STATIC ANALYSIS OF A SINGLE STAGE HYDRAULIC CYLINDER

Abstract

-In this study the static analysis of a single stage hydraulic cylinder is considered. A complete theoretical model is developed that allows the consideration of all the factors that affect the statics of a hydraulic cylinder in its action as a compression member. The scheme is based on the classical Euler-Bernoulli beam theory, and makes detailed account of all the loadings present, and of the various types of boundary conditions. Keywords-Scheme of analysis, Hydraulic cylinder, Single stage, New factors I. INTRODUCTION Hydraulic cylinders are compression members consistingof parts having different rigidity. In the simplest casethere are two parts (Fig. 1), but in more complicated cases,such as telescopic cylinders, there are several parts [1],[2], [3]. Anumber of different combinations of support conditions atthe ends are encountered in these problems. In the simplestcase there are pinned supports at both ends, while in othercases the supports may be pinned-fixed, doubly-fixed, orfixed-free. In exceptional conditions, hydraulic cylindersoperate solely in the vertical condition, but morecommonly they operate in an inclined position or in acompletely horizontal position. In these latter positions theself-weight of the cylinder and the hydraulic fluid oftenprovide a transverse load that increases the eccentricity ofaxial loads. Further factors requiring consideration are thesliding joint between the rod and cylinder, and thelooseness in the joints, implying elasticity in theconnections or supports. The components forming thehydraulic cylinder have step-variations in their stiffness,and thus the equation governing the deflection isdiscontinuous over the domain, which complicates theanalysis. In the technical literature a number of approaches for theanalysis of compression members have been presented [4[, [5], [6], [7], but none has completely addressed the full details thatare encountered with practical hydraulic cylinders. Articles and thestudy of the various catalogs provided by suppliers ofhydraulic cylinders indicate that some details related tohydraulic cylinders are not taken into consideration, andthat approximate approaches of analysis are applied, whichmay in cases lead to non-conservative results [8], [9], [10]. The industry produces a variety of hydraulic cylinderproducts, and generally carries out complete designs for itsproducts. Nevertheless, there is no available methodology,appropriate for comprehensive analysis of hydrauliccylinders, which accounts for both transverse and axialloads. Thus a comprehensive scheme of calculation isrequired which considers completely the various loadingand support conditions that may arise, and whichultimately leads to a safe product having economicaldimensions. A. Stability analysis of compression members. The classical method of stability analysis of a compressionmember is described by Timoshenko [11]. Other methodsexist which offer a more detailed consideration of theproblem [12], [13], [14]. These methods include the classical Euler-Bernoullimethod based on an approximate differentialequation for the elastic bending of a beam, methods basedon semi-empirical formulas, the method of the -coefficient for the reduction of the admissible stress, energymethods, the method of the parameters of the origin, themethod of the integration of the differential equation, thefinite element method, the secant formula for the case ofcolumns with eccentric load, and the method of limit loadsfor the case of the loss of stability due to simultaneouslongitudinal and transverse bending. Most of thesemethods cover only compression members having constantrigidity, and thus cannot be applied directly to hydrauliccylinders. It has been shown that the method of parametersof the origin to determine the critical load, whilepermitting the analysis of structures with variable rigidity,is excessively complicated in solution if all the factorsaffecting the problem are to be considered [15].