Analysis 1 - Exsiting Moment of inertia

Analysis 1 is to determine the moment of inertia of one shaft with spacer, gears, and blades. The dimensions come from drawings from a previous engineer on the project. No information of the material that the parts are made of, so an assumption is made that all parts are AISI 5160. The density on MatWeb for this material is 0.284 lb/in^3. Assumptions were also made that the gear teeth and keys are negligible in the calculation. The total moment of inertia for 1 of the shafts is 6.652 lb-in^2. (Appendix A-1 for calculations)

 

Analysis 2 - Transfered Torque and Speed

Analysis 2 is to determine the horsepower, torque, and rounds per minute of the shaft. This is needed to complete the requirement of having enough force to be able to shred carbon fiber with a feed rate that exceeds 1’ per minute on pieces less than 6” in length. The motor and its specifications are found on McMaster-Carr, model number 6136K512. The torque value used is when the motor is in continuous operation. The existing gear ratio of 7:22 is used. The results give; 113.78 in-lbs toque, 3.18 HP, and 5534.6 rpm. These values will be use with the moment of inertia in designing a flywheel.

Analysis 3 – Force to shear carbon fiber

Analysis 3 is to determine the force required to shear the carbon fiber. The given dimensions of the carbon fiber are 3in wide by 0.35 in high. These are used to find the cross-sectional area being sheared at once. The shear force is coming from both sides from multiple teeth but due to the fact they are spaced very close to each other and should be exerting the same force each it is assumed that the shear force is distributed evenly in one direction. The shear strength of carbon fiber is found on MatWeb to be 12,574 psi. The force required to shear is 13,202.7 lbs. This value will be used in the calculation in finding the moment of inertia needed to satisfy the requirement of choking not occurring when shedder feed rate exceeds 1’ per minute on pieces less than 6”.

Analysis 4 – Time to shred 6in of carbon fiber

Analysis 4 is to determine the time it will take to shred 6 in of carbon fiber at max speed. First the circumference of the cutting wheel is found using the given 1.5 in radius. This value of 9.42 in is used in finding the number of rotations to shred 6 in of carbon fiber, coming out to 0.64 rotations. With the bug assumption of a constant max speed this value is round up to the nearest rotation of 1. Time is found by dividing by the max speed given as 560 RPM and then converting form minutes to seconds. The time calculated to shred through 6 in of carbon fiber is 0.11 seconds. This value will be used in the calculation in finding the moment of inertia needed to satisfy the requirement of choking not occurring when shedder feed rate exceeds 1’ per minute on pieces less than 6”.

Analysis 5 – Moment of Inertia of Flywheel

Analysis 5 is to determine the moment of inertia needed from the flywheel. This will take the calculated needed moment of inertia and the calculated existing moment of inertia. So, with the existing known the needed will first be calculated. This is done using moment and impulse calculations. Impulse is the time of cutting the carbon fiber multiplied by the torque applied. The torques of both the motor adding impulse and the cutting taking away impulse are used. Then the moment is found using the rpms the shaft is spinning at. A factor of safety of 2.5 is used to give a moment of inertia needed from the flywheel of 51 lb/in^2. This will satisfy the requirement of shredding 6” of carbon fiber without binding.

Analysis 6 – Dimensions of Flywheel

Analysis 6 is to determine the dimensions of the flywheel. This was done in excel using the moment of inertia formula of a cylinder and subtracting the bore area. The moment of inertia formula is rearranged to find the outer diameter. The density and thickness of the wheel is assumed to be 0.284 lb/in^2 and thickness of 1”. The calculated outer diameter of a solid wheel is 6.34” with a weight of 33.6 lbs. This flywheel would be easily manufactured and be able to satisfy the requirements of being able to cut 6” of carbon fiber without choking and using the already provided 1” shaft.

Analysis 7 – Chain Length

Analysis 7 uses mechanical design to calculate the required length of chain around the two sprockets to keep the iteraaction between the chain and the sprockets as tight as possible.

Analysis 8 – V Belt Pulley Moment

Analysis 8 is the measurement of the area moment of inertia of v-belt pulleys from McMaster-Carr. Most flywheels found online are manufactured for cars and are quite expensive. The process of manufacturing a flywheel is complex when it comes to balancing, the available machinery in current facilities would make it difficult to do this. A large V-Belt pulley would be a simple inexpensive substitute that will get the job done. This meets both the budget requirement and increases moment of inertia to be able to shred 6” of carbon fiber scrap. Multiple CAD files are downloaded from McMaster-Carr of V-Belt pulleys and solid works mass properties command is used to compare mass moment of inertia. The cast iron 9.75” diameter flywheel is found to have the closest moment of inertia to !@#$%^&&* of !#%$^#@%.

Analysis 9 – Carbon Fiber Friction

Analysis 9 is the measurement of the minimal angle of slope required for the shredded pieces of carbon fiber to slip on a piece of steel sheet metal. This resulted is needed to meet the requirement that the carbon fiber shreds must exit the shredder. The process to calculate this angle is done through testing. Calculations can be done; however, they will give a ballpark solution when testing gives more accurate results. Testing is done by dropping already shredded pieces of carbon fiber on an angled piece of steel and observing if the carbon fiber slips down the metal or stays on it. The tested angles are 30, 45, and 60 degrees. The carbon fiber did not slide off the metal when at 30 degreed but did at both 45 and 60. Therefore, the minimum required angle is found to be 45 degrees.

Analysis 10 – Shaft Stress

Analysis 10 measures the stress on the current installed shaft and tested to see if it would fail under load. The given load by the cutting wheels is the cutting force divided by the number of blades. The load of one blade is 600lbs. Using bending stress and shear stress analysis. Both stresses of 94,300 psi of bending and 47,150 psi of shear prove to be significantly lower than the critical stresses and prove the original shaft will be able to handle the load sufficiently. This satisfies the requirement of using parts from the previous model of shredder.

Analysis 11 – Housing Stresses

Analysis 11 measures the shear stress on the key that holds the blades from rotating on the shaft. Using the shear stress formula, the blades will be putting 15,352 psi of force on the key that can withstand 53,700 psi. This shows the key can withstand the forces applied to it. The key already purchased will be able to complete this task so the requirement of reusing parts can be met as well.

Analysis 12 – Mounting Stresses

Analysis 12 measures the shear stress on the key that transmits power from the sprocket to the shaft. The same formula of shear stress is used to calculate the stress on the key. The stress is 22,189 psi which is well below the critical stress of 53,700. New key stock will have to be purchased to do this, but the device will not be able to function without it.