User:Samantha787/weeklyupdate

Project Preference
1 MakerBot PLA, 2 Smart Shoe, 3 Mobile Robot Hallway Navigation

Problem Statement
Our group aims to discover the material properties of the PLA product used with the makerbot. We are currently on the design phase of the project and intend to first discover which properties are important to users and second construct several test to quantify these properties.

Project Plan
This is a rough outline of weeks to come, subject to change.  Week 1- The main goal of week one is to research different material properties while keeping the user in mind. This will help the group decide which properties are the most important and they will have some background knowledge when the development of tests begin. Week 2- Team members will spend this week designing tests for the material properties chosen. Team members will also choose the shape of PLA needed for each test. Week 3- This week will be spent building prototype test apparatuses and collecting trial data. During this process the group will keep in mind ways to improve prototypes.  Week 4- The last week will be spent perfecting all prototypes into a polished, finished design to pass onto the implement phase of this project.

Week 1 Narrative
My personal objective this week was to research the material property of strength. The most valuable information I obtained was from my current ENES-140 textbook, Mechanics of Materials 2nd edition by Timothy A. Philpot. Trying to narrow down strength into one simple definition is not an easy task, but in general strength defines if an object is strong enough to withstand repeated loads without breaking, fracturing, or permanently deforming. Strength is quantified and evaluated by looking at the total stress in an object. In general, stress is given as the internal force over an object's cross-sectional area ( σ = P/A ) similar to and sharing units of pressure. Depending on whether the SI or FPS system is being used stressed is often given in units of MPa or ksi respectively. While there is one general definition of stress and strength, they can be further broken down into different components. Most aspects of strength/stress are found using the tensile test and graphing a stress-strain diagram. Links to a tensile test explanation and an example of a stress-strain diagram can be found below.  Normal Stress- stress which acts on a surface that is perpendicular to the direction of the internal force, an axial load causing compression or tension.  Shear Stress- stress which acts on a surface that is parallel to the direction of the internal force, mostly seen acting on bolts holding back an axial load.  Yield Stress- the stress that will induce a permanent amount of deformation in the material, usually defined at .2%. Ultimate Strength- after yielding the point at which fracturing begins seen by necking, a thinning in the material's diameter. Ultimate strength is the limit or maximum stress of the tensile test diagram, also known as tensile strength. Fracture Stress- the stress at which a specimen breaks into two separate pieces.

Stress-Strain Diagram

Tensile Test Explanation

 After researching strength, I believe the most relavant element is the stress-strain diagram and the critical points along it. These give us a window into many different aspects of the material that I believe the user would find essential to know. In order to proceed with our project I believe it is necessary to find a way to create our own stress-strain diagram using PLA specimens. My objective for next week will include more research on the tensile test and any way to recreate the test using economically fair materials. While I have a decent idea on the axial limits of an object, I need to spend more time investigating the shear limits and ways in which they can be tested as well next week.

Week 2 Narrative
Due to the economic constraints on the tension test, my goal this week was to look into alternative tests in order to find PLA's young's modulus. After searching online I found various values for PLA's young's modulus which ranged from 350 MPa to 3820 MPa. Idea 1 <br \> My initial thoughts for recreating the tension test in a cheap manner was the use of weights. We could hang a marked cylindrical PLA specimen and continue to add more and more weight while recording the deformation. Using the equation for deformation delta = PL/AE I did some preliminary calculations. P = delta(AE)/L after isolating P we can set up a relationship between the amount of deformation and the amount of force needed to obtain that value. Using a measurable deformation of 1mm and the lowest E value I could find online, I found it would take around 452 newtons, 46 kg, or 102 lbsf to produce this small deformation if not more due to the varied values of E. The data from this preliminary calculation shows the amount of weight needed to preform this type of tension test would prevent the experiment for being feasible. <br \><br \> Idea 2 <br \> One alternative to the tension test is a 3 point bending test. The setup is fairly simple, the specimen used is a long rectangular beams with dimensions of lxwxh. The beam is symmetrically supported on both sides while a central load of increasing magnitude is applied. The deflection delta = L^3*F/4wh^3*E, where L is the distance between the two outer supports and E is young's modulus. Rearranging the equation we can isolate F, in this case the applied central load, and find the force needed for a certain amount of deflection. F = E*4*wh^3*delta/L^3 as before using a measurable value of 1mm for deflection and the lowest value for E, it would take around 18 newtons, 1.8 kg, or 4 lbsf to produce this deflection. This preliminary data makes this method far more feasible than the tension test, but it does have its drawn backs. For one, deflection can be difficult to measure accurate giving rise to error. However this can be reduced by instead measuring the strain on the two surfaces of the beam by using strain gauges. The only issue with using strain gauges though is that strain is not evenly distributed about the surfaces. Since a concentration central loading is being applied having a strain gauge at that exact point will give the best results, but this placement can complicate the test. In order to rectify these sources of error I have looked into a similar but more accurate test, the four point bending test.

3 Point Bending Test Explained <br \> <br \> Idea 3 <br \> The 4 point bending test is very similar to the 3 point bending test, but offers some advantages. Like before the specimen used is a long rectangle beam of dimensions lxwxh and is supported symmetrically on both side. However, unlike the 3 point bending test, two concentrated loads are applied symmetrically on both sides. Having a symmetrical support and load system creates a surface, between the two applied loads, with a constant maximum stress/strain unlike before. Taking measurements of strain at this region will reduce error and give us far more accurate results than a 3 point bending test.

4 Point Bending Test Explained <br \> <br \> Idea 4 <br \> The only disadvantage of a 3 or 4 point bending test is being able to produce and reproduce an evenly distributed concentrated load. Our current resources may prevent us from having a gradual enough increase in load magnitude over time. Without many data points to graph, finding a viable young's modulus will be difficult. With these difficulties in mind I decided to think outside the realm of physical forces and applied loads taking some inspiration from my physics 3 class. The speed of a wave through a medium is solely dependent upon the medium it is traveling in. For instance the speed of sound changes, but is constant for every kind of substance it can travel through. Therefore, the speed of sound through a solid is a material property which can be calculated by v = sqrt(E/density). The velocity of a wave is also equal to its frequency multiplied by its wavelength, v = lamda*f. By substituting and rearranging we find E = (lamda*f)^2*density. If we can somehow send a sound wave through a long piece of PLA cable and record its wavelength and frequency on the other side, we will then have speed through the medium. The density of the material can then be found by measuring the mass of a sample m(kg) and finding the volume of that sample V(m^3) by using the water displacement method. Density can then be found by density rho = m/V. With these known values we can solve for E, conducting several trials and taking their averages would help reduce error.

Week 3 Narrative


<br \><br \><br \> My goal this week was to determine the accuracy of our current 3pt bending test setup before performing a dry run with a PLA specimen. The setup shown is simple yet effective, consisting of a few inexpensive parts. Two triangular wooden supports hold a test specimen horizontally along with a level in order to have a base with which to measure deflection. The supports are kept equidistantly 10 inches from the concentrated load, in this case held by a clamp located at the center of the beam. In order to check the accuracy of this setup I went to a home improvement store and purchased two different materials to test, pine wood and cpvc pipe.<br \><br \>

Before beginning my test on the wood specimen I found a known value of young's modulus for pine wood online and measured the piece with vernier calipers. The given value for pine wood's young's modulus is 1300 ksi. The dimensions of the wood beam to be tested was 24 inches long, 1.098 inches wide(w), and .2365 inches in height(h). The distance between the two outer supports was measured at 20 inches (L). I attached a clamp at the center point and first hung 2.5 lbf of weight. The deflection was then measured from the bottom of the level to the top of the beam as .4375 inches (d). Using the equation E= L^3*F/4*w*h^3*d, I calculated young's modulus to be around 789 ksi giving a percent error of 39.3%. This is a significantly large amount of error so it was necessary to find the exact source of error. Using my calculated young's modulus and the same equation above I found the supposed deflection for 3 lbf which equated to about .525 inches. After conducting the experiment a second time with 3 lbf I measured a deformation of .4688 inches. Using this second measured deformation I calculated young's modulus a second time obtaining a value around 881 ksi. Since these two experimental values were similar in magnitude the main source of error was not coming from the setup, results were reproducible. After conducting some research on the elastic modulus of wood I found that most given values are for forces applied along the grain. Although I could not find any specific values for pine wood against the grain, I did find that the elastic modulus can be significantly lower with such forces. In order to prove my source of error I continued the experiment a third time using a specimen with a much more specific given value for young's modulus, Cpvc piping.<br \><br \>

Once again I followed the same method as the wooden beam and began by getting a known value for young's modulus and dimensions. Fortunately the Cpvc had a U.S code printed on it "ASTM D 2846", this lead me to a website that had an exact value for this particular type of pvc, E= 370 ksi. The cpvc pipe was setup exactly the same as the beam, 24 inches long with 20 inches between both outer supports (L) but in this case it was circular in shape. The outer diameter of the pipe was .642 inches (Do) and the inner diameter was .4755 inches (Di). Due to the change in shape the equation for finding E changes as well. The new equation goes as follows E= L^3*F/48*d*(pi/64)*(Do^4-Di^4). Since the pipe was far more flexible than the beam I decided to only do one trial with 2.5 lbf. After securing the pipe and adding the weight I measured a deflection of .25 inches (d) giving a value of E to be about 286 ksi. This give us an error of 22.7%, still relatively high but much smaller than the previous test specimen. <br \><br \>

This trial run of our 3 point bending method has given us some important data on how to proceed with our prototype. While this system can replicate results it is still far from perfect and still carries more error than I had hoped. Moving forward, we must improve this design to be more accurate by continuing tests on well known materials. While conducting this experiment I have already found several areas of improvement and made note of them. For example, I did not have a wide range of weights to choose from, by increasing the amount of data points collected we can take the average of all calculated values and reduce error. Another source of error was my weighing system, since I did not have labeled weights I used objects from around the house and measured them on a everyday scale only precise to one decimal place. Lastly, since the measured values of deflection are so small it is important to leave out as much human measuring error as possible. During this experiment I was holding tools and measuring by hand. If there was some way to mount a measuring device or to digitally measure our deflection that would greatly reduce our error.<br \><br \><br \><br \><br \><br \><br \><br \><br \>

Week 4 Narrative
<br \> Coming to the end of the design cycle, I spent this week making sure the next group had all the information they needed to continue. My ultimate goal was to write an easy to follow experimental procedure for the 3 point bending test. The procedure is very similar to my test in week three with a few changes. One major improvement this week was the use of a hanging weight set. By having labeled masses, I could easily and accurately measure the force applied to the beam. Another improvement was how deflection was measured. Last week I measured deflection by hand with a small ruler incorporating a significant amount of error. This week I placed a piece of paper behind the beam and marked the top surface's initial position as a base line. After each addition of mass I would mark the new location of the beam's top surface. After marking all the deflections I removed the paper from the set up. I then measured the distance from the base line to each deflection mark with vernier calipers and recorded it in a chart. I measured the deflection from 5 different weights and calculated the elastic modulus for each. My experimental average value for PLA's elastic modulus was calculated at 2.41 GPa. In order to see how accurate my experimental value was, I predicted the amount of deflection of an unused mass. My calculated deflection for 1150 g, 11.28 N, was 5 mm. After conducting the experiment I measured the amount of deflection to be 4.7 mm. This gives me a percent error of 6% showing my results were reproducible, a huge improvement from last week's error of 23%. Links to the experiment process and my dry run of it can be found below.<br \><br \>

General experimental process the next group will use to calculate the elastic modulus of PLA: 3 Point Bending Experiment

Example of the experimental process preformed: 3pt Dry Run

<br \> Moving forward, the implement group will need to study multiple factors that could affect PLA's elastic modulus. These include fill direction, color of PLA, temperature, and any other variable the implement group can think of. The above general experimental process can be used to test all these variables by performing the procedure while changing one variable and holding all the others constant.