Design of a New Hydraulic Accumulator for Transient Large Flow Compensation

energies

Article Design of A New Hydraulic Accumulator for Transient Large Flow Compensation

Donglai Zhao, Wenjie Ge *, Xiaojuan Mo, Bo Liu and Dianbiao Dong Department of Mechanical Engineering and Automation, School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China * Correspondence: [email protected]; Tel.: +86-135-7209-3855

Received: 29 June 2019; Accepted: 9 August 2019; Published: 13 August 2019

Abstract: Hydraulic accumulators are widely used in industry due to their ability to store energy and absorb fluid shock. Researchers have designed kinds of novel accumulators with better performance in these specific areas. However, the pressure in these accumulators decreases significantly when the fluid oil is continuously supplied from the accumulator to the hydraulic system. This limitation leads to a transient large pressure drop, especially in a small hydraulic system with varied working frequency. In this research, a combined piston type accumulator is proposed with a relatively steady pressure property. The gas chamber and the fluid chamber are separated by a cam mechanism. By using the nonlinear property of the cam mechanism, the nonlinear relationship between the pressure and the volume of the gas can be offset. Hence, the fluid pressure can be maintained in a relatively steady range. The defect of the traditional accumulator in the frequency varied system is analyzed in detail. Then, the structure of the new accumulator is proposed and modeled based on the traditional piston type accumulator. The mathematical equation of the cam mechanism is built under the assumption that the nitrogen gas works in an adiabatic process. A simulation system based on the Amesim platform is constructed, and mathematic equations of the system are given. Preliminary experiments are conducted to evaluate the performance of the new accumulator. The comparison results show that the adaptability of the new accumulator is obviously larger than that of the traditional accumulator in a frequency varied system.

Keywords: new hydraulic accumulator; pressure oscillation; cam mechanism; frequency varied system

1. Introduction A hydraulic accumulator is a rigid tank separated into two regions, one filled with nitrogen gas and the other filled with hydraulic fluid. The bladder type accumulator, the diaphragm type accumulator, and the piston type accumulator are the most widely used accumulators in the industry. An accumulator commonly plays two roles in a hydraulic system; one is to store energy and provide additional fluid power, and the other is to reduce pressure fluctuation and absorb shock. To improve the efficiency of the rotational motion load systems, Triet Hung Ho designed a closed loop hydraulic energy regenerative system using one high pressure accumulator and one low pressure accumulator [1,2]. Henderson designed a novel hydraulic power take-off system with a high pressure accumulator to convert the wave energy [3]. FO António analyzed a general wave energy converter model with a low pressure accumulator and a high pressure accumulator [4]. Zengguang Liu et al. used an accumulator to eliminate fluctuation and intermittence of the hydraulic wind turbine [5,6]. Midgley modeled a hydraulic regenerative braking system with a high pressure accumulator and a low pressure accumulator for an articulated heavy vehicle [7]. Bravo, R. R. S. presented a new concept of a parallel hydraulic pneumatic regenerative braking system. By using the hydraulic accumulator and air

Energies 2019, 12, 3104; doi:10.3390/en12163104 www.mdpi.com/journal/energies Energies 2019, 12, 3104 2 of 17 reservoir, the new system has great flexibility to recover braking energy [8]. Bing Xu et al. designed a speed control system of variable voltage variable frequency (VVVF) hydraulic elevator with the accumulator, and they validated that adding the accumulator could improve the efficiency of the whole system [9]. Bingbing Wang modeled and analyzed a valve controlled system in which the accumulator worked as the oil supplying component and had a sustained pressure decline [10]. Ruichen Wang et al. designed a regenerative hydraulic shock absorber system and analyzed the influence of the accumulator parameters [11]. However, there is an inherent weakness of the traditional accumulator. When working in a hydraulic system that has a large vibration of the flow rate in one cycle, the accumulator has a significant pressure oscillation. To decrease the drop of the pressure, people usually choose a sufficiently large accumulator. However, this method cannot be applied in the mobile system in which the hydraulic system is set with the limitation of volume and weight. People have made plenty of attempts to improve the property of the traditional accumulator. When an accumulator works with a large holding time, the thermal loss during the large charge and discharge cycle can be quite high. Pourmovahed analyzed the thermal loss with and without elastomeric foam in the gas side. The result showed that the gas temperature could maintain nearly constant in a fully foam-filled accumulator, and thermal losses decreased to only 1% [12]. Van de Ven JD designed a flywheel type accumulator that stored the energy in both rotating kinetic and compressed gas. By increasing the angular velocity of the flywheel to 500 rad/s, the energy stored in the flywheel type accumulator could be almost 10 times greater than a normal hydraulic accumulator [13,14]. Joshua J. Cummins et al. designed an advanced strain energy accumulator using carbon nanotube (CNT) embedded rubber [15,16]. Van de Ven JD proposed a new hydraulic accumulator concept that could keep a constant pressure when it worked. By using a variable area piston and a rolling diaphragm, the accumulator could vary the equivalent section area of the gas chamber and keep the fluid pressure constant [17]. In this paper, a combined piston type hydraulic accumulator working with low pressure drop is designed. Contrary to a traditional piston type accumulator, the new accumulator’s fluid cavity and gas cavity both have a piston for sealing and transferring force. The two pistons are connected through a rotary cam mechanism. Using the nonlinear characteristic of the cam mechanism, the nonlinear relationship between the pressure and the volume of the gas can be offset, and the fluid pressure can be maintained in a relatively steady range. In Section2, the flow compensation process of the traditional accumulator in a steady system and a frequency increased system is described. The defect of the traditional accumulator is also discussed. In Section3, the structure design of the new accumulator is given, and the equation of the cam mechanism is built based on the energy equation. In Section4, the simulation models of the new accumulator and the single cylinder hydraulic system are constructed in the Amesim platform. The dynamic equations of the main components are presented. In Section5, the experimental platform is constructed based on the simulation model. The fluid pressures of the new accumulator with different pre-charge gas pressures are tested at a fixed flow rate. The comparison between the new accumulator and the traditional accumulator in a specific example as the working frequency instantly increases from 0.25 Hz to 0.5 Hz is discussed in detail. The effective regions of the new accumulator and the traditional accumulator are also gauged. In Section6, conclusions about the effectiveness of the new accumulator and future work are summarized.

2. Defect of the Traditional Accumulator in the Frequency Varied System The fluid in a hydraulic system is supplied by the hydraulic pump. The flow rate is decided based on the system requirement. Although the variable pump has superiority in the flow rate regulation, considering its size and weight, people prefer to choose a fixed displacement pump in some small hydraulic systems. The flow rate regulation is achieved by the speed regulation of the motor or the engine. Moreover, because the velocity of the cylinder varies in a large range, the flow rate of the pump usually matches the average flow rate of the entire hydraulic system, and the fluctuation of the flow rate is compensated by the accumulator. EnergiesEnergies 20192019, 12, 12, x, 3104FOR PEER REVIEW 3 of3 of18 17

A typical single cylinder hydraulic system is depicted in Figure 1. The diameters of the cylinder A typical single cylinder hydraulic system is depicted in Figure1. The diameters of the cylinder piston are 40 mm/20 mm, and the stroke length is 0.16 m. To simplify the analysis, the cylinder motion piston are 40 mm/20 mm, and the stroke length is 0.16 m. To simplify the analysis, the cylinder motion is designed as a 0.25 Hz sine wave, and the flow rate of the cylinder is calculated and illustrated in is designed as a 0.25 Hz sine wave, and the flow rate of the cylinder is calculated and illustrated in Figure 1. The peak value of the flow rate in extension and retraction of the cylinder is different due Figure1. The peak value of the flow rate in extension and retraction of the cylinder is di fferent due to to the different effective areas in the cap-end chamber and the rod-end chamber. The pump flow rate the different effective areas in the cap-end chamber and the rod-end chamber. The pump flow rate satisfies Equation (1): satisfies Equation (1): 1 ZT T QQdt≥ 1 (1) Qppr0 Qrdt (1) ≥ TT 0 wherewhere QQpp is the the pump pump flow flow rate, rate, QQr isr isthe the flow flow rate rate of the of theentire entire hydraulic hydraulic system, system, and andT is Ttheis the periodperiod time. time.

Vout1 Vout 2

Vin2 Vin3 Vin1

FigureFigure 1. 1. TheThe flow ﬂow rate rate of of the the cylinder cylinder an andd the the pump pump in in a asingle single cylinder cylinder hydraulic hydraulic system: system: (1) (1) motor; motor; (2)(2) fixed ﬁxed displacement displacement pump; pump; (3) (3) hy hydraulicdraulic accumulator; accumulator; (4) (4) proportional proportional valve; valve; (5) (5) cylinder; cylinder; (6) (6) tank; tank; (7)(7) relief relief valve. valve.

DuringDuring a acomplete complete cycle cycle of of the the cylinder cylinder motion motion,, when when the the pump pump flow flow rate rate is is lower lower than than the the cylindercylinder flow flow rate, rate, the the accumulator accumulator compensates compensates the the flow flow rate rate with with a adecrease decrease of of pressure. pressure. When When the the pumppump flow flow rate rate is is larger larger than than the the cylinder cylinder flow flow rate, rate, the the extra extra fluid fluid oil oil flows flows into into the the accumulator. accumulator. WhenWhen the the accumulator accumulator pressure achievesachieves the the rated rated pressure, pressure, the the extra extra fluid fluid oil flowsoil flows through through the reliefthe reliefvalve. valve. From From the view the view of effi ofciency, efficiency, the energy the energy loss of loss the reliefof the valve relief should valve should be minimized. be minimized. The pressure The pressurefeature infeature a steady in a working steady working system issystem that the is pressurethat the pressure of the accumulator of the accumulator can get backcan get to theback rated to thepressure rated afterpressure an entire after workingan entire cycle. working The volumecycle. The of the volume accumulator of the shouldaccumulator satisfy should Equation satisfy (2): Equation (2):   Vout1 V1 V2  ≤ −  V VVV+≤−V V V V (2)  out 1out112out2 in2 1 2   − ≤ − VinVVVVV1 + V+−≤−in2 + Vin3 Vout1 + Vout2  out12212 out in ≥ (2)  ++≥ + VVVin123 in in V out 1 V out 2 where V1 and V2 are the gas volumes of the accumulator in the lowest required pressure and the rated working pressure. Where V1 and V2 are the gas volumes of the accumulator in the lowest required pressure and the In a valve controlled system, the system pressure is usually higher than the working pressure rated working pressure. of the cylinder. When the system pressure decreases, to ensure the actuator works well, the valve In a valve controlled system, the system pressure is usually higher than the working pressure of opening is increased. Since the valve opening has a maximum value, there is a minimum value for the cylinder. When the system pressure decreases, to ensure the actuator works well, the valve the system pressure under which the valve and the cylinder cannot work well. This minimum value opening is increased. Since the valve opening has a maximum value, there is a minimum value for is named as the lowest required pressure. Ignoring the uncertain disturbance at the force load, the the system pressure under which the valve and the cylinder cannot work well. This minimum value working pressure of the actuator cylinder can be approximately calculated when given a certain motion. is named as the lowest required pressure. Ignoring the uncertain disturbance at the force load, the The lowest required pressure can be calculated from the working pressure and the pressure drop of working pressure of the actuator cylinder can be approximately calculated when given a certain the valve. motion. The lowest required pressure can be calculated from the working pressure and the pressure When the pump flow rate is equal to the average flow rate, the energy loss of the relief valve can drop of the valve. be reduced to the minimum value. However, this pump flow rate is not robust enough for a frequency When the pump flow rate is equal to the average flow rate, the energy loss of the relief valve can be reduced to the minimum value. However, this pump flow rate is not robust enough for a frequency

Energies 2019, 12, 3104 4 of 17 Energies 2019, 12, x FOR PEER REVIEW 4 of 18 varied system. As As shown in Figure 22a,a, whenwhen thethe workingworking frequencyfrequency increasesincreases suddenly,suddenly, thethe pumppump flowflow rate cannot cannot match match the the new new flow flow rate rate of of the the sy systemstem immediately immediately because because of the of thehysteresis hysteresis of the of themotor motor speed speed regulation. regulation. Therefore, Therefore, there there is isa atr transitionansition process process between between two two different different working frequencies. The The transition transition process process contains contains two two stages: speed speed regulation regulation stage stage and and recovery recovery stage. stage. The speedspeed regulationregulation stage stage starts starts when when the the working working frequency frequency changes changes and and ends ends when when the pumpthe pump flow rateflow matchesrate matches the new the average new average flow rate flow again. rate Duringagain. During the speed the regulationspeed regulation stage, the stage, fluid the volume fluid andvolume the pressureand the pressure in the accumulator in the accumulator decrease continuously.decrease continuously. The recovery The stagerecovery starts stage after starts the speed after regulationthe speed regulation stage and endsstage whenand ends the pressurewhen the returns pressure to thereturns rated to pressure. the rated pressure. To reducereduce thethe didifficultyfficulty ofof thethe analysis, the example model in Figure1 1 is is idealizedidealized withoutwithout forceforce load and uncertain disturbance. Because the motion of the cylinder in the Figure 1 1 is is aa sinesine wave,wave, thethe working pressure increases whenwhen the motion frequency increases. Thus, the lowest required pressure increases as well. If the increase of the working frequency is large enough, the accumulator pressure drops belowbelow thethe lowestlowest requiredrequired pressure pressure during during the the speed speed regulation regulation stage, stage, as as illustrated illustrated in Figurein Figure2b. Therefore,2b. Therefore, the accuracythe accuracy of the of cylinderthe cylinder motion motion is aff isected affected during during the transitionthe transition process. process.

Vout4 Vout6 Vout8

Vout5 Vout7 V Vout2 out3 Vout1 Vin5 V Vin6 Vin7 Vin8 Vin9 Vin2 in3 Vin4 Vin1

Figure 2. Performance of a traditional accumulator in a single cylinder hydraulic system when the working frequency is suddenly doubled: (a) flowflow rate of the pump and the cylinder; (b) oscillation of the accumulator pressure andand thethe lowestlowest requiredrequired pressure.pressure. There are usually two ways to decrease the excessive pressure drop—increasing the pump flow There are usually two ways to decrease the excessive pressure drop—increasing the pump flow rate or increasing the volume of the accumulator. The former increases the energy loss of the relief valve rate or increasing the volume of the accumulator. The former increases the energy loss of the relief at low working frequency, and the latter increases the weight of the whole system. Considering energy valve at low working frequency, and the latter increases the weight of the whole system. Considering efficiency and weight limit, the above-mentioned ways are not suitable for the small hydraulic system. energy efficiency and weight limit, the above-mentioned ways are not suitable for the small hydraulic This defect of the traditional accumulator is due to the nonlinear characteristic of the gas. The system. exponential compression and expansion processes of the gas cause a large pressure variation during This defect of the traditional accumulator is due to the nonlinear characteristic of the gas. The exponential compression and expansion processes of the gas cause a large pressure variation during the working process. To ease this problem, the gas chamber and the fluid chamber in the accumulator

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theEnergies working 2019, 12 process., x FOR PEER Toease REVIEW this problem, the gas chamber and the fluid chamber in the accumulator5 of 18 should be isolated, and the force between the gas and the fluid should be transmitted through ashould nonlinear be isolated, device. Theand nonlinearthe force between device is the to ogaffsets and the the nonlinear fluid should variation be transmitted of the gas pressurethrough a and maintainnonlinear the device. fluid pressureThe nonlinear in a steady device area. is to offset the nonlinear variation of the gas pressure and maintain the fluid pressure in a steady area. 3. Modeling of the New Accumulator 3. Modeling of the New Accumulator 3.1. Structure of the New Accumulator 3.1. Structure of the New Accumulator When the nitrogen gas is compressed, the pressure of the gas can be calculated using the gas state equation.When the nitrogen Whether gas the is workingcompressed, cycle the is pressu an adiabaticre of the process gas can orbe ancalculated isothermal using process, the gas the relationshipstate equation. between Whether the pressurethe working and cycle the volumeis an ad ofiabatic the gas process is nonlinear. or an isothermal Although process, the change the of relationship between the pressure and the volume of the gas is nonlinear. Although the change of the the gas pressure is nonlinear, the nonlinearity can be offset through anther nonlinear transformation. gas pressure is nonlinear, the nonlinearity can be offset through anther nonlinear transformation. In In the traditional mechanisms, the nonlinear property exists in multi-bar linkages, variable ratio gears, the traditional mechanisms, the nonlinear property exists in multi-bar linkages, variable ratio gears, and cam mechanisms. Considering the complexity and the size, a rotary cam mechanism is chosen to and cam mechanisms. Considering the complexity and the size, a rotary cam mechanism is chosen to achieve this nonlinear transformation. achieve this nonlinear transformation. AsAs illustrated illustrated in Figure Figure 3,3 ,the the new new accumulator accumulator is a iscombined a combined piston piston type accumulator. type accumulator. The fluid The fluidchamber chamber and the and gas the chamber gas chamber are separated are separated by the piston by the and piston the cam and mechanism. the cam mechanism. The fluid chamber The fluid chamberis between is betweenthe fluid theend fluidcover end andcover the fluid and pist theon. fluid The piston. gas chamber The gas is between chamber the is gas between end cover the gas endand cover the gas and piston. the gas The piston. rotary cam The mechanism rotary cam is mechanism fixed in the ismiddle fixed inof the cylinder middle ofwith the two cylinder angular with twocontact angular ball contactbearings ball and bearings a thrust andnut. aThere thrust are nut. four There grooves are fouron the grooves cylinder’s on thewall, cylinder’s which are wall, whichsymmetrically are symmetrically distributed distributed along the alongaxial theline. axial Each line. piston Each has piston a steel has shaft a steel to shafttransfer to transferforce and force anddisplacement, displacement, and andthe steel the steelshaft shaftextends extends from the from grooves. the grooves. Each steel Each shaft steel contacts shaft with contacts the profile with the profileof the ofcam the mechanism cam mechanism through through needle needlebearings. bearings. These grooves These grooves convert convertthe rotary the motion rotary of motion the cam of the cammechanism mechanism into intothe linear the linear motions motions of the ofpistons. the pistons. To decrease To decrease the friction, the friction, the needle the bearing needle is bearing used is usedbetween between the steel the steel shaft shaft and andthe thegroove. groove. The Theend endcovers covers and andthe thepistons pistons are aresealed sealed with with O-rings, O-rings, recordingrecording to to the the structure structure ofof thethe traditionaltraditional piston piston type type accumulator. accumulator.

Figure 3. Mechanism structure of the new accumulator. Figure 3. Mechanism structure of the new accumulator.

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3.2.3.2. ShapingShaping ofof thethe CamCam MechanismMechanism

AsAs shownshown in in Figure Figure4, 4, the the cam cam mechanism mechanism has ha twos two profiles: profiles: one one is the is fluidthe fluid cam profilecam profileL1 andL1 and the other is the gas cam profile L2. In Figure4, the dash line is the previous position of the needle bearing, the other is the gas cam profile L2 . In Figure 4, the dash line is the previous position of the needle andbearing, the solid and the line solid is the line latter is the position latter position of the needle of the bearing. needle bearing. When the When fluid the flows fluid in flows and outin and of theout newof the accumulator, new accumulator, the energy the energy stored instored the fluid in the chamber fluid chamber can be expressedcan be expressed as: as: Z Z Z Z P Adr=−− P Adr fdr fdr P LLLLAdrfg11= PgAdr 2f dr1 2f dr (3)(3) f 1 12121 2 1 2 L1 L2 − L1 − L2 Z P AdrZ=++ P AdrZ fdrZ fdr LLLLfg21 2 1 2 (4) 1212 P f 2Adr1 = PgAdr2 + f dr1 + f dr2 (4) L1 L2 L1 L2 where Pf 1 and Pf 2 are the fluid pressures when the fluid flows out and in, Pg is the pressure of where P f 1 and P f 2 aref the fluid pressures when the fluid flows out and in, Pg is the pressure of the the nitrogen gas, is the friction of the piston, A is the cross-sectional area of the piston, and r1 nitrogen gas, f is the friction of the piston, A is the cross-sectional area of the piston, and r1 and r2 are and r are the arc lengths along L1 and L2 . the arc2 lengths along L1 and L2.

PA− f PA+ f y f 2 y f 1 Δ Δ y1 y1 Δr Δr 1 Fluid cam profile L1 1 Fluid cam profile L1

RΔθ RΔθ

x x

Δr Δr 2 Δ 2 Δ y2 y2 + Gas cam profile L2 − Gas cam profile L2 Pg Af PAg f ()a ()b

FigureFigure 4.4. Model of the cam mechanismmechanism inin 2D:2D: ((aa)) chargingcharging process;process; ((bb)) dischargingdischarging process.process.

The pressure P f 2 is larger than the pressure P f 1 because of the piston friction. The fluid pressure in The pressure Pf 2 is larger than the pressure Pf 1 because of the piston friction. The fluid the accumulator can be decomposed into two parts—the ideal fluid pressure P f (idea) and the disturbed pressure in the accumulator can be decomposed into two parts—the ideal fluid pressure Pf ()idea and pressure P ( ). The disturbed pressure in this paper is defined as a pressure caused by the piston f dis P friction.the disturbed The disturbed pressure pressure f ()dis . The causes disturbed a deviation pressure between in this the pape real fluidr is defined pressure as anda pressure the ideal caused fluid pressure.by the piston Thus, friction. the energy The distur Equationsbed pressure (3) and (4) causes can also a deviation be expressed between as: the real fluid pressure and the ideal fluid pressure. Thus, the energy Equations (3) and (4) can also be expressed as: Z Z P f (idea) P f (dis) Adr1 = PgAdr2 E f (5) L ()P − −=−P AdrL P Adr E− 1 LLfidea() fdis () 12 g 2 f (5) 12 Z Z ()P+=+ P Adr P Adr E PLLf (ideaf()) idea+ P f (dis f () dis) Adr1 1= gPgAdr 22 + f E f (6)(6) 12 L1 L2 E wherewhereE f isf the is the work work of of the the piston piston friction. friction. FromFrom EquationsEquations (5)(5) andand (6),(6), itit cancan bebe seenseen thatthat thethe fluidfluid pressurepressure inin thethe newnew accumulatoraccumulator cancan maintainmaintain aa minimumminimum pressurepressure oscillationoscillation whenwhen thethe idealideal pressurepressure PPf (f idea()idea) is is constant. constant. Therefore,Therefore, thethe key of the new accumulator is the design of the cam profiles that can keep the P f (idea) as a constant. key of the new accumulator is the design of the cam profiles that can keep the Pf ()idea as a constant. Ignoring the friction effect, the ideal energy stored by the fluid should be equal to the energy Ignoring the friction effect, the ideal energy stored by the fluid should be equal to the energy stored by the compressed gas. Assuming the compression and the expansion processes of the nitrogen stored by the compressed gas. Assuming the compression and the expansion processes of the gas obey the ideal gas Equation (7): nitrogen gas obey the ideal gas Equation (7): n n P0V0 = PgVg (7) nn= P00VPVg g (7) where Pg0 and Vg0 are pre-charge pressure and gas volume of the accumulator, n is the polytrophic exponent, and Pg and Vg are the current pressure and the gas volume of the accumulator.

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where Pg 0 and Vg 0 are pre-charge pressure and gas volume of the accumulator, n is the polytrophic exponent, and Pg and Vg are the current pressure and the gas volume of the accumulator.Energies 2019, 12 , 3104 7 of 17 The energy equation of the new accumulator is a second curvilinear integral along the profile of L L the camThe mechanism. energy equation Since of the1 and new accumulator2 are continuously is a second differentiable curvilinear curves, integral the along energy the equation profile of canthe cambe transformed mechanism. as Since EquationL1 and (8):L2 are continuously differentiable curves, the energy equation can be transformed as Equation (8): n θθPV A θθ= gg00 PAkRdfidea() 1 kRd 2 (8) 00− nn Z θ Z ()θVAyg 02 Pg0Vg0A P f (idea)Ak1Rdθ = n k2Rdθ (8) where k and k are the slopes0 of the profiles, R0 and(Vg 0θ areAy2 the) radius and the rotation angle of 1 2 − the cam mechanism, and y2 is the displacement of the gas piston and can be expressed as Equation where k1 and k2 are the slopes of the profiles, R and θ are the radius and the rotation angle of the cam (9): mechanism, and y2 is the displacement of the gas piston and can be expressed as Equation (9): θ y =Z kRdθ (9) 220 θ y2 = k2Rdθ (9) 0 To simplify the design, the profile L2 can be set as a fixed slope line, and the displacement of = θ the gasTo simplifypiston is the y22 design,kR the. The profile nonlinearL2 can betransformation set as a fixed slopecan be line, achieved and the by displacement the profile of L the1 . Assuminggas piston the is y 2working= k2Rθ .process The nonlinear in the accumulator transformation is fast can enough be achieved to be treated by the profile as an adiabaticL1. Assuming process, the theworking value processof the n incan the be accumulator set as 1.4. Then is fast, the enough slope of to the be treatedprofile asL1 an can adiabatic be given process, from Equations the value (8) of andthe n(9).can be set as 1.4. Then, the slope of the profile L1 can be given from Equations (8) and (9).

1.41.4 PPVg0V kk2 k ()θ = gg002g0 k1(1θ) = 1.4 (10)(10) PVAkR() − θ 1.4 P fidea()V gg 0Ak 2Rθ f (idea) 0 − 2 = = = = = GivenGiven the the parameters parameters as as Pgg00 =6060 barbar,V, gV0 g00.2= 0.2L , kL2, k20.35= 0.35, Pfidea(), P f (idea60) bar= ,60A bar19.625, A = cm19.625and cm andR = 4.6R = cm4.6, thecm ,real the cam real camprofiles proﬁles of the of new the new accumulato accumulatorr in the in theexperiment experiment can can be calculated. be calculated. The The resultresult is is shown shown in in Figure Figure 55..

FigureFigure 5. 5. RealReal cam cam profiles proﬁles of of the the new new accumulator accumulator in in the the experiments. experiments.

3.3.3.3. Different Different Pre-Change Pre-Change Gas Gas Pressure Pressure in in the the New New Accumulator Accumulator OnceOnce the the parameters parameters of of Equation Equation (10) (10) are are fixed, fixed, the the profile profile of of the the cam cam mechanism mechanism can can be be decided. decided. AlthoughAlthough thethe designdesign of of the the new new accumulator accumulator is to is closely to closely maintain maintain the fluid the pressurefluid pressure at a given at pressurea given P f (idea), a new, relatively steady fluid pressure with a different pre-charge gas pressure can also be pressure Pf ()idea , a new, relatively steady fluid pressure with a different pre-charge gas pressure can achieved. Assuming the new pre-charge gas pressure is Pg , the new energy equation in the new also be achieved. Assuming the new pre-charge gas pressure 1is P , the new energy equation in the accumulator can be expressed as Equation (11): g1 new accumulator can be expressed as Equation (11): Z n Z n θ Pg0V nnk2 θ Pg1V A θθPVg0 k PV A g0 P f (new)A gg002Rdθθθ= = gg 10 k2Rdθ (11) PAfnew()nnn Rd kRd 2 n (11) 0 00P ( PVAy)(V()g0 −−Ay2) () VAy0 (Vg0 Ay2) f ideafidea()02 g− g 02−

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From Equation (11), the new ﬂuid pressure P f (new) is derived as Equation (12):

Pg1P f (idea) P f (new) = = constant (12) Pg0

Ignoring the effect of the friction, the new fluid pressure P f (new) is proportional to the new pre-charge pressure Pg1. Therefore, the new accumulator can achieve a series of steady fluid pressure with different pre-charge gas pressures, which is validated in Section5.

4. Mathematic Model of the Single Cylinder Valve Controlled System

4.1. Simulation Model To compare the flow compensation property of the traditional accumulator and the new accumulator, a simulation model of the new accumulator is constructed in the Amesim platform, as shown in the lower right dashed frame of Figure6. Considering the piston friction of the new accumulator, the simulation model uses two cylinders to simulate the fluid chamber and the gas chamber. The transformation property of the cam mechanism is built using two rotary-linear modulated transformer submodels. One rotary load submodel is used to simulate the inertia moment of the cam mechanism. The slope of the cam profile L1 is set with the function f (x) according to Equation (10). The slope of the cam profile L2 is set as constant value k2. A traditional bladder type accumulator is Energiesconnected 2019, with 12, x FOR the portPEER of REVIEW the gas chamber, which provides the dynamic property of the compressed9 of gas. 18

Figure 6. Simulation model constructed on Amesim. Figure 6. Simulation model constructed on Amesim. The entire hydraulic system model in the simulation contains the fluid power part, the proportional directionalAs is well valve, known, the actuatorthe dynamic cylinder, of the and hydrauli the loadc system part. has In thea high fluid nonl powerinearity. part, Some a commercial complex controlthree-phase methods asynchronous such as feedback motor is linearization used to drive method, a constant adaptive pump, control, and the and motor sliding speed mode is controlled control haveby a frequencybeen used inverter.to achieve The a better relief performance. valve and the De newspite accumulator the difficult are control the other of the two hydraulic parts of thesystem, fluid thepower traditional part. The PID load control part,as algorithm shown in can the upperstill get right an acceptable dashed frame performance of Figure4 ,in consists the low of anfrequency inertial motion.load and To a simplify force load. the To analysis, simplify the the new simulation, accumulato ther system cylinder and in thethe forcetraditional load uses accumulator the same system size as usethe actuatorthe same cylinder PID controller in the main settings system. in Usingthis paper. a solenoid The flow valve compensation to switch theflow properties direction, of thethe forcetwo accumulatorsload can provide are acompared steady force. in low frequency.

4.2. Proportional Valve Compared with the servo valve, pressure drop and energy loss are lesser in the proportional valve. For energy efficiency purposes, the proportional valve is a better choice in a low frequency hydraulic system. The flow property of the proportional valve can be described by Equation (13) as follows:

2 QCAx=Δ() P dvρ (13)

where Cd is the flow coefficient at the valve port, A()xv is the opening area decided by the valve π ρ Δ−θ spool displacement xv , is the fluid oil density, and P is the pressure difference 2 between the inlet and the outlet of the proportional valve. The equation A()xv achieves a maximum valve Amax when the valve opening percent reaches 100%. With the maximum valve Amax , the lowest required pressure of the system can be calculated given a certain cylinder motion.

4.3. The New Accumulator The bladder accumulator uses a rubber bladder to separate the nitrogen gas and the fluid oil, which is widely used in the low pressure system. Compared with the piston accumulator, the bladder accumulator has a better response velocity. In this paper, the bladder accumulator is considered as a fast response accumulator without response delay in the low frequency system. Different from the bladder accumulator, the new accumulator uses the cam mechanism and two pistons to transform force

Energies 2019, 12, 3104 9 of 17

Another simulation model using the traditional accumulator submodel to replace the new accumulator model is also constructed in the Amesim platform. Because the new simulation model is the same as those in the simulation of Figure6 except the accumulator, the new simulation model is not illustrated in this paper. As is well known, the dynamic of the hydraulic system has a high nonlinearity. Some complex control methods such as feedback linearization method, adaptive control, and sliding mode control have been used to achieve a better performance. Despite the diﬃcult control of the hydraulic system, the traditional PID control algorithm can still get an acceptable performance in the low frequency motion. To simplify the analysis, the new accumulator system and the traditional accumulator system use the same PID controller settings in this paper. The ﬂow compensation properties of the two accumulators are compared in low frequency.

4.2. Proportional Valve Compared with the servo valve, pressure drop and energy loss are lesser in the proportional valve. For energy efficiency purposes, the proportional valve is a better choice in a low frequency hydraulic system. The flow property of the proportional valve can be described by Equation (13) as follows: s 2 Q = C A(xv) ∆P (13) d ρ where Cd is the flow coefficient at the valve port, A(xv) is the opening area decided by the valve spool π displacement xv, ρ is the fluid oil density, and ∆P θ is the pressure difference between the inlet 2 − and the outlet of the proportional valve. The equation A(xv) achieves a maximum valve Amax when the valve opening percent reaches 100%. With the maximum valve Amax, the lowest required pressure of the system can be calculated given a certain cylinder motion.

4.3. The New Accumulator The bladder accumulator uses a rubber bladder to separate the nitrogen gas and the fluid oil, which is widely used in the low pressure system. Compared with the piston accumulator, the bladder accumulator has a better response velocity. In this paper, the bladder accumulator is considered as a fast response accumulator without response delay in the low frequency system. Different from the bladder accumulator, the new accumulator uses the cam mechanism and two pistons to transform force and displacement. Considering the friction force and the moment of inertia, the dynamic equation of the new accumulator is represented by Equation (14):  .  ( ) + ( ) + ( ) = Jω  PgA sgn v f p f mgpagp k2 P f A sgn v f p f m f pa f p k1 θ R  −a k k v k k− × − ×  f p 1 2− f p 10 2  agp = 2 (14)  k  . 1  ω = agp/k2R where Pg and P f are the pressures of the gas chamber and the fluid chamber, A and f are the section area and the friction of the piston in the new accumulator, mgp and m f p are the piston masses in the gas . chamber and the fluid chamber, J and ω are the moment of inertia and the angular acceleration of the cam mechanism, agp and a f p are the accelerates of the two pistons in the gas chamber and the fluid chamber, v f p is the piston velocity in the fluid chamber where the velocity is positive when the gas expands, and sgn(x) is the step function as Equation (15):   1 if x > 0  sgn(x) =  0 if x = 0 (15)   1 if x < 0 − Energies 2019, 12, 3104 10 of 17

Given a certain ﬂow variation, the ﬂuid pressure in the new accumulator can be computed as: " . # 1 1 Jω 1 P f = P f (idea) sgn(v f p) f (1 + ) + (mpagp + ) + m f pa1 (16) − A k1(θ) R k1(θ)

From Equation (16), we can see that the fluid pressure can vibrate along the set value P f (idea). The effect of the inertial force as the second and the third term in the square brackets is much less than the effect of the friction in the low working frequency. Therefore, the dynamic property of the new accumulator is mainly decided by the piston friction.

4.4. The Driving Cylinder In this paper, we use a constant pressure subsystem to supply a constant force load. The subsystem is set with a large enough ﬂow rate to ensure a steady force load. The inertial load slides on the rail by the sliding bearings, which can be treated as an ideal inertial load without friction. The dynamic equation of the inertial load can be written as Equation (17):

. h . . i .. P A P A sgn(x) f + f + P (H(x)A + H( x)A ) = mx (17) 1 1 − 2 2 − 1 2 load 1 − 2 where P1 and P2 are the pressures in the piston side chamber and the rod side chamber, A1 and A2 are effective areas of the piston side chamber and the rod side chamber, f1 and f2 are the friction forces in the driving cylinder and the force load cylinder,m and x are the mass and the displacement of the inertial load, Pload is the pressure in the force load, and the flow rates in the two chambers of the driving cylinder are represented in Equation (18):  q h i  2 . .  Q1 = CdA(xv) ρ H(x) √Ps P1 + H( x) √P1 Pt  q − − − (18)  2 h . . i  Q = C A(xv) H(x) √P Pt + H( x) √Ps P 2 d ρ 2 − − − 2 where Ps and Pt are the supply pressure and the tank pressure of the main system, and H(x) is a function defined by Equation (19) as: ( 1 if x 0 H(x) = ≥ (19) 0 if x < 0

5. Simulation and Experiment Results

5.1. Experiment Platform To test and compare flow compensation properties between the new accumulator and the traditional accumulator, a hydraulic platform based on the previous simulation model is erected, as shown in Figure7. There are two hydraulic circuits—the main actuator circuit and the force load circuit—in the experimental platform. The main circuit uses a three-phase asynchronous motor with 2.2 kw rated power and 2840 r/min rated speed to drive a constant displacement pump. The asynchronous motor is controlled by a SIEMENS frequency inverter. The actuator cylinder is connected to a Hoyea proportional valve BFWNE-02-3C2-32 with electrical position feedback. To ensure the steady of the force load, the flow in the force load circuit is sufficiently supplie by another motor and pump. Rated pressures in the main circuit and the force load circuit are set to 63 bar and 35 bar. The two cylinders with the same size are deployed in the main circuit and the force load circuit. The motion of the actuator cylinder rod is measured by a linear displacement transducer. The working pressure of the main circuit is measured by a pressure transducer. An ADVANTECH PCI-1716 data acquisition card is used to convert the analog signals and send out the valve command. The parameters of the main components of the experiment platform are shown in Table1. Energies 2019, 12, x FOR PEER REVIEW 11 of 18

5. Simulation and Experiment Results

5.1. Experiment Platform To test and compare flow compensation properties between the new accumulator and the traditional accumulator, a hydraulic platform based on the previous simulation model is erected, as shown in Figure 7. There are two hydraulic circuits—the main actuator circuit and the force load circuit—in the experimental platform. The main circuit uses a three-phase asynchronous motor with 2.2 kw rated power and 2840 r/min rated speed to drive a constant displacement pump. The asynchronous motor is controlled by a SIEMENS frequency inverter. The actuator cylinder is connected to a Hoyea proportional valve BFWNE-02-3C2-32 with electrical position feedback. To ensure the steady of the force load, the flow in the force load circuit is sufficiently supplie by another motor and pump. Rated pressures in the main circuit and the force load circuit are set to 63 bar and 35 bar. The two cylinders with the same size are deployed in the main circuit and the force load circuit. The motion of the actuator cylinder rod is measured by a linear displacement transducer. The working pressure of the main circuit is measured by a pressure transducer. An ADVANTECH PCI-1716 data acquisition Energiescard is 2019used, 12 to, 3104convert the analog signals and send out the valve command. The parameters of the11 main of 17 components of the experiment platform are shown in Table 1.

Figure 7. The experiment platform.

Table 1. Main parameters of the simulation and experiment system.

NameName ValueValue Unit Unit DiameterDiameter of piston/piston of piston/piston rod rodof the of the cylinder cylinder 32/16 32/16 mm mm StrokeStroke of the of cylinder the cylinder 15 15 cm cm Mass of the inertial load 20 Kg Mass of the inertial load 20 Kg Displacement of the pump in the main system 6 ml/r DisplacementCracking pressure of the of pump the relief in valvethe main in the system main system 63 6 bar ml/r CrackingCracking pressure pressure of the of therelief relief valve valve in inthe the main force system load part 35 63 bar bar Cracking pressureDiameter of the relief of the valve new accumulatorin the force load part 50 35 mm bar Moment of inertia of the cam mechanism 0.0014 Kg m2 Diameter of the new accumulator 50 · mm Initial gas volume of the new accumulator 0.2 L Moment of inertia of the cam mechanism 0.0014 Kg·m2 Initial gas pressure of the new accumulator 60 bar InitialInitial gas gas volume volume of of the the new traditional accumulator accumulator 0.46 0.2 L L InitialInitial gas gas pressure pressure of of the the new traditional accumulator accumulator 40 60 bar bar Initial gas volume of the traditional accumulator 0.46 L 5.2. Fluid Pressures with Diﬀerent Pre-Charge Pressures

To verify the effectiveness of the new accumulator design, a preliminary experiment focusing on the steady of the fluid pressure is conducted in this subsection. The first experiment is to gauge the fluid pressure when the fluid flows in and out from the new accumulator at a fixed flow rate. In Figure8, the red lines are three ideal fluid pressures, 15 bar, 40 bar, and 70 bar. The pre-charge gas pressure is calculated from Equation (12). The lines with symbols are real fluid pressures tested by the experiment at a steady piston speed of 0.02 m/s. The pressures during acceleration and deceleration processes are not illustrated in this figure. The black arrow indicates the flow direction of the new accumulator. With the effect of the friction, the real fluid pressure when the fluid flows in is larger than the real fluid pressure when the fluid flows out. Therefore, the new accumulator has two levels of pressure, high pressure and low pressure. As shown in Figure8, when the ideal fluid pressure is 15 bar, the average gap between the ideal fluid pressure and real fluid pressure is 1.2 bar. Meanwhile the fluid pressure can maintain almost steady at a certain value, which means the variation of the pressure gap can be neglected in low pressure. When the ideal fluid pressure increases to 40 bar, the average pressure gap increases to 2.8 bar. Moreover, the pressure gap increases with the increase of the fluid charging percent. The maximum variation of the pressure gap is 0.5 bar at the 40 bar ideal Energies 2019, 12, x FOR PEER REVIEW 12 of 18

Initial gas pressure of the traditional accumulator 40 bar

5.2. Fluid Pressures with Different Pre-Charge Pressures To verify the effectiveness of the new accumulator design, a preliminary experiment focusing on the steady of the fluid pressure is conducted in this subsection. The first experiment is to gauge the fluid pressure when the fluid flows in and out from the new accumulator at a fixed flow rate. In Figure 8, the red lines are three ideal fluid pressures, 15 bar, 40 bar, and 70 bar. The pre-charge gas pressure is calculated from Equation (12). The lines with symbols are real fluid pressures tested by the experiment at a steady piston speed of 0.02 m/s. The pressures during acceleration and deceleration processes are not illustrated in this figure. The black arrow indicates the flow direction of the new accumulator. With the effect of the friction, the real fluid pressure when the fluid flows in is larger than the real fluid pressure when the fluid flows out. Therefore, the new accumulator has two levels of pressure, high pressure and low pressure. As shown in Figure 8, when the ideal fluid pressure is 15 bar, the average gap between the ideal fluid pressure and real fluid pressure is 1.2 bar. Meanwhile the fluid pressure can maintain almost steady at a certain value, which means the variation of the pressure gap can be neglected in low pressure. When the ideal fluid pressure increases to 40 bar, the average pressure gap increases to 2.8 bar. Moreover, the pressure gap increases with the increase of the fluid charging percent. The maximum variation of the pressure gap is 0.5 bar at the 40 bar ideal pressure. When the ideal fluid pressure increases to 70 bar, the average pressure gap increases to 4.5 bar. The maximum variation of the pressure gap increases to 1.8 bar at the 70 bar ideal pressure. As discussed in the previous sections, the pressure gap is mainly caused by the friction of the new accumulator. Because the friction in the new accumulator increases with the increase of the pressure, the pressure gap in the high pressure is larger than that in the low pressure. The variation of the pressure Energies 2019, 12, 3104 12 of 17 gap increases with the increase of the pressure, which is mainly due to the inaccuracy of the ideal gas equation at the high pressure. Another pressure characteristic is that the pressure gap when the fluid flowspressure. in is larger When than the idealthe pressure ﬂuid pressure gap when increases the fluid to flows 70 bar, out. the This average is due to pressure the different gap increases lubrication to conditions4.5 bar. The of maximum the two processes. variation of the pressure gap increases to 1.8 bar at the 70 bar ideal pressure.

FigureFigure 8. TheThe fluid fluid pressure pressure of the the new accumulator with a 0.02 m/s m/s piston speed. As discussed in the previous sections, the pressure gap is mainly caused by the friction of the new 5.3. Comparison in A Large Instant Flow Compensation Process accumulator. Because the friction in the new accumulator increases with the increase of the pressure, the pressureTo show gap the in different the high flow pressure compensation is larger than properties that in theof lowthe pressure.two accumulators, The variation a detailed of the experimentpressure gap with increases working with frequency the increase instantly of the increasing pressure, from which 0.25 is mainlyHz to 0.5 due Hz to is the tested. inaccuracy Based on of the averageideal gas flow equation rate, the at thepump high speeds pressure. are set Another to 820 pressurer/min and characteristic 1700 r/min, iscorrespondingly. that the pressure The gap first when 4 s inthe the fluid experiment flows in isrepresent larger than the thefluid pressure charging gap stage. when In thethis fluid stage, flows the motor out. This starts is duefrom to zero the dispeedfferent to thelubrication fixed speed, conditions and the of accumulator the two processes. is charged from pre-charged pressure to the rated pressure. The sine signal starts at the fourth second, and the working frequency is set to 0.25 Hz. After two entire cycles,5.3. Comparison the working in A frequency Large Instant increases Flow Compensation instantly from Process 0.25 Hz to 0.5 Hz. Then, the motor is regulated to 1700To showr/min the to dimatchfferent the flow new compensation average flow properties rate. The of theflow two compensation accumulators, properties a detailed experimentof the two with working frequency instantly increasing from 0.25 Hz to 0.5 Hz is tested. Based on the average

flow rate, the pump speeds are set to 820 r/min and 1700 r/min, correspondingly. The first 4 s in the experiment represent the fluid charging stage. In this stage, the motor starts from zero speed to the fixed speed, and the accumulator is charged from pre-charged pressure to the rated pressure. The sine signal starts at the fourth second, and the working frequency is set to 0.25 Hz. After two entire cycles, the working frequency increases instantly from 0.25 Hz to 0.5 Hz. Then, the motor is regulated to 1700 r/min to match the new average flow rate. The flow compensation properties of the two accumulators are compared in three stages—0.25 Hz steady stage at 4–12 s, transition stage at 12–18 s, and 0.5 Hz steady stage at 18–24 s.

5.3.1. Pressure Comparison To achieve a smooth simulation curve, some parameters in the Amesim model, such as the stiffness of the hoses and the flow rate pressure gradient of the relief valve, are tuned reasonably. Additionally, flow rate of the pump is carefully designed based on the required motion. Therefore, during the two steady stages and the transition stage, there is little fluid flowing through the relief valve. For a better speed regulation, the parameters of the asynchronous motor are considered in the Amesim model. Moreover, some noise from the transducer is removed. As shown in Figure9, the charging process of the accumulator begins from 0 s. Before the new accumulator is fully charged, the fluid pressure can maintain an approximate steady value. There is an end to the cam profile, as shown in Figure3. When the needle bearing reaches the end of the cam profile, the new accumulator is fully charged, and the fluid pressure increases and reaches the cracking pressure of the relief valve. Therefore, when the new accumulator is fully charged at approximately 3 s, there is a pressure increment from the new accumulator pressure to the cracking pressure of the relief valve. Energies 2019, 12, x FOR PEER REVIEW 13 of 18 accumulators are compared in three stages—0.25 Hz steady stage at 4–12 s, transition stage at 12–18 s, and 0.5 Hz steady stage at 18–24 s.

5.3.1. Pressure Comparison To achieve a smooth simulation curve, some parameters in the Amesim model, such as the stiffness of the hoses and the flow rate pressure gradient of the relief valve, are tuned reasonably. Additionally, flow rate of the pump is carefully designed based on the required motion. Therefore, during the two steady stages and the transition stage, there is little fluid flowing through the relief valve. For a better speed regulation, the parameters of the asynchronous motor are considered in the Amesim model. Moreover, some noise from the transducer is removed. As shown in Figure 9, the charging process of the accumulator begins from 0 s. Before the new accumulator is fully charged, the fluid pressure can maintain an approximate steady value. There is an end to the cam profile, as shown in Figure 3. When the needle bearing reaches the end of the cam profile, the new accumulator is fully charged, and the fluid pressure increases and reaches the cracking pressure of the relief valve. Therefore, when the new accumulator is fully charged at approximately 3 s, there is a pressure increment from the new accumulator pressure to the cracking pressure of the relief valve. When working in two steady stages, the fluid pressures of the two accumulators vibrate regularly. Fluid pressures in both accumulators can return to the initial levels at the end of each working cycle. The oscillation of the pressure is continuous and derivable in the traditional accumulator. The oscillation of the pressure is rectangular in the new accumulator. Through the transformation of the cam mechanism, the pressure in the new accumulator keeps approximately constant if the flow direction is not changed. When the frequency of the sine signal suddenly increases from 0.25 Hz to 0.5 Hz, the flow of the pump cannot match the requirement instantly, and the accumulator supplies the extra flow. The transition stage consists of the speed regulation stage and the pressure recovery stage. Before the motor speed reaches the new value, the pressure of the traditional accumulator continuously decreases and falls below the lowest required pressure. After the speed regulation phase, the pressure gradually recoversEnergies 2019 to, the12, 3104steady area. It is different in the new accumulator that the pressure can still vibrate13 in of 17a steady area.

Figure 9. Comparison of two pressures of the two accumulator systems when the sine signal frequency suddenly increases from 0.25 Hz to 0.5 Hz: (a) pressure of the traditional accumulator; (b) pressure of

the new accumulator.

When working in two steady stages, the fluid pressures of the two accumulators vibrate regularly. Fluid pressures in both accumulators can return to the initial levels at the end of each working cycle. The oscillation of the pressure is continuous and derivable in the traditional accumulator. The oscillation of the pressure is rectangular in the new accumulator. Through the transformation of the cam mechanism, the pressure in the new accumulator keeps approximately constant if the flow direction is not changed. When the frequency of the sine signal suddenly increases from 0.25 Hz to 0.5 Hz, the flow of the pump cannot match the requirement instantly, and the accumulator supplies the extra flow. The transition stage consists of the speed regulation stage and the pressure recovery stage. Before the motor speed reaches the new value, the pressure of the traditional accumulator continuously decreases and falls below the lowest required pressure. After the speed regulation phase, the pressure gradually recovers to the steady area. It is different in the new accumulator that the pressure can still vibrate in a steady area.

5.3.2. Comparison of the Valve Motions As shown in Figure 10, when working in two steady stages, the proportional valves in the two systems move regularly. Because the pressure in the traditional accumulator vibrates continuously, the motion of the valve is continuous, too. The valve motion in the new accumulator system is slightly diﬀerent than that in the traditional accumulator system. The opening percent of the valve quickly increases or decreases when the pressure in the new accumulator vibrates from low pressure to high pressure. During the transition stage, the pressure in the traditional accumulator falls below the lowest required pressure. In this condition, the valve command saturates, and the valve is fully open. After the speed regulation phase, the pressure recovers gradually, and the valve control returns to Energies 2019, 12, x FOR PEER REVIEW 14 of 18

Energies 2019During, 12, 3104 the transition stage, the pressure in the traditional accumulator falls below the14 oflowest 17 required pressure. In this condition, the valve command saturates, and the valve is fully open. After the speed regulation phase, the pressure recovers gradually, and the valve control returns to normal. normal.Compared Compared with withthe thetraditional traditional accumulator accumulator system, system, the the valve valve can can still workwork wellwell in in the the new new accumulatoraccumulator system system because because of theof the special special pressure pressure characteristic. characteristic.

FigureFigure 10. 10.Comparison Comparison of theof the valve valve motions motions of theof the two tw systemso systems when when the the sine sine signal signal frequency frequency suddenlysuddenly increases increases from from 0.25 0.25 Hz toHz 0.5 to Hz.0.5 Hz. 5.3.3. Cylinder Motion Comparison 5.3.3. Cylinder Motion Comparison During two steady stages, the motions of the actuator cylinders in the two systems can both During two steady stages, the motions of the actuator cylinders in the two systems can both stably stably track the input signal by the PID algorithm, as shown in Figure 11. The two tracking errors track the input signal by the PID algorithm, as shown in Figure 11. The two tracking errors both increase both increase with the increase of the working frequency. Moreover, due to the extra inertia load and with the increase of the working frequency. Moreover, due to the extra inertia load and friction, the friction, the cylinder motion in the new accumulator system has a small phase delay compared with cylinder motion in the new accumulator system has a small phase delay compared with the traditional the traditional accumulator system. The tracking error in the new accumulator system is slightly larger accumulator system. The tracking error in the new accumulator system is slightly larger than that in than that in the traditional accumulator system. theEnergies traditional 2019, 12, accumulatorx FOR PEER REVIEW system. 15 of 18 However, during the speed regulation phase, the tracking error of the traditional accumulator system increases obviously, while the tracking error of the new accumulator system can still vary steadily. Because the valve command saturates, the cylinder of the traditional accumulator system cannot track well. In this situation, the maximum tracking error of the traditional accumulator system is about two times larger than that of the new accumulator system.

FigureFigure 11. Cylinder 11. Cylinder motion motion comparisons comparisons of the of twothe two systems systems when when the sinethe sine signal signal frequency frequency suddenly suddenly increasesincreases from from 0.25 0.25 Hz toHz 0.5 to Hz: 0.5 (Hz:a) cylinder (a) cylinder motions motions of the of twothe two systems; systems; (b) tracking(b) tracking errors errors of the of the twotwo systems. systems.

5.4. Effective Region of the Traditional Accumulator and the New Accumulator The increment of working frequency from 0 Hz to 0.4 Hz is tested to achieve the effective regions of the traditional accumulator and the new accumulator. The horizontal axis is the working frequency increment with the basic frequency 0.25 Hz. As shown in Figure 10, when the increment is zero, pressures of two accumulator are all higher than the lowest required pressure, which means the two accumulators can work well in this working frequency. With the increment increases, the lowest pressure of the traditional accumulator decreases exponentially during the transition process. The high pressure and the low pressure of the new accumulator increases and decreases gradually. The lowest required pressure of the system also increases. When the increment increases to 0.18 Hz, the pressure curve of the traditional accumulator is equal with the lowest required pressure curve, which is illustrated as point A in Figure 10. In other words, the increment 0.18 Hz is a critical value for the traditional accumulator, above which the cylinder of the traditional accumulator system cannot track the desired motion well. Similarly, the new accumulator has two critical values of 0.31 Hz and 0.38 Hz, which are illustrated as point B and point C in Figure 10. Since the value of point B is less than that of point C, the frequency value 0.31 Hz is the critical value for the new accumulator. As shown in Figure 12, the frequency increment that the new accumulator can adjust is 0.13 Hz more than that of the traditional accumulator. Therefore, the new accumulator has a larger effective region than the traditional accumulator.

Energies 2019, 12, 3104 15 of 17

However, during the speed regulation phase, the tracking error of the traditional accumulator system increases obviously, while the tracking error of the new accumulator system can still vary steadily. Because the valve command saturates, the cylinder of the traditional accumulator system cannot track well. In this situation, the maximum tracking error of the traditional accumulator system is about two times larger than that of the new accumulator system.

5.4. Effective Region of the Traditional Accumulator and the New Accumulator The increment of working frequency from 0 Hz to 0.4 Hz is tested to achieve the effective regions of the traditional accumulator and the new accumulator. The horizontal axis is the working frequency increment with the basic frequency 0.25 Hz. As shown in Figure 10, when the increment is zero, pressures of two accumulator are all higher than the lowest required pressure, which means the two accumulators can work well in this working frequency. With the increment increases, the lowest pressure of the traditional accumulator decreases exponentially during the transition process. The high pressure and the low pressure of the new accumulator increases and decreases gradually. The lowest required pressure of the system also increases. When the increment increases to 0.18 Hz, the pressure curve of the traditional accumulator is equal with the lowest required pressure curve, which is illustrated as point A in Figure 10. In other words, the increment 0.18 Hz is a critical value for the traditional accumulator, above which the cylinder of the traditional accumulator system cannot track the desired motion well. Similarly, the new accumulator has two critical values of 0.31 Hz and 0.38 Hz, which are illustrated as point B and point C in Figure 10. Since the value of point B is less than that of point C, the frequency value 0.31 Hz is the critical value for the new accumulator. As shown in Figure 12, the frequency increment that the new accumulator can adjust is 0.13 Hz more than that of the traditional accumulator. Therefore, the new accumulator has a larger effective region than the traditionalEnergies 2019, accumulator.12, x FOR PEER REVIEW 16 of 18

Figure 12.12. PressurePressure variations variations of theof twothe accumulatorstwo accumulators withdifferent with different increment increment of the working of the frequency. working frequency. 5.5. Energy Output of the Pump in the Two Systems 5.5. EnergyAlthough Output the of new the accumulatorPump in the Two can Systems maintain pressure in a transient large flow compensation, energy loss and efficiency should be analyzed for a better understanding and use of the new accumulator. Although the new accumulator can maintain pressure in a transient large flow compensation, Based on the above experiment, the energies out of the pump in the two systems are measured, energy loss and efficiency should be analyzed for a better understanding and use of the new as shown in Figure 13. During the first 4 s and the transition stage, the charging energy of the new accumulator. accumulator system is larger than that of the traditional accumulator system. During the two steady Based on the above experiment, the energies out of the pump in the two systems are measured, as stages, the mean values of the output power of the pump in the two systems are almost the same. shown in Figure 13. During the first 4 s and the transition stage, the charging energy of the new Due to the friction between the piston and the cylinder, there exists energy loss at the new accumulator system is larger than that of the traditional accumulator system. During the two steady accumulator, and the efficiency of the new accumulator is lower than the traditional accumulator. stages, the mean values of the output power of the pump in the two systems are almost the same.

Figure 13. Energy out of the pump in the two systems.

Due to the friction between the piston and the cylinder, there exists energy loss at the new accumulator, and the efficiency of the new accumulator is lower than the traditional accumulator. The energy efficiency of the new accumulator in the two steady stages can be simply calculated as Equation (20): η = PPout in (20)

where Pin and Pout are the charging and the discharging pressures of the new accumulator. Using Equation (20), the efficiencies of the new accumulator during the two steady stages are 88.7% and 85.5%. Compared with the new accumulator, the traditional bladder type accumulator works with high efficiency and can be treated without energy loss in this paper.

6. Conclusions

Energies 2019, 12, x FOR PEER REVIEW 16 of 18

Figure 12. Pressure variations of the two accumulators with different increment of the working Energies 2019frequency., 12, 3104 16 of 17

5.5. Energy Output of the Pump in the Two Systems The energy efficiency of the new accumulator in the two steady stages can be simply calculated as EquationAlthough (20): the new accumulator can maintain pressure in a transient large flow compensation, energy loss and efficiency should be analyzed for a better understanding and use of the new η = Pout/Pin (20) accumulator. where PBasedin and onPout theare above the experiment, charging and the the energies discharging out of the pressures pump in of the the two new systems accumulator. are measured, Using as Equationshown (20),in Figure the e ffi13.ciencies During of the the first new 4 accumulators and the transition during thestage, two the steady charging stages energy are 88.7% of the and new 85.5%.accumulator Compared system with is the larger new than accumulator, that of the the traditional traditional accumulator bladder type system. accumulator During the works two with steady highstages, efficiency the mean and canvalues be treatedof the output without power energy of th losse pump in this in paper. the two systems are almost the same.

FigureFigure 13. 13.Energy Energy out out of theof the pump pump in thein the two two systems. systems.

6. ConclusionsDue to the friction between the piston and the cylinder, there exists energy loss at the new accumulator,To decrease and the the pressure efficiency drop of of the the new traditional accumulator accumulator is lower than in the the valve traditional controlled accumulator. hydraulic The systemenergy when efficiency the system of the working new accumulator frequency increases in the two instantly,a steady stages new combinedcan be simply piston calculated type accumulator as Equation is proposed(20): in this paper. The entire structure is designed, and the mathematical equation of the cam mechanism is built based on the ideal gas equation.η = A simulation model is constructed in the Amesim PPout in (20) platform, and an experimental platform is also built with the same parameters. whereFrom thePin and experimental Pout are the results charging of the singleand the cylinder discharging system, pr theessures lowest of the pressure new accumulator. of the traditional Using accumulatorEquation decreases(20), the efficiencies exponentially of the during new the accumulator transition process. during Underthe two the steady basic workingstages are frequency 88.7% and 0.2585.5%. Hz, the Compared critical valueswith the of new the accumulator, frequency increment the traditional are 0.18 bladder Hz for type the accumulator traditional works accumulator with high andefficiency 0.31 Hz forand the can new be treated accumulator. without When energy the loss frequency in this paper. increment is above the critical value, the cylinder cannot track the desired motion well, and the tracking error obviously increases during the transition6. Conclusions process. An example as the working frequency instantly increases from 0.25 Hz to 0.5 Hz is tested. Results shows that, during the transition process, the pressure of the traditional accumulator system drops below the lowest required pressure, and the maximum tracking error is almost double that of the steady stage. On the contrary, the pressure and the tracking error of the new accumulator system can still maintain steady during the transition process. Different from the traditional accumulator, the hydraulic force in the new accumulator is transferred through the steel shaft and the cam mechanism. Therefore, the pressure range of the new accumulator is limited to the flexural strength of the steel shaft and the contact strength of the cam mechanism. As shown in Figure8, the new accumulator works well in the low pressure, and the pressure curve deviates gradually from the ideal pressure in the medium pressure. Considering this fact, the prototype and the experiment are not validated in high pressure. The purpose of this paper is to propose a new type accumulator and validate it preliminarily. Further research will concentrate on decreasing the piston friction and pressure oscillation amplitude of the new accumulator. The new accumulator’s structure should be further optimized for a more compact size and a larger pressure range. A more accurate gas equation, which is suitable from low pressure to high pressure, should be used to design the profile of the cam. Additionally, a detailed application in a specific small hydraulic system with the new accumulator will be studied. Energies 2019, 12, 3104 17 of 17

Author Contributions: Conceptualization, D.Z.; Methodology, D.Z.; Software, X.M.; Validation, D.Z. and B.L.; Writing-Original Draft Preparation, D.Z.; Writing-Review & Editing, D.D.; Funding Acquisition, W.G. Funding: This work was supported by the National Natural Science Foundation of China (50975230) and the Research Fund for the Doctoral Program of Higher Education of China (20136102130001). Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

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