ECGR 3120: Project Description

Instructor: Dr. Soumitra R Joy

Total Marks: 70

Submission Rules:

It is a group project, each group consists of no more than three people. You can use Python, MATLAB, or any other convenient platform for script writing and animation. Create a video demonstration of the project, and narrate the video, and upload in youtube. Upload all of your scripts in Github. Submit a pdf containing the project report, a link to your Youtube Video demonstration and a link to your Github scripts. Add a cover page. The cover should mention the name of the group members.

The project has 5 parts. Part 1,2,3 should be submitted by November 10. Part 4,5 should be submitted by December 5.

Description

An inkjet printer is shooting charged droplet towards a letter size paper. A capacitor is placed along its path so as to control the direction of motion of the droplet. Assume that, if a voltage V is applied across the capacitor, then the field E inside of the capacitor would be V=EW. The electric field E will add a vertical component of velocity (Vy) on the droplet according to the equation: $V_y= a_y T$ . Here T is the time the droplet spends inside the capacitor, and is the vertical acceleration of the droplet, $a_y = \frac{F}{m} = \frac{qE}{m}$ . Here m is the mass of the droplet, and q is the charge of droplet.

The time T that the droplet spends inside the capacitor can be determined by this relation: $L1=V_x T$, where $V_x$ is the horizontal velocity of the droplet, and L1 is the length of the capacitor.

Therefore, the velocity of the droplet, after it exits the capacitor would be $V= \sqrt{V_x^2 + V_y^2}$. After it exits the capacitor, no further change of velocity will occur, assuming the effect of gravity is negligible.

Requirements/Steps

1. Simulate the motion of the droplet when no voltage is applied across the capacitor. How much time would it take for the droplet to reach the center of the paper? Points = 5

2. Simulate the act of drawing a vertical line (similar to the letter “I” ) along the center of the paper at 300 dpi resolution. How much time would it take to draw the letter ‘I’? Points = 10

3. Plot the profile of applied voltage V(t) across the capacitor versus the time t for drawing the letter ‘I’. This profile of V(t) should look like a staircase. V(t) will remain constant until a droplet exits the capacitor chamber, and immediately it will switch to the next value in order to control the next incoming droplet. How big the letter ‘I’ could be drawn on the paper? Points = 10

4. Resimulate the act of drawing letter ‘I’ as big as possible consuming as small time as possible for each of the following adjustment of the parameter:

   a. The distance between the capacitor and the paper L2 is threefold increased, and everything else remains same

   b. L1 is twofold increased, and everything else remains same

   c. Droplet diameter is tenfold increased, and everything else remains same

   d. The horizontal speed at which the gun shoots the droplet is twofold increased, and everything else remains same

   e. The charge of the droplet is fivefold increased, and everything else remains same. Plot the profile of applied voltage V(t) versus time t. Points = 20

5. If you want to draw the letter ‘H’ on the paper, you have to add an additional capacitor to impose a velocity component to the droplet. Design the additional capacitor to draw the biggest possible ‘H’ on the paper. You have to decide the design parameter of the capacitors to draw the ‘H’ shape (length, width of the capacitor plates, and their spacing). Simulate the entire process of drawing the biggest possible ‘H’ shape in 300 dpi resolution. Plot the voltage profile V(t) applied across the capacitor vs time t for both the capacitor. Both the voltage profile would look like a staircase. Points = 25

How to run

• Python 3 must be installed along with pip and pipenv
  
• Once downloaded, run pipenv shell.
  
• Run the first 2 blocks. After this, you can run any simulation math along with its plotting block, which is always right after.
  
• You can either show the animations live, or save them to a .mp4 file. Uncomment whichever you would like.
  

Part 1

1. According to the simulation, it takes 0.00015 seconds to reach the end of the paper, traveling at 20m/s with only 1 droplet and no voltage being applied to the parallel plates. Below is a gif showing the droplet. A video is also stored in videos.
   

2. According to the simulation, the time it took to draw the 'I', which was 5.346023303062736 mm long, took, 0.009 seconds. This was at 300DPI. Below is a gif showing the drawing, with a video also stored in videos.
   

3. According to the simulation, the time it took to draw the 'I', which was 5.346023303062736 mm long, took, 0.0045 seconds, at 300DPI. In testing, it was found that 5.346023303062736 was about as large that it could draw, before it started to hit the parallel plates. Below is a gif showing the drawing, with a video also in videos.
   Below is also an image of the voltage vs time graph. This is the same for both question 2 and 3
   

Part 2

4. Part A. Below is a gif showing what happens if the distance betwene the capacitor and paper is increased 3x.
   Below is also an image of the voltage vs time graph.
   Part B. Below is a gif of what happens if the distance L1 is 2x larger.
   Below is also an image of the voltage vs time graph.
   Part C. Below is a gif that shows what happens if the droplet diameter is 10x larger.
   Below is also an image of the voltage vs time graph.
   Part D. Below is a gif that shows what happens if the droplets are shot at 2x the speed.
   Below is also an image of the voltage vs time graph.
   Part E. Below is a gif that shows what happens if the droplets have 5x the charge.
   Below is also an image of the voltage vs time graph.
   

5. 2 parallel plates, the same size, were used in this section. Below is a gif that shows the results. It essentially draws 3 lines, and changes the voltage of each parallel plate to accomplish this.
   Below is also an image of the voltage vs time graph, for the y axis.
   Below is also an image of the voltage vs time graph, for the z axis.