# PD ISO TS 13725-2016

Hydraulic fluid power — Method for evaluating the buckling load of a hydraulic cylinder PD ISO/TS 13725:2016 BSI Standards Publication WB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06National foreword This Published Document is the UK implementation of ISO/TS 13725:2016. It supersedes BS ISO/TS 13725:2001 which is withdrawn. The UK participation in its preparation was entrusted by Technical Committee MCE/18, Fluid power systems and components, to Panel MCE/18/-/3, Cylinders. A list of organizations represented on this committee can be obtained on request to its secretary. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. © The British Standards Institution 2016. Published by BSI Standards Limited 2016 ISBN 978 0 580 89989 8 ICS 23.100.20 Compliance with a British Standard cannot confer immunity from legal obligations. This Published Document was published under the authority of the Standards Policy and Strategy Committee on 30 June 2016. Amendments/corrigenda issued since publication Date Text affected PUBLISHED DOCUMENT PD ISO/TS 13725:2016© ISO 2016 Hydraulic fluid power — Method for evaluating the buckling load of a hydraulic cylinder Transmissions hydrauliques — Méthode d’évaluation du flambage d’un vérin TECHNICAL SPECIFICATION ISO/TS 13725 Reference number ISO/TS 13725:2016(E) Second edition 2016-06-01 PD ISO/TS 13725:2016 ISO/TS 13725:2016(E)ii © ISO 2016 – All rights reserved COPYRIGHT PROTECTED DOCUMENT © ISO 2016, Published in Switzerland All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of the requester. ISO copyright office Ch. de Blandonnet 8 • CP 401 CH-1214 Vernier, Geneva, Switzerland Tel. +41 22 749 01 11 Fax +41 22 749 09 47 copyright@iso.org www.iso.org PD ISO/TS 13725:2016 ISO/TS 13725:2016(E)Foreword iv Introduction v 1 Scope . 1 2 Symbols and units . 1 2.1 General . 1 2.2 Additional notations . 2 3 General principles . 3 3.1 Purpose 3 3.2 Description . 3 3.3 Dimensional layout of hydraulic cylinder 3 3.4 Common calculation of maximum stress in the rod (for all mounting types) σ max. 5 3.4.1 Deflexion curve 6 3.4.2 Bending moment . 6 3.4.3 Maximum value of the bending moment 6 3.4.4 Maximum stress of the piston rod 7 3.4.5 Mounting types of the cylinder tube and piston rod 7 4 Case of pin-mounted hydraulic cylinders . 8 4.1 Model of the hydraulic cylinder and unknown values 8 4.2 Linear system . 9 4.3 Critical buckling load . 9 4.4 Greatest allowable compressive load .10 5 Case of hydraulic cylinders fixed at the beginning of the cylinder tube and pin mounted at the end of the piston rod .10 5.1 Critical buckling load 10 5.2 Linear system 10 6 Case of hydraulic cylinders pin mounted at the beginning of the cylinder tube and fixed at the end of the piston rod 11 6.1 Critical buckling load 11 6.2 Linear system 11 7 Case of hydraulic cylinders fixed at both ends .12 7.1 Critical buckling load 12 7.2 Linear system 12 8 Case of hydraulic cylinders fixed at the beginning of the cylinder tube and free at the end of the piston rod .13 8.1 Critical buckling load 13 8.2 Linear system 14 9 Case of hydraulic cylinders fixed at both ends with free movement allowed at the end of the piston rod .15 9.1 Critical buckling load 15 9.2 Linear system 15 Annex A (informative) Example of numerical results 17 Bibliography .19 © ISO 2016 – All rights reserved iii Contents Page PD ISO/TS 13725:2016 ISO/TS 13725:2016(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 on the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information The committee responsible for this document is ISO/TC 131, Fluid power systems, Subcommittee SC 3, Cylinders. This second edition cancels and replaces the first edition (ISO/TS 13725:2001), which has been technically revised.iv © ISO 2016 – All rights reserved PD ISO/TS 13725:2016 ISO/TS 13725:2016(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 Technical Specification has been developed to comply with the requirements formulated by ISO/TC 131.© ISO 2016 – All rights reserved v PD ISO/TS 13725:2016 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. NOTE This method is based mainly on original work by Fred Hoblit. [2]This method has been established in reference to the standard NF PA/T3.6.37. [1] 2 Symbols and units 2.1 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 1e outside diameter of the cylinder tube mm D 1i inside diameter of the cylinder tube mm D 2 outside diameter of the piston rod mm e a , e d distance where the loading of an eccentrically loaded column is equivalent to a concentric axial force F and end moment M = F [x] e mm E 1 modulus of elasticity of cylinder tube material N/mm 2 TECHNICAL SPECIFICATION ISO/TS 13725:2016(E) © ISO 2016 – All rights reserved 1 PD ISO/TS 13725:2016 ISO/TS 13725:2016(E) Symbol Meaning Unit E 2 modulus of elasticity of piston rod material N/mm 2 F maximum allowable compressive axial load; modified by the factor of safety, (see k below), it creates in the piston rod a maximum stress equal to the yield stress of the piston rod material N F critical Euler buckling load of the cylinder N I 1 moment of inertia of the cylinder tube mm 4 I 2 moment of inertia of the piston rod mm 4 k factor of safety [see Clause 1, c)] — L 1 cylinder tube length (in accordance with Figure 1) mm L 2 piston rod length (in accordance with Figure 1) mm L 3 length of the portion of rod situated inside the cylinder tube, i.e. the distance between the centre points of the piston and the piston rod bearing (in accord- ance with Figure 1) with the rod fully extended mm Lp length of the piston mm M a fixed-end moment at the beginning of the cylinder tube of a fixed hydraulic cylinder N·mm M bc moment at the junction of cylinder tube and piston rod N·mm M d fixed-end moment at the end of the piston rod of a fixed hydraulic cylinder N·mm M max maximum moment in the piston rod N·mm R a reaction at the beginning of the cylinder tube N R d reaction at the end of the piston rod N R bc 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 2 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 deflection curve of the piston rod (see Figure 2) rad ρ 1 mass per unit volume of cylinder tube material kg/mm 3 ρ 2 mass per unit volume of piston rod material kg/mm 3 σ stress N/mm 2 σ e yield point of a material N/mm 2 σ max maximum compressive stress N/mm 2 φ a angle of the deflection curve at the beginning of the cylinder tube rad φ b angle of the deflection curve at the end of the cylinder tube rad φ c angle of the deflection curve at the beginning of the piston rod rad φ d angle of the deflection curve at the end of the piston rod rad ψ a angle at the beginning of the cylinder tube (see Figure 2) rad ψ d angle at the end of the piston rod (see Figure 2) rad 2.2 Additional notations The following additional notations are also used in this document: s 1= sin (q 1 L 1 ) (1) c 1= cos (q 1 L 1 ) (2)Table 1 (continued) 2 © ISO 2016 – All rights reserved PD ISO/TS 13725:2016 ISO/TS 13725:2016(E) s 2= sin (q 2 L 2 ) (3) c 2= cos (q 2 L 2 ) (4) q 1= × × 11(5) q 2= × × 22(6) NOTE The origin of these notations (used for calculation) comes from the original work of Hoblit (see Reference 2]. 3 General principles 3.1 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 Technical Specification is to determine the maximum allowable force, F max , that avoids reaching yield stress of the rod material, σ e , as well as buckling. 3.2 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 equations 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 13). There are as many equations as unknown values. Six types of fixation are treated (Table 2). The system of equations can be solved for an F value previously set. However, it is important to establish a particular value of F, noted F critical . F criticalcancels the determinant of the system of equations. This value should 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 max ) between the zero value (in fact ε·F critical ) and F critical(in fact [1- ε]·F critical ) that leads the stress in the rod to reach the yield stress of the rod material (when σ max= σ e ). NOTE ε is a seed value used in the method of proportional parts to solve the set of equations. 3.3 Dimensional layout of hydraulic cylinder Figures 1 and 2 depict the variables and principles used within this Technical Specification. In the event that the external load F on the cylinder is at its maximum with the rod fully extended, the worst case occurs when the cylinder is in the horizontal position. In this case, the maximum allowable compressive load is at its lowest and creates the maximum stress in the piston rod. For this reason, and also considering the way of calculation where L 3is insignificant compared with L 1and L 2 , L 3is the shortest distance between the two centre points of the piston and the bearing.© ISO 2016 – All rights reserved 3 PD ISO/TS 13725:2016 ISO/TS 13725:2016(E) When an almost retracted cylinder is loaded with a pushing force, there might be a risk of internal buckling of the rod. Therefore, the rod is to be calculated separately if this is regarded as a risk. NOTE is a possible minimum value of L 3 . Figure 1 — Cylinder4 © ISO 2016 – All rights reserved PD ISO/TS 13725:2016 ISO/TS 13725:2016(E) Rotational spring joining the two columns Cylinder tube: 1 column Piston rod: 1 column Geometrical relation between Ψ a , Ψ d , φ b , φ cand θ tg. to deflection curve of the cylinder tg. to deflection curve of the rod This relation is: θ - Ψ a- Ψ d+ φ b- φ c= 0 Key 1 cylinder 2 rod portion inside the cylinder 3 rod Figure 2 — Model of the hydraulic cylinder 3.4 Common calculation of maximum stress in the rod (for all mounting types) σ max The piston rod can be considered as the critical part of the cylinder if the thickness of the cylinder tube is sufficient. This condition should be verified before