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3 Process of parameters calculation for accumulators When doing experiments, shutoff valve 3 and shutoffvalve 10 were first opened before running of water pump 4.Then, the water pump was controlled at the minimumspeed 150 rpm by variable-frequency motor 6 and vari-able-frequency power source 5. Next, the working pressurewas adjusted to 2.0 9 106Pa by regulating throttle valve 8.Finally, the valve port of throttle valve 8 was kept constant,and the working pressure was adjusted to 3.0 9 106,5.3 9 106, 8.0 9 106, 10.0 9 106Pa by raising currentfrequency of variable-frequency power source to increasethe speed of variable-frequency motor.When the water pump ran at different working pressureadjusted above, the corresponding pressure pulsations andflowrate through nozzle data were collected and shown inFig. 8.For the next thing, the bladders of accumulators wereremoved and the anterior pipelines of accumulators wereblocked by screws, namely there were no accumulators toabsorb pressure pulsation for the water pump. Then the testprocess mentioned above was done again, and the corre-sponding pressure pulsation curves without accumulatorsand flowrate through nozzle were displayed in Fig. 9.Figures 8 and 9 present the pressure pulsation curves atdifferent working pressure. Then, the maximum value pd-max and minimum value pdmin of each pressure pulsationare calculated as follows, and the pressure pulsation factorsare represented in experiment column of Table 4.pdmax ¼P Rm¼1pdmaxðmÞRpdmin ¼P Rm¼1pdminðmÞR8> > > > > > <> > > > > > :ð17ÞIn Fig. 8 and experiment column of Table 4, the pres-sure pulsation factors are 0.83, 0.71, 0.85, 0.78 and 0.81 %corresponding to the working pressure of 2.0 9 106,3.0 9 106, 5.3 9 106, 8.0 9 106and 10.0 9 106Pa. Therewas some difference between experiment and simulationowing to the influence of pipes, valves and so on. But,similar to the pressure pulsation factors in simulation, thesefactors in experiment were also in close proximity to 0.8 %and reached maximum value at the working pressure of2.0 9 106and 5.3 9 106Pa, namely the first pressure spotand the second pressure spot.From Fig. 9 and experiment column of Table 4, it canbe seen that the pressure pulsation factors were about16–28 %, which were slightly less than the simulation24 68 00.40.81.20Working pressure /Pa×106×10-3Net volume of accumulators /m310 12 14pc1 pc2 pc3Fig. 4 Net volume of accumulator with different working pressureFig. 5 Pressure pulsation curves in simulation with multipleAccumulators results. This was because the outlet pipe of the water pumpcould absorb a little pressure pulsation as a chamber. Be-sides, the pressure pulsation factors were also much largerthan that of water pump with accumulators.So, the experimental results are in good agreement withthe simulation results. Meanwhile, the simulation methodfor the water pump with multiple accumulators was valid.6 ConclusionsIn this paper, we advance a calculation method for opti-mizing multiple accumulators which could richly absorbpressure pulsation all along when outlet pressure of wa-ter pump varied in HWPS. According to actual working4765Data acquisitionsystemAccumulatorsM1236489 1017F1F2P5Fig. 7 Pressure pulsationtesting system. a Testing site,b principle of pressure pulsationtesting system 1 water tank, 2filter, 3,10 shutoff valve, 4 waterpump, 5 variable-frequencypower source, 6 variable-frequency motor, 7 pressuretransmitter, 8 throttle valve, 9flow transmitterTable 4 Pressure pulsation factors of simulation/experimentWorking pressure (Pa) 2.0 9 106(%) 3.0 9 106(%) 5.3 9 106(%) 8.0 9 106(%) 10.0 9 106(%)Simulationdp with accumulators 0.76 0.72 0.81 0.67 0.79dp without accumulators 19 20 23 27 31Experimentdp with accumulators 0.83 0.71 0.85 0.78 0.81dp without accumulators 16 18 21 24 28Fig. 6 Pressure pulsation curves in simulation without accumulator conditions of HWPS and parameters of water pump, somesimulations and experiments have been done. And severalsignificant conclusions are obtained as follows:1. Calculation and determination of pressure spots pci arethe most key steps. The bladder volume and chargedpressure are close to pci. The number N and value of pcishould be calculated iteratively from the structuralpattern of water pump, working pressure range pmin-pmax, and allowable value of pressure pulsations factor[dp].2. The net volume of accumulators alters with the changeof outlet pressure of water pump, and reaches mini-mum when outlet pressure is pressure spots pci. Then,the capability of accumulators to absorb pressurepulsation reached the lowest point.3. On the basis of parameters of physical model, thepressure pulsation has been simulated and tested. Thepressure pulsation factors in simulation and experimentare very consistent and are both quite close to theallowable value 0.8 % with accumulators and 16–31 %without accumulators. All of the results support thevalidity of the mathematical model Eqs. 1–5 andoptimal calculation method Eqs. 6–16, and the accu-mulators can efficiently absorb the pressure pulsationof the axial piston water pump.4. The methods advanced in this study (accumulatorsdesigned to different flowrate) are effective for avariable displacement type piston pump. A fixeddisplacement type piston pump(used in this paper)discharges different flowrate by changing rotationspeed, namely the flowrate is proportional to therotation speed.