Date: Fri, 29 Mar 2024 01:40:53 -0500 (CDT)
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Problem Specification
A preeminent bicycle company is disappointed with the negative feedback =
they have received on their latest model, and they have pinpointed the prob=
lem to an outdated bicycle crank design that they assumed would still withs=
tand typical loads. To protect their reputation, they have outsourced the t=
ask of analyzing the crank to you, providing you with the geometry of the b=
icycle crank and attached pedal shaft shown below. The dimensions are given=
in inches. The material they selected has an Young's modulus E =
=3D 2.8x107 psi and Poisson ratio =CE=BD=3D0.3. =
p>
Higher Resoluti=
on Image
Using ANSYS, determine the mechanical response due to a load of 100 lbf =
applied vertically downward at the end of the pedal shaft as shown in the f=
igure below. Assume that the crank is attached rigidly to a fixed shaft fit=
ted into the hole near the left end of the crank. This means you can constr=
ain the surface of the left hole in X, Y and Z d=
irections as indicated below.
Calculate the deflection, strain and stress distributions in the crank/ped=
al shaft combination for this loading condition. Use the ANSYS results to e=
valuate the degree of stress concentration in the vicinity of the cut-out i=
n the crank geometry.
Go to =
Step 1: Pre-Analysis & Start-Up
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earning Modules
Step 1: Pre-Analysi=
s & Start-Up
From the problem statement, we know that we are solving static structura=
l problem.
Start ANSYS Workbench
With the new release of ANSYS 12, there have been a lot of improvement i=
n term of overall flow. We start our simulation by first starting the ANSYS=
workbench.
Start > All Programs > ANSYS 12.0 > Workbench<=
/p>
Following figure shows the workbench window.
Higher Resolution Image
At the left hand side of the workbench window, you will see a toolbox fu=
ll of various analysis systems. In the middle, you see an empty work space.=
This is the place where you will organize your project. At the bottom of t=
he window, you see messages from ANSYS.
Select Analysis Systems
Higher Reso=
lution Image
Since our problem involves static analysis, we will select the Static Structural (ANSYS) component on the left panel.
Left click (and hold) on =
Static Structural (ANSYS), and drag the icon to th=
e empty space in the Pro=
ject Schematic.
Since we selected Static Structural (ANSYS), each cell of the system cor=
responds to a step in the process of performing the ANSYS Structural analys=
is. Rename the project to Crank.
Now, we just need to work out each step from top down to get to the resu=
lts for our solution.
- We start by preparing our geometry
- We use geometry to generate a mesh
- We setup the physics of the problem
- We run the problem in the solver to generate a solution
- Finally, we post process the solution to gain insight into the results<=
/li>
Specify Material Properti=
es
We will first specify the material properties of the crank. The material=
has an Young's modulus E=3D2.8x107 psi and Poisson's ratio =CE=
=BD=3D0.3.
In the Crank cell, double click on Engineering Data. This will bring you to=
a new page. The default material given is Structural Steel. We will use this =
material and change the Young's modulus and Poisson's ratio.
Left click on Structu=
ral Steel once and you will see the details of Structu=
ral Steel material properties under =
Properties of Outline Row 3: Structural Steel. Under Isotropic Ela=
sticity, change Young's Modulus and Poisson's Ratio to E=3D2=
.8e7 psi and =CE=BD=3D0.3. Remember to change the unit accordingly.
Higher Resolutio=
n Image
Press the Return to P=
roject to return to Workbench Project Schematic window.
Go to =
Step 2: Geometry
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Step 2: Geometry
Note: You can import geometry from Solidworks. Just make sure that when =
you create your geometry in Solidworks, you have the Crank body and Handle =
body.
In the Crank cell, right click on Geometry, and click New Geometry...
At this point, a new window, ANSYS Design Modeler will be opened. You will=
be asked to select desired length unit. Select Inch unit and click OK.
Creating a Sketch
Like any other common CAD modeling practice, we start by creating a sket=
ch.
Start by creating a sketch on the XYPlane. Under Tree Outline, select XYPlane, th=
en click on Sketching next to <=
em>Modeling tab. This will bring up the Sketching Toolboxes.
Note: In sketching mode, there is Undo features that you can use if you mak=
e any mistake.
On the right, there is a =
Graphic window. At the lower right hand corner of =
the Graphic window, click on the +Z axis to have a normal look of the XY Plane.=
p>
Under Sketching Toolb=
oxes, click on =
Draw tab. We will first create the outline=
of the crank. Select Re=
ctangle and draw in the Graphics window as shown below. M=
ake sure that the rectangle is coincident with the x-axis (Letter C will ap=
pear).
Note: You do not have to worry about dimensions for now, we can dimension =
them properly in the later step. Next draw the semi-circular arc at both en=
d of rectangle. Under Dr=
aw Tab, select =
Arc by Center and execute the drawing as s=
hown.
Draw the crank circular hole next. Under Draw tab, click on Circle and execute=
the drawing as shown.
Next, we will dimension the current drawing. Under Sketching Toolboxes, sel=
ect Dimensions tab. You will see a list of dimensioning options. We will use t=
he default General<=
/strong> option. Execute the geometry dimensioning as shown below.=
p>
Input value for D2, H3, L1 respectively under Details View tab.
D2 =3D 0.5 in
H3 =3D 3.3465 in
L1 =3D 1.299 in
Note: Your dimension naming might not be the same as the one shown here. I=
t is fine. Just make sure your value correspond to correct dimensions.
Next, we need to make sure that the sketch is symmetric on both side. Unde=
r Sketching Toolboxes, select <=
em>Constraints tab. Select Midpoint and constrain the geo=
metry in the Graphics window as shown below.
=
Next, we will make sure that the both circular hole is of same dimension. =
Under Constraints=
strong> tab, select <=
em>Equal Radius. Execute constraint in the Graphics windo=
w as shown below.
We will next trim off the unwanted edge. Under Modify tab, select Trim. Execute =
the trimming in Graphics=
window as shown below.
At this point, we have the outline of the crank done. We need to add the c=
ut out in the middle of the crank. First start with a sketching of the cut-=
out. Under Draw tab, click on <=
em>Line and execute drawing in Graphic window as shown=
below.
We would want the four corners of the cut out we created to be of followin=
g coordinate.
(-0.7972, 0.1642)
(0.7972, 0.3248)=
code>
(0.7972, 0.9744)
(-0.7972, 1.1368)
Unfortunately, there is no easy way in specifying the coordinates of a poi=
nt. So we will have to dimension them accordingly using the dimensioning to=
ols. Click on Dimensions=
tab and use General tool and execute the dimensioning as=
shown.
Under Details View, enter the value for the dimensions.
H5 =3D 0.7972 in
H6 =3D 0.7972 in
L4 =3D 0.1642 in
L7 =3D 0.3248 in
L8 =3D 0.3248 in
L9 =3D 0.1642 in
Next we will add fillet to the corner of the cut out. Click on Modify tab and=
select Fillet. Enter a Rad=
ius value of 0.177 in. Execute the command in Graphics wi=
ndow as shown.
Now we have the sketch of the crank done. Next we will perform extrude fea=
ture on this sketch.
Create > Extrude
Under Details View, =
Sketched1<=
/span> is automatically selected as default Base Object.
Next to FD1, Depth (&=
gt;0), enter value 0.5 in. Click Generate.
Note that after you click <=
em>Generate, you see a new part created under the Tree Outline=
span>. This is what you should have in the Graphics window at this point.
Now let's keep moving by adding a handle to this crank. Under Tree Outline, =
click on XY Plane=
strong> and click on =
New Sketch . This will create a new sketch under XY Plane. You will=
see Sketch2 created under =
XYPlane. Click on the Sketching tab to start sketching th=
e handle. The base sketch for the handle is just a cycle. Under Draw tab, clic=
k on Circle.
Execute the drawing in the =
Graphics window as shown below.
At this point, we have the crank handle sketch done. We can continue addin=
g Extrude<=
/span> feature to the sketch. Click =
Extrude, make sure that Sketch2 is selected n=
ext to Base Object<=
/strong>. Next to Operation change Add Material to Add Frozen. This is becaus=
e we want to create the crank as two separate bodies. If we use the default=
Add Material, both the crank and crank handle will be created as a single bod=
y. Next to FD1, Depth (&=
gt;0) enter value of 2.645. We can now Generate this feat=
ure. Under Tree Outline, you will see that we now have 2 Parts and 2 Bodies=
. Select both parts and perform Form New Part operation.
=
In the Graphics window, this is what you should have now.
Congratulations! We are done with the Geometry setup. Let's close the Desi=
gn Modeler and go back to the Workbench (Your work will be saved. Don't wor=
ry).
Go to =
Step 3: Mesh
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Step 3: Mesh
In the Crank cell, right click on Model, and click Edit...
A new window Mechanical Modeler will open. We will start with the defaul=
t mesh generation method. Under Outline, right click on Mesh and click Generate Mesh<=
/span>. This will give us mesh that ANSYS mesher thinks appropriate for our=
geometry. We see that ANSYS is smart enough to create a mesh that sweep ac=
ross the cross sectional area of the crank. This is the type of mesh we are=
seeking for our geometry. However, sizing wise, the mesh is too coarse. We=
will have to increase the number of elements.
Under Outline, click on =
Mesh. Next under Details of "Mesh", expand the Sizing tab an=
d we will specify the element size that we desire. Element size of 0.125 in=
seems to be a good start. Next to <=
strong>Element Size, enter 0.125. Finally, click o=
n Generate Mesh again.
This is the mesh that appear in the Graphics window on the right.
Higher Resolution Image
You should have 18205 nodes and 3582 elements for your mesh. Click on Statistics under Details of "Me=
sh" to see that.
For future reference, the default mesh might not produce the desir=
able mesh that we want. To specify our own mesh control, right click on Mesh a=
nd select Insert. This way, we can insert meshing type and control that we des=
ire. To learn more about different meshing methods, please refer to the Mechanical Help at the top menu.
Go to Step 4: Setup (Physics)
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Step 4: Setup (Physics)
We have two loading conditions to specify. First we must fix the hole wh=
ere the crank would attach to the bicycle. Then we apply our loading condit=
ion of 100 lb on the end of the shaft.
Fixed Support
Under Outline, right click on Static Structural (F5), move the mouse cursor to=
Insert and select Fixed Su=
pport.
Now in the Graphics=
em> area, select the cylindrical hole and click Apply next to =
the Geometry under Details =
of "Fixed Support". You will see the fixed support bou=
ndary condition shown in the Graphics window.
Force on Shaft
Now we will apply 100 lb force at the end of the shaft. This time, I wil=
l show you another way of inserting boundary condition.
Under Outline, left click on Static Structural (F5). Third menu at the top wil=
l show different type of boundary conditions. Left click on Loads and select <=
span style=3D"color: rgb(102,0,153);">Force. In the Graphics<=
/strong>Details o=
f "Force" window, select the circular area at the end =
of the shaft. Under , click =
Apply next to Geometry. The selected area in the Grap=
hics window will be applied with this boundary condition. Next we will ente=
r the value of 100 lb force. Next to Define By, change Vector to Components. Enter a=
value of -100 next to Y=
Component. In the Graphics window, you will see the d=
irection of force applied.
Congratulations! We are done setting up the boundary conditions.
Go to =
Step 5: Solution
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Step 5: Solution
Now that we have set up the boundary conditions, we can actually solve f=
or a solution. Before we do that, let's take a minute to think about what i=
s the post-processing that we are interested in. We are interested in the d=
eflection and stress on the crank. Let's set up those post-processing param=
eters before we click solve button.
Under Outline, left click on Solution (F6). At the top third menu, insert <=
span style=3D"color: rgb(102,0,153);">Total Deformation and von Mi=
ses Stress. Finally click Solve at the top menu.
Go to =
Step 6: Results
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Step 6: Results
Let first look at Total Deformation. Under Solution (F6), click on Total Deformation<=
/span>. The Total Deformation plot is then shown in the Graphics window. Th=
e maximum deflection is 0.026644 in. We should check that our results make =
sense. It appears that the boundary conditions have been satisfied as the t=
ip of the shaft moves downward and the hole at the other end of the crank i=
s held in place.
Higher Resolution =
Image
Note: To show the original undeformed crank, go to third menu click and click on
Notice the deformation is exaggerated, revealing that deformation is pri=
marily caused by torsion.
You can also animate the deformation by clicking play button right under=
Graphics<=
/span> window.
Von Mises Stress
Now let's look at the stress on the crank. Left clicking on Equiva=
lent Stress under Solution (F6). In the Graphics window show the crank stre=
ss contour. The maximum stress is 27897 psi.
Higher Resolution Image
Here's the view without the handle.
Higher Resolution =
Image
Note: To hide the crank handle, select the appropriate body in the Graphic=
s window and right click and select =
Hide Body. Do the same to unhide a body. <=
br class=3D"atl-forced-newline">Go to Step 7: Verification & Validation=
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Step 7: Verificat=
ion & Validation
It is very important that you take the time to=
check the validity of your solution. This section leads you through some o=
f the steps you can take to validate your solution.
Simple Checks
Does the deformed shape look reasonable and agree with the applied bound=
ary conditions? We checked this in step 6.
Do the reactions at the supports balance the applied forces for static e=
quilibrium? To check this, select
Outline > Solution (F6) > Insert > Probe > For=
ce Reaction
Under Details of "For=
ce Reaction", select Fixed Support as Boundary Condition. At=
the top menu, click Solve to Evaluate All Results.
The forces in the X and Z directions are essentially zero and the total =
Y Axis is 100.00 (lbf) as expected.
Refine Mesh
Let's repeat the solution on a finer mesh with more smaller element size=
. Repeat the mesh steps, but this time use element size of 0.05 instead of =
0.125. This will create 10 divisions through the thickness of the crank ins=
tead of 4.
Obtain a new solution and compare both solution.
. |
Coarser Mesh |
Finer Mesh |
Max Deformation
|
0.0257in |
0.0258in |
Max Stress <=
/p> |
27897psi |
27978psi |
The difference in maximum displacement at the tip of the crank handle is=
less than 0.4%.
The difference in maximum stress at the cut out area is less than 0.3%.<=
/p>
This means that our mesh is refine enough and the solution obtained usin=
g the original mesh is probably good enough.
Do keep in mind that one would have to make more detailed comparisons be=
tween the solutions on the two meshes before we can make a definitive state=
ment about the mesh independence of our results.
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