Hopper (Cartridge) Team Lead: Dalton Mead Mike Zack

Transcription

1 Hopper (Cartridge) Team Lead: Dalton Mead Mike Zack Background The cartridge (hopper) will be the subsystem that holds the material mixture before the experiment is executed as well as drain the material to the transfer surface. The hopper will also be receiving the mixture from a recirculation system. The receiving of the mixture from the recirculation system will a design decision made by both subcommittees following the approval of our design at the Phase III presentation. Notebook calculations will be in Attachments 1-3. Below are the sketches showing the dimensions of the cartridge. Figure 1. This can easily be built with a piece of square aluminum tubing.

2 Below is the location of the suspension system at the Center of Mass Figure 2 Figure 2. shows the location of the center of mass by using two approaches. The verification of which approach will be correct can be tested after the hopper has been built, and before the suspension system is designed, since the height of the pivot arms will be determined by the locale of the center of mass. Design Choices Pugh Charts See Attachment 7. Method of Initiation/Stop of Experiment The hypotenuse of the triangle will be a separate piece of aluminum that will act as a door that transverses along the hypotenuse. This door will allow us to know the exact geometry of the opening which in turn will allow us to control the mass flow rate of the material as it exits the hopper. This door will be powered by a linear actuator. This is a motor that pulls and pushes along a transverse path and could connect to the door easily. The speed and power of this linear actuator have not been calculated at the time of the Phase III review. The calculations will need to account for the weight of the material pressing down against the door, which will result in a friction force between the metal plate and the system attaching it to the hopper. This friction force will have to be overcome by the power of the motor. Dimensions These dimensions were chosen based upon a Customer requirement to hold about 2kg of the particle mixture. During a recent test, the team members and myself took some samples of toner and carrier particles, supplied by Dr. Marcos Esterman, and found the densities of the different particles. Once these were established, I combined the most dense toner with the most dense carrier particle. The mass concentrations were 2% of the toner and 98% of the particles. These calculations with be reflected in Attachment 4. Once this density was calculated, the

3 volume of 2kg of this mixture was calculated and given a safe margin of error in case the customer decided in the future to use less dense mixtures in the future. This current design of the hopper will hold liters of any mixture you put into it, with some extra height to give room for whatever system is decided to receive the circulating particles into the top of the hopper. Center Of Mass Calculations The center of mass was calculated by two different approaches and were competed in MATLAB. Both codes will be present in Attachments 5 & 6. The first approach was accomplished by using equation 1. When m is the mass of the material and x is the location of the geometric COM of that material. The hopper was broken up into two geometric shapes, the rectangle and the lower triangle section. The rectangle is referred to as section 1 in the MATLAB code and the triangle is referred to section 2. COM X= sum(m_i*x_i)/sum(m_i) Eq 1. Using the density data we found during the test previously mentioned, the volume of the tested mixture was calculated in order to see how much volume the mixture would fill up the hopper in these dimensions. The mixture filled up the lower triangle, section 2, 100% and the COM was assumed to be at the same location as the geometric COM. However, the mixture did not fill section 1 100% of the way. This height was calculated by subtracting the volume of section 2 and using the volume of the hopper to find the height. This COM location was found for the mixture and a similar calculation was made for the hopper. This resulted in the following variables: mass of aluminum in section 1 (mal1), mass of mixture in section 1 (mmix1), mass of aluminum in section 2 (mal2), and mass of mixture in section 2 (mmix2). The location variables were noted as: x & y location of aluminum in section 1 (xal1, yal1), x & y location of mixture in section 1 (xmix1, ymix1), and the rest were repeat for section 2. Using equation 1, for both the X and Y coordinate, the calculation resulted in the mass COM as shown in Figure 2. The second approach was calculated by taking the means of the distance between each of the verticies. This gave us a geometric center of mass based on the dimension chosen. This MATLAB code is presented in Attachment 6 and resulted in the mean vertices result in Figure 2. These two results can be test by simply holding the hopper and the coordinates and see if the hopper rotates of stays balanced. Material Aluminum was chosen as the material for the hopper because it is a light and inexpensive material. It is also allowable to be used with the charged particles because the carrier particles and the toner particles will each have an opposite charge, and when mixed, should result in a zero charge since each carrier particle is carrying enough toner particles to negate the charge of the carrier. Since there is no excess charge in the particles, there will be no charge lost to the hopper before or during the experiment. This assumption was given to us by our team s subject matter expert, John Knapp, who worked in the cascade development sector of Xerox.

4 Angle of Repose Doing some research for how steep the angle of the triangle bottom section revealed a concept called the angle of repose. This concept is defined as the angle of a granular material that is the maximum angle that the material will achieve before they slip along each other, resulting in a event similar to that of an avalanche or a landslide. This angle can be calculated by using a humungous equation that needed properties of the mixture we did not have and could not easily find. To account for this inability to use the equation. We took the densest mixture we used in the previous experiment, and poured it onto a flat surface till the circumference of the pile grew to which that it was easy to measure. We used calipers to measure the diameter and height of the pile. Using equation 2 below and the law of sines, we were able to find the angle of repose for this specific material to be degrees. AngleofRepose=(atan(2*h/dia))*180/pi Eq 2. This angle was then used to create the dimension of the triangle using the cross sectional dimension of the tube as the base of the triangle to find the neccessary height of the triangle in section 2. The height was calculated to be 1.76 inches. Since this measurement will be very hard to be accurate when constructing, I increased the height to 1.875, which makes the angle steeper and accounts for a higher angle of repose that might be a quality of other material mixtures. This angle of repose set the angle of the triangle to insure that the material will for a fact flow out of the hopper and onto the transfer surface without any material being left in the hopper. Flow Down Explanation This hopper will be used to contain the particles prior to and during the experimentation of the material inside it so they are not lost into the surrounding environment. The door of the hopper will act as the initiation and stop mechanism of the experiment and will allow the mass flow rate to be predicted using the open area. This will allow the mass flow rate to be preset and the adjust will be able to be automated through Labview, given that the linear actuator will be compatible with Labview user interface. Future Test Procedures One test we would need to perform to confirm this design will work would be to use your fingers at the different center of mass locations to confirm which results are correct. There will also be a tension test on the door, using a tensile tester, when the hopper is filled with a mixture of particles to check that the model set to predict the power of the motor is correct. Once the door begins to move, record that force and use MATLAB to calculated the power needed.

5 General BOM - Square Aluminum tubing - can be cut down to proper size as long as inner dimensions are correct - Linear actuator - power to be determined at a later date - next action item for this design - Aluminum plate (door) Budget Aluminum materials $20 Linear Actuator $80-$250 Risk Assessment ID Risk Item Effect Cause L S I Action to Minimize Risk Owner 1 Linear Actuator not strong enough for future materials Won t be able to open door Not enough power to overpower friction force Do our best to predict power correctly and create factor of safety Team Effort 2 Machine Shop mistake in measurement Create the need to order more parts Cut dimensions incorrectly Measure twice, cut once Team Effort and User 3 Linear Actuator breaks budget Cause us to find a weaker motor, resulting in risk 1 Too highly priced Shop around, Coupons, Mailed in rebates, Groupons Team and User 4 Machine shop user gets injured Use of first aid kit or hospital trip Someone doesn t follow machine shop safety standards Follow safety and preferably have a buddy with you Team Team Positives for Phase III - great team communication - good note taking - team members were vocal about tardiness or absences - offered solutions to overcome their missed presence - Action items were clear and understood - Achieve the acquisition of lab room - Began running tests on toner & carrier particles - Beginning prototyping phase - Once team ran some tests, they got actual values to calculate with

6 - resulted in more specific design specifications Personal Deltas for Phase III - Better initiative on action items - took me longer than I wished to actually get started on calculations - would have allowed an SME to look at my design and check its validity - would have allowed team to see results and give better input to design choices

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10 Attachment 4 clear all; close all; clc; format compact; %!!!!!!!!! 90mircons %Volume in ml % mass in grams %Density in g/ml V_lc=[ ]; m_lc=[ ]; d_lc=m_lc./v_lc; Density_LC=mean(d_LC) %Carrier FC563 V_fc=[ ]; m_fc=[ ]; d_fc563=m_fc./v_fc; Density_FC563=mean(d_FC563) %Carrier FWC938 V_fwc=[ ]; m_fwc=[ ]; d_fwc938=m_fwc./v_fwc; Density_FWC938=mean(d_FWC938) %Toner %Magenta V_M=[ ]; m_m=[ ]; d_m=m_m./v_m; Density_Magenta=mean(d_M) %Yellow V_Y=[ 3.5 3]; m_y=[ ]; d_y=m_y./v_y; Density_Yellow=mean(d_Y) %Blue V_B=[1]; m_b=[0.55]; d_b=m_b./v_b; Desnity_Blue=mean(d_B) Density_LC = Density_FC563 = Density_FWC938 = Density_Magenta = Density_Yellow = Desnity_Blue =

11 Attachment 5 clc;clear all; close all; format compact; mal1=271.8; %g mmix1= ; %g mal2=42.126; %g mmix2= ; %g xal1=2.065; %in yal1= ; %in xmix1=2.065; %in ymix1= ; %in xal2= 1.375; %in yal2=1.25; %in xmix2=1.375; %in ymix2=1.25; %in %% %Center of Mass of Cartridge %COMx X=((mal1*xal1+mmix1*xmix1)/(mal1+mmix1))+((mal2*xal2+mmix2*xmix2)/(mal2+mmix2)); %COMy Y=((mal1*yal1+mmix1*ymix1)/(mal1+mmix1))+((mal2*yal2+mmix2*ymix2)/(mal2+mmix2)); COM=[X,Y] COM =

12 Attachment 6 clc;clear all;close all;format compact; xdata=[ ]; ydata=[ ]; xcenter = mean(xdata) ycenter = mean(ydata) %Graphically you can check with: plot(xdata,ydata,'b'); hold on plot(xcenter,ycenter,'r*') xcenter = ycenter =

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