AnAlysis of pulsAtion of the sliding-vAne pump for selected settings of hydrostAtic system AnAlizA pulsAcji ciśnieniA pompy łopAtkowej dlA wybrAnych nAstAw pArAmetrów ukłAdu hydrostAtycznego*

Sliding-vane pumps are widely used as sources of the flow in hydrostatic power transmission systems. A noticeable tendency in hydrostatic systems is revealed in the form of minimization of the mass, overall dimensions and at the same time increasing of a power density delivered by pumps. The article presents the preliminary results of the studies related to a pressure pulsation of the hydraulic system equipped with the sliding-vane pump (T7BS type manufactured by Parker & Denison Company). During the studies the pressure pulsation in selected places of pressure line were recorded. A series of measurements were performed for selected settings of the system. The recorded characteristics were analysed in time and frequency domains.


Introduction
Despite significant progress in the development of hydraulic drive systems, users of the systems fitted with hydrostatic drives [1,17] still experience a number of displacement pump failures.The process of diagnosing such devices is complicated and requires applying advanced tools [2,5] or data processing algorithms.Additionally most of these devices are not diagnose susceptible [3,18], what results from operating conditions [6] and external interferences.
Displacement pump diagnostic methods include vibroacoustic techniques, flow and pressure measurements, temperature control etc.However, each of those methods has its limitations and requires extensive knowledge [20][21][22].
The most commonly measured parameter of the hydrostatic systems is pressure [4].Based on the analysis of phenomena relating to displacement pump pressure pulsation, it is possible to determine a number of system operating parameters demonstrating failures [7,10,12,16] or detuning.Vibration due to pressure pulsation is caused by the uneven flow of hydraulic fluid from the pump to the system, which results in the accelerated wear of pump's elements [13,14], increased emission of noise and reduction in the accuracy of the receivers' positioning.In the experiment presented in this article, the analysis of pressure pulsation in the discharge line was performed on the Parker & Denison T7BS rotary vane pump and the results have been compared with the simulation carried out on the proprietary model.

Mathematical and simulation models of the rotary vane pump efficiency
Figure 1 presents the operating diagram of a single acting rotary vane pump.Temporary efficiency [19] of a pump results from the infinitesimal area circled by the vanes of a pump during the phase of crossing the transitory zone between the suction and discharge zones.In order to derive the formula to calculate temporary efficiency of the considered pump, the following simplifying assumptions have been adopted: outline of the stator track (in the form of a perfect circle), • transverse dimensions of a pump vane (zero thickness), • coordinate system -polar coordinate system has been adopted • for the analysis (with the pole placed in the axis of the rotor revolution), motion of the fluid -raising the fluid while the vanes travel • from suction to discharge zone.In relation to the adopted assumptions, efficiency of the pump has been determined as the capacity between two temporary positions of the vane in the transitory zone: The relation defining the value of temporary area circled by the vane travelling from suction to discharge zoned A, described in the polar coordinate system, takes the following form: where: r z -temporary radius of the point of contact between the vane and stator track [m], R -pumprotor radius [m], ω -rotor angular speed [rad/s].The relation enabling determination of the area circled by the opposite vane will take the same form as equation 2, with the only difference being other radius of the contact between the vane and track.After inserting equation 2 in the equation 1, the following formula for the pump temporary efficiency has been obtained: where: r u -radius of the contact of the opposite vane travelling from discharge to suction zone [m].Temporary radii of the pump vanes' contact may be expressed as: Taking into consideration the conditions determined using formula 3, the equation identifying the values of temporary radii of pump vanes' contact is as follows: R Z (5) where: φ -temporary angular position of the vane in the transitory zone from suction to discharge.Having considered that angle φ changes within the range (-π/z÷π/z), where z stands for the number of vanes, theoretical flow output of the single acting rotary vane pump with 12 vanes may be presented in the form of the characteristics shown in Fig. 2.
In case of the considered pump, the irregularity of efficiency, obtained based on the developed mathematical model, was 3,45%.
The acquired simulation characteristics of the flow output of the pump have been implemented in the measurement system model [8,9,15], developed in the Matlab-Simulink environment (Fig. 3).The suction line (between the source of stream and maximum valve)has been modeled as the collection of modules consisting of Simscape Hydraulic library function blocks oriented for the purposes of the simulation: hydraulic resistance of the supply bus, capacity of the hydraulic hose and fluid inertia in the hose [11,23].
The simulation has been carried out in relation to two selected cases (Fig. 4), with the adopted rotational speedn n of the pump shaft of 735 rpm: discharge line with no extra capacity, • discharge line with extra capacity of the hydraulic fluid.• Values of the pressure pulsation obtained as a result of the simulation and laboratory measurements suggest the proper selection of parameters for the adopted model.The simulation characteristics do not reflect the impact of the maximum valve dynamics on the examined

Measuring station and experiment plan
Measuring system (Fig. 5) consists of the double acting rotary vane pump (T7BS B09 3R00 A1M0 manufactured by Parker & Denison) powered by the AC asynchronous motor with frequency con-verter, L90LS valve block and receivers (hydraulic rotary motor and three hydraulic cylinders).
The pump has been connected with the valve block by means of the elastic discharge pipe of the following parameters: internal diameter d w =16mm (5/8"), two steel braids (type 2SN), hose length 5m.Pressure sensors SCPT-160-C2-05 have been installed at the pressure flange and before the valve block.Additionally, a flow meter SCFT-060-C2-05has been installed before the valve block.Working fluid temperature was monitored using temperature sensor SCLTSD-370-00-07, installed in the oil tank.Results were monitored and saved using ServiceMaster Plus instrument.Measurements were taken according to Table 1.Variable parameters included pressure and rotational speed of the pump shaft (regulation of the volumetric flow rate).

Station-based testing
Operating principle of displacement pumps involving periodical changes in the capacity of working areas is the reason of flow output and the pumping pressure fluctuation connected with temporary efficiency.Only screw pumps are free from this defect.The examined pump T7BS B09 3R00 A1M0 from Parker & Denison is a double acting rotary vane pump with fixed efficiency.Such construction enables relieving the pump shaft from the impact of axial forces coming from the pumping pressure and doubling the efficiency(as compared with the single acting rotary vane pump of the similar size).
As far as pump T7BS is concerned, the rotor is fitted with 12 vanes, and therefore the frequency of vanes travelling from the suction to discharge zone, equal with the frequency of the expected flow output of the pump f p , is as follows: ) where: i -a number of vanes, n -rotational speed of the pump shaft [rpm].
Table 2 summarizes the expected values of the pressure peak frequency, resulting from rotation of the pump shaft (f n ) and the subsequent vanes entering the discharge phase (f p ).
Summary results of measuring pressure on the discharge line of the pump were presented in the time (Table 3) and frequency domains (Table 4).
Besides the pulsation triggered by the pump vanes travelling from suction to discharge zone, in frequency spectrums one can notice (Fig. 10-13) pump shaft rotation frequency and its first harmonic (the reason is eccentricity of the pump shaft in relation to the stator ring track).Juxtaposition of pressure values in the time and frequency domains was presented in Tables 3 and 4. Furthermore, peak-to-peak value of the pressure measured by the pump is significantly lower than peak-to-peak value of pressure measured by the valve block (L90LS).What's more, in frequency spectrums measured by the valve block, one can observe pressure fluctuations that are almost invisible in the pressure spectrums by the pump.
The reason of the phenomenon connected with the occurrence of additional frequencies is a maximum valve installed in the block L90LS.During measurements, the stream provided by the examined pump to the block L90LS, was flowing through two-stage maximum valve to the discharge pipe line and then to the tank.Operating characteristics of maximum valve, where the main stage poppet operates with variable valve opening, causes self-excited pressure pulsation in case of the valve with not sufficient damping of poppet vibration.In the described case, it is maximum valve that is responsible for the additional pressure pulsation.The sampling frequency of recorded signals amounted to 1000 Hz.At the data processing method the authors adopted 2048 FFT samples analyzed with a function of the Flat Top window.Frequency spectrums were subjected to averaging in a domain of the four groups of samples.Due   to limitations of the measurement device recording the first harmonic responsible for entering successive blades in the discharge phase f p at high speeds was not possible (Table 4).As can be observed, a factor that has strong influence on pressure pulsation amplitudes resulting from eccentricity (frequencyf n ) is temperature, and at the same time hydraulic fluid viscosity.Pulsation amplitude resulting from the fact of vanes entering discharge zone is much lower.Additionally, it may be noticed (Table 4) that low frequency of pressure pulsation f n (circa 12 Hz) is damped by the hose connecting the pump with valve block.
Amplitudes of pressure pulsation resulting from the fact of vanes entering discharge zone (f p ) are several times lower;one may, however, notice their reinforcement by the discharge line.
In case of higher rotational speed of the pump shaft, one may observe strengthening of pressure pulsation at the discharge line between the pump and valve block not only in case of frequencyf p , but also frequencyf n (here equal to circa 24 Hz).In the extreme case, 4 times stronger pressure pulsation of 24 Hz and 12 times stronger pressure pulsation of 290 Hz.
The impact of discharge pressure on the pulsation amplitude at the pressure flange of the pump (pressure p 1 ) is not dominating.Nevertheless, it may be observed that the amplitude of pressure pulsation in relation to the frequency of pump shaft rotation f n increases with increase of discharge pressure.It may be a sign of the increase of pump shaft eccentricity, which should not happen taking into consideration its design (double acting pump is fitted with the shaft relieved from the radial forces coming from the discharge pressure).
The obtained results of experimental tests were compared with the respective simulation results (Fig. 4 and Table 5).
Despite discrepancies between the obtained values it should be stated that model tests of the impact of pump pulsation on the measurements of discharge pressure are close to the actual measurements to such extent that it is possible to use them for the process of designing new hydraulic systems.Another stage in the development of a mathematical model will be the process of tuning parameters, in order to develop the diagnostic model based on the pump equations.

Conclusions
The acquired results are to a large extent compatible with expectations.Due to small irregularities in the efficiency of rotary vane pump (theoretically lower by 3,5%),the observed pressure pulsation is characterized by low peak-to-peak values, in the worst case not exceeding 0,73bar (p s =120 bar, n n =1441 rpm, t s =40 o C).Spectrum analysis indicates the necessity of paying attention to the relationship between the amplitude of pressure pulsation with the rotation frequency of a pump shaft dependent on the fluid viscosity and discharge pressure.

Fig. 1 .
Fig. 1.Operating diagram of a single acting rotary vane pump ) where: B -width of the vane of the considered pump [m], dA -temporary area circled by the vane while travelling from suction to discharge zone [m 2 ], dA u -temporary area circled by the opposite vane travelling from discharge to suction zone [m 2 ].

Fig. 2 .Fig. 3 .
Fig. 2. Diagram of the theoretical temporary pulsation of a rotary vane pump with 12 vanes (vane width 60 mm, stator track diameter 160 mm, eccentricity value 25 mm, rotational speed of the pump shaft n n =735 rpm)

Fig. 4 .
Fig. 4. Characteristics of pressure pulsation obtained as a result of experimental tests and simulation (n n = 735 rpm, p s = 60 bar, temperaturets=40°C): a) with no extra capacitance of the discharge line, b) with extra capacitance of the discharge line

Fig. 6 .
Fig. 6.`Time courses of the pressure values with low rotational speed of the pump with no extra capacitance (experiment P1 -Tab. 1, n n =735rpm, t s =25 o C, p s =60 bar)

Fig. 7 .Fig. 8 .
Fig. 7. Time courses of the pressure values with fast rotational speed of the pump with no extra capacitance (experiment P7 -Tab. 1, n n =1470 rpm, t s =25 o C, p s =60 bar)

Table 1 .
Parameters of the experiment

Table 2 .
Expected values of the characteristic frequencies

Table 3 .
Comparison of pressure pulsation values in time domain

Table 4 .
Comparison of pressure pulsation values in frequency domain

Table 5 .
Comparison of the results of simulation and experimental tests