Toastmaster: Toasting in Style!
This product is a produced by Toastmaster and has an approximate cost of 14 dollars. The product is used to toast bread, bagels, Toaster Strudels, Poptarts, English Muffins, and many other bread products.
How It Works
1. Bread product is placed in toaster slots.
2. With toaster plugged in, handle is manually pressed down and dial/button is set to desired conditions.
3. When handle is lowered, converting springs close wire bread clamps. A plastic piece on the handle is wedged in between electrical prongs, completing the circuit. This activates the electromagnet, and a flat piece of metal attached to the handle mechanism is attracted to the magnet, thus holding down the bread product.
4. The heating elements are composed of nichrome wire wrapped around mica sheets. These are activated simultaneously with completion of the circuit. The pattern found on the bread products is a result of being in contact with the wire bread clamps.
5. The bread is released at a time dependent on the user’s input settings. The circuit is interrupted, and the electromagnet turned off. The handle mechanism is released, and the toasted product is forced upward.
6. The toasted product is then removed and enjoyed by the user.
The table belows lists the individual parts of the toaster:
|Part #||Part Name||Category||Function||Material||Picture|
|1||White plastic cover||Structural||Houses all inner components, protects user, and provides aesthetic appeal||Polypropylene (Recycling code: #5)|
|2||Gray plastic base containing circuit boards and other electrical components||Input and Structural||Operates and provides controls to heating elements, supports other components (circuit boards), and provides structural support||Polypropylene (Recycling code: #5)|
|3||Heating elements (x 3)||Output||Supplies heat to toast bread to perfection||Mica sheets, nichrome wire|
|4||Toast holder support||Structural||Provides anchoring point for toast holding troughs; moves up and down with handle mechanism||Steel|
|5||Metal handle component||Input||Positions and clamps bread for toasting||Treated steel|
|6||Toast holder (x2)||Support Element||Catches and supports bread for toasting||Treated steel|
|7||Wire bread clamps (x4)||Output||Clamps to hold bread; also heats to help toasting||Steel|
|8||Screws (x9)||Support||Holds together cover and base; holds in electrical components||Steel|
|9||Converting Springs||Motion conversion elements||When handle is pushed down, springs pull together to close wire bread clamps||Wire|
|10||Side wall (x2)||Structural||Holds heating elements in place; provides connection between inner components and plastic base.||Treated steel|
Time to toast
Calculating the time for the surface of the toast to reach the temperature necessary for the chemical reaction that causes bread to brown to occur:
Complete hand calculations for heat transfer analysis
1. Beginning temperature of system
2. Conduction coefficients of involved elements (wire, bread)
3. Emissivitiy of wire
4. Convection constant for air
5. Input voltage and current
6. Dimensions of toast, heating element, and toast slot
1. 1-D heat transfer
2. Ideal insulation
3. Thermal equilibrium in wire has been reached
4. Toast at final temperature for energy balance
5. All 4 heating elements exactly the same
6. constant thermal properties at room temperature
7. Toaster initially at room temperature
8. No conduction through sides of toaster
10. Only heat transfer due to radiation reaches toast
11. Convection heat transfer escapes through toast slots
12. No conduction through wire bread clamps
13. Bread product has uniform density
14. Bread product is square
15. Heat transfer to bread is uniform
16. Symmetric configuration on both sides of bread
Key thermal properties (see Figure 2):
•Verification Analysis Procedure (see Figure 3):
•Subsystem diagram (see Figure 4):
Heat transfer from radiation to toast: 101.2 W
Time to toast: 22.5 seconds
Efficiency of heating element: 40.5%
The time to toast, or the time it takes between turning on the toaster and the bread product reaching the temperature needed for the surface to begin browning, was the engineering specification related to the ‘ease of sensing and controlling state’ user requirement. It is desirable to minimize the time to toast. Minimizing the time to toast can be done through increasing the efficiency of the toaster, or the ratio of the heat transfer into the bread product to the power input into the heating elements. This can be increased or decreased by changing the geometric or thermal properties as described above. For example, decreasing the toast slot opening will decrease the convection constant, therefore decreasing the amount of heat lost through the top of the toaster to the environment. Or, a different material for the heating element wire could be chosen with a higher emissivity so there is more heat transfer to the bread by radiation. The conduction constant of the insulation should likewise be high so as to decrease the amount of heat lost through the toaster. The time to toast that was found through this procedure is within the correct range observed through actually toasting slices of bread.
To improve the design, a material with a higher emissivity could be chosen for the heating element wire, this would allow more energy to be transferred to the bread through radiation. The toast slots on top of the toaster could be made smaller or have a cover that slides over them while toasting so as to reduce the convection heat transfer constant by inhibiting air flow. This would decrease the heat lost to the surroundings and more would be transferred to heating the inside of the toaster. The current, which affects power input could be increased so as to provide more power which becomes heat transfer to the toast, although there are quite possibly safety regulations that this would violate. The thermal conductivity of the mica insulation, assumed here to be ideal, could be increased since heat is lost through this, even though it was considered negligible here. Cost is an important tradeoff as materials and manufacturing for creating a cover for the toast slots as well as a more insulating material for the heating elements are not cheap. Geometrical values to keep in mind in the design include the dimensions of the heating element wire. The surface area should be great enough to allow for maximum heat transfer to the toast, but not so large that the wire does not provide enough thermal resistance for optimal heat generation.
Maximum toast height at exit
Calculating the maximum height the toast will reach upon release of the electromagnet:
Equations for maximum toast height analysis
1. Mass of entire moving system (toaster parts and bread product)
2. Spring deflection
3. Spring stiffness
1. Spring is linear
2. Friction may be neglected in calculations
3. Static friction is great enough so that spring does not deflect when bread put in toaster
k = stiffness of spring
x = spring deflection
m = mass of moving system (includes bread product, handle, spring, toast holders, toast holder support, wire bread clamps, converting springs)
g = acceleration due to gravity
h = maximum height of the toast upon release of electromagnet
•Verification Analysis Procedure (see Figure 5):
In order for the toast to rise after the spring is released, the force of the spring must be greater than the force caused by the weight of the system.
•Subsystem diagram (see Figure 6):
Spring Stiffness, k: 46.7 N/m
Deflection in toaster, x: 0.06 m
Mass of the moving system, m: 0.185 kg
Maximum toast height at exit, h: 4.63 cm
The maximum height of the toast upon release of the electromagnet (at the toast exit) was the engineering specification related to the ‘force and motion control' and 'safety' user requirements. It is desirable to minimize the maximum height the toast will reach upon exit. Minimizing the meximum height of the toast may be accomplished through increasing the mass of the system or by decreasing the spring stiffness or spring deflection. The maximum height of the toast (4.93 cm) that was found through this procedure is approximately what would be expected from a toaster and what was observed while the toaster was in operation.
To improve the design, different spring stiffnesses or deflections could be changed so as to result in a desired maximum toast height depending on what the user wants. Greater spring stiffnesses could however lead to higher frictional forces which would be bad for wear of materials and would make analysis more difficult as friction could not be neglected. Increasing or decreasing spring deflection would be confined to the size of the toaster leaving not much room for improvement. The design may also be improved by changing the mass of the system (most likely done by choosing different materials). Changing the materials within the toaster could have multiple trade-offs such as costs, and thermal property changes. Thermal property changes would result in needing to perform a new thermal analysis of the toaster which would take time and other resources.
Force to fully deflect handle
Calculating the downward force that must be exerted on the handle to fully encase bread in the toaster.
A virtual model of the mechanism was created in Pro/E and then imported to MSC.ADAMS. First, the model was given weight by specifying the material density and activating the gravity option. Next, a spring was attached to the handle and grounded, and the stiffness was indicated (46 N/m). The handle was constrained to move only up and down the post (no rotation). Next, it was specified that the handle component would deflect downwards 6 centimeters, thus stretching the spring. A linkage mechanism was created to make the wire clamps move inward as the handle was pushed down, thus representing the motion of the “converting springs.” This was not intended to be part of the force analysis, but was included to visually display how the entire mechanism moved. The force required to fully deflect the handle was recorded in a graph (see below in “Results”).
1. In the MSC.ADAMS model, a piece of bread was not included. The above diagram is only to show a general representation of the mechanism and its relation to the toast. It is assumed that the weight of the bread would only assist in pushing down the handle, so it was decided that required force would be measured using an unloaded mechanism.
2. The force of friction is show in the diagram above. This is showing that the presence of friction is acknowledged, but in the MSC.ADAMS it is neglected. The required downward force is dominated by the spring, and thus friction is negligible.
•Animation of MSC.ADAMS Model:
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Required Force for 6cm-deflection: 2.65 Newtons
Equation of line: y = (-0.442x)
The engineering specification was defined as the force required to fully encase the bread in the toaster. These results are a direct measurement of this specification. The plot shows that a force of approximately 2.65 N is required to deflect the handle 6 centimeters. The plot of shows a linear relationship between the two quantities, and thus to deflect the handle any given amount, the required force can be expressed as y=(-0.442x).
These results verify the quality of the design by proving the required force is of a reasonable magnitude. The force required for full deflection is 2.65Newtons which is equivalent to approximately 0.595 pound-force. This is well within reason. It can be expected that most users would be able to exert this force. Only in extreme cases of disability could this be a challenge. Because this product could be used by the majority of consumers, its design could be considered of good quality (with regards to consumer usability).
The following table lists changes that could be made to the design of the toaster, the potential improvements, and also the possible downsides.
Interested in toasters or just a fan of toast? You can further explore the wild, wonderful world of toasters at the below links.
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