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x.4.1 The 1st pressure spot and accumulatorparametersThe minimum working pressure is taken as the 1st pressurespot, namely pc1 = pmin. By Ref [11], the 1st accumula-tor’s bladder volumeVAq1 ¼ dVm11 ð2 ½dp 2 þ½dp Þ1Kdp ¼ 2ðpdmax pdminÞðpdmax þ pdminÞ:8> > > > <> > > > :ð6ÞAccording to Ref [12], pulsating volume dVm1 isdVm1 ¼ pqrzpZ pzp0maxcosðpzp bÞzp sinpzp 1p; 00B @1C Adb ¼ CdqrCd ¼R pzp0pzpmaxcosðpzp bÞzp sinpzp 1p; 00B @1C Adb;8> > > > > > > > > <> > > > > > > > > :ð7Þwhere Cd is worked out only by the piston number of thewater pump,and b is angle integral variable.Equation 7 shows that the pulsation volume dVm1 isonly related to the delivery capacity qr and piston numberzp of the water pump, and not related to the output flowrateand pressure.When the first accumulator is used to absorb pressurepulsation most effectively, the recommended value of thecharged pressure could be calculated as below by Ref [11].pAq1 ¼ 0:6pc1 ð8ÞWhen the 1st accumulator is working at the 1st pressurespot, its net volume isVAr ¼ pAq1pc1VAq1 ¼ 0:6VAq1: ð9ÞIf the output pressure of water pump is larger than pminand the total net volume of all accumulators is not less thanthe minimum net volume VAr, the pressure pulsation willbe richly absorbed.4.2 The 2nd pressure spot and accumulatorparametersWhen output pressure pc1 = pmin and the net volume isVAr, the charged pressure of the 2nd accumulator must bepAq2 ¼ pc1: ð10ÞAssuming that the 2nd pressure spot is pc2, the 1st ac-cumulator can also absorb pressure pulsation at pc2, but thenet volume becomes smaller. So pc2 must be present at thefollowing equation:pAq1pc2VAq1 þ pAq2pc2VAq2 ¼ VAr: ð11ÞTransforming Eq. 11, the 2nd pressure spot pc2 could beobtained aspc2 ¼ VAq1VArðpAq1 þ pAq2Þ: ð12Þ4.3 The ith (i > 2) pressure spot and accumulatorparametersAccording to Eq. 10, the charged pressure of the 3rd-ithaccumulator ispAqi ¼ pcði 1Þ: ð13ÞAccording to Eq. 11, pci at the ith pressure spot could becalculated as belowpAq1pciVAq1 þ pAq2pciVAq2 þ þ pAqipciVAqi ¼ VAr: ð14ÞThenpci ¼ VAq1VArðpAq1 þ pAq2 þ þ pAqiÞ: ð15Þ4.4 The number of pressure spots NAccording to Eqs. 13 and 15, pAqi and pci are loop com-puted untilpci\pmax\pcðiþ1Þ: ð16ÞThen, N = i.To sum up sects. 4.1–4.4, the calculation process of thebladder volume and charged pressure of N accumulatorsare displayed in Fig. 3.5 Simulations and experiments5.1 Calculated parameters of accumulatorsBased on the actual size and parameters of the water pump(shown in Table 1), the main parameters of accumulatorsand net volume under different working pressure are cal-culated by Eqs. 6– 16 and shown in Table 2 and Fig. 4,respectively.Table 2 and Fig. 4 show the number N, minimum netvolume VAr, bladder volume VAqi, pressure spot pci andcharged pressure pAqi of accumulators. From the results, itcan be seen that three accumulators, whose bladder vol-umes are all 0.67 9 10-3m3and whose charged pressuresare 1.2 9 106, 2.0 9 106, 5.3 9 106Pa, respectively, areneeded to keep the pressure pulsation within 0.8 % whenworking pressure range is between 2 9 106and10 9 106Pa. In this case, the net volume is always largerthan 0.40 9 10-3m3and reaches the minimum valuewhen working pressures are 2.0 9 106and 5.3 9 106Pa.5.2 Simulation of pressure pulsationFor reasons of compact construction, outlet chamber iscircumferentially connected with six accumulators whosebladder volumes are all 0.335 9 10-3m3. Among these sixaccumulators, every two are charged the same gas pressure.Thus there are three pairs of accumulators whose chargedpressures are 1.2 9 106, 2.0 9 106and 5.3 9 106Pa,respectively.On the basis of mathematical Eqs. 1–5 which are built todescribe the accumulators absorbing pressure pulsation, thepressure pulsations under various working pressures weresimulated and are shown in Fig. 5 and simulation columnof Table 4 according to the simulation parameters inTables 1, 2, and 3. Meanwhile, the pressure pulsationswithout accumulators are shown in Fig. 6 and simulationcolumn of Table 4 when VAi = 0.Figure 5 shows the pressure pulsation curves whenworking pressure is varied over a range on the order from2.0 9 106Pa to 10.0 9 106Pa by adjusting the rotationspeed of the water pump. From the five typical pressurepulsation curves, it can be observed that the pressure pul-sations factor dp are basically controlled under 0.8 %.When working pressure is 2.0 9 106and 5.3 9 106Pa, thecorresponding total net volume is at the minimum value0.4 9 10-3m3that causes the pressure pulsation factor dpto reach the maximum. When working pressure is different,the larger the corresponding total net volume shown inFig. 4, the smaller the pressure pulsations factor dp.Figure 6 shows the pressure pulsation curves at thepressure range 2.0 9 106–10.0 9 106Pa when water pumpis not provided with accumulators. The curves display thatthe pressure pulsation factor dp is about 20–30 %, and muchlarger than that of water pump with accumulators. Thesefindings reflect that accumulators can efficiently decreasethe pressure pulsation of the axial piston water pump.5.3 Experiment of pressure pulsationAccording to the parameters listed in Table 1, 2, and 3, thewater pump and accumulators, whose construction draw-ings are shown in Fig. 1, are designed and manufactured.And three pairs of accumulators are charged pressures1.2 9 106, 2.0 9 106and 5.3 9 106Pa. For measuring thepressure pulsation, a testing system is designed and shownin Fig. 7.pc1=pminVolume of No.1 accumulator by Eq.(6)&Eq.(7) VAq1Filling pressure of No.2 accumulator by Eq.(10) pAq2Filling pressure of No.1 accumulator by Eq.(8) pAq1qr, zpNo.2 Pressure spotpc2…No.i Pressure spotpAqipci<pmaxFilling pressure of No.i accumulator by Eq.(13) Filling pressure of No.(i+1) accumulator by Eq.(13) pAq(i+1)No.(i+1) Pressure spotpc(i+1)>pmaxEndN=i Net volume of accumulator by Eq.(9) VArFig.