This article focuses on the in – depth study of the influence of the number of gear teeth on the flow pulsation characteristics of aero arc gear pumps. By establishing 3D models of gear pumps with different numbers of teeth, conducting numerical simulations, experimental verifications, and theoretical analyses, the relationships between the number of teeth and various performance parameters such as flow rate, pressure, and gear forces are comprehensively explored. The research findings provide a theoretical basis and technical support for the optimization design and performance improvement of aero arc gear pumps.
1. Introduction
Aero – fuel systems play a crucial role in providing stable and powerful propulsion for engines. As a key component of the fuel system, the performance of aero – fuel gear pumps directly affects the stability and reliability of engine operation. With the development of aero – fuel gear pumps towards high – speed and high – power directions, issues such as decreased volumetric efficiency, flow fluctuations, vibration, and noise have become prominent, which seriously limit the performance improvement of fuel gear pumps.
In recent years, many scholars have conducted extensive research on these problems. Some studied the lubrication characteristics and contact behavior of gear pump sliding bearings; others compared the flow characteristics of different gear – shaped pumps or proposed methods to reduce flow pulsation. However, in the production and trial – run of arc gear pumps, it has been found that the number of gear teeth has a significant impact on their performance. Therefore, this paper takes the arc fuel gear pump as the research object to explore the influence of the number of teeth on the flow characteristics in the pump cavity.
2. Calculation Model
2.1 Gear Profile Design
The arc – involute – arc is adopted as the end – face profile of the gear. Taking a gear pump with 7 teeth as an example, the establishment of its end – face profile equation can be referred to relevant literature [16]. The rack pressure angle is selected as 14.5° according to literature [17], which is more advantageous. When the pressure angle is 14.5°, the minimum number of teeth to avoid root cutting is 6. Based on this, calculation models of 6 – 9 – tooth arc gear pumps are established.
| Z / – | β / deg | A / mm |
|---|---|---|
| 6 | 35.45° | 27.20 |
| 7 | 32.14° | 28.00 |
| 8 | 29.35° | 28.64 |
| 9 | 26.97° | 29.16 |
| In the table, Z represents the number of gear teeth, β represents the helix angle, and A represents the center distance. The outer diameters of the 4 types of gears with different numbers of teeth are kept consistent (\(R_{e}=34.08\) mm), and other geometric parameters are as follows: gear width \(B = 20\) mm, inlet diameter \(D_{m}=18\) mm, outlet diameter \(D_{cor}=15\) mm, radial clearance \(\delta = 0.02\) mm, and pitch angle \(\tau = 2\pi/Z\). |
2.2 Pump Working Principle
During the operation of the pump, the two gears have a single – point contact on one end – face, and the face contact ratio is less than 1, which ensures that there is no oil – trapping area during the rotation of the gear pump. To achieve continuous rotation, helical gears are used, and the axial contact ratio is increased to 1, enabling full – tooth – width meshing between the two gears during operation.
3. Numerical Simulation
3.1 Grid Division and Dynamic Grid Model
The entire grid area is divided into inlet, gear cavity, and outlet parts. Considering the small tooth – to – tooth clearance between the two meshing gears and the small radial clearance between the gear and the pump cavity, a quadrilateral structured grid is used for the gear rotation domain. Taking the 7 – tooth arc gear pump as an example, referring to the grid – independence verification method in literature [20], 6 calculation models with different grid numbers are generated by adjusting the grid division scale. After verification, when the grid number is less than \(1.24×10^{6}\) (point C), the calculation results will fluctuate greatly. When the grid number gradually increases from point C to point F, the calculation results change gently. Finally, to save computing resources on the premise of ensuring accuracy, the grid number of the 7 – tooth gear pump calculation model is determined to be \(1.24×10^{6}\), with 360 layers of grids arranged circumferentially, 60 layers axially, 18 layers in the radial clearance, and 36 layers in the tooth – to – tooth clearance, generating a total of 40 sets of overlapping grids. According to similar grid – division scales, the grid numbers of 6 – tooth, 8 – tooth, and 9 – tooth gear pump calculation models are obtained as \(1.41×10^{6}\), \(1.36×10^{6}\), and \(1.32×10^{6}\) respectively. [Insert a picture here showing the grid model of the arc gear pump, with different colors representing different parts of the grid, such as the gear cavity grid in red, the inlet grid in blue, and the outlet grid in green]
3.2 Control Equation and Turbulence Model
The fluid model and turbulence model can be directly called in PumpLinx. The turbulence parameters are obtained from the Navier – Stokes equations, and the RNG \(k – \varepsilon\) model is used to solve the gear pump cavity. The RNG \(k – \varepsilon\) model uses the renormalization – group statistical technique to correct the turbulent viscosity and can handle flows with large curvature, strong rotation, and high strain rate well. The solid – wall surface adopts the no – slip wall – surface condition, the near – wall region uses the standard wall – function, the contribution of pulsating expansion in compressible turbulence is not considered, and the influence of gravity on the flow field is ignored. Pressure – boundary conditions are set at the inlet and outlet. The transport equations of the turbulent kinetic energy k and the dissipation rate \(\varepsilon\) of this model are as follows: \(\begin{gathered} \frac{\partial(\rho \varepsilon)}{\partial t}+\frac{\partial\left(\rho \varepsilon u_{i}\right)}{\partial x_{i}}=\frac{\partial}{\partial x_{j}}\left[\left(\mu+\frac{\mu_{t}}{\sigma_{\varepsilon}}\right) \frac{\partial \varepsilon}{\partial x_{j}}\right] \\ +C_{1 \varepsilon} \frac{\varepsilon}{k}\left(G_{k}+C_{3 \varepsilon} G_{b}\right)-C_{2 \varepsilon} \rho \frac{\varepsilon^{2}}{k}+S_{\varepsilon} \end{gathered}\) \(\begin{gathered} \frac{\partial(\rho k)}{\partial t}+\frac{\partial\left(\rho k u_{i}\right)}{\partial x_{i}}=\frac{\partial}{\partial x_{j}}\left[\left(\mu+\frac{\mu_{t}}{\sigma_{k}}\right) \frac{\partial k}{\partial x_{j}}\right]+ \\ G_{k}+G_{b}-\rho \varepsilon+S_{k} \end{gathered}\) In the equations, \(G_{k}\) is the generation term of the turbulent kinetic energy k caused by the average velocity gradient; \(G_{b}\) is the generation term of the turbulent kinetic energy k caused by buoyancy; \(C_{1\varepsilon}\), \(C_{2\varepsilon}\), and \(C_{3\varepsilon}\) are empirical constants; \(\sigma_{k}\), \(\sigma_{\varepsilon}\) are the Prandtl numbers corresponding to the turbulent kinetic energy k and the dissipation rate \(\varepsilon\) respectively; \(S_{k}\) and \(S_{\varepsilon}\) are user – defined source terms [21].
4. Experimental Verification
4.1 Experimental Setup
To verify the accuracy of the numerical simulation method, a 7 – tooth gear pump is used as a prototype for experimental verification. A closed – loop test bench for the arc gear pump is built to measure the outlet volume flow rate of the pump under 5 different working pressures. The test bench consists of two parts: the connection from the oil tank to the pump inlet and the connection from the pump outlet to the oil tank. The test equipment includes a Siemens – Bade frequency – conversion motor with a power of 7.5 kW; according to the motor configuration, pressure, and flow requirements, the frequency converter is selected as S200 – G7.5/P11T4B, the pressure sensor is selected as MIK – P300 30MPa with a measurement accuracy of 0.5%, the flowmeter is selected as LC – A2 – 0.2/AIGFI with a range of \(0.3 – 3m^{2}/h\) and a measurement accuracy level of 0.5, the data collector is a USB3200 – type with a sampling rate of 500ks/s, the throttle valve has a diameter of DN20, and the safety valve has a diameter of DN10. The test medium is hydraulic oil. [Insert a picture here showing the gear pump test bench, with clear labels for each component, such as the oil tank, motor, pump, pressure sensor, flowmeter, etc.]
4.2 Experimental Process
During the test, the inlet pressure of the prototype (5) is fixed at 0. As the motor (6) drives the prototype to operate, the hydraulic oil is transported from the oil tank (1) into the hydraulic pipeline. The pressure control valve (9) is placed on the pump outlet side to facilitate the adjustment of the pump outlet pressure. To ensure experimental safety, the outlet pressure of the prototype is adjusted to the minimum value through the pressure control valve. After the system runs stably, the outlet pressure is gradually adjusted through the pressure control valve. The pressure gauges (4/7) detect the pressure in the pipeline, and the flowmeter (8) detects the flow rate in the pipeline. Finally, the pressure and flow rate values are transmitted to the data collector in the form of analog signals, and the data collector transmits them to the upper – computer. After processing, the data is displayed on the visual interface of the upper – computer.
4.3 Comparison of Experimental and Simulation Results
The comparison between the numerical prediction and experimental results of the arc gear pump at 2000r/min is shown in the figure. It can be seen that under different inlet – outlet pressure – difference operating conditions, the numerical calculation values are higher than the experimental values, and the error is within 4.21%. The volume flow rate obtained from the numerical calculation is in good agreement with the experimental value. As the inlet – outlet pressure difference increases, the deviation between the experimental and numerically predicted volume flow rate values increases. The main reasons are that the pressure difference has a great impact on the volumetric efficiency, and the volumetric loss increases rapidly with the increase of the pressure difference. In addition, the numerical calculation ignores the mechanical losses caused by bearings, gears, and mechanical seals, as well as the errors in simplifying the 3D model of the arc gear pump rotation domain. Overall, using the RNG \(k – \varepsilon\) turbulence model to predict the performance of this pump has good accuracy and reference value.
5. Results and Analysis
5.1 Influence of the Number of Teeth on the Outlet Flow Characteristics of the Arc Gear Pump
The relationship curves between the outlet flow rate and volumetric efficiency of 6 – 9 – tooth gear pumps under different working conditions are shown in the figure. It can be seen that the number of teeth has a significant impact on the pump outlet flow rate. With the increase of the inlet – outlet pressure difference, the outlet flow rates and volumetric efficiencies of gear pumps with different numbers of teeth show a linear decrease.
| Operating Condition | 6 – tooth Pump | 7 – tooth Pump | 8 – tooth Pump | 9 – tooth Pump |
|---|---|---|---|---|
| 2MPa, 2000r/min | Average Outlet Flow Rate: [value 1], Volumetric Efficiency: [value 2] | Average Outlet Flow Rate: [value 3], Volumetric Efficiency: [value 4] | Average Outlet Flow Rate: [value 5], Volumetric Efficiency: [value 6] | Average Outlet Flow Rate: [value 7], Volumetric Efficiency: [value 8] |
| 10MPa, 2000r/min | Average Outlet Flow Rate: [value 9], Volumetric Efficiency: [value 10] | Average Outlet Flow Rate: [value 11], Volumetric Efficiency: [value 12] | Average Outlet Flow Rate: [value 13], Volumetric Efficiency: [value 14] | Average Outlet Flow Rate: [value 15], Volumetric Efficiency: [value 16] |
| As the pressure increases, the pressure gradient in the cavity increases, the internal leakage increases, and the shaft power of the pump decreases, resulting in a decrease in the average outlet flow rate. With the increase of the number of gear teeth, the proportion of the gear volume increases, and the effective volume for transporting fluid in the pump cavity decreases. The theoretical displacement of 6 – 9 – tooth pumps shows a downward trend, but it has a positive effect on the improvement of the volumetric efficiency. When the number of teeth increases to 9, the decrease range of the pump’s average outlet flow rate and volumetric efficiency is the smallest. |
The relationship between the flow pulsation coefficient and the number of teeth under different working conditions is shown in the figure. The flow pulsation coefficient is defined as \(\delta_{Q}=\frac{Q_{max } – Q_{min }}{Q_{ave }}\), where \(Q_{max}\), \(Q_{min}\) are the maximum and minimum outlet flow rates respectively, and \(Q_{ave}\) is the average outlet flow rate. The number of teeth has a significant impact on the pump’s flow pulsation. In the process of the inlet – outlet pressure difference increasing from 2MPa to 10MPa, the flow pulsation coefficients of gear pumps with different numbers of teeth all show an upward trend. Taking the 2000r/min working condition as an example, the 6 – tooth pump has the largest increase amplitude of 0.43, the 7 – tooth pump has the smallest increase amplitude of 0.03, and the 8 – tooth and 9 – tooth pumps increase by 0.35 and 0.07 respectively. At the same inlet – outlet pressure difference, 7 – tooth and 9 – tooth pumps can maintain a lower flow pulsation. [Insert a picture here showing the relationship curves between the outlet flow rate, volumetric efficiency, and flow pulsation coefficient and the number of teeth under different working conditions, with clear legends for different lines and symbols]
5.2 Influence of the Number of Teeth on the Internal Flow Characteristics of the Arc Gear Pump
Taking the simulation data of 6 – 9 – tooth pumps under the working conditions of 8MPa and 2000r/min as an example, the influence of the number of teeth on the internal flow characteristics and performance of the pump is analyzed. The outlet instantaneous flow rate characteristics curves of 6 – 9 – tooth gear pumps within one cycle are shown in the figure. The outlet instantaneous flow rates of gear pumps with different numbers of teeth show periodic changes, and the number of flow pulsations at the pump outlet is equal to the number of gear teeth. The number of teeth has a significant impact on the outlet flow rate pulsation of the pump. Among them, the flow rate reduction values from the peak to the trough of 7 – tooth and 9 – tooth pumps are relatively small, decreasing by 2.84L/min and 1.76L/min respectively. The flow rate reduction values of 6 – tooth and 8 – tooth pumps from the peak to the trough are relatively large, decreasing by 5.53L/min and 4.90L/min respectively. 6 – 9 – tooth gear pumps all have different degrees of secondary flow pulsation. When the number of teeth increases to 9, its pulsation characteristic curve gradually changes from an “M” – shaped peak to a “V” – shaped peak, and the pulsation amplitude decreases. In the process of the gradual increase of the number of teeth, the change of the flow pulsation amplitude within one cycle does not show a strictly linear decrease with the increase of the number of teeth, and the decrease ranges are different. The average outlet flow rates of pumps with different numbers of teeth also do not show a strictly linear decrease with the increase of the number of teeth.
The outlet instantaneous flow rate of the arc gear pump is related to the number of teeth, the volume of the tooth – cavity control area, and also related to factors such as the pitch angle \(\tau\), helix angle \(\beta\), and meshing angle \(\varphi\) of the two gears (these parameters change with the change of the number of teeth). The mathematical expression of the outlet instantaneous flow rate of the arc gear pump is derived from a mathematical perspective. Considering the arc helical gear as composed of countless arc spur gears with a thickness of dx staggered by an angle \(\beta\), the instantaneous flow rate model of the helical gear can be obtained by integrating the instantaneous flow rate of the arc spur gear with a thickness of dx.
5.3 Influence of the Number of Teeth on the Internal Pressure Characteristics of the Arc Gear Pump
The central section in the gear width direction is set as the pressure monitoring surface. The schematic diagrams of the internal pressure distribution of 6 – 9 – tooth gear pumps when they mesh and rotate by τ/4 are shown in Figure 14. It can be seen that as the number of teeth increases, the number of serially – connected transition chambers in the gear cavity gradually increases. Taking the first rotation position in Figure 14(a – d) as an example, the pressure differences between independent chambers of 6 – 9 – tooth pumps are as follows: 4.38MPa, 3.50MPa (for 6 – tooth, between 2D – 3D and 3D – 4D); 2.65MPa, 2.51MPa, 2.82MPa (for 7 – tooth, between 2D – 3D, 3D – 4D, and 4D – 5D); 1.99MPa, 2.01MPa, 2.01MPa, 1.93MPa (for 8 – tooth, between 1D – 2D, 2D – 3D, 3D – 4D, and 4D – 5D); 2.00MPa, 2.01MPa, 1.98MPa, 2.01MPa (for 9 – tooth, between 1D – 2D, 2D – 3D, 3D – 4D, and 4D – 5D). The pressure difference between adjacent independent chambers decreases step by step, and the pressure drop gradient gradually decreases. Moreover, as the number of teeth increases, the pressure distribution in the independent chambers when the gear rotates by τ/4 becomes more and more similar.
In the process of gear meshing, the areas of the high – pressure and low – pressure regions in the pump cavity change periodically. Due to the high inlet – outlet pressure difference, the shear force acting on the fluid element and the relative motion of fluid particles increase, and the continuity of the flow weakens, resulting in a large pressure difference change during the fluid transfer. At the inlet end, due to the local vacuum formed by the increase in the variable volume of the bottom cavity hole, vortices are likely to occur below the tooth – space opening. In addition, the pressure difference between the inlet end and the first rotating 1D/1S control volume is large, and the fluid velocity in the cavity is easily distorted at the extrusion point, and vortex flows appear below the left and right gear – cavity walls. As the gear rotates, part of the vortex flow moves along with the gear rotation, forming vortices within the effective volume between the gear and the cavity wall, and these vortices are distributed axially. The fluid velocity at this position is greater than that of the surrounding fluid, which enhances the flow instability. With the increase in the number of teeth, the position where the vortices concentrate gradually shifts from the center of the effective volume towards the edge of the cavity wall, which has a positive effect on the stability of the fluid motion in the cavity. Part of the vortex flow at the inlet end remains there, disturbing the fluid that subsequently enters the gear cavity, causing wear on the gear – cavity wall and impact losses, and some also leaks along the flow channel.
As the gear continues to rotate, the vortices continue to evolve towards the outlet end. Due to the interaction between the left and right gears, a pair of counter – rotating vortices are formed in the front and rear of the outlet end. Due to the effects of the helix angle and gear width, the flow states and sizes of this pair of counter – rotating vortices in the front and rear of the outlet are different, and they are asymmetric along the central axis direction, which affects the unbalance of the fluid pressure on the two gears. This unbalance is caused by the structure of the arc gear itself. Although theoretically, the arc gear pump can “completely eliminate” flow pulsation, due to the evolution of the vortex pairs in the gear – cavity wall, the unbalance of the forces on the two gears, and the leakage at the gaps, the fluid in the arc gear pump cavity shows instability.
In addition, the influences of tooth – to – tooth leakage and radial leakage on the internal pressure characteristics are mainly considered. The leakage amount between two gears depends on the opening area and the pressure difference between the upper and lower parts of the opening. Different numbers of teeth result in different action lines of a pair of meshing helical gears, and thus different changes in the opening area. For radial leakage (the radial clearance in this model is set to 0.02mm), since the geometric shape of the clearance is not a single – layer thin – film lubrication clearance, the flow here can be laminar or turbulent (depending on the Reynolds number, and the transition between laminar and turbulent flow is achieved using the hyperbolic tangent function, specifically represented in \(c_{p}\)). Therefore, the radial leakage model [4] uses the modified leakage equation: \(Q = c_{p}A_{k}\sqrt{\frac{2|\Delta P|}{\rho}}\), where \(c_{p}\) is defined as the flow coefficient in the literature [4], \(A_{k}\) is the orifice opening area between the tooth tip and the cavity wall, and \(\rho\) is the fluid density. As the number of teeth increases, the \(\Delta P\) between adjacent transition chambers decreases, which has a certain inhibitory effect on radial leakage. Therefore, appropriately increasing the number of teeth can effectively suppress the flow instability caused by the pressure difference during the pump operation.
5.4 Influence of the Number of Teeth on the Arc Gear Excitation Force
The two gears are symmetrically distributed and rotate synchronously in opposite directions. Taking the driven gear as the research object, its radial force and axial force are analyzed. The pulsation amplitude diagrams of the forces on the 6 – 9 – tooth driven gear within one cycle are shown in Figure 15. The radial force is the resultant force of the components in the x – y direction, and the axial force is the absolute value of the force along the z – axis. It can be seen from Figure 15 that the radial and axial forces on gears with different numbers of teeth change periodically, and the number of force pulsations on the gear is in a multiple relationship with the number of teeth. Assuming that the hydraulic oil is incompressible, this is mainly because the periodic movement of the gear pump causes the volumes of each control volume (1D – 9D, 1S – 9S) to change periodically, resulting in a periodic change in the internal flow field of the pump.
The change in gear force is related to gear meshing and the interaction between the gear and the fluid in the cavity. As the number of teeth increases, \(F_{x}\) decreases, \(F_{y}\) first decreases and then increases. For the resultant force F, as the number of teeth increases, the maximum value of the 9 – tooth gear is 71.38% less than that of the 6 – tooth gear, and the maximum value of \(F_{z}\) is 79.37% less. Within one cycle, as the number of teeth increases, the radial and axial forces on the gear gradually decrease, and the pulsation amplitude gradually becomes stable. Since the 6 – tooth gear has fewer transition chambers, the pressure difference between the transition chamber and the high – pressure chamber at the outlet is large, and a backflow phenomenon is likely to occur, resulting in an opposite acting force on the gear. Moreover, the effective volume in the 6 – tooth gear cavity is larger, making it more prone to flow separation and secondary flow phenomena.
By performing wavelet transform on the radial and axial forces through Matlab, with the bandwidth and center frequency set as cmor1 – 1.5, the scale is converted into frequency, the corresponding continuous wavelet coefficients are solved, and the wavelet responses (pulsation intensities) of the original functions (the radial and axial forces on the gear) in the time – domain and frequency – domain are obtained. Figure 16a shows the pulsation frequency spectrum of the radial force on the 6 – 9 – tooth gear within one cycle, displaying the time – scale change, frequency – scale change, wavelet response intensity, and phase distribution of the radial force on the gear within one cycle. Each pair of gear meshing forms a tooth – frequency cycle. When the gear rotates one week, a total of Z pairs of gears alternately mesh to form a rotation – frequency cycle. Within one rotation – frequency cycle, processes such as meshing entry, single/double – tooth meshing, and meshing disengagement occur, resulting in multiple volume mutations of the effective volume, which are specifically presented in the low – and high – frequency parts of the figure. As the gear rotates, the positive and negative phases of the wavelet response alternate, and the alternating frequency is related to the multiple of the number of teeth. Therefore, the periodic change of the gear radial force is related to gear meshing. It can be seen from the figure that the main frequencies of the radial force pulsation of gears with different numbers of teeth all appear at 1 – times the tooth – frequency, and the vibration amplitude at this position is the largest, indicating that this is the main influencing factor of the gear force pulsation. The wavelet response intensity decreases step by step from low frequency to high frequency, and the frequencies of the sub – frequencies are all multiples of the tooth – frequency. Therefore, the change in the wavelet response intensity is related to the meshing rotation of the two gears and the dynamic – static interference between the gear and the pump cavity.
As the number of gear teeth increases, the maximum wavelet response intensities of the radial force pulsation amplitudes of 7 – 9 – tooth driven gears change compared to the 6 – tooth gear as follows: – 54.37%, – 23.41%, – 21.83%, and the reduction in the wavelet response intensity in the main frequency band is obvious. However, the frequency of the gear force pulsation increases with the increase in the number of teeth.
Figure 16b shows the pulsation frequency spectrum of the axial force on the driven gear within one cycle. The maximum wavelet response intensities of the axial forces of 7 – 9 – tooth gears change compared to the 6 – tooth gear as follows: – 46.08%, – 75.42%, – 55.42%. The gear force pulsation is affected by the superposition of the rotation – frequency, tooth – frequency, and tooth – frequency multiples. During the rotation of the gear pump, the inlet – outlet pressure difference and the rotational speed of the gear pump have a certain influence on the harmonic components of the frequency spectrum. The inlet – outlet pressure difference affects the pulsation amplitude of the force, and the rotational speed affects the phase of the force pulsation, and their influences occur simultaneously.
It can be found from Figure 11b that the action line of a pair of meshing arc gears is not parallel to the rotation axis, so there is an axial component in the contact force generated, and the arc gear is thus subjected to a certain axial load. It can be found from Figure 14 that due to different numbers of teeth, there are differences in the pressure distribution in the D and C chambers at the same height of the main and driven gears in the monitoring surface. Therefore, the reaction forces of the fluid in the cavity acting on the two gears are asymmetric, making the pressures on the two gears unbalanced. This also reflects from the side that only at a specific number of teeth can the pulsation of the gear force in the gear pump be well eliminated. In addition, the increase in the number of teeth also has an impact on the lightweight design of the pump.
6. Conclusions
This paper studies the influence of the number of teeth on the flow, pressure characteristics, and gear force characteristics of arc gear pumps based on the CFD numerical method. The main research conclusions are as follows: (1) Numerical predictions and experiments show that the simulation values are in good agreement with the experimental values. The numerical simulation method used in this paper can well predict the flow characteristics of arc gear pumps. When the number of teeth changes, the helix angle and pitch angle change immediately. The flow characteristics in the pump cavity are not only affected by the number of teeth but also by the combined effects of the number of teeth, helix angle, pitch angle, etc. Therefore, as the number of teeth increases, the flow fluctuation coefficient does not show a strictly linear decrease. The simulated average outlet flow rate of the 7 – tooth gear pump is the largest; the theoretical outlet flow rate of the 9 – tooth gear pump is the smallest. Under the working conditions of 8MPa and 2000r/min, the volumetric efficiencies of 7 – 9 – tooth gear pumps change compared to the 6 – tooth gear pump as follows: + 18.34%, + 7.15%, + 20.70%. (2) As the number of teeth increases, the number of serially – connected transition chambers gradually increases, the pressure drop gradient between adjacent chambers of the pump decreases, the internal pressurization effect gradually stabilizes, and the leakage of the pump is improved to a certain extent. At the same time, the vector values of the gear radial and axial excitation forces decrease, and the pulsation intensities of the radial and axial forces decrease. The radial and axial forces are affected by the rotation – frequency, tooth – frequency, and their multiples. The inlet – outlet pressure difference and rotational speed have some influence on the harmonic components of their frequency spectra. This reflects that when the operating conditions of the pump are determined, only at a specific number of teeth can the pulsation of the pump be effectively reduced.
