Paper towel dispenser innovation
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Our group realized that determining Mspring and Mratchet from calculations of actual spring forces, dimensions, and friction forces is inefficient, and also inaccurate. Thus, we tested the actual model at different angles, incremented theta by 45 degrees, and reported forces to obtain Mspring and Mratchet values. To find force, we attached a reference spring to the end of sheet of paper towel and pulled until it reaches certain angle and stays at equilibrium. Then we measure the stretch of spring to find out the force. We applied the same method is used for both of Mspring and Mratchet, but we isolated the two values from each other and tested them separately. | Our group realized that determining Mspring and Mratchet from calculations of actual spring forces, dimensions, and friction forces is inefficient, and also inaccurate. Thus, we tested the actual model at different angles, incremented theta by 45 degrees, and reported forces to obtain Mspring and Mratchet values. To find force, we attached a reference spring to the end of sheet of paper towel and pulled until it reaches certain angle and stays at equilibrium. Then we measure the stretch of spring to find out the force. We applied the same method is used for both of Mspring and Mratchet, but we isolated the two values from each other and tested them separately. | ||
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''Calculation of Mspring and Mratchet'' | ''Calculation of Mspring and Mratchet'' | ||
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M<sub>spring, i</sub> = (D/2) Fspring, i = 0.05 Fspring, i Nm , where i = 0, 45°, 90°, …315°, 360 ° (eq.1) | M<sub>spring, i</sub> = (D/2) Fspring, i = 0.05 Fspring, i Nm , where i = 0, 45°, 90°, …315°, 360 ° (eq.1) | ||
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''Summary of results'' | ''Summary of results'' | ||
Revision as of 10:17, 5 December 2009
Mechanical Analysis
In our new paper towel dispenser, we incorporated a ratchet mechanism to prevent spindle from turning more than needed due to its inertia and causing paper towel to be rolled back in. For engineering analysis, we calculated and investigated to compare the effect of the additional inertia of the ratchet as well as the new resistance moment it will provide. First, we varied rotation angle of spindle and performed static analysis to measure force required for users to pull a paper towel with the original paper towel dispenser and with our new design. Then we assumed the average time it takes for a person to pull a paper towel to be 1 sec, and performed dynamic analysis of systems to find out required pulling force with and without ratchet mechanism.
Fig.1: left view of spindle (left) and right view of spindle(right) with ratchet mechanism indicated by red box
Free Body Diagram
Where:
D = diameter of spindle = 0.1m
Θ = angle displacement of spindle from initial state
W = weight of the spindle and ratchet gear
Fbase,y = force applied by axle of the base to the spindle in y-axis
Fapplied = force applied by user by pulling paper towel
Mresistant = Mspring + Mratchet
Mspring = moment from lever arm springs on the left side of spindle(varies with θ, angle of rotation of spindle, see Table 1)
Mratchet = moment from ratchet mechanism (moment due to friction force between ratchet gear and pawl, normal force being ratchet spring force and reaction force from axle of the base)
Determination of Mspring and Mratchet
Our group realized that determining Mspring and Mratchet from calculations of actual spring forces, dimensions, and friction forces is inefficient, and also inaccurate. Thus, we tested the actual model at different angles, incremented theta by 45 degrees, and reported forces to obtain Mspring and Mratchet values. To find force, we attached a reference spring to the end of sheet of paper towel and pulled until it reaches certain angle and stays at equilibrium. Then we measure the stretch of spring to find out the force. We applied the same method is used for both of Mspring and Mratchet, but we isolated the two values from each other and tested them separately.
Calculation of Mspring and Mratchet
References spring constant, k = 163.3 N/m
Initial length of reference spring constant, Linitial = 0.023 m
Fspring, i = k ∆xi = (163.33)∆xi N where ∆ xi = Lengthspring,i - Linitial = (Lengthspring,i - 0.023) m
Mspring, i = (D/2) Fspring, i = 0.05 Fspring, i Nm , where i = 0, 45°, 90°, …315°, 360 ° (eq.1)
Summary of results
The difference between Mspring and Mratchet is that unlike Mspring, Mratchet does not depend on angle of rotation. We found that Mratceht is relatively small compared to Mspring (approx. 2% of Mspring). Therefore we believe that adding ratchet mechanism would not cause a huge difference.
Table 1: Resistant forces, moments at different angles of rotation
Fig.3: Resistant moments at different angles of rotation
