1. CheesePot: Engineering Analysis By: James Weglarz

2. Outline Performed analysis on the CheesePot Vertical Fingers that are used to mix the cheese. Assumed heavy duty use cycle Using PTC Parametric 3.0 Show detail drawings of design parts Explain Design Constraints Engineering Standards used

3. Usage Heavy duty use cycle assumed to be twice a day for three years. Maximum load would be on startup Looked on code to find start up ques, total of 4 per cycle. Weekly start times = 8 Per week = 8 times per day * 7 days = 56 Weeks per calendar year = 52 Motor starts per calendar year = 52 * 56 = 2912 starts per year 2912 * 3 years = 8736 cycles for analysis

4. Drawing: Vertical Fingers Rev. A

5. Assumptions To determine the applied shear force per vertical member (total of 6), we need to find the area of fluid that each member will be under. CheesePot is usually filled halfway to produce ½ pound of cheese, so assumed that each vertical member will be halfway submerged. According to the drawing, 3.5 / 2 = 1.75 inch for height 1.75 * 0.5 = 0.875 inches 2 for area of finger that will be under Cheese. A = 0.875 inches 2

6. Formula Used to find Shear Stress In order to do this calculation, we will use the shear stress formula which is τ = F/A τ = shear stress F = Force applied A = cross sectional area of material that is under fluid

7. Fluid Mechanics Because the Vertical Ringers are rotating around an axis, in a circle, the velocity inside will be smaller than the exterior velocity. Since this involves finding shear stress by fluid viscosity and the coefficient of proportionality µ is called the shear, or ‘ordinary’ viscosity coefficient, we need to use équation 22c below.

8. Fluid Mechanics Equation 22c calculates the shear stress for a system that is linearly proportional. Thus, velocity is not the same for each vertical finger, we need to calculate the velocity difference per member (Dv/dy) in order to find force using equation 22c.

9. Fluid Mechanics R1, R2, and R3. From left to right Du/dr = ω r2 – ω r1 / r 2 – r 1 Du/dr = Dv/dy

10. Calculations Finger 1: Du/dr = ω r2 – ω r1 / r 2 – r 1 0.938 * 120rpm * 2π / 60 = 11.78 inches per second 11.78 inches per second / 0.938 inches = 12.56 inches per second difference Finger 2: 1.50 inches * 120rpm * 2π / 60 = 18.85 inches per second 18.85 inches per second / 1.50 inches = 12.56 inches per second difference Finger 3: 1.875 inches * 120rpm * 2π / 60 = 23.56 inches per second 23.56 inches per second / 1.875 inches = 12.56 inches per second difference

11. Calculations cont. Assuming that the velocity is 0 at the center. Thus the first finger’s distance was used from the center of rotation. Now that we have our velocity difference per each member as Dv/dy, we can use this value to calculate F shear by manipulating the equation. τ = F/A F shear = (A)(µ)(Du/dr)

12. Viscosity Calculations Exact cheese viscosity could not be obtained, so Axle Grease viscosity @ 40 degrees Celsius was assumed to be equal to the viscosity of cheese. Viscosity @ 40 C= 460 cST (centistokes) 460 cST = 460 centiPoise 6 894 759.09 × lbf·s/in² = cP 460 / 6894759.09 = 0.000066717 × lbfs/in²

13. Getting F-shear τ = F/A F shear = (A)(µ)(Du/dr) F shear =(0.875 in 2 )(0.000066717 lbfs/in² )(12.56 in/s) F shear = 7.3 * 10 -4 lbf

14. Torque Since this analysis will need peak torque (because we want to see the fatigue from multiple startups per cycle), we will use 0.1151 Nm as torque value. Below is a chart for the engine specs of the servo motor used to spin the vertical fingers.

15. Stainless Steel Properties Stainless Steel Properties were obtained from EduPack 2013.

16. Simulation The properties were then inserted into the material used for simulation.

17. Simulation Next, 7.3 * 10 -4 lbf was inserted into the simulation with each side of vertical fingers going opposite directions. This was the F-shear that we calculated earlier. The screw holes were used as a constraint since that’s the center of rotation and where the part will be constrained.

18. Results After the load test, the maximum stress values in PSI were obtained. 1.193 psi was the max

19. Design optimization Design optimization was done with the addition of a round in the middle with 0.05 inches of clearance in order to reduce stress spots.

20. Vertical Fingers Rev. B

21. Results for Optimized Design

22. With design optimization, the overall stresses were reduced, however there was a greater max stress value. 1.304 psi compared to without the round at 1.193 psi. I believe there was problems in applying the round correctly to the model which may have resulted in the higher max stress.

23. Fatigue Analysis “Confidence of Life” was performed with 8736 cycles, as calculated before. Peak-Peak was the amplitude type at the motors torque value of 0.1151 Nm Input data is shown in next slide

24. Fatigue Analysis

25. Fatigue Analysis Results

26. Fatigue Analysis The results indicated that there is no concern for fatigue. The stress amplitude was never enough to reach the Fatigue limit of Stainless Steel. On the right is a S-N Curve, which is used for Fatigue Life Evaluation

27. Vertical Stat An additional design that was made was the Vertical Stat. The vertical stat was used with the vertical fingers to cut and mix the cheese. The hoops on the bottom of the stat help capture the cheese curds and assist with draining of the excess resin. No analysis was needed for Vertical Stat because this is a stationary piece. However, testing can be done to determine how effective the design is in real world usage.

28. Vertical Stat

29. Vertical State Drawing Rev. A

30. Design Constraints The designs were constrained by the height and width of our stainless steel pot. The height of the Vertical Fingers needed to be tall enough to reach the servo motor on the lid of the pot. The Vertical Stat hoops needed to be wide enough to fit into the pot. The induction plate also needed to be big enough to be able to fit the pot on top (not shown). Because we were able to reverse engineer existing products for use, the only design we needed to make was for mixing application of our system

31. Assembled together

32. Engineering Standards Drawings and quality management are used following ISO 9001:2008 standards

33. Thank you! Any questions, please visit us at www.CheesePot.com Sincerely, James Weglarzwww.CheesePot.com