Power Scissors

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Computer Rendered Components

Drive Belt System

Isometric View

Top View

Side View

Annotated View

Paper Advancing Rollers

Isometric View

Front View

Side View

Cool Animated Videos

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Animated Printer Carriage

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Animated Paper Feed Mechanism

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Analysis

Analysis Of The Belt System

Scope of Analysis

The two engineering specifications that are quantified for the printer belt tensioning system, are the force on the belt required to accelerate the printer head to its maximum speed, and the force to stop the printer carriage and change direction. Both of these specifications pertain to the Dots Per Inch design parameter. The best design is to obtain the maximum DPI rating in the quickest printing time. To achieve this goal, the belt must be able to cope with the forces to accelerate the printer carriage.

Key Properties

• Printer Prints 4 pages a minute at 300 DPI
• Mass of Carriage With Ink Cartridge = 0.14 kg
• Moment of Inertia of Pulley = 0.5 (.002kg)(0.005^2m) = 2.5 x 10^8
• The belt is a trapezoidal design, meaning each tooth has the shape of the trapezoid
• The belt is made out of polyurethane which has good wear resistance and low friction

Assumptions

Friction force exerted by the slider on the carriage is always constant when moving, and should have been reduced to a minimum by the manufacturer. Lower friction would reduce the force the stepper motor has to supply to move the carriage. Since it is difficult to measure the exact amount of friction force, and it is relatively small compared to the acceleration forces, friction can be neglected.

Finding The Speed

Since, the actual printer head speed I could not be found, a few assumptions had to be made with the available information. The printer has a 300 DPI rating, which means that it can print 90,000 dots per square inch. It can print 4 pages of text per minute. Assuming that it prints 8.5” x 11” pages with a 1” top and bottom margin, and 1.25” side margins, it leaves a total of 54 square inches of text. This equates to 4.86 x 10^6 dots per page. Multiply the dots per page by the pages per minute, and that results in 2.43 x 10^7 dots per minute. 2.43 x 10^7 dots per minute is the average printing rate for the printer. However, if we assume the format is 12 point, Times New Roman font, the total area per line of text is 1.95 in^2 (6.5” x .3”) 0.54 square inches per page multiplied by 4 pages per minute, divided by 1.95 square inches per pass, and taking the reciprocal, yields .009 minutes per line, which is 0.54 seconds per line. Every line is 6.5 inches long, which means that the printer head moves at 12 inches per second. Since information on the acceleration of the printer carriage could not be obtained, it was instead estimated. After careful observation of other inkjet printers, the carriages reach their top speed almost instantaneously, so it was estimated that it takes 0.2 seconds to reach maximum velocity, and 0.25 seconds to stop and change direction.

Calculations

• Acceleration of Carriage From Rest

Acceleration of Carriage = max velocity/ time = (0.3048 m/s) / 0.2 s = 0.15 m/s2

Mass of Carriage With Ink Cartridge = 0.14 kg

F = ma = (0.14)(0.15) = 0.021 N

Therefore, it takes .021 N to accelerate the carriage from rest to the max velocity

• Stopping and Changing Direction

Change in velocity = (0.3048+.03048) = 0.6096 m/s

Change in Time = 0.25 s

F = (Mass*Change in Velocity)/ Change in time = 0.34 N

Therefore, the maximum force exerted on the belt due to the change in direction is 0.34 N.

As seen in Figure 10 below, the maximum force to pull the carriage is related to the torque supplied by the motor pulley. Furthermore, the carriage is fixed to one side of the belt, so it translates directly with the belt. During the analysis, the entire carriage is treated as a point mass and represented as a block. Figure 11 shows the free body diagram of the motor pulley. It is evident that the torque from the pulley is directly related to the force on the belt during acceleration.

Figure 10: Free Body Diagram Of System

Figure 11: Free Body Diagram Of Motor Pulley

The analysis through Adams produced results that were similar to the calculated values. The maximum force, as seen in Figure 12, reached 1 N which was very close to the calculated value of 0.34 N.

Figure 12: Force of the Drive Belt During Acceleration

Improvements

To increase the maximum force that the belt could handle, a few options are available. The cross-sectional area could be increased to decrease the stress on the belt. According the stress equation, stress = load / area , the stress can be reduced by increasing the cross sectional area to compensate for load force. The cross sectional area can be increased by making the belt wider or thicker. Making it wider would be more beneficial because it would provide a greater surface area for the toothed pulley to grip onto. The drawbacks for increasing the surface are the increase in stiffness and cost of manufacturing. Making the belt thicker would reduce its flexibility, making it harder for it to move around the pulley. It would require more torque form the input motor to compensate. Making the belt wider would force the pulleys to be wider, which drives up the cost of the system.

Another method to increase the stress capacity of the belt would be to use a curvilinear design instead of the current trapezoidal design. The curvilinear design looks very similar to the gear sprocket of a bicycle. Instead of a trapezoid shape, the curvilinear design uses a half circle shape. Therefore, the teeth are deeper in the gear which makes it less probable for tooth jumping during high accelerations. Furthermore, there is less material at the edges of the gear, which lowers the moment of inertia, allowing the gear to accelerate faster. [1]

Figure 13: Photoelastic Stress Pattern [1]

Figure 13 shows the photoelastic stress pattern of both designs, and it is evident that the curvilinear shape distributes stress more evenly. This is due to the larger tooth cross section. Since the curvilinear shape handles stress better than the trapezoidal shape, a narrower curvilinear belt could be used in place of a wider trapezoidal belt, thus, saving material and cost. [1] The trade off may be in increased cost to manufacture, since curvilinear belts are not as common as trapezoidal belts.

A final option to consider is to change the material of the belt. Using a more durable and stress resilient material such as steel or composites, may work better. However, it is most likely that these materials are more difficult to manufacture, which increases the cost

References

(1) SDP/SI : The World Of Timing Belts

Analysis Of The Paper Feeder

Part 1

The engineering specification chosen to analyze for this dissection was the force that was exerted on the two interlocking gears that managed the motion of the paper feed mechanism. This force was then translated into a stress and then examined to see if the gears would deform under the load. Both the geometry of the paper feeder and the size and type of motor contributed significantly to the loading of this problem. The larger the moment of inertia of the paper rollers and the center rod, the more resistance there is to the motion of the entire system, resulting in a larger gear force. The motor that was used in this model was a stepper motor. This was most likely chosen for its usefulness for moving the paper at a given increment. However, the stop and go nature of this motor increased the gear force by creating sudden starts and stops of the system rotation.

Part 2

Analysis will have to be performed on the operating conditions of the printer. The coefficient of the rubber wheels on the paper will have to be found along with all of the geometric parameters of the system. For example, the radii of the wheels, their thickness, and their density will all have to be found in order perform the analysis in ADAMS. All geometric parameters, moments of inertia and yield strengths will be have to be found to perform the analysis. Finally, the force that is necessary to slide the paper (adding to the resistance of the motion) will also need to be found. This will be found by using the coefficient of friction mentioned earlier.

Simplifications in the model can be made in this analysis. Since we are only concerned with what is going on at the gears, the yield stresses will be unnecessary for the rod and the wheels. Also, the wheels (which are composed of both rubber and plastic) can be considered to be entirely rubber since the density of rubber is greater than that of plastic. If the calculations indicate that stresses are such that they are close to the yield stress, than this simplification will have to be done away with in order to get a more accurate value for the gear force.

Part 3

Engineering Specification for Paper Feeder

Gear Force (and Stress)

• The force that is exerted on the two gears at their intersection (and the stress that results from this force).
• Target Value: Force < 1e5 N (from the 40 MPa Tensile Strength of Plastic)
• Direction of Improvement: Down (smaller gear force)
• Related user requirement: Paper feeds smoothly

Design decisions/parameters affected

• Geometry of System
• Size and Type of Motor

Key geometric, inertia, and material properties

• Length, radius, density of rod (stainless steel)
• Thickness, radius, density of Wheels (rubber)
• Thickness, radius, density of Gears (steel and plastic)
• Moment of inertia for all components

Analysis

Brittle Fracture Analysis: Maximum Normal Stress Theory

Results

Gear Force

From this graph, the maximum gear force was found to be about 0.3 N. This value is much less than the force at which the plastic gear would deform (1e5 N), verifying that the design is a safe for operation. This also verifies that this design meets the user requirement that the gear set up would not fail due to deformation.

Improvements

From this analysis, it is clear that the smaller plastic gear is more robust than is necessary. The amount of force that is applied to the gear is no where near a force that would cause any significant deformation. However, it is important to remember that this analysis is only of one aspect of the forces that are applied to this gear. It is possible that cyclic loading forces the gear to be as large as it is. Also, it is possible that this gear size is either easily manufactured or readily available. Therefore, it would be less expensive to use this gear rather than manufacture a gear that is of a different size.

1. What is the primary function of the device? How does it accomplish it? The primary function of the device is to cut through different materials. There are two blades, the bottom one stays stationary, and the top blade moves rapidly, opening and closing. This action allows the tool to cut through things.

2. List possible user requirements for your product. Provide rationale for each requirement. a. Blades are sharp enough to cut different materials i. Have a sharpening function b. Easy to use i. Has a low weight ii. Has a small size iii. Comfortable to hold iv. Wireless v. Easily accessible buttom to start c. Aestheically Pleasing i. More likely to be bought d. Long battery life, chargeable e. Changeable blades for different materials to cut f. Doesn’t break if dropped

3. List possible engineering specifications. Which user requirement(s) do these correlate to? (Are there any engineering specifications which do not correlate to a user requirement? How about any user requirement which has no associated engineering specification?) 1. Material for jaws is sharper than cutting materials strength 2. Battery Life is ______ long 3. Force of scissors is greater than _____ 4. Weight is less than _______ (5 lbs?) 5. Scissors retain sharpness for _______ (amt of time) 6. torque on motor is ______ 7. External casing can withstand ______ force, to avoid being dropped