隔膜压缩机膜片破裂理论分析
|
摘要
隔膜压缩机膜片裂纹通常产生在支板最外圈环槽边沿及中间处,且裂纹呈周向分布,因此径向应力过大是导致膜片破裂的主要原因。隔膜压缩机中柱塞泵不稳定工作会导致油缸内油量不足,在此情况下当活塞运动到下止点时膜片会紧贴支板,环槽处膜片承受贴合支板引起的大挠度变形径向应力及环槽处附加变形引起的小挠度变形径向应力。该文利用薄板大挠度及小挠度理论对两种应力进行了求解,计算结果表明:当进气压力为1.7MPa,最外圈环槽两边沿处及中间处膜片总径向应力为272.6MPa、275.7MPa、220.4MPa,大于膜片许用径向应力170MPa,其中小挠度变形径向应力为140.1MPa、138.2MPa、107.4MPa,因此附加变形对膜片寿命影响很大。
The diaphragm fracture in a diaphragm compressor occurred frequently in the edge and middle regions above the outer circular groove of a perforated plate. The circumferential crack indicated that exceeded radial stress was the main reason of failure. Due to the oil shortage in an oil cylinder caused by the unstable operation of a plunger pump, the diaphragm would cling to the perforated plate while the piston reached the bottom dead center. The part of the diaphragm above the groove would endure radial stresses caused by the large deflection deformation while the diaphragm clung to the perforated plate, and by the additional deformation in the groove region, respectively. In this paper, two kinds of radial stresses were calculated with the theory of a thin plate with large and small deflections, respectively. When the suction pressure was 1.7MPa, the combined radial stresses in the two edges and the middle region of the outer groove were 272.6MPa, 275.7MPa and 220.4MPa, which all exceeded an allowable radial stress, 170 MPa. Meanwhile, the radial stresses caused by additional deformation were 140.1MPa, 138.2MPa and 107.4MPa. Thus, the fatigue life of a diaphragm was decreased by its additional deformation.
The diaphragm fracture in a diaphragm compressor occurred frequently in the edge and middle regions above the outer circular groove of a perforated plate. The circumferential crack indicated that exceeded radial stress was the main reason of failure. Due to the oil shortage in an oil cylinder caused by the unstable operation of a plunger pump, the diaphragm would cling to the perforated plate while the piston reached the bottom dead center. The part of the diaphragm above the groove would endure radial stresses caused by the large deflection deformation while the diaphragm clung to the perforated plate, and by the additional deformation in the groove region, respectively. In this paper, two kinds of radial stresses were calculated with the theory of a thin plate with large and small deflections, respectively. When the suction pressure was 1.7MPa, the combined radial stresses in the two edges and the middle region of the outer groove were 272.6MPa, 275.7MPa and 220.4MPa, which all exceeded an allowable radial stress, 170 MPa. Meanwhile, the radial stresses caused by additional deformation were 140.1MPa, 138.2MPa and 107.4MPa. Thus, the fatigue life of a diaphragm was decreased by its additional deformation.
引文
[1]郁永章,刘勇.特种压缩机[M].北京:机械工业出版社,1989:16.Yu Yongzhang,Liuyong.Special compressors[M].Beijing:China Machine Press,1989:16.(in Chinese)
[2]何福保,沈亚鹏.板壳理论[M].西安:西安交通大学出版社,1993:65.He Baofu,Shen Yapeng.Theory of plates and shells[M].Xi’an:Xi'an Jiaotong University Press,1993:65.(in Chinese)
[3]张国祥,魏伟.一种新型的C1阶协调任意四边形薄板弯曲单元[J].工程力学,2005,22(6):69―75.Zhang Guoxiang,Wei Wei.A new C1 conforming quadrilateral thin plate bending element[J].Engineering Mechanics,2005,22(6):69―75.(in Chinese)
[4]雷光宇,郑照北.薄板大挠度广义协调有限元分析[J].工程力学,2003,20(2):11―14.Lei Guangyu,Zheng Zhaobei.Large deflection analysis of thin plates using generalized conforming element[J].Engineering Mechanics,2003,20(2):11―14.(in Chinese)
[5]DaS ilva P P,Krauth W.Numerical solution of the von Karman equations for a thin plate[J].International Journal of Modern Physics C,1997,8(2):427―434.
[6]Qian Weichang,Ye Kaiyuan.On the large deflection of circular plate[J].Acta Physica Sinica,1954,10(3):209―238.
[7]Liu R H,Zou R P.Nonlinear bending of a corrugated circular plate with a plane boundary region a non-deformable rigid-body at center under compound load[J].International Journal of Non-linear Mechanics1993,28(3):353―364.
[8]秦力一.圆薄板卡门大挠度的两步变分解法[J].工程力学,1989,6(4):109―113.Ching Liyi.A two-step variational method on problems of Karman's for large deflection circle plate[J].Engineering Mechanics,1989,6(4):109―113.(in Chinese)
[9]Manfred D.Hofer diaphragm compressors[EB].http://www.andreas-hofer.de/E/down loads/diaphragmcompressor10-02.pdf,2012.
[10]王迪生,冯海芃.隔膜压缩机双函数构造膜腔曲面[J].西安交通大学学报,1989,23(3):25―32.Wang Disheng,Feng Haipeng.Design of diaphragm chamber curve surface shape with double function of a diaphragm compressor[J].Journal of Xi’an Jiaotong University,1989,23(3):25―32.(in Chinese)
[2]何福保,沈亚鹏.板壳理论[M].西安:西安交通大学出版社,1993:65.He Baofu,Shen Yapeng.Theory of plates and shells[M].Xi’an:Xi'an Jiaotong University Press,1993:65.(in Chinese)
[3]张国祥,魏伟.一种新型的C1阶协调任意四边形薄板弯曲单元[J].工程力学,2005,22(6):69―75.Zhang Guoxiang,Wei Wei.A new C1 conforming quadrilateral thin plate bending element[J].Engineering Mechanics,2005,22(6):69―75.(in Chinese)
[4]雷光宇,郑照北.薄板大挠度广义协调有限元分析[J].工程力学,2003,20(2):11―14.Lei Guangyu,Zheng Zhaobei.Large deflection analysis of thin plates using generalized conforming element[J].Engineering Mechanics,2003,20(2):11―14.(in Chinese)
[5]DaS ilva P P,Krauth W.Numerical solution of the von Karman equations for a thin plate[J].International Journal of Modern Physics C,1997,8(2):427―434.
[6]Qian Weichang,Ye Kaiyuan.On the large deflection of circular plate[J].Acta Physica Sinica,1954,10(3):209―238.
[7]Liu R H,Zou R P.Nonlinear bending of a corrugated circular plate with a plane boundary region a non-deformable rigid-body at center under compound load[J].International Journal of Non-linear Mechanics1993,28(3):353―364.
[8]秦力一.圆薄板卡门大挠度的两步变分解法[J].工程力学,1989,6(4):109―113.Ching Liyi.A two-step variational method on problems of Karman's for large deflection circle plate[J].Engineering Mechanics,1989,6(4):109―113.(in Chinese)
[9]Manfred D.Hofer diaphragm compressors[EB].http://www.andreas-hofer.de/E/down loads/diaphragmcompressor10-02.pdf,2012.
[10]王迪生,冯海芃.隔膜压缩机双函数构造膜腔曲面[J].西安交通大学学报,1989,23(3):25―32.Wang Disheng,Feng Haipeng.Design of diaphragm chamber curve surface shape with double function of a diaphragm compressor[J].Journal of Xi’an Jiaotong University,1989,23(3):25―32.(in Chinese)