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According to the analysis in “Theoretical flow ripple characteristics” Section of this paper, the periodic change of gear meshing leads to the change of the internal flow channel structure of the gear pair, and the flow ripple will also undergo periodic changes, which makes the flow field of the oil in the pump also undergo periodic changes. The pump studied in this paper has 10 teeth, therefore, when the gear pump rotates a circle, the flow field of oil will occur 10 times of periodic change, in each cycle, the flow state of different positions will be very different, in order to fully understand the whole cycle flow change process of the pump, it is necessary to analyze the flow field in different positions of the pump. The simulation calculation results at speed of 1200 r/min and outlet pressure of 12 MPa were selected for analysis because it was the rated pump condition in which the system could run stably and maintain high volume efficiency under this condition. The setting of boundary conditions and oil properties were referred to “Initial and boundary conditions” Section. In the calculation process, in order to ensure the accuracy of the results and facilitate the effective analysis of the flow field at different moments, the external gear was set to simulate 5 turns, and 720 calculations were made for each turn, that is, one calculation was made for every 0.5° of gear rotation and the results were saved.

The pressure distribution of the internal flow field of the gear pump after calculation convergence is shown in Fig. 11, the pressure contours could not represent the change quantitatively due to the pressure gradient of tooth cavity is large, so the monitoring points were inserted into the tooth cavity of the central section of the external gear and the internal gear ring respectively during the simulation for the convenience of analysis, Point 1 in the tooth cavity of the external gear and Point 2 in the tooth cavity of the internal gear ring. The two monitoring cavities are apical cavity and root cavity corresponding to a pair of meshing target teeth, its initial positions are shown in Fig. 12, The external gear is the main driving gear and drives the internal gear ring to move clockwise. The oil suction cavity is on the left and the oil discharge cavity is on the right. When the gear rotates, the monitoring point rotates at the same angular velocity with the corresponding tooth cavity.

When the rotation angle is between 162° and 295°, the monitoring cavity is in the oil discharge cavity; When the rotation angle is between 295° and 302°, the monitoring cavity is in the trapped oil cavity formed by the engagement of the front and back teeth. The difference of tooth shape results in the change of trapped oil pressure of the pump is different from that of the involute gear pump. Therefore, the change of trapped oil pressure of the meshing tooth was discussed and analyzed in detail at point (4) of the conclusion. After the rotation Angle exceeds 302°, the monitoring tooth cavity is connected with the oil suction cavity and enters the oil suction cavity again. After that, the monitoring tooth cavity continues to rotate and return to the starting position for the next cycle. The pressure of the monitoring tooth cavity in the pump suction and oil discharge cavity fluctuates little, and is basically consistent with the pressure of the inlet and outlet. The pressure of the oil suction cavity is about 0.1 MPa, and the pressure of the oil discharge cavity is about 12.1 MPa.

When the rotation angle changes between 295° and 300°, the front and back teeth engage at the same time to form oil trapped phenomenon, which results in a wide range of pressure changes in the tooth cavity. The pressure changes in the tooth cavity during this period are plotted separately, as shown in Fig. 14. The tooth cavity pressure field along with the change of rotation angle when oil trapped phenomenon occurs is shown in Fig. 15, the selected section is the section of the central position of the internal flow field. When the rotation angle is about 295°, the gear pair is about to enter the two-tooth meshing state, and the high-pressure oil enters the meshing line of the front and back teeth and the end cover of the pump to form a closed space, resulting in oil trapped.

It can be seen from Figs. 14 and ​and1515 that the pressure of trapped oil cavity drops sharply and reaches the lowest when the rotation angle is about 300°. Different from involute gear pumps, the pressure of trapped oil cavity pressure does not have a sharp rise stage, because the pump"s special tooth shape determines that its trapped oil volume has been increasing in the trapped oil process, only the expansion without compression process, so as to avoid gear, shaft and bearing by a large radial force, improve the stability of the pump operation

The velocity streamline diagram of the pump is shown in Fig. 16, which shows an overview of the velocity distribution and the flow state of the pump. The oil velocity in the rotor area and delivery passageway was significantly higher than that in the oil distribution area and the suction due to the continuous engagement of the gear pair to draw in and discharge oil. As can be seen from the previous analysis, the pressure difference of gear tooth meshing region is large and the meshing gap is very small. The constant change of meshing position will make the speed field in this region constantly change. Therefore, the speed field of the gear tooth meshing region is analyzed emphatically. According to the working principle, the number of external gears of the pump is 10, and 10 periodic changes will occur when the external gears rotate once a week. The corresponding rotation angle range of one meshing cycle is 36°, for the convenience of analysis, the monitoring tooth is the same as that in the pressure field analysis, and the velocity field in one meshing cycle is drawn, as shown in Fig. 17.

When the liquid is dissolved into the gas, the pressure in the liquid is reduced to the gas separation pressure under the local thermodynamic state, the gas dissolved in the liquid will be precipitated; when the pressure inside the liquid down to the saturated vapor pressure under the local thermodynamic state, the fluid medium will change from liquid phase to gas phase, both of which are called cavitation. In practical engineering, the oil will inevitably dissolve into a certain amount of gas, and the internal pressure of the gear pump changes violently during operation, and its cavitation state is often the coexistence of gas cavitation and vapor cavitation

Based on Figs. 18, ​,1919 and ​and20,20, the following conclusions can be drawn about cavitation characteristics of the pump:As can be seen from Fig. 18, the total gas volume fraction in rotor region changes periodically with the rotation of the external gear. The volume fraction fluctuates within the range of 0–0.13% with a change period of about 36°, which is just the angle required to rotate a pair of meshing teeth;

As can be seen from Fig. 19, the gas volume fraction released by gas cavitation is almost the same as that of the total gas in the process of cavitation, while the vapor volume fraction is almost 0, indicating that gas cavitation plays a dominant role in the pump when cavitation occurs, and the gas generated by vapor cavitation is very little, almost none. Also, it indicates that there is no pressure drop below 400 Pa in the rotor region under this working condition.

Combined with Figs. 18 and ​and20,20, it can be seen that cavitation gas is generated at almost all angles in the rotation process, but there are certain differences in the amount of gas generated at different angles, the location and range of the region where the gas is generated. The location of cavitation is concentrated in the region close to the meshing point of the oil suction cavity, and the emergence of cavitation phenomenon at each position will undergo an evolution process of initiation, development and intensification, and gradual dissipation. During this evolution process, the cavitation intensity (the amount of cavitation gas generated) will undergo a weak-strong–weak process. The cavitation range (the area where cavitation gas is produced) will undergo a process from small to large to small, and the corresponding degree of cavitation will also undergo a process from mild cavitation to severe cavitation to mild cavitation. Combined with the working principle, pressure and velocity analysis results of the pump, a pair of gear teeth in front of the meshing point are detached, the volume expansion of the oil suction cavity at the place causes the oil suction empty, which reduces the pressure of the oil suction cavity, on the other hand, after the oil passes through the narrow gap between the teeth, the oil velocity is too large, which leads to the further reduction of local pressure. When the pressure is lower than the gas separation pressure, gas cavitation will occur.

According to the previous analysis, when the gas in the oil is separated out, the fixed volume in the oil suction chamber is occupied by bubbles, resulting in a decrease in the effective volume in the chamber, and the amount of bubbles produced is different with the degree of cavitation of the pump, which will certainly affect the pump outlet oil flow ripple characteristics. In order to control the cavitation degree and ensure that the regulating parameters will not affect the other performance of the pump, it can only be achieved by controlling the gas mass fraction in the oil. Multiple groups of different gas mass fraction were set and numerically calculated. The corresponding cavitation degree was from weak to strong, and the settings of other boundary conditions remained unchanged and consistent. The flow ripple results and the flow ripple characteristics at the pump outlet under different gas mass fraction were shown in Figs. 21 and ​and2222.

With the increase of gas mass fraction, the flow ripple amplitude at the pump outlet increases, the average flow rate of output decreases, and the flow ripple rate increases. As the degree of cavitation intensifies, more bubbles are precipitated in the oil, when these bubbles are transported to the high-pressure part of the rotor region, the bubbles will compress and break under the action of high pressure, which reduces the stability of the oil flow and increases the flow ripple amplitude. At the same time, the bubbles generated by cavitation will occupy the volume of the suction and discharge chamber, so that the effective working volume of the pump decreases, when the cavitation intensifies, the gas generated will increase, and the volume of the cavity occupied will increase, leading to the decrease of the average flow rate of output and the increase of the flow ripple rate.

Therefore, suppressing cavitation can reduce flow ripple at the pump outlet and improve volumetric efficiency. In general, cavitation is alleviated by setting unloading groove at locations where cavitation is severe, as shown in Fig. 23, on the one hand, when vacuum-suction occurs, the unloading groove can timely supplement the oil from the oil suction cavity through the end face of the gear to the tooth cavity, on the other hand, the existence of the groove can alleviate the oil speed and improve the stability of oil suction and discharge. The effect of the unloading groove on the cavitation of the pump is explained by comparing the cavitation of the pump under the two conditions with or without the unloading groove, Fig. 23 shows the cavitation field without and with the unloading groove. By comparison, it can be seen that the cavitation position of the pump is basically the same under the two conditions, but the cavitation degree of the area near the unloading groove is obviously weakened with the unloading groove. Figure 24 shows the variation of gas volume fraction in the rotor region without and with unloading groove. The gas volume fraction fluctuates between 0 and 0.19% in gear pump without unloading groove, but fluctuates between 0 and 0.13% in gear pump with unloading groove. The gas volume fraction in the rotor region with unloading groove is significantly lower than that without unloading groove at the same rotation angle. It can be seen that reasonable setting of unloading groove can effectively reduce the cavitation degree of the pump.

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Bucher Hydraulics located in Klettgau-Griessen, Germany is the internationally active hydraulic division of the Swiss conglomerate Bucher Industries, Niederweningen (ZH), a corporation listed on the SWX Swiss Stock Exchange.

Bucher Hydraulics develops and produces drive and control technology for the mobile and industrial hydraulics sector. Their range includes products for mobile and industrial hydraulics, elevator hydraulics, hydraulic drives for high-voltage switches and height-adjustable workbenches. Some of the many components produced include hydraulic pumps, hydraulic motors, valves, cylinders, power units, electronic devices and associated systems.

Their acquisitions include the Italian company "Hidroirma" (1994), "Beringer Hydraulik" in Neuheim, Switzerland (1996), "Hydrotechnik" in Frutigen, Switzerland and "Dingkind" in Taiwan (1997), "Truninger AG" in Solothurn, Switzerland (2000), "Monarch Hydraulics" (2007) and "Command Controls" (2008) in the United States, and "Eco Sistemas" (2013) in Brazil.

The Bucher Hydraulik corporate group was formed in 1996 with its business management in Klettgau-Grießen. Bucher Hydraulics became the company"s umbrella brand name in 2001.

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We insist on the principle of development of "High quality, Efficiency, Sincerity and Down-to-earth working approach" to provide you with excellent service of processing for Pool Pump Cartridge Filter System, Hydraulic Pump High Pressure, Displacement Pump Types, Our products are widely recognized and trusted by users and can meet continuously developing economic and social needs.

In addition to the simple mechanical structure, the use of advancedhydraulic oil can reduce the mechanical surface and the wear and tear of the functional parts. Eckerle gear chestnut can run at high pressure, even if the use of general hydraulic oil, it is not easy to wear pieces.

We often stay with the principle "Quality Very first, Prestige Supreme". We have been fully committed to supplying our consumers with competitively priced high-quality goods, prompt delivery and skilled provider for Factory For Eckerle Internal Gear Pump Export to Eindhoven, The product will supply to all over the world, such as: Amsterdam, Namibia, UK, Our company has already have pass the ISO standard and we are fully respect our customer "s patents and copyrights. If the customer provides their own designs, We will guarantee that they will be the only one can have that products. We hoping that with our good products can bring our customers a great fortune.

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