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2G1计算书
目录
1.中法兰强度计算·······················································································2
2.闸阀力计算·······························································································8
3.闸板、阀杆拉断计算·············································································10
4.闸板应力计算·························································································13
5.压板、活节螺栓强度计算·····································································15
1.基本条件:
公称通径DN50mm,公称压力PN1.6MPa,阀体材料CF8,闸板材料CF8,阀杆材料0Cr18Ni9,密封面材料CF8
2.中法兰计算
2.1输入参数
2.1.1基本参数:
口径(DN)=50mm
压力等级(CLASS)=150LB
阀种(TYPE)=闸阀
设计温度(T0)取常温380C。
设计压力(P)按GB/T1224-2005取值15.3kgf/cm2
法兰许用应力(FQB)按ASME第Ⅱ卷(2004版)材料D篇表1A,乘以铸件系数0.8
取值138MPa(14Kgf/mm2)
螺栓许用应力按GB/T3098.6-2000表2抗拉强度为700MPa,根据钢铁材料手册不锈钢卷提供的抗拉许用应力安全系数取3--4,取n=3.5。
抗剪许用应力是抗拉许用应力的0.5--0.8,取0.7。
所以抗剪许用应力为:
[τ]=700MPa÷3.5×0.7=140MPa=14.29kgf/mm2
垫片密封压力,按ASME第Ⅷ卷(2004版),取值Y=7.03,垫片系数取值M=3.00
2.1.2法兰基本尺寸
垫片宽度N=4.5mm,垫片外径D=98mm,
斜度高度H=16.6mm,壁厚G0=6.5mm,根部厚G1=G0+H/5=9.82mm
法兰内径BB=50mm,法兰外径A=165mm,螺栓中心距C=125mm,法兰有效厚度T=16mm
螺栓公称直径d=3/4”,螺栓数量n=4
2.1.3法兰形状系数
2.1.3.1法兰斜度修正系数f
根据按ASME第Ⅷ卷第一册(2004版)P304图2-7.6查得,取F=1.00
2.1.3.2一体形法兰计算系数F按ASME第Ⅷ卷第一册(2004版)P302图2-7.2,取FF=0.880
2.1.3.3一体形法兰计算系数V按ASME第Ⅷ卷第一册(2004版)P302图2-7.3,取V=0.410
2.2计算说明
2.2.1考虑腐蚀余量1mm后的参数调态(法兰计算尺寸)
中腔直径BB=BB+2=52mm,壁厚G0=G01-1=5.5mm,根部厚G1=G1-1=8.82mm
2.2.2垫片有效宽度B,按ASME第Ⅷ卷第一册(2004版)P300表2-5.2,B=4.5mm
2.2.3垫片压紧力作用中心圆直径G=D-2B=98-2×4.5=89mm
2.2.4法兰根部应力修正系数f=1
2.2.5系数G1/G0=9.82/6.5=1.51
2.2.6系数H/H0=H/(BB×G0)1/2=16.6/(50×5.5)1/2=1
2.2.7系数K=A/BB=3.3
2.2.8系数U=[K2(1+8.55246lgk)-1]/[1.36136(K2-1)(K-1)]
=[3.32×(1+8.55246lg3.3)-1]/[1.36136×(3.32-1)×(3.3-1)]
=1.879
2.2.9系数Y=[0.66845+5.7169K2lgK/(K2-1)]/(K-1)
=[0.66845+5.7169×3.32×lg3.3/(3.32-1)]/(3.3-1)
=1.710
2.2.10系数Z=(3.32+1)/(3.32-1)=1.202
2.2.11系数TT=[K2(1+8.55246lgk)-1]/[(1.04720+1.9448K2)(K-1)]
=[3.32×(1+8.55246×lg3.3)-1]/[(1.04720+1.9448×3.32)×(3.3-1)]
=1.689
2.2.12系数L=[T×FF(BB×G0)1/2+1]/TT+T3/[U×(BB×G0)1/2/V]
=[16×0.88×(52×5.5)1/2+1]/1.689+163/[1.879×(52×5.5)1/2/0.41]
=194.42
2.2.13内压力产生的全载荷HH=π×G2×P/400=π×892×15.3/400=951.35N
2.2.14使用状态下,需要的最小垫片压紧力(HP)
HP=π×B×G×M×P/50=π×4.5×89×3×15.3/50=1154.45N
2.2.15使用状态下,需要的最小螺栓载荷Wm1(WM1)
WM1=HH+HP=951.35+1154.45=2105.8N
2.2.16紧固状态下,需要的最小螺栓载荷Wm2(WM2)
WM2=π×B×G×Y=π×4.5×89×1.710=2150.44N
2.2.17使用状态下,需要的最小螺栓有效截面积Am1(AM1)
AM1=WM1/BQB=2105.8/14.29=147.36mm2
2.2.18紧固状态下,需要的最小螺栓截面积Am2(AM2)
AM2=WM2/BQB=2150.44/14.29=150.49mm2
2.2.19需要的最小螺栓有效截面积(AM),取AM1,AM2中的最大值,即AM=150.49mm2
2.2.20实际使用螺栓总有效截面积AB=BS×N=230.75×4=923mm2
2.2.21使用状态螺栓载荷WO=WM1=2105.8N
2.2.22紧固状态螺栓载荷
WG=(AM+AB)×BQB/2=(150.49+923)×14.29/2=7670.06N
2.2.23内压力作用于法兰内径截面的载荷
HHD=π×BB2×P/400=π×522×15.3/400=32.94N
2.2.24垫片载荷
HHG=WO-HH=2105.8-951.35=1154.45N
2.2.25内压力产生的全载荷与内压力作用于法兰内径截面的载荷之差
HHT=HH-HHD=951.35-32.94=918.41N
2.2.26螺栓中心至HHD作用点的距离
HD=(C-BB)/2-0.5G1=(125-50)/2-0.5×9.82=32.59mm
2.2.27螺栓中心至HHG作用点的距离
HG=(C-G)/2=(125-89)/2=18mm
2.2.28螺栓中心至HHT作用点的距离
HT=[(C-BB)/2+HG]/2=[(125-52)/2+18]/2=27.25mm
2.2.29内压力作用于法兰内径截面的弯矩
MD=HHD×HD=32.94×32.59=1073.51N.mm
2.2.30垫片载荷所需的弯矩
MMG=HHG×HG=1154.45×18=20780.1N.mm
2.2.31HHT产生的弯矩
MT=HHT×HT=918.41×27.25=25026.67N.mm
2.2.32使用状态下,作用于法兰的全弯矩
M0=MD+MMG+MT=1073.51+20780.1+25026.67=46880.28N.mm
2.2.33紧固状态下,作用于法兰的弯矩(MG)
MG=WG×(C-G)/2=7467.81×(125-89)=268841.2N.mm
2.2.34法兰轴向应力计算内径
当BB<20×G1且F1≥1,SS=BB+G0=50+6.5=56.5mm
2.2.35使用状态法兰轴向应力
QH0=F×MO/(L×G12×SS)==1×46880.28/(194.42×9.822×56.5)
=0.044Kgf/mm2≤FQB合格
2.2.36使用状态法兰径向应力
QR0=[1.33T×FF/(BB×G0)1/2+1]×M0/(L×T2×BB)
=[1.33×16×1/(52×6.5)1/2+1]×46880.28/(194.42×162×52)
=0.039Kgf/mm2≤FQB合格
2.2.37使用状态法兰周向应力
QT0=Y×M0/(T2×BB)-Z×QR0=1.71×46880.28/(162×52)-1.202×0.039
=5.975Kgf/mm2≤FQB合格
2.2.38使用状态合成应力
Q00=(QH0+QR0)/2=(0.044+0.039)/2=0.0415Kgf/mm2≤FQB合格
Q01=(QH0+QT0)/2=(0.044+5.975)/2=3.01Kgf/mm2≤FQB合格
2.2.39紧固状态法兰轴向应力
QHG=F×MG/(L×G12×SS)=1×268841.2/(194.42×9.822×619.5)
=13.6Kgf/mm2≤1.5FQB合格
2.2.40紧固状态法兰径向应力
QRG=[1.33T×FF/(BB×G0)1/2+1]×MG/(L×T2×BB)
=[1.33×16×0.88/(52×6.5)1/2+1]×268841.2/(194.42×162×52)
=1.4Kgf/mm2≤FQB合格
2.2.41紧固状态法兰周向应力
QTG=Y×MG/(T2×BB)-Z×QRG=11.88Kgf/mm2≤FQB合格
2.2.42紧固状态合成应力
QG0=(QHG+QRG)/2=(13.6+8.71)/2=11.16Kgf/mm2≤FQB合格
QG1=(QHG+QTG)/2=(13.6+6.49)/2=10.05Kgf/mm2≤FQB合格
2.2.43螺栓应力
BOLT=0.0703π×CLASS×D2/4AB
=0.0703π×600×6482/(4×27561.36)=505Kgf/cm2≤633Kgf/mm2合格
2.2.44垫片最小有效宽度
N-MIN=AB×BQB/(2π×G×Y)
=27561.36×17.6/(2π×631.28×4.869)≤22合格
3.闸阀力的计算
3.1密封比压计算
3.1.1介质静压力FJ
阀座密封内径d1=48mm阀座密封面宽W=10mm
介质压力按ASMEB16.34-2004取值P=1.6MPa
FJ=[π(d1+w)2×P]/4=[π(48+10)2×1.6]/4=2640.74N
3.1.2所需密封力Fm
密封所需比压
q=[(3.5+P)/(0.1×w)1/2]×1.4=[(3.5+1.6)/(0.1×10)1/2]×1.4=7.14MPa
Fm=π(d1+w)×w×q=π(48+10)×10×7.14=13003.368N
3.1.2密封面比压Sa
Sa=[(d1+w)2×P]/(4d1×w)=[(48+10)2×1.6]/(4×48×10)
=2.8MPa≤250MPa(250MPa为STL.6的许用密封比压)
3.2压紧力Ft计算
3.2.1关闭时闸板上的轴向力F1:
θ:
闸板楔半角θ=50
φ:
密封面摩擦角取u=0.2φ=tg-10.2=11.30°
F1=FJtg(θ+φ)=1815972.7×tg(2.86660+11.30)=487533.8N
3.2.2介质作用于阀杆的轴向力
阀杆直径d=18mm
F2=(π/4)d2×P=(π/4)×182×1.6=406.944N
3.2.3阀杆与填料的摩擦力F3:
杆与填料摩擦系数u1=0.1;填料总高h=39mm
Pp:
压套作用于填料的面压力Pp=25MPa
F3=u1πdhPp=0.1×π×70×53.9×25=29618.1N
Ft=F1+F2+F3=487533.8+39272.8+29618.1=529424.6N
3.3扭矩的计算
3.3.1阀杆与阀杆螺母的摩擦的扭矩T1
阀杆螺纹中径dm=65.616mm,阀杆螺纹导程l=16.93mm
阀杆螺纹升角β=arctg(l/πdm)=arctg[16.93/(π×65.616)]=4.70°
按《阀门设计》表9-5摩擦系数u2=0.15
摩擦角ρ=arctg(u2)=arctg(0.15)=8.53°
摩擦半径RFM=dM/(2tg(β+ρ))=dm(l+u2πdm)/[2(πdm+u2.l)]
=65.616×(16.93+0.15×π×65.616)/[2×(π×65.616+0.15×16.93)]
=7.525mm
T1=Ft×RFM/1000=529424.6×7.52/1000=3984N.m
3.4阀杆强度计算
[σ]:
阀杆许用应力,对ASTMA182F6a即1Cr13阀杆调质200~230HB,根据ASTMA370,σb=650~760MPa,取[σ]=σb/3=217MPa
阀杆螺纹小径ds=61.47mm
阀杆压应力σ=4×Ft/(π×ds×ds)
=4×529424.6/(π×61.47×61.47)=178.5MPa
σmax=0.5×σ×(1+sqrt(1+16×tg(β+ρ)×tg(β+ρ)))
=0.5×178.5×(1+sqrt(1+16×0.195×0.195))
=202.4MPa≤[σ]合格
4.闸板、阀杆拉断强度计算
4.1阀杆螺纹的拉断力PL(见下图)
螺纹中径dm=65.616mm(见右图)
螺纹小径di=61.47mm
阀杆材料抗拉强度按ASTMA182F6a,200~230HB硬度,
根据ASTMA370,对应的:
σb=650MPa
阀杆平均直径下的截面积Sg
Sg=π/4×[(dm+di)/2]2
=π/4×[(65.616+d61.47)/2]2=3165.3mm2
PL=Sg.σb=3165.3×650=2057445.0N
4.1.1I-I断面的拉断力P
I-I截面的面积SI=3696.9mm2
PI=SI.σb=3696.9×650=2402985.0N
4.1.2Ⅱ-Ⅱ断面的剪切力τII
Ⅱ截面的剪切面积SII=4620mm2
τII=2×SII×0.6×σb=2×4620×0.6×650=3603600N
4.1.3I-I截面的安全系数
nI=PI/PL=2402985.0/2057445.0=1.17≥1.1合格
4.1.4Ⅱ-Ⅱ断面的安全系数
nII=τII/PL=3603600/2057445.0=1.94≥1.5合格
4.2闸板的拉断计算(见下图)
闸板头部示意图
截面为2ד┫”的拉断计算(见下图)
截面为2ד┫”形的闸板梯形槽示意图
闸板材料抗拉强度,按ASME第Ⅱ卷D(2004版)篇表1A,
闸板材质WCB(20)取σb=485MPa
4.2.1I-I断面的合成力PW
e1=(aH2+bd2)/(2×(aH+bd))=(170×55.82+99×502)/[2×(170×55.8+99×50)]=26.91mm
e2=H-e1=55.8-26.91=28.89mm
h=e1-d=26.91-50=-23.09mm
惯性矩JX=[B.e13/-bh3+a.e23]/3={269×29.893/[-99×(-23.09)3+]a.e23}/3=3519937.7mm4
力臂L=(C-A)/4+e2=(85-51)/4+28.89=37.39mm
截面模量wX1=JX/e2=3519937.7/28.89=121839.3mm3
I-I断面的面积SI=bd+aH=99×50+170×55.8=14436mm2
PW=2σb/(L/wX1+1/SI)=2×650/(37.39/121839.3+1/14436)=2578752.3N
4.3Ⅱ-Ⅱ断面的剪应力
Ⅱ-Ⅱ断面的面积SII=(N-M).B=(88-45)×269=7310mm2
PT=2×SII×0.6×σb=2×7310×0.6×650=4254420N
4.4I-I断面的安全系数
nI=Pw/PL=2578752.3/2057445=1.36≥1.05合格
4.5Ⅱ-Ⅱ断面的安全系数
nII=Pτ/PL=4254420/2057445=2.17≥1.65合格
5.闸板应力计算
5.1闸板的应力
闸板应力计算示意图
设计压力P=10.21MPa;
通道半径a=232mm;闸板中轴半径b=150mm;闸板单板厚h=48mm
泊松比v=0.3
闸板材料应力强度值,根据ASME第Ⅱ卷D篇(2004版)表2A
材质为WCB取Sm=161MPa
5.2简支,内周边固定(垂直方向可移动),沿内周作用分布载荷
A11=1/2×{(1-v)×a2/[(1+v)a2+(1-v)b2]}[1-(1+2lna/b)(a2/b2)]
=1/2×{(1-0.3)×2322/[(1+0.3)×2322+(1-0.3)×1502]}×{1-[1+2ln(232/150)]×(2322/1502)}
=-0.77
B11=2b2/[(1+v)a2+(1-v)b2][(1+v)lna/b+1]
=2×1502/[(1+0.3)×2322+(1-0.3)×1502][(1+0.3)×ln(232/150)+1]
=0.82
σ11=3b2P/4h2{2(1+v)(A11+lna/b-(1-v)(1-B11a2/b2)}
=3×1502×10.21/4×482×{2×(1+0.3)×(-0.77+ln(232/150)-(1-0.3)×[1-0.82×(2322/1502)]}
=144.74MPa≤Sm合格
5.3简支,内周边固定(垂直方向可移动),受均布连续载荷
A15=1/4{a2/[(1+v)a2+(1-v)b2]}{(3+v)a2/b2+(1-v)[(4lna/b+3)a2/b2-2]}
=1/4×{2322/[(1+0.3)×2322+(1-0.3)×1502]}×{(3+0.3)×2322/1502+(1-0.3)×[(4×ln(232/150)+3)×2322/1502-2]}
=8.05
B15=b2/[(1+v)a2+(1-v)b2]{(3+v)-[(5+v)+4(1+v)lna/b]b2/a2}
=1502/[(1+0.3)×2322+(1-0.3)×1502]×{(3+0.3)-[(5+0.3)+4(1+0.3)×ln(232/150)]×1502/2322}
=0.04
σ15=3Pa2/8h2{(3+v)b2/a2+4(1+v)(A15+lna/b)b2/a2-(1-v)(2b2/a2+B15×a2/b2)}
=3×10.21×2322/8×482{(3+0.3)×1502/2322+4(1+0.3)(8.05+ln(232/150))×1502/2322-(1-0.3)(2×1502/2322+0.04×2322/1502)}
=90.11MPa≤Sm
总计算应力:
σ0=〡σ11〡+〡σ15〡=144.74+90.11=234.85MPa≤1.5Sm
5.4中腹厚t
密封面平均直径C=476mm
t=[sqrt(1.24×10.21/161)]×476=66.7mm
故闸板中腹厚取67mm
6.压板与活节螺栓的计算
6.1活节螺栓的计算
压板与活节螺栓计算示意图
填料函直径DS=95.4mm;阀杆直径ds=70mm,活节螺栓孔距L=220mm
压套作用于填料的面压力取Pp=25MPa
螺栓的许用应力σ1:
按ASME第Ⅱ卷(2004版)材料D篇表3,螺栓材质B7,取σ1=17.6kgf/mm2.
螺栓内径dso={[(Ds2-ds2).Pp]/(2σ1)}1/2={[(95.42-702)×25]/(2×17.6)}1/2=17.47mm
故选取1-8活结螺栓.
6.2压板计算
压板外圆D=134mm;压板内孔直径d1=74mm
压板应力强度值根据ASME第Ⅱ卷D篇(2004版)表2A,
材质为WCB(20),取Sm=161MPa
由高使用压力决定的载荷PY
PY=(π/4)((Ds2-ds2).Pp=(π/4)×((95.42-702)×25=82447.8N
压板厚度h={6PY.L/[5(D-d1)Sm]}1/2={6PY×220/[5×(134-74)×161]}1/2=47.5mm
实际厚度为52mm,合格.
6.3销轴计算
销轴剪应力τ=110.4MPa
销轴直径ds=[PY/(π.τ)]1/2=[82447.8/(π×110.4)]1/2=15.42mm
实际直径为20mm,合格.
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