Phd Thesis presentation

1. Tilt effect of pressure balance in
high pressure up to 500 MPa
December 4, 2018
Gigin Ginanjar (gigin@kriss.re.kr)
1

2. ‹#›
 Background
 Definition of pressure balance
 Tilt effect in pressure balance
 Introduction
 Absolute tilt effect
 Relative tilt effect
 Analysis of tilt effect
 Theoretical approach of piston tilt
 Simulation approach of piston tilt
• 2D/3D FEA simulation in perpendicular Condition
• 3D FEA simulation in tilt condition
• 3D FEA simulation result
 Minimization of the tilt effect
 Tilt adjustment method
 PCA Exchange method
 Conclusion 2
Content

3. ‹#›
3
Background(1)
Piston
Cylinder
Mass
 The main part is the Piston-Cylinder Assembly (PCA). The
piston is mounted vertically and freely rotates inside the
cylinder
 The pressure to be measured, 𝑷, is applied to the base of
the piston, generating upward vertical force. The force , 𝑭,
is equilibrated by the gravitational downward force due
to masses ,M, placed on the top of the piston and
gravitational acceleration, g
 Definition of the Pressure Balance (PB)
 Based on the physical principle of pressure equal to force
divided by area
𝑷 =
𝑭
𝑨
=
𝑴𝒈
𝑨
=
(1)

4. ‹#›
4
Background (2)
Piston
Cylinder
Mass
𝒎 is the individual mass value of each weight applied on the piston,
including all floating elements
𝝆 𝒂 is the density of air and 𝝆 𝒎 is the density of each weight
𝒈 is gravitational acceleration
𝒄 is piston circumference and 𝝈 is oil surface tension
𝑨 𝟎 is the effective area of the PCA at zero pressure
𝑷 𝑵 is nominal pressure,
𝜶 is the linear thermal expansion coefficient of the PCA
𝒕 is temperature of PCA and 𝒕 𝒓 is reference temperature of PCA
𝜽 is the angle of deviation of the piston axis from verticality
 Full Definition of the PB
𝑭=𝒎 𝟏 −
𝝆 𝒂
𝝆 𝒎
𝒈 + 𝒄𝝈
𝑨 𝒆 = 𝑨 𝟎 𝟏 + 𝝀𝑷 𝑵 𝟏 + 𝜶 𝒕 − 𝒕 𝒓
𝑷 =
𝑭
𝑨 𝒆
𝒄𝒐𝒔𝜽
𝝀 is distortion coefficient of piston and cylinder
(2)
(3)

5. ‹#›
5
Background (3)
 Tilt effect in pressure balance
 Conventional concept on pressure balance cosine effect
𝑷 𝒔 =
𝑭 𝒔
𝑨 𝒔
𝒄𝒐𝒔 𝜽
Ps
Std. pressure
Pt
testee. pressure
Test gauge

Tilt
(min)
Difference
(x10-6
)
1 0.0
2 0.2
5 1.1
10 4.2
15 9.5
30 38
60 152
0 20 40 60
0
30
60
90
120
150
1x10
-5
Rel.difference(x10
-6
)
Tilt (min)
15'
(4)

6. ‹#›
6
 Absolute tilt effect
 PCA standard : 100, 500 MPa
 Pressure balance: 5300 series
 Testee to be calibrated : Paros Scientific with 0.001 MPa resolution
 Temperature sensor: RTD
 Level adjustment : electronic level with 0.1’ resolution
3.5 mm
10 mm2
W/C
W/C
1.6 mm
2 mm2
Steel
W/C
Nom. Dia.
Nom. Area
Piston Mat.
Cylinder Mat.
100 MPa 500 MPa
Introduction(1)
Test gauge
Experimental Setup of Absolute Tilt Effect

7. ‹#›
Introduction(2)
-25 -20 -15 -10 -5 0 5 10 15 20
0.99996
0.99997
0.99998
0.99999
1.00000
1.00001
Ideal Case
100 MPa
500 MPa
NormalizedPressure
PB Body Tilt (minute)
5x10-6
 Result of absolute tilt effect
 100 MPa PCA nearly similar to the ideal case
 500 MPa PCA deviated from cosine behavior
7

8. ‹#›
Introduction(3)
 Relative tilt effect
 Effective area evaluation by cross-float method
 Tilt has no direction effect
 PCA standard : 100 MPa
 Testee to be calibrated : 100 MPa – 200 MPa – 500 MPa
 Pressure balance: 5300 series
 Temperature sensor: RTD
 Level adjustment : electronic level with 0.1’ resolution
8

9. ‹#›
9
Introduction(4)
9
0 10 20 30 40 50
0.9998
0.9999
1.0000
1.0001
1.0002
1.0003
RelativeEffectiveAreaChange(x10-6
)
Tilt angle ( Minute)
(100 -100) MPa
(100 -200) MPa
(100 -500) MPa
Ideal Case Before
1 x 10-4
 Comparison result of 100 MPa vs 500 MPa PCA
 Deviated from cosine behavior
 Comparison result of 100 MPa vs 100/200 MPa PCA
 Follow cosine behavior
 High sensitivity  repeatable results according to tilt angle

10. ‹#›
 Tilt in pressure balance
 The tilt is mainly caused by body/cylinder tilt b and piston tilt
p
 Possible condition of pressure balance
 Perpendicular Condition : b= p = 𝜖=0 and
 Assumption 1 : b≠0, p ≅ 0 and 𝜖=0: Cosine effect
 Assumption 2 : b≠0, p≠0 and 0< 𝜖<1: Theoretical, FEA simulation
(body/cylinder tilt including piston tilt)
Analysis of tilt effect
b
p
Piston
Cylinder
10
(p=0, 𝜖=0)
10
b
p
10Assumption 1 Assumption 2
Perpendicular Condition
(p=max, 𝜖=1)
𝜖 fraction of p , b ≫p
b= p = 𝜖=0

11. ‹#›
Theoretical Approach(1)
𝜕
𝜕𝑧
𝜌
𝜂
ℎ3
𝜕𝑝
𝜕𝑧
+
𝜕
𝜕
𝜌
𝜂
ℎ3
𝜕𝑝
𝜕
= 0
𝜕
𝜕𝑧
𝑒−𝛼𝑝ℎ3
𝜕𝑝
𝜕𝑧
+
𝜕
𝜕
𝑒−𝛼𝑝ℎ3
𝜕𝑝
𝜕
= 0
(5)
(6)
 General Equation of continuity
 Assumption for oil medium in high pressure
 Constant Density
 Viscosity exponential function of pressure 𝜂 = 𝜂0 𝑒 𝛼𝑝
 Based on equation by Dadson
 Not influenced by material properties of PCA
 Undistorted condition
11

12. ‹#›
 Incase of pressure balance in tilt condition gap at ( z,) position
 𝑝0=pressure in perpendicular condition
 𝑝′ =pressure distribution as function of (z,𝜑)
𝜕2
𝑝′
𝜕𝑧2
+
𝜕2
𝑝′
𝜕2
− 2𝛼
𝜕𝑝0
𝜕𝑧
𝜕𝑝′
𝜕𝑧
−
6
𝑙
𝜕𝑝0
𝜕𝑧
𝑠𝑖𝑛

𝑟0
= 0
𝐹 𝜖𝑝′ =
1
2 −2/𝑙
+2/𝑙
0
2𝜋𝑟0
𝜖𝑝′
𝜕ℎ
𝜕𝑧
𝑑𝑑𝑧
Theoretical Approach(2)
(9)
(10)
 Applying (7) (8) to equation of continuity from (6) become
 Solution of 𝑝′ by solving differential equation (5) and apply to resultant force
12
(7)
(8)𝑝(𝑧, ) = 𝑝0(𝑧) + ϵ𝑝′(𝑧, )
ℎ(z,)= ℎ0 1 − 𝜖
2𝑧
𝑙
𝑠𝑖𝑛

𝑟0
12
𝐹 𝜖𝑝′ = 6𝜖2
𝑝1 − 𝑝2
𝑟0
2
𝑙2
ℎ0 𝜋𝑟0 1 −
1
2
1
𝛼 𝑝1 − 𝑝2
𝑒 𝛽1 𝑒 𝑙 2𝑟0 𝐸𝑖 −𝛽2 − 𝐸𝑖 −𝛽1 + 𝑒−𝛽1 𝑒− 𝑙 2𝑟0 𝐸1
∗
𝛽2 − 𝐸1
∗
𝛽1
𝑐𝑜𝑠ℎ(
𝑙
2𝑟0

13. ‹#›
Theoretical Approach(3)
• 𝐸𝑖 𝛽 and 𝐸𝑖
∗
𝛽 Evaluated from tables of exponential Integral
• 𝛼𝑝1=4
• 𝛽j =
−𝑒
−𝛼𝑝 𝑗
𝑒−𝛼𝑝2−𝑒−𝛼𝑝1
𝑙
𝑟
(j = 1,2)
𝐸𝑖 𝛽 = − −𝛽
∞
𝑒−𝑡 𝑑𝑡, 𝐸1
∗
𝛽 = −
𝛽
∞
𝑒−𝑡
𝑑𝑡
Where
 Result of effective area at ( 𝜖=1)
 ~3 ppm for 500 MPa PCA
 ~1 ppm for 100 MPa PCA
13
Represent to a change in coefficient of viscosity of roughly 50:1 between
bottom and top of PCA
𝐴 𝑒(𝜖𝑝′
) = 𝜋𝑟0
2
1 +
ℎ 𝑜
𝑟0
1 + 𝜃t
𝜃t = 6𝜖2
𝑟0
2
𝑙2
1 −
1
2
1
𝛼 𝑝1 − 𝑝2
𝑒 𝛽1 𝑒 𝑙 2𝑟0 𝐸𝑖 −𝛽2 − 𝐸𝑖 −𝛽1 + 𝑒−𝛽1 𝑒− 𝑙 2𝑟0 𝐸1
∗
𝛽2 − 𝐸1
∗
𝛽1
𝑐𝑜𝑠ℎ(
𝑙
2𝑟0
With
(11)
(12)
 Expression of effective area 𝐴 𝑒(𝜖𝑝′)
Too small compared to experiment results
}

14. ‹#›
Simulation Approach(1)
 Finite Element Analysis (FEA)
 FEA to investigate piston tilt effect
 PCA to be simulated :
• 100 MPa PCA (W/C-W/C)
• 500 MPa PCA (W/C-W/C) & (Steel-W/C)
 Simulation Condition :
• 2D & 3D PCA simulation in perpendicular condition
• 3D PCA simulation in piston tilted condition
PCA artifacts for high pressure measurements
14

15. ‹#›
 2D FEA Simulation PCA at perpendicular Condition
 It had been well developed to calculate 𝝀 which results are
comparable to experimental result
Simulation Approach (2)
Effective Area
𝑝 𝑧 = 𝑝 1 −
0
𝑧 𝜌 𝑝 𝑧
𝜂 𝑝 𝑧
1
ℎ 𝑝 𝑧
3 𝑑𝑧
𝑜
𝑙 𝜌 𝑝 𝑧
𝜂 𝑝 𝑧
1
ℎ 𝑝 𝑧
3 𝑑𝑧
Pressure Distribution
15
b=0, p=0 and 𝜖 = 0
Tilt condition
(14)
(13)𝐴 𝑒 = 𝜋𝑟0
2
1 +
ℎ0
𝑟0
+
1
𝑟0 𝑝 0
𝑙
𝑝 𝑧
𝑑 𝑢(𝑝 𝑧) + 𝑈(𝑝 𝑧)
𝑑𝑧
𝑑𝑧

16. ‹#›
 Result of 2D FEA Simulation PCA at perpendicular
Condition
2D PCA Effective area equation & Pressure Distribution
0.0 0.2 0.4 0.6 0.8 1.0
1.7660
1.7665
1.7670
1.7675
1.7680
RadialDistortion(mm)
Normalized Engagement length
0 MPa
20 MPa
40 MPa
60 MPa
80 MPa
100 MPa
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
NormalizedPressureDistribution
Normalized Engagement length
20 MPa
40 MPa
60 MPa
80 MPa
100 MPa
Radial Displacement
Pressure Distribution
PCA Parameters & Material Properties
16
Simulation Approach(3)

17. ‹#›
 3D FEA at Perpendicular condition
 Generation of 3D Model using PCA nominal value
 Generation of suitable mesh from 3D model
 Node selection from the mesh generated previously
 Conversion for calculation gap between piston & cylinder
 To combine APDL and workbench program
 Modified equation for calculating effective area and pressure
distribution
 The result should be same with 2D FEA result
Simulation Approach(4)
3D PCA Modeling PCA Radius r( 𝝋,z) & R( 𝝋,z)
Distorted “Unwrap” gap region
Piston Radius r(𝝋,z) +u
PCA Radius r( 𝝋,z) & R( 𝝋,z)
Distorted “Unwrap” gap region
17

18. ‹#›
 3D FEA Simulation Flow Chart perpendicular Condition
ℎ𝑖 𝜑, 𝑧 = 𝑅 𝜑, 𝑧 − 𝑟 𝜑, 𝑧
Assume the initial pressure distribution is linear
Calculation pressure distribution base on density and viscosity,
PCA gap
Calculation PCA gap using gridding method to
convert from Cartesian coordinate to
cylindrical coordinate
Modeling the PCA
Meshing the PCA model
Cal gap width hi(𝜑,z)
Fluid Flow
problem Fluid flow equation
Cal section Ao, Ae, l
Structural Problem
Cal deformation 𝑢 𝑧 ( 𝜑, 𝑧),
( 𝜑, 𝑧) &hi+1( 𝜑, 𝑧)
ℎ𝑖(𝜑, 𝑧) = ℎ𝑖+1(𝜑, 𝑧)
ℎ𝑖 𝜑, 𝑧 − ℎ𝑖+1(𝜑, 𝑧)
ℎ𝑖 𝜑, 𝑧
< 10−6
𝑝𝑖(𝜑, 𝑧) = 𝑝𝑖+1(𝜑, 𝑧)
Modelling PCA
Simulation Approach(5)
18
b=p= 𝜖=0
𝑝𝑖 𝜑, 𝑧 − 𝑝𝑖+1(𝜑, 𝑧)
𝑝𝑖 𝜑, 𝑧
< 10−6
𝐴 𝑒 =
0
2𝜋
𝜋𝑟0
2 1 +
ℎ0
𝑟0
+
1
𝑟0 𝑝 0
𝑙
𝑝 𝑧
𝑑 𝑢 𝑝 𝑧
+ 𝑈 𝑝 𝑧
𝑑𝑧
𝑑𝑧 𝑑𝜑
0
2𝜋
𝑑𝜑
(15)
18

19. ‹#›
 2D vs 3D FEA result in perpendicular condition
 100 MPa (W/C-W/C)
 500 MPa (W/C-W/C)
 2D and 3D FEA  Same result
Simulation Approach(6)
19
Experiment 2D FEM 3D FEM
Ao (mm2 ) 9.805570 9.805569 9.805569
l (10-7 /MPa) 8.6 8.5 8.5
Experiment 2D FEM 3D FEM
Ao (mm2 ) 1.961063 1.961063 1.961063
l (10-7 /MPa) 7.8 7.7 7.7

20. ‹#›
Simulation Approach(7)
 3D FEA in tilt condition
 Generation of 3D Models using PCA nominal value with tilt
condition
 Calculation of undistorted effective area in tilt condition
 Modified equation for calculating effective area (undistorted) /
pressure distribution
 Next step : same as in perpendicular condition
Meshing &
Node Selection
Piston Radius r(𝝋,z)
undistorted
Piston Radius r(𝝋,z)
Undistorted for example only
3D PCA Modeling
20

21. ‹#›
 FEA Simulation Flow Chart in tilt condition
ℎ𝑖 𝜑, 𝑧 = 𝑅 𝜑, 𝑧 − 𝑟 𝜑, 𝑧
Assume the initial pressure distribution is linear
Calculation pressure distribution base on density and viscosity,
PCA gap
Calculation PCA gap using gridding method to
convert from Cartesian coordinate to
cylindrical coordinate
Modeling the PCA
Meshing of the PCA model
Cal gap width hi(𝜑,z)
Fluid Flow
problem Fluid flow equation
Cal section Ao, Ae, l
Structural Problem
Cal deformation u(𝜑, 𝑧),
U(𝜑, 𝑧) &hi+1(𝜑, 𝑧)
ℎ𝑖(𝜑, 𝑧) = ℎ𝑖+1(𝜑, 𝑧)
ℎ𝑖 𝜑, 𝑧 − ℎ𝑖+1(𝜑, 𝑧)
ℎ𝑖 𝜑, 𝑧
< 10−6
𝑃𝑖 𝜑, 𝑧 − 𝑃𝑖+1(𝜑, 𝑧)
𝑃𝑖 𝜑, 𝑧
< 10−6
𝑃𝑖(𝜑, 𝑧) = 𝑃𝑖+1(𝜑, 𝑧)
Modelling PCA
Simulation Approach(8)
𝐴 𝑒 =
0
2𝜋
𝜋𝑟0
2 1 + ℎ0
𝑟0
+ 1
𝑟0 𝑝 0
𝑙
𝑝 𝑧
𝑑 𝑢(𝑝 𝑧) + 𝑈(𝑝 𝑧)
𝑑𝑧
𝑑𝑧 𝑑𝜑
0
2𝜋
𝑑𝜑 21
p≠0 and 0< 𝜖<1
ℎ1(z,)= ℎ0 1 − 𝜖
2𝑧
𝑙
𝑠𝑖𝑛

𝑟0

22. ‹#›
 Pressure distribution of 500 MPa PCA (Steel-W/C)
 At the piston position at 𝝋 =0o ,pressure distribution is increasing, but
piston position at 𝝋 = 180O ,pressure distribution is decreasing
 At the piston position 𝝋 = 90O, 270O nearly the same as perpendicular
condition
0 5 10 15 20 25 30
0
100
200
300
400
500
0o
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
Pressure/MPa
Engagement Length / mm
0 5 10 15 20 25 30
0
100
200
300
400
500
90o
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
Pressure/MPa
Engagement Length / mm
0 5 10 15 20 25 30
0
100
200
300
400
500
180o
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
Pressure/MPa
Engagement Length / mm
0 5 10 15 20 25 30
0
100
200
300
400
500
270o
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
Pressure/MPa
Engagement Length / mm
0 90 180 270 360
0
100
200
300
400
500
z=0.1
z=0.5
Pressure/MPa
Angle / Degrees
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
z=0.9
-50 0 50 100 150 200 250 300 350 400
0
200
400
Pressure/MPa
Angle / Degree
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
z=0.01
z=0.5
z=0.99
22
Simulation Approach(9)

23. ‹#›
 Gap profile 500 MPa PCA (Steel-W/C)
 At the piston position at 𝝋 =0o ,gap profile is increasing, but piston
position at 𝝋 = 180O ,gap profile is decreasing
 At the piston position 𝝋 = 90O, 270O gap profile is nearly the same as
perpendicular condition
23
-50 0 50 100 150 200 250 300 350 400
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
Gap/mm
Angle / Degree
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
z=0.99
z=0.5
z=0.01
-50 0 50 100 150 200 250 300 350 400
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
Gap/mm
Angle / Degree
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
z=0.1
z=0.5
z=0.9
0 5 10 15 20 25 30
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
0o
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
Gap/mm
Engagement Length / mm
0 5 10 15 20 25 30
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
90o
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
Gap/mm
Engagement Length / mm
0 5 10 15 20 25 30
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
180o
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
Gap/mm
Engagement Length / mm
0 5 10 15 20 25 30
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
270o
0 E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
Gap/mm
Engagement Length / mm
23
23
Simulation Approach(10)

24. ‹#›
 Qualitative result of FEA simulation
 Estimation effective area of 500 MPa PCA
• Estimation of PCA radius from “neutral surface” in distorted & tilt
condition
• 𝐴 𝑒 max at 𝝋= 0o and 𝐴 𝑒min at 𝝋= 180o. At 𝝋= 90o & 270o , 𝐴 𝑒nearly
similar to perpendicular condition
• Effective area change depend of change difference between 𝝋= 0o &
𝝋= 180o
0 5 10 15 20 25 30
0.7895
0.7900
0.7905
0.7910
0.7915
Piston
Radii/mm
Engagement length / mm
Effective Radii 0.5E 0o
Effective Radii 0.5E 180o
Effective Radii 0.5E 90o
/270
Distorted Tilt 0.5E 0o
Distorted Tilt 0.5E 180o
Distorted Tilt 0.5E 90o
/270o
Cylinder
0 5 10 15 20 25 30
0.79034
0.79036
0.79038
0.79040
0.79042
0.79044
0.79046
0.79048
0.79050
Radii/mm
Engagement length / mm
0.0E
0.1 E
0.2 E
0.3 E
0.4 E
0.5 E
24
Simulation Approach(11)

25. ‹#›
 FEA Simulation result for PCA with tilted condition
 Effective area change for tilted piston
• Limited only for piston tilt from 0≤ 𝜖 ≤ 0.5
• 100 MPa PCA (W/C-W/C) small effective area change: less than 1 ppm
• 500 MPa PCA (W/C-W/C) small effective area change ~1 ppm
• 500 MPa PCA (Steel-W/C) significant effective area change ~6 ppm
• In case 𝜖>0.5
Simulation Approach(12)
FEA result according to piston tilt
25
-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6
-2
0
2
4
6
8
10
𝜖
Ae/Ae(x10-6)
Tilt ( )
100 MPa Simulation
500 MPa W/C Piston Simulation
500 MPa SS Piston Simulation
𝐴 𝑒 =
0
2𝜋
𝜋𝑟0
2 1 + ℎ0
𝑟0
+ 1
𝑟0 𝑝 0
𝑙
𝑝 𝑧
𝑑 𝑢(𝑝 𝑧) + 𝑈(𝑝 𝑧)
𝑑𝑧
𝑑𝑧 𝑑𝜑
0
2𝜋
𝑑𝜑

26. ‹#›
 FEA simulation result (extrapolation)
 The extrapolation of FEA simulation was applied from 0.5< 𝜖<1
which extend the possibility of beyond limitation of 3D FEA
simulation (contact problem)
26
•
𝛿𝐴 𝑒
𝐴 𝑒
= 𝑎1 𝜖 𝑎2(max 20 ppm, R=0.99917)
•
𝛿𝐴 𝑒
𝐴 𝑒
= 𝑎1 𝜖 𝑎2(max 5 ppm, R=0.99915)
Simulation Approach(13)
0.0 0.2 0.4 0.6 0.8 1.0
0
5
10
15
20
𝜖
Ae/Ae(x10-6)
Tilt ( )
100 MPa Simulation
500 MPa W/C Piston Simulation
500 MPa SS Piston Simulation
500 MPa WC Piston Simulation Extrapolated (Poly)
500 MPa SS Piston Simulation Extrapolated(poly)
100 MPa Piston Extrapolated

27. ‹#›
 Discussion of 3D FEA Result
 The probable condition of piston tilt, p , condition in relation to
body tilt condition;
• In case of b small enough : b  0 , 𝜖 propotional to b
• In case of b big: b  0 , 𝜖=1
• In case of b very big : b 0, 𝜖=1, possibility of additional
upper part of piston tilt with sensitivity issue such as contact
problem, fast rotation time
b
p
h
27
Simulation Approach(14)
h

28. ‹#›
-30 -20 -10 0 10 20 30
100.476
100.478
100.480
100.482
100.484
100.486
100.488
Pressure(MPa)
Tilt angle (min)
-8 -7 -6 -5 -4
-8
-7
-6
-5
-4
y-axis(min)
x-axis (min)
Mean value
Zero tilt measurement
Schematic Diagram of Tilt Adjustment
Pressure change according To tilt
Zero tilt Estimation Result
Minimization of tilt Effect (1)
 Tilt Adjustment
 Using precise electronic level meter
 Maximum pressure at vertical PCA condition
 Using precise pressure monitor at 100 MPa
28

29. ‹#›
𝐴′ 𝑡 =
𝐹𝑡
′
𝐹𝑠
′ 1 +
𝜃𝑠
′2
2
−
𝜃𝑡
′2
2
+ 𝛼 ∆𝑇𝑠
′
− ∆𝑇𝑡
′
𝐴 𝑠
𝑃 =
𝐹
𝐴(1 + 𝛼 ∆𝑇)
𝑐𝑜𝑠𝜃
𝐴 𝑡 =
𝐹𝑡
𝐹𝑠
𝑐𝑜𝑠𝜃𝑡
𝑐𝑜𝑠𝜃𝑠
1 + 𝛼∆𝑇𝑠
1 + 𝛼∆𝑇𝑡
𝐴 𝑠
𝐴 𝑡 =
𝐹𝑡
𝐹𝑠
1 +
𝜃𝑠
2
2
−
𝜃𝑡
2
2
+ 𝛼 ∆𝑇𝑠 − ∆𝑇𝑡 𝐴 𝑠
𝐴 𝑡
′
=
𝐹𝑡
′
𝐹𝑠
′
𝑐𝑜𝑠𝜃′ 𝑡
𝑐𝑜𝑠𝜃′ 𝑠
1 + 𝛼∆𝑇′ 𝑠
1 + 𝛼∆𝑇′ 𝑡
𝐴′ 𝑠
 PCA exchange method
 Applicable for PB with exchangeable PCA with same mounting post of
P/C
 Only exchanging PCA and other PB part remain at the same place
29
Minimization of tilt Effect(2)

30. ‹#›
0 20 40 60 80 100 120
9.8052
9.8054
9.8056
9.8058
9.8060
9.8062
9.8064
EffectiveArea(mm
2
)
Pressure (MPa)
before exchange
after exchange
mean value
2x10
-5
𝐴 𝑡 =
𝐴 𝑡 + 𝐴 𝑡
′
2
=
1
2
𝐹𝑡
𝐹𝑠
+
𝐹𝑡
′
𝐹𝑠
′ +
𝐹𝑡
𝐹𝑠
𝛼 𝑇𝑠 − 𝑇𝑡 +
𝐹𝑡
′
𝐹𝑠
′ 𝛼 𝑇𝑠
′
− 𝑇𝑡
′
+
𝐹𝑡
𝐹𝑠
𝜃𝑠
2
2
−
𝜃𝑡
2
2
+
𝐹𝑡
′
𝐹𝑠
′ (
𝜃𝑠
′2
2
−
𝜃𝑡
′2
2
) 𝐴 𝑠
m T 
Force/Mass Temperature Tilt
𝐴 𝑡
𝐴 𝑡
′
𝐴 𝑡
 Average Of Exchange PCAs
 Average of the exchange PCA  possible to compensate the
systematic error of calibration
 In special case  Can remove offset: not only tilt but also mass and
temperature
30
Minimization of tilt Effect(3)

31. ‹#›
 Offset of Tilt Term
 Compensation of tilt
 Only with assumption :Same Nominal Pressure
 Both PB body are remain in the same condition during PCA exchange
𝐹𝑡
𝐹𝑠
𝜃𝑠
2
2
−
𝜃𝑡
2
2
+
𝐹𝑡
′
𝐹𝑠
′
𝜃𝑠
′2
2
−
𝜃𝑡
′2
2
≅
𝐹𝑡
𝐹𝑠
𝜃𝑠
2
2
−
𝜃𝑡
′2
2
+
𝜃𝑠
′2
2
−
𝜃𝑡
2
2
= 0
=0 =0
𝐹𝑡
𝐹𝑠
≅
𝐹𝑡
′
𝐹𝑠
′
𝜃𝑠 = 𝜃′ 𝑡
Std tilt sensor
Test tilt sensor
𝜃𝑡 = 𝜃′ 𝑠
31
Minimization of tilt Effect(4)

32. ‹#›
 Tilt effect of pressure balance
 The experimental results of pressure balance with tilt effect for absolute and
relative tilt method
• 100 MPa PCA follow cosine effect
• 500 MPa PCA with a small diameter deviate from cosine effect
 To investigate piston tilt effect for PCA with a small diameter
• Theoretical method has been developed for maximum tilt of piston with
limitation such as undistorted problem, constant density, etc.
• 3D FEA simulation of PCA with tilt condition has been developed with
distorted condition of PCA. The simulation result shows significant
effective area change at maximum piston tilt
 Piston tilt effect can contribute to bigger estimation of the uncertainty
especially for smaller diameter piston in high pressure condition
 Future works
 Improvement of 3D FEA simulation in PCA with the tilt condition
• Adding actual dimension of PCA
• Different analysis of flow inside PCA gap for better understanding of
contact problem at top piston
Conclusion
32

33. Thank you
감사합니다
Terima kasih
표준이 올라가면 생활이 즐거워 집니다!
33