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Stress analysis in contact zone between the segments of telescopicbooms of hydraulic truck cranesMile Savkovia,n, Milomir Gaia, Goran Pavlovib, Radovan Bulatovia,Neboja ZdravkoviaaUniversity of Kragujevac, Faculty of Mechanical and Civil Engineering Kraljevo, Dositejeva 19, 36000 Kraljevo, SerbiabColpart d.o.o-Beograd, irovljeva 5, 11030 Beograd, Serbiaarticle infoArticle history:Received 16 April 2014Received in revised form11 September 2014Accepted 13 September 2014Available online 2 October 2014Keywords:Hydraulic truck craneTelescopic boomLocal stressExperimental testingFinite element analysisabstractThis paper presents the analysis of local stress increases at the contact zone between the inner and outersegments of telescopic booms of truck cranes. A portion with a relevant length was singled out of theouter segment and a mathematical model was created describing its stressstrain state as a function ofgeometrical parameters. The obtained results were veried by the nite element method as well as byexperimental testing of the truck crane TD-6/8. Comparison of results revealed high compliance betweenthe analytical model and the results obtained by the nite element method and experimental testing,which conrmed all the hypotheses. The presented methodology as well as the veried analyticalexpressions give guidelines for optimum design of box-like telescopic segments and other structureswith local stress increase in contact zone.& 2014 Elsevier Ltd. All rights reserved.1. IntroductionThe most important element for payload lifting and transportby telescopic hydraulic truck cranes is the boom. The telescopicboom consists of segments that retract or extend during operation.By changing its position in space, the boom of the truck cranetransfers load onto the substructure of the crane and the vehicleand represents its most responsible part. Reduction of dead weightof the boom opens the possibility for increasing the payload, thelifting speed as well as the speed of retraction and extension of thesegments.In recent years, world manufacturers of truck cranes have beenassigning great importance to the determination of an optimumform of the boom cross section, which would provide an increasein bending and torsional stiffness along with the reduction ofmass. However, during overhaul and regular checks of telescopicbooms of truck cranes, certain deformations and damages in thecharacteristic zone of boom segments have been noticed. Thatcharacteristic zone is located at the contact zone between theinner and outer segments when the inner segment is extended tothe maximum position. This fact indicates that stresses at thosezones are considerably higher than the stresses along the boomsegment. Determination of values of those stresses is the subject ofthis paper.Two model types of telescopic booms of the truck crane can befound in literature: mathematical models of the entire boom andmathematical models of interaction in contact zones betweensegments, which is the subject of this research, too.Papers 1,2 pay special attention to the contact zones betweenthe segments as well as the connection between the rst (outer)telescope segment and the hydrocylinder. These models consist ofthe corresponding equivalent masses and springs, where 1considers the boom with two telescopic segments, while 2 hasthree telescopic segments and a modal analysis done.Paper 3 points out the importance of contact zones betweenthe segments as well as the change of stresses at those points forvarious boom crane designs. The model which covers the inuenceof sliding and the inner telescope extended length at differentelevation angles of the boom is presented in paper 4. Thelocation of sliding contacts in relation to the outer and innertelescope segment is particularly emphasized. The paper 5analyzed the inuence of the extension length on loads distribu-tion through sliding contacts along the boom. Paper 6 analyzesthe problem of contacts between box-like segments of the tele-scopic truck crane by using the software package ANSYS, with thepresentation of the load transfer problem and buckling shapes.The mentioned papers examine interaction between the segmentsand load transfer from the inner telescope segment to the outerContents lists available at ScienceDirectjournal homepage: /locate/twsThin-Walled Structures/10.1016/j.tws.2014.09.0090263-8231/& 2014 Elsevier Ltd. All rights reserved.nCorresponding author. Tel.: 381 36 383392; fax: 381 36 383380.E-mail address: savkovic.mmfkv.kg.ac.rs (M. Savkovi).Thin-Walled Structures 85 (2014) 332340one. The generalized model of the telescopic truck crane (Fig. 1)isfrequently considered by a large number of authors.Paper 7 presents the mathematical model of the truck cranethat denes the control mode for reducing the oscillations of thesystem. It shows the global model of the boom and does not takeinto account the inuence of load transfer between the segments.Paper 8 also presents a mathematical model of the truck crane,which denes the way for reducing the oscillations and precisepositioning of payload. Paper 9 gives another mathematical modelof the truck crane and denes the inuence of lifting the boom by ahydro cylinder on dynamic reactions. Minimization of forces valuesin the hydro cylinders as well as their control while lifting andtransporting the payload in the working position are presented inpaper 10. Similar problems are discussed in paper 11,wheretheaccent is put on restricting the lifting load for the purpose of safecrane operation. Paper 12considers the inuence of differentparameters on motion of the payload and structure load. Theinuence of hydraulic drive system as well as the manner of itscontrol on dynamic behavior of truck cranes is the subject of paper13. Paper 14 presents a dynamic model of truck crane emphasiz-ing the control of change of the telescope length, change of theangle of inclination and rotation of the boom. The inuence ofexibility of soil on dynamic stability of the truck crane as well ason positioning of payload during rotation is presented in paper 15.Dynamic stability of a laboratory model of a truck crane wasexamined in paper 16. The model presented in this paper enablesdetermination of load conditions and geometrical characteristics atwhich there may occur a loss of stability. The paper 17 analyseddynamic stability of truck crane depending on the angular ballbearing deformation at connection between the substructure andsuperstructure through dynamic model with ve degrees of free-dom. A discrete model of truck crane and examination of oscilla-tions while lifting the payload, depending on the length and theangle of inclination of the boom, are presented in paper 18.Minimisation of load in relation to oscillation while lifting thepayload and rotation of the boom was presented in paper 19.Papers 20,21 also present modelling and simulation of a truckcrane as a complex model which takes into account all motions(load lifting, extension of the telescope, rotation of the boomwithout damping) using the Bond Graph method. Experimentaltesting and simulations were performed for the actual model andthe correctness of the created model was conrmed. Paper 22puts a special accent, in operation of cranes with the boom, on theinuence of wind, which is often neglected although it is veryimportant for the global stability of the crane in operation.Paper 23 presents the manner of decreasing the load at thetip of the boom by reducing payload pendulations, i.e. excitationat the tip of the boom, by using two-dimensional and three-dimensional models. It is shown that signicant reduction can beaccomplished by appropriate selection of cable speeds and length.Analysis of load transfer from the inner telescope segmentto the outer one is very important because it is the zone with thehighest stress values. This is also a conclusion of many investiga-tions conducted not only on cranes but on other structures as well.The conclusions obtained in those investigations are importantfor the hypotheses and creation of the model presented in thispaper. The results in 2433 show the approaches in modell-ing and inuence of local stresses at the contact zones of varioustypes of beams. Also, they underline the importance of deningmaximum loads that will not cause any plastic deformationsof the beams and, hence, will not endanger the functionality ofthe object.The generalized and simplied models of truck crane telescopicboom are presented in Fig. 1, with marked contact zones betweenthe inner and outer segments of the telescope (lines aa and bb).2. Denition of analytical modelDuring payload lifting, load is transferred from the innermovable segment to the outer segment through the correspondingsliding pads, Fig. 2. The sliding pads are placed at the front end ofthe outer segment and at the rear end of the inner segment.Therefore, the sliding pads placed at the outer segment are treatedas stationary, while the sliding pads placed at the inner segmentare treated as movable. Taking into account that the segment isconsiderably longer than the sliding pad, this paper starts with theassumption that the load from the inner segment sliding pad istransferred to the outer segment as continuously distributed loadof a constant value (Fig. 3).As the inner segment moves, position of the sliding padschanges in relation to the front end of the outer segment (coordi-nate x-Fig. 3). Therefore, the absolute value of continuous loadchanges with the change of the coordinate x. Still, remains constanton the sliding pads surface.This paper considers the inuence of local bending of the outersegment during load transfer. To make a successful research of thelocal stress increase due to contact load, the paper introduces thefollowing assumptions:Fig. 1. Model of truck crane telescopic boom: (a) generalized, (b) simplied.M. Savkovi et al. / Thin-Walled Structures 85 (2014) 332340 333C0 the zone of stress local increase does not extends beyond alength equal to height of the segment cross-section per side ofthe sliding pads (amaxr2 h), Fig. 4;C0 the inuence of transverse forces on stresses and deformationsof the plate is neglectable in comparison to external load andreactive moments;C0 the inuence of forces acting in the plate plane on normalstresses is neglectable in comparison to other loads;C0 elastic deformations of the supports (x0 and xa) areneglectable in comparison to the deformations that occur dueto the action of external load (Fig. 4).The singled out portion of length a is disassembled to itsconstituent ange and web plates. The disassembled ange andweb plates are considered as freely supported, whereby theirmutual inuence is taken into account by using the correspondingbending moments. The physical model, which includes the men-tioned assumptions, is presented in Figs. 4 and 5.Within the stressstrain analysis of ange plates, it is assumedthat the vertical web plates have sufcient stiffness and do notconsiderably inuence the local values of stress and deformations.Also, in the stressstrain analysis of vertical web plates, the angeplates represent the elastic support. External load input is pre-sented in Fig. 5.2.1. Bending equation for the top ange plateAccording to real-life solutions, it is assumed that the angeplates and the web plates have the same thickness (1and 2),which does not affect the generality of consideration. Afterdisassembling the segment portion, the stressstrain analysisstarts from the top ange plate, upon which the external loadacts. The differential equation for the transversely loaded plate hasthe form 34,35:4wux42C24wux2y24wuy4qx;yD1where:DE31=12 1C02C0C1the bending stiffness of the plate.The displacement function is assumed in the form:wux;y1m 1fuyC2sinmxaC16C172and it satises the boundary conditions by which the values ofdisplacement and the bending moments at the beginning (x0)and end of the segment (xa) are zero, i.e.:wujx 00;2wux2jx 00; wujx a0;2wux2jx a0; 3If the following designations are introduced:aa2C0a1; nC2a;mC2b; c coshC2b; s sinhC2b;P2C2C2bC0cC2s; R1C2bC2cC02sC22C2cC01;R22C2C2bsC21C0c;M a1C0a2C2cos C2a2amC2C2 sin C2a2C0sin C2a1hi;N cos C2b1C0C1C0 cos C2b2C0C1 cos C2b3C0C1C0 cos C2b4C0C1C2C3;Fig. 2. Sliding pads locations on the outer and inner segment.Fig. 3. Load transfer on the outer segment via sliding pads.Fig. 4. The portion of box-like segment loaded via two sliding pads.Fig. 5. Model for analysis: (a) before disassembling the plates (b) after disassem-bling the plates.M. Savkovi et al. / Thin-Walled Structures 85 (2014) 332340334and if it is assumed that the particular solution of Eq. (2) has theform:fpyKpC2 sinmybC16C174the value of the constant Kpis obtained:KpqcoDC2222;where:qco4nC2mC22C2q0a2C0a1C2M C2NThe function of deection of the top ange plate can now bewritten in the form:wux;y1n1mfuyC2sin C2x 5where:fuyBuC2yC2ch C2yCuDuC2yC2sh C2yKpC2 sin C2yC0C1:6As this is the case with a symmetric plate which is symme-trically loaded, the change of bending moments at the ends of theplate (for y0 and yb) can be written in the form:Ml;uMr;u 1m 1Emysin x 7If the following boundary conditions are used:wujy 00; C0D2wuy2jy 0 1m 1Emysin x;wujy b0; C0D2wuy2jy b 1m 1Emysin x;the values of constants in Eq. (6) are obtained in the followingform:Au0; BuEm2C2C2DC2cC01s; CuEmC2b2C2C2DC2cC01s; DuC0Em2C2C2D;2.2. Bending equation for the web platesBox-like beam portion has two identically supported andloaded web plates (Fig. 5). The differential equation of the leftweb plate has the form:4wlx42C24wlx2y24wly40 8The displacement function is assumed in the form:wlx;y1m 1flyC2sinmxaC16C179where function flyis adopted in the formflyAlBlC2yC2ch yClDlC2yC2sh y 10The solution of the differential Eq. (8) reads:wlx;y1m 1AlBlC2yC2ch yClDlC2yC2sh yC2C3sin x11If the boundary conditions are used (Fig. 5):wljy 00; C0D2wly2jy 0 1m 1Emysin x;wljy h0; C0D2wly2jy h 1m 1Embysin x;the values of constants for the left web plate are obtained:Al0; BlEmC2cC0Emb2C2C2DC2s; ClEmbC2cC0Em2C2C2DC2s2C2b; DlC0Em2C2C2D;Differential calculus for the right web plate is identical, onlywith index “r” instead of “l”.2.3. Bending equation for the bottom ange plateThe nature of supports and load transfer for the bottom angeplate is the same as for the web plates. So, the bending equationfor the bottom ange plate has the same form (8). The displace-ment functions correspond to Eqs. (9) and (10), so that the solutionof the differential equation of displacement of the bottom angeplate is obtained in the form:wbx;y1m 1AbBbC2yC2ch yCbDbC2yC2sh yC2C3sin x12By using the boundary conditions:wbjy 00; C0D2wby2jy 0 1m 1Embysin x;wbjy b0; C0D2wby2jy b 1m 1Embysin x;the values of constants are obtained:Ab0; BbEmbC2cC012C2C2DC2s; CbEmbC2cC012C2C2DC2s2C2b; DbC0Emb2C2C2D;Using the condition of equality of slope and deection of theange and web plates at the joints, the following values areobtained:EmQ C2R1C2 cosC2bP C2R2; EmbEmC2PQ C2cosC2bP;where:Q 2C2C2DC2s2C2KpC2:3. Presentation and verication of results3.1. Stressstrain analysis by using the analytical modelBased on the obtained expressions, the values of stresses anddeformations can be calculated for any point in any cross section ofthe considered box-like portion with length a (Fig. 4). In order tocheck the correctness of the calculation of stresses and deforma-tions, the values of geometrical parameters that correspond to theobject subjected to experimental testing are adopted. Tested objectis the hydraulic truck crane TD-6/8 from the production pro-gramme 36,inFig. 6.The relevant cross section where stresses and deformations arechecked is above the moving sliding pad at the maximumFig. 6. Hydraulic truck crane TD-6/8.M. Savkovi et al. / Thin-Walled Structures 85 (2014) 332340 335extension of the inner segmentsection aa (Fig. 1). The dimen-sions of the cross section of the box-like boom segment of thecrane (Fig. 5) are: b350 mm,h350 mm, 110 mm,210 mm. In order to perform the analytical calculation, it isnecessary to dene the value of force between sliding pad and theouter segment of the boom. The value of this force directlydepends on the length of extension of the inner segment, i.e. thecoordinate x (Fig. 3).Using Fig. 7, the force Plscan be determined in relation toextension length of the moving inner segment of the boom, i.e.coordinate x:PlsQ C2 2C2LtsC0xC02C2eC2hsGtsC2 LtsC0xGkoC2 2C2LtsC0x4C2x13where: the wrap angle of the rope over the upper pulley at thetop of the boom (901), -the coefcient of friction between therope and the pulley (0.15), Gko0.4 kN-the weight of the pulleyblocks, Gts4 kN-the weight of the inner boom segment 36.While testing the truck crane TD-6/8, the following values wereestablished: Q8.5 kN,Lts3750 mm,xmin885 mm,hs350 mm,a2a1250 mm,b2b180 mm. Based on these values and Eq. (13),the value of the force per sliding pad is obtained: Pls20 kN. Thevalue of continuous load (Figs. 4 and 5)is:qoPlsa2C0a1C2b2C0b114Obtained results of stresses and deformations are presentedlater on in comparative diagrams with experimental results andresults obtained by FEM.3.2. Experimental determination of stress values in the physicalmodelThe object of testing, hydraulic truck crane TD-6/8, is shown inFig. 5, the measuring points in Fig. 8 and the layout of measuringpoints and the connection scheme of measuring devices in Fig. 9.The measuring point 1 (Fig. 8) is above the centerpoint of thesliding pad surface and