Quick solution method of trapped oil unloading area of gear pump / motor with different module and same tooth profile

Abstract

The application discloses a quick solution method for trapped oil unloading area of a gear pump / motor under different module numbers of the same tooth profile parameter, and the unloading area Am(x) under the same tooth profile parameter and different module numbers is equal to the unloading area A1(x) under a unit module number multiplied by the square of an actual module number m, namely A m (x)=m 2 A1(x)(2-ε≤x≤1). For the trapped oil phenomenon of the pump / motor, the method better realizes precise evaluation of extreme trapped oil pressure and effective control in product design, and is beneficial to acceptance and application of general engineering technicians.

Description

Technical Field

[0001] This invention relates to the technical field of hydraulic external gear pumps / motors, and specifically to a rapid solution method for the oil trapping and unloading area of ​​gear pumps / motors with the same tooth profile parameters but different modules. Background Technology

[0002] External gear pumps / motors, or simply pumps / motors, are a pair of hydraulic components with opposite principles but essentially the same structure. Their core component, the gear pair, typically consists of two involute gears of the same size. While simple in structure and widely used, they all suffer from oil trapping phenomena, such as hydraulic shock caused by maximum oil trapping pressure due to a contact ratio greater than 1, and cavitation caused by minimum oil trapping pressure. These phenomena significantly affect the service life of the pump / motor and restrict its further development, especially in high-speed applications, where the greater the contact ratio, the more severe the oil trapping phenomenon. The tooth profile shape and size of the gear pair directly determine the oil trapping performance. Just as a circle represents shape and a diameter reflects size, the number of teeth, pressure angle, engagement angle, addendum coefficient, clearance coefficient, displacement coefficient, and even width coefficient only reflect the shape of the gear and are collectively called tooth profile parameters. Only the module truly reflects the size of the gear and is called the size parameter. The tooth profile parameters of pumps / motors are fixed after being designed for specific objectives, such as the lightweight tooth profile parameters of CN109372743B, CN213117359U, and CN111442074A, and the low-pulsation tooth profile parameters of CN111520454B and CN111079269A. Based on these fixed tooth profile parameters, different modules combined with gear width adjustments are typically used to meet the actual operating requirements of the product, such as pump displacement requirements. Currently, using a double unloading groove configuration with the gear pair centerline as the symmetrical line is the most effective measure to alleviate oil trapping, as seen in CN111502986B, CN209164073U, and CN209164074U. The effectiveness of this mitigation depends primarily on the calculation of the trapped oil pressure and its extreme value assessment and control. The accurate calculation of the trapped oil pressure depends entirely on the calculation method and accuracy of the unloading area, as seen in CN114704460A. Although the unloading area can be calculated using the sweeping area method, it involves many factors and a large amount of calculation, especially the calculation error is even greater when the root is cut, which is extremely unfavorable for general engineering technicians to accept and use.

[0003] Currently, most engineering technicians are proficient in using 3D software, and surface measurement based on the 3D features of the unloading area is an efficient and quick method. Even so, measuring the unloading area one by one for different modules with the same tooth profile parameters remains inefficient. Therefore, it is necessary to explore the intrinsic relationship between the unloading area and the module under the same tooth profile parameters. Summary of the Invention

[0004] To address the shortcomings of the prior art, this invention researches and designs a rapid solution for the oil trapping and unloading area of ​​gear pumps / motors with the same tooth profile parameters but different modules: the unloading area Am(x) under the same tooth profile parameters but different modules is equal to the unloading area A1(x) under the unit module multiplied by the square of the actual module m. This method better addresses the oil trapping phenomenon in pumps / motors, enabling more accurate assessment of extreme oil trapping pressure and effective control in product design, and is readily accepted and applied by general engineering technicians.

[0005] The technical solution of this invention is:

[0006] A rapid solution method for determining the oil trapping unloading area of ​​a gear pump / motor with the same tooth profile parameters but different modules, wherein the gear pump / motor includes a gear pair and a symmetrical double rectangular unloading groove, the gear pair and the symmetrical double rectangular unloading groove comprising four parts: a driving involute gear, a driven involute gear, and front and rear floating side plates on both sides of the gear pair. The driving and driven involute gears are identical, and the front and rear floating side plates are identical. Both the front and rear floating side plates have symmetrical double rectangular unloading grooves on their contact surfaces with the gear pair. The rapid solution method comprises the following steps:

[0007] Step 1: Determine the oil trapping zone and its position variables from the gear pair meshing process:

[0008] During the periodic meshing process of a gear pair, due to the transmission requirement that the gear pair overlap ratio ε is greater than 1, there exists an oil trapping chamber and its oil trapping process, enclosed by double-tooth meshing and floating side plates at both ends. Let F be the length of the meshing line from node P to the first meshing point N1 in the double-tooth meshing, and let x = 2F / Pb be a dimensionless positional variable that reflects the oil trapping process, where Pb is the base circle pitch, equal to the length of the meshing line from N1 to the last meshing point N2. Therefore, the compression range of the oil trapping process in the symmetrical double-rectangular unloading groove and large-backlash involute gear pair is...

[0009] 2-ε≤x≤1(1) and the expansion range of the trapped oil process are

[0010] 1≤x≤ε(2)

[0011] Step 2: The steps for creating the unloading area fitting polynomial with the same tooth profile parameters and unit module are as follows:

[0012] Step 1: Draw a 3D model of the gear pair with the same gear parameters and unit module;

[0013] Step 2: Draw the meshing line and the unloading groove opening line, and project the tooth profile curves of the driving involute gear and the driven involute gear that enclose the unloading area.

[0014] Step 3: Extrude the 3D model that encloses the unloading area;

[0015] Step 4: Measure the 9 unloading area values ​​at the 8 equal divisions of the trapped oil compression zone under the unit modulus;

[0016] Step 5: Based on the 9 unloading area values ​​measured in Step 4, derive the fitting polynomial of the unloading area A1(x) in the trapped oil compression range under unit modulus.

[0017] Among them, the unloading area within the oil-trapped expansion range under the same tooth profile parameter unit modulus is obtained by symmetry of A1(x) about x=1.0;

[0018] Step 3: Calculation of unloading area under different modules with the same tooth profile parameters:

[0019] The unloading area Am(x) under the same tooth profile parameters but different modules is equal to the unloading area A1(x) under the unit module multiplied by the square of the actual module m, that is...

[0020] A m (x)=m 2 A1(x)(2-ε≤x≤1)(3)

[0021] Among them, the unloading area in the oil expansion range under different moduli with the same tooth profile parameters is obtained by symmetry of Am(x) about x=1.0.

[0022] Preferably, the drawing software used in step two is UGNX / GC toolbox.

[0023] The beneficial effects of this invention are:

[0024] This invention obtains the unloading area under different modules with the same tooth profile parameters by multiplying the surface measurement value of the three-dimensional feature of the unloading area under unit module by the square of the actual module. The method is efficient and fast, thus providing efficient and reliable unloading area data for the accurate calculation of the subsequent trapped oil pressure of pumps / motors and its extreme value evaluation, as well as for effective control in the design. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the gear pair and floating side plate structure;

[0026] Figure 2 A schematic diagram of the trapped oil compression zone and its positional variables;

[0027] Figure 3 A schematic diagram comparing the measured unloading area values ​​under the same tooth profile parameters and different modules of 1, 1.5, and 2;

[0028] Wherein: 1. Driving involute gear, 2. Driven involute gear, 3. Front floating side plate, 4. Rear floating side plate, 5. Symmetrical double rectangular unloading groove, 6. Large side clearance, 7. Large side clearance oil trapping chamber, 8. Unloading area region, O1. Center of driving involute gear, O2. Center of driven involute gear, N1. First point of engagement in double-tooth meshing, N2. Second point of engagement in double-tooth meshing, P. Node, F is the meshing line length between PN1, x is the dimensionless positional variable during the oil trapping process, A m A. Unloading area under different modules with the same tooth profile parameters; B. Setting dimensions of symmetrical double rectangular unloading grooves; α′. Meshing angle. Detailed Implementation

[0029] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0030] like Figures 1-3 As shown, a rapid solution method for the oil trapping and unloading area of ​​a gear pump / motor with the same tooth profile parameters but different modules is presented. The gear pump / motor includes a gear pair and a symmetrical double rectangular unloading groove. The gear pair and the symmetrical double rectangular unloading groove include four parts: a driving involute gear 1, a driven involute gear 2, and front floating side plates 3 and rear floating side plates 4 on both sides of the gear pair. The driving involute gear 1 and the driven involute gear 2 are identical. The front floating side plate 3 and the rear floating side plate 4 are identical. The front floating side plate and the rear floating side plate 4 are both provided with symmetrical double rectangular unloading grooves 5 on their contact surfaces with the gear pair. The rapid solution method includes the following steps:

[0031] Step 1: Determine the oil trapping zone and its position variables from the gear pair meshing process:

[0032] During the periodic meshing process of a gear pair, due to the transmission requirement that the gear pair overlap ratio ε is greater than 1, there exists an oil trapping cavity and its oil trapping process, which is formed by double-tooth meshing and floating side plates at both ends. Let F be the length of the meshing line from node P to the first meshing point N1 in the double-tooth meshing, and x = 2F / P. b Let P be a dimensionless positional variable that reflects the oil trapping process. b The base circle pitch is equal to the length of the meshing line between N1 and the final engagement point N2. Therefore, the compression range of the involute gear pair during the oil trapping process, characterized by the symmetrical double rectangular unloading groove 5 and the large backlash 6, is...

[0033] 2-ε≤x≤1(1) and the expansion range of the trapped oil process are

[0034] 1≤x≤ε(2)

[0035] Step 2: The steps for creating the unloading area fitting polynomial with the same tooth profile parameters and unit module are as follows:

[0036] Step two can be performed using 3D software such as UGNX / GC toolbox: 1) Draw a 3D model of the gear pair with the same gear parameters and unit module; 2) Draw the meshing line and unloading groove line in the UGNX / Sketch design features, and project the tooth profile curves of the driving and driven involute gears that enclose the unloading area region; 3) Extrude the 3D model that encloses the unloading area region using the UGNX / Extrude design features; 4) Measure the 9 unloading area values ​​at the 8 equal divisions of the oil-trapping compression interval under the unit module using the UGNX / Moving Object design features and the measurement surface analysis function; 5) Obtain the fitting polynomial of the unloading area A1(x) in the oil-trapping compression interval under the unit module using the EXCEL add trend line function from these 9 unloading area values. The unloading area in the oil-trapping expansion interval is obtained by symmetry of A1(x) about x = 1.0.

[0037] Step 3: Calculation of unloading area under different modules with the same tooth profile parameters:

[0038] Unloading area A under different modules with the same tooth profile parameters m (x) is equal to the unloading area A1(x) under unit modulus multiplied by the square of the actual modulus m, that is

[0039] A m (x)=m 2 A1(x)(2-ε≤x≤1)(3) where the unloading area within the trapped oil expansion interval is determined by A m (x) is obtained by symmetry about x = 1.0.

[0040] The theoretical proof of formula (3) states that the size of the unloading area is uniquely determined by the geometric dimensions of the gear pair and the setting dimensions of the symmetrical double unloading grooves. The setting dimension is the distance between the double unloading grooves in the direction perpendicular to the centerline of the gear pair. For gear pairs with the same tooth profile parameters, since the geometric dimensions of the gear pair in both the centerline direction and its perpendicular direction are linearly related to the module, for the double rectangular unloading grooves, the setting dimension B is...

[0041] B = P b cosα'=πmcosαcosα'(4) where α′ is the meshing angle, and B also has a linear relationship with the module. Therefore, it can be deduced that the gear pairs and their unloading grooves corresponding to different modules with the same tooth profile parameters are the same as the gear pairs and their unloading grooves corresponding to the unit module, magnified by the module multiple. Just as the length and width of a rectangle are magnified by the module multiple, the square of the area of ​​the rectangle (length multiplied by width) is magnified by the module multiple. Similarly, the unloading area under different modules with the same tooth profile parameters is the same as the square of the unloading area under the unit module, magnified by the module multiple.

[0042] Example

[0043] The example uses three standard gears with parameters of 14 teeth, pressure angle α = 20°, meshing angle α′ = 20°, and module m = 1, 1.5, and 2. The overlap ratio is calculated to be ε = 1.463.

[0044] A rapid solution method for calculating the unloading area of ​​trapped oil in gear pumps / motors with the same tooth profile parameters but different modules involves four parts: the driving involute gear 1, the driven involute gear 2, and the front floating side plates 3 and rear floating side plates 4 on both sides of the gear pair. The driving involute gear 1 and the driven involute gear 2 are identical, as are the front floating side plates 3 and the rear floating side plates 4. Both the front floating side plates 3 and the rear floating side plates 4 have symmetrical double rectangular unloading grooves 5 on their contact surfaces with the gear pair. Figure 1 As shown.

[0045] A rapid solution method for calculating the unloading area of ​​trapped oil in gear pumps / motors with the same tooth profile parameters but different modules includes the following steps:

[0046] Step 1: Determine the oil trapping zone and its position variables from the gear pair meshing process;

[0047] Step 2: Creating the unloading area fitting polynomial with the same tooth profile parameters and unit module;

[0048] Step 3: Calculation of unloading area under different modules with the same tooth profile parameters.

[0049] In step one, due to the transmission requirement that the gear pair overlap ratio ε is greater than 1 during the periodic meshing process, there exists an oil trapping chamber and its oil trapping process, formed by double-tooth meshing and floating side plates at both ends. Figure 2 As shown. Let F be the length of the meshing line from node P to the first engagement point N1 in the double-tooth meshing, and x = 2F / P. b Let P be a dimensionless positional variable that reflects the oil trapping process. b The base circle pitch is equal to the length of the meshing line between N1 and the final engagement point N2. Therefore, the compression range of the symmetrical double-rectangular unloading groove and the large backlash involute gear pair during the oil trapping process is...

[0050] 2-ε=0.537≤x≤1(1) and the expansion range of the trapped oil process are

[0051] 1≤x≤ε=1.463(2)

[0052] Step two: 1) Use 3D software such as UGNX / GC toolbox to draw a 3D model of the gear pair with the same gear parameters and unit module; 2) In the design features of UGNX / Sketch, draw the meshing line and unloading groove line, and project the tooth profile curves of the driving and driven involute gears that enclose the unloading area region; 3) Use the design features of UGNX / Extrude to extrude the 3D model that encloses the unloading area region; 4) Use the design features of UGNX / Moving Object and the analysis function of the measurement surface to measure the unloading area A1(x) corresponding to different oil trapping positions x in the oil trapping compression interval with unit module. The measured values ​​of the unloading area for three standard gears with module m = 1, 1.5, and 2, and the oil trapping compression interval divided into 8 equal parts, are shown below. Figure 3 As shown.

[0053] Step two can be performed using 3D software such as UGNX / GC toolbox: 1) Draw a 3D model of the gear pair with the same gear parameters and unit module; 2) Draw the meshing line and unloading groove opening line in the UGNX / Sketch design features, and project the tooth profile curves of the driving and driven involute gears that enclose the unloading area region; 3) Extrude the 3D model that encloses the unloading area region using the UGNX / Extrude design features; 4) Measure the 9 unloading area values ​​at the 8 equal divisions of the oil-trapping compression interval under the unit module; 5) Obtain the fitting polynomial of the unloading area A1(x) in the oil-trapping compression interval under the unit module from these 9 unloading area values. The unloading area in the oil-trapping expansion interval is obtained by symmetry of A1(x) about x = 1.0.

[0054] Step three is a summary of the nine unloading area measurements taken from the three standard gears with modules m=1, 1.5, and 2 in step two, and the eight equal divisions of the oil-trapped compression range, to obtain the unloading area A under different modules with the same tooth profile parameters. m (x) is equal to the unloading area A1(x) under unit modulus multiplied by the square of the actual modulus m, that is

[0055] A m (x)=m 2 A1(x)(2-ε≤x≤1)(3) where the unloading area within the trapped oil expansion interval is determined by A m (x) is obtained by symmetry about x = 1.0.

[0056] The theoretical proof of formula (3) states that the size of the unloading area is uniquely determined by the geometric dimensions of the gear pair and the setting dimensions of the symmetrical double unloading grooves. The setting dimension is the distance between the double unloading grooves in the direction perpendicular to the centerline of the gear pair. For gear pairs with the same tooth profile parameters, since the geometric dimensions of the gear pair in both the centerline direction and its perpendicular direction are linearly related to the module, for the double rectangular unloading grooves, the setting dimension B is...

[0057] B(m)=P b cosα'=πmcosαcosα'(4) where α′ is the meshing angle, and B also has a linear relationship with the module. It can be inferred that the gear pairs and unloading grooves corresponding to different modules with the same tooth profile parameters are the same as the gear pairs and unloading grooves corresponding to the unit module. Just like the length and width of a rectangle are both magnified by the module, and the area of ​​the rectangle with the length multiplied by the width is magnified by the square module, the unloading area under different modules with the same tooth profile parameters is the same as the unloading area under the unit module is magnified by the square module.

Claims

1. A rapid solution method for the unloading area of ​​trapped oil in a gear pump / motor under different modules with the same tooth profile parameters, wherein the gear pump / motor includes a gear pair and a symmetrical double rectangular unloading groove, the gear pair and the symmetrical double rectangular unloading groove comprising four parts: a driving involute gear, a driven involute gear, and front and rear floating side plates on both sides of the gear pair, wherein the driving and driven involute gears are identical, the front and rear floating side plates are identical, and both the front and rear floating side plates are provided with symmetrical double rectangular unloading grooves on their contact surfaces with the gear pair, characterized in that: The fast solution method includes the following steps: Step 1: Determine the oil trapping zone and its position variables from the gear pair meshing process: During the periodic meshing process of the gear pair, due to the transmission requirement that the gear pair overlap ratio ε is greater than 1, there exists an oil trapping cavity and its oil trapping process, which is formed by double tooth meshing and floating side plates at both ends. Let F be the length of the meshing line from node P to the first meshing point N1 in the double tooth meshing, and let x = 2F / Pb be a dimensionless position variable that can reflect the oil trapping process, where Pb is the base circle pitch, which is equal to the length of the meshing line from N1 to the last meshing point N2. Thus, the compression range of the oil trapping process of the symmetrical double rectangular unloading groove and the large backlash involute gear pair is 2-ε≤x≤1(1) and the expansion range of the oil trapping process is 1≤x≤ε(2). Step 2: The steps for creating the unloading area fitting polynomial with the same tooth profile parameters and unit module are as follows: Step 1: Draw a 3D model of the gear pair with the same gear parameters and unit module; Step 2: Draw the meshing line and the unloading groove opening line, and project the tooth profile curves of the driving involute gear and the driven involute gear that enclose the unloading area. Step 3: Extrude the 3D model that encloses the unloading area; Step 4: Measure the 9 unloading area values ​​at the 8 equal divisions of the trapped oil compression zone under the unit modulus; Step 5: Based on the 9 unloading area values ​​measured in Step 4, derive the fitting polynomial of the unloading area A1(x) in the trapped oil compression range under unit modulus. Among them, the unloading area within the oil-trapped expansion range under the same tooth profile parameter unit modulus is obtained by symmetry of A1(x) about x=1.0; Step 3: Calculation of unloading area under different modules with the same tooth profile parameters: The unloading area Am(x) under the same tooth profile parameters but different modules is equal to the unloading area A1(x) under the unit module multiplied by the square of the actual module m, that is... A m (x)=m 2 A1(x)(2-ε≤x≤1)(3) where the unloading area in the oil expansion range under different moduli with the same tooth profile parameters is obtained by Am(x) being symmetrical about x=1.

0.

2. The method for rapidly calculating the oil trapping unloading area of ​​a gear pump / motor with the same tooth profile parameters but different modules, as described in claim 1, is characterized in that: The drawing software used in step two is UGNX / GC Toolbox.

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