Research and Improvement of the Hydraulic Suspension System for a Heavy Hydraulic Transport Vehicle

applied sciences

Article Research and Improvement of the Hydraulic Suspension System for a Heavy Hydraulic Transport Vehicle

Jianjun Wang 1,2,3,4, Jingyi Zhao 1,3,4,5,* , Wenlei Li 1,3,4, Xing Jia 6 and Peng Wei 6

1 Hebei Provincial Key Laboratory of Heavy Machinery Fluid Power Transmission and Control, Yanshan University, Qinhuangdao 066004, China; [email protected] (J.W.); [email protected] (W.L.) 2 College of Mechanical Engineering, Anhui Technical College of Mechanical and Electrical Engineering, Wuhu 241000, China 3 Key Laboratory of Advanced Forging & Stamping Technology and Science, Yanshan University, Qinhuangdao 066004, China 4 Hebei Key Laboratory of Special Delivery Equipment, Yanshan University, Qinhuangdao 066004, China 5 State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China 6 Tianjin Key Laboratory of Aerospace Intelligent Equipment Technology, Tianjin Institute of Aerospace Mechanical and Electrical Equipment, Tianjin 300458, China; [email protected] (X.J.); [email protected] (P.W.) * Correspondence: [email protected]; Tel.: +86-13603358270

Received: 1 July 2020; Accepted: 27 July 2020; Published: 29 July 2020

Featured Application: Adding an accumulator in a suspension system can eﬀectively reduce the hydraulic impact caused by an uneven road, and the appropriate accumulator parameters can be obtained through combined simulation.

Abstract: In order to ensure the ride comfort of a hydraulic transport vehicle in transportation, it is important to account for the eﬀects of the suspension system. In this paper, an improved hydraulic suspension system based on a reasonable setting of the accumulator was proposed for a heavy hydraulic transport vehicle. The hydraulic transport vehicle was a multi-degree nonlinear system, and the establishment of an appropriate vehicle dynamical model was the basis for the improvement of the hydraulic suspension system. The hydraulic suspension system was analyzed, and a mathematical model of the hydraulic suspension system with accumulator established and then analyzed. The results revealed that installing the appropriate accumulator can absorb the impact pressure on the vehicle, while a hydraulic suspension system with an accumulator can be designed. Further, it was proved that a reasonable setting for the accumulator can reduce the impact force on the transport vehicle through simulation, and the optimal accumulator parameters can be obtained. Finally, an experiment in the ﬁeld was set up and carried out, and the experimental results presented to prove the viability of the proposed method.

Keywords: ride comfort; hydraulic shock; hydraulic suspension; accumulator; combined simulation

Appl. Sci. 2020, 10, 5220; doi:10.3390/app10155220 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 15

1. Introduction The suspension system is one of the most important components of a transport vehicle, which can improve the ride comfort, running stability, and reduce the impact force caused by an uneven road.Appl. Sci. Therefore,2020, 10, 5220 it is very important to select the suspension design scheme and suspension2 of 15 parameters in a reasonable way. The large impact force on the vehicle load-bearing platform will aggravateup and down the vibration up and down of the vibration tire, affect of the the adhesion tire, affect between the adhesion the wheel between and the the ground, wheel and and aff theect ground,the braking and force, affect which the braking will cause force, a greatwhich impact will cause on the a stabilitygreat impact of the on vehicle the stability [1–3]. Theof the hydraulic vehicle [1suspension–3]. The hydraulic system hassuspension great advantages, system has one great of advantages, the main functions one of the is to main reduce functions the impact is to reduce on the thevehicle impact load-bearing on the vehicle platform. load-bearing The hydraulic platform. suspensionThe hydraulic system suspension has been system used ha fors been a long used time, for aand long it time can not, and only it can improve not only the improve ride comfort the ride of comfort the vehicle, of the but vehicle, also realize but also raising realize and raising lowering and loweringof the body. of the The body. transportation The transportation requirements requirements are ride comfort, are ride stability, comfort, and stability safety, and but because safety but of becausethe poor of compressibility the poor compressibility of hydraulic of oil, hydraulic the rigidity oil, of the the rigidity hydraulic of suspension the hydraulic is substantial suspension and is substantialthe absorption and ofthe the absorption impact force of the is impact poor. Through force is poor. simulation Through analysis, simulation Banerjee, analysis, S. improved Banerjee, the S. improvedvibration reduction the vibration of a reduction vehicle and ofoptimized a vehicle and the parametersoptimized the of theparameters hydro-pneumatic of the hydro suspension-pneumatic [4]. suspensChoi, S.B.ion realized [4]. Choi, vibration S.B. realized control vibration through control a synovial through control a synovial strategy control [5]. strategy Francois. [5]. compared Francois. compareddifferent gas different models gas to calculatemodels to the calculate spring forcethe spring of a hydro-pneumatic force of a hydro-pneumatic suspension suspension and found thatand foundthe hydro-pneumatic that the hydro- suspensionpneumatic suspension model on considering model on considering energy conversion energy was conversion more accurate was more [6]. accurateWang, G.Y. [6]. improved Wang, G the.Y. rideimproved comfort the of ride a vehicle comfort by changingof a vehicle the dampingby changing of the the suspension damping of under the suspensiondifferent working under conditionsdifferent working [7]. Through conditions simulation, [7]. Through Ansari, simulation, F.A. obtained Ansari, the best F.A. parameters obtained the for bestaccumulator parameters pressure for accumulator for a heavy pres trailersure suspension for a heavy [8 trailer]. Zhang, suspension S.Z. obtained [8]. Zhang, a calculation S.Z. obtained method a calculationfor the suspension method accumulatorfor the suspension according accumulator to the limiting according working to the condition limiting working [9]. Zhao, condition J.Y. studied [9]. Zhao,the compliance J.Y. studied of self-adaption the compliance suspension of self- groupadaption systems suspension in self-propelled group systems transporters in self [-10propelled]. Liu, X. transportersproposed an observer-based[10]. Liu, X. proposed active fault-tolerant an observer- controllerbased active for afault vehicle-tolerant suspension controller system for a [11 vehicle]. Gui, suspensionZ. analyzed system the effects [11]. of Gui, an uneven Z. analyzed road on the a multi-axleeffects of an vehicle uneven with road hydraulic on a multi suspension-axle vehicle and found with hydraulicthat increasing suspension the axle and number found of the that multi-axle increasing vehicle the axl cane e numberffectively of suppress the multi the-axle dynamic vehicle load can on effectivelythe frame andsuppress suspension the dynamic [12]. load on the frame and suspension [12]. The heavy heavy hydraulic hydraulic transport transport vehicle vehicle studied studied is shown is shown in Figure in Figure 1. It is1. a Itspecial is a special transport transport vehicle, notvehicle, a conventional not a conventional road vehicle. road It vehicle.is mainly It used is mainly for transportation used for transportation in construction in construction sites. sites.

Figure 1. TheThe hydraulic hydraulic transport vehicle.

Based on on the the previous previous work, work, an improved an improve methodd method for a hydraulic for a hydraulic suspension suspension system is proposed system inis proposedthis paper. in First, this thepaper. structure First, ofthe the structure suspension of the system suspension was analyzed system andwas expressed analyzed byand a mathematicalexpressed by amodel. mathematical The main model. function The of main the accumulators function of the in accumulators a hydraulic suspension in a hydraulic system suspension of a transport system vehicle of a transportis to absorb vehicle the impact is to absorb pressure, the impact so the pressure, diaphragm so typethe diaphragm accumulator type was accumulator selected. The was hydraulic selected. Thesuspension hydraulic system suspension with accumulators system with was accumulators designed, thenwas thedesigned, mathematical then the model mathematical of the accumulator model of theand accumulator the dynamic and model the ofdynamic the vehicle model established. of the vehicle Finally, established. the combined Finally, simulation the combined was realizedsimulation by waADAMSs realized and by AMESim, ADAMS and and the AMESim, optimal and parameters the optimal of the parameters accumulator of the obtained. accumulator The experiment obtained. wasThe experimentcompared with was thecompared simulation, with which the simulation, verified the which correctness verified of the the correctness simulation of and the design. simulation and design. 2. Analysis of the Suspension System 2. AnalysiThe suspensions of the Suspension system is the System key component of the hydraulic transport vehicle. Its main function is to support the vehicle load-bearing platform and buffer the load. It can also control the lifting action of the whole vehicle [13]. Therefore, the suspension system is very important as it affects the stability of the vehicle. Each axis of a hydraulic transport vehicle is equipped with two sets of hydraulic Appl.Appl. Sci.Sci. 20202020,, 1010,, xx FORFOR PEERPEER REVIEWREVIEW 33 ofof 1515

TheThe suspensionsuspension systemsystem is is thethe keykey componentcomponent ofof thethe hydraulichydraulic transporttransport vehiclevehicle.. ItsIts mainmain functionfunction isAppl.is toto support Sci.support2020, 10 thethe, 5220 vehiclevehicle loadload--bearingbearing platformplatform andand bufferbuffer thethe load.load. ItIt cancan alsoalso controlcontrol thethe liftinglifting actionaction3 of 15 ofof thethe wholewhole vehiclevehicle [13][13].. Therefore,Therefore, thethe suspensionsuspension systemsystem isis veryvery importantimportant asas itit affectsaffects thethe stabilitystability ofof the the vehicle. vehicle. Each Each a axisxis of of aa hydraulichydraulic transporttransport vehicle vehicle isis equipped equipped with with twotwo sets sets of of hydraulic hydraulic suspensionsuspension systems,systemssystems, each, each each set set set of ofwhich of which which is separately is is separately separately connected connected connected with the with with frame the the throughframe frame through through a rotary aa support. rotaryrotary supportThesupport composition.. TThehe compositioncomposition of the hydraulic ofof thethe hydraulichydraulic suspension suspensionsuspension system is systemsystem shown is inis shownshown Figure 2 inin. FigureFigure 22..

Rotary Support SSuspensionuspension FFramerame CylinderCylinder Rotary Support BalanceBalance ArmArm

BrakeBrake SystemSystem

WheelWheel

FigureFigure 2.2. SchematicSchematic diagram diagram of of the the suspension suspensionsuspension system. system.

TheThe single single hydraulichydraulic suspensionsuspension suspension systemsystem system cancan can bebe be simplifiedsimplified simpliﬁed intointo into aa mechanismamechanism mechanism asas as shownshown shown inin inFigureFigure Figure 33.. 3 .

a a CC B DD B 2 c L1 L c L1 L2 WheelWheel G C ' G bb C ' FF

DD''

Figure 3. The simplified mechanism. Figure 3. TheThe simplified simpliﬁed mechanism. The initial angle between the suspension frame and the suspension balance arm is a. It is The initial initial angle angle between between the the suspension suspension frame frame and theand suspension the suspension balance balance arm is a arm. It is is assumed a. It is assumed the rotation angle of the suspension balance arm relative to the suspension frame is c, and assumedthe rotation the angle rotation of the angle suspension of the suspension balance arm balance relative arm to therelative suspension to the framesuspension is c, and frame the strokeis c, and of the stroke of the corresponding suspension cylinder is x. The following equation can be obtained. the stroke corresponding of the corresponding suspension cylinder suspension is x. cylinder The following is x. The equation following can equation be obtained. can be obtained.

q 2 2 L  x  L2 AB  L2 BC  2L L cos(a  c) (1) LL AC+xx= LL2 AB + L2 BC 22LL ABLL BCcoscos((a +a c)c) (1) ACAC AB BC − ABAB BCBC According to the moment balance equation of the suspension mechanism, Equation (2) is According to to the the moment moment balance balance equation equation of the of suspension the suspension mechanism, mechanism, Equation Equation (2) is obtained (2) is obtained as follows. obtainedas follows. as follows. FL1 = GL2 (2) Appl. Sci. 2020, 10, 5220 4 of 15 where F is the force of the suspension cylinder, G is the load on each suspension. According to the triangle area equation, Equation (3) can be obtained.

1 1 L L sin(a + c b) = (L + x)L (3) 2 AB BC − 2 AC 1

So L1 and L2 can be obtained as follows.

LABLBC sin(a + c b) L1 = p − (4) L2 + L2 2L L cos(a + c b) AB BC − AB BC −

L = LBD cos(a + c j) (5) 2 − So, Equation (2) can be transformed as follows, which is the relationship between the force on each suspension and the force of one suspension cylinder.

LABLBC sin(a + c b) F p − = G LBD cos(a + c b) (6) · L2 + L2 2L L cos(a + c b) · − AB BC − AB BC − The full load G on each hydraulic suspension is 17 t, the force F of the suspension cylinder is related to the geometric parameters of the suspension structure, and it can be obtained from Equation (6). The force is 382.52 N and the working pressure of each suspension hydraulic cylinder is 21.3 MPa when the vehicle is fully loaded. When the transport vehicle is running on an uneven road, it can be adjusted freely by the telescopic movement of the suspension cylinders, so that the load-bearing platform is always in a horizontal state, but there will be a hydraulic impact on the suspension cylinder. The main reason for hydraulic impact is that the kinetic energy of the hydraulic oil is converted into pressure energy instantaneously. According to the law of conservation of energy, the dynamic energy of hydraulic oil is converted into elastic potential energy, Equation (7) can be obtained as follows:

1 1 V ρVv2 = ∆P2 (7) 2 2 K0 where V is the volume of the hydraulic oil, v is the average ﬂow velocity, ρ is density of the hydraulic oil, K’ is the equivalent bulk modulus of the hydraulic oil, ∆P is the impact pressure. So, the impact pressure can be obtained as follows: s K ∆P = ρ 0 v = ρcv (8) ρ where c is the transmission velocity of the pressure shock wave in the pipeline. According to the above theory, two simple hydraulic cylinders can be selected as approximate suspension hydraulic cylinders for analysis. There are multiple suspension hydraulic cylinders in the hydraulic transport vehicle similar to this. The two states of the two hydraulic cylinders are shown in Figure4. The two hydraulic cylinders are the same. In the initial position, the two cylinders are in the same horizontal position and the pressure value is the same. It is assumed that the oil is incompressible. According to the change of oil volume in the two cylinders, the following equations can be obtained.

V1 + V2 = 2V0 (9)

d 2 V V = π( ) Y (10) 2 − 1 2 Appl. Sci. 2020, 10, 5220 5 of 15

where V0 is the initial oil volume of the two cylinders, V1 is the oil volume of the left cylinder after change, V2 is the oil volume of the right cylinder after change, ∆V is the changed oil volume, d is the diameter of the cylinder, Y is the change of road surface. According to Equations (9) and (10), ∆V can be obtained as follows.

πd2 ∆V = V V = Y (11) 2 − 0 8 According to the relationship between volume and flow, the changed oil flow Q can be obtained from Equation (12) while the average flow velocity can be obtained as Equation (13).

d∆V πd2 dY Q = = (12) dt 8 · dt Q 1 dY v = = (13) d 2 2 · dt π( 2 ) The relationship between the average ﬂow velocity and the road unevenness is shown as Equation (13). However, it is a simpliﬁed model, in practice, there is a certain angle between the position of the suspension cylinder and the vertical direction, which should be further considered in an accurate calculation. According to Equation (13), Equation (8) can be transformed as follows.

1 dY ∆P = ρc (14) 2 dt From Equation (14), it can be seen that the impact pressure is mainly related to the change of the road surface and the time used. Because the type of hydraulic oil and pipeline has been selected and the unevenness of the road cannot be changed, improving the stability of the transport vehicle can only be achieved by lowering the speed of the vehicle and setting the accumulator. The main function of the accumulator in the suspension system is the gas spring. During transportation, the compression and release of gas can absorb well the impact pressure of the suspension cylinder caused by the uneven Appl.road Sci. surface 2020, 10, and x FOR impact PEER REVIEW load. 5 of 15

V1 V0 V0 V2

(a) (b)

Figure 4. (a) The initial state; (b) the state of encountering an uneven road. Figure 4. (a) The initial state; (b) the state of encountering an uneven road. 3. Improvement of the Suspension Hydraulic System The two hydraulic cylinders are the same. In the initial position, the two cylinders are in the same3.1. Accumulatorhorizontal position Setting and the pressure value is the same. It is assumed that the oil is incompressible. According to the change of oil volume in the two cylinders, the following equations can be obtained. The accumulator is an important elastic element in the suspension system of the transport vehicle, so the accumulator selected was the diaphragm type accumulator. When the transport vehicle is V V  2V running, the accumulator and the hydraulic cylinder1 2 can form0 a hydraulic spring suspension, which( can9) be used to absorb the impact and vibration transmitted by the road. When the transporter is lifting d 2 and lowering, the load will change andV theV motion  ( will) Y be out of sync. This is due to the( poor10) 2 1 2 where V0 is the initial oil volume of the two cylinders, V1 is the oil volume of the left cylinder after change, V2 is the oil volume of the right cylinder after change, ΔV is the changed oil volume, d is the diameter of the cylinder, Y is the change of road surface.

According to Equations (9) and (10), ΔV can be obtained as follows.

d 2 V V V  Y (11) 2 0 8 According to the relationship between volume and flow, the changed oil flow Q can be obtained from Equation (12) while the average flow velocity can be obtained as Equation (13).

dV d 2 dY Q    (12) dt 8 dt Q 1 dY v    d (13)  ( )2 2 dt 2 The relationship between the average flow velocity and the road unevenness is shown as Equation (13). However, it is a simplified model, in practice, there is a certain angle between the position of the suspension cylinder and the vertical direction, which should be further considered in an accurate calculation. According to Equation (13), Equation (8) can be transformed as follows.

1 dY P  c (14) 2 dt From Equation (14), it can be seen that the impact pressure is mainly related to the change of the road surface and the time used. Because the type of hydraulic oil and pipeline has been selected and the unevenness of the road cannot be changed, improving the stability of the transport vehicle can only be achieved by lowering the speed of the vehicle and setting the accumulator. The main function of the accumulator in the suspension system is the gas spring. During transportation, the compression and release of gas can absorb well the impact pressure of the suspension cylinder caused by the uneven road surface and impact load. Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 15

3. Improvement of the Suspension Hydraulic System

3.1. Accumulator Setting The accumulator is an important elastic element in the suspension system of the transport vehicle, so the accumulator selected was the diaphragm type accumulator. When the transport vehicle is running, the accumulator and the hydraulic cylinder can form a hydraulic spring suspension, which can be used to absorb the impact and vibration transmitted by the road. When the transporter is lifting and lowering, the load will change and the motion will be out of sync. This is due to the poor load resistance of the accumulator. In order to solve this problem, the suspension hydraulic system with accumulator was designed as shown in Figure 5. It is composed of a three- position four-way hydraulic directional control valve, a two-position four-way electromagnetic directional control valve, a two-position two-way electromagnetic directional control valve, and throttling orifices.

When the transport vehicle is ready to lift, the two-position two-way electromagnetic reversing control valve is electrified to change the direction and cut off the accumulator from the hydraulic Appl.system. Sci. 2020 At , the10, 5220 same time, the two-position four-way electromagnetic directional control valve6 of 15 is electrified, and the two hydraulic control ports of the hydraulic directional control valve are respectively connected with the hydraulic cylinder and the accumulator to realize the pressure loadcompensation resistance to of the the hydraulic accumulator. cylinder. In order After to solvethe lifting this problem,operation the is completed, suspension the hydraulic all directional system withcontrol accumulator valves return was to designed the initial as shownstate, and in Figurethe accumulator5. It is composed can be ofreconnected a three- position into the four-way system hydraulicwithout impact. directional Because control the valve, pressures a two-position in the accumulator four-way electromagnetic and the hydraulic directional cylinder control are always valve, aequal, two-position connection two-way without electromagnetic impact of the accumulator directional control can be valve, realized. and throttling oriﬁces.

Suspension hydraulic cylinder Accumulator

2/2 electromagnetic directional valve

2/4electromagnetic directional valve

Throttling orifice 3/4 hydraulic directional valve P T P1 Main pressure circuit Pressure compensation circuit

Figure 5. The schematic diagram of the accumulator setting.

3.2. TheWhen Improved the transport Hydraulic vehicle System is of ready Suspension to lift, the two-position two-way electromagnetic reversing control valve is electrified to change the direction and cut off the accumulator from the hydraulic system. At theThe same schematic time, the diagram two-position of the suspension four-way electromagnetic hydraulic system directional of the transport control vehicle valve isafter electrified, adding andthe accumulators the two hydraulic is shown control in ports Figure of the6. The hydraulic load sensing directional technology control valve was areadopted respectively in the connectedhydraulic withsystem. the The hydraulic output cylinder flow and and system the accumulator pressure of to the realize pump the can pressure be changed compensation with the to demand the hydraulic of the cylinder.load and Aftermaintain thes lifting a good operation flow with is completed,pressure matching the all directional. The multi control-way valve valves can return maintain to the a initialgood state,proportional and the characteristic,accumulator can which be reconnected can reduce into the the powe systemr loss without of the impact. system. Because The inlet the and pressures outlet inpressure the accumulator of the proportional and the hydraulic multi-way cylinder valve can are be always kept equal,constant, connection so that the without output impact flow of the accumulatorproportional canmulti be-way realized. valve cannot be affected by the load.

3.2. The Improved Hydraulic System of Suspension The schematic diagram of the suspension hydraulic system of the transport vehicle after adding the accumulators is shown in Figure6. The load sensing technology was adopted in the hydraulic system. The output flow and system pressure of the pump can be changed with the demand of the load and maintains a good flow with pressure matching. The multi-way valve can maintain a good proportional characteristic, which can reduce the power loss of the system. The inlet and outlet pressure of the proportional multi-way valve can be kept constant, so that the output flow of the proportional multi-way valve cannot be affected by the load. Appl. Sci. 2020, 10, 5220 7 of 15 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 15 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 15

Suspension hydraulic cylinder Suspension hydraulic cylinder Accumulator Accumulator Explosion Explosionproof valve proof valve

Pressure Pressure P1 compensation P1 compensation circuit circuit

Emergency Emergencylowering valve lowering valve

Lifting valve Lifting groupvalve group

Switching Switchingvalve group valve group

Load sensitive variable Load displacementsensitive variable pump displacement pump

Figure 6. The schematic diagram of the improved suspension hydraulic system. FigureFigure 6.6. The schematic diagramdiagram ofof thethe improvedimproved suspensionsuspension hydraulichydraulic system.system.

4. Modeling4. Modeling and and Simulation Simulation 4. Modeling and Simulation WithWith the the wide wide application application of theof the hydraulic hydraulic transport transport vehicle vehicle in transportation,in transportation, the the requirements requirements With the wide application of the hydraulic transport vehicle in transportation, the requirements onon ride ride comfort comfort are are becoming becoming higher higher and and higher, higher, to ensureto ensure the the safety safety of theof the transportation. transportation. In orderIn order on ride comfort are becoming higher and higher, to ensure the safety of the transportation. In order to verifyto verify that that the the accumulator accumulator can can reduce reduce the the impact impact on on the the vehicle, vehicle, and and for for the the optimal optimal parameter parameter to verify that the accumulator can reduce the impact on the vehicle, and for the optimal parameter selectionselection of of the the accumulator, accumulator, a a simulation simulation of of the the vehicle vehicle withwith thethe accumulators wa wass carried carried out. out. selection of the accumulator, a simulation of the vehicle with the accumulators was carried out.

4.1.4.1. Mathematical Mathematical Model Model Analysis Analysis of Accumulatorof Accumulator 4.1. Mathematical Model Analysis of Accumulator WhenWhen the the accumulator accumulator is connectedis connected to theto the system, system, it isit generallyis generally connected connected through through a section a section of of When the accumulator is connected to the system, it is generally connected through a section of pipeline,pipeline, which which has a has great a inﬂuence great influence on the characteristics on the characteristics of the accumulator. of the accumulator. Therefore, when Therefore, modeling when pipeline, which has a great influence on the characteristics of the accumulator. Therefore, when themodeling accumulator, the accumulator, the connecting the pipeline connecting can bepipeline considered can be as considered a part of the as accumulator. a part of the Inaccumulator. practical modeling the accumulator, the connecting pipeline can be considered as a part of the accumulator. application,In practical the application, connecting pipelinethe conn betweenecting thepipeline accumulator between and the the accumulator suspension cylinder and the should suspension be In practical application, the connecting pipeline between the accumulator and the suspension as shortcylinder as possible.should be The as short accumulator as possible. system The diagram accumulator is shown system as Figurediagram7. is shown as Figure 7. cylinder should be as short as possible. The accumulator system diagram is shown as Figure 7.

Accumulator Hydraulic cylinder Accumulator Hydraulic cylinder

K K

Pa Qa Pa P2 Qa P2 Orifice v Orifice v

P1 P1 la

a la

d a d

FigureFigure 7. The7. The accumulator accumulator system system diagram. diagram. Figure 7. The accumulator system diagram.

In addition,In addition, the the following following assumptions assumptions should should be be made made when when modeling modeling the the accumulator accumulator [14 [14,15,].15]. In addition, the following assumptions should be made when modeling the accumulator [14,15]. TheThe charge charge pressure pressure of theof the accumulator accumulator is ais slow a slow process, process, so so the the change change of gasof gas pressure pressure and and volume volume The charge pressure of the accumulator is a slow process, so the change of gas pressure and volume cancan be be seen seen as as an an isothermal isothermal process; process; the the dischargingdischarging processprocess of the accumulator accumulator is is fast, fast, and and th thee gas can be seen as an isothermal process; the discharging process of the accumulator is fast, and the gas does not exchange heat with the outside world, so it can be considered as an adiabatic process does not exchange heat with the outside world, so it can be considered as an adiabatic process approximately; the compressibility of hydraulic oil is quite different from gas, so it can be ignored; approximately; the compressibility of hydraulic oil is quite different from gas, so it can be ignored; Appl. Sci. 2020, 10, 5220 8 of 15 gas does not exchange heat with the outside world, so it can be considered as an adiabatic process approximately; the compressibility of hydraulic oil is quite different from gas, so it can be ignored; and the flow of hydraulic oil in the accumulator can be regarded as laminar flow. The approximate flow continuity equation of the accumulator can be expressed as follows. s 2 Qa = C A ∆P (15) d d ρ 0 where Qα is the flow into accumulator, Cd is the orifice discharge coefficient, Ad is the orifice area, and ∆P’ is the pressure difference before and after the orifice. The motion equation of the hydraulic oil in the connecting pipeline and the accumulator is as follows. dQa L + RQa = P Pa (16) dt 1 − where L is the liquid inductance, R is the fluid resistance, P1 is the pressure of the pipeline. L and R are expressed as follows. l L = ρ a (17) Ad

128µla R = (18) 2 πda where µ is the kinetic viscosity, la is the length of the pipeline between accumulator and hydraulic cylinder, da is the diameter of the pipeline. The main function of the accumulator is to absorb the impact pressure of the system. The type of gas charged in the accumulator is nitrogen. The required volume of the accumulator can be calculated according to the Equation (19). 0.004QP2(0.0164la t) V = − (19) a P P 2 − 1 where Va is the required volume of the accumulator, Q is the ﬂow in the pipeline, P2 is the maximum allowable impact pressure, t is the time from the beginning to the end of impact. After calculation and analysis, the accumulator (075-1315-042-711) of Integral Corporation is selected. As the air spring, the accumulator absorbs the impact pressure, and its spring stiﬀness K is equal to the ratio of the force ∆F exerted by the volume change of accumulator gas on the suspension cylinder to the displacement ∆x of the cylinder. It is shown as follows.

k ∆F ∆P A dP kPaV K = = 0 · = A2 = A2 2a (20) ∆x ∆V /A dV k+1 0 V1a where ∆V’ is the changed volume of the gas in the accumulator, V1a is the gas volume in the initial state, V2a is the gas volume in the impact state, A is the area of the cylinder, k is the isentropic exponent of the gas, Pa is the pressure of the accumulator at any moment.

4.2. Motion Equation of the Vehicle The transport vehicle is a complex multi-body system, which has not only an interaction force and relative displacement between the components, but also an interaction between the tire and the road. Therefore, it is very diﬃcult to establish an accurate dynamic model of the whole vehicle. According to the structure of the transport vehicle studied, the following assumptions can be made when building a vehicle motion model [16]. The compressibility of the liquid can be considered as a spring, and the throttle eﬀect of the valve and the leakage of the hydraulic cylinder can be considered as damping. The elasticity of the frame, the load-bearing platform, and the driver’s cab is much less than that of the suspension system, Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 15

The compressibility of the liquid can be considered as a spring, and the throttle effect of the valve Appl.and Sci.the2020 leakage, 10, 5220 of the hydraulic cylinder can be considered as damping. The elasticity of the frame,9 of 15 the load-bearing platform, and the driver’s cab is much less than that of the suspension system, and they are regarded as rigid bodies without considering elastic deformation. The vibration influence of andthe diesel they are engine, regarded transmission as rigid bodies shaft, without and gearbox considering on the elasticwhole deformation.vehicle is ignored. The vibration Because influence only the ofsuspension the diesel system engine, of transmission the vehicle is shaft, studied, and gearboxthe influence on the of whole the steering vehicle system is ignored. is not Because considered. only theThe suspension center of gravity system of of goods the vehicle is assumed is studied, to remain the influence unchanged of the under steering full load system condition. is not considered. The center of gravity of goods is assumed to remain unchanged under full load condition. TheThe simplifiedsimplified dynamic model of the vehicle is modeled as as show shownn in in Figure 8 8,, andand MM isis thethe massmass ofof thethe vehiclevehicle load-bearingload-bearing platform,platform, mmii isis thethe massmass ofof wheel,wheel, kkii isis thethe stistiffnessffness ofof thethe hydraulichydraulic suspension,suspension, kktiti isis the the stiffness stiffness of ofthe the tire, tire, ζi isζ thei is damping the damping of the of hydraulic the hydraulic suspension, suspension, zi0 is thezi0 verticalis the verticaldisplacement displacement of the ofconnection the connection point, point, zi is zthei is verticalthe vertical displacement displacement of of the the tire tire center, center, yyi i isis the the unevennessunevenness of of the the road, road,Z Z1 1is is the the vertical vertical displacement displacement ofof the the mass mass center, center,θ θx,x,and andθ θyy isis thethe angleangle ofof rotationrotation around the the XX--axisaxis and and YY-axis.-axis.

Z1 Z30 Z20 θx

M Z40 L2 X

Z10 k3 ζ 3 k2 ζ 2 Y θy k1 k4 ζ 1 ζ 4 z3 z2 m3 m2 kt3 kt2 z1 z4 y3 m1 y2 m4

kt1 kt4

y1 y4

FigureFigure 8.8. The dynamic modelmodel ofof thethe vehicle.vehicle.

AccordingAccording to Newton’sNewton’s law and the dynamic model model of of the the vehicle, vehicle, the the forceforce andand verticalvertical displacementdisplacement ofof thethe connectionconnection pointpoint cancan bebe obtainedobtained asas followsfollows [[17].17]. . . Fi = ki[zi zi0] + ci[zi zi0](i = 1, 2, 3, 4) (21) Fi  ki[z−i  zi0 ] ci[−zi  zi0 ](i 1,2,3,4) (21)   z = Z 0.5L θ 0.5L θ  10z  Z1  0.51Lx  0.52 Ly  10 1− 1 −x 2 y  z20 = Z1 + 0.5L1θx 0.5L2θy  z  Z  0.5L− 0.5L  (22)  z3020= Z1 1 0.5L1θ1x +x 0.5L2θy2 y   − (22)  z z =ZZ+0.50.L5Lθ+0.50L.5Lθ  40 30 1 1 1 1x x 2 2y y  According to Equations (21) andz (22),40  theZ1  three0.5L direction1 x  0.5L motion2 y equations of the vehicle load- bearing platform can be obtained as Equation (23). The motion equation of the unsprung mass is According to Equations (21) and (22), the three direction motion equations of the vehicle obtained as Equation (24). load- bearing platform can be obtained as Equation.. (P23). The motion equation of the unsprung mass  MZ = F  1 i is obtained as Equation (24).  ..  IXθx = 0.5[(F2 + F4) (F1 + F3)]L1 (23)  .. −  IYθy = 0.5[(F3 +F4) (F1 + F2)]L2 MZ1  − Fi ..  mizi + ζi(zi zIi0) + ki(0zi.5[(ziF0) + Fkti()zi (Fyi) =F0)](iL= 1, 2, 3, 4) (24) − X x − 2 4 − 1 3 1 (23)   where IX is the rotation inertia of theIY platform y  0.5 about[(F3  theF4 )X-axis,(F1 IYFis2 )] theL2 rotation inertia of the platform about the Y-axis.

The vibration equationmi zi  ofi ( thezi  wholezi0 )  systemki (zi  canzi0 ) be obtainedkti(zi  y asi )  follows.0(i 1,2,3,4) (24)

.. . where IX is the rotation inertia of the platform about the X-axis, IY is the rotation inertia of the platform [M]Z + [ζ]Z + [K]Z = [Kt]Y (25) about the Y-axis. where M is the mass matrix, ζ is the damping matrix, K is the stiﬀness matrix, Kt is the tire stiﬀness matrix, Q is the unevenness matrix of the road. Appl.Appl. Sci.Sci. 20202020,, 1010,, xx FORFOR PEERPEER REVIEWREVIEW 1010 ofof 1515

TheThe vibrationvibration equationequation ofof thethe wholewhole systemsystem cancan bebe obtainedobtained asas follows.follows.   [[MM]]ZZ[[]]ZZ[[KK]]ZZ [[KKtt]]YY ((2525)) Appl. Sci. 2020, 10, 5220 10 of 15 wwherehere MM isis thethe massmass matrixmatrix,, ζζ iiss thethe dampingdamping matrix,matrix, KK isis thethe stiffnessstiffness matrix,matrix, KKtt isis thethe tiretire stiffnessstiffness matrix,matrix, QQ isis thethe unevennessunevenness matrixmatrix ofof thethe roadroad.. 4.3. The Simulation Model 4.3.4.3. TheTheBecause SimulationSimulation hydraulic ModelModel transport vehicles are used to transport heavy goods, the class B road is selected in theBecauseBecause simulation, hydraulic hydraulic a 3D road transport transport is established vehicles vehicles with are are used used a length to to transport transport of 10 m and heavy heavy a width goods, goods, of 3 the the m. class class The tire B B road road is also is is selectanselect importanteded inin thethe part simulation,simulation, of the vehicle, aa 3D3D roadroad so isis the establishedestablished accuracy withwith of the aa length tirelength model ofof 1010 plays mm andand an aa width importantwidth ofof 33 m.m. role TheThe in tire thetire ischaracteristicsis alsoalso anan importantimportant of the part transportpart ofof thethe vehicle vehicle,vehicle, model. soso thethe The accuracyaccuracy suspension ofof thethe system tiretire modelmodel of the playsplays whole anan vehicleimportantimportant is studied, rolerole inin thenotthe characteristics onlycharacteristics the vertical of of force the the transport transport of the tire, vehicle vehicle but also model model the.. longitudinal The The s suspensionuspension force system system and external of of the the whole whole force should vehicle vehicle be is is studied,considered,studied, notnot only soonly the thethe UA verticalvertical tire type forceforce is ofof selected thethe tire,tire, [ 18 bubu].tt alsoalso According thethe longitudinallongitudinal to the tire forceforce type andand and externalexternal speciﬁc forceforce parameters shouldshould bebe of considered,theconsidered, transport soso vehicle, thethe UAUA a tiretire tire typetype model isis selectedselected is obtained. [18].[18]. According ThisAccording hydraulic toto thethe transport tiretire typetype vehicle andand specificspecific is self-propelled, parametersparameters of soof the the transportwheelstransport are vehicle,vehicle, added aa totiretire drive modelmodel directly isis obtained.obtained. in the ThisThis model. hydraulichydraulic The ﬁnal transporttransport vehicle vehiclevehicle model isis selfself is established--propelled,propelled, soso as thethe shown wheelswheels in areFigureare addedadded9. toto drivedrive directlydirectly inin thethe model.model. TheThe finalfinal vehiclevehicle modelmodel isis establishedestablished asas shownshown inin FigureFigure 9.9.

FigureFigure 9. 9. TheThe model model of of the the whole whole vehicle. vehicle.

ThenThen the the AMESim AMESim model model of of the the suspension suspension system system isis built. built. And And the the ADAMS ADAMS model model is is imported imported intointointo thethe AMESimAMESim AMESim model,model, model, thethe the combinedcombined combined simulationsimulation simulation modelmodel model cancan can bebe obtained beobtained obtained asas shownshown as shown inin FigureFigure in Figure 10.10. TheThe 10 . parametersTheparameters parameters ofof thethe of model themodel model areare aresetset setaccordingaccording according toto tothethe the design.design. design. TheThe The ssamplingampling sampling intervalinterval interval isis is setset set asas as 0.010.01 0.01 ss in in ADAMS,ADAMS, andand inin orderorderorder to toto observe observeobserve the thethe simulation simulationsimulation process processprocess clearly, clearly,clearly, the thethe sampling samplingsampling period periodperiod is is setis setset as asas 0.001 0.0010.001 s in ss inAMESimin AMESimAMESim [19 [19].[19].]. In In theIn thethe simulation, simulation,simulation, an anan impact impactimpact load loadload 10 4 1010N44 N N is is addedis addedadded to toto the thethe vehicle vehiclevehicle load-bearing loadload--bearingbearing platform platformplatform at attheat thethe 10th 10th10th second. secosecond.nd.

ZS_X4 GT_F1 ZS_X4 GT_F1 ZSZS__VV44 GT_X4 ZS_F1 GT_X4 ZS_F1 GTGT__VV44 GT_F2 ZSZS__XX33 GT_F2 ZSZS__VV33 ADAMS ZS_F2 ADAMS GTGT__XX33 ZS_F2 For GTGT__VV33 For ZS_X2 GT_F3 AMESimAMESim ZS_X2 GT_F3 ZSZS__VV22 GT_X2 ZSZS__FF33 GT_X2 GTGT__VV22 ZS_X1 GTGT__FF44 ZS_X1 ZSZS__VV11 GT_X1 ZSZS__FF44 GT_X1 GTGT__VV11

Figure 10. The combined simulation model. Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 15 Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 15 Appl. Sci. 2020, 10, 5220 11 of 15 Figure 10. The combined simulation model. Figure 10. The combined simulation model. 4.4. The Parameter Selection of the Accumulator 4.4. The Parameter Selection of the Accumulator 4.4. The Parameter Selection of the Accumulator The initial charging pressure of the accumulator is 30 bar in the simulation, the pressure fluctuation The initial charging pressure of the accumulator is 30 bar in the simulation, the pressure curvesThe of initialone suspension charging hydraulic pressure of cylinder the accumulator are obtained is by 30 taking bar in di thefferent simulation, accumulator the volumes, pressure fluctuation curves of one suspension hydraulic cylinder are obtained by taking different accumulator fluctuationas shown in curves Figure of 11 one. It suspension can be seen hydra that theulic fluctuations cylinder are of obtained cylinder by pressure taking different are relatively accumulator small in volumes, as shown in Figure 11. It can be seen that the fluctuations of cylinder pressure are relatively volumes,the first 3 as s, shown because in the Figure system 11. isIt can not be stable seen when that the it is fluctuations first started. of Aftercylinder 5 s, pressure it can be are seen relatively that the small in the first 3 s, because the system is not stable when it is first started. After 5 s, it can be seen pressuresmall in the fluctuation first 3 s, ofbecause the cylinder the system is relatively is not stable small whenwhen theit is accumulator first started. volume After 5 iss,0.75 it can L, be and seen the that the pressure fluctuation of the cylinder is relatively small when the accumulator volume is 0.75 thatfluctuation the pressure range fluctuation is within 5 bar.of the The cylinder pressure is relatively fluctuations small are when relatively the accumulator large under othervolume volumes, is 0.75 L, and the fluctuation range is within 5 bar. The pressure fluctuations are relatively large under other whichL, and the obviously fluctuation cannot range meet is within the requirements. 5 bar. The pressure Therefore, fluctuation the accumulators are relatively volume large is under selected other as volumes, which obviously cannot meet the requirements. Therefore, the accumulator volume is volumes,0.75 L. which obviously cannot meet the requirements. Therefore, the accumulator volume is selected as 0.75 L. selected as 0.75 L.

20 20 0.5L 15 0..755LL 15 0.751LL 11.L5L 10 1.5L 10 5

bar

bar P / 0 P 0 -5 -5 -10 -10 -15 -15 0 5 10 15 20 25 0 5 10 15 20 25 T/s T/s Figure 11. The pressure fluctuations of the cylinder under different volumes of accumulator. FigureFigure 11. 11. TheThe pressure pressure fluctuations ﬂuctuations of of the the cylinder cylinder under different diﬀerent volume volumess of accumulator.

After the accumulator volume is set to 0.75 L, the pressure fluctuation curves of the suspension After the accumulator volume is set to 0.75 L, the pressure fluctuation fluctuation curves of the suspension hydraulic cylinder are obtained under the different accumulator charging pressures, as shown in hydraulic cylinder are obtained under the different different accumulator charging pressures, as shown in Figure 12. It can be seen that the pressure fluctuation of the cylinder is at a minimum when the Figure 12.12. It It can can be be seen seen that that the the pressure pressure fluctuation fluctuation of of the the cylinder is at a minimum when the charging pressure is 30 bar. Under other charging pressures, the pressure fluctuations of the charging pressure pressure is is30 30bar. bar. Under Under other other charging charging pressures, pressures the pressure, the pressure fluctuations fluctuations of the suspension of the suspension hydraulic cylinder are too large to meet the requirements. Therefore, the charging suspensionhydraulic cylinder hydraulic are cylinder too large are to meet too large the requirements. to meet the Therefore,requirements. the charging Therefore, pressure the charging of the pressure of the accumulator is selected as 30 bar. pressureaccumulator of the is selectedaccumulator as 30 is bar. selected as 30 bar.

15 15 10bar 10 1030barbar 10 3050barbar 5070barbar 5 70bar 5 0

bar

bar P / -5 P -5 -10 -10 -15 -15 -20 -20 0 5 10 15 20 25 0 5 10 15 20 25 T/s T/s Figure 12. The pressure fluctuations of the cylinder under different charging pressures of the FigureFigure 12. 12.The The pressure fluctuations ﬂuctuations of ofthe the cylinder cylinder under under different diﬀ erentcharging charging pressures pressures of the of accumulator. the accumulator. accumulator. 5. Analysis of the Experiment and Simulation 5. Analysis Analysis of of the Experiment and Simulation When the vehicle is running with full load, the ride comfort standard of this special transport When the vehicle is running with full load, thethe ride comfortcomfort standard of this special transport vehicle is such that the impact pressure of the suspension hydraulic cylinder is no more than 20 bar, vehicle is such that the impact pressure of the suspension hydraulic hydraulic cylinder cylinder is is no no more more than than 2 200 bar, bar, and the height change of the vehicle platform should be less than 50 mm [20–22]. and the height change of the vehicle platform should be less than 50 mmmm [[2020––2222].]. Appl. Sci. 2020, 10, 5220 12 of 15

Appl.Appl. Sci. Sci. 2020 2020, ,10 10, ,x x FOR FOR PEER PEER REVIEW REVIEW 1212 of of 15 15 From the above simulation results, it can be concluded that the accumulator setting plays a FromFrom the the above above simulation simulation results, results, itit can can be be concluded concluded that that the the accumulator accumulator setting setting plays plays a a positiveFrom role the in suspensionabove simulation impact results, reduction. it can In order be concluded to verify the that simulation the accumulator results, the setting experiment plays a positivepositive role role in in suspension suspension impact impact reduction. reduction. In In order order to to verify verify the the simulation simulation results, results, the the experiment experiment inpositive the ﬁeld role was in suspension carried out asimpact shown reduction. in Figure In 13 order. to verify the simulation results, the experiment inin thethe fieldfield wawass carriedcarried outout asas shownshown inin FigureFigure 13.13.

FigureFigureFigure 13.13. 13. The The experimentexperiment inin thethe ﬁeld.field. field.

TheTheThe datadatadata acquisitionacquisitionacquisition ininin thethethe experimentexperimentexperiment isisis based basedbased on onon LabVIEW LabVIEWLabVIEW software. software.software. TheThe principleprincipleprinciple ofof datadatadata transmissiontransmissiontransmission isis is shownshown shown inin in FigureFig Figureure 1414 14... The The data data ofof sensorssensor sensorss cancan bebe convertedconvert converteded intointo into voltage voltage signals,signal signals,s, anda andnd thethe the correspondingcorrespondingcorresponding pressure pressurepressure value valuevalue can cancan be bebe obtained obtainedobtained after afterafter conversion conversionconversion and andand calculation. calculation.calculation. Data DataData measuring measuringmeasuring in the inin

ﬁeldthethe fieldfield experiment experimentexperiment is shown isis shownshown in Figure inin FigureFigure 15. 1515..

Signal acquisition Signal system

Signal acquisition Signal system Signal acquisition Signal system GNDGND

++2424VV R PressurePressure sensor sensor 4 4 +24V RR OutOut put put:0:0--2020mAmA AGNDAGND

+24V Pressure sensor 3 ++2424VV RR PressurePressure sensor sensor 3 3 R SignalSignal 4 4 OutOut put put:0:0--2020mAmA

Signal 3 (

Signal 3 ( Input

Signal 3 ( Input +24V Input ++2424VV R PressurePressure sensor sensor 2 2 RR SignalSignal 2 2 Out put:0-20mA :

Out put:0-20mA : : :

Out put:0-20mA 0

5000

- 5000 SignalSignal 1 1 5000 ++2424VV R PressurePressure sensor sensor 1 1 +24V RR

Pressure sensor 1 mV mV

OutOut put put:0:0--2020mAmA mV

)

) )

FigureFigureFigure 14.14. 14. The The principleprinciple ofof datadata transmissiontransmission and and acquisition. acquisitionacquisition. .

Figure 15. Data measuring in the field. FigureFigureFigure 15.15. 15. Data Data measuringmeasuring inin thethe ﬁeld.field.field.

5.1.5.1.5.1. PressurePressure ofof thetthehe SuspensionSuspension CylinderCylinderCylinder InInIn thethethe experiment,experiment,experiment, thethe cementcement blocksblocks are are selectedselected as as the the load, load, and and the the speed speed is isis set setset to toto 10 1010 km/h. kmkm/h./h. TheTheThe pressure pressurepressure curves curvescurves of of of one one one suspension suspensionsuspension cylinder cylinder cylinder are areare obtained obtained obtained and and and compared compared compared with with with the the the combined combined combined simulationsimulation as as shown shown in in Figure Figure 16. 16. It It can can be be seen seen that that the the input input impac impactt load load causes causes the the impact impact pressure pressure atat thethe 10th10th second.second. WWhenhen thethe accumulatoraccumulator isis connected,connected, thethe impactimpact pressurepressure isis obviouslyobviously reduced,reduced, Appl. Sci. 2020, 10, 5220 13 of 15

Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 15 Appl.simulation Sci. 2020 as, 10 shown, x FOR PEER in Figure REVIEW 16 . It can be seen that the input impact load causes the impact pressure13 of 15 and the maximum reduction is 12 bar. From Figure 16, it can be seen that the pressure fluctuation of at the 10th second. When the accumulator is connected, the impact pressure is obviously reduced, the suspension hydraulic cylinder is large when the accumulator is disconnected, the maximum and and the maximum reduction reduction is is 12 12 bar. bar. F Fromrom Figure Figure 16,16, it it can can be be seen seen that that the the pressure pressure fluctuation fluctuation of of minimum pressure are 227 bar and 207 bar in the experiment; but when the accumulator is connected, thethe suspension suspension hydraulic hydraulic cylinder is large when the accumulator is disconnected, the maximum and and the pressure fluctuates within 7 bar, and the fluctuation is relatively smooth. The experimental results minimum pressure are 227 bar and 207 207 bar bar in in the the experiment; experiment; but but when when the the accumulator accumulator is is connected, connected, are basically consistent with the combined simulation results, which shows the correctness of the thethe pressure pressure fluctuates fluctuates within 77 bar, andand thethe fluctuationfluctuation isis relativelyrelatively smooth.smooth. TheThe experimentalexperimental results simulation, and further verifies the rationality of the accumulator parameter selection. are basically consistent with with the combined simulation results, results, which which shows shows the the correctness of of the simulation, and and further further verifies verifies the the rationality rationality of ofthe the accumulator accumulator parameter parameter selection. selection.

230 Simulation 230 Experiment Simulation 230 Experiment 225 Simulation 230225 Experiment Simulation Experiment

225220 225220

bar

bar /

220 / P

215 P 220215

bar

/ P 215210 P 215210 210 210 205 205 0 5 10 15 20 25 0 5 10 15 20 25 205 T/s 205 T/s 0 5 10 15 20 25 0 5 10 15 20 25 (a) T/s (b) T/s (a) (b) Figure 16. The pressure of one cylinder: (a) Accumulator off; (b) accumulator on. Figure 16. The pressure of one cylinder: (a) Accumulator oﬀ;(b) accumulator on. Figure 16. The pressure of one cylinder: (a) Accumulator off; (b) accumulator on. 5.2. Ride Comfort of the Vehicle 5.2. Ride Comfort of the Vehicle 5.2. RideIn order Comfort to ofverify the Vehicle the correctness of the design, the change curves of the vehicle load-bearing In order to verify the correctness of the design, the change curves of the vehicle load-bearing platformIn order center to areverify collected the correctness as shown ofin theFigure design 17. ,When the change the accumulator curves of the is on, vehicle it can load be seen-bearing that platform center are collected as shown in Figure 17. When the accumulator is on, it can be seen that the the height of the vehicle platform changes smoothly, and the displacement change of the vehicle platformheight of center the vehicle are collected platform as changes shown smoothly, in Figure and17. When the displacement the accumulator change is ofon, the it can vehicle be seen platform that platform in the vertical direction is obviously reduced. thein the height vertical of the direction vehicle is platform obviously changes reduced. smoothly, and the displacement change of the vehicle platform in the vertical direction is obviously reduced.

80 40

8040 4020

mm /

400 / 200

mm /

0 / 0 D D -40 -20

--4080 --2040 0 5 10 15 20 25 0 5 10 15 20 25 -80 T/s -40 T/s 0 5 10 15 20 25 0 5 10 15 20 25 (a)T /s (b)T /s (a) (b) Figure 17. The platform height change: (a) Accumulator off;(b) accumulator on. Figure 17. The platform height change: (a) Accumulator off; (b) accumulator on. 6. ConclusionsFigure 17. The platform height change: (a) Accumulator off; (b) accumulator on. 6. Conclusions The suspension system of a newly developed hydraulic transport vehicle was studied in this 6. Conclusions paper.The The suspension suspension system system of of a the newly transport developed vehicle hydraulic was analyzed transport in detail, vehicle and wa thes impactstudied force in th onis thepaper. transportThe The suspension suspension vehicle causedsystem system byof theofa newlythe uneven transport developed road vehicle analyzed hydraulic wa ands analyzed calculated.transport in vehicledetail, Based onand wa the sthe studied analysis impact in offorce th theis paper.accumulatoron the Thetransport suspension mathematical vehicle system caused model of by the and the transport the uneven whole vehicleroad vehicle analyzed wa motions analyzed and equation, calculated. in detail, the 3D Basedand model the on includingimpact the ana forcelysis the onroadof the and transport accumulator vehicle vehicle were mathematical created, caused and by the model modeluneven and imported roadthe wholeanalyzed into vehicle AMESim and calculated. motion model, equation, and Based finally on the the a 3D combined ana modellysis ofsimulationincluding the accumulator the carried road out. and mathematical vehicle The simulation we modelre created, results and the and show whole the that model vehicle a reasonable imported motion into selection equation, AMESim of the accumulator model, 3D model and includingparametersfinally a combined the can road reduce simulation and the vehicle impact carried we pressurere out. created, The of simulation andthe suspension the model results importedcylinder. show that Finally,into a reasonable AMESim a real vehicle model, selection field and of finalexperimentaccumulatorly a combined was parameters carried simulation out, can and reduce carried the datathe out. impact of The one simulation suspensionpressure resultsof hydraulic the suspensionshow cylinder that a cylinder.reasonable with the Finally, accumulator selection a real of accumulatoronvehicle and field off under experimentparameters full load wacan collecteds reducecarried theout, when impact and the the vehicle pressure data of was one of runningthe suspension suspension at normal hydraulic cylinder. speed. cylinder Finally, The researchwith a real the vehicleaccumulator field experiment on and off uwanders carried full load out, collected and the whendata of the one vehicle suspension was running hydraulic at normal cylinder speed. with Thethe accumulatorresearch results on andshow off that under the settingfull load of collected the accumulator when the and vehicle a reasonable was running selection at normal of parameters speed. The not research results show that the setting of the accumulator and a reasonable selection of parameters not Appl. Sci. 2020, 10, 5220 14 of 15 results show that the setting of the accumulator and a reasonable selection of parameters not only have a great effect on the impact pressure reduction of the suspension cylinder, but also have a positive effect on the ride comfort of the transport vehicle.

Author Contributions: J.Z. proposed the research method. The simulation and experiments were performed and the manuscript was written by W.L. and J.W. The creation of models and the manuscript revision were performed by X.J. and P.W. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Key Research and Development Program of China (2019YFB2005204), National Natural Science Foundation of China (51675461, 11673040), Key Research and Development Program of Hebei Province (19273708D), the Scientific Research Project Foundation of Anhui Education Department (KJ2019A1161), the Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems (GZKF-201922) and the Open Project Program of Tianjin Key Laboratory of Aerospace Intelligent Equipment Technology, Tianjin Institute of Aerospace Mechanical and Electrical Equipment. Conflicts of Interest: The authors declare no conflict of interest.

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