User:Samantha787/weeklyupdate2

Project Preference
1 Makerbot, 2 Powerwheel, 3 Smart shoe

Problem Statement
Determine a value for the modulus of elasticity for PLA and discover which factors have an affect on it.

Project Plan
Subject to Change Week 1: Determine if and how the color of PLA affects modulus of elasticity.  Week 2: Determine if and how fill direction of PLA affects modulus of elasticity.  Week 3: Determine if and how temperature affects modulus of elasticity.  Week 4: Determine how there variables affect PLA's yield stress and ultimate stress.

Week 1 Narrative
My first goal this week was to prove that the given procedure from the design phase had repeatable results. In order to do this I followed the procedure keeping all variables used constant. These included using the same beam, the neon green beam printed with length by width cross sections, and increments of weight used. After following the procedure I received and calculated the values shown in the table below.

Beam Dimensions: L= .189 m   w= .01 m   h= .00544 m       Beam Color: Neon Green           Fill direction: L x w cross sections

Averaging the calculated E from each trial gives a value of E= 2.33 GPa. The average calculated value for the previous dry run under these condition was E= 2.41. In order to evaluate if these two values were considered "repeatable", I calculated their percent difference, %D= (Difference between the two values)/(Average of the two values). In this case %D= 3.38%, this is a relatively small value leading to the conclusion that this experiment produces repeatable results.

Having proved the success of the experimental procedure, I moved onto my next goal of determining how the color of PLA affects its modulus of elasticity. Each member of the team was assigned a different color of PLA to conduct the three point bend test. All other variables such as temperature and fill direction were kept constant for all colors. The color assigned to me this week was clear PLA. After conducting the given procedure I received and calculated values shown in the table below.

Beam Dimensions: L= .189 m   w= .00989 m   h= .00521 m       Beam Color: Neon Green           Fill direction: L x w cross sections<br \>

Averaging the calculated E from each trial gives a value of 2.85 GPa. In order to see if color has any affect on PLA's modulus of elasticity the values of E for a range of colors must be evaluated. I judged how different the values for E(neon green) and E(clear) were by using percent difference. The value of percent difference between these two colors is around 20.1%, a fairly large amount. The next step in analyzing these values is to define which value of percent difference warrants color as an attributing factor of PLA's elastic modulus. In my opinion a percent difference of 20.1% is a noticeable amount, but before making the assumption that color has a profound affect on PLA's modulus of elasticity the values of all colors experimentally found by my team mates must be compared.

Week 2 Narrative


The group's goal this week was to collect enough data to statistically analyze the affect of color on PLA's modulus of elasticity. I was assigned the colors neon green and clear to conduct the experimental procedure on and instructed to obtain ten different data points. Since I had completed two trials on neon green in the past I only needed to conduct eight additional trials. Likewise, clear only required nine additional trials. The group met in the engineering lab and simultaneously conducted the experiment to increase efficiency. Since the triangular supports are relatively long, two beams can be tested at a time. The picture to the right shows the workshop setup. After obtaining all the deflection data, I calculated E and E average for every trial, results can be seen in the table below. In order to prevent error and to find these mass amounts of calculated values in a timely manner; I wrote a simple Matlab program which took a vector of forces along with a vector of corresponding deflections and calculated the E value for each of the five weights used per trial. The program then found the average value of E for the presented trial. Since I had 17 trials to calculate values for this program drastically reduced the time needed to complete the task. The code used can be seen in the picture on the left and the .m file used for calculating E and E average can be downloaded here: Matlab Finding E Code.<br \><br \>

Beam Dimensions: L= .189 m   w= .01002 m   h= .00542 m  <br \>     Beam Color: Neon Green      <br \>     Fill direction: L x w cross sections<br \>

<br \> Beam Dimensions: L= .189 m   w= .00995 m   h= .00533 m  <br \>     Beam Color: Clear      <br \>     Fill direction: L x w cross sections<br \>

<br \>The group has plans to meet within the next few days to statistically analyze the data for the five colors tested. The initial idea is to use a 2-sample Z test to compare the colors and finally determine if color has an impact on PLA's stiffness.

Week 3 Narrative


Our goal this week was to determine the affect of fill direction on PLA's modulus of elasticity. Three beams were printed each with a different cross sectional fill direction. Seen to the right, the cross sectional areas included were L x w, L x h, and w x h. By doing these series of tests in a new color of PLA, blue, we could determine if fill direction had an affect while comparing a new color to our previous week's experiment. My first task was to recreated the same set-up and procedure as last week, with the blue L x w cross sectional beam. The results of my 10 trials can be seen below.<br \> <br \> Beam Dimensions: L= .19 m   w= .01009 m   h= .00539 m  <br \>     Beam Color: Blue      <br \>     Fill direction: L x w cross sections<br \>

<br \> My next task was to run 10 trials with the new blue w x h cross sectional beam. Due to the limited printing height of the makerbot, the w x h beam's length was reduced from the normal 220 mm to 150 mm. This created issues when trying to recreate the previous set-up and procedure. The reduced length caused the amount of deflection from the same added force to be much smaller than before since deflection is proportional to length. This made the normal starting weight of 250g and increases of 300g difficult to measure and distinguish between marks. To create more readable data the starting weight was changed to 500g with an increase of 500g per increment. In order to add so much weight at a given time, two weight hangers were used instead of one and the set-up was altered slightly. The set-up can be seen in the picture to the left. My first trial with the new set-up and weight increments can be seen below, followed by the averages of all 10 of my trials. <br \><br \>

Beam Dimensions: L= .12966 m   w= .01004 m   h= .00517 m  <br \>     Beam Color: Blue      <br \>     Fill direction: w x h cross sections<br \>

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Week 4 Narrative


The goal this week was to evaluate the ultimate stress of PLA. This value describes the maximum load the material can withstand before breaking. In order to experimentally test this value, the group used the 2 point bending test. A beam was placed at the end of a table and clamped tightly, creating a fixed end. Weights were then added in increments of 200g while measuring the new distance from the force to the fixed end due to deflection. This process was repeated until the beam broke. The mass and distance at the moment of breaking were then used in the equation below to calculate the normal stress due to bending in the beam. The procedure was then repeated for all colors of PLA by using beams from previous experiments. <br \><br \>

2 point: $$\sigma =\left ( \frac{6FL}{wh^2} \right )$$ <br \>

F = Force applied to beam<br \> L = Length from force to fixed end (an average value of .1325 m was used for all beam calculations) <br \> w = Width of beam<br \> h = Height of beam<br \> <br \>

The table below shows the maximum endured stress for each colored beam. Since the makerbot was unable to print for the past week only one trial per color was conducted, for more accurate results this procedure must be completed at least 9 more times to obtain enough data to statistically analyze. However this table gives us some idea on the maximum stress a simple shaped piece of PLA can withstand depending on its color.

<br \><br \> Another way to test these values would be to conduct the 3 point bend process. While the 3 point bend test would require more weight, it incorporates less error due to the value of L staying constant with each increment of mass. The formula for normal stress due to bending in a beam for 3 point can be seen below. <br \> <br \> 3 point: $$\sigma =\left ( \frac{3FL}{2wh^2} \right )$$ <br \>

F = Force applied to beam<br \> L = Length between two outer supports<br \> w = Width of beam<br \> h = Height of beam<br \> <br \> Using the previously calculated value of ultimate stress and beam dimensions the minimum amount of endured stress can be seen in the glow beam. This beam would only require 26.96 N or 2.75 kg to recreate breaking in the 3 point set-up. The maximum amount of endured stress can be seen in the green beam. This beam would require 55.01 N or 5.61 kg to recreate breaking in the 3 point set-up. These values are feasible, after completing the procedure in the 3 point set-up one could confirm 2 point values along with reducing error.