Tilt Effect Pressure balance

1. Tilt effect of pressure balance in
high pressure up to 500 MPa
19 September 2014
Gigin Ginanjar (gigin@kriss.re.kr)
In-Mook CHOI (mookin@kriss.re.kr)

2. ‹#›
Backgrounds
v Tilt effect of pressure balance
Ø Normally negligible if the tilt angle is small
Ø Not easy to align PCA perpendicular to gravity axis with levels
because a piston is not perfectly perpendicular to its piston
head
Ø Can be cancelled out by Swapping two PCAs in cross float
method if they can be adopted in the same body of the
pressure balance
Ø Sensitivity issue and effective area change due to a lateral
force component
v Tilt adjustment and its effect analysis
Ø Tilt adjustment by a precision pressure gauge
Ø Experimental effect due to PCA tilt
Ø FEA analysis for verification

3. ‹#›
Absolute Tilt Effect
v P/C Assembly Tilt Effect
Ø Pressure balance cosine effect
Ø Direct pressure difference
Ps
Std. pressure
Pt
Std. pressure
 =


 
Test gauge
q , Tilt
Tilt
(min)
Difference
(x10-6)
1 0.0
2 0.2
5 1.1
10 4.2
30 38
60 152
120 609
0 20 40 60
150
120
90
60
30
0
1x10-5
Rel. difference (x10-6)
Tilt (min)
15'

4. ‹#›
5x10-6
0 20 40 60 80 100 120
9.8062
9.8060
9.8058
9.8056
9.8054
9.8052
Effective Area(mm2)
Pressure (MPa)
0' Before Swap
0' After Swap
10' Before Swap
10' After Swap
Mean of 10' results
Experimental results by cross-float
Max. point
Absolute PCA tilt adjustment
v Tilt effect
Ø Relative tilt effect between pressure balances
can be eliminated
• Only PCA swap
Ø Absolute tilt adjustment
• Precise electronic level meter
• Maximum pressure at vertical PCA condition
• Use of Precise pressure gauge
Experimental Setup
y=0
X
Y
y=-x
y=x
x=0
Axis x (min) y (min)
x=0, y=0 -4.09 -6.79
x=0, y=x -4.42 -4.42
x=0, y=-x -4.83 -6.79
y=0, y=x -4.42 -4.42
y=0, y=-x -4.83 -6.79
y=x, y=-x -4.53 -7.34
Result ̅ 
Mean -4.52 -5.84
Std. Dev. 0.31 1.30

5. ‹#›
Relative PCA Tilt Effect
v Relative P/C Assembly Tilt Effect
Ø Effective area evaluation by cross-float method
Ø Tilt effect has no direction effect
Ø Swapping only PCAs è Removing the systematic error caused by tilt,
mass, and temperature etc.
Pj , Jacket pressure
Ps
Std. pressure
q , Tilt
Pt
Testee pressure
 =


=
  

= 
 =


=
  

= 
 =
 + 

=




   +

 
≅



 =
  


 =

 


6. ‹#›
Swapping effect of PCA
v Mean value of effective area by Swapping cross-float
method
Ø Effect by swapping piston/cylinder assembly
qs , STD Tilt qt , TEST Tilt
Ps
STD. pressure
Pt
Test pressure
 =
 + Δ  
  + Δ
=
 + Δ  
  + Δ
= 
 =
 + Δ
 + Δ
 
 
 + Δ
 + Δ

= 

 + Δ

− Δ


 + 
 − 

  + Δ − Δ 
Before swapping condition

7. ‹#›
qs , TEST Tilt qt , STD Tilt
Ps
STD. pressure
Pt
Test pressure
 
=
 
 + Δ
  
 + Δ
=
 
+ Δ  
  + Δ
=  
 
=
 
+ Δ
 
+ Δ
 
 
 + Δ
 + Δ

=  
  − Δ


+ Δ


 − 
 + 

  − Δ + Δ 
Swapping effect of PCA
v Mean value of effective area by Swapping cross-float
method
Ø Effect by Swapping piston/cylinder assembly
After swapping condition

8. ‹#›
Swapping effect of PCA
v Removal of all the offset of pressure balances
Ø Most significant effect è tilt of PCA
 =
 +  

≅




+
 
 
v Comparison experiments between high pressure
balances with tilt effect
Ø Main objective è to investigate tilt effect
Ø Symmetric results with respect to the tilt angle according to the
nominal diameter of piston/cylinder
Ø Sensitivity issue and effective area change due to a lateral force
component by tilted PCA è FEA verification(?)

9. ‹#›
Experiments
v Comparison experiments between high pressure
balances with tilt effect
Ø Pressure standard : 100 MPa
Ø Testee to be calibrated : 100 MPa – 200 MPa – 500 MPa
Ø Pressure balance: 5300 series
Ø Temperature sensor: RTD
Ø Level adjustment with electronic level of 0.1’ resolution
3.5 mm
10 mm2
W/C
W/C
1.6 mm
2 mm2
Steel
W/C
2.5 mm
5 mm2
W/C
W/C
3.5 mm
10 mm2
W/C
W/C
Nom. Dia.
Nom. Area
Piston Mat.
Cylinder Mat.
100 MPa 100 MPa 200 MPa 500 MPa

10. ‹#›
Experiments
v Comparison of 100 MPa vs 100 MPa
Ø Symmetrical results between before and after swapping PCA
Ø High sensitivity à repeatable results according to tilt angle
Ø Not distinguishable verticality with low tilt angle
0 20 40 60 80 100 120
9.8080
9.8070
9.8060
9.8050
9.8040
9.8030
Before 0'
After 0'
Before 10'
After 10'
Before 20'
After 20'
Before 30'
After 30'
Before 40'
After 40'
Before 50'
After 50'
Effective Area (mm2)
Pressure (MPa)
1x10-4
Before Swap
After Swap
Ideal Case Before
Ideal Case After
0 10 20 30 40 50
9.8070
9.8065
9.8060
9.8055
9.8050
9.8045
9.8040
9.8035
Effective Area(mm2)
Tilt Angle (Minute)
x 10-4
Effective area Effective area change

11. ‹#›
Before Swap
After Swap
Ideal Case Before
Ideal Case After
0 10 20 30 40 50
4,9045
4,9040
4,9035
4,9030
4,9025
Effective Area(mm2)
Tilt Angle (Minute)
Experiments
v Comparison of 100 MPa vs 200 MPa
Ø Not so symmetrical results between before and after swapping PCA
Ø Bad sensitivity when the 200 MPa PCA has a big tilt angle
Ø Not distinguishable verticality with low tilt angle
Effective Area (m2) Pressure (MPa)
20 40 60 80 100
4,90450
4,90400
4,90350
4,90300
4,90250
Before Swap 0'
After Swap 0'
Before Swap 10'
After Swap 10'
Before Swap 20'
After Swap 20'
Before Swap 30'
After Swap 30'
Before Swap 40'
After Swap 40'
Effective area Effective area change

12. ‹#›
Experiments
v Comparison of 100 MPa vs 500 MPa
Ø Non-symmetric results
Ø No cosine behavior, but a little linear characteristics according to tilt
Ø Worse sensitivity than (100 vs 100) and (100 vs 200) MPa
20 40 60 80 100
1.96200
1.96180
1.96160
1.96140
1.96120
1.96100
Effective Area (m2)
Pressure(MPa)
Before Swap 0'
After Swap 0'
Before Swap 10'
After Swap 10'
Before Swap 20'
After Swap 20'
Before Swap 30'
After Swap 30'
Before Swap 40'
After Swap 40'
Before Swap
Aftter Swap
Ideal Case Before
Ideal Case After
0 10 20 30 40
1.9617
1.9616
1.9615
1.9614
1.9613
1.9612
1.9611
1.9610
Effective Area (mm2)
Tilt Angle (Arc Minute)
Effective area Effective area change

13. ‹#›
Results and Discussion
v Comparison of 100 MPa vs 500 MPa
Ø Symmetry is getting worse according to piston diameter
• 100 MPa vs 100 MPa è Mean (0.0 ± 3.3)´10-6
• 100 MPa vs 200 MPa è Mean (6 ± 12)´10-6
• 100 MPa vs 500 MPa è Mean (6 ± 15)´10-6
Ø 500 MPa PCA should be evaluated up to 500 MPa to verify the tilt
characteristic clearly (500 MPa vs 500 MPa)
0 10 20 30 40 50
1.0003
1.0002
1.0001
1.0000
0.9999
0.9998
Relative Effective Area Change(x 10-6)
Tilt angle ( Minute)
(100 -100) Before
(100 -100) After
(100 -200) Before
(100 -200) After
(100 -500) Before
(100 -500) After
Ideal Case Before
Ideal Case After
100 MPa vs 100 MPa
100 MPa vs 200 MPa
100 MPa vs 500 MPa
0 10 20 30 40 50
1.000075
1.000050
1.000025
1.000000
0.999975
0.999950
0.999925
Relative Effective Area Change(x 10-6)
Tilt Angle (Minute)
Effective area change Average Effective area change

14. ‹#›
Results and Discussion
v Comparison of 500 MPa vs 500 MPa
Ø Same material of cylinder, but different material of piston
Ø Hard steel piston vs W/C piston with same nominal area
Ø Hard steel piston
• Relatively large shift according to tilt angle
Ø W/C piston
• Relatively small shift according to tilt angle
0 100 200 300 400 500 600
1.9624
1.9620
1.9616
1.9612
1.9608
Effective Area (mm2)
Pressure (MPa)
Before 0'
After 0'
Before 10'
After 10'
Before 20'
After 20'
Before 30'
After 30'
Before 40'
After 40'
100 200 300 400 500
1.9628
1.9624
1.9620
1.9616
1.9612
Hard steel piston & W/C cylinder W/C piston & cylinder
Effective area (mm2)
Pressure (MPa)
Before 0'
After 0'
Before 10'
After 10'
Before 20'
After 20'
Before 30'
After 30'
Before 40'
After 40'

15. ‹#›
Results and Discussion
v Hard steel piston and W/C cylinder
Ø Difficult to align the PCA verticality
Ø Tilt error due to re-installation of PCA
Ø Non-linear behavior in small tilt angle
Ø Linear behavior with large tilt angle
Ø Non-Repeatable measurement because sensitivity issue
Ø Effective Area Change
• Little-Symmetric behavior
• Non cosine effect
Ø No distortion coefficient change, but Little-symmetric behavior
Before Swap
After Swap
Ideal Case Before
Ideal Case After
0 10 20 30 40
1,96165
1,96160
1,96155
1,96150
1,96145
1,96140
1,96135
Effective Area (mm2)
Tilt Angle (Minute)

16. ‹#›
Results and Discussion
v W/C piston and cylinder
Ø Relatively easy to align the PCA verticality
Ø Small tilt error due to re-installation of PCA
Ø Linear behavior in small tilt angle
Ø Distortion coefficient change in high press range in case of large tilt
Ø Remove at 100 MPa
Ø Effective Area Change
• Symmetric behavior
• clearly not cosine effect
Ø Significant distortion coefficient change, but symmetric behavior
0 10 20 30 40
1.0
0.8
0.6
0.4
Before
After
Distorsion Coefficient (x10-6/MPa)
Tilt Angle (min)
After Swap
Before Swap
Ideal Case Before
Ideal Case After
0 10 20 30 40
1,9614
1,9612
1,9610
1,9608
Effective Area (mm2)
Tilt Angle (Minute)

17. ‹#›
Results and Discussion
v 500 MPa Tilt Comparison Steel-W/C PCA vs W/C-W/C PCA
Ø Effective Area Change
• Relatively symmetric behavior
• Relatively similar behavior at small tilt angle, Very different behavior at
big tilt angle
WC-WC 500 Before Swap
WC-WC 500 After Swap
Steel-WC 500 Before Swap
Steel-WC 500 After Swap
Ideal Case Before Swap
Ideal Case After Swap
0 10 20 30 40
1.00008
1.00004
1.00000
0.99996
0.99992
Relative Effective Area Change (x 10-6)
Tilt Angle (Minute)

18. ‹#›
Results and Discussion
v Pressure Balance Sensitivity
Ø Piston Fall Rate
• Relative small change for PCA with bigger diameter (100,200) MPa
• For small diameter PCA increasing change fall rate proportional to tilt due to
oil viscosity, PCA gap change and temperature effect
• Big change for Steel-carbide PCA due installation problem
Ø Piston Free Rotation time
• Significant decreasing change (above 20’) for Piston with big diameter
• For PCA with smaller diameter relative small decreasing change
Piston Fall Rate
0 10 20 30 40 50
Piston Free Rotation time
Piston Free Rotation time
25
20
15
10
5
0
Piston Free Rotation Time (Minute)
Tilt Angle (Arc Minute)
Steel-W/C 500 MPa (500 MPa)
W/C -W/C 500 MPa (500 MPa)
0 10 20 30 40 50
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
Piston Rate of Fall(mm/min)
Tilt Angle (Arc Minute)
W/C - W/C 100 MPa (100 MPa)
W/C - W/C 200 MPa (100 MPa)
Steel - W/C 500 MPa (500 MPa)
W/C - W/C 500 MPa (500 MPa)

19. ‹#›
Results and Discussion
v Theoretical Approach ( by Dadson )
Ø Gap piston cylinder at ∈ angle
Ø Resultant Force at ∈ tilt angle
Ø Consider Three Cases
 =   −∈
• Density constant, viscosity constant
• Density constant, viscosity proportional to P
• Density proportional to P, viscosity constant





 ∈  =



  ∈ 


/
/
q≠ϵ
 =   +


 + 
 = 6ϵ 
 1 −
2
2
cosh

2
 = 6ϵ 
 1 +
1
2
1
  − 
 

  − +  − +   
 
∗  + 
∗ 
cosh 
2
relation between and ϵ maximum tilt angle
 = 6ϵ 
 1 −
1
2





 ∫ 
 +  

 ∫ 

cosh 
2

20. ‹#›
Results and Discussion
v Simulation Approach ( FEM )
Pz along the clearance to be
calculated using the
following equation:
ö
ö
( )
( ) ÷ ÷ ÷ ÷ ÷
ø
æ
ç ç ç ç ç
è
÷ ÷ ÷ ÷ ÷
ø
æ
ç ç ç ç ç
è
= -
ò
ò
dz
p
( )
p
z
h
r
( )
z
p h
dz
p h
p P
z
l
z
z
z
z
z
3
0
3
0
1
h
( )
1
( )
1
r
R
r
Ø 2D -FEM
h
l
z=l
z=0
P1 = 0
P2 = Ps
R’
r’
h’
l
z=l
z=0
P1 = 0
U
P2 = Ps
u
z=l
z=0
P1 = 0
P2 = Ps
Un-distorted structure
Ø Simplified 3D -FEM
Distorted structure
P(z=l) = 0 and P(z=0) = P
u U dp
h
1
(0)
( ) ( )
ïþ
ïý ü
ïî
ïí ì
= + p
- ò + dz
A r z
dz
e p p z z
r r P
l
p p
p p
0
2
(0)
(0)
p (0) 1
Ps↑ à Ae↑
l
viscosity (η) and density (ρ))
depend on Pz .
Un-distorted structure
• Piston gap profile along
engagement length
• 3D- pressure profile Pz
• Effective area Change

21. ‹#›
Summary
v Tilt effect of pressure balance
Ø Not easy to adjust absolute tilt parallel to gravity axis
Ø Cosine effect is not negligible.
Ø Absolute tilt adjustment is possible using precise pressure gauge of
high resolution
Ø In case of swappable PCAs, the tilt effect can be eliminated, but the
behavior of PCA over 200 MPa is not eliminated well. In case of a PCA
with a small diameter, it caused a significant effective area change and
a sensitivity issue.
Ø Tilt effect is more significant in case of a PCA with a small diameter
v Future Works
Ø Analytical approach for understanding the effective area and
distortion coefficient change due to the tilt
Ø Quantitative evaluation of sensitivity according to tilt angle
Ø FEM analysis for the verification of experimental effective area change
• Simplified 3D model required

22. Thank you
감사합니다
Terima kasih
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