1. Seal Analysis Jeremy Osguthorpe Mitchell Woolf Jon Blotter 7 / 12 / 2007

2. Project Objectives Develop a finite element model of the seal using the geometry model provided. Using generic material properties determine the displacement and stress as functions of time using 80 psi and 100 psi instantaneous pressure loads. 2

3. Model Assumptions Constraining Seal –The metal cage was removed from the model and the effects of the cage were applied as boundary conditions. Diaphragm Material Properties –Density =.00106 lbm/in^3 –Modulus of Elasticity = 3,500 psi –Poisson’s Ratio ≈ 0.50 –Damping Coefficient = 0.1 –Isotropic Material

4. Model Assumptions Loading –The pressure will reach a maximum value within 0.0001 sec. and then remains constant throughout the analysis. This is a perfect (instantaneous) pressure loading. A flow analysis could be done to verify this result. –A uniform pressure distribution is applied over the diaphragm

5. Analysis Procedure Meshed Seal –The seal was meshed using a 2D surface mesh followed by a solid tetra mesh. –The mesh element size is a result of refining the seal until there was a convergence of results.

6. Analysis Procedure Constraining Seal –The seal was constrained as shown in the figures. Appropriate surfaces were selected to represent the effect of the gun barrel and cage on the seal. -Constraints A were constrained in the direction of the barrel -Constraints B were constrained in the radial direction -Constraints C were constrained in all directions

7. Analysis Procedure Applying Pressure to the Seal –A dynamic load was applied to the appropriate surfaces of the seal as shown. The figure is a profile view of how the pressure is applied to the entire seal. –Uniform pressure loads of 80 psi and 100 psi were used in the static and transient analysis.

8. Static Analysis Results Original ShapeDeformed Shape

9. Static Analysis Results The yellow mesh represents the deformed shape and the purple represents the undeformed shape

10. Static Analysis Results Figure- Side view of deformed shape Figure- The yellow mesh represents the deformed shape and the purple represents the undeformed shape

11. Static Analysis Results Stress on the Seal –The stresses throughout the seal are shown in the figures according to color contour on the following slide –The maximum stress experienced by the seal is 3,430 psi.

12. Static Analysis Results Isometric view of stress contours

13. Transient Analysis Results Transient analysis requires large amounts of computer processing resulting in large amounts of computation time. Transient analysis of the entire seal is redundant and is avoidable due to the symmetrical geometry. A single point inside of the seal was chosen for analysis. This point was chosen because it experiences the largest displacement and is a point of interest in relation to the paintball.

14. Transient Analysis Results The transient results are plotted on the following slide. The load is applied at a time of 0.001 seconds. The load is nearly instantaneous. The maximum displacement of the diaphragm is reached approximately 0.001sec later at a time of 0.002 sec. The diaphragm oscillates for approximately 15 milliseconds and then finally settles at a displacement of 0.328”. This displacement value was also confirmed using static analysis.

15. Static Analysis Results Isometric view of stress contours – 100 psi

16. Static Analysis Results Top view of stress contours – 100 psi

17. Static Analysis Results Side view of stress contours – 100 psi

18. Transient Analysis Results Dynamic displacements - inside of the seal with a load - 100 psi

19. Transient Analysis Results Dynamic displacements - inside of the seal - 80 psi

20. Transient Analysis Nominal dimensions of seal

21. Transient Analysis Maximum displacement with 100 psi Seal will fully close under these conditions (inner diameter = 0.0”)

22. Transient Analysis Final displacement values for 100 psi Inner Diameter = 0.093”

23. Transient Analysis Maximum displacement values for 80 psi Inner Diameter = 0.147”

24. Transient Analysis Final displacement values for 80 psi Inner Diameter = 0.223”

25. Analysis Summary Conclusions For the 100 psi load, the maximum displacement of 0.376” was reached in ~1 msec. The steady state displacement reached at ~12 msec is ~ 0.325”. The maximum stress experienced by the seal was 3,430 psi. For the 80 psi load, the maximum displacement of 0.310” was reached in ~1 msec. The steady state displacement reached at ~10 msec is ~ 0.262”.