machine design, Vol.3(2011) No 1, ISSN pp

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1 machne desgn, Vol.3(211) No 1, ISSN pp Prelmnary note CAD/CAE INVESTIGATION OF A LARGE HYDRAULIC МINING EXCAVATOR Rosen MITREV 1, * - Radoslav GRUYCHEV 2 - Petr POBEGAILO 3 1,2 Techncal Unversty of Sofa, Faculty of Mechancal Engneerng, Sofa, Bulgara 3 NPO Teknokon, Moscow, Russa Receved ( ); Revsed ( ); Accepted ( ) Abstract: The present work s devoted to CAD/CAE nvestgaton of the mechancal system of large mnng excavator wth Trpower system. The nvestgaton s performed n Autodesk Inventor envronment and ts dynamcal smulator. A 3D model of the excavator workng equpment s developed and t s used for nvestgaton of the geometrcal, force, knematcal and dynamcal parameters of the mechancal system. Also nvestgaton of these parameters for an operatng cycle of the excavator s performed. Key words: CAD/CAE, excavator knematcs, dynamcs, Trpower 1. INTRODUCTION The excavators are popular multfunctonal constructon and mnng machnes. Excavator conssts of travelng body, swng body and front dggng manpulator, by whch dggng operatons are performed. The dggng manpulator conssts of a number of movng elements, man of whch are boom, stck and bucket, connected by rotatonal jonts. These elements are powered by hydraulc cylnders, whch are connected to the excavator lnks and workng tools drectly or through transmsson mechansms. Actuaton of the elements s by extenson and retracton of the hydraulc cylnders, commanded by the operator. Fg.1. Knematcal scheme of the workng attachment wth Trpower system When mnng operatons are performed t s desrable to keep the constant nclnaton of the bucket along the path of dggng and transportaton of the materal. Usually, because of the bucket s attached to the stck, ts nclnaton depends on the nclnaton of the boom and stck. That s why durng the moton an addtonal correcton of the bucket nclnaton by bucket cylnder s necessary to keep ts preset nclnaton. Constant nclnaton of the bucket could be acheved by mechancal lnkages or by hydraulcs. There are few possbltes to desgn such types of lnkages and the most advanced of them s the patented by O&K Trpower system. The Trpower system was nvented by a O&K engneer n 1989 to make workng for the operator easer by actuaton of only one cylnder for bucket crowd and lftng. Although the patent expred n 2, Terex s stll the only one manufacturer of excavators wth Trpower system. The knematcal scheme of the Trpower system s shown at Fg.1. The mechansm conssts of 9 lnks (ncludng ground) and has 3 degrees of freedom. Boom 1, stck 2 and bucket 3 are actuated by hydraulc cylnders 4, 5 and. The hydraulc cylnders 4 and 5 are not drectly connected to the boom 1, but through a trangular rotatable element 8. Ths element s connected to a superstructure va a rod wth constant length 7. The preset nclnaton of the bucket s acheved n two cases: 1) When the cylnder 4 extends (cylnder 5 also could extend or could be blocked), t lfts the boom 1 and element 8 rotates clockwse. Because of cylnder s blocked, t acts as a rod wth constant length. Element 8 pulls the bucket 3 and t rotates counterclockwse, keepng ts preset nclnaton; 2) Cylnder 5 extends and cylnders and 4 are blocked. In ths case the bucket also keeps the preset nclnaton. Modelng and nvestgaton of the excavator, partcularly knematcs and dynamcs of the dggng manpulator s a challengng task and a topc of ncreasng mportance for desgners, due to presence of potental for reducng prototypng costs and provdng the better understandng of the mechancal system behavor. In the present paper, an nvestgaton of geometrcal, force, knematcal and dynamcal parameters of a large hydraulc excavator wth Trpower system s presented. 2. LITERATURE SURVEY There s a massve collecton of papers whch consders the nvestgaton of mechancal system parameters, especally knematcs and dynamcs of excavators work attachment. *Correspondence Author s Address: Techncal Unversty of Sofa, Faculty of Mechancal Engneerng, blvd. Klment Ohrdsk 8, 1 Sofa, Bulgara, rosenm@tu-sofa.bg

2 Some authors have derved the knematc relatonshps that relate jont angles of a backhoe to the locaton and orentaton of the bucket tp [8]. Other authors [5,11] have developed a knematc model for an excavator by usng the wdely used n robotcs Denavt Hartenberg approach. The forward and nverse knematc relatons representng the pose of the bucket, the angular postons of the jonts, and the lengths of the hydraulc actuators are presented n [8,11]. The dynamcs of the excavator and smlar earthmovng machnes s also has been studed by numerous researchers. A forward dynamc model of an excavator performng dggng operatons s presented n [11]. The equatons of moton of the excavator are obtaned by usng of the Newton-Eulers formulaton. The model takes as nput the forces generated by the hydraulc actuators and provdes as output the poston of the bucket. The authors of [1] have proposed a Lagrangan formulaton of wheel loader dynamcs where the machne s represented as a three lnk manpulator. Another model based on the Newton-Euler method s developed n [18]. Other researchers [14] also have used a smlar formulaton to model excavators modfed for forestry applcatons. Dynamc modelng of mnng hydraulc shovel excavators s presented n [4]. Dynamc models of the hydraulc shovel excavator have derved for ts boom, stck and bucket, and are analyzed as free body dagrams usng the teratve Newton-Euler method. Mathematcal model for a hydraulc actuator wth pump-controlled system s presented n [1] and the moton of the boom of hydraulc excavator s modeled and smulated as an example. The author of [21] has used the Lagrange equatons for the dynamcs of the hydraulc excavator. The modelng of the excavators and smlar machnes as multbody systems s not wdely consdered n the publshed lterature. The paper [1] descrbes a geometrc method for formulaton of constraned multloop lnkage dynamcs whch s appled to large mnng excavator wth Trpower system. Doman decomposton method wth teraton s proposed and appled to dynamc smulaton of hydraulc excavator n [9]. A method to obtan a low order dynamc model for multlnk flexble hydraulc cranes s presented n [13]. A mathematcal model of large-scale moble constructon manpulator s represented by a coupled system of nonlnear ordnary dfferental equatons, formulated n mnmal coordnates s developed n [7]. Based on Kane dynamc equatons, the method of establshng analytcal dynamc model for DOF ndustral robotc manpulators contanng closed chan for sprayng s put forward, and the dynamc equatons n explct form are derved n [12]. Reference [19] nvestgates the modellng and control of a full-scale unmanned excavator vehcle. The developed model takes nto account the knematcs and dynamcs of the moble platform (vehcle) and the excavaton arm. The authors of paper [2] have adopted the multbody approach and DAE formulaton of excavator and front loader dynamcs. 3. THEORETICAL APPROACH FOR DYNAMICAL INVESTIGATION OF THE EXCAVATOR Мechansms can be generally categorzed nto open-loop mechansms and closed-loop mechansms. The dfference s that the jont degrees of freedom (DOF) n open loop mechansms are ndependent of one another whereas n closed-loop mechansms they are not ndependent. Extensve nformaton on open- and closed-loop mechansms s avalable from standard engneerng books. The lnkage of the Trpower system could be presented as multbody mechancal model contanng lnks, whch forms open and closed knematc loops. The dynamc smulaton of the closed-loop system s more dffcult then the open-loop system. In comparson wth open-loop systems, closed-loop systems tend to possess relatvely few degrees of freedom compared to the number of connected bodes. Knematc loops ntroduce two dffcultes: 1) there s no longer one-to-one correspondence between the jont varables and the moton freedoms of the system due to the loop closure equatons; 2) to defne the confguraton of the system unambguously more number of coordnates than the degrees of freedom s needed. A number of methods are avalable to formulate dynamcs of multbody system, ncludng the teratve Newton-Euler dynamc formulaton, the Lagrangan formulaton, Kane s method, and others. Of course, all methods have benefts and drawbacks. Sutable for modelng of the consdered mechancal system are well establshed n the analytcal mechancs Lagrange equatons of the frst knd. They are used for dervng the equatons of moton of the multbody system components: d dt L L + q& q m j = 1 φ j λ j q = Q = 1,2,..., n where L=T-U s the Lagrangan functon; T s the knetc energy of the system; U s the potental energy of the system; q, =1,2,..n are set of n dependent coordnates; Q generalzed externally appled forces, actng along the dependent coordnates; φ j, j=1,2, m - set of ndependent constrant equatons; λ Lagrange multplers. Equaton (1) represents n equatons wth (n+m) unknowns. In order to have a suffcent number of equatons, t s necessary to supply m more equatons. The obvous choce s to use the algebrac constrants equatons (2) whch along wth (1) consttute a set of dfferental algebrac equatons (DAE s) of ndex three: φ j = j = 1,2,..., m (2) Thus, the nterconnecton orented modelng descrbes the dynamc behavor of the sngle body and the couplng of the subsystems by algebrac equatons. Ths approach leads to a large system of loosely coupled equatons that can be solved for the coordnates and Lagrange multplers. The vector of Lagrange multplers can be used to determne the generalzed reacton forces. Takng nto account Lagrange equatons (1), expressons for knetc and potental energes of the bodes, constrant equatons and expressons for generalzed forces we can generate equatons of moton of the multbody system. The consdered lnkage conssts of 11 bodes (f hydraulc cylnders are consdered as consstng of two bodes) and (1) 18

3 12 rotatonal and 3 translatonal knematcal pars. The system of equatons whch descrbes the moton of multbody system consst of 33 dfferental equatons of second order and 3 algebrac equatons. Numercal soluton of such large DAE system s dffcult because of computatonal and numercal problems. More ratonal way for modelng of the consdered system s to use a dedcated software. 4. CAD/CAE APPROACH FOR DYNAMICAL SIMULATION OF THE EXCAVATOR An easy appled and wdely used n engneerng practce approach for smulaton of the excavator as a multbody system s a modelng by way of general purpose mechancal dynamcs software [3,15,17]. In the present work, Autodesk Inventor package and ts dynamc smulator are used for modelng and smulaton. A 3D CAD model of real lfe machne Terex/O&K RH-12E s developed-see Fg.2. At the fgure are also drawn workng zone of the excavator and global axes, accordng whch all quanttes are computed. results from the nvestgaton of some of the mechancal system parameters Bucket nclnaton Properly desgned lnkage must ensure that the bucket wll be kept to preset constant angle of nclnaton whle dggng and lftng the bucket wth excavated materal. Ths condton s acheved at the stage of mechansm synthess through choce of sutable geometrcal parameters of the elements and ther connecton to other elements. For evaluaton of the bucket nclnaton along the dggng or transportaton path, a seres of smulatons are performed. Bucket nclnaton s evaluated when the boom s lfted (moton down-up) by ts hydraulc cylnder and all other cylnders are blocked. The receved results are depcted at Fg St roke, mm Fg.3. Inclnaton of the bucket as a functon of the boom cylnder stroke Fg.2. 3D CAD model of excavator workng equpment There s provded one to one correspondence between geometrcal, force, knematcal and mass-nertal propertes of real lfe machne and CAD model. From the vewpont of dynamcal smulaton the excavator mechansm s vewed as a set of rgd bodes nterconnected to each other by jonts that constran, but not restrct, relatve moton between any two bodes. Common jonts used n excavator mechansm nclude revoluton, prsmatc and fxed (grounded) jont. Тhe process of creatng dynamc smulaton study conssts of 4 core steps: 1) creaton of cad model of the system; 2) creaton of jonts between components that have relatve moton between them; 3) creaton of envronmental condtons to smulate realty; 4) performance of smulaton and assessment of results. As a result of performed smulaton tasks are receved results for geometrcal and force parameters, velocty and acceleraton of bodes and t s characterstc ponts. The man drawback of the receved results s ts fragmentary nature, that s why we can not fnd overall relatons between the system parameters, whch determne the receved soluton. Below are represented and commented There are shown relatons between the stroke of the boom hydraulc cylnder and the bucket tlt for dfferent combnatons of relatve stuaton of the workng equpment elements. Obvously, n all cases the bucket nclnaton changes along the moton path. Several addtonal experments show that ths change s larger around the border of workng space (up to 15 ). When dggng or transportaton operatons n ths zone are performed, t s possble to spll the excavated materal or change the dggng process parameters, that s why a manual correcton of the bucket nclnaton from the operator s needed. In the zones around the center of the workng space devaton from the preset nclnaton s much smaller (4 5 ) whch cannot cause the mentoned problems 4.2. Potental dggng force along the dggng path Аcordng to adopted termnology [2], the potental (n other words-possble) dggng force s the tangental dggng force on the bucket tooth top, whch can be realzed when dggng s performed by hydraulc cylnders and the pressure n them s maxmal. To determne ths potental dggng force along the dggng path, two experments are performed: 1) The boom s lfted by ts cylnder and the value of the dggng force s 19

4 determned for dfferent values of the boom cylnder stroke; 2) The stck s lfted by ts cylnder and the value of the dggng force s determned for dfferent values of the stck cylnder stroke. The executon of the mentoned experments needs determnaton of such value of tangental dggng force, whch keeps n equlbrum the system along the dggng path for known maxmal value of force n the hydraulc cylnder (of the stck or the boom) see Fg.4. The nvestgaton s performed for dfferent strokes of the correspondng cylnders: for the boom cylnder - 5mm., 1mm., 15mm., 2mm.; for the stck cylnder- mm., 15mm., 3mm. Fg.4. The scheme for determnaton of the unknown value of the potental dggng force Results (Fg.5) for the determned dggng force are depcted as relaton between the force and the relatve heght of the bucket over ts lowest poston Boom 5 mm. Boom 1 mm. Boom 15 mm. Boom 2 mm. Stck mm. Stck 15 mm. Stck 3 mm. performed by the moton of the stck, the potental dggng force could be accepted as constant along the dggng path Velocty and acceleraton of the cuttng tooth top Veloctes and acceleratons of the workng equpment lnks nfluence some mportant machne parameters: technologcal and techncal-economcal parameters, nertal forces on the lnks and excavated materal, parameters of the nteracton between the control system and the operator etc. Knematcal parameters of the cuttng tooth top are mportant prmarly for velocty of the sol cuttng, whch nfluences the workng resstance of the sol and also t determnes the speed of cuttng tooth wear. At the Fg. are shown results for the velocty and acceleraton of the bucket tooth top, receved for dfferent constant veloctes (5mm/s, 1mm/s, 15 mm/s, 2mm/s, 25mm/s) of the boom hydraulc cylnder (moton down-up). One can see that the lnear ncrease of the velocty of the hydraulc cylnder (5 mm/s, 1 mm/s, 15 mm/s, 2 mm/s, 25 mm/s) leads to approxmately unform ncrease of the tooth velocty (24mm/s, 48mm/s, 72mm/s, 9mm/s, 12mm/s for relatve heght = ). From the other sde, the acceleraton of the same pont s nonlnear. Increase of the relatve heght.8 leads to small change of the velocty and respectvely small values of acceleraton. After the ponted value of relatve heght velocty decreases sharply and acceleraton ncreases. Values of the acceleratons are small and the excted nertal forces are mnmal Relatve heght Fg.5. Values of dggng force as a functon of relatve heght One can observe that: 1) When the dggng s performed by the moton of the boom, the potental dggng force ncreases when the relatve heght ncreases and ths ncrease s stronger around the upper part of the workng zone (relatve heght>.7); 2) When the dggng s V 5 mm/s V 1 mm/s V 15 mm/s V 2 mm/s V 25 mm/s A 5 mm/s A 1 mm/s A 15 mm/s A 2 mm/s A 25 mm/s Fg.. Values of the velocty and acceleraton of the cuttng tooth as a functon of relatve heght 4.4. Mechancal system parameters durng the operatng cycle Smulaton of the operatng cycle allow us to nvestgate the change of the mechancal system parameters for a operatng cycle, to determne ther maxmal values for a cycle and stuaton of the workng equpment elements n ths moment of tme. Also we can determne the duraton 2

5 of the operatng cycle and mnmze t by executon of concurrent motons of the dfferent lnks whch wll lead to ncrease n excavator performance. An approxmate operatng cycle wth duraton of 37s s smulated. The sequence of motons and ther duratons are shown at the Fg.7. Veloctes of the hydraulc cylnders rods are 2mm/s. At the same pcture are shown duratons of dfferent forces actng on the workng equpment durng the cycle - dggng force kn, weght of materal n the bucket 294kN and weghts of all elements. One can see that after the bucket unloadng (21-24s.) n backward moton the motons of the bucket, stck and boom are executed together. The theoretcal calculated excavator performance for 15m 3 bucket and 37s duraton of cycle s 291t/h whch value s close to publshed by manufacturer value of 3t/h n test condtons. At Fg.8 we can observe the change of velocty of the cuttng tooth top and ts components durng the consdered operatng cycle. Maxmal value of the cuttng tooth velocty s about 44mm/s whch value s acheved durng the rotaton of the workng equpment around vertcal Z axs (see Fg.2). At the perod of backward moton (when the motons of bucket, stck and boom are performed together) the maxmal velocty s about 2 mm/s. In all other parts of the operatng cycle the value of velocty s much smaller than ponted values. At the Fg.9 are depcted results for acceleraton of the peak pont of the cuttng tooth. Agan, the maxmal value of acceleraton s observed durng the rotaton of workng equpment around the vertcal axs. Ths acceleraton has a value approxmately 13 mm/s 2 and s caused from rotaton of the workng equpment around vertcal axs (centrfugal acceleraton). Such a bg acceleraton causes addtonal nertal load on the workng equpment lnks, especally n the forward moton when the bucket s full A, mm/s^2 Ax,mm/s^2 Ay,mm/s^2 Az,mm/s^2 Acceleraton, mm/s Fg.9. Acceleraton of the cuttng tooth top and ts components durng the operatng cycle Fg.7. Sequence of lnks motons durng operatng cycle (cycle pattern) From the Fg.1 we can trace the change of the forces n the hydraulc cylnders of the stck and boom durng the operatng cycle. We can see that for forward moton (untl 24 s. - end of bucket unloadng) the forces n hydraulc cylnders have sgnfcant values. After unloadng of materal forces become neglgble Force h.c boom, N Force h.c stck, N Velocty, mm/s Force h.c., N Tme, s Fg.8. Velocty of the cuttng tooth top and ts components durng the operatng cycle Fg.1. Forces n the hydraulc cylnders durng the operatng cycle 21

6 The developed CAD model of the excavator can be used for nvestgaton of the nverse knematcs and dynamcs, especally for trajectory generatons. The computed forces n the knematcal pars together wth the appled external forces can be used for FEM smulaton of the mechancal system. 5. CONCLUSION The used CAD/CAE approach for nvestgaton of large mnng excavator s sutable for performng geometrcal, force, drect and nverse knematcal and dynamcal analyss of the workng equpment mechancal system. By smulaton t s possble to nvestgate the change of parameters durng operatng cycle and optmze t duraton. Although the used CAD/CAE system has no bult-n tools for optmzaton of the mechancal system parameters, optmzaton could be performed by tral and error method. REFERENCES [1] ALAYDI, J., Mathematcal Modelng for Pump Controlled System of Hydraulc Drve Unt of Sngle Bucket Excavator Dggng Mechansm. Jordan journal of mechancal and ndustral engneerng, Volume 2, Number 3, Sep. 28 ISSN , Pages [2] DANTCHEV, D., Hydromechancal synthess of excavator drvng mechansms. D.Sc. dssertaton, Techncal unversty of Sofa, Bulgara, [3] DING, G., QIAN, Z., FENG, P., PAN, S. Actve Vbraton Control of Excavator Workng Equpment wth ADAMS. North Amercan ADAMS User Conference, Orlando, FL, 2. [4] FRIMPONG, S., YAFEI, H., INYANG, H., Dynamc Modelng of Hydraulc Shovel Excavators for Geomaterals. Internatonal Journal of Geomechancs, Jan28, Vol. 8 Issue 1, pp.2-29; [5] HOFSTRA, C., HEMMEN, A., MIEDEMA, S., HULSTEYN, J., Descrbng the poston of backhoe dredges. Texas A&M 32nd Annual Dredgng Semnar. Warwck, Rhode Island, June 25-28, 2. [] HEMAMI, A., DANESHMEND, L., Force analyss for automaton of the loadng operaton n LHD- Loader. Proc IEEE nternatonal conference on robotcs and automaton, IEEE, Pscataway, N.J., [7] HILLER, M., Modellng, smulaton and control desgn for large and heavy manpulators. Robotcs and Autonomous Systems 19, 199, [8] HSIN-SHENG, L., SHINN-LIANG, C., KUO- HUANG, L., A study of the desgn, manufacture and remote control of a pneumatc excavator. Internatonal Journal of Mechancal Engneerng Educaton. Volume 32, Issue 4, 24, pp [9] IMANISHI, E., NANJO, T., HIROOKA, E., SUGANO, N., Fast smulaton on flexble multbody dynamcs usng doman decomposton technque. Journal of system desgn and dynamcs. Vol.1, No3, 27, pp [1] JANSSEN, B, NIEVELSTEIN, M., Mult-loop Lnkage Dynamcs va Geometrc Methods: A Case Study on a RH2 Hydraulc Excavator. Internshp report. Endhoven Unversty of Technology. Department of Mechancal Engneerng, October 23. [11] KOIVO, A., THOMA, M., KOCAOG-LAN, E., ANDRADE-CETTO, J., Modelng and control of excavator dynamcs durng dggng operaton. Journal of Aerospace Eng., 9(1), 199, pp [12] LIN, G., WANG D., XU, L., GAO,S., The analytcal dynamc model of sx-dof ndustral robotc manpulators of contanng closed chan.mechansm and Machne Theory 4 (25) [13] LINJAMA, M., VIRVALA, T., Low-order dynamc model for flexble hydraulc cranes. Proc.Instn. Mech Engrs. Vol 213 Part I, pp , [14] PAPADOPOULOS, E., SARKAR, S., On the dynamc modelng of an artculated electrohydraulc forestry machne. Proceedngs of the 199 AIAA Forum on Advanced Developments n Space Robotcs, Madson, WI, August 1-2, 199 [15] PARK, C., LIM, K., A Smulaton Envronment for Excavator Dynamcs. MSC.Software Vrtual Product Development Conference 24, Calforna. [1] SARATA, S., SATO, K., YUTA, S., Moton control system for autonomous wheel loader operaton. Proceedng of the Internatonal Symposum on Mne Mechanzaton and Automaton, 1995,pp [17] VADHE, R., DAVE, V., Multbody smulaton of earthmovng equpment usng Motonvew/Motonsolve. 4th Inda/ASEAN HyperWorks Technology Conference 28, Bangalore, Inda [18] VAHA, P., SKIBNIEWSKI, M., Dynamc Model of an Excavator. ASCE Journal of Aerospace Engneerng. (2), Aprl, [19] ZWEIRI, Y., SENEVIRATNE, L., ALTHOEFER, K., Modellng and control of an unmanned excavator vehcle. Proc. Instn Mech. Engrs Vol. 217 Part I: J. Systems and Control Engneerng, 23 pp [2] FOX,B., JENNINGS L., ZOMAYA, A., On the modelng of actuator dynamcs and the computaton of prescrbed trajectores. Computers and structures (8), 22, [21] JANOSEVIC, D., Analyss of hydraulc excavator dynamc stablty, XVII Internatonal Coference on Materal flow, machne and devces n ndustry, Belgrade,