Open cmflannery opened 7 years ago
10/14 - Hoop Stress Calculation
Structural Analysis (Sources) http://www.engineeringtoolbox.com/stress-thin-walled-tube-d_948.html
Thin-Wall Cylinders -FS of 1.5: ~ 30.9k psi -FS of 2.0: ~ 41.2k psi -Material Interest: Phenolic -Properties are unknown due to limited info on Loki Rocketry Products. -Garolite(phenolic of nozzle) is used as an estimate: ~32-40k psi
Thermal Analysis (Sources) http://www.g10fr4.com/g10_fr4_technical_data_specifications.html http://www.matweb.com/search/datasheet.aspx?matguid=8337b2d050d44da1b8a9a5e61b0d5f85&ckck=1
Temperature Max = 3500 F CTE @ T = 68 F = 5.50* 10^-6 Young's Modulus: 19000 psi (shear) -FS of 1.5 ~ 548.6 psi -FS of 2.0 ~ 731.5 psi
Overall Comments -Phenolic Liners well above FS of 1.5, but below FS of 2.0
Phenolic Liner Liner thickness; 1/8" Liner Length: 7' 6.5" = 91.5"
Casting Tubes: Thickness: 1/8" Length: 15"
Grains Length: 14" OD: 6.90" ID: 2.75"
Phenolic Liner Hoop Stress Calculations
Using http://www.engineeringtoolbox.com/stress-thin-walled-tube-d_948.html
Hoop Stress = (745.9793426 psi * 7.062 in) / 2 * .25 in = 10536.2122348824 psi
Per http://www.g10fr4.com/g10_fr4_technical_data_specifications.html
19,000 psi max
Therefore a F.S. of ~1.8.
The purpose fo the phenolic liner is to act as a thermal barrier between the combustion chamber and the aluminum casing. The phenolic liner doesn't need to take hoop stress. The heat transfer through the phenolic liner to the aluminum should be calculated and then the hoop stresses in the aluminum liner should be compared against its yield stress.
The tolerances on the liner and the aluminum casing need to be large enough to allow the liner to slide into the airframe. Hoop stress calculation and material calculations should be completed on the liner to ensure the pressure in the combustion chamber doesn't cause the liner to fracture.
Look into other possible solutions.