Three-component proportional controller parameter calculation method

Abstract

The invention provides a method for calculating parameters of a three-component proportional controller, which comprises the following steps of: S1, calculating and determining the height of a shell of each set of the proportional controller and the unit displacement of a volume metering component of the proportional controller according to the component proportion and the height of the proportional controller; s2, according to the geometric structure relation and boundary dimension constraint of the volume metering component of the proportional controller, calculating and determining the diameter of a leakage-resistant rotor blade, the diameter of a leakage-resistant rotor transmission shaft, the diameter of a displacement rotor blade and the diameter of a displacement rotor transmission shaft; s3, calculating the internal leakage rate and the proportional error of the volume metering part of the proportional controller, evaluating whether the proportional controller meets the design requirement or not according to the proportional error, and if the design requirement is not met, executing the steps S1 to S2 again; and S4, according to the rotating speed relationship between the displacement rotor and the leakage-proof rotor, calculating and determining the modulus and the tooth number of a linkage gear of the leakage-proof rotor and the displacement rotor. According to the method, designers can be assisted to quickly obtain reasonable key structure parameters of the three-component proportional controller.

Description

Technical Field

[0001] The invention relates to a controller parameter calculation method, in particular to a three-component proportional controller parameter calculation method, and belongs to the technical field of flow measurement and control. Background Art

[0002] The three-component ratio controller is a key component of the underwater thermal power energy supply system. Its ratio and ratio accuracy determine the energy efficiency of the three-component propellant, which in turn affects the efficiency and stability of the thermal power system. Figure 1 As shown, the three-component proportional controller is essentially composed of three sets of volumetric metering components with the same structure and the same rotation speed in parallel. The three components of the propellant enter the flow channel separately as shown in FIG. Figure 2 The three sets of volumetric metering components of the proportional controller shown in the figure then enter the downstream mixer through their respective outflow channels. In theory, the volumetric flow ratio of the three components depends on the size ratio of the three sets of volumetric metering components and is not affected by the external environment. Therefore, compared with the regulating valve proportional controller, the volumetric proportional controller has the advantages of simple structure, no need for complex feedback control, good adaptability to working conditions, etc., and has good engineering application potential in underwater thermal power energy supply systems.

[0003] In actual operation, the volume metering component of the three-component proportional controller must have a matching clearance, which inevitably causes internal leakage, resulting in a decrease in the accuracy of the three-component propellant ratio, thereby affecting the performance of the three-component propellant. The internal leakage of the three-component proportional controller is determined by the structural parameters of the volume metering component, the working pressure difference and the matching clearance. The internal leakage of the volume metering component can be theoretically analyzed to evaluate the ratio error of the proportional controller, providing a reference for the design of the three-component proportional controller.

[0004] The design task of the three-component proportional controller is to calculate the total volume flow rate of the three-component propellant according to the given Q , Proportional controller component ratio A i , Working speed n , Overall dimensions: length, width and height L × W × H Under these conditions, the structural parameters of the three-component proportional controller that meets the requirements of proportion and accuracy are calculated, such as Figure 3 As shown, its structural parameters include the height of each housing of the proportional controller B i , leakage-proof rotor blade diameter D b 、 Diameter of the transmission shaft of the leakage-proof rotor D bh , Displacement rotor blade diameter D p, displacement rotor drive shaft diameter D ph At the same time, its design tasks also include evaluating the internal leakage of each set of volumetric metering components Q Li And the proportional error E i , determine the module of the leakage-blocking rotor and displacement rotor gear m and number of teeth z .

[0005] The structural design of the three-component proportional controller is extremely complex, and its application scenarios are relatively special. At present, the relevant field lacks a systematic and process method for the design and calculation of the structural parameters of the proportional controller, as well as a theoretical calculation model for the internal leakage of the volumetric metering components. This has limited its iterative optimization and engineering application to a certain extent. Summary of the invention

[0006] Based on the above background, the purpose of the present invention is to provide a method for calculating parameters of a three-component proportional controller to solve the problems described in the background technology.

[0007] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions: A method for calculating parameters of a three-component proportional controller, the method comprising the following steps: S1. According to the component ratio and the height of the proportional controller, calculate and determine the height of each housing of the proportional controller and the unit displacement of the volumetric measuring component of the proportional controller; S2. According to the geometric structure relationship and the external dimension constraint of the volume metering component of the proportional controller, the diameter of the leakage-proof rotor blade, the diameter of the leakage-proof rotor drive shaft, the diameter of the displacement rotor blade and the diameter of the displacement rotor drive shaft are calculated and determined, wherein the geometric structure relationship and the external dimension constraint include the following relationship: ; In the formula, D p is the displacement rotor blade diameter, D ph is the displacement rotor drive shaft diameter, D b To prevent leakage, the rotor blade diameter is D bh To prevent leakage, the rotor drive shaft diameter is t To prevent leakage, the thickness of the rotor blade edge is ph is the minimum distance between the displacement rotor blade and the leakage-blocking rotor blade, s For the matching clearance, L is the proportional controller length, kis the shell thickness, W is the proportional controller width, q r The unit displacement of the volumetric measuring component of the proportional controller; S3, calculating the internal leakage of the volumetric measuring component of the proportional controller and the proportional error, and evaluating whether the proportional controller meets the design requirements according to the proportional error. If it does not meet the design requirements, re-execute steps S1 to S2; if it meets the design requirements, continue to execute step S4; S4. According to the rotational speed relationship between the displacement rotor and the leakage-blocking rotor, the module and the number of teeth of the linkage gear between the leakage-blocking rotor and the displacement rotor are calculated and determined.

[0008] Preferably, the step S1 specifically includes the following steps: Component ratio A i , Proportional controller height H And the height of each housing of the proportional controller B i The relationship between them is: ; The sum of the heights of the three shell layers is equal to the height of the proportional controller; Total volume flow Q , component ratio A i 、Height of each shell B i and proportional controller speed n Volumetric metering components with proportional controllers Unit displacement q r The relationship between them is: ; Solve the combined equations to calculate the height of each housing of the proportional controller B i and proportional controllers volumetric metering components unit displacement q r .

[0009] Preferably, the component ratio A i , Proportional controller height H And the height of each housing of the proportional controller B i The specific relationship includes: ; The total volume flow Q , component ratio A i 、Height of each shell B iand proportional controller speed n Volumetric metering components with proportional controllers Unit displacement q r The specific relationship includes: .

[0010] Preferably, in step S2, the relational expression between the geometric structure relation and the external dimension constraint specifically includes: .

[0011] Preferably, in step S2, the minimum distance between the displacement rotor blade and the leakage-blocking rotor blade is ph The value is 1mm, and the clearance s The value is 0.02mm, the shell thickness k The value is 7mm.

[0012] Preferably, in step S3, calculating the internal leakage amount and the proportional error of the volumetric measuring component of the proportional controller specifically comprises the following steps: Internal leakage of volumetric measuring components of proportional controller Q Li , working pressure difference Δ P , fit clearance s , component viscosity μ i The relationship between them is: ; In the formula, is the laminar leakage term, is the orifice flooded outflow leakage term, C l is the laminar outflow coefficient, C v is the orifice outflow coefficient, B i is the characteristic width of the clearance between the displacement rotor and the leakage-blocking rotor, S i is the characteristic length of the clearance between the displacement rotor and the leakage-blocking rotor, P i is the component density Proportional Error E i , total volume flow Q , component ratio A i , Leakage in the volumetric measuring component of the proportional controller Q Li The relationship between them is: .

[0013] Preferably, the proportional error E i , total volume flow Q , component ratio A i , Leakage in the volumetric measuring component of the proportional controller Q Li The specific relationship includes: .

[0014] Preferably, in step S3, evaluating whether the proportional controller meets the design requirements specifically includes the following steps: The absolute value of the proportional error is compared with a preset threshold value. If the absolute value of the proportional error is less than the preset threshold value, the proportional controller meets the design requirements; otherwise, the proportional controller does not meet the design requirements.

[0015] Preferably, the step S4 specifically comprises the following steps: Number of gear teeth z , leakage-proof rotor diameter D b and displacement rotor drive shaft diameter D ph The relationship between them is: .

[0016] In the formula, z 1 To prevent leakage, the number of rotor gear teeth is: z 2 is the number of teeth on the displacement rotor gear, and z 1 and z 2 The relationship between z 1 = z 2 .

[0017] Compared with the prior art, the present invention has the following advantages: A three-component proportional controller parameter calculation method of the present invention provides a systematic and standardized design calculation method for the structural parameters of the three-component proportional controller, which overcomes the shortcomings of traditional design that relies on personal experience, can assist designers to quickly obtain reasonable key structural parameters of the three-component proportional controller, and conveniently and quickly evaluate the proportional error of the designed proportional controller. This method can be combined with a computer for programmed design and optimization, overcoming the problems of traditional manual design that is difficult to optimize and has low design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0019] Figure 1 It is a three-dimensional structural schematic diagram of a three-component proportional controller in the prior art; Figure 2 It is a schematic diagram of the internal structure of the volume metering component of the three-component proportional controller in the prior art; Figure 3 It is a schematic diagram of the structural parameters of a three-component proportional controller in the prior art; Figure 4 It is a flow chart of a method for calculating parameters of a three-component proportional controller according to the present invention; Figure 5 It is a schematic diagram of the internal leakage analysis software of the proportional controller in the present invention; Figure 6 It is a schematic diagram of the gear set structure of the proportional controller in the present invention; Figure 7 This is a physical diagram of a three-component proportional controller designed and processed according to a three-component proportional controller parameter calculation method of the present invention; Figure 8 It is an experimental data diagram of a three-component proportional controller designed and processed according to a three-component proportional controller parameter calculation method of the present invention; In the figure: 1. displacement rotor; 2. displacement rotor drive shaft; 3. leakage-proof rotor; 4. leakage-proof rotor drive shaft; 5. displacement rotor gear; 6. leakage-proof rotor gear. DETAILED DESCRIPTION

[0020] The technical solution of the present invention is further described in detail below through specific embodiments and in conjunction with the accompanying drawings. It should be understood that the implementation of the present invention is not limited to the following embodiments, and any form of modification and / or change made to the present invention will fall within the protection scope of the present invention.

[0021] In the present invention, unless otherwise specified, all parts and percentages are weight units, and the equipment and raw materials used can be purchased from the market or are commonly used in the art. The methods in the following embodiments, unless otherwise specified, are conventional methods in the art. The components or equipment in the following embodiments, unless otherwise specified, are universal standard parts or components known to those skilled in the art, and their structures and principles are known to those skilled in the art through technical manuals or conventional experimental methods.

[0022] An embodiment of the present invention discloses a method for calculating parameters of a three-component proportional controller, the method comprising the following steps: S1. According to the component ratio and the height of the proportional controller, calculate and determine the height of each housing of the proportional controller and the unit displacement of the volumetric measuring component of the proportional controller; S2. According to the geometric structure relationship and the external dimension constraint of the volume metering component of the proportional controller, the diameter of the leakage-proof rotor blade, the diameter of the leakage-proof rotor drive shaft, the diameter of the displacement rotor blade and the diameter of the displacement rotor drive shaft are calculated and determined, wherein the geometric structure relationship and the external dimension constraint include the following relationship: ; In the formula, D p is the displacement rotor blade diameter, D ph is the displacement rotor drive shaft diameter, D b To prevent leakage, the rotor blade diameter is D bh To prevent leakage, the rotor drive shaft diameter is t To prevent leakage, the thickness of the rotor blade edge is ph is the minimum distance between the displacement rotor blade and the leakage-blocking rotor blade, s For the matching clearance, L is the proportional controller length, k is the shell thickness, W is the proportional controller width, q r The unit displacement of the volumetric measuring component of the proportional controller; S3, calculating the internal leakage of the volumetric measuring component of the proportional controller and the proportional error, and evaluating whether the proportional controller meets the design requirements according to the proportional error. If it does not meet the design requirements, re-execute steps S1 to S2; if it meets the design requirements, continue to execute step S4; S4. According to the rotational speed relationship between the displacement rotor and the leakage-blocking rotor, the module and the number of teeth of the linkage gear between the leakage-blocking rotor and the displacement rotor are calculated and determined.

[0023] The embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of the embodiments of the present invention. However, one or more embodiments may also be implemented by those skilled in the art without these specific details.

[0024] 1. Design calculation and evaluation of three-component proportional controller Given conditions Table 1 gives the given conditions and data for calculating the structural parameters of the three-component proportional controller. The working medium is a three-component propellant. The density and viscosity of the three components are P 1 =1000kg / m 3 , P 2 =1200kg / m 3 , P 1 =2040kg / m 3 and 1 =2.4mPa×s, 2 =1.8mPa×s, 3 =1.0mPa×s, total volume flow rate of three-component propellant Q =60L / min, component ratio A 1 =1.0, A 2 =2.0 and A 3 =3.0, proportional controller working speed n =625r / min, the proportional controller dimensions are length × width × height: L =104mm× W =90mm× H =60mm.

[0025] Table 1 Input conditions for the design calculation of the structural parameters of the three-component proportional controller

[0026] 2. Design Calculation Tasks The design calculation task is to obtain the key structural parameters and performance parameters of the three-component proportional controller, including: the height of each housing of the proportional controller B i , leakage-proof rotor blade diameter D b 、 Diameter of transmission shaft of leakage-proof rotor D bh , Displacement rotor blade diameter D p , displacement rotor drive shaft diameter D ph , module of linkage gear m Number of teeth z 、The internal leakage of each set of volume measuring components Q Li , proportional error E i .

[0027] 3. Design Calculation Process like Figure 4 As shown, the design calculation is divided into four steps, namely: 1. Calculate and determine the height of each housing of the proportional controller B i and unit displacement q r ; 2. Calculate and determine the diameter of the leakage-proof rotor blade of the volumetric metering component D b 、 Diameter of the transmission shaft of the leakage-proof rotor D bh , Displacement rotor blade diameter D p , displacement rotor drive shaft diameter D ph ; 3. Calculate the internal leakage of each set of volumetric measuring components Q Li and proportional error E i ; 4. Calculate and determine the module of the linkage gear between the leakage-blocking rotor and the displacement rotor m and number of teeth z .

[0028] Step 1: According to A i / H - B i and A i / Q / B i / nq r Relationship, calculate and determine the height of each housing of the proportional controller B i and unit displacement q r Specific steps: Component ratio A i Theoretically equal to the height of the three-layer shell B i The ratio between the three layers of shell height B i The sum is equal to the total height of the proportional controller H , the functional relationship between the three is ; Solving the equations, we can obtain the heights of the three shell layers: B 1 =10mm, B 2 =20mm and B3 =30mm.

[0029] Total volume flow Q Ratio to components A i Determines the volume flow of each component, and the height of each shell B i and operating speed n Unit displacement with proportional controller q r Negative correlation, there is a functional relationship, that is, ; Solve the equation to get the unit displacement of the volumetric measuring component of the proportional controller q r =1.25mL / r.

[0030] Step 2: Calculate and determine the diameter of the leakage-blocking rotor blades based on the working principle and geometric relationship of the volumetric metering component of the proportional controller D b 、 Diameter of the transmission shaft of the leakage-proof rotor D bh , Displacement rotor blade diameter D p , displacement rotor drive shaft diameter D ph Four key structural parameters. Specific steps: The two displacement rotors and the leakage-blocking rotor work alternately without interfering with each other. The displacement rotor blade diameter D p The diameter of the drive shaft D ph , leakage-proof rotor blade diameter D b The diameter of the drive shaft D bh , and the related gaps have a functional relationship, that is, ; In the formula d t To prevent leakage, the thickness of the rotor blade edge is ph is the minimum distance between the displacement rotor blade and the leakage-blocking rotor blade, s For the matching clearance.

[0031] Two-row rotor blade diameter D p and their center distance largely determine the length of the proportional controller L , taking into account the shell thickness k, there is a geometric function relationship, that is, ; Displacement rotor blade diameter D p The diameter of the drive shaft D ph , leakage-proof rotor blade diameter D b and shell thickness k Determines the proportional controller width W , there is a geometric function relationship, that is, ; According to the working principle of the volumetric measuring component, its displacement q r and D p , D ph There is a functional relationship, namely ; When designing, the fit clearance is generally 0.02mm. d s =0.02mm, the minimum distance between the displacement rotor blade and the leakage-blocking rotor blade is generally 1.0mm. ph =1.0mm, the shell thickness is generally around 7.0 k =7.0mm.

[0032] At this time, the volume measuring component only has D p , D ph , D b and D bh The four key parameters have not yet been determined, so solving the above equations together can give D b =47mm, 、D bh =8mm, D p =41, and D ph =10mm.

[0033] Step 3: Calculate the internal leakage of the volumetric metering component based on the gap leakage theory Q Li and proportional error E i Specific steps: The internal leakage of the proportional controller is divided into laminar flow under the action of pressure difference shear and orifice submerged outflow under the action of pressure difference. The end face clearance and radial clearance leakage between the displacement rotor and the leakage-blocking rotor belong to laminar flow leakage, while the fitting clearance leakage between the leakage-blocking rotor and the displacement rotor belongs to orifice submerged outflow.

[0034] After the key parameters of the volumetric metering component of the proportional controller are determined, its internal leakage Q Li and working pressure difference Δ P , fit clearance s and component viscosity μ i There is a functional relationship, namely ; The first term is laminar leakage, and the second term is orifice submerged leakage. C l is the laminar outflow coefficient, C v is the orifice outflow coefficient, S i is the characteristic length of the clearance between the displacement rotor and the leakage-blocking rotor, from which the internal leakage can be calculated Q Li .

[0035] The theoretical flow rate of each volumetric metering component depends on the total volume flow rate Q and A i , and according to the calculated internal leakage Q Li , the proportional error of each set of volumetric measuring components is calculated by the following function E i ,Right now ; The internal leakage of each volumetric measuring component can be calculated by the above two formulas: Q Li and proportional error E i , evaluate the performance of the designed proportional controller. According to the above formula, the proportional controller internal leakage analysis software was developed, which can easily and quickly obtain the internal leakage of the proportional controller, such as Figure 5 Table 2 shows the internal leakage and proportional error of each set of volumetric measuring components of the proportional controller.

[0036] Table 2 Internal leakage and proportional error at working pressure difference of 0.1 MPa

[0037] Step 4: According to the speed relationship between the displacement rotor and the leakage-blocking rotor, calculate and determine the module of the linkage gear between the leakage-blocking rotor and the displacement rotor. m and number of teeth z Specific steps: The center distance of the gear set is equal to the center distance between the displacement rotor and the leakage-blocking rotor. The number of teeth on the leakage-blocking rotor gear is z 1 and displacement rotor gear teeth z 2 With leakage rotor diameter D b and displacement rotor drive shaft diameter D pb , there is a functional relationship, that is ; When designing, the module and pressure angle of the gear are generally 0.5 and 20°. m =0.5 and α=20°, and the number of teeth of the leakage-proof rotor gear z 1 is the number of teeth on the displacement rotor gear z 2 2 times, from which the number of teeth can be determined z 1 =38 and z 2 =19. The gear set designed is as follows Figure 6 shown.

[0038] So far, the key structural parameters of the three-component proportional controller have been obtained. According to the above ideas and methods, the three-component proportional controller was designed and processed. Figure 7 In addition, the performance of the designed three-component proportional controller is tested experimentally, as shown in Figure 8 As shown in the figure, it can be seen that the component ratio of the three-component proportional controller is relatively stable within the full flow range.

[0039] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core ideas of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating parameters of a three-component proportional controller, characterized in that: The method comprises the following steps: S1. According to the component ratio and the height of the proportional controller, calculate and determine the height of each housing of the proportional controller and the unit displacement of the volumetric measuring component of the proportional controller; S2. According to the geometric structure relationship and the external dimension constraint of the volume metering component of the proportional controller, the diameter of the leakage-proof rotor blade, the diameter of the leakage-proof rotor drive shaft, the diameter of the displacement rotor blade and the diameter of the displacement rotor drive shaft are calculated and determined, wherein the geometric structure relationship and the external dimension constraint include the following relationship: ； In the formula, D p is the displacement rotor blade diameter, D ph is the displacement rotor drive shaft diameter, D b To prevent leakage, the rotor blade diameter is D bh To prevent leakage, the rotor drive shaft diameter is t To prevent leakage, the thickness of the rotor blade edge is ph is the minimum distance between the displacement rotor blade and the leakage-blocking rotor blade, s For the matching clearance, L is the proportional controller length, k is the shell thickness, W is the proportional controller width, q r The unit displacement of the volumetric measuring component of the proportional controller; S3, calculating the internal leakage of the volumetric measuring component of the proportional controller and the proportional error, and evaluating whether the proportional controller meets the design requirements according to the proportional error. If it does not meet the design requirements, re-execute steps S1 to S2; if it meets the design requirements, continue to execute step S4; S4. According to the rotational speed relationship between the displacement rotor and the leakage-blocking rotor, the module and the number of teeth of the linkage gear between the leakage-blocking rotor and the displacement rotor are calculated and determined.

2. A three-component proportional controller parameter calculation method according to claim 1, characterized in that: The step S1 specifically includes the following steps: Component ratio A i , Proportional controller height H And the height of each housing of the proportional controller B i The relationship between them is: ； The sum of the heights of the three shell layers is equal to the height of the proportional controller; Total volume flow Q , component ratio A i 、Height of each shell B i and proportional controller speed n Volumetric metering components with proportional controllers Unit displacement q r The relationship between them is: ； Solve the combined equations to calculate the height of each housing of the proportional controller B i and proportional controllers volumetric metering components unit displacement q r .

3. A three-component proportional controller parameter calculation method according to claim 2, characterized in that: The component ratio A i , Proportional controller height H And the height of each housing of the proportional controller B i The specific relationship includes: ； The total volume flow Q , component ratio A i 、Height of each shell B i and proportional controller speed n Volumetric metering components with proportional controllers Unit displacement q r The specific relationship includes: 。 4. A three-component proportional controller parameter calculation method according to claim 1, characterized in that: In step S2, the relationship between the geometric structure relationship and the external dimension constraint specifically includes: 。 5. A three-component proportional controller parameter calculation method according to claim 1, characterized in that: In step S2, the minimum distance between the displacement rotor blade and the leakage-blocking rotor blade ph The value is 1mm, and the clearance s The value is 0.02mm, the shell thickness k The value is 7mm.

6. A three-component proportional controller parameter calculation method according to claim 1, characterized in that: In step S3, calculating the internal leakage amount and the proportional error of the volumetric measuring component of the proportional controller specifically includes the following steps: Internal leakage of volumetric measuring components of proportional controller Q Li , working pressure difference Δ P , fit clearance s , component viscosity μ i The relationship between them is: ； In the formula, is the laminar leakage term, is the orifice flooded outflow leakage term, C l is the laminar outflow coefficient, C v is the orifice outflow coefficient, B i is the characteristic width of the clearance between the displacement rotor and the leakage-blocking rotor, S i is the characteristic length of the clearance between the displacement rotor and the leakage-blocking rotor, P i is the component density Proportional Error E i , total volume flow Q , component ratio A i , Leakage in the volumetric measuring component of the proportional controller Q Li The relationship between them is: 。 7. A three-component proportional controller parameter calculation method according to claim 6, characterized in that: The proportional error E i , total volume flow Q , component ratio A i , Leakage in the volumetric measuring component of the proportional controller Q Li The specific relationship includes: 。 8. A three-component proportional controller parameter calculation method according to claim 1, characterized in that: In step S3, evaluating whether the proportional controller meets the design requirements specifically includes the following steps: The absolute value of the proportional error is compared with a preset threshold value. If the absolute value of the proportional error is less than the preset threshold value, the proportional controller meets the design requirements; otherwise, the proportional controller does not meet the design requirements.

9. A three-component proportional controller parameter calculation method according to claim 1, characterized in that: The step S4 specifically comprises the following steps: Number of gear teeth z , leakage-proof rotor diameter D b and displacement rotor drive shaft diameter D ph The relationship between them is: ； In the formula, z 1 is the number of teeth on the leakage-proof rotor gear, z 2 is the number of teeth on the displacement rotor gear, and z 1 and z 2 satisfies the relationship z 1= z 2.

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