Analytical Methods for Trapped Oil Pressure and its Extreme Values ​​in Gear Pumps / Motors

Abstract

An analytical method for determining the trapped oil pressure and its extreme values ​​in gear pumps / motors includes the following steps: Step 1, determining the trapped oil region and its positional variables based on the gear pair meshing process; Step 2, an analytical solution method for the trapped oil pressure; Step 3, a fitting formula method for obtaining the unloading area; Step 4, an analytical solution method for determining the extreme trapped oil pressure and its occurrence location. This invention offers a simpler method, more reliable results, and more accurate extreme values ​​and their occurrence locations; it significantly simplifies existing numerical methods for determining trapped oil pressure; it clarifies that the extreme value of the trapped oil pressure occurs at the point where the unloading groove is about to close, rather than at the actual closure point, and the specific extreme value location depends on the size of the unloading area in the area where the unloading groove is about to close; the method, obtained from 3D feature measurement of the unloading area and an Excel trend line, is highly efficient, fast, and accurate, providing a reliable basis for the accurate evaluation of the extreme trapped oil pressure in external gear pumps / motors and effective control in product design.

Description

Technical Field

[0001] This invention relates to the technical field of hydraulic gear pumps / motors, and specifically to an analytical method for the trapped oil pressure and its extreme values ​​in gear pumps / motors. Background Technology

[0002] External gear pumps (referred to as gear pumps) and external gear motors (referred to as gear motors) are two types of positive displacement hydraulic components with completely opposite working principles but basically identical structures. The core component of a gear pump / motor is a large-backlash involute gear pair composed of two gears of the same size (referred to as a gear pair). Compared to other types of hydraulic pumps and motors, it has the simplest structure and the widest application. However, the need for gear pair transmission with a contact ratio greater than 1 also causes inherent oil trapping defects in both types of pumps / motors. The hydraulic shock caused by the maximum oil trapping pressure and the cavitation phenomenon caused by the minimum oil trapping pressure are harmful, greatly affecting and restricting the service life and further development of the product, especially in the pursuit of high-speed development. Among these, the extreme value assessment and effective control of the maximum and minimum oil trapping pressures are important aspects of gear pump / motor design. In recent decades, scholars both domestically and internationally have conducted extensive research on oil trapping pressure through numerical simulation, prototype testing, and control measures. However, prototype testing is only applicable to low-speed conditions, and numerical simulation places high demands on fundamental theoretical knowledge and programming skills. Currently, although the industry has provided estimation formulas for extreme trapped oil pressure, they are all based on the assumption that the unloading flow rate of trapped oil through the unloading groove opening is equal to zero. The reliability of the results and the quality of the extreme trapped oil pressure assessment are questionable and need further improvement. Summary of the Invention

[0003] This invention addresses the shortcomings of the prior art. Taking a gear pump / motor with, but not limited to, symmetrical double rectangular unloading grooves and a large backlash gear pair as an example, it provides an analytical method for determining the trapped oil pressure with respect to the trapped oil position variable. This method is based on the instantaneous balance relationship between the trapped oil flow rate, leakage flow rate, and unloading flow rate within the trapped oil chamber, without neglecting the unloading flow rate of trapped oil through the unloading groove opening. Through further theoretical derivation, an analytical method for determining the trapped oil pressure with respect to the trapped oil position variable is proposed. Furthermore, by ensuring that the first derivative of the obtained analytical expression for the trapped oil pressure with respect to the trapped oil position variable is zero, the extreme values ​​of the trapped oil pressure and their locations can be quickly obtained. The purpose of this invention is to better achieve accurate assessment of extreme trapped oil pressure and effective control in product design for the trapped oil phenomenon in external gear pumps / motors.

[0004] The analytical method for the trapped oil pressure and its extreme values ​​in a gear pump / motor involves a gear pair and symmetrical double rectangular unloading grooves, comprising four parts: the driving involute gear-shaft, the driven involute gear-shaft, and the front and rear floating side plates on both sides of the gear pair. The driving and driven involute gears are identical, as are the front and rear floating side plates. Both the front and rear floating side plates have symmetrical double rectangular unloading grooves on their contact surfaces with the gear pair.

[0005] A method for analyzing the trapped oil pressure and its extreme values ​​in a gear pump / motor, the method comprising the following steps:

[0006] Step 1: Determine the oil trapping zone and its position variables from the gear pair meshing process;

[0007] Step 2: Analytical solution method for trapped oil pressure;

[0008] Step 3: Method for obtaining the fitting formula of the unloading area;

[0009] Step 4: Analytical solution method for extreme oil trapping pressure and its location. In Step 1, during the periodic meshing process of the gear pair, due to the gear pair overlap... ε The transmission requirement is greater than 1, so there is a double-tooth meshing oil trapping process. Let... f For nodes p In double-tooth meshing, the first point of engagement is reached. m The length of the meshing line between nodes is a positional variable that reflects the oil trapping process. p After entering the meshing point in double-tooth engagement. n The length of the meshing line between them is p b -f The base circle pitch is p b Therefore, a periodic oil trapping zone under the symmetrical double rectangular unloading groove and the large backlash gear pair is obtained as follows: ,

[0010] Among them, the compression sub-interval of the trapped oil interval is ,

[0011] The expansion sub-interval of the trapped oil interval is .

[0012] In step two, the flow exchange between the trapped oil medium within the trapping chamber and the input and output media outside the chamber mainly involves the volume change rate of the trapped oil medium itself caused by the trapping chamber. Q T (Referred to as trapped oil flow rate), unloading area through rectangular unloading slot. R unloading flow rate Q R and leakage flow through the axial gaps at both ends of the gear pair Q Z The three parts, including the compression of trapped oil. Q T When the oil flows out of the trapped oil cavity, it is negative. Q R 、Q ZThe result is positive; ignoring the flow rate change caused by the compression of the trapped oil itself, the instantaneous balance of the flow rates within the trapped oil chamber yields... ,

[0013] in ,

[0014] In the formula, b The width of the gear pair. p To trap oil pressure, ω For rotational speed, h z This is the total tooth height of the gear. c z This is the axial gap value. μ For the viscosity of the medium, α′ The engagement angle, p i To import pressure, p o Due to export pressure, p io This represents the average value of import and export pressure. Z It is a constant. C For flow coefficient, generally C =0.62, ρ For the density of the medium, C The number 2 at the beginning indicates that there are unloading grooves at both ends of the gear pair;

[0015] From equation (4), we get ,

[0016] Right now ,

[0017] In the formula, p>p o When "±" and "∓" are in the upper "+" and "-", they are in the lower "-" and "+" respectively.

[0018] make ,

[0019] Substituting equation (8) into equation (7), then from ,

[0020] have to ,

[0021] Without considering the effect of cavitation pressure on the trapped oil pressure in the expansion sub-section, the trapped oil pressure in the compression sub-section and the trapped oil pressure in the expansion sub-section are relative to the average values ​​of the inlet and outlet pressures. p io Symmetry allows for the calculation of the trapped oil pressure within the expansion sub-interval. p(f) The fitting method for obtaining the unloading area in step three: for the trapped oil pressure in equation (10) p(f)The exact solution depends entirely on the unloading area. R(f) With the further development of 3D software such as UGNX, the 3D feature measurement technology based on the unloading area and the 6th-order polynomial fitting technology of the trend line in the Excel table are efficient and fast methods for obtaining the calculation method and its accuracy. The 3D feature measurement steps of the unloading area are as follows: 1) Create a 3D model of the gear pair using the UGNX / GC toolbox; 2) Divide the oil trapping compression sub-section into several oil trapping positions; 3) In the design features of UGNX / Sketch, 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; 4) Using the design features of UGNX / Extrude, extrude the 3D model of the unloading surface by selecting the boundary curve of the area enclosed by the unloading groove opening line, the meshing line and the tooth profile curve; 5) Using the design features of UGNX / Move Object, rotate the 3D model of the gear pair to these several equally divided oil trapping positions, and calculate the equally divided rotation angle. θ The 3D model of the unloading surface will also change synchronously; 6) After the 3D model of the gear pair rotates to each oil trapping position, the unloading area under that oil trapping position is measured in time using the analysis function of UGNX / measurement surface. To ensure the high accuracy of the subsequent 6th order polynomial fitting, the number of decimal places in the measurement data is 8, thus obtaining several high-precision unloading area data under the equal division of the oil trapping compression sub-interval. The main steps of the 6th order polynomial fitting are: 1) Import the obtained position variable values ​​with 8 decimal places and the corresponding unloading area data in the oil trapping compression sub-interval into an Excel table in two rows. The first row is several position variable values, and the second row is several corresponding unloading area data; 2) Subtract a value x from each of these position variable values ​​so that the position variable values ​​in the first column become 1; 3) To ensure the high accuracy of the unloading area, especially at the unloading closed position of 0.5 p b To achieve high-precision fitting in the vicinity, these corresponding unloading area data values ​​are all magnified by a factor greater than 100. M 4) In the XY (scatter plot) of the above two rows of data, add a trend line for a 6th-order polynomial, and display the number of decimal places as 8 and the coefficients as follows: a 0、 a 1. a 2. a 3. a 4. a 5. a 6. Fitting multiple formulas; 5) The high-precision fitting polynomial for the unloading area obtained from this is: .

[0022] The analytical solution method for the extreme trapped oil pressure and its location in step four is derived from the first derivative of equation (10). dp / dfEqual to 0, that is, by

[0023] or ,

[0024] Determine the maximum trapped oil pressure and its location.

[0025] in ,

[0026] Without considering the effect of cavitation pressure on the trapped oil pressure within the expansion sub-section, the average value of the inlet and outlet pressures is obtained by using the minimum trapped oil pressure within the expansion sub-section and the maximum trapped oil pressure within the compression sub-section. p io Symmetry allows for the calculation of the minimum trapped oil pressure within the expansion sub-interval. The beneficial effects of this invention are: The proposed analytical formula for the trapped oil pressure and its extreme values ​​in gear pumps / motors is simpler, more reliable, and provides more accurate extreme values ​​and their locations; it not only improves existing analytical methods for finding the extreme trapped oil pressure when the unloading flow rate is zero, but also greatly simplifies existing numerical methods for solving the trapped oil pressure; it clarifies that the extreme value of the trapped oil pressure occurs at the point where the unloading groove is about to close, rather than at the actual closure point, and the specific extreme value location depends on the size of the unloading area in the area where the unloading groove is about to close, thus providing direction for the effective control of the extreme trapped oil pressure; the 6th-order fitting polynomial obtained from the 3D feature measurement of the unloading area and the Excel trend line is efficient, fast, and has high fitting accuracy, thus providing an effective and reliable basis for the accurate evaluation of the extreme trapped oil pressure of external gear pumps / motors and effective control in product design. Attached Figure Description

[0027] Figure 1 Schematic diagram of gear pair - shaft and floating side plate structure;

[0028] Figure 2 A schematic diagram of the trapped oil zone and its location variables;

[0029] Figure 3 A schematic diagram comparing the measured and fitted values ​​of the unloading area;

[0030] Figure 4 A schematic diagram of trapped oil pressure in a case where cavitation pressure is not considered.

[0031] The components include: 1. Driving involute gear-shaft; 2. Driven involute gear-shaft; 3. Front floating side plate; 4. Rear floating side plate; 5. Symmetrical double rectangular unloading grooves; 6. Large backlash; o1. Center of the driving involute gear. o 2. The center of the driven involute gear, m In double-tooth meshing, the first tooth to enter the engagement point... n After the two teeth mesh, they enter the engagement point. c, are the side gap points, p ,node, f For nodes p To the engagement point m The length of the meshing line between them, R Unloading area ω Rotation speed p i Import pressure p o Export pressure p Oil pressure, p io ① Average inlet and outlet pressures; ② Meshing line; ③ Unloading groove opening line; ④ Tooth profile curves of the driving and driven involute gears that enclose the unloading area. Detailed Implementation

[0032] The present invention will be further described below with reference to specific embodiments.

[0033] Example

[0034] The example uses a standard gear with 14 teeth, a module of 6, a contact ratio of 1.463, and a tooth width of [missing information]. b =30 mm; gear pump speed 2500 RPM ω =261.8 rad / s, viscosity of medium μ =0.09 pa.s, axial gap value c z =0.15 mm, flow coefficient C =0.62, medium density ρ =870 Kg / m 3 Inlet pressure of gear pump p i =0.1 Pa, outlet pressure p o =5 MPa, inlet pressure of gear motor p i =5 MPa, outlet pressure p o =0.1 MPa, magnification factor M =100. Therefore, the trapped oil compression sub-range can be calculated to be 4.75824954 mm ≤ f The trapped oil expansion sub-interval is ≤8.85639430 mm. f ≤12.95453906 mm, x =3.75824954 mm, p io = 2.55 MPa. For example... Figures 1 to 4 As shown, the analytical method for the trapped oil pressure and its extreme values ​​in a gear pump / motor involves a gear pair and symmetrical double rectangular unloading grooves, comprising four parts: the driving involute gear-shaft 1, the driven involute gear-shaft 2, and the front floating side plates 3 and rear floating side plates 4 on both sides of the gear pair. The driving and driven involute gears are identical, as are the front and rear floating side plates 3 and 4. Both the front and rear floating side plates 3 and 4 have symmetrical double rectangular unloading grooves 5 on their contact surfaces with the gear pair. The analytical method for the trapped oil pressure and its extreme values ​​in a gear pump / motor includes the following steps:

[0035] Step 1: Determine the oil trapping zone and its position variables from the gear pair meshing process;

[0036] Step 2: Analytical solution method for trapped oil pressure;

[0037] Step 3: Method for obtaining the fitting formula of the unloading area;

[0038] Step 4: Analytical solution method for extreme trapped oil pressure and its location.

[0039] In step one, during the periodic meshing process of the gear pair, due to the overlap of the gear pair... ε The transmission requirement is greater than 1, so there is a double-tooth meshing oil trapping process. Let... f For nodes p In double-tooth meshing, the first point of engagement is reached. m The length of the meshing line between nodes is a positional variable that reflects the oil trapping process. p After entering the meshing point in double-tooth engagement. n The length of the meshing line between them is p b -f The base circle pitch is p b Therefore, a periodic oil trapping zone under the symmetrical double rectangular unloading groove and the large backlash gear pair is obtained as follows: ,

[0040] Among them, the compression sub-interval of the trapped oil interval is ,

[0041] The expansion sub-interval of the trapped oil interval is .

[0042] In step two, the flow exchange between the trapped oil medium within the trapping chamber and the input and output media outside the chamber mainly involves the volume change rate of the trapped oil medium itself caused by the trapping chamber. Q T (Referred to as trapped oil flow rate), unloading area through rectangular unloading slot. R unloading flow rate QR and leakage flow through the axial gaps at both ends of the gear pair Q Z The three parts, including the compression of trapped oil. Q T When the oil flows out of the trapped oil cavity, it is negative. Q R 、Q Z The result is positive; ignoring the flow rate change caused by the compression of the trapped oil itself, the instantaneous balance of the flow rates within the trapped oil chamber yields... ,

[0043] in ,

[0044] In the formula, b The width of the gear pair. p To trap oil pressure, ω For rotational speed, h z This is the total tooth height of the gear. c z This is the axial gap value. μ For the viscosity of the medium, α′ The engagement angle, p i To import pressure, p o Due to export pressure, p io This represents the average value of import and export pressure. Z It is a constant. C For flow coefficient, generally C =0.62, ρ For the density of the medium, C The number 2 in front indicates that both ends of the gear pair have unloading grooves; from equation (4), we get ,

[0045] Right now ,

[0046] In the formula, p>p o When "±" and "∓" are in the upper "+" and "-", they are in the lower "-" and "+" respectively.

[0047] make ,

[0048] Substituting equation (8) into equation (7), then from ,

[0049] have to .

[0050] The fitting formula for obtaining the unloading area in step three is as follows: for the trapped oil pressure in formula (10) p(f) The exact solution depends entirely on the unloading area. R(f) With the further development of 3D software such as UGNX, the 3D feature measurement technology based on the unloading area and the 6th-order polynomial fitting technology of the trend line in the Excel table are efficient and fast methods for obtaining the calculation method and its accuracy. Among them, the 3D feature measurement steps of the unloading area are mainly as follows: 1) Create a 3D model of the gear pair using the UGNX / GC toolbox; 2) Divide the oil trapping compression sub-interval 8 into 9 oil trapping positions; 3) In the design features of UGNX / Sketch, draw the meshing line ① and the unloading groove opening line ②, and project the tooth profile curves ③ of the driving involute gear and the driven involute gear that enclose the unloading area; 4) Using the design features of UGNX / Extrude, extrude the 3D model of the unloading surface by selecting the boundary curve of the area enclosed by the meshing line ①, the unloading groove opening line ② and the tooth profile curve ③; 5) Using the design features of UGNX / Move Object, rotate the 3D model of the gear pair to these 9 oil trapping positions, with the rotation angles equally divided. θ =0.74367783°, the 3D model of the unloading surface will also change synchronously; 6) After the 3D model of the gear pair is rotated to each oil trapping position, the unloading area under the oil trapping position is measured in time using the analysis function of UGNX / measurement surface. In order to ensure the high accuracy of the fitting of the subsequent 6th order polynomial, the number of decimal places of the measurement data is 8, thus obtaining 9 high-precision unloading area data under the equal division of the oil trapping compression sub-interval.

[0051] The main steps of fitting the trend line using a 6th-order polynomial in the Excel spreadsheet are: 1) Import the nine positional variable values ​​(each with eight decimal places) and their corresponding unloading area data within the obtained oil compression sub-interval into the Excel spreadsheet in two rows. The first row contains the nine positional variable values, and the second row contains the nine corresponding unloading area data. 2) Subtract the decimal places from each of these nine positional variable values. x =3.75824954 mm, making the position variable value of the first column 4.75824954 mm become 1; 3) To ensure the unloading area, especially the unloading groove closed position 0.5 p b = The fitting accuracy is high around 8.85639430 mm, and the unloading area data values ​​at all 9 locations are enlarged. M =Multiples of 100; 4) Add a trend line for a 6th-order polynomial to the XY (scatter plot) of the above two rows of data, thereby showing that the coefficients are respectively a 0 = 1490.97983061 a 1 = -419.09651704 a 2 = -113.93957736 a 3 = 92.60310644a 4 = -30.27733395 a 5 = 5.21819192 a 6 = -0.35205648 is the fitting formula; 5) The high-precision fitting polynomial for the unloading area obtained from this is ,Depend on R ( f The fitted value of (11) is completely consistent with the measured value, indicating that the fitting polynomial shown in equation (11) has very high accuracy.

[0052] Neglecting the effect of cavitation on the trapped oil pressure within the expansion sub-section, the trapped oil pressure within the expansion sub-section is determined by the trapped oil pressure within the compression sub-section with respect to point (0.5). p b , p io That is, (8.89 mm, 2.55 mm). The result is obtained symmetrically from MPa). The analytical result obtained from equation (10) is completely consistent with the numerical result obtained by combining equations (4) and (5). For example, f=p b - 0.5 εp b The 8.32 MPa at 4.76 mm demonstrates the correctness of the derivation process of equation (10).

[0053] The analytical solution method for the extreme trapped oil pressure and its location in step four is derived from the first derivative of equation (10). dp / df Equal to 0,

[0054] That is, by or ,

[0055] Determine the maximum trapped oil pressure and its location.

[0056] in ,

[0057] The maximum trapped oil pressure of the gear pump / motor is 26.27 / 24.09 MPa, and the location of occurrence is [missing information]. f =7.93 mm; the minimum trapped oil pressure is -21.17 / -18.99 MPa, and the location of occurrence is... f =9.78 mm, where the minimum trapped oil pressure is determined by the maximum trapped oil pressure with respect to point (0.5). p b , p io That is, (8.89 mm, 2.55 mm). (MPa) is obtained symmetrically. Due to f= At position 7.93 mmR <0.6 mm 2 This corroborates that the extreme value of the trapped oil pressure occurred at the point where the unloading trough was about to close. f= The non-true closure point is 8.86 mm; the specific extreme location depends on the area near where the unloading channel is about to close. R Size, R The larger the value, the closer the extreme value is to the location. f= The unloading groove is closed at an angle of 8.86 mm. R The smaller the value, the further away the extreme value is from the location. f= The 8.86 mm unloading groove closing position points to the direction for innovation in unloading grooves that increase the unloading area in the vicinity.

Claims

1. An analytical method for the trapped oil pressure and its extreme values ​​in gear pumps / motors, characterized in that: The parsing method includes the following steps: Step 1: Determine the oil trapping zone and its position variables from the gear pair meshing process; Step 2: Analytical solution method for trapped oil pressure; Step 3: Method for obtaining the fitting formula of the unloading area; Step 4: Analytical solution method for extreme trapped oil pressure and its location; In step one, during the periodic meshing process of the gear pair, due to the overlap of the gear pair... ε The transmission requirement is greater than 1, so there is a double-tooth meshing oil trapping process. Let... f For nodes p In double-tooth meshing, the first point of engagement is reached. m The length of the meshing line between nodes is determined to reflect the positional variables during the oil trapping process. p After entering the meshing point in double-tooth engagement. n The length of the meshing line between them is p b -f The base circle pitch is p b Therefore, a periodic oil trapping zone under the symmetrical double rectangular unloading groove and the large backlash gear pair is obtained as follows: , Among them, the compression sub-interval of the trapped oil interval is , The expansion sub-interval of the trapped oil interval is ; In step two, the flow exchange between the trapped oil medium within the trapping chamber and the input and output media outside the chamber involves the volume change rate of the trapped oil medium itself caused by the trapping chamber. Q T Unloading area through rectangular unloading slot R unloading flow rate Q R and leakage flow through the axial gaps at both ends of the gear pair Q Z The three parts, including the compression of trapped oil. Q T When the oil flows out of the trapped oil cavity, it is negative. Q R 、Q Z The result is positive; ignoring the flow rate change caused by the compression of the trapped oil itself, the instantaneous balance of the flow rates within the trapped oil chamber yields... , in , In the formula, b The width of the gear pair. p To trap oil pressure, ω For rotational speed, h z This is the total tooth height of the gear. c z This is the axial gap value. μ For the viscosity of the medium, α′ The engagement angle, p i To import pressure, p o Due to export pressure, p io This represents the average value of import and export pressure. Z It is a constant. C For flow coefficient, C =0.62, ρ For the density of the medium, C The number 2 at the beginning indicates that there are unloading grooves at both ends of the gear pair; From equation (4), we get , Right now , In the formula, p>p o When "±" and "∓" are in the upper right corner, take the "+" and "-" signs respectively; otherwise, take the "-" and "+" signs respectively. make , Substituting equation (8) into equation (7), then from , have to , Without considering the effect of cavitation pressure on the trapped oil pressure in the expansion sub-section, the trapped oil pressure in the compression sub-section and the trapped oil pressure in the expansion sub-section are relative to the average values ​​of the inlet and outlet pressures. p io Symmetry allows for the calculation of the trapped oil pressure within the expansion sub-interval. p(f) ; The high-precision fitting polynomial for the unloading area is: , a i M is a coefficient, where M is a multiple greater than 100; The analytical solution method for the extreme trapped oil pressure and its location in step four is derived from the first derivative of equation (10). dp / df Equal to 0, that is, by , or , Find the maximum trapped oil pressure and its location, where .

2. The analytical method for the trapped oil pressure and its extreme values ​​in a gear pump / motor as described in claim 1, characterized in that: The gear pair and symmetrical double rectangular unloading groove involved in the analytical method include four parts: the active involute gear-shaft, the driven involute gear-shaft, and the front floating side plate and the rear floating side plate on both sides of the gear pair. The active involute gear and the driven involute gear are completely identical, and the front floating side plate and the rear floating side plate are completely identical. The front floating side plate and the rear floating side plate are provided with symmetrical double rectangular unloading grooves on the contact surface with the gear pair.

3. The analytical method for the trapped oil pressure and its extreme values ​​in a gear pump / motor as described in claim 1, characterized in that: The fitting method for obtaining the unloading area in step three includes a 3D feature measurement step for the unloading area: 1) Create a 3D model of the gear pair using the UGNX / GC toolbox; 2) Divide the oil-trapping compression sub-section into several oil-trapping positions; 3) In the UGNX / Sketch design features, 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 region; 4) Using the UGNX / Extrude design features, extrude the 3D model of the unloading surface by selecting the boundary curve of the region enclosed by the unloading groove opening line, the meshing line, and the tooth profile curve; 5) Using the UGNX / Move Object design features, rotate the 3D model of the gear pair to each of these several equally divided oil-trapping positions, and calculate the equally divided rotation angles. θ The 3D model of the unloading surface will also change synchronously; 6) After the 3D model of the gear pair is rotated to each oil trapping position, the unloading area under the oil trapping position is measured in time using the analysis function of UGNX / measurement surface. In order to ensure the high accuracy of the subsequent 6th order polynomial fitting, the number of decimal places of the measurement data is 8, thus obtaining several high-precision unloading area data under the equal division of the oil trapping compression sub-interval.

4. The analytical method for the trapped oil pressure and its extreme values ​​in a gear pump / motor as described in claim 3, characterized in that: The steps of the 6th-order polynomial fitting are as follows: 1) Import the obtained position variable values ​​(8 decimal places) and corresponding unloading area data within the trapped oil compression sub-interval into an Excel spreadsheet in two rows. The first row contains the position variable values, and the second row contains the corresponding unloading area data; 2) Subtract a value x from each of these position variable values ​​so that the position variable values ​​in the first column become 1; 3) To ensure the unloading is closed at position 0.5... p b To achieve high-precision fitting in the vicinity, these corresponding unloading area data values ​​are all magnified by a factor greater than 100. M 4) Add a trend line for a 6th-order polynomial to the XY scatter plot of the above two rows of data, and display the number of decimal places as 8 and the coefficients as follows: a 0、 a 1. a 2. a 3. a 4. a 5. a The fitting formula for 6.

Images