Aerial work platform truck

Dynamic Characteristics Simulation of Aerial Work Platform Truck Luffing system Based on Mutlab/SimulinkAbstract：In this paper，the principle of work of aerial work platform truck luffing system is introduced and The mathematics model is established. With Matlab/Simulink the simulation model of luffing system is constructed, meanwhile the dynamical characteristics is implemented. By analysising the simulation results, this paper provides theoretical foundation for design and improve of luffing system.Keywords：Aerial Work Platform Truck；Luffing system；Mutlab/Simulink；Dynamic Simulation0. IntroductionEngineering machineries extensively applied on departments of the economic development. And it occupies a very important position in economic development. Aerial work platform truck as an important branch of engineering machineries field, is widely used in ship、architecture、port 、public works etc. Aerial work platform truck which has a wide horizon of development is an emerging industry. Our country’s aerial work platform is only 20 or 30 years old. In the early period its development wasn’t very good with a limit on economic environment and technological level[1-3].So the improvement of working performance has important practical significance. Luffing system is one of the main work units of aerial work platform truck, whether the choice of the parameters and the designing of structural parameters are reasonable affect the reliability and advanced character. Accordingly, luffing system is discussed in detail in this paper.Matlab/simulink is a soft package which is used to model、simulate and analysis. It Provides many modules, such as sinks、source、nonlinear、continuous and discrete etc[4]. Its application not only shortens the research cycle, but also reduces the development costs and enhances the work efficiency.1. Structure and working principle of Luffing systemAerial work platform truck’s luffing means changing the distance between platform and the spool thread with poly-centers of slewing, this distance is called radius. Derricking mechanism extends its operation radius from up-down orientation to one side. In this paper luffing mechanism adopt fluid cylinder movement[5].The structure of luffing system of aerialwork platform truck is shown in Fig.1Fig.1. Luffing system of aerial work platform truck1-Hydraulic Pump; 2- overflow valve;3-3position 4 port reversed valve; 4-balance valve 5-Hydraulic cylinder; 6-oil filterThe luffing of arm is controlled by 3position 4 port reversed valve(figure M). Hydraulic Pump 1 droved by electric machine when the reversed valve works (pos.no.3, right frame), outputting pressure oil , then it is sent to the reversed valve(pos. no. 3, right frame) passing hydraulic pipe, eventually enters the rodless cavity of hydraulic cylinder after passing the balance valve 4. The hydraulic oil of sucker rodof hydraulic cylinder pass reversed valve (pos. no. 3, right frame), then flows back to tank passing oil filter [6]. The pressure of system is controlled by overflow valve 2. Balance valve 4 can make the hydraulic loop produce proper resistance, preventing the hydraulic cylinder and working parts gliding under tare load or the uneasing motion which is caused by speeding under tare load in the descend movement. 2. Building of mathematical models(1)Building of mathematical models of the reversed valve[7]v x is the displacement of the slide valve,Q 1 is the flow which enter the left cavity of piston passing slide valve, Q 2 is the flow that right cavity flows back to tank passing slide valve, so the average flow of system can be defined as follows:122Q Q +The average flow output from slide valve, after linearization can be defined as follows:l q v c l Q K x K P =- (1)Where, K q is the flow magnifying coefficient , K c is the pressure flow magnifying coefficient, P l is the output pressure.(2) The flow continuity equation of luffing hydraulic cylinder (asymmetrical hydraulic cylinder).This paper takes the internal leakage coefficient and external leakage coefficient of the hydraulic cylinder into consideration, and it is laminar flow. So the equation of oil enter cavity of hydraulic cylinder can be defined as follows1111121()e dV V dp ic ec dt dtQ C p p C p β=-+++⋅ (2) The equ ation of oil flow back to cavity ofhydraulic cylinder can be described by2222122()e dV V dp ic ec dt dtQ C p p C p β=----⋅ (3) Where, C ic is the internal leakage coefficient of hydraulic cylinder, C ec is theexternal leakage coefficient of hydraulic cylinder, V 1 is the volume of oil enter cavity of hydraulic cylinder, V 2 is the volume of oil flow back to cavity of hydraulic cylinder, βe is the bulk modulus of hydraulic fluid.The total volume of working chamber of hydraulic cylinder can be described by [8]1011V V A y =+ (4)2022V V A y =- (5)Where, V 01 is the initial volume of oil enter cavity of hydraulic cylinder, V 02 is the initial volume of oil flow back to cavity of hydraulic cylinder. Y is the piston displacement.Simplifying the equation 2, 3, 4 can get equation as follows101024()e l p tc l l l Q A s y C p V s p V s p β=⋅⋅+⋅+⋅⋅+⋅⋅ (6)Where, tc C is the total leakage coefficientof hydraulic cylinder, it can be described by12tc ic ec C C C =+ (7)A p is the cross section of hydraulic cylinder, it can be described by12A A p A +=(8)Where, A 1 is the cross section of rodless cavity of hydraulic cylinder, A 2 is the cross section of sucker rod of hydraulic cylinder.(3)Establishing force equilibrium equationsbetween hydraulic cylinder loadAccording to practical application, this paper takes the quality and viscous damping coefficient into consideration, neglecting spring loadanddisturbanceload,excludingnonlinear(coulomb friction ,for example) and oil quality, so the force equilibrium equations can be written as2212()d y dyl dt dtA A p mB -=+ (9) Where, m the total quality of piston andload , B is the viscous damping coefficient of piston and load [9].4.Building of transfer function and simulation modelAfter laplace alternation , the equation1, 6,9 can be rewrote as followsl q v c l Q K x K P =- (10)10102()e l p tc l l l Q A s y C p V s p V s p =⋅⋅+⋅+⋅⋅+⋅⋅ (11)212()l p p A A p ms x Bs x -=⋅+⋅ (12)According to Equations10, 11 and 12, after eliminating middle variable(Q l 、P l ) can get the output equation of hydraulic cylinder as follows12()12()()320102010222222124()()4()()12121212[)][]k qvA A A A m V V mkB V V BK ce ceA A A A A A A A A A e e x s s sy ββ-+++-----++++=(13)Where, K ce is the flow-pressurecoefficient, it can be described byce c tc k k C =+ (14)It is easy to get the transfer function between piston displacement and slide valve displacement as follows12()12()()320102010222222124()()4()()12121212[)][]k q A A A A vm V V mk B V V BK ce ce A A A A A A A A A A e e y x s s sββ-+++-----++++=(15)With the transfer function between piston displacement and slide valve displacemen is constructed, the selection of initial parameters is needed. The system initial parameters are listed in table 1.Table 1. Parameters of systemParameterValue Unit K ce 6.71×10-11 m 3.MP a .s -1A 1 0.009 m 2 A 2 0.005 m 2 V t 5.635×10-3m 3 βe 1.8×109 N .m -2 m 3000 kg B 1.2×103N . s ..m -1 K q2m 2.s -15. Simulating and optimizing of Dynamic CharacteristicsAccording to the initial parameters, the displacement and speed of hydraulic cylinder are shown in Fig.2 and Fig.3.Fig.2. displacement of hydraulic cylinder according to initial parametersFig.3. speed of hydraulic cylinder accordingto initial parametersFig.2 and Fig.3 shows that the reaction time of system is about 0.37 second, after that the system is tending towards stability, and it is clear that the system has a bigger oscillation at first. So the system optimizing is needed.The each parameter of hydraulic system has a great effect on its dynamic quality. Based on preceding simulation, it can easily get the influence of parameters changes on the dynamic characteristics, so it is important to reaches the best performance by the reasonable selection of parameters, then it offers important reference to the optimization of design of hydraulic system [10].(1) When the bulk modulus of hydraulic fluid βe changes from 1.8×109(N/m 2) to 1.4×109(N/m 2), the displacement and speed of hydraulic cylinder are shown in Fig.4 and Fig.5Fig.4. displacement of hydraulic cylinder changing the bulk modulus of hydraulic fluid βeFig.5. speed of hydraulic cylinder changing the bulk modulus of hydraulic fluid βe It is clear in Fig.3 and Fig.4 that when the bulk modulus of hydraulic fluid βe is declined, the dynamic response time of system expands to about 1 second, and the oscillation deepens. This demonstrates that the dynamic characteristics worsen when the bulk modulus of hydraulic fluid βe is declined. There are many factors that affect the dynamic characteristics of system, among which air mixing into oil has the greatest on it [11]. So it is necessary to strictly control the proportion of air in the oil in order to increase the reaction time of system.(2) When the total quality of piston andload(m )increases from 3000kg to 5000kg, thedisplacement and speed of hydraulic cylinder areshown in Fig.6 and Fig.7Fig.6. displacement of hydraulic cylinder increasing the total quality of piston and load(m )Fig.7.speedofhydrauliccylinderincreasing the total quality of piston and load(m )Fig.6 and Fig.7 show that the response time of system becomes longer when increase the total quality of piston and load(m ). It needs about 0.5 second to reach steady state, and the oscillationamplitudeincreases.Thisdemonstrates that the dynamic characteristics under the low-load condition is better than high-load field. So controlling the total quality of piston and load (m ) is essential.(3) When increase the flow magnifying coefficient (K q ), the displacement and speed ofhydraulic cylinder are shown in Fig.8 and Fig.9Fig.8. displacement of hydraulic cylinder increasing the flow magnifying coefficient (K q )Fig.9. speed of hydraulic cylinder increasing theflow magnifying coefficient (K q ) From Fig.8 and Fig.9 it is easy to see thatthe response time of system becomes longer when increase the flow magnifying coefficient (K q ). It needs about 0.6 second to reach steady state, and the oscillation amplitude increases. Therefore, it is essential to control the flow magnifying coefficient (K q ) within reasonable area.(4)It is known that PID controller is the most widely used in modern industry due to its simplicity and clear functionality. In order to further improve the performance of system, PID controller has been equipped [12-13]. So the simulation model can be easily got Fig.11asfollowsFig.11. simulation model equipping PIDcontrollerRunning simulate program can get theFig.12 and Fig.13 as followsFig.12. displacement of hydraulic cylinderequipping PID controllerFig.13. speed of hydraulic cylinder equipping PID controllerThe simulation results show that system performance has been further improved. The PID controller results in greatly reducing the time of the system tending towards stability , a nd reduces the oscillation amplitude by a big range. 6. ConclusionsThis paper introduces the principle, structure, and working process of luffing system. Byusingmutlab/simulink software,weestablished a simulation model and performed a performance simulation. Following conclusions can be drawn:(1) The simulation is implemented bychanging the parameters of the system before designing the actual system, by observing the curve can makes it clear that the effect of parameters disturbance on system performance. This can help designers select proper parameters, design reasonable system. Consequently, it shortens the research cycle and reduces the development costs.(2) By using the closed-loop PID controller, the system dynamic performance can be greatlyimproved.(3) Mutlab/simulink software can raise the design efficiency of luffing system , it is simple, accurate, this supplies effective way to analyse and improve the dynamic characteristics of luffing system. References[1] Zhao jing-yi, Ma yu-liang, Liu Hua. Research ofElectro-hydraulic Control Sytem of Aerial WorkPlatform TLK21[D]. Yanshan university, 2007,5. [2] XU Zhen-bao. Study of Electro-hydraulic Control Sytem for Raise-rise Arm of High Task Vehicle[D]. Shandong University of Science and Technology. 2007,5.[3] KONG De-Qin, The Design and Research of Folding-Arm Aerial Cage ′s Hydraulic System [D]. Herfei University of Technology. 2009,2[4] W ANG Xin, SONG Xiao-guang, XUE Lin.. 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