Upload
others
View
16
Download
1
Embed Size (px)
Citation preview
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
F100 Turbine Exhaust Case
Stress Analysis of Strut Cracks
Cap. Shani Eitan, Propulsion Branch, IAF
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Background
โข Turbine Exhaust Case (TEC) is a part of Low Pressure Turbine (LPT) module of the F100-220/220E-DPI engine.
โข TECs consist of 8 Struts that straighten the turbine exit flow.
โข Some of the struts also contain oil lines for the bearings.
โข IAF has experienced a high number of cracks on the Strutsโ airfoils, that were beyond T.O. limit.
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Objectives
โข To estimate the risk of flying with a cracked strut
โข The objectives of this investigation is to calculate:โข Critical crack length ๐๐๐โข Static Margin of safety (M.S.) as a function of crack length (a)
๐. ๐. ๐ =๐๐ข๐โ 1, ๐ = ๐ ๐ฟ๐๐ด๐ท๐, ๐
แ๐๐๐ = ๐๐.๐.=0
= ?
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Challenges
โข Analysis:โข Stress calculation of a cracked part (not crack propagation,
not fatigue, but margin of safety at next flight).
โข Boundary conditions
โข Thermal loads
โข Exotic material
โข Aerodynamic cross section
โข Operator stand point of view (not a designer):โข Design is unknown
โข Loads are unknown (at least initially)
โข Material properties
โข Dimensions
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsFree Body Diagram
L โ Lift โ aerodynamic forceD โ Drag โ aerodynamic forceM โ Moment/torque โaerodynamic loadT โ Temperature of turbine exit flow โ thermal condition
V โ Velocity of turbine exit flow
- Fixed displacement boundary condition
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsStrut Airfoil Mechanical Properties@ ~1300๐F
โข Strut Airfoil is made of Nickel INCONEL alloy AMS5599
โข Youngโs Modulus is E=200GPa
โข Ultimate strength is ๐๐ข =827Mpa
โข Thermal Expansion coefficient
โข is ๐ผ = 13.410โ6
๐พ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Velocity
V
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Velocity
โข Velocity represented by Flow Rate formula:
โข Flow Rate at the Exhaust is the sum of core air flow rate and fuel flow rate:
แถ๐๐๐ฅ = ฯ โ A๐๐ฅ โ V โ V =แถ๐๐๐ฅ
ฯ โ A๐๐ฅ
แถ๐๐๐ฅ = แถ๐๐ + แถ๐๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Velocity
โข Core air flow rate is calculated using F100-220 core-fan bypass ratio:
โข Known F100 flow rates (fuel including A/B, Engine Inlet Air flow):
ฮฒ =แถ๐๐
แถ๐๐น= 0.61
แถ๐๐ = 49,964๐๐โ
แถ๐๐ธ = 225๐๐๐
V =แถ๐๐๐ฅ
ฯ โ A๐๐ฅ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Velocity
โข Core air flow rate is calculated using F100-220 core-fan bypass ratio:
โข Fuel flow in seconds:
แถ๐๐
แถ๐๐ธ โ แถ๐๐= 0.61 โ แถ๐๐ =
0.61
1.61แถ๐๐ธ =
0.61
1.61โ 225 = 86๐๐๐
แถ๐๐ = 49,964๐๐
60 โ 60 โ ๐ = 14๐๐๐
V =แถ๐๐๐ฅ
ฯ โ A๐๐ฅ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Velocity
โข Gas flow rate thru the TEC can therefore be calculated:
โข Cross Sectional Area of the flow thru the TEC:
แถ๐๐๐ฅ = แถ๐๐ + แถ๐๐ = 86 + 14 = 100๐๐
๐ ๐๐
V =แถ๐๐๐ฅ
ฯ โ A๐๐ฅ
Aex = ฯ ๐ ๐2 โ ๐ ๐
2 = ฯ 15.6742 โ 6.3852 = 643.7 ๐๐2
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Velocity
โข Gas density in the TEC area:
V =แถ๐๐๐ฅ
ฯ โ A๐๐ฅ
ฯ =๐
ว๐ โ ๐=
44.8 ๐๐๐ผ
271๐ฝ
๐พ๐ โ ๐พโ 1362๐๐น
=308,885.1
๐
๐2
271๐ฝ
๐พ๐ โ ๐พโ 1012K
= 1.126๐๐
๐3
ฯ = 4.068 โ 10โ5๐๐
๐๐3
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Velocity
โข Velocity at TEC inlet can therefore be calculated:
V =แถ๐๐๐ฅ
ฯ โ A๐๐ฅ
๐ =แถ๐๐๐ฅ
ฯ โ A๐๐ฅ=
100
643.7 โ 4.068 โ 10โ5= 3,818
๐๐
๐ ๐๐= 97
๐
๐ ๐๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift L =
1
2๐๐2๐๐ถ๐ฟ
L
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข Surface Area of the airfoil:
L =1
2๐๐2๐๐ถ๐ฟ
S =๐ ๐1 + ๐2
2=225.8 โ 221 + 163.3
2= 43,388 ๐๐2 = 67.25 ๐๐2
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข Lift coefficient ๐ถ๐ฟ of a finite airfoil the sum of the 2D cross sectional ๐ถ๐:
โข Whereas, c(y) is the cross section length at each section of the airfoil:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐ฟ =1
๐เถฑ0
๐
๐ถ๐ ๐ฆ โ ๐ ๐ฆ ๐๐ฆ
๐ ๐ฆ =๐2 โ ๐1
๐๐ฆ + ๐1 = โ0.225๐ฆ + 221
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข ๐ถ๐ ๐ฆ is the 2D cross sectional lift coeff. At each section. A 2 sections interpolation will be used :
๐ถ๐ is calculated using lift-line theorem:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐ ๐ฆ =๐ถ๐2 โ ๐ถ๐1
๐๐ฆ + ๐ถ๐1
๐ถ๐1 = 2๐ ๐ผ1 +1
๐เถฑ
0
๐๐๐ง
๐๐ฅ1
๐๐๐ ๐ โ 1 ๐๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข 2D cross section airfoil line z(x) was derived from a SolidWorks model.
โข SolidWorks model was constructed using a swept protrusion of the 2 cross sections:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐1 = 2๐ ๐ผ1 +1
๐เถฑ
0
๐๐๐ง
๐๐ฅ1
๐๐๐ ๐ โ 1 ๐๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข 2D cross section airfoil line z(x) was interpolated using O(5) order level:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐1 = 2๐ ๐ผ1 +1
๐เถฑ
0
๐๐๐ง
๐๐ฅ1
๐๐๐ ๐ โ 1 ๐๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข 2D cross section airfoil line z(x) was interpolated using O(5) order level:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐1 = 2๐ ๐ผ1 +1
๐เถฑ
0
๐๐๐ง
๐๐ฅ1
๐๐๐ ๐ โ 1 ๐๐
=5E-10x5-3E-07x4 +8E-05x3-0.0087x2 +0.6387x + 0.211
Rยฒ =0.9957
-10
0
10
20
30
40
50
050100150200250
Y1
Y2
YM
Poly. (YM)
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข 2D cross section airfoil line ๐๐ง
๐๐ฅ 1was analytically
calculated:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐1 = 2๐ ๐ผ1 +1
๐เถฑ
0
๐๐๐ง
๐๐ฅ1
๐๐๐ ๐ โ 1 ๐๐
๐ง1 ๐ฅ
= 5 โ 10โ10๐ฅ5 โ 3 โ 10โ7๐ฅ4 + 8 โ 10โ5๐ฅ3 โ 0.0087๐ฅ2 + 0.6387๐ฅ + 0.211
๐๐ง
๐๐ฅ1
= 25 โ 10โ10๐ฅ4 โ 12 โ 10โ7๐ฅ3 + 24 โ 10โ5๐ฅ2 โ 0.0174๐ฅ + 0.6387
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข Integrals were calculated using transformation x-๐, and using MAPLE:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐1 = 2๐ ๐ผ1 +1
๐เถฑ
0
๐๐๐ง
๐๐ฅ1
๐๐๐ ๐ โ 1 ๐๐
แป๐ฅ = ฮค๐ 2 (1 โ ๐๐๐ ๐
เถฑ
0
๐๐๐ง
๐๐ฅ1
๐๐๐ ๐ โ 1 ๐๐ = โ2.93
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข Integrals were calculated using transformation x-๐, and using MAPLE:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐1 = 2๐ ๐ผ1 +1
๐เถฑ
0
๐๐๐ง
๐๐ฅ1
๐๐๐ ๐ โ 1 ๐๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข Integrals were calculated using transformation x-๐, and using MAPLE:
โข Angle between two cross sections was measured:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐1 = 2๐ ๐ผ1 +1
๐เถฑ
0
๐๐๐ง
๐๐ฅ1
๐๐๐ ๐ โ 1 ๐๐
๐ถ๐1 = 2๐ ๐ผ1 โ 2.93
๐ถ๐2 = 2๐ ๐ผ2 โ 2.72
๐ผ1 โ ๐ผ2 = 110 = 11 โ๐
180= 0.192.
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข Turbine exit velocity angle of attack at the last rotor stage is relatively small:
โข ๐ผ 1 โ 0๐
โข ๐ผ 2 โ 10๐ ๐๐๐๐ ๐ข๐๐๐
L =1
2๐๐2๐๐ถ๐ฟ
๐ผ1, ๐ผ2
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
LoadsCalculation of Lift
โข Lift force acting on the strut airfoil can now be calculated:
L =1
2๐๐2๐๐ถ๐ฟ
๐ถ๐ฟ =1
๐เถฑ0
๐
๐ถ๐ ๐ฆ โ ๐ ๐ฆ ๐๐ฆ =1
43,388เถฑ
0
225.8
0.0112๐ฆ โ 18.41 โ0.225๐ฆ + 221 ๐๐ฆ = 17.508
L =1
2๐๐2๐๐ถ๐ฟ =
1
2โ 1.126 โ 972 โ 0.043388 โ 17.508 = 4,023 ๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads interim summery
L=4000 N
V=97 m/s
D
M
T=1300F
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Drag force Calculation
D
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Drag force Calculation
โข Drag force on a finite wing is expressed using the formula:
D =1
2๐๐2๐๐ถ๐ท
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Drag force Calculation
โข Drag coefficient on a finite wing is expressed using the formula:
๐ถ๐ท =8
๐2๐ถ๐ฟ2
๐๐ด๐ ; ๐ด๐ =
๐2
๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Drag force Calculation
โข Drag force can be therefore calculated:
D =4๐ ๐๐๐ถ๐ฟ
2
๐2๐3=4 โ 1.126 97 โ 0.043388 โ 17.5 2
0.2252๐3= 15,500 ๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Aerodynamic Moment Calculation
M
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Aerodynamic Moment Calculation
โข Aerodynamic moment acting on a finite wing is expressed using lift-line theorem according to the formula:
M =1
2๐๐2๐ถ๐เถฑ
0
๐
๐2(๐ฆแป๐๐ฆ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Aerodynamic Moment Calculation
โข Aerodynamic moment coefficient of a finite wing formula:
๐ถ๐ =1
0๐๐2(๐ฆแป๐๐ฆ
เถฑ
0
๐
แป๐(๐ฆ 2๐ถ๐(๐ฆแป๐๐ฆ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Aerodynamic Moment Calculation
โข Aerodynamic moment coefficient as a function of location, using 2 cross section interpolation method:
๐ถ๐ ๐ฆ =๐ถ๐2 โ ๐ถ๐1
๐๐ฆ + ๐ถ๐1
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Aerodynamic Moment Calculation
โข Aerodynamic moment coefficient of 2D cross sections:
๐ถ๐1,2 =1
2เถฑ
0
๐๐๐ง
๐๐ฅ1,2
๐๐๐ 2๐ โ ๐๐๐ ๐ ๐๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Aerodynamic Moment Calculation
โข Aerodynamic moment integrals were calculated using MAPLE:
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Aerodynamic Moment Calculation
โข Aerodynamic moment integrals were calculated using MAPLE:
๐ถ๐ ๐ฆ = โ0.0033๐ฆ + 0.6416
๐ถ๐ =1
0๐๐2(๐ฆแป๐๐ฆ
เถฑ
0
๐
๐ ๐ฆ 2๐ถ๐ ๐ฆ ๐๐ฆ = 0.999
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads Aerodynamic Moment Calculation
โข Aerodynamic moment can now be calculated:
M =1
2๐๐2๐ถ๐เถฑ
0
๐
๐2 ๐ฆ ๐๐ฆ = 58.4 ๐ โ๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Loads summery
L=4000 N
V=97 m/s
D=15500 N
M=58N-M
T=1300F
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress Analysis
โข Sress analysis (calculation of ๐แป was conducted using 3 different methods.
โข Numerical analysis:โข Finite Elements Method (FEM) โ Ansys Workbench
โข Analytical method:โข Nominal stress of degraded moments of inertia due to
crack presence in a critical cross section.
โข Stress intensity factor K1C method
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisFEM โ Physical Model
FREE AFT ENDFREE OUTER
SURFACE
FREE INNER
SURFACE
FIXED SURFACE END
(ATTACHED TO LPT)
โข TEC is attached (fixed) to the aft outer perimeter of the LPT. Rest of the surfaces are free.
โข Struts are attached (fixed) to the inner and outer case surfaces.
โข Struts โfeelโ air flow aerodynamic forces and high temprature
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisFEM โ Computational Model -Geometry
FREE AFT ENDFREE OUTER
SURFACE
FREE INNER
SURFACE
FIXED SURFACE END
(ATTACHED TO LPT)
โข One TEC strut was modeled in Solidworks, attached to inner and outer platforms representing the case.
โข One strut model saves computational memory in comparison to a full TEC model.
FIXED SURFACE END
(ATTACHED TO LPT)
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisFEM โ Computational Model โ Crack Geometry
crackโข Crack width 0.1mm was modeled.
โข Several different crack lengths: 0โ, 0.5โ, 1.5โ, 3.0โ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisFEM โ Computational Model - Mesh
โข SOLID187 3D Element was used. Element size 0.1 mm in crack and 1 mm in near crack surface.
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisFEM โ Computational Model โ Loads and Boundary Condition
FIXED
FIXED
LOADS
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisFEM โ Computational Model โMaterial Properties
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisFEM โ Computational Model โ Results
๐ = 163๐๐๐M.S.= +4.07
No Crack (a=0โ)
๐ = 415๐๐๐M.S.= +0.99
a=0.50โ
๐ = 538๐๐๐M.S.= +0.54
a=1.50โ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisFEM โ Computational Model โ Results
๐ = 855๐๐๐M.S.= -0.02
a=3.0โ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Stress in the strut consists of different loads and stress conditions (moment, shear, bending, torque). And therefore would be calculated with VON-MISES formula:
๐ = ๐๐ตโ๐ฟ๐ท + ๐๐2 + 3 ๐๐ฟ๐ท + ๐๐
2
๐ = ๐2 + 3๐2
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Strut was considered as a fixed supported beam under a uniform load consists of lift, drag, moment and thermal stress
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Geometric properties were calculated using a CAD model:
I๐ฅ๐ฅ1 = 67497.36๐๐4
I๐ฆ๐ฆ1 = 994338.67๐๐4
๐ฝ = 994338.67๐๐4
Area = 425.08 millimeters^2
I๐ฅ๐ฅ2 = 142470.71๐๐4
I๐ฆ๐ฆ2 = 2259760.67๐๐4
๐ฝ = 2259760.67๐๐4
Area = 561.99 millimeters^2
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Uniform force is the vector sum of Lift and drag:
โข Maximum bending moment and shear is at the smallest section profile (least area and inertia):
๐ค =๐ฟ2 + ๐ท2
๐=
40002 + 155002
225.8= 71
๐
๐๐
๐ =๐ค๐2
12=71 โ 225.82
12= 301,665 ๐ โ ๐๐
V =๐ค๐
2=71 โ 225.8
2= 8016 ๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Maximum stresses due to lift and drag at the beam are:
โข Torque due to aerodynamic moment:
๐๐ต =๐
๐ผ๐ฅ๐ฅ๐ง =
301665 โ 21
67500= 93 ๐๐๐
๐๐ฟ๐ท =V
๐ด=8016
425.8= 18.825 ๐๐๐
๐๐ =๐๐
๐ฝ=58400 โ 80
994338.67= 4.7 MP๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Thermal stress is due to strutโs thermal expansion:
โข Inner and outer diameters of the TEC also expand, and therefore compensate the strutโs expansion:
๐ =โ๐
๐= ๐ผโ๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Strut potential expansion is:
โข Outer case perimeter expansion:
โ๐ = 225.8 โ 13.4 โ 10โ6 โ 1012 =3mm
๐ =โ๐
๐= ๐ผโ๐
๐1 = ๐0 ๐ผโ๐ + 1 = 2๐๐ 0 ๐ผโ๐ + 1
๐1 = 2๐ โ 15.674 13.4 โ 10โ6 โ 1012 + 1 = 99.81"
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Outer Case radius expansion is therefore:
โข Inner case is calculated the same way = 2.2mm
๐ 1 =๐12๐
โ๐ = ๐ 1 โ ๐ 0 = 5.23๐๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Expansion superposition summery:Outer case expands 5.23
mm
Inner case expands 2.20 mm
The gap between inner and outer case expands 3.03 mm
The strut expands 3.00 mm
The strut expands additional 0.03 mm due to cases
tension
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach
โข Thermal stress due to 0.03mm expansion is:
โข Total stress can now be calculated using VON-MISES criteria:
๐๐ = ๐ธ๐ = 200,000 โ0.03
225.8= 26 MPa
๐ = 26 + 93 2 + 19 + 5 2 = 121 MP๐
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach โ classic approach
โข Stress rise due to loss of geometrical stiffness:
๐ โ โ ๐ด โ , ๐ผ๐ฅ๐ฅ โ โ ๐ =๐
๐ผ๐ฅ๐ฅ๐ง โ , ๐ =
๐
๐ดโ
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach โ classic approach
โข Stress rise due to loss of geometrical stiffness:
CrackLength [mm]
CrackLength [inch]
CrackLength
[cm]
Cross section area A [mm^2]
Ixx [mm^4]Bending
Stress riseShear Stress
rise
00.00056214247100
12.70.501.27545.281360895%3%
25.41.002.54528.8612800211%6%
38.11.503.81512.5611867220%10%
50.82.005.08496.210880131%13%
63.52.506.35479.849893044%17%
76.23.007.62463.488905960%21%
88.93.508.89447.127918880%26%
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
M.S. VS Crack length (a)
M.S
. (M
argi
n o
f Sa
fety
)
CmInch Crack
length (a)
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach โ Fracture Mechanics
โข In Fracture Mechanics theorem we define a critical stress intensity factor K1C.
โข K1C is a material property โ for INCONEL 625 itโs 59 Mpa ๐.
โข The stress intensity is calculated using the formula:
K1 = ฮฒฯ ฯa
โข The Margin of Safety would therefore be
๐พ1๐K1
โ 1
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach โ Fracture Mechanics
โข Definition of ๐ and ๐ฝ
ฮฒd/ba/dBda[inch]
1104.34.30
1.0210.124.34.30.5
1.0510.234.34.31
1.0810.354.34.31.5
1.1310.464.34.32
1.2810.584.34.32.5
1.510.74.34.33
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Stress AnalysisAnalytical Approach โ Fracture Mechanics
โข M.S. calculations:
M.S.
๐พ1๐K1
โ 1K1CK1ฮฒฯ[MPa]a[m]a[inch]
-590.0112100
1.3934855924.71.021210.01270.5
0.6440945935.91.051210.02541
0.3068245945.11.081210.0381.5
0.0802455954.61.131210.05082
-0.147035969.21.281210.06352.5
-0.335555988.81.51210.07623
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Summery of Results
-1
0
1
2
3
4
5
0 0.5 1 1.5 2 2.5 3 3.5
M.S
.
a [inch]
Results Summery - 3 methods of crack M.S.
Classic Fracture Mechanics FEA
6.11.2014, ืืืื ืืื, ืืื ืืขื ืกืืืื ืืืืจืืื ืืช ืื13-ืืื ืขืืื ื, ืขื ืฃ ืื ืขืโืืื ืืืืืืจ
Conculsion
โข Construction of a decision making tool for fleet managers having a logistic maintenance issue.
โข Calculation of M.S. using three different methods
โข Results show good correlation between methods in range of 1โ-2โ crack length
โข M.S.=0 in a=3โ according to FEM method
โข M.S.=0 in a=2.2โ according to K1C method
โข Engine manufacturer approved a temporary limit of 3โ as long as a visual inspection is done after/before every flight
โข Investigation helped in keeping availability of the fleet until logistics was solved (procurement and repair implemented)