Cooling Pipes: Force Analysis
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Thermal forces
Disc deflections
Manufacturing tolerance forces
Glue joint analysis
Friction forces
Thermal forces
Temperature decrease 40 K
primary
secondary
radial force
[N]
tangential
force [N]
torque
[Nmm]
middle
0.1
0.1
0.05
0.2
18
34
outer
0.1
0.1
22
middle
0.7
3.8
0
outer
0.7
3.8
0
inner
Thermal 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
Manufacturing 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
Manufacturing tolerance forces
One end displaced 0.1 mm in tangential direction
all 6 DOFs fixed
primary
secondary
1 rot DOF free
rad
[N]
tang
[N]
torque
[Nmm]
rad
[N]
tang
[N]
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
middle
0.3
17.8
147
0
4.6
outer
0.1
9.5
94.3
0
2.4
Actual 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  2.2  1.6
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
Forces
Manufacturing Tolerance
[mm]
0.1
0.2
0.3
0.5
highest force [N]
highest torque
[Nmm]
4.6
9.2
13.8
49.4
-
-
-
294
(Highest forces and torques occur at the inserts of
the secondary middle cooling blocks)
Disc 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
Disc Deflection
n = 92
force per insert
[N]
Manufacturing tolerance [mm]
0.1
0.2
0.3
0.4
0.5
1.5
3.1
4.6
10.6
16.6
disc deflection
24.2 48.4 72.6 167
262
[m]
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
Analytical glue joint analysis
glue
 max
Force
G T
 1

G
1



with  

t glue    E1  t1
t glue  E1  t1 E2  t2 
Filling in all properties:
max = 0.4 MPa (with 0.5 mm manufacturing
tolerance)
Analytical glue joint analysis
Torque
glue
 max
GM
with   G   1  1 



t glue    G1  t1
t glue  G1  t1 G2  t2 
Filling in all properties:
max = 5.7 MPa (with 0.5 mm manufacturing
tolerance)
Considerations
• 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
Numerical glue joint analysis
19.8 MPa
Numerical glue joint analysis
8.9 MPa
Numerical glue joint analysis
11.3 MPa
Prestressed 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
Concluding 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