CALCS PROC070
HYDRAULIC CYLINDER

CONTENTS

Guidance: Application, Input, Output & Theory
Notation
Input Data Format
Project Example
PROC070 Theory

GUIDANCE

APPLICATION

Hydraulic cylinders subject to hydraulic pressure on either side of the piston
See also: PROC013 PROC016 PROC037

INPUT TO PROCEDURE

Include 1Pr & DNV in section$ indicator as required.
Cylinders differ in configuration and to include checks on aspects as appropriate enter data as follows:
Nm_th<>0 for threaded connection strength
Nm_e<>0 for eyes under tension loading
Nm_chf<>0 for flat cylinder heads
Pb<>0 for bolt tension strength
The proc calculates an effective length on the basis of a perfectly stiff cylinder and flexible ram.
The cylinder hoop stress is related to the ram force (+ve tension or -ve compressive) acting on an annular surface or disc respectively.

OUTPUT FROM PROCEDURE

Buckling & yield strength checks

THEORETICAL BASIS

1st Principles, DNV CN 2.9 & API 2C AnnexD

NOTATION

Nmnumber material _c cylinder _th thread _e eye _chf cylinder head flat
AbCSA bolt - minor dia
Dbminor bolt diameter
Dco Dcicylinder outer & inner diameter
De deeye outer & inner diameter
Dro Drirod outer & inner diameter
fhcylinder hoop stress (tens +ve)
fdccylinder direct stress
fdrrod direct stress
Lram actual length for buckling
Lcram length closed
Leram Euler buckling length (effective)
Lsram design stroke max
phydraulic fluid pressure
pththread pitch
Pforce
Pbbolt tension force
Pcram compressive force (-ve)
Ptram tension force (+ve)
Peeye plate single force
Pmaxyielding force +ve or -ve
Plmaxforce compressive max length - for buckling
tthickness

INPUT DATA FORMAT

P."PROC070 HYDRAULIC CYLINDER 150726"
LET Nmc%=:Nmr%=:Ngrc%=:Ngrr%=:Nk%=:Nkb%=DNV
LET Dco=:Dci=:Dro=:Dri=0
LET Lcl=:Ls=:Lp=Lcl+1*Ls
LET Lf=(Lcl-Ls)/5:Lr=Ls+2*Lf:Lc=Lcl+Ls-Lr:Lbe=0
LET Pc=-1:Pcb=-1:Pt=0:REM Case 5 Elev 63deg
PROC070:REM General
PROC070a:REM DNV Buckling
PROC070b:REM DNV Cyl Thickness
LET Nm%=:Nk%=DNV:P=:Lth=:dth=:pth=:PROC070c:REM DNV thread shear?
LET Nm%=:P=Pt:t=:D=:d=:PROC070d:REM DNV Eye Plate Tension
LET Nm%=:Ngr%=:Nk%=API:tch=:Cf=.33:DF=3:Ew=1:REM API Data
PROC070e:REM API Cyl Head Flat
PROC070h:REM API Buckling TBC
PROC070i:REM API t_cyl
LET Nm%=:Ngr%:pth=:dmaj=:dmin=:Lth=:P=:DF=:PROC070j:REM API Thread Shear

PROJECT EXAMPLE

PROCtitle("Ax-H Hyd Cyl TBC"," "," ")
P."PROC070 HYDRAULIC CYLINDER 150726"
LET Nmc%=steel:Nmr%=steel:Ngrc%=S355:Ngrr%=S355:Nk%=DNV:Nkb%=DNV
LET Dco=49.5:Dci=40:Dro=30:Dri=0
LET Lcl=D01:Ls=D03:Lp=Lcl+1*Ls
LET Lf=(Lcl-Ls)/5:Lr=Ls+2*Lf:Lc=Lcl+Ls-Lr:Lbe=0
LET Pc=L11:Pcb=L01:Pt=0
PROC070:REM General
PROC070a:REM DNV Buckling
PROC070b:REM DNV Cyl Thickness

PROC070 HYDRAULIC CYLINDER 150726
LET Nmc%=steel:Nmr%=steel:Ngrc%=S355:Ngrr%=S355:Nk%=DNV:Nkb%=DNV
LET Nmc%=2:Nmr%=2:Ngrc%=2:Ngrr%=2:Nk%=3:Nkb%=3
LET Dco=49.5:Dci=40:Dro=30:Dri=0
LET Dco=49.5:Dci=40:Dro=30:Dri=0
LET Lcl=D01:Ls=D03:Lp=Lcl+1*Ls
LET Lcl=620:Ls=487:Lp=1107
LET Lf=(Lcl-Ls)/5:Lr=Ls+2*Lf:Lc=Lcl+Ls-Lr:Lbe=0
LET Lf=26.6:Lr=540.2:Lc=566.8:Lbe=0
LET Pc=L11:Pcb=L01:Pt=0
LET Pc=-403.6:Pcb=-308.2:Pt=0
Ax-H Hyd Cyl TBC - P070 Hydraulic Ram 150726 -
p= ABS(Pc)*4/(PI*Dci^2)= 0.3212
p= ABS(-403.6)*4/(3.142*40^2)= 0.3211
pt= Pt*4/(PI*(Dci^2-Dro^2))= 0
pt= 0*4/(3.142*(40^2-30^2))= 0
Ar= PI*(Dro^2-Dri^2)/4= 706.9
Ar= 3.142*(30^2-0^2)/4= 707
Ir= PI*(Dro^4-Dri^4)/64= 3.976E4
Ir= 3.142*(30^4-0^4)/64= 3.977E4
Ic= PI*(Dco^4-Dci^4)/64= 1.69E5
Ic= 3.142*(49.5^4-40^4)/64= 1.691E5
Ax-H Hyd Cyl TBC - P070 Cyl & Rod Stresses -
fh= p*(Dco^2+Dci^2)/(Dco^2-Dci^2)= 1.53
fh= 0.3212*(49.5^2+40^2)/(49.5^2-40^2)= 1.53
UF_059= fh/(dac(Nk%,Kd%)*mgr(Ngrc%,Fy%))= 0.9912
UF_059= 1.53/(0.4348*3.55)= 0.9912
fc= Pc/Ar= -0.571
fc= -403.6/706.9= -0.5709
UF_060= ABS(fc)/(dac(Nk%,Kd%)*mgr(Ngrr%,Fy%))= 0.3699
UF_060= ABS(-0.571)/(0.4348*3.55)= 0.3699
Ax-H Hyd Cyl TBC - P070 1stPr Buckling Length Lbe 150726 -
LET Lre=Lp-Lc:Lbe=Lre*3/2
LET Lre=540.2:Lbe=810.3
function was = TAN(PI*Lre/Lbe)+PI*Lc/Lbe
Bisection Method - 15 iterations to find soluton 843.1
Ax-H Hyd Cyl TBC - P070a DNV CN2.9 3.7.4 Buckling -
L= Lc+Lr= 1107
L= 566.8+540.2= 1107
Z= Lc/Ic+Lr/Ir+(1/Ir-1/Ic)*(L/(2*PI))*SIN(2*PI*Lc/L)= 0.01668
Z= 566.8/1.69E5+540.2/3.976E4+(1/3.976E4-1/1.69E5)*(1107/(2*3.142))*SIN(2*3.142*566.8/1107)= 0.01668
Pcr= mat(Nm%,E%)*PI^2/(L*Z)= 1106
Pcr= 2070*3.142^2/(1107*0.01668)= 1107
UF_062= ABS(Pcb)/(dac(Nkb%,Kcr%)*Pcr)= 0.6408
UF_062= ABS(-308.2)/(0.4348*1106)= 0.6409
Ax-H Hyd Cyl TBC - P070b DNV CN2.9 3.7.6 t_cyl -
Note: p & Fy same units and 0.3mm corrosion allowance neglected
t= p*(Dci/2)/(1*(mgr(Ngrc%,Fy%)*dac(Nk%,Kd%))*1-.5*p)= 4.645
t= 0.3212*(40/2)/(1*(3.55*0.4348)*1-.5*0.3212)= 4.645
UF_063= (2*t)/(Dco-Dci)= 0.9779
UF_063= (2*4.645)/(49.5-40)= 0.9779
END070