAdvanced Utility Window and the ANSYSOutput Window.

The ANSYS Advanced Utility Window,also known as the Graphical User Interface(GUI), is the location where all the userinterface takes place.

The Output Window documents all actionstaken, displays errors, and solver status.

Graphical User Interface

Output Window


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The main utility window can be broken upinto three areas. A short explanation of eachwill be given.

First is the Utility Toolbar:

From this toolbar you can use the commandline approach to ANSYS and access multiplemenus that you can’t get to from the mainmenu.

Note: It would be beneficial to take some time and explorethese pull down menus and familiarize yourself with them.

Second is the ANSYS Main Menu as shownto the right. This menu is designed to use atop down approach and contains all thesteps and options necessary to properly pre-process, solve, and postprocess a model.

Third is the Graphical Interface windowwhere all geometry, boundary conditions,and results are displayed.

The tool bar located on the right hand sidehas all the visual orientation tools that areneeded to manipulate your model.


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With ANSYS 8.0 open select> File > Change Jobname

and enter a new job name in the blank fieldof the change jobname window.

Enter the problem title for this tutorial.> OK

In order to know where all the output filesfrom ANSYS will be placed, the workingdirectory must be set in order to avoid usingthe default folder: C:\Documents andSettings.

> File > Change Directory > then select the location that you wantall of the ANSYS files to be saved.

Be sure to change the working directory atthe beginning of every problem.

With the jobname and directory set theANSYS database (.db) file can be given atitle. Following the same steps as you didto change the jobname and the directory,give the model a title.

Knuckle Joint PinPreprocessing

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To begin the analysis, a preference needs tobe set.

> Main Menu > Preferences

Place a check mark next to the Structuralbox. This determines the type of analysis tobe performed in ANSYS.

> Ok

The ANSYS Main Menu should now beopened. Click once on the “+” sign next toPreprocessor.

> Main Menu > Preprocessor

The Preprocessor options currently avail-able are displayed in the expansion of theMain Menu tree as shown to the right.


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As mentioned previously, the ANSYS MainMenu is designed in such a way that oneshould start at the beginning and worktowards the bottom of the menu in prepar-ing, solving, and analyzing your model.

Note: This procedure will be shown throughout the tuto-rial.

Select the “+” next to Element Type or clickon Element Type. The extension of themenu is shown to the right.

> Element Type

Select Add/Edit/Delete and the Elementtype window appears. Select add and theLibrary of Element Types window appears.

> ADD/EDIT/DELETE > Add

In this window, select the types of elementsto be defined and used for this problem.

For this model Pipe16 elements will beused. We will define them as having asolid shaft rather than an inner diameter.

> Pipe > Elast straight16> OK

In the Element Types window Type 1Pipe16 should be visible signaling thatthe element type has been chosen.

Close the Element Types window.> Close


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The properties for the pipe 16 elements needto be chosen. This is done by adding a RealConstant.

> Preprocessor > Real Constants > Add/Edit/Delete

The Real Constants window should appear.Select add to create a new set.

> Add

The Element Type for Real Constants win-dow should appear. From this window,select Pipe16 as the element type.

> Type 1 Pipe16 > OK

The Real Constant Set Number 1, forPipe16 window will appear. From this win-dow you can interactively customize the ele-ment type.

From the problem statemen the outsidediameter of the pin should be 0.5 inches.Since the pin is a solid, the thickness of theelements should be equal to the radius ofthe outside diameter (should be .25 inches).

Enter the values in to the table as shown tothe right.

> Ok

Close the window.> Close


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The material properties for the Pipe16 ele-ments now need to be defined.

> Preprocessor > Material Props > Material Models

The Define Material Models Behavior win-dow should now be open.

This window has many different possibili-ties for defining the materials for yourmodel. We will use isotropic, linearly, elas-tic, structural properties.

Select the following from the MaterialModels Available window:

> Structural > Linear > Elastic > Isotropic

The window titled Linear IsotropicProperties for Material Number 1 nowappears. This window is the entry point forthe material properties to be used for themodel.

Enter 30e6 (30 Mpsi) in for EX (Young'sModulus) and 0.3 for PRXY (Poission’sRatio).

> OK

Close the Define Material Model Behaviorwindow.

> Material > Exit


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The next step is to define the keypoints(KP’s) where loads and constraints will beapplied:

> Preprocessor > Modeling> Create Keypoints > In Active CS

The Create Keypoints in Active CS win-dow will now appear. Here the KP’s will begiven numbers and their respective (XYZ)coordinates.

Enter the KP numbers and coordinatesfor the pin definition. Select Applyafter each KP has been defined.

Note: Be sure to change the keypoint numbereverytime you click apply to finish adding a key-point. If you don’t it will just move the last keypoint youentered to the new coordinates you just entered.

KP # 1: X=0, Y=0, Z=0KP # 2: X=0.25, Y=0, Z=0KP # 3: X=0.6875, Y=0, Z=0KP # 4: X=1.0625, Y=0, Z=0KP # 5: X=1.5, Y=0, Z=0KP # 6: X=1.75, Y=0, Z=0

Select OK when complete.

In the case that a mistake was made in creat-ing the keypoints, select:

> Preprocessor > Modeling > Delete > Keypoints

Select the inappropriate KP’s and select Ok.

The created KP’s should look similar to theexample to the right except the KP’s couldbe labeled with the KP numbers.


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At times it will be helpful to turn on the key-point numers.

> PlotCtrls > Numbering > put a checkmark next to keypointnumbers > OK

Other numbers (for lines, areas, etc..) can beturned on in a similiar manner.

The next step is to create lines between theKP’s.

> Preprocessor > Modeling > Create > Lines > Lines > Straight Lines

The Create Straight Lines window shouldappear. You will create 5 lines. Create line 1between the first two keypoints.

For line 1: MB1 KP1 then MB1 KP 2.

The other lines will be created in a similiarmanner.

For line 2: MB1 KP2 then MB1 KP 3.For line 3: MB1 KP3 then MB1 KP 4.For line 4: MB1 KP4 then MB1 KP 5.For line 5: MB1 KP5 then MB1 KP 6.

Verify that each line only goes between thespecified keypoints. When you are donecreating the lines click ok in the CreateStraight Lines window.

> Ok

If you make a mistake, use the following todelete the lines:

> Preprocessor > Modeling > Delete > Lines Only


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Now that the model has been created, itneeds to be meshed. Only meshed modelscan be run to find a solution. Models aremeshed with elements.

First, the element size will be specified.> Preprocessor > Meshing> Size Cntrls > Manual Size > Lines > All Lines

The Element Sizes on All Selected Lineswindow should appear. From this windowthe number of elements per lines segementcan be defined along with the Element edgelength.

Since the length of the pin is 1.75 in, approx-imately 20 elements along the length of thepin will produce reasonable results.

Enter 0.0875 into the Element edge lengthfield since 1.75/20=0.0875 in.

> Ok

Note: you could change the element edge length after com-pleting the tutorial to a different value and rerun the solu-tion to see how it affects the results.

With the mesh parameters complete thelines representing the pin can now bemeshed. Select:

> Preprocessor > Meshing > Mesh > Lines

From the Mesh Lines window select PickAll.

> Pick all

This will select all the line segments andmesh them all at the same time.

The meshed line should appear similar asshown to the right.

Knuckle Joint PinSolution

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We will now move into the solution phase.

Before applying the loads and constraintsto the pin, we will select to start a newanalysis

> Solution > Analysis Type > NewAnalysis

For type of analysis select Static and selectOk.

The constraints will now be added.

For this problem the two upward actingforces act as simple constraints or reactionforces. The reaction forces can be modeledas constraints in the X and Y direction.

To apply constraints select:> Solution > Define Loads > Apply > Structural > Displacement > On Keypoints

The Apply U, ROT on KP’s window nowappears. It will be easier to select the key-points if the keypoint numbers are turnedon as previously explained. However, thecurrent view probably shows just the ele-ments and not the keypoints. The Plotmenu can change the way you see yourmodel. You can see both the elements andthe keypoints on the screen by selecting:

> Plot > Multiplots

To see just the keypoints;> Plot > Keypoints > Keypoints

Use the plot menu to view your model inway most helpful to completing the step intutorial.


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With the Apply U, ROT on KP’s windowopen select KP 2 and KP 5 from the ANSYSgraphics window.

> Apply

The Apply U, ROT on KP’s large windowshould appear. From this window thedegrees of freedom can be specified.

To the right of DOFs to be constrainedselect UX, UY, ROTX, and ROTY.

> Apply.

The contstraints now apppear at keypoints 2and 5.

Now select KP 3 and KP 4.> Apply

The Apply U, ROT on KP’s large windowshould reappear.

Unselect UX, UY, ROTX, and ROTY byusing MB1 and then select UZ and ROTZ.

> Ok

The final constraints should now be on KP 3and KP 4.

The constrained model should appear simi-lar to the right.


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The loads will now be applied to the pin.> Solutions > Define Loads > Apply> Structural > Force/Moment > On Keypoints

The Apply F/M on KP’s window shouldappear.

Select KP 3 and KP 4 in the graphics win-dow.

> Apply

The expanded Apply F/M on KP’s windowshould appear. From this window the direc-tion of the force and magnitude can be spec-ified.

Select FY for the Direction of force/moment.Select Constant Value for Apply as.

The total force of 1000 lb will be dividedequally between the two pins.

Enter 500 in the Force/moment value fieldwhich will apply a -500 lb force.

Verify that all the fields match those of thefigure shown to the right.

> Ok

The fully loaded and constrainedmodel should appear similar tothe picture shown on the right.


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The next step in completion of the tutorial isto solve the current load step that has beencreated. Select:

> Solution > Solve > Current LS

The Solve Current Load Step window willappear. To begin the analysis select Ok.

The analysis should begin and when com-plete a Note window should appear thatstates the analysis is complete.

Close both the Note window and /STATUSCommand window.

Knuckle Joint PinPost Processing

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Results are viewed by using post processingcommands.

From the ANSYS Main Menu select:> General Postproc > Element Table> Define Table

The Element Data Table window shouldappear and should be empty. This windowshows which types of results will and can beplotted. Select add.

> Add

The Define Additional Element TableItems window should appear. From thiswindow the types of results of interest canbe selected to be used for analysis.

From the problem statement it says to esti-mate the maximum bending stress for theloading assumption in part c. To obtain thestress, select Stress from the Item, Comp,Results data item drag down menu. Fromthe drag down menu to the right of thestress selection, select von Mises SEQV.

> Stress > Von Mises SEQV> Ok

The picture to the right shows the line thatshould be added to the Element Data Table.

With the result type selected the results canbe plotted.

Select Close in the Element Data Tablewindow.

> Close

Knuckle Joint PinPost Processing

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To view results:> General Postproc > Element Table> Plot Elem Table

The Contour Plot of Element Table Datashould appear. From this window the vari-ous types or results that could have beenpreviously defined can be accessed.

Select SEQV fromto the right of Item to beplotted.

Select No- do not average for the Average atcommon nodes field.

>Ok

A plot now appears that shows the vonMises stress contour and the deformationalso.

In the top left hand corner of the plot thetext SMX = 17825 is displayed. This repre-sents the maximum bending stress in thepin and the location is defined on the pinwhere its says MX.

The text DMX = .345E-03 represents themaximum deflection of the pin. The colorcontour of the pin is gaged according to thescale at the bottom of the window to refer-ence various points along the pin.

To validate the results from ANSYS, thehand calculations for the pin configurationdesired are provided on the next page.

Knuckle Joint PinHand Calculations

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Problem Statement:A pin in a knuckle joint carrying a tensileload F deflects somewhat on account of thisloading, making the distribution of reactionand load shown. The usual designer’sassumption of loading is shown in part c;others sometimes choose the loading inpard d. If a=.5 in, b=.75 in, d=.5 in andF=1000 lb, estimate the maximum bendingstress.

Following the loading assumption of Part cwhich we modeled, we will now present theclosed form solution.

Sigma = Mc/I Maximum Bending StressI =(PI*d4)/64c = d/2M = maximum moment

Solution:I = (PI*(.5)4)/64=.003067961576 in4

c=.5/2=.25 in

The maximum moment is found by usingshear/moment diagrams.

From Moment diagram M=218.75 lb-in.To solve for maximum bending stress subvalues into sigma.

Sigma = Mc/I= (218.75)(.25)/(.003067961576)

Sigma = 17,825.353 psi Answer

Part c

b/2

a + b a/2 a/2

500

-500

M (lb-in)

218.75

í (lb)

Shear and Bending MomentDiagrams