The PBJ Cookie Company Inc. has hired our team to design a cam-driven peanut-butter pump for their new 600/minute cookie assembly line. These 1.25" square cookies are hoped to be a serious competitor to the popular Gaucho¨ cookie line. The cookie tops and bottoms are carried through an oven, side by side on a constant-velocity conveyor belt and are spaced on 3" centers in the direction of travel.

    The cookie-bottoms exit the oven and continue on the same conveyor to the PB station where a uniform thickness of peanut butter is applied as the cookie-bottom passes by the PB nozzle at constant velocity. The cookie-tops travel in parallel on the same conveyor to the jelly station where a uniform thickness of Welch’s Grape Jelly¨ is applied as the cookie top passes by the jelly nozzle at constant velocity. Further down the line, a linkage flips the jellied top onto the PB’d bottom to make the world’s most delicious cookie. (Well, to each his own.)

    The jelly application is fine but PBJ Inc. is having trouble with the peanut-butter side of the line. Peanut butter is a difficult material to handle. It belongs to a class of non-Newtonian fluids called Bingham fluids. There is a substantial amount of entrained air in the PB which makes it slightly compressible. Laboratory tests have shown that if you attempt to pump it at a constant flow-rate with a piston pump, there will be a lag at the beginning as the entrained air is compressed. After it reaches steady state, it will flow at a uniform rate if the piston moves at constant velocity. But then, at the end of the piston’s stroke, the stored energy in the compressed, entrained air comes back to haunt you and causes a case of "peanut-butter drool" which makes for a messy cookie.

    So, in order to get a sharp-edged start to the "patch" of peanut butter, and to prevent the "dreaded PB drool", we need a special cam design to drive the piston pump. Figure P9-2 on page 392 of Design of Machinery shows a similar setup to that of this peanut-butter pump. This figure shows a cam driving a follower attached to a piston pump which, in our case, contains peanut butter instead of saline. The (non-crunchy) peanut butter will flow out of the "pressure outlet". The accumulator with its air charge represents the entrained air in the PB.

    Extensive laboratory tests have shown that we need an extra "kick" at the beginning of the pumping cycle to wind up the "air spring" in the PB, followed by a period of constant velocity motion to lay down a uniform thickness of PB. Then, at the end of the "patch" of PB, we need to provide a "sniff" to rapidly retract the piston and prevent drool. The piston is then returned to the start point to refill the pump and repeat the cycle.

    You can calculate the necessary velocity of the piston/follower for the steady-state portion of the cycle from the above information. The velocity of the "kick" appears to be optimal at about 3 times the steady-state velocity and should be of as short a duration as possible within reasonable acceleration bounds. The velocity of the "sniff" appears to be optimal at about 4 times the steady-state velocity and should be of as short a duration as possible within reasonable acceleration bounds.

    Your task is to design the PB piston-driver cam for good dynamic operation and to size it in a reasonable package.

    As with any design problem, there is an infinity of solutions possible. You are expected to come up with the best solution you can design. To do so you will have to try out many alternate designs and iterate to your 'best' solution. You should expect to typically go through at least ten iterations before arriving at an acceptable one. Some measures of "better" designs will be: lower peak accelerations, smoother jerk, smaller physical cam size, good pressure angles and reasonable follower size. You may use either a flat faced or roller follower. You are required to compute the s, v, a, j functions, the pressure angles and radii of curvature of the entire cam and draw the cam profile. All of these tasks can be accomplished with program Dynacam.

    You are also required to document your solution in a professional engineering report which adheres to the Project Report Specifications document previously distributed. This report will document the process by which you iterated to your final design as well as the design itself. Do not just describe the final result. Rather show me how you arrived at it, including the failures encountered along the way. This will demonstrate to me that you understand the engineering concepts and the relevant course material. Note that unreferenced and undiscussed computer or other illustrations will be considered to be report "filler" and be ignored. Do not put anything in the report unless you discuss its meaning. NO model of your design is required. But, please do include a computer disk with your DYNACAM solution files on it.

    For this project, no background research is required beyond your textbook. See Chapters 9 and 17 and section 2-15. Begin your report with the goal statement and task specifications followed by the design description phase of the design process. No need to include any background research. The report must include the following figures IN THE ORDER LISTED!

-    S-V-A-J diagrams in one plot

-    separate S, V, A, J plots (4 figures)

-    pressure angle plot

-    radius of curvature plot

-    the (3) boundary condition tables for each of your segments

-    a cam profile

-    any other data you think necessary

IMPORTANT! IMPORTANT!