ISO/PRF TS 13725

Hydraulic fluid power -- Method for evaluating the buckling load of a hydraulic cylinder

Transmissions hydrauliques -- Méthode d'évaluation de la charge de flambage d'un vérin hydraulique

General Information

• Status: Published
• ICS: 23.100.20 - Cylinders
• Technical Committee: ISO/TC 131/SC 3 - Cylinders
• Drafting Committee: ISO/TC 131/SC 3/WG 1 - Hydraulic cylinder mounting dimensions

RELATIONS

• Revised: ISO/TS 13725:2016 - Hydraulic fluid power -- Method for evaluating the buckling load of a hydraulic cylinder
• Effective Date: 24-Jul-2021

Standards Content (sample)

TECHNICAL ISO/TS
SPECIFICATION 13725
Third edition
Hydraulic fluid power — Method
for evaluating the buckling load of a
hydraulic cylinder
Transmissions hydrauliques — Méthode d'évaluation de la charge de
flambage d'un vérin hydraulique
PROOF/ÉPREUVE
Reference number
ISO/TS 13725:2021(E)
ISO 2021
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ISO/TS 13725:2021(E)
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© ISO 2021

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Published in Switzerland
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ISO/TS 13725:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Symbols and units ............................................................................................................................................................................................... 2

4.1 General ........................................................................................................................................................................................................... 2

4.2 Additional notations ........................................................................................................................................................................... 3

5 General principles ............................................................................................................................................................................................... 3

5.1 Purpose .......................................................................................................................................................................................................... 3

5.2 Description ................................................................................................................................................................................................. 3

5.3 Dimensional layout of hydraulic cylinder ........................................................................................................................ 4

5.4 Common calculation of maximum stress in the rod (for all mounting types) σ .....................

max 5

5.4.1 General...................................................................................................................................................................................... 5

5.4.2 Deflexion curve ...................................................................... ............................................................................................ 6

5.4.3 Bending moment ............................................................................................................................................................. 6

5.4.4 Maximum value of the bending moment .................................................................................................... 6

5.4.5 Maximum stress of the piston rod .................................................................................................................... 7

5.4.6 Mounting types of the cylinder tube and piston rod ........................................................................ 7

6 Case of pin-mounted hydraulic cylinders ................................................................................................................................... 8

6.1 Model of the hydraulic cylinder and unknown values .......................................................................................... 8

6.2 Linear system ........................................................................................................................................................................................... 8

6.3 Critical buckling load ......................................................................................................................................................................... 9

6.4 Greatest allowable compressive load .................................................................................................................................. 9

7 Case of hydraulic cylinders fixed at the beginning of the cylinder tube and pin

mounted at the end of the piston rod ...........................................................................................................................................10

7.1 Critical buckling load ......................................................................................................................................................................10

7.2 Linear system ........................................................................................................................................................................................10

8 Case of hydraulic cylinders pin mounted at the beginning of the cylinder tube and

fixed at the end of the piston rod ......................................................................................................................................................11

8.1 Critical buckling load ......................................................................................................................................................................11

8.2 Linear system ........................................................................................................................................................................................11

9 Case of hydraulic cylinders fixed at both ends ...................................................................................................................12

9.1 Critical buckling load ......................................................................................................................................................................12

9.2 Linear system ........................................................................................................................................................................................13

10 Case of hydraulic cylinders fixed at the beginning of the cylinder tube and free at

the end of the piston rod ...........................................................................................................................................................................14

10.1 Critical buckling load ......................................................................................................................................................................14

10.2 Linear system ........................................................................................................................................................................................15

11 Case of hydraulic cylinders fixed at both ends with free movement allowed at the

end of the piston rod .....................................................................................................................................................................................16

11.1 Critical buckling load ......................................................................................................................................................................16

11.2 Linear system ........................................................................................................................................................................................17

Annex A (informative) Example of numerical results ......................................................................................................................18

Bibliography .............................................................................................................................................................................................................................20

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ISO/TS 13725:2021(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso .org/

iso/ foreword .html.

This document was prepared by Technical Committee ISO/TC 131, Fluid power systems, Subcommittee

SC 3, Cylinders.

This third edition cancels and replaces the second edition (ISO/TS 13725:2016) which has been

technically revised.
The main changes compared to the previous edition are as follows:
— Formulae (18) and (27) have been corrected.
— The key to Figure A.1 has been corrected.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/ members .html.
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ISO/TS 13725:2021(E)
Introduction

Historically, cylinder manufacturers in the fluid power industry have experienced very few rod buckling

failures, most likely due to the use of adequately conservative design factors employed during cylinder

design and to the recommendation of factors of safety to the users. Many countries and some large

companies have developed their own methods for evaluating buckling load.

The method presented in this document has been developed to comply with the requirements

formulated by ISO/TC 131.
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TECHNICAL SPECIFICATION ISO/TS 13725:2021(E)
Hydraulic fluid power — Method for evaluating the
buckling load of a hydraulic cylinder
1 Scope
This document specifies a method for the evaluation of the buckling load which:

a) takes into account a geometric model of the hydraulic cylinder, meaning it does not treat the

hydraulic cylinder as an equivalent column,

b) can be used for all types of cylinder mounting and rod end connection specified in Table 2,

c) includes a factor of safety, k, to be set by the person performing the calculations and reported with

the results of the calculations,
d) takes into account possible off-axis loading,

e) takes into account the weight of the hydraulic cylinder, meaning it does not neglect all transverse

loads applied on the hydraulic cylinder,
f) can be implemented as a simple computer program, and
g) considers the cylinder fully extended.

The method specified is based on the elastic buckling theory and is applicable to single and double

acting cylinders that conform to ISO 6020 (all parts), ISO 6022 and ISO 10762. If necessary, finite

element analyses can be used to verify as well as to determine the buckling load.

The method is not developed for thin-walled cylinders, double-rods or plunger cylinders.

The method is not developed for internal (rod) buckling.
The friction of spherical bearings is not taken into account.
[2]

NOTE This method is based mainly on original work by Fred Hoblit . This method has been established in

[1]
reference to the standard NFPA/T3.6.37 .
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
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ISO/TS 13725:2021(E)
4 Symbols and units
4.1 General

The symbols and units used in this document are given in Table 1. See Figures 1 and 2 for labels of

dimensions and other characteristics.
Table 1 — Symbols and units
Symbol Meaning Unit

C stiffness of a possible transverse support at the free end of the piston rod N/mm

D outside diameter of the cylinder tube mm
D inside diameter of the cylinder tube mm
D outside diameter of the piston rod mm

e distance at the beginning of the tube where the loading of an eccentrically loaded mm

column is equivalent to a concentric axial force, F, and end moment, M = F [x] e
e distance at the end of the rod where the loading of an eccentrically loaded mm
column is equivalent to a concentric axial force, F, and end moment, M = F [x] e
E modulus of elasticity of cylinder tube material N/mm
E modulus of elasticity of piston rod material N/mm
F maximum allowable compressive axial load; modified by the factor of safety, N
(see k below), it creates in the piston rod a maximum stress equal to the yield
stress of the piston rod material
F Euler buckling load of the cylinder N
I moment of inertia of the cylinder tube mm
I moment of inertia of the piston rod mm
k factor of safety [see Clause 1, c)] —
L cylinder tube length (in accordance with Figure 1) mm
L piston rod length (in accordance with Figure 1) mm

L length of the portion of rod situated inside the cylinder tube, i.e. the distance mm

between the centre points of the piston and the piston rod bearing (in accord-
ance with Figure 1) with the rod fully extended
L length of the piston mm

M fixed-end moment at the beginning of the cylinder tube of a fixed hydraulic N·mm

cylinder
M moment at the junction of cylinder tube and piston rod N·mm

M fixed-end moment at the end of the piston rod of a fixed hydraulic cylinder N·mm

M maximum moment in the piston rod N·mm
max
R reaction at the beginning of the cylinder tube N
R reaction at the end of the piston rod N
R reaction between cylinder tube and position rod N
x distance from the end of a beam mm
y deflection of a slender beam at distance x mm
g gravitational acceleration mm/s

Δ elongation of the possible transverse support at the free end of the piston rod mm

θ angle (crookedness) between the deflection curve of the cylinder tube and the rad

deflection curve of the piston rod (see Figure 2)
ρ mass per unit volume of cylinder tube material kg/mm
ρ mass per unit volume of piston rod material kg/mm
σ stress N/mm
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ISO/TS 13725:2021(E)
Table 1 (continued)
Symbol Meaning Unit
σ yield point of a material N/mm
σ maximum compressive stress N/mm
max
φ angle of the deflection curve at the beginning of the cylinder tube rad
φ angle of the deflection curve at the end of the cylinder tube rad
φ angle of the deflection curve at the beginning of the piston rod rad
φ angle of the deflection curve at the end of the piston rod rad
ψ angle at the beginning of the cylinder tube (see Figure 2) rad
ψ angle at the end of the piston rod (see Figure 2) rad
4.2 Additional notations

The following additional notations are also used in this document (use Formulae (1) to (6)):

s = sin (q L) (1)
1 1 1
c = cos (q L) (2)
1 1 1
s = sin (q L) (3)
2 2 2
c = cos (q L) (4)
2 2 2
kF×
q = (5)
EI×
kF×
q = (6)
EI×

NOTE The origin of these notations (used for calculation) comes from the original work of Hoblit (see

Reference [2]).
5 General principles
5.1 Purpose

The cylinder is a system consisting of three parts (Figure 2). Two parts, the cylinder tube and the rod

outside of the tube, are considered as columns. This system is subject to compressive forces (F, -F). The

third part is the connection between these two parts in the form of the small piece of the rod inside the

tube and is modelled as a rotational spring. The purpose of this document is to determine the maximum

allowable force, F , that avoids reaching yield stress of the rod material, σ , as well as buckling.

max e
5.2 Description

The cylinder is in static equilibrium. The cylinder is subjected to a deformation due to the compression

forces (F, -F). This deformation is identified for each of the three parts of the cylinder by geometric

unknowns (angles) and static unknowns (forces, moments) and a specific relation (Hoblit model) due to

the rotational spring joining the cylinder tube and the rod.

Based on considerations of equilibrium and kinematics, a set of formulae is formulated. The type of

fixations (e.g. pin-mounted or fixed at the two ends) defines the number of unknown values (from 9 to

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ISO/TS 13725:2021(E)

13). There are as many formulae as unknown values. Six types of fixation are treated in this document

(Table 2).

The system of formulae can be solved for an F value previously set. However, it is important to establish

a particular value of F, noted F . F cancels the determinant of the system of formulae. This value should

c c

not be reached because it leads to an infinite value of the maximum stress of the rod (σ ).

max

It is therefore necessary to find the value of F (F ) between the zero value (in fact ε·F ) and F (in fact

max c c

[1- ε]·F ) that leads the stress in the rod to reach the yield stress of the rod material (when σ = σ ).

c max e
NOTE ε is a seed value used in the method of proport
...