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Automated Single-Stream Recycling Sorting System

Automate the process of sorting recyclables, reduce cost of sorting, and maintain the convenience of single-stream recycling. Implement a fan-based system to blow recyclables into designated bins. Mathematical model and sensitivity analysis included.

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Automated Single-Stream Recycling Sorting System

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  1. SCUDEM: Problem A Team members: Stas Kuzmenko, Lewis McAllister, Kate Perkins

  2. Problem summary: • Automate the process of sorting recyclables • Keep single-stream recycling (convenient for consumers) • Reduce cost of sorting by removing necessity of human labor Image Credit: recycle.georgetown.org

  3. Assumptions • Uniform distribution of paper and cardboard • Recyclables fall vertically and with no initial horizontal or vertical velocity • Force of fan is uniform, acts horizontally, and does not affect vertical motion of recyclables • There are no sources of wind other than the fan • Paper and cardboard are less dense than most other recyclables • Drag in horizontal direction (opposing fan wind) is negligible

  4. Physics principles • Drag (at low speeds) • Basic model, without drag • Gravity • Paper spends longer in the air & is blown on longer by fan • Speed of falling paper and cardboard

  5. Diagram of Setup Recyclables enter Fan blows recyclables outward Paper and cardboard Plastic, aluminum, other recyclables Image credit: http://www.rkairconindustries.com/industrial-fans.html

  6. Free-Body Diagram and Sum of Forces FfForce of wind from fan FgForce of gravity D Drag component in y-direction

  7. Vertical DE for Paper Products Substituting all known values... Substitute v for x’ and v’ for x’’ 0.0045v' = 0.0045*9.8 - 1/2*1.225*1.05*0.0142*v^2

  8. Vertical DE (cont.) Solving for v:Integrating for x: Accounting for initial conditions (x = 0, x’ = 0)

  9. Graph of Vertical DE

  10. Horizontal Sum of Forces and DE - Wind force equation from: engineeringtoolbox.com

  11. Solving Vertical and Horizontal Differential Equations For height 10 m and 12 m wide chute, x(t) = 10: t = 4.7 s v = c = 0.53 m/s wind speed, with 10 m height drop

  12. Sensitivity analysis (additional problem) Small change in height has greatest impact: • Paper falls for a longer time therefore blown longer by fan • Large surface area--force of fan’s wind is greater • Allowing recyclable size to vary means significant amounts of paper and plastic will end up in the wrong bin

  13. Full Drag • Now, there is drag in both x and y directions • Using reference frame of surrounding air particles Drag Drag Wind not moving in reference frame Wind from fan Wind force Gravity Gravity Direction of motion Direction of motion Our reference frame Reference frame of air, moving relative to ours

  14. Full Drag Variables and Constants • s, wind speed (m/s) • d, fan diameter (m) • h, height of conveyor (m) • m, mass of material (kg) • A, cross-sectional area of material (m2) • ∑Fx and ∑Fy, sum of forces in x and y directions • D, force of drag • xw and vw, the position and velocity in the wind’s reference frame • g, gravity constant (9.8 kg*m/s2) • ⍴, mass density of air (1.225 kg/m3) • Cd, drag coefficient of a rough sphere (0.5)

  15. Assumptions • x and y directions are independent • Recycling is roughly balled or folded • Fan blows perfectly perpendicular to gravity and does not affect materials below its bottom lip • Paper and cardboard are lighter than other recyclables • x axis is positive away from the fan, y axis is positive upwards

  16. They did the math (they did the monster math) • Materials have no initial velocity (v0 = 0) • Materials fall from height h, through a fan of diameter d, and have final height 0

  17. Conclusions Both a height of 10 m and a wind speed of .53 m/s are reasonable • Other types of recycling will be in paper section--some hand sorting still required • Model could be improved by also finding where recyclables other than paper end up horizontally

  18. Sources http://www.rkairconindustries.com/industrial-fans.html https://www.engineeringtoolbox.com/wind-load-d_1775.html

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