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압력용기 제조를 위한 D.D.I. 공정의 팁 클리어런스 설계

곽효서1, 박건영2, 김철3,#orcid

Design of Tip Clearance in the D.D.I. Process to Manufacture Pressure Vessel

Hyo Seo Kwak1, Gun Young Park2, Chul Kim3,#orcid
Journal of the Korean Society for Precision Engineering 2018;35(7):715-720.
Published online: July 1, 2018

1 부산대학교 기계기술연구원

2 부산대학교 기계융합기술학과

3 부산대학교 기계공학부

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# chulki@pusan.ac.kr TEL: +82-051-510-2489
• Received: August 2, 2017   • Revised: March 23, 2018   • Accepted: May 1, 2018

Copyright © The Korean Society for Precision Engineering

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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  • The liner of CNG pressure vessel was manufactured using a deep drawing and ironing (D.D.I.) process with a single punch. Tip clearance between billet and die suggested in the actual field has been widely used to reduce forming load and to improve die life. However, the analysis and design of tip clearance is necessary for the third stage of forming defect. In this study, the tip clearance of the third stage was determined to limit the ratio of reduction of cross-sectional area based on theoretical analysis. The proposed tip clearance was verified via finite element analysis. In addition, the simulation technique was established by comparing the forming load based on theoretical calculation with the load determined via FEM.
  • KEYWORDS: CNG pressure vessel, D.D.I. process, Tip clearance, Finite element analysis, Forming load
  • KEYWORDS: 압축천연가스 압력용기, D.D.I. 공정, 팁 클리어런스, 유한요소해석, 성형하중

A 31

Cross sectional area after 3rd drawing process

A 32

Cross sectional area after 3rd ironing process

C

Tip clearance

dd 31

Drawing die diameter of 3rd stage

di 32

Ironing die diameter of 3rd stage

dm 31

Effective diameter of liner

dp 3

Punch diameter of 3rd stage

Fd

Forming load of 3rd drawing process

Fi

Forming load of 3rd ironing process

m

Constant share friction coefficient

t 23

Billet thickness after 2nd process

t 31

Billet thickness after 3rd drawing process

t 32

Billet thickness after 3rd ironing process

ε¯

Effective strain

εr

Radial strain

εz

Axial strain

εθ

Tangential strain

μ

Coulomb friction coefficient

σn

Normal stress of die surface

σ 0

Von-mises stress of die surface

σ¯

Effective stress

τcoulomb

Coulomb friction force

τconst

Constant share friction force

ΔA3

Reduction ratio of cross sectional area of 3rd stage

Δt23→31

Reduction amounts of thickness after 3rd drawing process

Δt31→32

Reduction amounts of thickness after 3rd ironing process
압축천연가스(CNG) 저장용기는 딥 드로잉(Deep Drawing)과 아이어닝(Ironing)을 하나의 펀치를 이용하여 연속적으로 성형하는 D.D.I. (Deep Drawing and Ironing) 공정으로 제작된다. 이 공정은 각 성형단계 내에서 열처리를 생략하여 공정시간이 단축되고 생산성을 높일 수 있는 장점이 있다.1-3 Lie 등4은 FAD (Failure Assessment Diagram)기법을 이용하여 길이방향 표면 크랙이 있는 CNG 압력용기의 피로파괴에 대한 연구를 수행하였으며, Kang 등5은 CNG 압력용기(Type 2)의 구조 안전성 및 저장 용량 확보를 위하여 실린더부, 돔부 및 복합재층의 두께를 설계하였다. Walker 등6은 이방성을 고려한 Tsai-Wu 이론을 적용하여 복합재 압력용기 제조를 위한 제작 공차의 최적화에 관한 연구를 수행하였다. Choi 등7은 AUTO LISP및 ANSYS APDL을 이용하여 압력용기 라이너의 형상 및 피로수명 향상을 위한 자긴공정(Autofrettage Process) 설계를 위한 자동화 프로그램을 개발하였다. Lee 등8은 드로잉 및 아이어닝 공정의 설계인자에 따른 유한요소해석을 통하여, 성형 결함 방지를 위한 금형설계에 관한 연구를 수행하였다.
드로잉 공정에는 성형 하중 감소 및 금형 수명 향상을 위하여 소재와 금형 사이에 팁 클리어런스(Tip Clearance)를 부여한다. 기존의 CNG 압력용기 제조를 위한1차, 2차 및 3차 드로잉 공정의 팁 클리어런스는 현장의 경험을 토대로 제안된 값(각각 소재 두께의 5%, 5% 및 -5%)이 널리 적용되고 있다.2 기존의 연구에서는 드로잉 비(Drawing Ratio), 다이 사이의 거리 및 다이 곡률 반경 등의 설계인자를 고려한 D.D.I. 공정 설계가 이루어져 왔으나, 팁 클리어런스에 관한 연구는 이루어지지 않아 3차 공정의 불안전성으로 인한 주름(Wrinkling), 접힘(Folding) 및 찢어짐(Tearing)이 발생하여 이에 대한 체계적인 분석 및 설계가 필요하다.
이에 본 연구에서는 CNG 압력용기 라이너 제조를 위한 D.D.I 공정 중3차 공정의 불안전성을 방지하기 위하여 이론적 해석을 통한 3차 성형단계의 2차 공정인 아이어닝 공정의 한계 단면적 감소율을 만족하는 팁 클리어런스 값을 선정하였으며, 유한요소해석을 통하여 제안된 값의 타당성을 검증하였다. 또한, 이론 및 유한요소해석의 성형 하중을 비교하여 해석기법을 확립하였다.
2.1 라이너 제조를 위한 D.D.I. 공정 개요
CNG 저장을 위한 복합재 압력용기는 Fig. 1과 같이 탄소 및 유리섬유에 레진을 함침한 복합재층(Composite Layer)이 금속 라이너(Liner)에 와인딩된 형태이다. 라이너는 실린더부, 바닥부 및 돔부로 이루어져 있으며, 압력용기 제조를 위한 절차는 Fig. 2와 같다. 금속 라이너 성형을 위하여 2차 및 3차 성형단계에서는 D.D.I. 공정이 적용되는데, Fig. 3과 같이 하나의 펀치를 이용하여 소재의 직경을 감소시키는 드로잉 공정 및 두께를 감소시키는 아이어닝 공정이 짧은 시간(3초 이내) 내에 연속적으로 이루어지기 때문에 드로잉으로 인한 가공경화가 발생하지 않아 후처리 생략이 가능하여 비용 및 시간 절감 효과가 큰 장점이 있다. 1차 성형단계에서는 단동형 수직 프레스를 이용한 딥 드로잉 공정을 통해 초기 블랭크를 컵 형상으로 성형하며, 2차 성형단계에서는 수평식 프레스를 이용하여 재드로잉 및 2번의 아이어닝 공정이 이루어진다. 3차 성형단계에서는 재드로잉 및 아이어닝 공정을 통하여 최종 두께를 가지는 실린더부가 성형되고, 돔부 성형을 위한 스피닝 공정을 거친 후 라이너 제조가 완료된다.1 또한, 각 성형단계 완료 후 가공경화를 제거하기 위하여 완전 풀림, 구상화 열처리 공정 및 인산염 피막처리(Phosphate Coating)가 이루어진다.9,10
Fig. 1

CNG pressure vessel

KSPE_2018_v35n7_715_f001.jpg
Fig. 2

Process to manufacture CNG pressure vessel

KSPE_2018_v35n7_715_f002.jpg
Fig. 3

D.D.I. process to manufacture the liner of CNG pressure vessel

KSPE_2018_v35n7_715_f003.jpg
2.2 드로잉 공정의 팁 클리어런스
드로잉 공정에는 금형의 마모 감소로 인한 수명 증가, 펀치의 성형 하중 감소 및 인장력 제어를 위하여 소재와 펀치 및 다이 사이에 팁 클리어런스를 부여한다. 팁 클리어런스 값이 작으면 전단력이 작아지고 금형의 수명이 단축되므로, 적절한 팁 클리어런스 값을 선택해야 한다. 일반적으로 드로잉 공정에서 팁 클리어런스 값은 소재두께의 5%-20%이다.11 Fig. 4와 같이 직경 1,100 mm 및 두께 12.5 mm인 초기 블랭크를 이용하여 유효직경 337.36 mm, 두께 4.775 mm 및 총길이 1707.60 mm인 라이너 성형을 위한 드로잉 공정에서 팁 클리어런스는 기존의 현장의 경험을 토대로 1차 및 2차 드로잉에서는 소재두께의 5%, 3차에서는 소재두께의 -5%를 적용하고 있다.2 그러나, 3차 공정이 불안전하기 때문에 이론 및 유한요소해석을 통한 3차 드로잉 공정의 팁 클리어런스 설계를 수행하였다.
Fig. 4

The tip clearances in the D.D.I. process used in the actual field

KSPE_2018_v35n7_715_f004.jpg
기존 Yoon3의 연구에 의하면, 2차 성형단계에서 총 단면적 감소율이 50%를 넘지 않도록 하고, 3차 성형단계에서는 아이어닝 시 단면적 감소율이 35%를 초과하지 않도록 아이어닝 량을 결정한다. 본 연구에서는 3차 드로잉 공정의 팁 클리어런스에 따른 아이어닝 공정의 이론 단면적 감소율을 계산하여 주름, 접힘 및 찢어짐 현상을 방지하고자 한다. 또한, 아이어닝 공정에서 한계 단면적 감소율(35%)3을 초과하지 않도록 팁 클리어런스 값을 선정하였으며, 유한요소해석을 통하여 제안된 값을 검증하였다.
3.1 팁 클리어런스에 따른 단면적 감소율
기존의 팁 클리어런스 값인 -5%를 기준으로 5가지 모델(0%, -5%, -10%, -15% 및 -20%)을 생성하여, 식(1)부터 식(3)을 토대로 3차 성형단계의 펀치(dp3), 드로잉 다이(dd31) 및 아이어닝 다이(di32)의 치수를 Table 1에 계산하였다. i번째 성형단계(Stage)의 펀치 치수를 dpi, i번째 성형단계 및 j번째 공정(Process)의 드로잉 다이 치수는 ddij, i번째 성형단계 및j번째 공정의 아이어닝 다이 치수는 diij이다. dm31는 성형하고자 하는 최종 라이너의 유효직경(337.36 mm), t23은 2차 성형단계 완료 후 소재의 두께(9.048 mm) 및 C는 팁 클리어런스 값이다. 드로잉 공정 후 Fig. 5의 소재 단면적(A31) 및 아이어닝 공정 후 소재의 단면적(A32)을 이용하여 식(4) 부터 식(6)을 토대로 아이어닝 공정의 단면적 감소율(ΔA3)을 계산하고 Table 2에 나타내었다. 팁 클리어런스 값이 작아질수록 단면적 감소율이 감소하였고, -20%일 때 성형결함이 발생하지 않는 한계 단면적 감소율(35%)3 이내를 만족한다.
Table 1

Diameters of punches, drawing and ironing dies according to tip clearances of the 3rd stage

Table 1
Tip clearance (%) dp3 (mm) dd31 (mm) di32 (mm)
0 328.31 346.41 337.86
-5 328.76 345.96 338.31
-10 329.22 345.50 338.77
-15 329.67 345.05 339.22
-20 330.12 344.60 339.67
Fig. 5

Cross sectional areas (A31, A32) after the drawing and ironing processes in the 3rd stage

KSPE_2018_v35n7_715_f005.jpg
Table 2

Reduction ratios of cross sectional areas according to tip clearances of the 3rd stage

Table 2
Tip clearance (%) A31 (mm2) A32 (mm2) ΔA3 (%)
0 9,589.50 4,996.67 48.89
-5 9,110.03 5,003.46 45.08
-10 8,630.55 5,010.25 41.95
-15 8,151.08 5,017.03 38.45
-20 7,671.60 5,023.82 34.51
(1)
dp3=dm31-t231+C
(2)
dd31=dm31+t231+C
(3)
di32=dp3+2t32
(4)
A31=πdd312-dp324
(5)
A32=πdi322-dp324
(6)
∆A3=A31-A32A31
3.2 D.D.I. 공정의 유한요소해석
상기 제안된 팁 클리어런스 값(-20%)의 타당성 검증을 위해, 상용 소프트웨어인 Forge NxT 2.0를 이용한 유한요소해석을 수행하였다.

3.2.1 3D 모델 및 해석 조건

2차 성형단계 해석 완료 후 도출된 소재 형상을 3차 성형단계의 초기 모델로 적용하였으며, 1차 및 2차 성형공정의 펀치 및 다이 치수는 Fig. 6의 현장에서 제공받은 도면을 토대로 3D 모델링을 수행하였으며, 이를 Fig. 7에 나타내었다. 사면체(Tetrahedron) 요소를 이용하여 Fig. 8와 같이 빌렛에 24,429개의 격자를 생성하였으며, 공정이 진행됨에 따라 주기적으로 격자의 재구성(Remesh)이 일어난다.12 재료의 물성치는 온도에 따라 다르며 성형이 진행되면서 라이너 소재(34CrMo4)의 온도가 수시로 변하기 때문에, 해당 온도에 대한 물성치를 실시간으로 적용해야 한다. 따라서, Forge NxT 2.0에 내장되어 있는 Fig. 9의 온도에 따른 변형률-유동응력 선도를 적용하였으며, 다이 및 펀치는 강체(Rigid Body)로 설정하였다. 쿨롱 마찰계수(μ) 및 전단 마찰상수(m)가 식(7)에서 식(8)로부터 계산되며, 해석 과정에서 소재와 다이 사이에서 발생하는 마찰력은 두 값 중 작은 값이 실시간으로 적용된다.12 쿨롱 마찰계수(0.05) 및 전단 마찰상수(0.1)는 Fig. 10과 같이 Forge NxT 2.0에서 제공하는 34CrMo4의 값으로 정의하였다.12 여기서 σn및 σ0은 각각 다이 표면에 작용하는 수직응력 및 Von-Mises 응력이다. 해석시간 단축을 위해 Adjustment 기능을 이용하여 빌렛은 다이에, 펀치는 빌렛에 접촉하도록 설정하였으며, 펀치 속도는 현장에서 적용하고 있는 값인 50 mm/s로 설정하였다.
Fig. 6

Punch and die dimensions of D.D.I. process

KSPE_2018_v35n7_715_f006.jpg
Fig. 7

3D model for forming analysis of the 3rd stage

KSPE_2018_v35n7_715_f007.jpg
Fig. 8

Generation of mesh

KSPE_2018_v35n7_715_f008.jpg
Fig. 9

Strain-flow stress curve of 34CrMo4 according to temperature

KSPE_2018_v35n7_715_f009.jpg
Fig. 10

Coulomb friction coefficient and share friction factor of 34CrMo4 provided by Forge NxT 2.0

KSPE_2018_v35n7_715_f010.jpg
(7)
τcoulomb=μσn
(8)
τconst=mσ03

3.2.2 해석 결과 및 고찰

3차 드로잉 공정의 팁 클리어런스 값에 따른 유한요소해석의 결과로, 최대 드로잉 및 최대 아이어닝 하중을 Table 3에, 3차 성형단계의 2차 공정인 아이어닝 공정의 한계 단면적 감소율을 만족하는 팁 클리어런스 값이 -20%일 때 시간에 따른 펀치의 성형 하중을 Fig. 11에 나타내었다. 이 경우, 드로잉 하중(697.56 ton)이 가장 높은 반면 아이어닝 하중(431.84 ton)은 가장 낮음을 알 수 있고, 현장에서 사용중인 프레스 용량(1000 ton)1 이하이므로 성형이 가능함을 알 수 있다. Forge NxT의 후처리기에서는 해석 중 접힘이 발생하여 메쉬의 노드점이 서로 만나게 되면 Folds 값이 1이 되고, 접힘이 발생하지 않으면 0을 나타내는데, Fig. 12와 같이 팁 클리어런스 값이 -20%일 때 3차 성형단계 완료 후 라이너의 모든 부분에서 Folds의 값이 0으로 나타났다.
Table 3

Maximum drawing and ironing loads according to tip clearances of the 3rd stage

Table 3
Tip clearance
(%)		 Maximum
drawing load (ton)		 Maximum
ironing load (ton)
0 595.44 730.8
-5 632.55 539.77
-10 641.15 486.09
-15 681.50 455.83
-20 697.56 431.84
Fig. 11

Forming load according to time when tip clearance is -20%

KSPE_2018_v35n7_715_f011.jpg
Fig. 12

Liner shape after the 3rd stage when tip clearance is -20%

KSPE_2018_v35n7_715_f012.jpg
팁 클리어런스 값이 작아질수록 최대 드로잉 하중은 증가하는 반면 최대 아이어닝 하중은 감소하는데, 그 원인을 파악하기 위하여 각 공정에서 소재의 두께 감소량을 분석하였다. 소재의 두께는 다이와 펀치 사이의 거리이며, 식(9)를 이용하여 3차 드로잉 및 아이어닝 공정 후 소재의 두께(t31및 t32)를 계산하였다. 또한, 식(10)에서 식(11)을 이용하여 드로잉 공정 후 두께 감소량(Δt23→31) 및 아이어닝 공정 후 두께 감소량(Δt31→32)을 도출하였다. Table 4에 따르면, 값이 0 미만인 팁 클리어런스가 적용된 드로잉 공정으로 인하여 소재의 두께가 줄었으며, 팁 클리어런스 값이 작아질수록 드로잉 공정에서 두께 감소량이 늘어났고 아이어닝 공정에서는 두께 감소량이 감소하였다. 드로잉 공정의 팁 클리어런스를 음의 값(-20%)으로 설정함으로써, 3차 드로잉 공정에서의 두께도 미리 감소시켜 연속 가공되는 아이어닝 공정에서 성형결함을 방지하는 단면적 감소율을 한계 값(35%) 이내를 만족시켰다.
Table 4

Amounts of thickness reductions according to tip clearances of the 3rd stage

Table 4
Tip clearance
(%)		 t31
(mm)		 t32
(mm)		 Δt23→31
(mm)		 Δt31→32
(mm)
0 9.05 4.78 0.00 4.27
-5 8.60 4.78 0.45 3.82
-10 8.14 4.78 0.91 3.37
-15 7.69 4.78 1.36 2.92
-20 7.24 4.78 1.81 2.46
(9)
t31=dd31-dp32, t32=di32-dp32
(10)
∆t23→31=t23-t31
(11)
∆t31→32=t31-t32
유한요소해석의 타당성 검증을 위하여, 3차 드로잉 공정의 팁클리어런스가 -20%인 경우의 드로잉 및 아이어닝 공정 하중을 이론적으로 계산하였다. 식(12)에서 식(13)을 이용하여 유효 변형률(ε¯)을 구하고, 34CrMo4 소재의 변형률-유동응력 관계식(식(14)) 및 단면적(A)을 이용하여 식(15)으로부터 드로잉 하중(Fd) 및 아이어닝 하중을(Fi) 계산하였다. 그 결과, Table 5와 같이 드로잉 하중 및 아이어닝 하중이 각각 783.54 ton 및 473.84 ton으로 계산되었으며, 유한요소해석에서 도출된 값과 10.97% 및 8.86%의 오차를 보이는데, 이는 해석 프로그램의 정확도 및 메쉬의 조밀성 등에서 오차가 발생한 것으로 사료되며, 이는 D.D.I. 공정의 해석 기법이 타당성을 가짐을 알 수 있다.
Table 5

Comparison of the forming loads obtained from theoretical calculation and that from FEM

Table 5
Theory FEM Error
Drawing load 783.54 ton 697.56 ton 10.97%
Ironing load 473.84 ton 431.84 ton 8.86%
(12)
dε¯=23dεr-dεθ2+dεθ-dεz2+dεz-dεr2
(13)
ε¯=∫dε¯
(14)
σ¯=Kεn¯
(15)
F=σ¯A
여기서 소성계수 K는 90.42, 가공경화지수 n은 0.213이다.
본 연구에서는 CNG 압력용기 라이너 제조를 위한 D.D.I. 공정 중 3차 성형단계의 불안전성을 방지하기 위하여, 이론적 해석을 통한 3차 성형단계의 2차 공정인 아이어닝 공정의 한계 단면적 감소율을 초과하지 않는 팁 클리어런스 값을 선정하였다. 또한, 유한요소해석을 통하여 제안된 값의 타당성을 검증하였으며 본 연구의 결과를 요약하면 아래와 같다.
(1) 3차 성형단계의 2차 공정인 아이어닝 공정에서 한계 단면적 감소율을 초과하지 않게 하는 드로잉 공정의 팁 클리어런스를 구하기 위해, 5가지 모델(0%, -5%, -10%, -15% 및 -20%)을 생성하고 이론 단면적 감소율을 계산하였다. 그 결과, 팁 클리어런스 값이 작아질수록 단면적 감소율이 낮아졌고, -20%일 때 한계 단면적 감소율(35%) 이내를 만족했다.
(2) 상기의 제안된 팁 클리어런스 값(-20%)의 타당성 검증을 위하여 3차 성형단계의 1차 공정인 드로잉 공정의 팁 클리어런스 값에 따른 유한요소해석을 수행하였다. 그 결과, 값이 -20%인 경우 드로잉 하중이 697.56 ton 및 아이어닝 하중이 431.84 ton로 나타났으며, 이는 현장에서 사용중인 프레스 용량(1000 ton) 이하이므로 성형이 가능함을 알 수 있다.
(3) 3차 성형단계의 1차 공정인 드로잉 공정의 팁 클리어런스가 -20%인 경우의 드로잉 및 아이어닝 공정의 이론 하중이 783.54 ton 및 473.84 ton로 계산되었으며, 이는 유한요소해석에서 도출된 값과 비교하였을 때 각각 10.97% 및 8.86%의 오차를 보이나, 해석 프로그램의 정확도 및 메쉬의 조밀성 등에서 오차가 발생한 것으로 사료되며, 이는 D.D.I. 공정의 해석 기법이 타당성을 가짐을 알 수 있다.
본 논문의 연구 내용을 CNG 압력용기 제조를 위한 공정에 적용함으로써, 성형 결함 감소로 인한 생산성 향상에 큰 도움이 될 것으로 사료된다.
이 논문은 2015년도 정부(교육부)의 재원으로 한국연구재단의 지원을 받아 수행된 기초연구사업임(No. 201523870001).
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    10.1016/S1003-6326(11)61088-1
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    Choi, J., Jung, S., and Kim, C., “Development of an Automated Design System of a CNG Composite Vessel Using a Steel Liner Manufactured Using the DDI Process,” The International Journal of Advanced Manufacturing Technology, Vol. 24, Nos. 11-12, pp. 781-788, 2004.
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    Kim, E.-S., Kim, J.-H., Park, Y.-S., Kim, C., and Choi, J.-C., “Development of an Automated Design System of CNG Composite Vessel using Steel Liner Manufactured by DDI Process,” Journal of Korean Society of Precision Engineering, Vol. 20, No. 1, pp. 205-213, 2003.
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Design of Tip Clearance in the D.D.I. Process to Manufacture Pressure Vessel
J. Korean Soc. Precis. Eng.. 2018;35(7):715-720.   Published online July 1, 2018
DOI: https://doi.org/10.7736/KSPE.2018.35.7.715
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Design of Tip Clearance in the D.D.I. Process to Manufacture Pressure Vessel
J. Korean Soc. Precis. Eng.. 2018;35(7):715-720.   Published online July 1, 2018
DOI: https://doi.org/10.7736/KSPE.2018.35.7.715
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Design of Tip Clearance in the D.D.I. Process to Manufacture Pressure Vessel
Image Image Image Image Image Image Image Image Image Image Image Image
Fig. 1 CNG pressure vessel
Fig. 2 Process to manufacture CNG pressure vessel
Fig. 3 D.D.I. process to manufacture the liner of CNG pressure vessel
Fig. 4 The tip clearances in the D.D.I. process used in the actual field
Fig. 5 Cross sectional areas (A31, A32) after the drawing and ironing processes in the 3rd stage
Fig. 6 Punch and die dimensions of D.D.I. process
Fig. 7 3D model for forming analysis of the 3rd stage
Fig. 8 Generation of mesh
Fig. 9 Strain-flow stress curve of 34CrMo4 according to temperature
Fig. 10 Coulomb friction coefficient and share friction factor of 34CrMo4 provided by Forge NxT 2.0
Fig. 11 Forming load according to time when tip clearance is -20%
Fig. 12 Liner shape after the 3rd stage when tip clearance is -20%

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Design of Tip Clearance in the D.D.I. Process to Manufacture Pressure Vessel
Tip clearance (%) dp3 (mm) dd31 (mm) di32 (mm)
0 328.31 346.41 337.86
-5 328.76 345.96 338.31
-10 329.22 345.50 338.77
-15 329.67 345.05 339.22
-20 330.12 344.60 339.67
Tip clearance (%) A31 (mm2) A32 (mm2) ΔA3 (%)
0 9,589.50 4,996.67 48.89
-5 9,110.03 5,003.46 45.08
-10 8,630.55 5,010.25 41.95
-15 8,151.08 5,017.03 38.45
-20 7,671.60 5,023.82 34.51
Tip clearance
(%)		 Maximum
drawing load (ton)		 Maximum
ironing load (ton)
0 595.44 730.8
-5 632.55 539.77
-10 641.15 486.09
-15 681.50 455.83
-20 697.56 431.84
Tip clearance
(%)		 t31
(mm)		 t32
(mm)		 Δt23→31
(mm)		 Δt31→32
(mm)
0 9.05 4.78 0.00 4.27
-5 8.60 4.78 0.45 3.82
-10 8.14 4.78 0.91 3.37
-15 7.69 4.78 1.36 2.92
-20 7.24 4.78 1.81 2.46
Theory FEM Error
Drawing load 783.54 ton 697.56 ton 10.97%
Ironing load 473.84 ton 431.84 ton 8.86%
Table 1 Diameters of punches, drawing and ironing dies according to tip clearances of the 3rd stage
Table 2 Reduction ratios of cross sectional areas according to tip clearances of the 3rd stage
Table 3 Maximum drawing and ironing loads according to tip clearances of the 3rd stage
Table 4 Amounts of thickness reductions according to tip clearances of the 3rd stage
Table 5 Comparison of the forming loads obtained from theoretical calculation and that from FEM

Table 1

Table 2

Table 3

Table 4

Table 5

JKSPE : Journal of the Korean Society for Precision Engineering

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