MAE 3272 - Lecture Notes - Bike Crank 1_4!7!14

Lecture 9 - 7-April-14 M&AE 3272 - Spring 2014

1

WSachse; 4/2014;

Module 3:Bicycle Component Modeling and Testing

M&AE 3272 - Lecture 8 1

M&AE 3272: Mechanical Propertyand Performance Laboratory

Bikes of the Future?Bikes of the Future?Bikes of the Future?Bikes of the Future?

WSachse; 4/2014;

MAE 3272 Blackboard site



2

WSachse; 4/2014;



M&AE 3272: Mechanical Propertyand Performance Laboratory

A/D Conversion; Signal Processing;

and Display

WSachse; 4/2014;

Measurement Systems:


Stage 1 Stage n

Signal Conditioning/

Processing Stages

Output Stage

Materialor Systemunder Test

Control Stage

ActuatorSystemActuator

Sensing Element

TransductionSystem


3

WSachse; 4/2014;


Crank Geometry Crank designs based on past years M&AE 3250 designs

ANSYS Modeling Model with ANSYS to find two locations for strain gage rosettes:(1) High stress concentration; (2) Uniform stresses

Gaging and static testing Pre-machined crank arms provided; Gage with strain gage rosettes; Static loading; comparison with ANSYSmodeling

In-situ Testing Crank installed on bicycle: Pedal Force components; Crank Position; LabVIEW vi provided! (22 data sets)2 Strain gage rosettes (2 times 3 strain components)

Data Comparison Compare principal strains/directions with ANSYS model predictions

Virtual Presentations Group prepares Data Sheet critically comparing static measurements/modeling; Results of dynamic testing; and a 5-Slide Presentation of results


WSachse; 4/2014;




4

WSachse; 4/2014;

Module 3: ANSYS Component Modeling


1. Back-of-the-envelope estimates using beam theory

2. Import CAD geometry3. Mesh, Setup Physics and Solve4. Check results5. Add gauges to CAD geometry6. Calculate strain values for gages7. Compare with measured values

Original Slide from R Bhaskaran, 2014

Covered in MAE 3250

WSachse; 4/2014;




Use Euler-Bernoulli beam theory See Pre-Analysis step in the tutorial


5

WSachse; 4/2014;

Module 3: Strain Gage Modeling in ANSYS


Original Slide from R Bhaskaran, 2013, 2014

Extract average strain over the area covered by strain gage

Create a surface element for each strain gage Shell element: shell181 Use for strain/stress evaluation

only Gage nodal displacements are

calculated from underlying crank displacements

Not from stiffness matrix inversion Stiffness of gage is ignored

shell181: 4 nodes per element

WSachse; 4/2014;

Module 3: Strain Gage Modeling Procedure


Create surface on crank face Plane > Sketch > Surface from sketch

Bond surface to crank face Should happen automatically

Mesh surface with one shell181 element Insert Commands Tell ANSYS to use shell181 purely for post-processing

Solve and view results Use solution coordinate system to get strain component

in directionANSYS will do the transformation and averaging to find Original Slide from R Bhaskaran, 2014


6

WSachse; 4/2014;

Module 3: Strain Gage Modeling: Commands



See help for shell181 for more info

et: set element type et, matid, 181: set element type to 181 (i.e. shell181)

keyopt: set keyoption to control element behavior

keyopt, matid, 1, 2: set keyoption #1 to 2 (strain/stress evaluation only)

WSachse; 4/2014;

Module 3: Strain Gage Modeling: Mesh




7

WSachse; 4/2014;

Strain Gage Modeling: Solution Coordinate System



Local coordinate system for element

WSachse; 4/2014;

Verification of ANSYS Results:


Check that:

Boundary conditions on displacement and traction are satisfied

Equilibrium is satisfied: Reactions balance applied load

ANSYS results are reasonably independent of the mesh

ANSYS results compare well with Euler-Benoulli beam theory



8

WSachse; 4/2014;

ANSYS Modeling: Mesh Refinement



Need to check dependence of results on the mesh size

ANSYS (0.05 edge

sizing)

ANSYS (0.075 edge

sizing)

ANSYS(0.1 edge

sizing)Beam Bending

Theory

xx(micro-strain) -1239.9 -1239.4 -1239.0 -1227.9

WSachse; 4/2014;

Module 3: Modeling - Four Bicycle Crank Designs


Crank #1:

Crank #3: Crank #4:

Parasolid files of these geometries are available to you for direct input to ANSYS

Crank #2:


9

WSachse; 4/2014;



Geometry import procedure:https://confluence.cornell.edu/x/fQZoC

When both crank arm and pedal shaft are present, need to form new part to connect them.


WSachse; 4/2014;

Module 3: Modeling Loading Detail


Static Loading

Case

Pedal (Dynamic)

Loading Case


10

WSachse; 4/2014;M&AE 3272 - Lecture 8 19


Initial Mesh Undeformed/Deformed Shape

Refined Mesh

von MisesStress

WSachse; 4/2014;

Stresses and Deformations in Ductile Materials 2D State of Stress on Material Surface,

e.g. x, y and xy ; Plane strain applies: x, y and xy . Failure (yielding) of ductile materials (e.g. metals) is due to a

change of shape (twist, pull, bending). The 2nd Deviatoric Stress Invariant reaches a critical value.

von Mises Yield Criterion: Maximum Distortion Energy/Volume is less than the Distortion Energy/Volume of yielding:UD = 1/(6*G){12 1*2 + 22} where 1 and 2 are the principal stresses; G is the Modulus of Rigidity

For a tensile test: 1=Y; 2=0 (UD)Y = Y2/(6*G) . von Mises Yield Criterion: 12 1*2 + 22 < Y2

Define: von Mises stress {12 1*2 + 22}1/2 [MPa]M&AE 3272 - Lecture 8 20


11

WSachse; 4/2014;

Stresses and Deformations in Ductile Materials von Mises Yield Criterion: Maximum Distortion

Energy/Volume is less than the Distortion Energy/Volume of yielding:UD = 1/(6*G){12 1*2 + 22} where1 and 2 are the principal stresses;G is the Modulus of Rigidity.For a tensile test: 1=Y; 2=0 (UD)Y = Y2/(6*G) .von Mises Yield Criterion:12 1*2 + 22 < Y2


WSachse; 4/2014;

Module 3: ANSYS Component ModelingImport Parasolid crank design: File->Import->Para

Select solid facets display mode: Utility Menu->Plotctrls->Style->Solid Model Facets(Select Normal Faceting); Utility Menu->Plot->Volumes

Scale Object to `meters: Main Menu->Preprocessor->Modeling->Operate->Scale->Volumes (Pick all) RX, RY, RZ: 1000 each

Verify geometry: Utility Menu->List->Keypoint->Coordinates only(Compare keypoint locations with Solidworks drawing)

`Glue volumes to share common areas between crank

and pedal shaft:

Main Menu->Preprocessor->Modeling->Operate->Booleans->Glue->Volumes (Pick ALL)Check Command Window; look for GLUE VOLUMES

HINT: When using MESH200 elements, select the z-Face of both the crank arm and pedal shaft to insure that the nodes of each element coincide.

COMPUTE:(for best location of e-gages)

Region of maximum change of von-Mises stress;Region of most uniform deformation (large values!)

DELIVERABLES:(Annotate plots: Name; View)

Iso-metric views of original mesh; Refined mesh; Plot of element solution for von-Mises stress (Original/Refined).



12

WSachse; 4/2014;

Module 3: ANSYS Component Modeling - 2


COMPUTE (for best location of -gages): Region of maximum von-Mises stress; Region of most uniform deformation but large!

DELIVERABLES:

(Annotate plots: Name; View) Iso-metric views of original mesh Refined mesh Plot of von-Mises stress

(Original/Refined).

Saving Images in ANSYSMechanical

Saving Images in ANSYSMechanical


WSachse; 4/2014;



Initial Mesh Undeformed/Deformed Shape

Refined Mesh

von MisesStress


13

WSachse; 4/2014;

Measurement of Deflections, Strains and Stresses in a crank arm: Specimen surface is in a state of plane stress.

e.g. x, y and xy .

Equations of plane strain apply; e.g. x, y and xy . Measure strains x, y on the specimen surface. How can one measure the shear strain?

How can one determine the principal strains, 1, 2principal stresses, 1, 2 ,and their direction, ?

Solution: Three strain gages oriented at different directions mounted on the surface of the specimen.


WSachse; 4/2014;

Strain Gage Rosette:Determination of Principal Strains/Stresses


Three (3) strain gages mounted in different directions.Each gage measures longitudinal strain only (or corrections

for cross-sensitivity are made prior to data analysis.)All gages measure strain at the same point (close at least.)

Omega: SGD-1/350-RY83


14

WSachse; 4/2014;

Plane Strain Transformation Equations:


x = x cos2 + y sin

2 + xy sin cos

=1

2(x + y) +

1

2(x y) +

xy

2sin

y = x sin2 + y cos

2 xy sin cos

=1

2(x + y)

1

2(x y)

xy

2sin

xy = 2 (y x) sin cos + xy (cos2 sin2 )

= (x y) sin 2 + xy cos 2

WSachse; 4/2014;

Plane Strain Transformations: Mohrs Circle


`


15

WSachse; 4/2014;

Rectangular Strain Gage Rosette:Determination of Principal Strains


WSachse; 4/2014;

Rectangular Strain Gage Rosette:Principal Strains via Mohrs Circle


When the x-Axis coincides with the A-Gageand the y-Axis with the C-Gage :

Then . . . x = A ; y = C ; xy = 2B A C

1

2

3 3


16

WSachse; 4/2014;

Determination of Principal Stressesand von Mises Stress:


For a specimen in plane stress , we only have theprincipal strains 1 , 2 and principal stresses 1 , 2 :(E - Youngs Modulus ; - Poissons ratio )

Principal Stresses :

1 =E

(1 2)(1 + 2)

2 =E

(1 2)(2 + 1)

von Mises Stress :

vM =2

1 12 + 22 < Y

WSachse; 4/2014;

Module 3: Bicycle Crank Gaging


Cable Connector should be in direction of crank shaft.

Wires long-enough to overlap the end of the crank arm.

Wires on outside of crank arm! Wires should be firmly attached

to crank arm.


17

WSachse; 4/2014;

LabVIEW : cycle_test.vi


WSachse; 4/2014;



etc. . . etc. . . etc. . .


18

WSachse; 4/2014;

Mon, Mar 24, 2013 -- Module 3 ScheduleWEEK (March 24th-28th): ANSYS Tutorial and Assignment.All students are to work on the ANSYS Tutorial. There are two assigned problems/exercises which each of you will hand in.A dog-bone shaped crank arm with mounted strain-gage: (1) Find strain at gage center using Beam Theory; (2) Use ANSYS to compute average strain over gage area; (3) Repeat with gage rotated at 45-deg to x-axis.THIS WEEK (April 7th-11th): ANSYS Modeling of your Crank Arm.Each group of students is to carry out the modeling of their assigned crank subject to a 100 lb static load. You should reconnect with your Groups (same as Module 2THE NEXT WEEK: April 14th-18th OPEN LabsThe labs will be run as OPEN-LAB periods for the gaging of your crank arm. First get approval from your TA for your plans for mounting gages and the bag of parts for your crank arm. TA's will be in the Lab during your normal Lab Session times. You can reach them at other times as well. Any TA can approve your plans.Also static testing of your crank arm. Static Testing Schedule will be posted.AND THE FINAL TWO WEEKS:April 21st 25th: Static testing of your crank arm. Testing Schedule will be posted.April 28th- May 2nd: Dynamic testing of the class crank arm. Posted Schedule.Course Link: Syllabus and Schedule / Lab Schedule

Class Schedule (April 7th to May 2nd):


Due: Due: Due: Due: Friday, Friday, Friday, Friday, April April April April 11111111thththth, 6pm, 6pm, 6pm, 6pm

MAE 3272 - Lecture Notes - Bike Crank 1_4!7!14

Documents

Transcript of MAE 3272 - Lecture Notes - Bike Crank 1_4!7!14