Stress Analysis of Flange Ring Stress Analysis of Flange Ring under Preload Condition (1) Coordination Analysis of Flange Ring and Shell Deformation Analysis Total Radial Displacement of Flange Ring: w0f=wp0sf+wM0sf+wM0Hf Total External Torque: M0H=p0b(D0b-D0g)2=p0bS0 is obtained by the assumptions (2) and (5): wM0sf=0; wM0Hf=0; wp0sf=0.

Axial stress of the flange ring: The axial stress of the flange ring at the edge is equal to the axial stress of the shell at the edge. According to the assumption (4), the bending stress of the casing under the action of the edge moment M0s (here, the axial direction) is S0z=12M0sxD3, the flange ring is in contact with the inner edge of the casing, ie, x=-D2, reaching the axial direction. The maximum value of the compressive bending stress; at the point of contact with the outer edge of the casing, i.e., x = D2 reaches the maximum value of the axial tensile bending stress. x=D2, the axial stress reaches its maximum value (S0z)max=6M0sD2.

The radial stress of the flange ring is equal to the sum of the bending stress caused by the moment M0r and the radial stress caused by the edge force p0s. S0r=12M0rzt3f-p0sf, M0r=M0s-p0st3f2 The flange ring reaches the maximum value of the radial tensile stress at the inner diameter, z=tf2 (ie point a) 6M0rt2f-p0stf; and at the inner diameter of the flange ring, z When =-tf2 (ie, point b), the maximum value of the radial compressive stress is 6M0rt2f+p0stf.

The radial tensile stress of the flange ring at point a is greater than its compressive stress at point b. Therefore z = tf2, the radial stress maximum (S0r)max = 6M0rt2f - p0stf. The circumferential stress of the flange ring is equal to the sum of the circumferential bending stress caused by the corner H0f and the circumferential film stress caused by the pressure -p0stf.

S0t=SH0ft+Sp0st=EfH0fzr-p0stfD0+Di2(D0-Di), lnD0Di≈2(D0-Di)D0+Di When r=Di2, z=tf2 (ie, point a), the flange ring is stretched circumferentially The maximum stress reaches EftfDiH0f+p0stflnD0Di; when r=Di2,z=-tf2 (ie, point b), the circumferential compressive stress of the flange ring reaches its maximum value EftfDiH0f-p0stflnD0Di.

The circumferential tensile stress of the flange ring at point a is greater than its compressive stress value at point b, so z=tf2, the circumferential stress maximum (S0t)max=EftfDiH0f+p0stflnD0Di. Flange ring torque analysis Figure 1.2.2 Stress analysis of flange ring under operation (1) Coordination analysis of flange ring and shell deformation Total radial displacement of flange ring wpf=wpsf+wMpsf+wMpHf+wpcf External torque MpH=ppgsp+p1(Dpb-Di2)+p2(2Dpb-Di-Dpg4) According to the assumptions (2) and (4), the radial displacement of the flange ring is wpf=0.

The total radial displacement of the shell wpH=wpsH+wMpsH+wpcH where: wpsH=pps2k3D; wMpsH=Mps2k2D; wpcH=pcD2i8EfD0(2-L) the total corner of the shell HpH=HpsH+HMpsH+HpcH;HpsH=-pps2k2D ;HMpsH=-MpskD; HpcH=0 According to hypothesis (4), the radial displacement of the flange ring and the casing are equal, the rotation angle is the same, ie wpf=wpH; Hpf=HpH and Hpf=12MptQEft3flnD0Di, Mpt=MpH+(Mps -ppstf2)PDi2PQ81 Supplement Zhang Qingya et al.: Strength Reliability Analysis of Gasket Bolt Flange Connection System Page4

Mps=MpHPDi+k3Dr3tfpc2EfD(2-L)-kr2t3fpclnD0Di12DiD(2-L)Eft3flnD0Di12kDDi+1+ktf2Hpf=MpHPDi+k2DD3ipc(2-L)(1+ktf)8EfDEft3flnD0Di6Di+(2+ktf) axis of the flange ring Directional stress: The axial stress at the edge of the flange ring is equal to the transverse stress of the shell at the edge. According to the hypothesis (6), the total axial stress of the shell under the action of the edge moment Mps and the internal pressure pc is Spz=12MpsxD3+pc(Di+D)4D. When x=D2, the axial tensile stress reaches the maximum value. It is 6MpsD2-pc(Di+D)4D; when x=-D2, the maximum value of axial compressive stress is 6MpsD2+pc(Di+D)4D.

The maximum value of the axial tensile stress is greater than its compressive stress. Therefore, the maximum axial stress (Spz)max=6MpsD2-pc(Di+D)4D. The radial stress of the flange ring: should be equal to the Mpr moment The sum of the induced bending stress, the internal pressure strength pc, and the radial stress caused by the edge force pps.

Spr=12Mprzt3f-ppstf+pc, Mpr=Mps-ppstf2 flange ring at the inner diameter, z=tf2 (ie point a) reaches the maximum value of radial tensile stress is 6M0rt2f-p0stf+pc; At the inner diameter, when z=-tf2 (ie, point b), the maximum value of the radial compressive stress is 6M0rt2f+p0stf-pc. The radial tensile stress of the flange ring at point a is greater than its compressive stress at point b. Therefore, z = tf2, the radial stress maximum (S0r)max = 6M0rt2f - p0stf + pc.