Dynamic Simulation of the Harvester Boom Cylinder

Article Dynamic Simulation of the Harvester Boom Cylinder

Rongfeng Shen *, Xiaozhen Zhang and Chengjun Zhou

School of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou 350002, China; [email protected] (X.Z.); [email protected] (C.Z.) * Correspondence: [email protected]; Tel.: +158-0607-7197

Academic Editor: Robert Parkin Received: 25 December 2016; Accepted: 17 March 2017; Published: 17 April 2017

Abstract: Based on the complete dynamic calculation method, the layout, force, and strength of harvester boom cylinders were designed and calculated. Closed simulations for the determination of the dynamic responses of the harvester boom during luffing motion considering the cylinder drive system and luffing angle position control have been realized. Using the ADAMS mechanical system dynamics analysis software, six different arm poses were selected and simulated based on the cylinder as the analysis object. A flexible model of the harvester boom luffing motion has been established. The movement of the oil cylinder under different conditions were analyzed, and the main operation dimensions of the harvester boom and the force condition of the oil cylinder were obtained. The calculation results show that the dynamic responses of the boom are more sensitive to the luffing acceleration, in comparison with the luffing velocity. It is seen that this method is very effective and convenient for boom luffing simulation. It is also reasonable to see that the extension of the distance of the bottom of the boom is shortened by adjusting the initial state of the boom in the working process, which can also effectively reduce the workload of the boom—thus improving the mechanical efficiency.

Keywords: boom; hydraulic cylinder; dynamical simulation

1. Introduction Harvesters are employed effectively in level-to-moderately steep terrain for clearcutting areas of forest [1,2]. For very steep hills or for removing individual trees, humans working with chain saws are still preferred in some countries. In northern Europe, small and maneuverable harvesters are used for thinning operations, and manual felling is typically only used in extreme conditions where tree size exceeds the capacity of the harvester head or by small woodlot owners [3]. The luffing movement is usually driven by the modern automobile crane’s hydraulic motor or cylinder. Dynamic force can be generated in the drive system during starting or braking, which is harmful to the safety of the crane, but also to the crane driver’s health. Because of the payload of the suspender, the motion of the pendulum and the dynamic force can be very significant. For this reason, many crane dynamics studies have been reported in the literature [4]. Most of the published articles concentrate on dynamic responses of booms during rotating and hoisting motions, such as Guangfu Sun’s [5] research of the lifted load motion considering changes in rotating, booming, load hoisting, and support system. Chin et al. [6] demonstrated the effects of a platform motion on the dynamic stability of the boom crane. Keum-Shik Hong et al. [7] investigated the influences of transverse and travel motions of a three-dimensional overhead crane system on the payload pendulum. Recently, David Blackburn et al. [8] studied the dynamics of a slewing-crane. The majority of input-shaping theory is based on linear analysis. M.A. Hannan [9] presented a numerical investigation of the nonlinear dynamic response of a fully submerged payload hanging from a fixed crane vessel.

Machines 2017, 5, 13; doi:10.3390/machines5020013 www.mdpi.com/journal/machines Machines 2017, 5, 13 2 of 9

Machines 2017, 5, 13 2 of 8 Only a few works have paid attention to the luffing motion of harvester booms. Sawodny et al. [10] proposed a dynamic model for the boom luffing of a rotary crane and used this model to control the payloadOnly a p fewendulum works during have luffingpaid attention motion. to However, the luffing the model motion is of only harvester rigid, without booms. considerationSawodny et al. of [10 the] proposed boom deformation. a dynamic Hirokazu model for et the al. boom[11] showed luffing another of a rotary control crane model and used for level this luffingmodel to motion control of thea crane payload with pendulum a combination during of luffing feedback motion. and However,feedforward. the However model is, only the workrigid, withoutfocused considerationonly on the control of the strategy, boom deformation. and the dynamic Hirokazu behavior et al. [ 11of] the showed boom another was not control considered. model Kilicaslianfor level luffing et al. [ motion12] used of a a multi crane-body with dynamic a combination theory of similar feedback to the and principle feedforward. of “kinematic However, force the” workin the focused crane, only wherein on the the control amplitude strategy, of and luffing the dynamic motion driven behavior by of hydraulic the boom waspressure not considered. having a specifiedKilicaslian speed et al. [ and12] used time a is multi-body assumed dynamicto be cycloid. theory This similar is similar to the principle to the principle of “kinematic of ‘‘kinematic force” in forcing’’.the crane, Because wherein of the the amplitude large inertia of luffingl forces motionof the crane driven structure, by hydraulic for the pressure start-up having and braking a specified of a cranespeed system, and time the is assumeddriving force to be and cycloid. torque This generated is similar by to thethe principlemotor or ofcylinder “kinematic are time forcing”.-complicated Because functions.of the large These inertial driving forces forces of the p cranelay an structure, important for role the in start-up exerting and dynamic braking responses of a crane and system, control the effects.driving Inforce this and paper, torque the generated luffing boom’s by the motor cylinder or’s cylinder dynamic are behaviortime-complicated will be functions.considered. These The calculationdriving forces will play be realized an important for a hydraulic role in exerting harvester dynamic boom. responses Because andthe boom control structure effects. In is thissubject paper, to notthe luffingonly elastic boom’s deformation, cylinder’s flexible dynamic multi behavior-body willdynamic be considered. theory will The be calculationused to describe will be the realized boom luffingfor a hydraulic motion. harvesterThe drive boom. system Because is cylind therical boom, and structure is described is subject using to hydraulic not only elasticand control deformation, theory. Theflexible generalized multi-body cylinder dynamic driving theory forces will bewill used be derived to describe using the the boom virtual luffing work motion. principle. The driveSimulations system ofis cylindrical,crane luffing and motion is described will be usingcarried hydraulic out. As a and numerical control theory.simulation The example, generalized a dynamic cylinder analysis driving offorces the will harvester be derived was using carried the virtual out by work the principle. mechanical Simulations system of dynamic crane luffing analysis motion software will be ADAMScarried out.—first Asly a numericaldesigning simulation and calculating example, thea dynamic boom, analysis secondly of the analyzing harvester force, was carried and finally out by calculatingthe mechanical column system stability. dynamic In analysissummary, software the three ADAMS—firstly-dimensional model designing of the and boom calculating was est theablished boom, bysecondly the SolidWorks analyzing software, force, and and finally was calculating imported columninto the stability. ADAMS In simulation summary, software. the three-dimensional The boom’s differentmodel of working the boom conditions was established were simulated by the SolidWorks and analyzed software, by ADAMS and was to imported obtain working into the area ADAMS and stresssimulation situation software. [13]. The The results boom’s can different provide workingthe important conditions parameters were for simulated the assembly andanalyzed design, and by ADAMSprovide a toreference obtain workingfor selecting area reasonable and stress pose situation parameters. [13]. The results can provide the important parameters for the assembly design, and provide a reference for selecting reasonable pose parameters. 2. The Method of Complete Dynamic Calculation 2. The Method of Complete Dynamic Calculation The harvester hydraulic pump translates mechanical energy from the engine into hydraulic energy,The drive harvesters hydraulic hydraulic oil pumpto the translatesmulti-way mechanical valve block energy, and fromthen the, controlled engine into by hydraulicthe cab control energy,, handledrives hydraulics the core oil position to the multi-way of the integrated valve block, valve and block then, in controlled accordanc bye thewith cab the control, principle handles of load the sensingcore position control of [ the14] integrated. Its main work valve progress block in accordanceis turning by with rotating the principle bodies, ofmain load boom sensing lifts, control telescopic [14]. boomIts main extension work progress, and other is turning movements by rotating [15,16] bodies,. The worki mainng boom condition lifts, telescopic of the harvester boom extension, boom is relativelyand other movements complex. The [15 , main16]. The hydraulic working cylinder, condition the of the secondary harvester hydraulic boom is relatively cylinder, complex.and the telescopicThe main hydraulic cylinder are cylinder, all large the flow secondary components, hydraulic and cylinder, other hydraulic and the telescopic components cylinder interact are and all worklarge flowtogether components, [17]. A virtual and other prototype hydraulic model components was created interact in order and to work study together the boom [17 ].(Figure A virtual 1). Becauseprototype the model harvester was createdboom rotation in order is tolimited study by the the boom cockpit (Figure, the1 ).maximum Because theload harvester of the boom boom is 12rotation,300 N is— limitedthe sum by of the the cockpit, weight theof the maximum load that load must of thebe able boom to issupport 12,300 N—thethe logging sum head of the and weight the weightof the load of the that tree must. Figure be able 2 shows to support the structure the logging of the head harvester and the weightboom; the of the linkages tree. Figure are connected2 shows the by pivotstructure pins. of Static the harvester analysis boom;of the theboom linkages is a prerequisite are connected for dynamic by pivot pins.simulation Static analysisanalysis. ofDuring the boom the movementis a prerequisite of the for boom, dynamic the simulation maximum analysis.bending momentDuring the on movement the end of of the the boom boom, occurs the maximum when it extendsbending to moment the farthest on the end end of of the the working boom occurs range. when At this it extendspoint, the to boom the farthest acts as end a rigid of the body working, and accordingrange. At this to point,the connection the boom acts of each as a rigid assembl body,y, and the according main boom to the and connection the second ofary each boom assembly, are articulatedthe main boom in the and column the secondary on the cantilever boom are beam. articulated in the column on the cantilever beam.

Figure 1. The boom model and structure diagram diagram..

Machines 2017, 5, 13 3 of 8 Machines 2017, 5, 13 3 of 9

I J G F E F2 F1 M2(F) α β K B θ C D A M1(F) m1g

m2g

FigureFigure 2. 2. BoomBoom structure structure and and force force diagram diagram..

2.12.1.. Calculation Calculation of of the the Main Main Cylin Cylinderder

2.1.12.1.1.. Force Force Analysis Analysis TheThe main main cylinder cylinder is is the the boom’s boom’s lifting lifting power power in in order order to to provide provide enough enough hoisting hoisting force force [17 [17]. ]. TheThe force force does does not not act act directly directly on on the the jib, jib, but but is is transmitted transmitted to to the the jib jib through through intermediate intermediatess such such as as thethe pusher pusher and and link, link, and and is is then then transmitted transmitted to to the the harvesting harvesting head head at at the the end end of of the the telescopic telescopic arm. arm. TheThe axial axial force force FF ofof the the main main hydraulic hydraulic cylinder cylinder is is calculated calculated on on its its piston piston area. area.

π2 π 2 2 −3 2 S1SD=D 2=  ×110110 2 = 94989498 mm mm 2 = 9.4989.498  10× 310 m 2 m (1)(1) 1 4444 5 F1 = S1 × Pmax = 9498 × 25 = 2.37 × 10 N (2)       5 π FSP1π 1 max 9498 25 2.37 10 N (2) S = (D2 − d2) = × (1102 − 772) = 4844 mm2 = 4.844 × 10−3 m2 (3) 2 4 4 2 2 2 2 25  3 2 S( DF 2 d= ) S × P (110max = 4844 77 ) × 484425 = mm1.21 ×  4.84410 N  10 m (3) (4) 2 44 where S1 represents the piston (rodless cavity) area; S2 represents the rod-side annular area of the piston 5 (with rod cavity); F1 representsFSP the2  hydraulic max force 4844 acting  25  on 1.21 the  10 piston N (thrust force); F2 represents(4 the) hydraulic force acting on the ring area of the side of piston rod (pulling force); Pmax represents the max wherepressure S1 represents of the hydraulic the piston circuit, (rodless value 25cavity) MPa; areaD represents; S2 represents outside the diameter rod-side ofannular hydraulic area cylinder, of the pistonvalue 110(with mm; rodd represents cavity); F1 therepresents diameter the of the hydraulic piston rod,force value acting 77 mm.on the piston (thrust force); F2 represents the hydraulic force acting on the ring area of the side of piston rod (pulling force); Pmax represents2.1.2. Column the max Stability pressure Calculation of the hydraulic circuit, value 25 MPa; D represents outside diameter of hydraulicThe boom’scylinder movement, value 110 ismm powered; d represents by hydraulic the diameter cylinder of and the determinespiston rod, thevalue stability 77 mm. of the load of the entire boom, so it is necessary to check the column stability of the piston rod. 2.1.2. ColumnThe secondary Stability moment Calculation of the piston rod inertia moment I: The boom’s movement is powered by hydraulic cylinder and determines the stability of the π × d4 π × 0.0774 load of the entire boom, so it isI =necessary =to check the column= 1.72 ×stability10−6 m of4 the piston rod. (5) 64 64 The secondary moment of the piston rod inertia moment I:

Cross-sectional area of piston rod S44: d 0.077 I   1.72  1064 m (5) 64 64 πd2 π × 0.0772 S = = = 4.65 × 10−3 m2 (6) Cross-sectional area of piston rod4 S: 4

22 Critical load of piston rod Fk: d 0.077 S   4.65  1032 m (6) 44 nπ2EI 1 × 3.142 × 2.1 × 1011 × 1.72 × 10−6 F = = = 1 × 106 N (7) Critical load of pistonk Lrod2 Fk: 0.82 2 2 11 6 where n represents the end conditionn EI 1  factor, 3.14  the 2.1 main  10 cylinder  1.72  10 for the two-point6 hinge, value n = 1; E Fk   1  10 N (7) represents elastic modulus valueL22 of the piston rod0.8 material, value E = 2.1 × 1011 Pa; L represents the wherelength n ofrepresents the piston the rod; endI represents condition factor, the secondary the main moment cylinder of for the the piston two- rodpoint inertia hinge moment., value n = 1; E represents elastic modulus value of the piston rod material, value E = 2.1 × 1011 Pa; L represents the length of the piston rod; I represents the secondary moment of the piston rod inertia moment.

Machines 2017, 5, 13 4 of 8

6 Fk 1 × 10 5 = = 5 × 10 NFmax (nk is stability safety factor), satisfying condition. nk 2

2.2. Calculation of the Second Cylinder

2.2.1. Force Analysis The second cylinder is generally arranged on the main boom, and connects the triangular pusher with the main boom. The axial force F of the second hydraulic cylinder is calculated based on its piston area. π π S = D2 = × 902 = 6358 mm2 = 6.358 × 10−3 m2 (8) 1 4 4 5 F1 = S1 × Pmax = 6358 × 25 = 1.59 × 10 N (9) π π S = (D2 − d2) = × (902 − 632) = 3243 mm2 = 3.243 × 10−3 m2 (10) 2 4 4 4 F2 = S2 × Pmax = 3243 × 25 = 8.11 × 10 N (11) where S1 represents the piston (rodless cavity) area; S2 represents the rod-side annular area of the piston (with rod cavity); F1 represents the hydraulic force acting on the piston (thrust force); F2 represents the hydraulic force acting on the ring area of the side of piston rod (pulling force); Pmax represents the max pressure of the hydraulic circuit, value 25 MPa; D represents outside diameter of the hydraulic cylinder, value 90 mm; d represents the diameter of the piston rod, value 63 mm.

2.2.2. Column Stability Calculation The secondary moment of the piston rod inertia moment I:

π × d4 π × 0.0634 I = = = 7.7 × 10−7 m4 (12) 64 64 Cross-sectional area of piston rod S:

πd2 π × 0.0632 S = = = 3.1 × 10−3 m2 (13) 4 4

Critical load of piston rod Fk:

nπ2EI 1 × 3.142 × 2.1 × 1011 × 7.7 × 10−7 F = = = 1.96 × 106 N (14) k L2 0.92 where n represents the end condition factor, the second cylinder for the two-point hinge, value n = 1; E represents elastic modulus value of piston rod material, value E = 2.1 × 1011 Pa; L represents the length of piston rod; I represents the secondary moment of the piston rod inertia moment.

6 Fk 1.96 × 10 5 = = 9.84 × 10 NFmax(nk is stability safety factor), satisfying condition nk 2

3. Dynamic Simulation of the Cylinder

3.1. The Preprocessor of the Boom’s Virtual Prototyping After importing the SolidWorks model into ADAMS, the ADAMS working environment is set up including units, gravitational acceleration, and grid. The constraints between the different components are deﬁned according to the movement of the various components of the boom. Between the hydraulic cylinder and piston rod, the paper can use translational to analysis. In the ADAMS software, the constraints of each part of the working arm are shown in Table1. Machines 2017, 5, 13 5 of 9

3. Dynamic Simulation of the Cylinder

3.1. The Preprocessor of the Boom’s Virtual Prototyping After importing the SolidWorks model into ADAMS, the ADAMS working environment is set up including units, gravitational acceleration, and grid. The constraints between the different components are defined according to the movement of the various components of the boom. Between the hydraulic cylinder and piston rod, the paper can use translational to analysis. In the ADAMSMachines 2017 software,, 5, 13 the constraints of each part of the working arm are shown in Table 1. 5 of 8

Table 1. Virtual constraints between components of the boom. Table 1. Virtual constraints between components of the boom. Part i Part j Constraint Relationship Part i Base GroundPart j FixedConstraint Relationship BaseBase Main cylinder Ground Revolute Fixed BaseBase MainBoom cylinder Revolute Revolute BaseCylinder Piston Boom rod Translational Revolute Cylinder Piston rod Translational MainMain boom boom Second Second boom boom Revolute Revolute JibJib Telescopic Telescopic boom boom Translational Translational PusherPusher Puller Puller Revolute Revolute

3.23.2.. The Boom’s Movement Law The process of the harvester is a a cycle cycle of of snatching, snatching, luffing lufﬁng,, and and rotation rotation.． ItIt can achieve working conditionconditionss with different different working working range range and and lifting lifting capacity capacity in in the the operating operating range range.． In the whole movement, the the cylinder cylinder is is the the only only power power controlling controlling the movementthe movement of the of boom: the tilt,boom: sweep, tilt, expand. sweep, expand.By changing By changing the working the working position ofposition the boom of the (Figure boom3) (Figure several times3) several to complete times to a complete whole telescopic a whole processtelescopic in process different in states, different the forcestates, curve the force of the cu hydraulicrve of the cylinderhydraulic under cylinder various under working various conditions working conditionscan be obtained can be based obtained on the based dynamic on simulationthe dynamic of thesimulation harvester of boom. the harvester The cylinder boom. force The is analyzedcylinder forcein the is whole analyzed working in the process. whole working This will process. help reduce This will the help difﬁculty reduce of the the difficulty operator’s of work,the operator but also’s work,reduce but the energyalso reduce consumption the energy of theconsumption machine. In of the the ADAMS machine. software, In the thereADAMS are twosoftware, kinds ofthere driving are twoconditions kinds of of driving the working conditions arm: of one the is working the main arm oil: one cylinder is the drive,main oil and cylinder the other drive, is the and secondary the other iscylinder the secondary drive. cylinder drive.

(a) (b) (c)

Figure 3. The main cylinder lufﬁngluffing and three typical operation conditions. ( a)) working condition condition 1; 1; (b) working condition 2;2; ((c)) workingworking conditioncondition 3.3.

3.33.3.. Cylinder Drive In simulating thethe mainmain cylindercylinder motion, motion, the the drive drive function function is is set set to to realize realize the the movement movement of theof the jib jiband and telescopic telescopic boom boom by movingby moving the the master master cylinder. cylinder. The The extension extension of the of the main main cylinder cylinder can can drive drive the themain main boom, boom, jib, andjib, and telescopic telescopic boom boom to rotate to rotate around around the hinge the hinge point point B at the B at left the end left of end the of main the boom.main Theboom. working The working width and width load and of the load boom of the are boom affected are by affected a single by telescopic a single telescopicmotion. The motion. following The followingthree typical three conditions typical areconditions selected are from: selected working from condition: working 1 is condition the vertical 1 is position the vertical of the position jib (−90 ◦of), workingthe jib (−90°), condition working 2 is condition the jib at − 245 is◦ theand jib a at horizontal −45° and line, a horizontal and working line, conditionand working 3 is condition the extension 3 is theof the extension jib to the of far the end. jib to the far end.

3.4. Secondary Cylinder Drive

In simulating the motion of the second cylinder, the main cylinder and telescopic boom movement are determined first, and only the second cylinder can be telescopic. The expansion of the second cylinder drives the jib and the embedded telescopic boom rotating around the hinge point C (the hinge point of the main boom and secondary boom). The working range of the boom and its weight are only affected by the secondary cylinder. The master cylinder is set in different states, the boom is set to different initial working states, and the main cylinder and telescopic cylinder are locked. Next, the simulation drive parameters of the secondary cylinder are set, and the simulation time is set to 10 s. The three conditions show the selection of the first luffing angle as −20◦, 0◦, and 45◦ in Figure4. Machines 2017, 5, 13 6 of 9 Machines 2017, 5, 13 6 of 9 3.4. Secondary Cylinder Drive 3.4. Secondary Cylinder Drive In simulating the motion of the second cylinder, the main cylinder and telescopic boom movementIn simulating are determined the motion first , andof the only second the second cylinder, cylinder the can mai ben telescopic. cylinder and The telescopic expansion boomof the movementsecond cylinder are determined drives the firstjib and, and the only embedded the second telescopic cylinder boom can be rotating telescopic. around The the expansion hinge point of the C second(the hinge cylinder point drives of the the mai jibn andboom the and embedded secondary telescopic boom). boomThe working rotating range around of thethe hinge boom point and itsC (theweight hinge are point only affectedof the mai byn the boom secondary and secondary cylinder. boom). The master The workingcylinder isrange set in of different the boom states, and theits weightboom isare set only to differentaffected by initial the secondary working statecylinder.s, and The the master main cylinder is and set telescopic in different cylinder states, theare boomlocked is. Next, set to the different simulation initial drive working parameters states ,of and the thesecondary main cylinder cylinder and are telescopicset, and the cylinder simulation are lockedtimeMachines is. setNext,2017 to, 5 10,the 13 s. simulationThe three conditions drive parameters show the of selection the secondary of the firstcylinder luffing are angle set, and as − the20°, simulation 0°, and6 45 of° 8 timein Figure is set 4to. 10 s. The three conditions show the selection of the first luffing angle as −20°, 0°, and 45° in Figure 4.

(a) (b) (c) (a) (b) (c) Figure 4. The secondary cylinder luffing and three typical operation conditions. (a) Working Figure 4. The secondary cylinder lufﬁng and three typical operation conditions. (a) Working condition; Figurecondition; 4. The(b) W secondaryorking condition cylinder 5; ( luffingc) Working and condition three typical 6. operation conditions. (a) Working (b) Working condition 5; (c) Working condition 6. condition; (b) Working condition 5; (c) Working condition 6. 4. Results Analysis 4. Results Analysis 4. Results Analysis Figure 5 shows that the maximum operating amplitudes of work condition 1, work condition 2, Figure5 shows that the maximum operating amplitudes of work condition 1, work condition 2, and Figurework condition 5 shows that3 are the 4.8 maximum m, 6.9 m ,operating and 8.2 m. amplitudes The figure of show works thecondition “length” 1, workfor the condition end of the 2, and work condition 3 are 4.8 m, 6.9 m, and 8.2 m. The ﬁgure shows the “length” for the end of the andmain work cylinder condition trajectory 3 are, indicating4.8 m, 6.9 mthe, and displacement 8.2 m. The offigure the bottom shows theof the “length” auxiliary for armthe .end Figure of the 5a main cylinder trajectory, indicating the displacement of the bottom of the auxiliary arm. Figure5a mainshows cylinder that the trajectory motion and, indicating work of conditionsthe displacement 1, 2, and of 3 the are bottom different of. Thisthe auxiliary is because arm the. Figuremain arm 5a shows that the motion and work of conditions 1, 2, and 3 are different. This is because the main arm of showsof the workingthat the motion arm is upwardand work sloping of conditions as a result 1, 2of, and the 3decision are different to set. theThis initial is because position the as main working arm the working arm is upward sloping as a result of the decision to set the initial position as working ofcondition the working 1; when arm the is upward master cylindersloping asis retracted,a result of thethe maindecision arm to to set rotate the initialon the position side arm as will working rotate condition 1; when the master cylinder is retracted, the main arm to rotate on the side arm will rotate conditioninwards, and1; when the jibthe low master end cylinderdisplacement is retracted, decreases the gradually.main arm toThe rotate change on therule sides of workarm will condition rotate inwards, and the jib low end displacement decreases gradually. The change rules of work condition 2 inwards,2 and work and conditionthe jib low 3 end are displacement similar. It is decreases obvious that gradually. the reachabl The changee range rule ofs theof work three condition working and work condition 3 are similar. It is obvious that the reachable range of the three working conditions 2conditions and work are condition increasing 3 , are as the similar. working It is position obvious of that the thetelescopic reachabl arme rangecontrolled of the by three the secondary working are increasing, as the working position of the telescopic arm controlled by the secondary cylinder conditionscylinder is aredifferent. increasing According, as the toworking the load position spectrum, of the the telescopic maximum arm load controlled of working by condition the secondary 1 can is different. According to the load spectrum, the maximum load of working condition 1 can reach cylinderreach 3120 is different.kg, while According the maximum to the load load of spectrum,working condition the maximum 2 is 1910 load kg, of andworking the maximum condition lifting1 can 3120 kg, while the maximum load of working condition 2 is 1910 kg, and the maximum lifting capacity reachcapacity 3120 of kg, working while conditionthe maximum 3 is 1230 load kg.of working condition 2 is 1910 kg, and the maximum lifting of working condition 3 is 1230 kg. capacity of working condition 3 is 1230 kg.

(a) (b) (a) (b) Figure 5. Simulation of the main cylinder under three typical work conditions: (a) The end of the Figuremain cylinder 5. Simulation trajectory; of the (b ) mMainain ccylinderylinder underforce. three typical work conditions: (a) The end of the Figure 5. Simulation of the main cylinder under three typical work conditions: (a) The end of the main main cylinder trajectory; (b) Main cylinder force. cylinder trajectory; (b) Main cylinder force. Work conditions 4, 5, and 6 have the luffing angle of the main boom as negative, 0°, and positive.Work Figure condition 6 showss 4, 5that, and the 6 trendhave ofthe the luffing displacement angle of of the the main boom boom end asunder negative, three kinds 0°, and of Work conditions 4, 5, and 6 have the luffing angle of the main boom as negative, 0◦, and positive.working Figureconditions 6 shows are similar, that the with trend the of movement the displacement increasing of theand boom the working end under area three being kinds similar. of workingpositive. conditions Figure6 shows are similar, that the with trend the movement of the displacement increasing of and the the boom working end underarea being three similar. kinds of working conditions are similar, with the movement increasing and the working area being similar. The maximum operation area of work condition 4 is 5.1 m, for work condition 5 it is 5.6 m, and for work condition 6 it is 6.6 m. In order to analyze force change of the main cylinder under different working conditions, the load of the boom end was set to 1230 kg, the simulation time was set to 10 s (the first second is the preparation time of the boom, mainly to adjust movement of the secondary cylinder and telescopic cylinder and lock their luffing movement status), then the luffing motion of main cylinder simulation was carried out. From the force curve of the main cylinder, the first second is the boom’s position adjustment time. From 2 s onward, the force gradually reduced to the end of the action (the boom cylinder has stretching movement under working condition 1, and the force Machines 2017, 5, 13 7 of 9

The maximum operation area of work condition 4 is 5.1 m, for work condition 5 it is 5.6 m, and for work condition 6 it is 6.6 m. In order to analyze force change of the main cylinder under different working conditions, the load of the boom end was set to 1230 kg, the simulation time was set to 10 s (the first second is the preparation time of the boom, mainly to adjust movement of the secondary cylinder and telescopic cylinder and lock their luffing movement status), then the luffing motion of Machinesmain cylinder2017, 5, 13 simulation was carried out. From the force curve of the main cylinder, the first second7 of 8 is the boom’s position adjustment time. From 2 s onward, the force gradually reduced to the end of the action (the boom cylinder has stretching movement under working condition 1, and the force of ofthe the main main cylinder cylinder reach reacheses its its maximum. maximum. Th Thisis is isbecause because from from 2 2 s s onward onward,, the the jib jib is in a verticalvertical position,position, andand the the main main cylinder cylinder is inis maximum in maximum torque; torque with; with the main the main cylinder’s cylinder contraction,’s contraction, the boom the constantlyboom constantly lifted upward, lifted upward, reducing reducing the working the range.working The range lift resistance. The lift torque resistance was torque also decreasing, was also sodecreasing, the force so of thethe mainforce cylinderof the main continued cylinder to continue reduce.d After to reduc the boome. After movement, the boom themovement, force of thethe lufﬁngforce of cylinder the luffing increased cylinder slowly increas undered work slowly conditions under work 2 and condition 3. The mains 2 boom and 3 continuously. The main boom lifted upwardcontinuous withly thelifted continuous upward with contraction the continuous of the main contraction cylinder, of and the increasedmain cylinder, to its maximumand increas value.ed to 5 5 Theits maximum maximum value. force The of the max cylinderimum force is 1.92 of× the10 cylinderN under is 1.92 work × 10 condition5 N under 2, work while condition it is 2.33 × 2, 10whileN underit is 2.33 work × 10 condition5 N under 3.work The condition data of the 3. six The work data conditions of the six work are organized condition ins are Table organized2. It can bein Table seen from2. It can the be table seen that from the the force table on thethat sub-cylinder the force on isthe also sub different-cylinder with is also changes different in the with initial changes position in the of theinitial main position boom. of With the themain increase boom. of With theboom the increase angle,the of the boom’s boom working angle, rangethe boom’s was reduced working and range the forcewas reduced of the cylinder and the gradually force of the reduced. cylinder For gradually work condition reduced 6,. withFor work shrinking condition of the 6, second with shrinking cylinder, theof the jib second moved cylinder, from outside the jib to move inside,d from the outside force of to the ins lufﬁngide, the cylinder force of reduced,the luffing and cylinder it reached reduc theed, minimumand it reache valued the at min aboutimum 5.5 s.value As the at about cylinder 5.5 continueds. As the cylinder to shrink, continue the processd to shrink, of resistance the process torque of alsoresistance increased. torque also increased.

(a) (b)

Figure 6. Simulation of secondary cylinder under three typical work conditions. (a) The end of the Figure 6. Simulation of secondary cylinder under three typical work conditions. (a) The end of the secondary cylinder trajectory; (b) Secondary cylinder force. secondary cylinder trajectory; (b) Secondary cylinder force.

Table 2. The comparison of luffing parameters of main and secondary cylinder. Table 2. The comparison of lufﬁng parameters of main and secondary cylinder. Max Working Range Max Force of Cylinder Average Force of

Max Working(mm) Range Max Force(N) of Cylinder AverageCylinde Force ofr (N) Cylinder (mm) (N) (N) Work condition 1 4798 1.06 × 105 0.78 × 105 5 5 WorkWork conditioncondition 1 2 47986923 1.061.92× × 10105 0.781.63× ×10 105 Work condition 2 6923 1.92 × 105 1.63 × 105 Work condition 3 8235 2.33 × 105 1.95 × 105 Work condition 3 8235 2.33 × 105 1.95 × 105 5 5 WorkWork conditioncondition 4 4 51485148 2.052.05× × 10105 1.271.27× ×10 105 WorkWork conditioncondition 5 5 55925592 1.81.8× × 101055 1.101.10× ×10 1055 WorkWork conditioncondition 6 6 66306630 0.480.48× × 101055 0.230.23× ×10 1055

5.5. ConclusionsConclusions AnalysisAnalysis of of thethe above above conditions conditions shows that the attitude of the boom boom and the the jib jib affects affects the the workingworking rangerange ofof thethe workingworking armarm ofof thethe harvesterharvester whenwhen thethe loadload isis constantconstant andand onlyonly thethe boomboom cylinderscylinders are are extended extended and and contracted. contracted. When When the load the isload determined is determined and only and the only main the boom main cylinder boom changescylinder its changes stretch, its thestretch, changing the changing position position of the main of the boom main and boom jib will and affect jib will the affect whole the boom’s whole work area. So, the force of the cylinder increases with the increase of the working range. When the secondary cylinder’s stroke makes the boom reach its maximum work area (work condition 3), the force of the cylinder also reaches its maximum. In harvesting processes, shortening the telescopic boom’s end can effectively reduce the load of the boom and enhance the mechanical efﬁciency by adjusting the telescopic boom’s initial working state. Generally, the force of the lufﬁng cylinder has a tendency to increase. A 3D boom model was built by SolidWorks software imported into ADAMS Machines 2017, 5, 13 8 of 8 dynamics simulation. Taking the main and secondary cylinders as the research objects, the design and calculations were carried out, and three working conditions were selected to simulate and obtain the working range and force of different working positions. The results show that the working position of the main and secondary boom affect the boom’s working range and the force of cylinders. In this paper, the pitching motion of the working arm is the main consideration, and the working arm can also be turned for further study.

Author Contributions: Rongfeng Shen conceived and designed the experiments and wrote the paper; Xiaozhen Zhang performed the experiments and analyzed the data; Chengjun Zhou contributed materials and analysis tools. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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