cooling pipes: force analysis
DESCRIPTION
Cooling Pipes: Force Analysis. Thermal forces Disc deflections Manufacturing tolerance forces Glue joint analysis Friction forces. Thermal forces. Temperature decrease 40 K. Thermal Deflections. Maximum deflection of the disc is 31 m - PowerPoint PPT PresentationTRANSCRIPT
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Cooling Pipes: Force Cooling Pipes: Force AnalysisAnalysis
• Thermal forces
• Disc deflections
• Manufacturing tolerance forces
• Glue joint analysis
• Friction forces
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Thermal forces Thermal forces
Temperature decrease 40 K
radial force [N]
tangential force [N]
torque [Nmm]
primary inner 0.1 0.05 18middle 0.1 0.2 34outer 0.1 0.1 22
secondary middle 0.7 3.8 0outer 0.7 3.8 0
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Thermal DeflectionsThermal Deflections
• Maximum deflection of the disc is 31 m
• Thermal deflection of the cooling pipe between two cooling blocks if one end would be free:
L = L · · T = 65 · 15 ·10-6 · 40 = 39 m
• A manufacturing tolerance of this value would result in the same forces
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Manufacturing toleranceManufacturing tolerance
• Analysis of pieces of cooling pipe between two adjacent blocks. One end gets a prescribed deflection, other end:– all six DOFs fixed– all DOFs fixed except one rotational DOF
• Random effect, the average disc deflection is zero, deflections because of standard deviation
• Stresses in the glue layer between insert and disc surface
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Manufacturing tolerance Manufacturing tolerance forcesforces
One end displaced 0.1 mm in tangential directionall 6 DOFs fixed 1 rot DOF free
rad [N]
tang [N]
torque [Nmm]
rad [N]
tang [N]
primary inner 0 1.6 35.7 0 0.6
middle 0 1.1 29.5 0 0.4
outer 0 1.9 37.6 0 0.7
secondary middle 0.3 17.8 147 0 4.6
outer 0.1 9.5 94.3 0 2.4
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Actual situationActual situation
• Holes in cooling blocks have diameter 2.2 mm, screws to attach cooling blocks to inserts are M1.6
• This means that the clearance between screw and hole is between 0 and 0.6 mm
• Below this tolerance, the rotation can be set free. In a worst case situation the rotation has to be fixed if the manufacturing tolerance > 0.3 mm
2.2 1.6
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ForcesForces
Manufacturing Tolerance [mm]
0.1 0.2 0.3 0.5
highest force [N]4.6 9.2 13.8 49.4
highest torque [Nmm] - - - 294
(Highest forces and torques occur at the inserts of the secondary middle cooling blocks)
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Disc DeflectionDisc Deflection
• Mean total force = 0, because of the random direction of the manufacturing tolerances, assume a normal distribution of the forces
• Standard Deviation of the total tangential force total = F · n
• Per insert: 4.2 · total /n = 4.2F/n (at Z = 4.2, the chance of exceeding this value is 0.1% in 18 discs)
• Take mean tangential force of the secondary cooling blocks and the number n as the overall amount of secondary cooling blocks
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Disc DeflectionDisc Deflection
n = 92 Manufacturing tolerance [mm]
0.1 0.2 0.3 0.4 0.5
force per insert [N]
1.5 3.1 4.6 10.6 16.6
disc deflection [m]
24.2 48.4 72.6 167 262
Same deflection as thermal deflection (31.2 m) will be reached at a manufacturing tolerance of 130 m
Maximum deflection of disc (200 m) will be reached at a manufacturing tolerance of about 400 m
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Analytical glue joint Analytical glue joint analysisanalysis
glueglue
max1 1glue
G T
t E t
with
1 1 2 2
1 1
glue
G
t E t E t
Filling in all properties:
max = 0.4 MPa (with 0.5 mm manufacturing tolerance)
Force
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Analytical glue joint Analytical glue joint analysisanalysis
glueTorque
max1 1glue
G M
t G t
with
1 1 2 2
1 1
glue
G
t G t G t
Filling in all properties:
max = 5.7 MPa (with 0.5 mm manufacturing tolerance)
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ConsiderationsConsiderations
• The calculated values for the shear stress are heavily depending on the boundaries of the glue joint
• By making a well-finished glue joint, stresses can be brought down
• Tests have to be done on the glue joint to get a good feeling of the glue strength
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Numerical glue joint Numerical glue joint analysisanalysis
19.8 MPa
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Numerical glue joint Numerical glue joint analysisanalysis
8.9 MPa
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Numerical glue joint Numerical glue joint analysisanalysis
11.3 MPa
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Prestressed screwsPrestressed screws
• Cooling blocks are attached to insert with M1.6
• Max. prestressing force Fs = max · A• If max = 150 MPa and A = 1.27 mm², then Fs
= 191 N per screw• Friction force Ff = 2·Fs· = 2·191·0.1 = 38.2
N• If manufacturing tolerance is 0.4 mm, then
the force and the torque together give a force of 31.6 + 147/22.8 = 38.0 N
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Concluding remarksConcluding remarks
• Keeping the manufacturing tolerance at 0.3 mm will be safe because of the low forces and zero moments
• If 0.3 mm cannot be reached, 0.4 mm is the absolute maximum with respect to disc deflections
• Glue joint analyses give very different results, because of the uncertatinties of the boundary geometry
• 0.4 mm is a limit if there wouldn’t be a positioning pin between cooling block and insert; the positioning pin can take a lot of the friction force away