CN203730300U - Fourier non-circular gear-driven four-blade differential pump - Google Patents

Abstract

The utility model discloses a four-blade differential speed pump driven by Fourier noncircular gears. The power of the utility model is output by the motor and transmitted to the input shaft through the coupling; the first Fourier non-circular gear and the second Fourier non-circular gear are fixed on the input shaft; the first conjugate Fourier non-circular gear is fixed on the input shaft; The circular gear is fixed on the output shaft and meshes with the first Fourier non-circular gear; the second conjugate Fourier non-circular gear and the second impeller are consolidated through the sleeve, and the sleeve is looped on the output shaft; the second The two-conjugate Fourier non-circular gear meshes with the second Fourier non-circular gear; the first impeller is fixed on the output shaft; the first impeller and the second impeller are equipped with two blades, and a single blade is installed inside each blade. Directional pressure relief valve, the direction of one-way pressure relief valve is consistent with the direction of blade rotation. The utility model has the advantages of large displacement, stable flow, and easy adjustment of unequal velocity law, and effectively solves the problems of pressure pulsation and trapped liquid in traditional differential pumps.

Description

Four-vane differential pump driven by Fourier non-circular gears

technical field

The utility model belongs to the technical field of displacement pumps and relates to a vane differential pump, in particular to a four-blade differential pump driven by Fourier non-circular gears.

Background technique

The liquid pumps commonly used in general machinery include piston pumps, plunger pumps, diaphragm pumps, roller pumps and centrifugal pumps. Among them: live (pillar) piston pumps have higher outlet pressure, but require a reliable seal between the piston and the cylinder. , and the pressure fluctuates greatly; the diaphragm pump can produce a relatively stable liquid flow when there are multiple cylinders, but the structure is complex; the displacement of the roller pump is uniform when the speed is stable, and the leakage increases with the increase of the pressure. The displacement and efficiency of the centrifugal pump are correspondingly reduced; the structure of the centrifugal pump is simple and easy to manufacture, but its displacement is large and the pressure is low, so it is used in occasions where the working pressure is not required. These pumps have their own defects, and they cannot meet the constant flow and high pressure requirements of some special machinery.

The existing differential pumps mainly have the following types according to the different driving mechanisms:

Rotating guide rod-gear vane differential pump, its drive system is subjected to alternating loads, which produces gear meshing noise, and impact noise will also be caused when the gaps between the moving pairs are large.

The universal joint gear mechanism drives the vane differential pump, and the angle between the input shaft and the output shaft of the universal joint mechanism is a key parameter affecting the performance of the pump. The larger the angle, the larger the displacement of the pump. However, with the increase of the angle, the flow pulsation of the pump increases and the transmission efficiency of the universal joint decreases.

Deformed eccentric circle non-circular gear drive vane differential pump, the adjustment parameters of the eccentric circle non-circular gear pitch curve are mainly eccentricity and deformation coefficient, the adjustment amount is limited, the adjustment accuracy is not high, resulting in transmission ratio optimization, inconvenient adjustment, poor design Flexibility is not conducive to further optimization of the design, and it is difficult to optimize problems such as pressure pulsation and trapped liquid.

Contents of the invention

The purpose of this utility model is to provide a four-blade differential pump driven by Fourier non-circular gears, which has large displacement, high pressure, stable flow and compact structure; The non-uniform velocity law is easy to adjust, which is convenient for performance optimization; by installing a one-way pressure relief valve in the blade, the adjacent closed cavity is opened when the pressure exceeds the limit, effectively solving the problem of trapped liquid in the existing differential pump.

The utility model comprises a driving part and a differential pump part.

The drive components include a drive gearbox, an input shaft, an output shaft, a first Fourier non-circular gear, a second Fourier non-circular gear, a first conjugate Fourier non-circular gear, a second conjugate Fourier non-circular gear Rifle non-circular gears and bushings. The motor drives the input shaft to rotate, and the input shaft is supported on both side walls of the drive gearbox through two bearings; the first Fourier non-circular gear and the second Fourier non-circular gear are fixedly installed on the input shaft; The two ends of the output shaft are respectively supported on the box wall of the drive gearbox and the pump casing through bearings, and the first conjugate Fourier non-circular gear is fixedly installed on the output shaft and meshes with the first Fourier non-circular gear; Both the second conjugate Fourier non-circular gear and the second impeller are fixed on the shaft sleeve, and the shaft sleeve is looped on the output shaft; the second conjugate Fourier non-circular gear and the second Fourier non-circular gear Engage;

The differential pump components include a pump casing, a first impeller, a second impeller and a one-way pressure relief valve; the pump casing is sequentially provided with a first discharge port, a first liquid suction port, a second The liquid discharge port and the second liquid suction port; the first impeller is fixed on the output shaft; the first impeller and the second impeller are symmetrically provided with two blades; along the circumferential direction, the blades of the first impeller and the second impeller The blades are arranged alternately; a one-way pressure relief valve is installed inside all blades.

According to the structure of the pump, the initial value a ₀ of the center distance between the first Fourier non-circular gear and the first conjugate Fourier non-circular gear is given, and then according to the closed condition of the pitch curve and the meshing condition, the center is obtained by using the advance and retreat method The exact value of distance a. The specific calculation is as follows:

The pitch curve expression of the first Fourier non-circular gear is:

Among them, a ₁ , a ₂ , b ₁ and b ₂ are the parameters of the Fourier function, the value range of a ₁ is 1~6, the value range of a ₂ is 1~3, and the value range of b ₁ is 0~2.3 , b ₂ ranges from 0 to 2.3, n is the order of the first Fourier non-circular gear, and the value is 2; is the rotation angle of the first Fourier non-circular gear, is the corresponding rotation angle of the first Fourier non-circular gear radial direction.

According to the principle of non-circular gear meshing, when the first Fourier non-circular gear rotates 360°, the angular displacement of the first conjugate Fourier non-circular gear:

Both the first Fourier non-circular gear and the first conjugate Fourier non-circular gear are second-order non-circular gears. Therefore, when the first Fourier non-circular gear rotates 360°, the first conjugate Fourier non-circular gear The circular gear also rotates 360°, and the iterative formula for calculating the center distance a can be obtained:

Take the initial value of the center distance a ₀ and use the advance and retreat method to search and calculate the exact value of the center distance a.

The input shaft and the output shaft are respectively arranged at two ends of the gearbox; one end of the input shaft extends out of the drive gearbox and is connected with the motor through a coupling.

The first liquid discharge port and the second liquid discharge port are arranged symmetrically, and the first liquid suction port and the second liquid suction port are symmetrically arranged.

The direction of all one-way pressure relief valves is consistent with the direction of vane rotation.

The structures of the first Fourier non-circular gear and the second Fourier non-circular gear are completely consistent, and the structures of the first conjugate Fourier non-circular gear and the second conjugate Fourier non-circular gear are completely consistent , the first Fourier non-circular gear, the second Fourier non-circular gear, the first conjugate Fourier non-circular gear and the second conjugate Fourier non-circular gear are all second-order non-circular gears; the first The initial installation phase difference between the Fourier non-circular gear and the second Fourier non-circular gear, and the initial installation phase difference between the first conjugate Fourier non-circular gear and the second conjugate Fourier non-circular gear are all 90 °.

The transmission ratio between the first Fourier non-circular gear and the first conjugate Fourier non-circular gear is:

The transmission ratio between the second Fourier non-circular gear and the second conjugate Fourier non-circular gear is:

Among them, θ is the initial installation phase difference between the first Fourier non-circular gear and the second Fourier non-circular gear, and the value is 90°.

Make the transmission ratio i ₂₁ of the first Fourier non-circular gear and the first conjugate Fourier non-circular gear equal to the transmission ratio i ₄₃ of the second Fourier non-circular gear and the second conjugate Fourier non-circular gear , four different corners can be obtained corner Take the minimum When , the angular displacement of the first Fourier non-circular gear is The angular displacement of the second Fourier non-circular gear is The rotation angles of the first impeller and the second impeller are respectively:

The center position angle of the first discharge port of the pump casing Center position angle of the first liquid suction port The center position angle of the second liquid discharge port ψ _{row 2} = ψ _{row 1} + π, the center position angle of the second liquid suction port ψ _{suction 2} = ψ _{suction 1} + π; the first liquid discharge port, the first liquid suction port, the second liquid suction port The liquid discharge port and the second liquid suction port are equal in size and 2-5° smaller than the vane angle θ _lobe of the blade; the value of the vane angle θ _lobe of the first impeller and the second impeller are both 40°-45°.

Minimum opening angle of two adjacent blades At this time, the closed cavity has the minimum volume:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}$

Among them, R is the radius of the blade, r is the radius of the impeller shaft, and h is the thickness of the blade.

Maximum opening angle of two adjacent blades At this time, the closed cavity has the maximum volume:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}$

The displacement calculation expression of the four-blade differential pump:

Q＝4×(V _max -V _min )＝2(Δψ _max -Δψ _min )(R ² -r ² )×h×10 ^-6

The instantaneous flow calculation expression of the four-blade differential pump:

$\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; dV</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h\&omega;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; |</span>$

Among them, V is the volume of the liquid discharge chamber; ω is the angular velocity of the first Fourier non-circular gear and the second Fourier non-circular gear, and its calculation formula is

Calculation expressions of the minimum volume and maximum volume trapped liquid pressure changes of the four-blade differential pump:

$\frac{{\mathrm{<span\; class="notranslate">\; dp</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h\&omega;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; |</span>$

$\frac{{\mathrm{<span\; class="notranslate">\; dp</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h\&omega;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; |</span>$

where K is the elastic modulus of the liquid.

The beneficial effect that the utility model has is:

The utility model adopts a Fourier non-circular gear mechanism, and the pitch curve of the Fourier non-circular gear has six adjustment parameters. The law of constant speed transmission is easy to adjust, and it is easy to realize the optimization of the displacement, pressure, flow and other performances of the differential pump. By installing a one-way pressure relief valve in the vane, the adjacent closed cavity is opened when the pressure exceeds the limit, which effectively solves the problem of trapped liquid in the existing differential pump. Due to the symmetrical suction port and liquid discharge port of the differential pump driven by the Fourier non-circular gear mechanism, the radial balance is good, and the non-constant speed transmission is a rotary motion, so the operation is stable and reliable, the radial working load is balanced, and the pulsation is controllable Good performance; many blades, large displacement, the inner surface of the pump casing and the shape of the blades are simple, and the volumetric efficiency is high.

The core mechanism of the utility model is two pairs of Fourier non-circular gears with different installation phases, with few parts and compact structure.

Description of drawings

Fig. 1 is a schematic diagram of the mechanism movement of the utility model;

Figure 2 is a sectional view of the overall structure of the differential pump components in the utility model;

Fig. 3 is a schematic diagram of the meshing relationship of Fourier non-circular gears in the initial installation position in the utility model;

Fig. 4 is the schematic diagram of the limit position of the blade of the present utility model;

Fig. 5-1 is the instantaneous flow diagram when the displacement of the utility model is maximum;

Fig. 5-2 is the meshing diagram of the Fourier non-circular gear pitch curve when the displacement of the utility model is maximum;

Fig. 6-1 is the instantaneous flow diagram when the displacement of the utility model is minimum;

Fig. 6-2 is the meshing diagram of the Fourier non-circular gear pitch curve when the displacement of the utility model is the minimum;

Fig. 7-1 is the instantaneous flow diagram when the utility model is used in parallel connection of multiple pumps;

Fig. 7-2 is the meshing diagram of the Fourier non-circular gear pitch curve when the utility model is used in parallel connection of multiple pumps.

In the figure: 1. Drive gearbox, 2. Input shaft, 3. Output shaft, 4. First Fourier non-circular gear, 5. Second Fourier non-circular gear, 6. First conjugate Fourier Non-circular gear, 7. Second conjugate Fourier non-circular gear, 8. Shaft sleeve, 9. Coupling, 10. Motor, 11. Pump casing, 11-1, First liquid discharge port, 11-2 , the first liquid suction port, 11-3, the second liquid discharge port, 11-4, the second liquid suction port, 12, the first impeller, 13, the second impeller, 14, one-way check valve.

Detailed ways

Below in conjunction with accompanying drawing and embodiment the utility model is further described.

As shown in Figures 1 and 2, a four-blade differential pump driven by a Fourier non-circular gear includes a driving part and a differential pump part.

The drive components include a drive gearbox 1, an input shaft 2, an output shaft 3, a first Fourier non-circular gear 4, a second Fourier non-circular gear 5, a first conjugate Fourier non-circular gear 6, a second Conjugate Fourier non-circular gear 7 and shaft sleeve 8 . The motor 10 transmits power to the input shaft 2 through the coupling 9, and the input shaft 2 is supported on both side walls of the drive gearbox 1 through two bearings; the first Fourier non-circular gear 4 and the second Fourier non-circular gear The gears 5 are all fixedly installed on the input shaft 2; the two ends of the output shaft 3 are respectively supported on the box walls of the drive gearbox 1 and the pump casing 11 through bearings, and the first conjugate Fourier non-circular gear 6 is fixedly installed on the output shaft. on the shaft 3, and meshes with the first Fourier non-circular gear 4; the second conjugate Fourier non-circular gear 7 and the second impeller 13 are fixed on the shaft sleeve 8, and the shaft sleeve 8 is looped on the output shaft 3 above; the second conjugate Fourier non-circular gear 7 meshes with the second Fourier non-circular gear 5 .

The differential pump components include a pump casing 11, a first impeller 12, a second impeller 13 and a one-way pressure relief valve 14; the pump casing 11 is sequentially provided with a first liquid discharge port 11-1 and a first liquid suction port 11 along the circumferential direction -2. The second liquid discharge port 11-3 and the second liquid suction port 11-4; the first liquid discharge port 11-1 and the second liquid discharge port 11-3 are symmetrically arranged, and the first liquid suction port 11-2 is connected to the The second liquid suction port 11-4 is arranged symmetrically; the first impeller 12 is fixed on the output shaft 3; the first impeller 12 and the second impeller 13 are all symmetrically provided with two blades; along the circumferential direction, the blades of the first impeller 12 and The blades of the second impeller 13 are arranged alternately; a one-way pressure relief valve 14 is installed inside all the blades, and the direction of the one-way pressure relief valve 14 is consistent with the rotation direction of the blades.

As shown in Figure 3, the structures of the first Fourier non-circular gear 4 and the second Fourier non-circular gear 5 are exactly the same, and the first conjugate Fourier non-circular gear 6 and the second conjugate Fourier non-circular gear The structure of the circular gear 7 is exactly the same, the first Fourier non-circular gear 4, the second Fourier non-circular gear 5, the first conjugate Fourier non-circular gear 6 and the second conjugate Fourier non-circular gear 7 are second-order non-circular gears; the initial installation phase angle of the first Fourier non-circular gear 4 is θ ₁ , and the initial installation phase angle of the second Fourier non-circular gear 5 is θ ₂ ; the first Fourier The initial installation phase difference between the non-circular gear 4 and the second Fourier non-circular gear 5, the first conjugate Fourier non-circular gear 6 and the second conjugate Fourier non-circular gear 7 is θ ₁ -θ ₂ , whose value is 90°, realizes the differential rotation of the first impeller 12 and the second impeller 13, so that the volume of the closed chamber of the differential pump changes periodically, at the first discharge port 11-1 and the second discharge port 11 -3 produces discharge, and produces suction at the first liquid suction port 11-2 and the second liquid suction port 11-4. Since the non-uniform speed transmission of the Fourier non-circular gear is continuous, when the closed cavity is completely sealed, the blades still rotate at a differential speed, which will cause the pressure in the closed cavity to exceed the limit value, and the one-way pressure relief valve 14 will be adjacent to the closed cavity Open up and release pressure to prevent trapped liquid.

The working principle of the four-blade differential pump driven by Fourier non-circular gears:

The motor 10 transmits power to the first Fourier non-circular gear 4 and the second Fourier non-circular gear 5 through the coupling 9 and the input shaft 2 . The first Fourier non-circular gear 4 meshes with the first conjugate Fourier non-circular gear 6, the second Fourier non-circular gear 5 meshes with the second conjugate Fourier non-circular gear 7, and the first conjugate The Fourier non-circular gear 6 transmits power to the first impeller 12 through the output shaft 3 , and the second conjugate Fourier non-circular gear 7 transmits power to the second impeller 13 through the shaft sleeve 8 . The installation phases of the two pairs of Fourier non-circular gear pairs are different to realize the differential rotation of the first impeller 12 and the second impeller 13, thereby realizing liquid suction and liquid discharge.

According to the structure of the pump, the initial value a ₀ of the center distance between the first Fourier non-circular gear 4 and the first conjugate Fourier non-circular gear 6 is given, and then according to the closed condition of the pitch curve and the meshing condition, the advance and retreat method is used to search Get the exact value of the center distance a. The specific calculation is as follows:

The pitch curve expression of the first Fourier non-circular gear 4 is:

Among them, a ₁ , a ₂ , b ₁ and b ₂ are the parameters of the Fourier function, n is the order of the first Fourier non-circular gear 4, and the value is 2; is the rotation angle of the first Fourier non-circular gear 4, Corresponding rotation angle for the first Fourier non-circular gear 4 radial direction.

According to the principle of non-circular gear meshing, when the first Fourier non-circular gear 4 rotates 360°, the angular displacement of the first conjugate Fourier non-circular gear 6 is:

Both the first Fourier non-circular gear 4 and the first conjugate Fourier non-circular gear 6 are second-order non-circular gears. Therefore, when the first Fourier non-circular gear 4 rotates 360°, the first conjugate Fourier non-circular gear Rifle non-circular gear 6 also rotates 360°, and the iterative formula for calculating the center distance a can be obtained:

Take the initial value of the center distance a ₀ and use the advance and retreat method to search and calculate the exact value of the center distance a.

After obtaining the accurate value of the center distance a, the center position of the discharge and suction ports of the pump casing, the displacement, instantaneous flow rate, and the minimum volume and maximum volume trapping pressure change expressions of the four-blade differential pump can be solved. The specific calculation is as follows:

The transmission ratio of the first Fourier non-circular gear 4 and the first conjugate Fourier non-circular gear 6 is:

The transmission ratio of the second Fourier non-circular gear 5 and the second conjugate Fourier non-circular gear 7 is:

Wherein, θ is the initial installation phase difference between the first Fourier non-circular gear 4 and the second Fourier non-circular gear 5, and the value is 90°.

Make the transmission ratio i ₂₁ of the first Fourier non-circular gear 4 and the first conjugate Fourier non-circular gear 6 equal to that of the second Fourier non-circular gear 5 and the second conjugate Fourier non-circular gear 7 transmission ratio i ₄₃ , four different corners can be obtained corner Take the minimum , the angular displacement of the first Fourier non-circular gear 4 is The angular displacement of the second Fourier non-circular gear 5 is The rotation angles of the first impeller 12 and the second impeller 13 are respectively:

As shown in Figure 4, the center position angle of the first discharge port of the pump casing Center position angle of the first liquid suction port The center position angle of the second liquid discharge port ψ _{row 2} = ψ _{row 1} + π, the center position angle of the second liquid suction port ψ _{suction 2} = ψ _{suction 1} + π; the first liquid discharge port, the first liquid suction port, the second liquid suction port The sizes of the liquid discharge port and the second liquid suction port are 2° smaller than the vane angle θ _lobe of the blade; the value of the vane angle θ _lobe of the first impeller 12 and the second impeller 13 is both 45°.

Minimum opening angle of two adjacent blades At this time, the closed cavity has the minimum volume:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}$

Among them, R is the blade radius, the value is 90mm; r is the impeller shaft radius, the value is 20mm; h is the blade thickness, the value is 50mm.

Maximum opening angle of two adjacent blades At this time, the closed cavity has the maximum volume:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}$

The displacement calculation expression of the four-blade differential pump:

Q＝4×(V _max -V _min )＝2(Δψ _max -Δψ _min )(R ² -r ² )×h×10 ^-6

The instantaneous flow calculation expression of the four-blade differential pump:

$\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; dV</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h\&omega;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; |</span>$

Among them, V is the volume of the liquid discharge chamber; ω is the angular velocity of the first Fourier non-circular gear 4 and the second Fourier non-circular gear 5, and its calculation formula is

Calculation expressions of the minimum volume and maximum volume trapped liquid pressure changes of the four-blade differential pump:

$\frac{{\mathrm{<span\; class="notranslate">\; dp</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h\&omega;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; |</span>$

$\frac{{\mathrm{<span\; class="notranslate">\; dp</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h\&omega;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; |</span>$

where K is the elastic modulus of the liquid.

By calculating the minimum volume and maximum volume of the four-blade differential pump, the trapped liquid pressure can provide a reference for the selection of the one-way pressure relief valve in the vane, and is generally used to determine the upper limit of the one-way pressure relief valve.

As shown in Figures 5-1 and 5-2, the parameters of the Fourier function in the pitch curve expression of the first Fourier non-circular gear 4 are a ₁ =5.025, a ₂ =2.568, b ₁ =0.013, b ₂ =0.013, the order of the first Fourier non-circular gear 4 is n=2, the initial value of the center distance a ₀ =15mm, the center distance a can be obtained as 32.3mm, and the rotation angle of the first Fourier non-circular gear 4 Obtain the minimum value of 46°, at this time, the angular displacement of the first Fourier non-circular gear 4 is 46°, the angular displacement of the second Fourier non-circular gear 5 is 136°, the rotation angle ψ ₁ of the first impeller 12 is 64°, the rotation angle ψ ₂ of the second impeller 13 is 115°, the center position angle ψ _{row 1} of the first liquid discharge port is 86.5°, and the center position of the first liquid suction port The angle ψsuction ₁ is 137.5°, the central position angle ψrow ₂ of the second liquid discharge port is 266.5°, and the central position angle ψsuction ₂ of the second liquid suction port is 317.5°. Under this parameter, the displacement of the four-blade differential pump is the largest, and its value is 10305.9ml. At this time, the instantaneous flow pulsation is obvious, the first Fourier non-circular gear 4, the second Fourier non-circular gear 5, the first common The pitch curves of the yoke Fourier non-circular gear 6 and the second conjugate Fourier non-circular gear 7 are obviously concave.

As shown in Figures 6-1 and 6-2, the parameters of the Fourier function in the pitch curve expression of the first Fourier non-circular gear 4 are a ₁ =2, a ₂ =2.568, b ₁ =0.013, b ₂ =0.013, the order of the first Fourier non-circular gear 4 is n=2, the initial value of the center distance a ₀ =20mm, the center distance a can be obtained as 40.5mm, and the rotation angle of the first Fourier non-circular gear 4 Obtain the minimum value of 46°, at this time, the angular displacement of the first Fourier non-circular gear 4 is 46°, the angular displacement of the second Fourier non-circular gear 5 is 136°, the rotation angle ψ ₁ of the first impeller 12 is 51°, the rotation angle ψ ₂ of the second impeller 13 is 128°, the center position angle ψ _{row 1} of the first liquid discharge port is 73.5°, and the center position of the first liquid suction port The angle ψsuction ₁ is 150.5°, the center position angle ψrow ₂ of the second liquid discharge port is 253.5°, and the center position angle ψsuction ₂ of the second liquid suction port is 330.5°. Under this parameter, the displacement of the four-blade differential pump is the smallest, and its value is 3318.25ml. At this time, the instantaneous flow curve is gentle, and the first Fourier non-circular gear 4, the second Fourier The pitch curves of the yoke Fourier non-circular gear 6 and the second conjugate Fourier non-circular gear 7 are concave.

As shown in Figures 7-1 and 7-2, the parameters of the Fourier function in the pitch curve expression of the first Fourier non-circular gear 4 are a ₁ =6, a ₂ =2, b ₁ =0.013, b ₂ =0.013, the order of the first Fourier non-circular gear 4 is n=2, the initial value of the center distance a ₀ =20mm, the center distance a can be obtained as 42.1mm, and the rotation angle of the first Fourier non-circular gear 4 Obtain the minimum value of 46°, at this time, the angular displacement of the first Fourier non-circular gear 4 is 46°, the angular displacement of the second Fourier non-circular gear 5 is 136°, the rotation angle ψ ₁ of the first impeller 12 is 62°, the rotation angle ψ ₂ of the second impeller 13 is 118°, the center position angle ψ _{row 1 of} the first liquid discharge port is 84.5°, and the center position of the first liquid suction port The angle ψsuction ₁ is 140.5°, the center position angle ψrow ₂ of the second liquid discharge port is 264.5°, and the center position angle ψsuction ₂ of the second liquid suction port is 320.5°. Under this parameter, the displacement of the four-blade differential pump is 9123.91ml. At this time, the top of the instantaneous flow curve is gentler than the bottom, which is suitable for multi-pump parallel connection. The first Fourier non-circular gear 4, the second Fourier non-circular gear 5 , The pitch curves of the first conjugated Fourier non-circular gear 6 and the second conjugate Fourier non-circular gear 7 are not obviously concave, and better gear transmission characteristics and performance of the four-blade differential pump can be obtained.

Claims (6)

1. A four-blade differential pump driven by Fourier non-circular gears, including drive components and differential pump components, characterized in that: The drive components include a drive gearbox, an input shaft, an output shaft, a first Fourier non-circular gear, a second Fourier non-circular gear, a first conjugate Fourier non-circular gear, a second conjugate Fourier non-circular gear Liye non-circular gear and shaft sleeve; the motor drives the input shaft to rotate, and the input shaft is supported on the two side walls of the drive gearbox through two bearings; the first Fourier non-circular gear and the second Fourier non-circular gear The gears are all fixedly installed on the input shaft; the two ends of the output shaft are respectively supported on the box wall of the drive gearbox and the pump casing through bearings, and the first conjugate Fourier non-circular gear is fixedly installed on the output shaft, and is connected with the second The first Fourier non-circular gear meshes; the second conjugate Fourier non-circular gear and the second impeller are fixed on the shaft sleeve, and the shaft sleeve is looped on the output shaft; the second conjugate Fourier non-circular gear Mesh with the second Fourier non-circular gear; The differential pump components include a pump casing, a first impeller, a second impeller and a one-way pressure relief valve; the pump casing is sequentially provided with a first discharge port, a first liquid suction port, a second The liquid discharge port and the second liquid suction port; the first impeller is fixed on the output shaft; the first impeller and the second impeller are symmetrically provided with two blades; along the circumferential direction, the blades of the first impeller and the second impeller The blades are arranged alternately; a one-way pressure relief valve is installed inside all blades; According to the structure of the pump, the initial value a ₀ of the center distance between the first Fourier non-circular gear and the first conjugate Fourier non-circular gear is given, and then according to the closed condition of the pitch curve and the meshing condition, the forward and backward method is used to search and obtain the center The exact value of distance a; the specific calculation is as follows: The pitch curve expression of the first Fourier non-circular gear is: Among them, a ₁ , a ₂ , b ₁ and b ₂ are the parameters of the Fourier function, the value range of a ₁ is 1~6, the value range of a ₂ is 1~3, and the value range of b ₁ is 0~2.3 , b ₂ ranges from 0 to 2.3, n is the order of the first Fourier non-circular gear, and the value is 2; is the rotation angle of the first Fourier non-circular gear, is the corresponding rotation angle of the first Fourier non-circular gear radial direction; According to the principle of non-circular gear meshing, when the first Fourier non-circular gear rotates 360°, the angular displacement of the first conjugate Fourier non-circular gear: Both the first Fourier non-circular gear and the first conjugate Fourier non-circular gear are second-order non-circular gears. Therefore, when the first Fourier non-circular gear rotates 360°, the first conjugate Fourier non-circular gear The circular gear also rotates 360°, and the iterative formula for calculating the center distance a can be obtained: Take the initial value of the center distance a ₀ and use the advance and retreat method to search and calculate the exact value of the center distance a. 2. Four-blade differential pump driven by Fourier non-circular gears according to claim 1, characterized in that: the input shaft and the output shaft are respectively arranged at two ends of the gearbox; one end of the input shaft The head extends out of the drive gearbox and is connected with the motor through a shaft coupling. 3. The four-blade differential pump driven by Fourier non-circular gears according to claim 1, characterized in that: the first liquid discharge port and the second liquid discharge port are arranged symmetrically, and the first liquid suction port and the second liquid discharge port are arranged symmetrically. The second liquid suction port is arranged symmetrically. 4. The four-vane differential pump driven by Fourier non-circular gears according to claim 1, wherein the direction of all the one-way pressure relief valves is consistent with the direction of rotation of the vanes. 5. Four-blade differential pump driven by Fourier non-circular gear according to claim 1, characterized in that: the structure of the first Fourier non-circular gear and the second Fourier non-circular gear is completely Consistent, the structure of the first conjugate Fourier non-circular gear and the second conjugate Fourier non-circular gear are exactly the same, the first Fourier non-circular gear, the second Fourier non-circular gear, the first conjugate Both the Fourier non-circular gear and the second conjugate Fourier non-circular gear are second-order non-circular gears; the initial installation phase difference between the first Fourier non-circular gear and the second Fourier non-circular gear, the first The initial installation phase difference between the conjugate Fourier non-circular gear and the second conjugate Fourier non-circular gear is 90°. 6. The Fourier non-circular gear-driven four-blade differential pump according to claim 1, wherein the transmission ratio of the first Fourier non-circular gear and the first conjugate Fourier non-circular gear is : The transmission ratio between the second Fourier non-circular gear and the second conjugate Fourier non-circular gear is: Among them, θ is the initial installation phase difference between the first Fourier non-circular gear and the second Fourier non-circular gear, and the value is 90°; Make the transmission ratio i ₂₁ of the first Fourier non-circular gear and the first conjugate Fourier non-circular gear equal to the transmission ratio i ₄₃ of the second Fourier non-circular gear and the second conjugate Fourier non-circular gear , four different corners can be obtained corner Take the minimum When , the angular displacement of the first Fourier non-circular gear is The angular displacement of the second Fourier non-circular gear is The rotation angles of the first impeller and the second impeller are respectively: The center position angle of the first discharge port of the pump casing Center position angle of the first liquid suction port The center position angle of the second liquid discharge port ψ _{row 2} = ψ _{row 1} + π, the center position angle of the second liquid suction port ψ _{suction 2} = ψ _{suction 1} + π; the first liquid discharge port, the first liquid suction port, the second liquid suction port The liquid discharge port and the second liquid suction port are equal in size, and are 2 to 5° _smaller than the vane angle θ of the blade; the _values of the vane angle θ of the first impeller and the second impeller are both 40° to 45°; Minimum opening angle of two adjacent blades At this time, the closed cavity has the minimum volume: ${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}$ Among them, R is the radius of the blade, r is the radius of the impeller shaft, and h is the thickness of the blade; Maximum opening angle of two adjacent blades At this time, the closed cavity has the maximum volume: ${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 6</span>}}$ The displacement calculation expression of the four-blade differential pump: Q＝4×(V _max -V _min )＝2(Δψ _max -Δψ _min )(R ² -r ² )×h×10 ^-6 The instantaneous flow calculation expression of the four-blade differential pump: $\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; dV</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h\&omega;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; |</span>$ Among them, V is the volume of the liquid discharge chamber; ω is the angular velocity of the first Fourier non-circular gear and the second Fourier non-circular gear, and its calculation formula is Calculation expressions of the minimum volume and maximum volume trapped liquid pressure changes of the four-blade differential pump: $\frac{{\mathrm{<span\; class="notranslate">\; dp</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h\&omega;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; |</span>$ $\frac{{\mathrm{<span\; class="notranslate">\; dp</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; h\&omega;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}<span\; class="notranslate">\; |</span>$ where K is the elastic modulus of the liquid.