Specific calculation method of flow and displacement of gear pump

The gear pump can be divided into two types: external engagement and internal engagement. The external engagement gear pump has several kinds of gears, such as straight teeth, helical teeth and human teeth. Generally, the involute profile is adopted, while the internal engagement gear pump adopts arc cycloid profile or involute profile
Gear pump engagement classification
The number of gears in the external gear pump is two gears in common use, and there is only one gear in the internal gear pump. The gear pump is suitable for conveying various liquids without solid particles. It can be used as a hydraulic pump in the oil pump, fuel pump, infusion pump and hydraulic transmission device. The viscosity of the conveying liquid can reach 5 × 105cst
Theoretical displacement and flow of gear pump
Theoretical displacement refers to the volume of liquid discharged from each revolution of the pump without leakage loss. When the number of teeth of two gears is the same, the theoretical displacement of the external gear pump is:
qth=πb/2(d20-a2-1/3t20-1/3b2tgbgβg)
Where B -- tooth width, m;
D0 -- diameter of gear top circle, m;
A - gear center distance, m;
T0 -- pitch of base circle, m;
BG -- helix angle on cylindrical surface, degree
The theoretical displacement per revolution of the uncorrected standard spur gear pump is:
gth=2πbm2(z+1-π2/12cos2a)10-3 cm3/r
Where m - gear module, mm;
Z -- number of gear teeth;
A - tool pressure angle, degree
The theoretical flow of gear pump can be calculated as follows:
Qth=qthn×10-3L／min
Where n -- pump speed, R / min
Considering the efficiency is the gear pump flow
Instantaneous flow of gear pump
The volume of liquid discharged by the pump is called instantaneous flow. The instantaneous theoretical flow of external gear is:
Q'th = 2 π Nb (ra2-r'2-r2g θ 2) × 10-6 L / min
Where ra - radius of wheel top circle, mm;
R '- pitch radius of gear, mm;
RG -- radius of base circle, mm;
N -- rotation speed, R / min;
B -- tooth width, bin;
θ - helix angle, degree
When the pump works, the meshing point of two gears moves along the meshing line, so 0 is variable, that is, the instantaneous flow of the pump is pulsating, and its pulsating frequency.
The flow pulsation of gear pump (causing pressure pulsation at the same time) will cause noise and vibration of gear pump. The pulsation degree of flow and pressure is related to the number of teeth. The flow pulsation is expressed by the flow nonuniformity coefficient
δ0=(Q’th max-Q’th min)/Q’th min
Where q'th max - large instantaneous theoretical flow;
Q'th min - small instantaneous theoretical flow
For the external meshing standard spur gear pump with equal number of teeth and overlapping coefficient e greater than l (the unloading groove is not opened), there are:
δ0=π2ε2cos2a/4(z+1)