HYDRAULIC HYDRAULIC CYLINDER CYLINDER

LOAD LOAD CAPACITYCAPACITY

VIC 26-27 May 2008

WP 2 DESIGN BY ANALYSIS• T2.1 STRUCTURAL ANALYSIS

Objectives: Buckling theoretical model of H.C for several boundary conditions

WP 6 TESTING AND MONITORING PROCEDURES• T6.1.1 FIELD TESTING• T6.1.2 LAB TESTING

Objectives: Experimental lab buckling of H.C for several boundary conditions(Bench Tests)Field buckling tests of H.C using real machines: Farm loader and back-hoeIndoor buckling tests of H.C using a real mini back-hoe machine

WORK PERFORMED DURING THE LAST PERIOD (37-48 months)

1. Bench tubular rods experimental buckling tests.

2. Bench experimental buckling tests with hydraulic cylinder with tubular rods

3. Bench experimental tests with hydraulic cylinder rods in order to evaluate the material resistance properties (Bending and Tensile Tests)

4. Visual Basic software for the mathematical model evaluation

5. Experimental tests with tubular rods filled with ceramic material(collaboration with BCE)

6. Collaboration with IFTR and ROQUET for a new design method for H.C based on probabilistic design

7. Field Tests: (Collaboration with HIDRAR)• Indoor test with backhoe (HIDRAR/UPC)

(cylinders and rods)

• Field test with backhoe (HIDRAR-BMH)

Factors Affecting Actuator Load Capacity

STATE OF THE ART year EXP

Initial Imperfection

Friction Torques

Load Eccentricity

Actuator Weight Fluid

Hoblit, Fred.Critical buckling for hydraulic actuating cylinders.

1950 is considered

is considered

K.L SeshasaiStress Analysis of Hydraulic Cylinders.

1975 as initial data

is considered

(Hoblit)

Bennett, M.CA Calculation of Piston rod Strength.

1978 as initial data

only for piston rod articulation

reaction in piston rod articulatio

n

Ravishankar, N.Finite Element Analysis of Hydraulic Cylinders.

1980

elastic rigidity in

connection point

as a distributed

load

Chai Hong YooColumn loadings on telescopic power cylinders.

1986 through FEMthrough

FEMthrough

FEM

S. BaragettiBending behaviour of double-acting hydraulic actuators.

2001initial

definition as sinusoidal

Equivalents for both

sides

Norma ISO/TS 13725(ISO/TC131 subcom. SC3) 2001

is considered

is considere

d

is considered

(Hoblit)

Yishou T., Wenwei, W.Stability analysis for hydraulic hoist cylinder of hi l k it t

2004is

considered

distributed load in

tube and d

is considered

(Hoblit)

Important parameters have been considered to achieve a better knowledge about H.CBUCKLING PHENOMENA:

1- Misalignment : rod / cylinder tube

2- Interaction in pin/bushing joint (Friction)

• Clearance between gland and rod• Cylinder body deformation due to oil pressure (CIMNE)• Guide ring wear effect (TRELLEBORG SS)

• Friction torques in hydraulic cylinder end joints

3-Mechanism layout effect on load capacity

( )

22 1 1 1 1 1 1 2 1 2 1 1 1

1 1 1 2 21 1

2 22 1 2

2 2 2 1 2 22

22 1 1 2 1 1 1 2

2 1 2 1 3 2 22

cos( ) cos( )( ) 0 0 1 02

0 cos( ) sen( ) 0 0 02 2

0 cos( ) sen( ) 1 02

L k L L q k L QL q L L q L qsen k L CPL P P PL P PPk k P

q L L qQk L k L C q qP P P P k P

L L QL q L L L q qk L k L C qPL PL PL P P k P

k

− − + − − −

− − − −

⎛ ⎞− − − − −⎜ ⎟⎝ ⎠

−( )

1

1

L

( )1 1 1 11 1 1 2 2 1 2 2 1 1 1

1

22 1 1 1 1

1 2 1 2

01 1 1 1 2 2

1

02 2 2 2 2

2

sencos( ) sen( ) cos( ) 0 1 0 sen

0 0 0 02

1 1 10 0 0 0

1 10 sen( ) cos( ) 0 0

c

C C C

Ce

Ce

k k L qk L k k L k k L Y k LP Pk

L L q L QLK P K K K q L LL L L

Y Qk M q L q LPL PL L P L

Y Qk k L k k L MPL PL L PL

θ θ

− − −

⎛ ⎞− − + + −⎜ ⎟

⎝ ⎠⎡ ⎤− − − + −⎢ ⎥⎣ ⎦

− − +

C

PP

=

THEORETICAL MODEL MATRIX

M23

3 = 4

2

13

14

4

3

2

M32

B

A

12

VA

M14

23

O

1st Caseω 2 > ω3 > 0

34(∞)

3 = 4

2

13

2

34( )

B

AVA 23

3

4

14

12 O

M23

M14

Actuator as a component of the mechanism

2nd Caseω3 > ω2 > 0

ANG. VELOCITY of rod is positive and

TORQUE in rod pin is positive

ROD TORQUE POWER IS POSITIVE ANG. VELOCITY of rod is positive and

TORQUE in rod pin is negative

ROD TORQUE POWER IS NEGATIVE

M23 is ACTIVE TORQUE M23 is RESISTIVE TORQUE

Experiments with hydraulic cylinders

ROD DIAMETER : 30mmGLAND DIAMETER :

30 30,2 30,4 30,6

Previous Experimental work

60

65

70

75

80

85

90

29,5 30 30,5 31 31,5 32 32,5

Diametro de Tapones (mm)

Car

ga m

áxim

a ad

mis

ible

(kN

)

D. D. taptapóónn (mm)(mm) 3030 30,230,2 30,430,4 30,630,6 3131 3232ImperfecciImperfeccióónn inicialinicial ΘΘ1 1

((gradosgrados)) 0,1360,136 0,1980,198 0,2750,275 0,3410,341 0,4730,473 0,8020,802

Pin diameter = 22mm and bush diameter = 25,6 mm

Gland diameter (mm)

Max

. Loa

d (k

N)

Theoretical model(frictionless)

Experimental results(frictionless)

Bush 25,6 mm

Gland mm

Misalig. Angle ( º )

Theoretical Model vs Experimental Results (frictionless)

60

80

100

120

140

160

180

29,8 30,3 30,8 31,3 31,8

Gland Internal Diameter (mm)

Max

. Adm

issi

ble

Load

(kN

)

Ajuste valores medios medidos, pasador de 25,6mm

Ajuste valores medios medidos, pasador de 22mmGland

Diameter (mm)

Θ1 (grades)

3030 0,1360,136

30,230,2 0,1980,198

30,430,4 0,2750,275

30,630,6 0,3410,341

3131 0,4730,473

3232 0,8020,802

FRICTION and FRICTIONLESS JOINTS COMPARISON

Full pin (25,6mm)=bushing

Small pin (22mm) and bushing=25,6mm

Including Friction

Frictionless

Pressure

Deflection

STRAINGAUGES

Strain gauges for bending moment measurement along the rod

225 225 30

567 mm

Lado 21 2 3

Lado 1

BENDING MOMENT DISTRIBUTION along ROD for several LOADS

-200

-100

0

100

200

300

400

500

0 100 200 300 400 500 600

position (rod side) X (mm)

Bend

ing

mom

ent (

N m

)

100 bar

200

300

400

500

600

700

750

770

Bending torques measured through strain gauges

225 225 30

567 mm

Lado 21 2 3

Lado 1

REAL BI-ARTICULATED CYLINDERS

DUMPER TRUCKP

Mechanisms (examples) Real behaviour

bi-articulated

Clamped-articulated with torques

bi-articulated with torques of different sense

Bi-articulated with torques of same sense

PP

P

Me2Me1

PP

Me1

M2

Carga

P

PP

M2M1

P

PP

M2M1

Bench experimental tests with hydraulic cylinder rodsin order to evaluate the material resistance properties

(Bending and Tensile Tests)

WORK PERFORMED DURING THE LAST PERIOD (37- 48 months)

UNIVERSAL TESTING MACHINE (3 Points Bending test)

H.Tubes St 37

30X20 and 30X24mm

L= 500mm

TUBE ROD

BENDING STRESS DETERMINATION

(TUBE AND BAR ROD BENDING TESTS)

Rod F-11430mm diameterL= 500mm

BAR ROD

Test NºMachine

(Limit force)(kN)

Max. load (Elastic Zone)

(kN)

Equivalent Stress(MPa)

1 25 15 707

2 200 14 660

.EXPERIMENTAL BENDING RESULTS WITH BAR RODS(30mm diameter and L=500mm)

Average: 684MPa

Tube Nº Wall Thickness

(mm)

Load(kN)

Equiv. Stress(MPa)

1 3 8 639

2 3 8,15 651

3 5 12,5 735

4 5 12,4 728

EXPERIMENTAL RESULTS WITH TUBULAR RODS(30/24 and 30/20 mm external/internal diameters)

Average: 688MPa

UNIVERSAL TESTING MACHINE (3 Points Bending test)

Tube 30X20mm

L=500mm

Load (kN)

Deflection (mm)

Tensile testmaterial-F114

specimen 15,2 mm diamter

0

100

200

300

400

500

600

0 0,0025 0,005 0,0075 0,01 0,0125 0,015

Strain (adimensional)

Stre

ss (M

Pa)

TENSILE TESTS

EXPERIMENTAL BUCKLING OF H.C(USING TUBULAR RODS)

ADVANTAGES:

1- H.C WEIGHT REDUCTION

2- ECONOMICAL IMPACT

3- ON-LINE MONITORING (SENSORS INSIDE ROD)

4- AESTHETIC ASPECT

Tube thickness

Pin Diameter

Test Nº Buckling Load

3 mm 22 mm 4 32,75 kN3 mm 22 mm 5 31 kN3 mm 25,6 mm 3 68,38 kN3 mm 25,6 mm 6 72,1 kN5 mm 22 mm 11 42,68 kN5 mm 22 mm 12 43,49 kN5 mm 25,6 mm 10 97,16 kN

TUBULAR RODS BUCKLING(30mm external diameters)

H.C Length (mm)

Experimental Load(kN)

EULERLoad(kN)

Relative "Error"

(%)1220 49 31,1 36,531320 36,8 26,6 27,7131420 29 23 20,681645 18,4 17,1 7,06

EXPERIMENTAL LOAD vs EULER LOAD- Tubular rods 30/24mm - Frictionless boundary conditions( SAME PIPE but DIFFERENT ROD LENGTH)

Standard

Bar- Exp.

Tube-Euler

Bar-EulerTube-Exp.

H.C Length(mm)s

CriticalLoad(kN)

EXPERIMENTAL H.C BUCKLING SUMMARY

Frictionless boundary conditions (Joint pin 22mm)

Tubular rods 30/24mm

Exper=Euler

Standard length

FRICTIONLESS

Critical Load(kN)

H.C Length(mm)

X

FRICTION BOUNDARY CONDITIONS (Pin joint 25,6mm)Tubular Rod 30/24mm)

Tube-Euler

Tube-Exp.

Bar-Euler

Tube-Exp.

Standard

WITH FRICTION

25,6 (pin)22 (pin)

Inertia (cm4)

rod (30)

tube(30x20)

tube(30x24)

167

88

3,94

102

70

3,19

73

49

2,35

0

20

40

60

80

100

120

140

160

180

Load

(KN

)

Buckling of hydraulic cylinderL= 1220 mm

25,6 (pin)22 (pin)

Inertia (cm4)

rod (30)

tube(30x20)

tube(30x24)

128,4

49,4

3,97

97,16

43,1

3,19

70

32

2,35

0

20

40

60

80

100

120

140

160

180

Load

(KN)

Buckling of simple rodsL= 1350 mm

L= 1350 mm

SUMMARY RESULTS

HYDRAULIC CYLINDERS SIMPLE RODS

BUCKLING OF TUBE RODS FILLEDWITH CERAMIC MATERIAL

BCE-UPC

BUCKLING TEST BENCH

Force cell(5000 pounds)

Bi-articulated rod(diam. 6mm) (L= 250 mm)

Bi-Clamped rod (6mm diameter)

Full sectionWith ceramic

Annular section

Ceramic filling

Rods with ceramic core –BCE/UPC

Full section Annular section Annular+Ceramic

BUCKLING TEST RESULTS- RODS

0

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

pin-pin lamp-clamp

lamp-clamp

pin-pin lamp-clamp

lamp-clamp

pin-pin lamp-clamp

lamp-clamp

Com

pr. F

orce

(N)

Euler model

FIELD TESTS

• Indoor test with backhoe (HIDRAR/UPC)(cylinders and rods)

• Field test with backhoe (HIDRAR-BMH)

Indoor tests with backhoe (HIDRAR/UPC)(cylinders and rods)

BACKHOE FRAME

MASTER CYLINDER

Cylindersubstituted by a simple rod(forbucklingpurposes)

MASTER CYLINDERMechanical advantage=8

BACKHOE

Rod test on backhoe machine

Rod D ext D int L

FULL SECTION 15 0 1.24020 0 1.24025 0 1.24030 0 1.240

ANNULAR SECTION 15 9 1.24020 14 1.24025 19 1.24030 24 1.240

1

2

4

3

1

2

4

3

Pressure (Master)

1

2

4

3

34 2

1Starting torque curve

Torque curve (just before buckling)

34 2

1

Starting torque curve

Torque curve (just before buckling)

Mid term curve

time

FARM LOADER

P3

P2P1

P3P4

Stre

ss (

MP

a)

Deflection rod curve

Moment curve

M 0

ISO 13.725Excel sheet application

FINAL CONCLUSIONS 1- ISO Standard 13725 does not include the misalignments and adherence

pin/bushing friction effects.2- adherence or friction pin/bushing represent a factor of 3 compared with ideal

bi-articulated joints.3- hydraulic cylinder own weight (aprox 100 N) has a negligible influence on

load capacity (only 2% reduction of load capacity)4- misalignment due to guide ring wear ( 5 % due to 1000 cycles) has a higher

influence on load capacity (reduction of load capacity about 10 %)

6- In real machines,mechanism layout can modify the hydraulic cylinder load capacity during the kinematics cycle due to the friction torques in pin/bushing joints. The friction torque can be an ACTIVE TORQUE or aPASSIVE TORQUE, depending on mechanism kinematics. Thisinnovative result has been demonstrated by the experimental bucklingresults experiments applied on real machines(Farm loader and Backhoe).

7- Buckling experimental results showed that tubular rods filled with ceramicmaterial did not gave the expected results

5- In the hydraulic cylinder tested, an eccentric load of 1 mm, reduced the load capacity about 12 %

ACHIEVEMENTS BEYOND THE STATE OF THE ART

•A theoretical model for different boundary conditions was developed and experimentally validated, describing the cylinder load capacity, including all those important factors affecting its load capacity, such as:

•Misalignment between cylinder rod and cylinder body due to assembly tolerances •Misalignment due to guide rings wear•Misalignment due to oil pressure•Frictions at end bearing supports and•Cylinder own weight.

•ISO 13725Excel sheet application for different boundary conditions has been developed. •Several typographic mistakes have been detected in ISO 13725 and should be transmitted to ISO Committee through UNACOMA/AIFTOP.•The mathematical model is implemented by Excel worksheet, using Visual Basic software, forload capacity and piston-rod diameter evaluations.•Experimental data base creation with more than 100 hydraulic cylinders which have been destructed using the buckling test bench for cylinder’s load capacity calculation.•Experimental results on real machines (Farm loader and Backhoe) demonstrated that layoutcan modify the hydraulic cylinder load capacity during the kinematics cycle, due to the friction torque in pin/bushing joints.