Advanced Tribology: Proceedings of CIST2008 & ITS-IFToMM2008

1033 Pages·2010·144.02 MB·English

by  Siwei Zhang (auth.), Prof. Jianbin Luo, Prof. Yonggang Meng, Prof. Tianmin Shao, Dr. Qian Zhao (eds.)

Jianbin Luo
Yonggang Meng
Tianmin Shao
Qian Zhao

Advanced Tribology
Proceedings of CIST2008 & ITS-IFToMM2008
Jianbin Luo
Yonggang Meng
Tianmin Shao
Qian Zhao

Advanced Tribology
Proceedings of CIST2008 & ITS-IFToMM2008

With 1609 figures
Editors
Prof. Jianbin Luo Prof. Yonggang Meng
State Key Laboratory of Tribology Tsinghua University State Key Laboratory of Tribology Tsinghua University
100084, Beijing, China 100084, Beijing, China
E-mail: [email protected]
E-mail: [email protected]

Dr. Qian Zhao
Prof. Tianmin Shao
State Key Laboratory of Tribology Tsinghua University
State Key Laboratory of Tribology Tsinghua University
100084, Beijing, China
100084, Beijing, China
E-mail: [email protected]
E-mail: [email protected]

ISBN 978-7-302-20422-0
Tsinghua University Press, Beijing

ISBN 978-3-642-03652-1 e-ISBN 978-3-642-03653-8
Springer Dordrecht Heidelberg London New York

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Content
Advanced Tribology
(cid:803)Proceedings of CIST2008 &
ITS-IFToMM2008
Edited by:
Jianbin LUO, Yonggang MENG,
Tianmin SHAO, Qian ZHAO
State Key Laboratory of Tribology,
Tsinghua University, Beijing, China
Tsinghua University Press Springer
1
Preface
Preface
The 5th China International Symposium on Tribology (CIST 2008), conjugated with the 1st International
Tribology Symposium of IFToMM (ITS - IFToMM 2008), was held from September 24 to 27, 2008 in Beijing,
China. The symposium was jointly organized by the State Key Laboratory of Tribology (Tsinghua University), the
State Key Laboratory of Solid Lubrication (Lanzhou Institute of Chemical Physics, Chinese Academy of
Sciences), and the Tribology Institution of Chinese Mechanical Engineering Society. Increasing activities in the
area of tribology of academia and industry in recent years were discussed during the symposium. Overall, a total of
463 abstracts were accepted for presentation and 378 participants took part in 41 oral sessions or in the poster area.
We gratefully acknowledge the financial support for the symposium from the National Natural Science
Foundation of China, International Federation for the Promotion of Mechanism and Machine Science (IFToMM),
STLE (USA), the State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics (China),
China University of Mining and Technology, SAE Magnetics (H.K.) Ltd. (Hongkong, China), NSK Ltd. (Japan),
ETT (Eureka Think Tank) (Japan) and Quaker Chemical (China) Co. Ltd. (USA).
The symposium brought tribologists together from industry to academia all over the world for the purpose of
sharing their research information and viewpoints. The topics of the symposium included:
Subjects Organizers
Prof. Yuanzhong Hu (China)
Lubrication
Prof. Jane Wang (USA)
Prof. Zhongrong Zhou (China)
Friction and wear
Prof. Valentin L. Popov (Germany)
Prof. Yonggang Meng (China)
Micro/Nano-tribology
Prof. Dae-Eun Kim (R. Korea)
Prof. Tianmin Shao (China)
Tribology of coatings, surface and interface
Prof. A. Erdemir (USA)
Prof. Shirong Ge (China)
Biotribology
Prof. Zhongming Jin (UK)
Prof. Weimin Liu (China)
Tribo-chemistry
Prof. S. Mori (Japan)
Prof. Xinchun Lu (China)
Industry tribology
Prof. Yongzheng Zhang (China)
We would like to thank all the organizers of the above subjects and the session chairs in the symposium. We
also would like to express our great gratitude to Profs. Siwei Zhang, Qunji Xue, Jianbin Luo, Hugh Spikes, and
Stven Granick, for their excellent plenary talks, to Profs. Y. Kimura, S. M. Hsu, W. M. Liu, Y. G. Meng, A.
Erdemir, and A.G. Wang, for their keynote speeches, to all of the invited presenters and all the participants in the
symposium.
In the social programme on Sep. 27, 2008, some participants took a short tour of the Beijing city, which just
successfully hosted the 29th Olympic Games and the Paralympics in August and September of 2008. Although the
I
Preface
games ended in a splendor of fireworks a few days before the symposium, many participants met the joy, the
warm, and the passion of Beijing in their journey. In the afternoon of Sep. 26, more than 100 participants visited
the State Key Laboratory of Tribology (SKLT), Tsinghua University, as the first state key laboratory in the field of
tribology in China and was established in 1988. Now there are more than 20 full-time staffs, about 20 part-time
research assistants, and 70 postgraduate students working on tribology in the laboratory.
The success of the symposium depends heavily on the colleagues and students in SKLT, and many friends
who played a role in organization. We would like to thank Profs. Yonggang Meng, Tianmin Shao, Hui Wang,
Xinchun Lu, Drs. Xiangjun Zhang, Yu Tian, Qian Zhao, Chenhui Zhang, Haosheng Chen, Jiadao Wang, Dan Guo,
Tianbao Ma, and Ms. Yuhua Qi, Ms. Xiaochen Chen, as well as Dr. Aiyang Zhang, Dr. Jingyun Fan, for their great
contribution to the symposium. We would also like to thank our student volunteers for their excellent works.
We now look forward to the 6th China International Symposium on Tribology to be held in 2011 in Lanzhou,
China.

Shizhu Wen

Jianbin Luo
State Key Laboratory of Tribology
Tsinghua University, Beijing 100084, China
II
Content
Content
Plenary Lectures
Current Industrial Activities of Tribology in China...........................................................................................Siwei Zhang(cid:3) 3
The Fullerene-Like Nanostructure Hydrogenated Carbon Films with Super-Low Friction....Qunji Xue, Junyan Zhang(cid:3) 4
Tribology in Nanomanufacturing—Interaction between Nanoparticles and a Solid Surface..........J. B. Luo, D. Guo(cid:3) 5
Tribology at Small Scales.....................................................................................................................................Steve Granick(cid:3) 11
Frontiers of Research in Liquid Lubrication.................................................................................................Hugh A. Spikes(cid:3) 12

Keynote Talks
EHL with Grease at Low Speeds..............................................................Yoshitsugu Kimura, Toshiaki Endo, Daming Dong(cid:3) 15
The Nature of Adhesion and Friction.............................................................................................................Stephen M. Hsu(cid:3) 20
Space Tribology of China........................................................................................................................................Weimin Liu(cid:3) 21
Active Control of Sliding Friction...................................................................................................Yonggang Meng, Yu Tian(cid:3) 22
Superhard and Low Friction Nanocomposite Coatings: Design, Synthesis, and Applications
.............................................................................................A. Erdemir, O. L. Eryilmaz, M. Urgen, K. Kazmanli, V. Ezirmik(cid:3) 23
Tribology of Metal-on-Metal Bearings at High Inclination Angles
............................................................................................................Reginald Lee, Aaron Essner, Aiguo Wang, Shirong Ge(cid:3) 24

Technical Sessions
(cid:265). Lubrication
Key Factors to Induce Cavitation-Erosion (Invited)....................................Darong Chen, Jiadao Wang, Haosheng Chen(cid:3) 31
Mechanical and Tribological Properties of TiC-Reinforced HSS-Based Composites with an Interpenetrating
Network for High Temperature Self-Lubrication Applications......................................Yanjun Wang, Zuomin Liu(cid:3) 32
Friction and Wear Characteristics of Advanced Space Lubricants (Invited)
................................................................................................Nobuyoshi Ohno, Sobahan Mia, Shigeki Morita, Shingo Obara(cid:3) 38
Lubrication Analysis of Journal Bearing and Rotor System Using CFD and FSI Techniques
...................................................................................................................Huiping Liu, Hua Xu, Peter Ellison, Zhongmin Jin(cid:3) 40
Oil Film Behavior under Minute Vibrating Conditions in EHL Point Contacts
........................................................................................................................Chen Feng, Taisuke Maruyama, Tsuyoshi Saito(cid:3) 42
Different Loading and Motion Applied on Hip Simulators Affects the Lubrication of
Metal-on-Metal Hip Implants...................................................Leiming Gao, Fengcai Wang, Peiran Yang, Zhongmin Jin(cid:3) 44
EHD Lubrication of Different Types of Gears...............................................................................................Vilmos Simon(cid:3) 46
The Role of Heat Partition in Elastohydrodynamic Lubrication (Invited)
.......................................................................................................................H. P. Evans, A. Clarke, K.J. Sharif, R.W. Snidle(cid:3) 48
Influence of Surface Roughness on Elastohydrodynamic Journal Bearings with Non-Newtonian Lubricants
................................................................................................................Chatchai Aiumpornsin, Mongkol Mongkolwongrojn(cid:3) 50
Theoretical Investigation of Journal Bearings with Non-Newtonian Fluids Included Thermal Effects
................................................................................................................Mongkol Mongkolwongrojn, Chatchai Aiumpornsin(cid:3) 52
Magnetic Fluid Based Squeeze Film Behavior between Transversely Rough Curved Plates
...........................................................................................................G.M.Deheri, Rakesh M. Patel, Nikhilkumar D. Abhangi(cid:3) 54
III
Content
Engine Lubrication System Analysis and Oil Pump Design Optimization..............................................Quanbao Zhou(cid:3) 56
Temperature-Dependent Rheology and Tribology of Lubrication Greases Investigated with New Flexible
Platform for Tribological Measurements on a Rheometer...............................................Jörg Läuger, Patrick Heyer(cid:3) 61
Study on Characteristic Parameters of Wear Particle Boundary...................................................Guobin Li, Delin Guan(cid:3) 64
Viscosity Variation Model and Its Application in Micro/Nano-Scale Clearance
.............................................................................................................................Dong Chun-liu, Zhang Chao-hui, Wang Yan(cid:3) 70
Numerical Solving Method for the Structural Stiffness of Gas Foil Bearings.........Geng Haipeng, Qi Shemiao, Yu Lie(cid:3) 75
Biotribological Properties of Natural Swine Joint Cartilage...................................................Cui Tao, Xiong Dangsheng(cid:3) 81
Effect of Surface Texturing on Lubrication Film Formation within Non-Conformal Contacts
.....................................................................................I. K(cid:2)upka, M. Hartl, R. Poliš(cid:3)uk, M. Vaverka, M. Vrbka, O. Šamánek(cid:3) 84
Experimental Investigation of Time-Dependent Oil Film Pressure in a Dynamically Loaded Journal Bearing
.............................................................................................................................Sun Meili, Xia Chengyong, Wang Xiangang(cid:3) 86
Experimental Research and Numerical Simulation of LY12 and HPb62-2 Ring Compression
......................................................................................................................Bin Guo, Feng Gong, Chunju Wang, Debin Shan(cid:3) 94
Application of Metal Self-Repairing Additives on Cylinder-Piston Ring Rubbing Pairs
.......................................................................................Lei Wang, X. C. Zhou, Q. Q. Li, C. Q. Yuan, X. P. Yan, Y. H. Chen(cid:3) 98
Wettability Study of Multiply-Alkylated Cyclopentanes (MACs) on Silicon Substrates.....Ying Wang, Mingwu Bai(cid:3) 102
Numerical Analysis on Hydrodynamics of Circular Translational Polishing under Mixed Lubrication
......................................................................................................................................................................W. Zhai, P. Feng(cid:3) 104
Micro-Tribological Analysis of POM-MoS2-Compounds.........................................R. Stengler, S. Schraube, X. G. Hu(cid:3) 109
On Lubrication Characteristics of Dual Tori Double-Enveloping Toroidal Worm Drive
...................................................................................................Yaping Zhao, Wenjun Wei, Xuezhu Dong, Jiancheng Zhou(cid:3) 110
Thermoelastohydrodynamic Lubrication Analysis of Crankshaft Bearing Considering Crankshaft
Deformation under Load..........................................................................................Jun Sun, Jianglin Liu, Changlin Gui(cid:3) 112
Transient Behavior of Elasto-Metal-Plastic Journal Bearing during the Stage of Stop
................................................................................................................................Jian Jin, Guoxian Zhang, Xiaojing Wang(cid:3) 116
Analyses on the Splashing Parameters of High-Speed Oil Impacted a Wall in Jet Lubrications
..................................................................................................................Le Gu, Zhenghuan Ye, Liqin Wang, Dezhi Zheng(cid:3) 120
Interferometry Measurement of Spinning Effect on Sliding EHL...........................................F. Guo, X. M. Li, B. Fan(cid:3) 122
Effect of Wide Dimples on Planar Contact Lubrication.....Jiadao Wang, Zhongling Han, Haosheng Chen, Darong Chen(cid:3) 125
Friction Properties and Microstructure of Al-Cu-Fe Nano Films........................Zhou Xi-ying, Liu Yan-hui, Xu Zhou(cid:3) 127
Tribological Properties of Ti6Al4V Alloy by FOTS Self-Assembled Monolayers Modification Treatment
...............................................................................................................................................Sun Changguo, Zhang Huichen(cid:3) 130
Influence of Spinning Effect on the Rolling EHL Films............................................................X. M. Li, F. Guo, B. Fan(cid:3) 134
A Study on Lubrication Characteristics between Piston Ring and Cylinder Bore of Bent-Axis Type Piston Pump
............................................................Jae-Youn Jung, Ihn-Sung Cho, Il-Hyun Beak, Hyun-Il Shin, Jae-Cheon Jo, Lu Hong(cid:3) 136
The Fabrication and Lubricant Performance of MoS2 Nanotubes Arrays.......................Caihong Sun, Changsheng Li(cid:3) 140
The Research on the Lubricant Aging under Durability Test of the Porous Sliding Bearings
..................................................................................................................Giemza Boleslaw, Kaldonski Tadeusz, Krol Artur(cid:3) 142
Models for Predicting Friction Coefficient and Parameters with Influence in Elastohydrodynamic Lubrication
.................................................P. Lafont Morgado, J. Echávarri Otero, J. B. Sánchez-Peñuela Lejarraga, J. L. Muñoz Sanz,
A. Díaz Lantada, J. M. Muñoz-Guijosa, H. Lorenzo Yustos, P. Leal Wiña(cid:3) 144
Elastohydrodynamic Film Thickness in Elliptical Contacts with Rolling and Spinning........................Tae-Jo Park(cid:3) 146
Experimental Study on the Tribological Properties of Pure Powder Lubrication under Plane Contact
......................................................................................................................Wang Wei, Liu Xiaojun, Liu Kun, Li Hongxian(cid:3) 151
IV
Content
Hydrodynamic Analysis and Experiment Verification of the High-Pressure Small-Flow Centrifugal Pump
................................................................................................................................Li Bao-liang, Jiang Qin-Yu, Pan Xing-he(cid:3) 153
Effect of Liquid Surface Tension and Viscosity on Micro-Bubble Induced by External Electric Field
..........................................................................................................................................................Xie Guoxin, Luo Jianbin(cid:3) 155
Study of Water Lubrication in Sliding Point Contact Friction Pairs with Hydrophobic Surfaces
............................................................................................................Zhizuo Ma, Chenhui Zhang, Shuhai Liu, Wenshi Zhu(cid:3) 157
A Simplified Numerical Elastic-Plastic Contact Model for Rough Surfaces
.............................................................................................Zhanjiang Wang, Wenzhong Wang, Yuanzhong Hu, Hui Wang(cid:3) 159
Film Characteristics of Grease in Point Contact under Micro-Swaying Motion
.............................................................................................Li Gang, Zhang Chenhui, Luo Jianbin, Liu Shuhai, Lu Xinchun(cid:3) 167
Effects of Solid Body Temperature on the Non-Newtonian Thermal EHL Behavior in Point Contacts (Invited)
.......................................................................................................................................................Xiaoling Liu, Peiran Yang(cid:3) 169
Numerical Analysis on Dynamic Characteristics of Flying Magnetic Head with Ultra Thin Spacing
......................................................................................................................................................Yao Hua-ping, Huang Ping(cid:3) 171
The Analysis of Higher Guide Bearing Pad Temperature and Its Fault Diagnosis
...........................................................................................................................Mei Gui, Gao Zhi, Liu Ying, Liu Xiangfeng(cid:3) 175
Pitting Life Prediction Based on a 3-D Line Contact Mixed EHL Analysis and Subsurface von Mises Stress
Calculation (Invited)................................................................................................Dong Zhu, Ning Ren, Q. Jane Wang(cid:3) 178
Numerical Lubrication Simulation of Metal-on-Metal Hip Joints: Ball-in-Socket Model and Ball-on-Plane Model
.......................................................................Wenzhong Wang, Fengcai Wang, Zhongmin Jin, D. Dowson, Yuanzhong Hu(cid:3) 180
Deterministic Simulation of Surfaces in Conformal-Contact Lubrication (Invited)
.....................................................................................................Shangwu Xiong, Chih Lin, Jane Q. Wang, Yansong Wang(cid:3) 182
Simulation and Experimental Validation of the Effect of Surface Texture on Fluid Film Formation
.............................................................................................Zhang Jinyu, Meng Yonggang, Le Chengning, Hideki OGATA(cid:3) 184
Marangoni Stress and Its Effects on the Flow in an Evaporating Sessile Droplet..............Xuefeng Xu, Jianbin Luo(cid:3) 186
Film Forming Characteristics of Oil-in-Water Emulsion with Super-Low Oil Concentration
...................................................................................................................................Ma Liran, Luo Jianbin, Zhang Chenhui(cid:3) 188
A Piston Lubrication Model Considering the Coupling between the Piston Secondary Motion and the
System Inertia Variation in an IC Engine.........................Xiaoxiang Zhang, Zhinan Zhang, Ping Wang, Youbai Xie(cid:3) 191
Analysis of the Combined Effect of the Surface Roughness and Inertia on the Performance of High-Speed
Hydrostatic Thrust Bearing..........................................................Yang Xuebing, Xiong Wanli, Lü Lang, Hou Zhiquan(cid:3) 197
Study on the Efficiency of the New-Style Reducer with the Green Lubricant
...............................................................................................Hu Junhong, Jin Yingli, Guo Dan, Ding Jinyuan, He Weidong(cid:3) 202
Pressure Dependence of the Limiting Shear Stress Coefficient of Liquid Lubricants......G. T. Y. Wan, P. L. Wong(cid:3) 206
A Method of Dual Number for the Aerodynamic Property Analysis of Gas-Lubricated Mechanism:
Self-Pressurizing Thrust Bearings and Non-Contacting Face Seals...............Wanfu Xu, Bin Geng, Chunjing Shi(cid:3) 211
A Model for the Calculation of the Micro-Pores Number of Compressively Molded Polyimide Porous
Materials.................................................................................................Yuping Pu, Jianmin Chen, Peng Zhao, Qunji Xue(cid:3) 216
Frictional Dynamics in a Two Dimensional Frenkel-Kontorova Model with Square Lattice Symmetry
...............................................................................................Ju-na Wei, Cang-long Wang, Wen-shan Duan, Jian-min Chen(cid:3) 220
Advances in investigation of Elasto-Aerodynamic Lubrication in Compliant Foil Bearings (Invited)
.........................................................................................................................................Lie Yu, Shemiao Qi, Haipeng Geng(cid:3) 225
Normal Stress Effects in Journal Bearing Lubrication with Maxwell Fluid
.........................................................................................................Li Xiaodi, Chen Haosheng, Chen Darong, Wang Jiadao(cid:3) 231
V
Content
(cid:266). Friction and Wear
Analysis of Bearing Outer Ring Creep with FEM..............................Jianjun Zhan, Kinji Yukawa, Hiromichi Takemura(cid:3) 237
Effect of Content of MoS on Sliding Tribological Behavior of Copper-Based Powder Metallurgy Materials
2
under Electrical Current..........Shangguan Bao, Zhang Yongzhen, Xing Jiandong, Sun Lemin, Hu Daochun, Qiu Ming(cid:3) 239
Research on Frictional Wear Properties of C/C Composite with Electric Current
...............................................................................................................L. X. Jia, Y. Z. Zhang, J. Li, L. M. Sun, Y. W. Zhao(cid:3) 242
Friction Behavior of C/C-SiC Braking Composites Fabricated by Warm Compacted-in situ Reaction
.....................................................................................................................Zhuan Li, Peng Xiao, Xiang Xiong, Su-hua Zhu(cid:3) 246
Tribological Properties of Hybrid Ag SiW O Nanoparticles Multilayer Films
4 12 40
..............................................................................................................Yanbao Guo, Deguo Wang, Siwei Zhang, Yuqi Xiao(cid:3) 250
Study on Fatigue Crack Behavior of Rail in Different Curve Radius..............Wen Zhong, Wenjian Wang, Qiyue Liu(cid:3) 255
Improvement in Wear Resistance of TiNi Alloy Processed by Equal Channel Angular Extrusion and
Annealing Treatment.......................................................................................................................Z. H. Li, X. H. Cheng(cid:3) 257
Self-Healing of a Soft Primer Coating Caused by Plasticization during Sliding against UHMWPE
...............................................................................................................Pieter Samyn, Koenraad Bonny, Gustaaf Schoukens(cid:3) 260
Performance of an Infinitely Long Transversely Rough Hydrodynamic Slider Bearing
....................................................................G. M. Deheri, Chandaniben D. Changela, H. C. Patel, Nikhilkumar D. Abhangi(cid:3) 262
Investigation on Fretting Fatigue Behavior of Ti811 Alloy at Elevated Temperature...Xiaohua Zhang, Daoxin Liu(cid:3) 264
Dry Sliding Wear Behavior of a Tribological Couple: Spray-Deposited Al-Si/SiC Composites/Brake Pads
p
......................................................................................................................................Teng Jie*, Chen Ding, Chen Zhenhua(cid:3) 268
Wear Behaviors of a Cu-Based Bulk Metallic Glass under Various Gas Atmosphere
........................................................................................................................................G. Q. Zhang, L. N. Wang, H. Z. Liu(cid:3) 270
A Study of the Correlation between Gear Wear and Vibration........Cao Yibo, Xie Xiaopeng, Liu Yan, Ding Tianhuai(cid:3) 273
Study on the Relationship between Microstructural Change in Friction-Induced Deformation Layer and
Friction Behavior of Austenitic Stainless Steel..............................Xue Zongyu, Zhou Sheng, Wei Xicheng, Li Jian(cid:3) 278
Abrasive Wear Behavior of Several Metallic Materials under Simulated Sand-Dust Environment
......................................................................................................................................................Chunxia Li, Fengyuan Yan(cid:3) 283
Wear Behavior of Plasma-Nitrided 2Cr13 Martensitic Stainless Steel under Air and Vacuum
............................................................................................Yang Jianqun, Liu Yong, Ye Zhuyu, Yang Dezhuang, He Shiyu(cid:3) 285
Sealing Performance and Wear Mechanism of PTFE Oil Seal.......................Ye Zibo, Huang Xing, Liang Rongguang(cid:3) 287
Fretting Corrosion Wear of Synergy between Mechanical and Electrochemical for Biomaterials in Hanks
Balanced Salt Solution.....................................................................................................................Li Ji-wu, A. Iwabuchi(cid:3) 292
Torsional Fretting Behaviors of UHMWPE against Different Counter-Bodies (Invited)
...................................................................................................................Z. B. Cai, M. H. Zhu, J. Yu, S. X. Qu, Z. R. Zhou(cid:3) 298
An Experimental Study on the Rotational Fretting Wear Behavior of LZ50 Steel
.............................................................................................................................J. L. Mo, M. H. Zhu, Z. J. Liao, Z. R. Zhou(cid:3) 300
Comparative Study of Tribological Properties with Different Fibers Reinforced PTFE/PEEK Composites
at Elevated Temperatures.........Mu Liwen, Feng Xin, Zhu Jiahua, Wang Huaiyuan, Sun Qingjie, Shi Yijun, Lu Xiaohua(cid:3) 302
Research on Friction Characteristic of End Faces of Mechanical Seals...............L. Wei, B. Q. Gu, X. Feng, J. J. Sun(cid:3) 304
Failure Mechanism of Hadfield Steel Crossing.....F. C. Zhang, B. Lv, T. S. Wang, C. L. Zheng, Q. Zou, M. Zhang, M. Li(cid:3) 309
Synthesis and Tribological Behavior of Surface Coated Cu Nanoparticles in Liquid Paraffin
............................................................................................Ling Zhang, Lei Chen, Hongqi Wan, Jianmin Chen, Huidi Zhou(cid:3) 311
Tribological Behaviors at High Load of MoS Films in Vacuum
2
....................................................................Xinxin Ma, Gang Wang, Guangze Tang, Yong Liu, Shiyu He, Dezhuang Yang(cid:3) 313
VI