User:ABielat/ENES-100/Project 2

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Week5 Narrative
For my week 5 task I printed a pentagonal prism

Week6 Narrative
Over the weekend of October 17, 2014 our team printed both the rectangular prism and triangular prism with the following variables:


 * Green PLA material (polylactic acid)
 * Both used 10% infill

undefined Our group was not able to print the circular or pentagonal prism in the green PLA material because the 3-D printer was malfunctioning. The malfunction was related to the extruder being clogged. To date our team has produced the following beams which are ready for testing: Note: All Beams used 10% infill

Our team plans to produce the circular and pentagonal prisms as soon as the 3-D printer is back up and running.

The following pictures represent the parts manufactured over the weekend:

The following video link shows a 3 point test being performed on a Rectangular Green Prism with 10% infill:

video of the Rectangular Prism

Next Steps:

1. The Engineering Lab ran out of red PLA material. As a result the testing of Red PLA material has been discounted for the remaining semester.

2. Beams manufactured out of black and yellow PLA material will now be used to compare to each other as well as the green PLA material.

3. The percent infill will still vary between 5% and 10% so that a economic evaluation can be performed on all of the PLA materials and shapes produced.

4. The triangular and the pentagonal prisms are going to be discontinued and replaced with a rectangular prisms with different height to width ratios but keeping the  cross-sectional area the same at 0.25 in^2. Both the triangular and the pentagonal prisms clearly where inferior to the rectangular prism in both strength and constructability which is the reason why they are being discontinued. The table below summarize the shapes which will be manufactured in the future at both infills and all 3 PLA colors.

5. The 2 point test is now discontinued for the remainder of the semester because the weight was sliding off of the free end of the beam. Professor Campo suggested we should not puncture the beam because it would comprise the material. She suggested the we focus on the 3 point test. With the 3 point test our team will be able to successfully compare the mechanical properties and economic ramifications of the various materials and beams.

6. After all of the beams are manufactured in all of the options of colors and infills 3 point testing will continue.

7. After all testing is complete and the data is complied calculations will be performed for mechanical properties of all of the prism beams manufactured.

Week7 Narrative
As of Friday October 23, 2014 both Makerbot Replicator 3D printers were down. Both had the same issue that the extruders were severely clogged. Professor Edlman is looking into repairing the fifth generation which may require a new part. It is imperative that one or both are up and running so that the bean prisms can be manufactured and tested. In the event that the printers can not be fixed this week I will suggest to the group that we consider the following back up plan.

 Backup Plan: Wood Prism Beams 

As a backup plan I suggest we use small wood beams to test in our testing apparatus and perform calculations to determine the material properties as well as an economic evaluation. Similarly to the PLA material we hold the cross sectional area constant and vary the the length and width to optimize the design.

 Testing Apparatus Issues 

1. Need more weights. The team is running out of weights as the prism beams have been stronger than anticipated. I suggest that we weigh items in the lab such as a cinder block and use it as a weight. The team would weigh the object to a tenth of a pound using a balance beam scale. We start with the 50 lbs that we currently have and when we reach the threshold of an object we replace the weights with the object and continue to add onto the object with the original 50 lbs in the increments that are necessary to complete the test. If we hit the threshold a second the process can be repeated. This should allow for the team to produce as much weight as necessary.

2. Weight Bucket Deformation and Weight Limits. The current weight bucket started to collapse and deform at about 40 lbs. At higher loads the bucket is almost closed shut. I suggest we use a strong crate which I will bring from home and attach it to the test specimens as seen figure below. This method will allow for our team to support several hundred pounds of weight if needed. The cord is wrapping around the members for stability and going under neath the crate for added strength.



3. Deflection Measurements. The team has struggled find a method to accurately measure deflection. I suggest we measure deflection as shown in the set-up below. The spacers will allow for the straight edge to clear the cord providing a accurate measurement with calipers.



4. Prism End Supports. The prism beam end supports need to be stabilized from rotation, particularly for the specimens with tall height to width ratios. The following setup detailed below will accomplish this.



 Current Test Results 

The red square beam prism with 10% infill failed at 74 lbs. The green square beam prism with 10% infill failed at 66 lbs. They were practice test runs. Future tests will calculate deflection at multiple loading increments to allow for a complete calculation and engineering analysis. The following pictures show a sample failure of a green 10% infill square prism beam.



 Engineering Calculations 

The engineering analysis will start with utilizing engineering mechanics for a simply supported beam with a concentrated load at the mid point. This will establish the Design Loads (Theoretical Loads) for each prism beam tested. All results will be tabulated in excel spreadsheet for manipulation of data for complete analysis. The following is the shear and moment diagram for our simply supported beam with a concentrated load.



The maximum shear value is:

Vmax = R = P/2 and will be measured in lbs.

The maximum moment will be at the midpoint and is:

Mmax = Pl/4 and will be measured in inch x lbs.

The maximum deflection will be at the midpoint and is:

deflection max = Pl^3/48EI

Where:

P = load in lbs

R = Reaction in lbs

V = Shear in lbs

l = span length in inches

M = moment in inch-lbs

E = modulus of elasticity

I = Moment of Inertia

The bending stress fb can be calculated by setting the design moment (theoretical moment) equal to the actual moment and solving for fb. The actual moment is calculated as follows:

Mact = Ixx/y * (fb)

Where:

M = moment in inch-lbs

fb = the bending stress at position y

Ixx = the Moment of Inertia about the x axis (strong axis)

The Moment at yield is at the extreme fiber when the distance y is at it's furthest distance from the neutral axis. This point will be established as y = c. Moreover, this will provide us the yield stress of the material fy.

M yield = Ixx/c * fy

Setting the deign moment equal to the yield moment and solving for fy will give us the experimental yield stress for each test.

M max = M yield

Mmax = Ixx/c * fy

Solving for fy:

fy = (Mmax * c )/ Ixx

Similarly, The deflection can be set equal to each of the deflections measured.

deflection tested = (Pl^3)/(48EI)

Solving for E:

E = (Pl^3)/ (deflection tested * 48 * Ixx)

The moment of Inertia about the neutral x axis can be calculated and seen as follows for our respective prism beams:



Comprehensive and detailed spreadsheets will be complied for all test specimens at all recorded levels. This will allow our team to establish the material properties of all of our tested specimens.

 Engineering Calculations for Red Square Prism Beam with 10% Infill 

Givens:

Span = 5.5 in

P = 74 lbs

b = .5 in

h= .5in

c = h/2 = .25 in

MDesign = Pl/4

MDesign = (74 lbs * 5.5 in)/4

MDesign = 101.75 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

fy = (Mmax * c )/ Ixx

fy = (101.75 in*lbs * 0.25 in)/ 0.005208 in^4

fy = 4,884 psi = 33.67 Mpa

This first go at a bending test and calculation for Red Square Prism Beam with 10% Infill is pretty close to values for wood as we would expect.

Week 8 Narrative
Thursday October 30, 2014 and Friday October 31, 2014 both Makerbot 3D printer's were down as several attempts throughout these days were made to make prints. On Friday at 11:36 AM notice was given that both printers were operational. Friday and Saturday were spent producing prism beams. On Monday the Makerbot 5th Generation 3D printer went down again. With the printer issues coupled with a backup log of engineering students trying to print their respective projects, our team was still able to produce and test the following beams:


 * Green cylindrical prism beam with 10% infill


 * Green pentagonal prism beam with 10% infill


 * Red cylindrical prism beam with 10% infill

Deflection spacers were also designed and produced on the 3D Makerbot printer. The second spacer was not produced until after the testing was completed. The improved deflection measurement system will be utilized from here on out.

Predicted Failure Engineering Calculations
The yield stress (fy) for all members of a specific PLA color and infill should be the same. All values will be averaged and extreme values will be eliminated such that our team will develop a working yield stress (fy) for future designs. As of now only one test was performed and the calculated yield stress was fy = 4,884 psi = 33.67 MPa for a red, square prism beam with 10% infill. Since this was the only tested value to date, this yield stress will be used to predict the failure of the green PLA cylindrical prism beam with 10% infill.

Given:

Length = 6.75 in

bearing = .625 in

span (l) = 5.5 in

diameter (d) = 0.5 in

radius (r) = 0.25 in

yc = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

Mmax = (Ixx/yc)* fy

fy = 4,884 psi = 33.67 MPa (from previous test)

Mmax = (0.003068/4)*4,884

Mmax = 59.96 in-lbs

Mdesign = Pl/4 (simply supported beam with single load at midpoint)

Set Mdesign = Max and solve for P

59.96 = Pl/4

P = 59.96*(4)/(5.5)

P = 43.6 lbs

Using the data base sample fy = 4,884 psi = 33.67 MPa predicts that the green PLA cylindrical prism beam (10% infill) with a diameter of 1 inch will fail at approximately 43 lbs. As more test are completed the fy value will be established allowing us to successfully engineer and predict test failures. We will find out in today's class how well we are doing at this point when we test the green PLA cylindrical prism beam (10% infill) with a diameter of 1 inch. Deflections will also be measured in future tests allowing us to establish elasticity (E) for the various PLA materials.

The actual failure was 40 lbs.

Engineering Calculations Red Cylindrical Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 40 lbs

diameter (d) = 0.5 in

radius (r) = 0.25 in

yc = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

MDesign = Pl/4

MDesign = (40 lbs * 5.5 in)/4

MDesign = 55.00 in lbs

fy = (Mmax * c )/ Ixx

fy = (55.00 in*lbs * 0.25 in)/ 0.003068 in^4

fy = 4,481.8 psi = 30.90 Mpa

Engineering Calculations Red Pentagonal Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 33 lbs

diameter (d) = 0.476 in

radius (r) = 0.238 in

yc = 0.238 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

MDesign = Pl/4

MDesign = (33 lbs * 5.5 in)/4

MDesign = 45.38 in lbs

fy = (Mmax * c )/ Ixx

fy = (45.38 in*lbs * 0.238 in)/ 0.00252 in^4

fy = 4,285.4 psi = 29.56 Mpa

Engineering Calculations Green Cylindrical Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 30 lbs

diameter (d) = 0.5 in

radius (r) = 0.25 in

yc = 0.25 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.003068 in^4

MDesign = Pl/4

MDesign = (30 lbs * 5.5 in)/4

MDesign = 41.25 in lbs

fy = (Mmax * c )/ Ixx

fy = (41.25 in*lbs * 0.25 in)/ 0.003068 in^4

fy = 3,361.4 psi = 23.18 Mpa

Engineering Calculations Green Pentagonal Prism Beam 10% Infill
Givens:

Span = 5.5 in

P = 32 lbs

diameter (d) = 0.476 in

radius (r) = 0.238 in

yc = 0.238 in

Ixx = (1/4)*pi*r^4

Ixx = (1/4)*pi*(0.25)^4

Ixx = 0.00252 in^4

MDesign = Pl/4

MDesign = (32 lbs * 5.5 in)/4

MDesign = 44.00 in lbs

fy = (Mmax * c )/ Ixx

fy = (44.00 in*lbs * 0.238 in)/ 0.00252 in^4

fy = 4,155.6 psi = 28.65 Mpa

Engineering Calculations for Green Square Prism Beam with 10% Infill
Givens:

Span = 5.5 in

P = 60 lbs

b = .5 in

h= .5 in

c = h/2 = .25 in

MDesign = Pl/4

MDesign = (60 lbs * 5.5 in)/4

MDesign = 82.5 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/12*b*h^3

Ixx = 1/12*.5*.5^2

Ixx = 0.005208 in^4

fy = (Mmax * c )/ Ixx

fy = (82.5 in*lbs * 0.25 in)/ 0.005208 in^4

fy = 3960.0 psi = 27.30 Mpa

Engineering Calculations for Green Triangular Prism Beam with 10% Infill
Givens:

Span = 5.5 in

P = 30 lbs

b = .5 in

h= .43 in

yc = h/3 = .14333 in

MDesign = Pl/4

MDesign = (30 lbs * 5.5 in)/4

MDesign = 41.25 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/36*b*h^3

Ixx = 1/36*.43*.5^3

Ixx = 0.001104 in^4

fy = (Mmax * c )/ Ixx

fy = (41.25 in*lbs * 0..1433 in)/ 0.001104 in^4

fy = 5,354.3 psi = 36.91 Mpa

Engineering Calculations for Red Triangular Prism Beam with 10% Infill
Givens:

Span = 5.5 in

P = 22.5 lbs

b = .5 in

h= .43 in

yc = h/3 = .14333 in

MDesign = Pl/4

MDesign = (22.5 lbs * 5.5 in)/4

MDesign = 30.94 in lbs

fy = (Mmax * c )/ Ixx

Ixx = 1/36*b*h^3

Ixx = 1/36*.43*.5^3

Ixx = 0.001104 in^4

fy = (Mmax * c )/ Ixx

fy = (30.94 in*lbs * 0..1433 in)/ 0.001104 in^4

fy = 4,015.7 psi = 27.69 Mpa

Summary of Results to Date
The following data table summarizes our testing and calculations to date (11-5-14).

A few of the data points seem to be outside the realm of what would be expected. Most notably, the Green Triangular prism beam with 10% infill as it's yield stress (fy) was way above the red triangular value as well as the average yield stress (fy) for the green PLA material. I suggest that we complete 2 more trials for prism beam for a total of 3 each and average the values. This will give our team much more accurate results and allow us to isolate odd-ball tests. This will not be possible for any of the red prism beams as the lab is out of red PLA material. Three total trials can be completed for the green PLA material and other colors that are available to produce.

Tested Specimens
The following picture shows the tested green pentagonal prism beam with 10% infill after failure.



The following picture shows the tested red rectangular prism beam with 10% infill after failure.



The following picture shows the tested green cylindrical prism beam with 10% infill after failure.



Videos of 3-Point Bending Test
The following video link shows a 3 point test being performed on a Pentagonal Red Prism with 10% infill measuring deflection:

Video of the Pentagonal Red Prism-Deflection

The following video link shows a 3 point test being performed on a Pentagonal Red Prism with 10% infill showing the failure point:

Video of the Pentagonal Red Prism-Failure

The following video link shows a 3 point test being performed on a Cylindrical Green Prism with 10% infill showing the failure point:

Video of the Cylindrical Green Prism

The following video link shows a 3 point test being performed on a Pentagonal Green Prism with 10% infill showing the failure point:

Video of the Green Pentagonal Prism

The following video link shows a 3 point test being performed on a Rectangular Green Prism with 10% infill showing the breaking point:

Video of the Green Rectangular Prism

Engineering As-Built Drawings
The following engineering as-built drawing represents the cylindrical prism beams:



The following engineering as-built drawing represents the rectangular prism beams:



The following engineering as-built drawing represents the triangular prism beams:



The following engineering as-built drawing represents the pentagonal prism beams: