Determination method, device and equipment for meshing rigidity of shifted herringbone gear and storage medium

Abstract

The invention relates to the technical field of gear mechanical calculation, in particular to a method, a device and equipment for determining meshing rigidity of a shifted herringbone gear and a storage medium, and the method comprises the following steps: discretizing a herringbone gear pair to obtain slice information, and determining initial load distribution information according to herringbone gear design parameters, working condition parameters and the slice information; determining meshing point coordinate information of each slice gear by utilizing slice information, and further determining a load angle; confirming the tooth body meshing rigidity based on the initial load distribution information, and calculating the deformation rigidity of a base body, so as to obtain the meshing rigidity of a gear pair; judging whether the meshing rigidity of the gear pair meets an iteration stop condition, and if not, calculating corrected load distribution information; returning to execute the confirmation of the tooth body meshing stiffness based on the initial load distribution information; according to the method disclosed by the invention, the nonlinear load transfer characteristic of the herringbone gear pair is considered, the influence of the displacement coefficient on the tooth surface contact characteristic is analyzed, and the prediction precision of the time-varying meshing stiffness model of the herringbone gear pair is improved.

Description

Technical Field

[0001] The present invention relates to the field of gear mechanics calculation technology, and in particular to a method, device, equipment and storage medium for determining meshing stiffness of a modified herringbone gear. Background Art

[0002] The herringbone gear is composed of left-handed and right-handed helical gears symmetrically combined along the center line. Its unique symmetrical structure can balance the axial force components of the gears on both sides, fundamentally eliminating the axial force problem in the helical gear transmission; the structural advantages of the herringbone gear make it show significant engineering application value under heavy load and high-speed conditions; at the same time, the gear displacement correction processing technology achieves multiple optimization goals on the basis of avoiding root cutting by adjusting the relative position of the tool and the wheel blank: it can not only improve the load-bearing capacity of the gear pair, but also adapt the center distance parameters and optimize the spatial layout of the transmission system.

[0003] However, the change in tooth profile geometry caused by displacement machining will lead to a significant change in the load distribution characteristics of the left and right helical gears of the herringbone gear; the adjustment of such geometric parameters will directly affect the distribution law of the meshing stiffness of the herringbone gear through the distribution of the meshing contact line and the load transfer path; there are still two key theoretical gaps in the current research field: first, the quantitative influence mechanism of the displacement coefficient on the load distribution characteristics of each meshing point of the double helical gear has not been elucidated; second, the influence law of the displacement parameters on the overall meshing stiffness of the herringbone gear lacks a systematic mathematical model analysis; when considering the displacement effect, the existing meshing stiffness calculation model generally has problems such as a single modeling dimension and incomplete parameter coupling relationship, which seriously restricts the scope of application and calculation accuracy of the model.

[0004] It can be seen that the existing technology still needs to be improved and enhanced. Summary of the invention

[0005] In order to overcome the deficiencies of the prior art, the present invention aims to provide a method for determining the meshing stiffness of a herringbone gear with a modified position, which can accurately determine the meshing stiffness of the herringbone gear pair during the meshing process of the herringbone gear pair under the influence of the modification coefficient.

[0006] A first aspect of the present invention provides a method for determining the meshing stiffness of a shifted herringbone gear, comprising: discretizing a herringbone gear pair to obtain slice information, and confirming the initial load distribution information of the herringbone gear pair based on the obtained design parameters and operating parameters of the herringbone gear and the slice information; determining the meshing point coordinate information of each sliced ​​gear obtained by the discretization processing based on the slice information, and confirming the load angle of the herringbone gear pair based on the meshing point coordinate information; confirming the tooth body meshing stiffness based on the initial load distribution information, and calculating the matrix deformation stiffness based on the confirmed load angle, and then calculating the gear pair meshing stiffness based on the tooth body meshing stiffness and the matrix deformation stiffness; judging whether a preset iteration stop condition is met based on the gear pair meshing stiffness, if not, confirming the modified load distribution information based on the initial load distribution information and the calculated gear pair meshing stiffness calculation; using the modified load distribution information as the initial load distribution information, and returning to execute the confirmation of the tooth body meshing stiffness based on the initial load distribution information.

[0007] Optionally, in a first implementation method of the first aspect of the present invention, the herringbone gear pair is discretized to obtain slice information, and based on the acquired design parameters and operating parameters of the herringbone gear and the slice information, the initial load distribution information of the herringbone gear pair is confirmed, including: discretizing the herringbone gear pair along the tooth width direction to obtain multiple left-handed helical gear slices, multiple right-handed helical gear slices and slice information, wherein the slice information includes the number of slices; obtaining the design parameters and operating parameters of the herringbone gear, wherein the design parameters include the normal pressure angle and helix angle of the left-handed helical gear and the normal pressure angle and helix angle of the right-handed helical gear, and the operating parameters include the torque transmitted by the driving wheel of the herringbone gear pair; based on the acquired design parameters and operating parameters of the herringbone gear, the slice information and the pre-constructed load equation, the initial load distribution information of the herringbone gear pair is confirmed.

[0008] Optionally, in a second implementation method of the first aspect of the present invention, the meshing point coordinate information of each sliced ​​gear obtained by discretization processing based on the slice information includes: constructing a local coordinate system, and establishing a reference line parallel to the width direction of the herringbone gear pair in the constructed local coordinate system; based on the constructed local coordinate system and the reference line, determining the meshing point coordinate information of each left-handed helical gear slice and each right-handed helical gear slice obtained by discretization processing.

[0009] Optionally, in a third implementation method of the first aspect of the present invention, confirming the load angle of the herringbone gear pair based on the meshing point coordinate information includes: confirming the pressure angle and tooth center distance at the meshing point based on the meshing point coordinate information; calculating the pitch circle radius at the meshing point based on the design parameters and operating parameters of the herringbone gear; and calculating the load angle of the herringbone gear pair based on the confirmed pressure angle and tooth center distance at the meshing point and the calculated pitch circle radius.

[0010] Optionally, in a fourth implementation method of the first aspect of the present invention, the confirmation of the tooth meshing stiffness based on the initial load distribution information includes: confirming the force information of the herringbone gear pair according to the acquired design parameters and operating parameters of the herringbone gear and in combination with the initial load distribution information, the force information including the radial component of the meshing force, the tangential component of the meshing force and the axial component of the meshing force; calculating the deformation stiffness of each sliced ​​gear based on the design parameters and operating parameters of the herringbone gear, the calculated initial load distribution information and the confirmed force information, the deformation stiffness including Hertz contact stiffness, tangential bending stiffness, tangential shear stiffness, radial compression stiffness, axial bending stiffness, axial shear stiffness and axial torsional stiffness; calculating the tooth meshing stiffness based on the calculated deformation stiffness of each sliced ​​gear.

[0011] Optionally, in a fifth implementation of the first aspect of the present invention, the matrix deformation stiffness is calculated based on the confirmed load angle, and then the gear pair meshing stiffness is calculated based on the tooth body meshing stiffness and the matrix deformation stiffness, including: calculating the matrix deformation stiffness based on the design parameters and operating parameters of the herringbone gear and the confirmed load angle; obtaining the matrix deformation correction coefficient, and calculating the meshing stiffness of the left-handed sliced ​​helical gear pair and the meshing stiffness of the right-handed sliced ​​helical gear pair based on the tooth body meshing stiffness, the matrix deformation stiffness and the matrix deformation correction coefficient; calculating the gear pair meshing stiffness based on the meshing stiffness of the left-handed sliced ​​helical gear pair and the meshing stiffness of the right-handed sliced ​​helical gear pair.

[0012] Optionally, in a sixth implementation method of the first aspect of the present invention, the gear pair meshing stiffness is used to determine whether a preset iteration stop condition is met. If not, the load distribution information is corrected based on the initial load distribution information and the calculated gear pair meshing stiffness, including: if the calculated gear pair meshing stiffness does not meet a preset convergence accuracy and the current number of iterations is less than a preset maximum number of iterations, the preset iteration stop condition is not met; the preset constraints and a pre-constructed objective function are obtained, and the meshing number information is confirmed based on the preset constraints, the initial load distribution information and the gear pair meshing stiffness; the pre-constructed objective function is corrected based on the meshing number information, and a genetic algorithm is used to solve the corrected objective function to obtain the corrected load distribution information.

[0013] The second aspect of the present invention provides a device for determining the meshing stiffness of a shifted herringbone gear, comprising: an initialization module, used to discretize a herringbone gear pair to obtain slice information, and confirm the initial load distribution information of the herringbone gear pair based on the obtained design parameters and operating parameters of the herringbone gear and the slice information; a confirmation module, used to determine the meshing point coordinate information of each sliced ​​gear obtained by the discretization process based on the slice information, and confirm the load angle of the herringbone gear pair based on the meshing point coordinate information; a calculation module, used to confirm the tooth meshing stiffness based on the initial load distribution information, and calculate the matrix deformation stiffness based on the confirmed load angle, and then calculate the gear pair meshing stiffness based on the tooth meshing stiffness and the matrix deformation stiffness; a judgment module, used to judge whether a preset iteration stop condition is met based on the gear pair meshing stiffness, and if not, to calculate and confirm the modified load distribution information based on the initial load distribution information and the calculated gear pair meshing stiffness; an iteration module, used to use the modified load distribution information as the initial load distribution information, and return to execute the confirmation of the tooth meshing stiffness based on the initial load distribution information.

[0014] The third aspect of the present invention provides a device for determining the meshing stiffness of a shifted herringbone gear, the device comprising: a memory and at least one processor, the memory storing instructions; at least one of the processors calling the instructions in the memory so that the device for determining the meshing stiffness of the shifted herringbone gear performs each step of the method for determining the meshing stiffness of the shifted herringbone gear described in any one of the above.

[0015] A fourth aspect of the present invention provides a computer-readable storage medium having instructions stored thereon, and when the instructions are executed by a processor, the various steps of any of the above-mentioned methods for determining the meshing stiffness of a herringbone gear are implemented.

[0016] In the technical solution of the present invention, the herringbone gear pair is discretized to obtain slice information, and the initial load distribution information is determined according to the herringbone gear design parameters, operating parameters and slice information; the meshing point coordinate information of each sliced ​​gear is determined by using the slice information, and then the load angle is confirmed; the tooth body meshing stiffness is confirmed based on the initial load distribution information, and the matrix deformation stiffness is calculated to obtain the gear pair meshing stiffness; it is determined whether the gear pair meshing stiffness meets the iteration stop condition, and if not, the corrected load distribution information is calculated; the execution is returned to confirm the tooth body meshing stiffness based on the initial load distribution information; the method disclosed in the present application can confirm the evolution law of the time-varying meshing stiffness of the herringbone gear by considering the nonlinear load transfer characteristics of the left-right helical gear pair and analyzing the influence mechanism of the displacement coefficient on the tooth surface contact characteristics, thereby significantly improving the prediction accuracy of the herringbone gear pair time-varying meshing stiffness model, that is, improving the accuracy and reliability of the output gear pair meshing stiffness. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A logic flow chart of a method for determining meshing stiffness provided by an embodiment of the present invention; Figure 2 A schematic diagram of the structure of a device for determining the meshing stiffness of a shifted herringbone gear provided by an embodiment of the present invention; Figure 3 A schematic diagram of the structure of a device for determining the meshing stiffness of a shifted herringbone gear provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the meshing analysis model of herringbone gear pairs; Figure 5 This is a schematic diagram of the contact line distribution law of the herringbone gear pair; Figure 6 This is the force analysis diagram of the left-handed slice gear; Figure 7 This is a schematic diagram of the load angle calculation model for herringbone gear pairs; Figure 8 This is a schematic diagram of the calculation results of the meshing stiffness of a herringbone gear pair. DETAILED DESCRIPTION

[0018] The present invention provides a method, device, equipment and storage medium for determining the meshing stiffness of a shifted herringbone gear. In the present invention, the terms "first", "second", "third", "fourth", etc. (if any) in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein. In addition, the terms "including" or "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0019] For ease of understanding, the specific process of the embodiment of the present invention is described below. Figures 1 to 8 , an embodiment of the method for determining the meshing stiffness of a modified herringbone gear in an embodiment of the present invention includes: 101. Discretize the herringbone gear pair to obtain slice information, and confirm the initial load distribution information of the herringbone gear pair based on the obtained design parameters and operating parameters of the herringbone gear and the slice information; In this embodiment, based on the idea of ​​"slicing method", the herringbone gear pair is discretized along the tooth width direction, which can reduce the difficulty of modeling the meshing stiffness of the herringbone gear pair and can accurately determine the meshing point coordinate information of each sliced ​​gear, which helps to deeply understand the meshing characteristics of the herringbone gear pair.

[0020] 102. Determine meshing point coordinate information of each sliced ​​gear obtained by discretization processing based on the slice information, and confirm the load angle of the herringbone gear pair based on the meshing point coordinate information; 103. Confirm the tooth meshing stiffness based on the initial load distribution information, calculate the matrix deformation stiffness based on the confirmed load angle, and then calculate the gear pair meshing stiffness based on the tooth meshing stiffness and the matrix deformation stiffness; 104. Determine whether a preset iteration stop condition is satisfied based on the meshing stiffness of the gear pair, and if not, calculate and confirm the modified load distribution information based on the initial load distribution information and the calculated meshing stiffness of the gear pair; 105. Use the modified load distribution information as the initial load distribution information, and return to execute confirmation of the tooth body meshing stiffness based on the initial load distribution information; In this embodiment, by solving the modified load distribution information and using the modified load distribution information as the initial load distribution information, returning to repeat the iteration, the calculation result of the load distribution can be continuously optimized until the preset iteration stop condition is met, thereby ensuring the accuracy and reliability of the gear pair meshing stiffness finally output.

[0021] The present application discloses a method for determining the meshing stiffness of a herringbone gear, which discretizes a herringbone gear pair to obtain slice information, and determines the initial load distribution information according to the herringbone gear design parameters, operating condition parameters and slice information; determines the meshing point coordinate information of each sliced ​​gear using the slice information, and then confirms the load angle; confirms the tooth body meshing stiffness based on the initial load distribution information, and calculates the matrix deformation stiffness, and then obtains the gear pair meshing stiffness; determines whether the gear pair meshing stiffness meets the iteration stop condition, and if not, calculates the corrected load distribution information; returns to execute the confirmation of the tooth body meshing stiffness based on the initial load distribution information; the method disclosed in the present application can confirm the evolution law of the time-varying meshing stiffness of the herringbone gear by considering the nonlinear load transfer characteristics of the left-right helical gear pair and analyzing the influence mechanism of the displacement coefficient on the tooth surface contact characteristics, thereby significantly improving the prediction accuracy of the herringbone gear pair time-varying meshing stiffness model, that is, improving the accuracy and reliability of the output gear pair meshing stiffness.

[0022] In the second embodiment of the method for determining meshing stiffness of a modified herringbone gear according to the embodiment of the present invention, step 101 comprises: 201. Discretize the herringbone gear pair along the tooth width direction to obtain a plurality of left-handed helical gear slices, a plurality of right-handed helical gear slices, and slice information, wherein the slice information includes the number of slices; In this embodiment, the meshing analysis model and contact line distribution law of the herringbone gear pair are as follows: Figure 4 and Figure 5 As shown; Figure 4 middle, R bi ( i = p , g , representing the master and slave wheels respectively) and w i Respectively represent gears i The base circle radius and rotation speed; According to previous research, herringbone gears can be regarded as equivalent models of left-handed and right-handed helical gears; Observation Figure 5 It can be seen that the contact line of the two helical gears is around A 3 B 3 The gears are symmetrically distributed along the axis and there are multiple contact lines. Any point on the contact line participates in the meshing, which undoubtedly increases the complexity of the meshing stiffness modeling of the herringbone gear pair. In order to simplify the modeling process, this embodiment draws on the concept of the "slice method" and takes the driving wheel as an example to discretize the herringbone gear along the tooth width direction. Figure 5 shown.

[0023] Figure 5 In the process, the slices are evenly distributed along the tooth width. d w = B / n is the tooth width of the sliced ​​herringbone gear, n is the number of slices, and B is the tooth width; each contact line is parallel to each other on the meshing plane and is separated by a base circle pitch. P bt , A 1 and B 1 are the intersection points of the meshing line of the herringbone gear pair and the tooth top circles of the driving and driven gears, B m is the length of the meshing plane.

[0024] 202. Obtain design parameters and operating parameters of the herringbone gear, wherein the design parameters include the normal pressure angle and the helix angle of the left-handed helical gear and the normal pressure angle and the helix angle of the right-handed helical gear, and the operating parameters include the torque transmitted by the herringbone gear pair driving wheel; Please refer to Table 1, which shows the design parameters and operating parameters of the herringbone gear pair studied in this embodiment.

[0025] Table 1 Gear design parameters and operating parameters

[0026] 203. Based on the obtained design parameters and operating condition parameters of the herringbone gear and the pre-constructed load equation, confirm the initial load distribution information of the herringbone gear pair; In this embodiment, it can be known from the meshing principle of the herringbone gears that the axial component of the meshing force of the left-handed part and the axial component of the meshing force of the right-handed part are equal, and the meshing force of the left-handed part and the meshing force of the right-handed part should correspond to the torque transmitted by the driving wheel. Therefore, based on the following pre-constructed load equation, the initial load distribution information of the herringbone gear pair can be confirmed: (1) In the formula, T p is the torque transmitted by the herringbone gear pair driving wheel, α nl and β l are the normal pressure angle and helix angle of the left-handed helical gear, α nr and β r are the normal pressure angle and helix angle of right-hand helical gear, For contact line kk Middle left-handed slice j The load borne, For contact line kk Middle right-hand slice j The load borne, F l The load distributed to the left-hand helical gear is a known value; The load distributed to the right-hand helical gear is a known value; R bp It is the base circle radius of the driving wheel of the herringbone gear pair, which is the set input value.

[0027] Based on the gear meshing principle, the number of contact lines of a helical gear pair generally does not exceed 4. In this embodiment, in the initial stage, the initial load distribution information of the herringbone gear pair is confirmed based on formula (1), and the initial load distribution information includes the initial load borne by each slice of the left-handed helical gear and the initial load borne by each slice of the right-handed helical gear in the herringbone gear; wherein, in the initial stage, it is defined that the initial load borne by each slice of the left-handed helical gear is equal, and the initial load borne by each slice of the right-handed helical gear is equal, that is, based on the number of slices, the initial load borne by each slice can be confirmed.

[0028] In a third embodiment of the method for determining meshing stiffness of a modified herringbone gear according to an embodiment of the present invention, step 102 includes: 301. Construct a local coordinate system, and establish a reference line parallel to the tooth width direction of the herringbone gear pair in the constructed local coordinate system; 302. Based on the constructed local coordinate system and reference line, determine the meshing point coordinate information of each left-handed helical gear slice and each right-handed helical gear slice obtained by discretization processing.

[0029] according to Figure 5 , the meshing point X of each slice herringbone gear pair is the intersection of the slice center line and the contact line; according to Figure 5 As shown, establish a local coordinate system x m - A 1 - y m , the coordinates of the meshing position X on each slice can be calculated through geometric relationships ( x m , y m ); Taking the left-handed sliced ​​helical gear in the driving wheel as an example, project point X to A 1 B 1 The meshing position of the left-handed helical gear and the herringbone gear can be determined on the meshing line A 1 B 1 Projection point on X ' ; According to the principle of gear meshing, X ' That is the projected meshing position of the left-handed sliced ​​helical gear of the herringbone gear corresponding to point X on the end face, from which the meshing parameters of the left-handed sliced ​​helical gear at point X can be determined.

[0030] Figure 5 It shows that the meshing point of the left-hand helical gear pair in the herringbone gear pair is from point A 1 Point B 3 Move, the meshing point of the right-hand helical gear pair from point A 2 Point B 3 Movement; through this meshing process, this embodiment can derive the change law of the contact line of the herringbone gear pair, which will not be described in detail here.

[0031] In order to reduce the workload of subsequent modeling, Figure 5 Select a line parallel to the width of the herringbone gear teeth mesh As a reference line; Figure 5 It can be seen that mesh There are intersections with both the left-handed sliced ​​helical gear and the right-handed sliced ​​helical gear, which is the intersection of the herringbone gear pair at that moment. mesh The coordinates of the meshing points on the , can be calculated by the following formula: (2) In the formula, kk For contact line kk(kk =1,2,3…,N , N is the number of contact lines), x mesh For Line mesh and x m The horizontal coordinate of the axis intersection point, slope kk For contact line kk The slope of b kk is the intercept of the contact line kk on the y-axis; through formula (2), the coordinate information of the meshing point between the left-handed helical gear and the right-handed helical gear can be obtained; In the fourth embodiment of the method for determining meshing stiffness of a modified herringbone gear in the embodiment of the present invention, step 102 further includes: 401. Confirm the pressure angle and tooth center distance at the meshing point based on the meshing point coordinate information; In this embodiment, the tooth center distance and pressure angle at the meshing point can be calculated based on the coordinate information of the meshing point; the meshing point is the point of action of load transmission. When the herringbone gears are meshed, the force is transmitted through the tooth surface contact point. The coordinates of each meshing point directly determine the position of the point on the tooth surface (such as close to the tooth top, tooth root or the middle of the tooth), affecting the effect of the tooth shape (change in tooth thickness due to displacement) on stiffness; and determines the direction and distribution of the contact line (the contact line of the helical gear is an oblique line, and the contact line of the herringbone gear is symmetrical for left and right rotation), thereby affecting the distribution of the load in the tooth width direction (for example, the force on the middle slice may be greater).

[0032] 402. Calculate the pitch circle radius at the meshing point based on the design parameters and operating parameters of the herringbone gear; 403. Calculate the load angle of the herringbone gear pair based on the confirmed pressure angle and tooth center distance at the meshing point and the calculated pitch circle radius.

[0033] Previous studies have shown that the meshing stiffness of the helical gear meshing tooth pair is related to its load angle; therefore, it is necessary to determine the load angle of the shifted helical gear; select the gear in the left-handed helical gear pair of the herringbone gear i Take the load angle calculation model as an example. Figure 7 As shown in the figure, X is the meshing point, R Xi Meshing point X To the gear i Tooth center O i The tooth center distance, A 1 X is the meshing line, R bi For gear i Base circle radius, αXikk,j,l and θ Xikk,j,l Gear i Pressure angle and load angle at the meshing point.

[0034] Depend on Figure 7 It can be seen that t Middle gear of left-hand helical gear pair i The load angle can be obtained by formula (3): (3) In the formula, z i and α i They are respectively the middle gear of the left-hand helical gear pair i The number of teeth and the pitch circle pressure angle, α Xikk,j,l ( kk =1,2,…, N , N is the number of contact lines, j =1,2,…, n , n is the number of slices) is the middle gear of the left-hand helical gear pair i At the meshing point X The pressure angle at inv ( x )=tan( x )- x is an involute function; if R Xi < R i , formula (3) takes the + sign, if R Xi ≥ R i , formula (3) takes - sign; R Xi and R i They are respectively the middle gear of the left-hand helical gear pair i At the meshing point X The tooth center distance and pitch circle radius at R i Through the gears i Calculation of number of teeth and module; ss i It is the middle gear of the left-hand helical gear pair i The pitch circle tooth thickness can be obtained by formula (4): (4) In the formula, m The module of the left-hand helical gear pair in the herringbone gear. x iIt is the middle gear of the left-hand helical gear pair i The displacement coefficient.

[0035] In the fifth embodiment of the method for determining meshing stiffness of a modified herringbone gear in the embodiment of the present invention, step 103 includes: 501. According to the acquired design parameters and working condition parameters of the herringbone gear, combined with the initial load distribution information, confirm the force information of the herringbone gear pair, wherein the force information includes a radial component of meshing force, a tangential component of meshing force, and an axial component of meshing force; In this embodiment, taking the left-handed sliced ​​helical gear in the herringbone gear as an example, its force condition is as follows: Figure 6 As shown; Figure 6 middle, F kk,j,l ( kk =1,2,…, N , N is the number of contact lines, j =1,2,…, n , n is the number of slices), , F mt and F ma They are respectively the load borne by each slice of the left-handed helical gear in the herringbone gear, the radial component of the meshing force, the tangential component of the meshing force and the axial component of the meshing force.

[0036] Depend on Figure 6 It can be seen that F mr , F mt and F ma It can be expressed as: (5) (6) (7) To facilitate subsequent derivation, the resultant forces of the left-handed sliced ​​helical gear on the end face in the radial and tangential directions are given as F a and F b , as shown in formula (8): (8) In the formula, α nl is the normal pressure angle of the left-hand helical gear, β l is the helix angle of left-hand helical gear.

[0037] 502. Calculate the deformation stiffness of each sliced ​​gear based on the design parameters and working condition parameters of the herringbone gear, the calculated initial load distribution information and the confirmed force information, wherein the deformation stiffness includes Hertz contact stiffness, tangential bending stiffness, tangential shear stiffness, radial compression stiffness, axial bending stiffness, axial shear stiffness and axial torsional stiffness; In this embodiment, according to the energy method, during the meshing process, the energy stored in the left-handed sliced ​​helical gear pair j(j =1,2,…, n , n The potential energy on the contact surface (is the number of slices) includes seven parts: Hertz contact potential energy U hj,l , tangential bending potential energy U tbikk,j,l , tangential shear potential energy U tsikk,j,l , radial compression potential energy U tcikk,j,l , axial bending potential energy U abikk,j,l , axial shear potential energy U asikk,j,l and axial torsional potential energy U atikk,j,l； The potential energy of these seven parts corresponds to the Hertz contact stiffness k hj,l , tangential bending stiffness k tbikk,j,l , tangential shear stiffness k tsikk,j,l , radial compression stiffness k tcikk,j,l , axial bending stiffness k abikk,j,l , axial shear stiffness k asikk,j,l and axial torsional stiffness k atikk,j,l , which can be obtained from material mechanics: (9) (10) (11) (12) (13) (14) (15) In the formula, E i , G i and vi Gear i The elastic modulus, shear modulus and Poisson's ratio, ρ Xi is the radius of curvature, Ax, Ix, h, d, x and dx are the meshing stiffness calculation parameters respectively; For gear i At the meshing point X The Hertzian contact half-width at is related to the distributed load of the gear and can be obtained by the following formula: (16) During the first iteration, the gear is calculated using the initial load distribution information. i At the meshing point X The Hertz contact half-width at is used to calculate the initial Hertz contact stiffness; in subsequent iterations, the modified load distribution information is used to calculate the gear i At the meshing point X The Hertzian contact half-width at is used to calculate the modified Hertzian contact stiffness, so as to continuously reduce the error and gradually approach the true solution.

[0038] 503. Calculate the tooth meshing stiffness based on the calculated deformation stiffness of each slice gear; In this embodiment, for example, the left-handed slicing helical gear pair j(j =1,2,…, n , n The meshing stiffness of the tooth body (where ( is the number of slices)) is shown in formula (17): (17) The parameters in the formula can be obtained by formula (9)-(15), For left-handed slicing helical gear pair j(j =1,2,…, n , n is the tooth meshing stiffness of the tooth body (number of slices).

[0039] In the fifth embodiment of the method for determining meshing stiffness of a modified herringbone gear according to the embodiment of the present invention, step 103 further includes: 601. Calculate the deformation stiffness of the matrix based on the design parameters and operating parameters of the herringbone gear and the confirmed load angle; In this embodiment, during the gear meshing process, the gear base will also deform to a certain extent, and the stiffness corresponding to this partial deformation is the base deformation stiffness. k fikk,j，l , can be obtained by the following formula: (18) In the formula, μ f is the distance from the meshing line and the focus of the gear tooth symmetry line to the tooth root circle,S f is the base circle arc corresponding to the entire gear tooth profile; , , and The coefficients can be obtained by the following polynomial: (19) In the formula, for , , and Any one of A , B′ , C , D , E′ and F′ See Table 2 for details. h f = r fp / r int , r fp is the root circle radius of the driving gear teeth, r int is the radius of the driving wheel gear shaft hole, θ f is the central angle of the tooth profile of the driving wheel.

[0040] Table 2 and The value of

[0041] 602. Obtain a matrix deformation correction coefficient, and calculate the meshing stiffness of the left-handed sliced ​​helical gear pair and the meshing stiffness of the right-handed sliced ​​helical gear pair based on the tooth meshing stiffness, the matrix deformation stiffness, and the matrix deformation correction coefficient; In this embodiment, for example, the meshing stiffness of the left-handed helical gear pair can be obtained by formula (20): (20) In the formula, ε i is the matrix deformation correction coefficient, generally 1.1, For left-handed slicing helical gear pair j meshing stiffness.

[0042] 603. Calculate the meshing stiffness of the gear pair based on the meshing stiffness of the left-handed sliced ​​helical gear pair and the meshing stiffness of the right-handed sliced ​​helical gear pair; In this embodiment, after obtaining the meshing stiffness of each left-handed sliced ​​helical gear pair, the meshing stiffness of the left-handed helical gear pair can be obtained by superimposing them along the tooth width direction and the contact line, as shown in formula (21): (twenty one) Similarly, the meshing stiffness of the right-handed helical gear pair can be obtained, which will not be repeated here; the meshing stiffness of the gear pair is the sum of the meshing stiffness of the left-handed helical gear pair and the meshing stiffness of the right-handed helical gear pair, as shown in the following formula: (twenty two) In the formula, k l and k r They are the meshing stiffness of left-hand helical gear pair and the meshing stiffness of right-hand helical gear pair respectively.

[0043] In the sixth embodiment of the method for determining meshing stiffness of a modified herringbone gear in the embodiment of the present invention, step 104 comprises: 701. If the calculated meshing stiffness of the gear pair does not meet the preset convergence accuracy and the current number of iterations is less than the preset maximum number of iterations, the preset iteration stop condition is not met; In this embodiment, when the calculated meshing stiffness of the gear pair is ≤ the preset convergence accuracy, or the current number of iterations is ≥ the preset maximum number of iterations, it indicates that the preset iteration stop condition is met. At this time, the meshing stiffness value of the gear pair calculated during the last iteration is output as the final meshing stiffness of the herringbone gear pair; the preset convergence accuracy is the preset true value of the meshing stiffness, which can be set in advance according to the actual working conditions.

[0044] 702. Obtain preset constraints and pre-built objective functions, and confirm meshing number information based on the preset constraints, initial load distribution information, and meshing stiffness of the gear pair, wherein the meshing number information includes a set of contact line numbers of the gear pair involved in meshing and a set of sliced ​​helical gear pair numbers; In this embodiment, it can be seen from formula (9) that the Hertzian contact stiffness of the left-handed helical gear pair is Related to the load it bears; left-handed slice j The load F kk,j,l ( kk =1,2,…, N , N is the number of contact lines) can be obtained from the slice load distribution equation: (twenty three) In the formula, F kk,j,l and S kk,j,l Contact line kkMiddle left-handed slicing helical gear pair j Loads and meshing errors, F kk,l , k kk,l and S kk,l Contact line kk The load, meshing stiffness and meshing error borne; this constraint condition reveals that the load distribution between slices must follow the principle of local balance.

[0045] In this embodiment, formula (23) is used to determine the number of the sliced ​​helical gear pair involved in the meshing; the specific method is as follows: first, the contact line is confirmed based on the initial load distribution information kk The load F kk,l , then F kk,l , the meshing stiffness of the slice helical gear pair calculated based on formula (20) and the meshing error of each slice helical gear pair are substituted into the slice load distribution equation to obtain the meshing force of each left-handed slice helical gear pair: F kk,j,l ;when F kk,j,l <0, indicating kk Contact line No. j The slice helical gear pair does not participate in the meshing, that is, the corresponding parameters are removed from the slice load distribution equation and the calculation is performed again until the number of the slice helical gear pair that finally participates in the meshing is determined.

[0046] The meshing load distributed to each contact line of the left-handed helical gear pair can be determined by the load coordination equation. The constraint condition formed by the load coordination equation reveals that the load distribution between the left-handed helical gear and the right-handed helical gear must satisfy the axial force balance and torque balance; the load coordination equation is shown in formula (24): (twenty four) In the formula, F l The load distributed to the left-hand helical gear is obtained by formula (1).

[0047] In this embodiment, equation (24) is used to determine the load borne by each contact line. F kk ; The specific method is: first, the meshing stiffness of each left-handed slice helical gear pair involved in the meshing is superimposed to obtain the contact line meshing stiffness , then , the load distributed by the left-hand helical gear determined by formula (1) F l Substituting the meshing error of each contact line into the load coordination equation, the load borne by each contact line can be obtained. Fkk,l ;when F kk,l <0, indicating kk If a contact line does not participate in the meshing, the corresponding parameter is removed from the load coordination equation and the calculation is performed again until the contact line number that finally participates in the meshing is determined.

[0048] Furthermore, it can be seen from equations (1), (23) and (24) that it is difficult to solve the load distribution of the left-handed helical gear and the right-handed helical gear in the herringbone gear. To address this problem, the present invention adopts a genetic algorithm to solve it. The objective function and constraint conditions are shown in equation (25): (25) In the formula, st .1. st .2 and st .3 are the objective functions f 1 And the objective function f 2 The constraints of st .1. st .2 are the slice load distribution equation and load coordination equation, including the case of left-hand slice gear and the case of right-hand slice gear; and According to equations (23) and (24), that is, under the constraints st .1 and st .2, determine the contact line number of the left-handed helical gear pair and the right-handed helical gear pair participating in the meshing and the set of the slice helical gear pair number; taking the left-handed helical gear pair as an example, when a slice helical gear pair on a specific contact line participates in the meshing, (kk, j, l) ∈ ,at this time, F kk,j,l > 0; On the contrary, when a specific contact line does not participate in meshing, or when a certain slice helical gear pair on a specific contact line does not participate in meshing, (kk, j, l) ,at this time, F kk,j,l =0.

[0049] 703. The pre-constructed objective function is modified based on the meshing number information, and the modified objective function is solved by a genetic algorithm to obtain modified load distribution information.

[0050] In this embodiment, when solving the modified load distribution information based on the genetic algorithm, firstly, the left-handed sliced ​​helical gear pairs participating in the meshing are calculated based on formula (23) using real number coding. j Load and right-handed slice helical gear pair jThe loads to be borne are arranged into vectors in sequence, and an initial population containing N individuals is randomly generated after the value range of the elements is determined; then the objective function is used as the fitness function to evaluate the quality of each individual; then the roulette selection method is used in combination with the elite retention strategy to perform a selection operation to select individuals with high fitness from the current population; then the selected individuals are crossovered in a single-point crossover manner and at a preset crossover probability to generate new individuals, and then the individuals are mutated in a uniform mutation manner and at a preset mutation probability; in each iteration process, it is determined whether the maximum number of iterations is reached or the fitness value of the best individual in the population is less than or equal to the preset fitness threshold. If not, the evaluation, selection, crossover, and mutation steps are repeated. If satisfied, the iteration is stopped, and the load distribution scheme corresponding to the individual with the smallest fitness value in the population is output as the modified load distribution information.

[0051] See also Figure 8 , Figure 8 This is a schematic diagram of the calculation results of the meshing stiffness of the herringbone gear pair; Figure 8 As shown, as the driving wheel transmits torque T p As the meshing stiffness of the herringbone gear pair calculated by the method disclosed in this embodiment increases, the main reason for this phenomenon is the nonlinear load characteristic of the Hertzian contact of the gear pair. Further observation Figure 8 It can be found that the meshing stiffness of the herringbone gear pair calculated by the method disclosed in this embodiment has slight fluctuations. This fluctuation phenomenon is attributed to the load distribution between the left-handed and right-handed helical gears, between the contact lines of the helical gears, and between the adjacent contact points of the helical gear contact lines. These distributions will change with the changes in the meshing parameters of the herringbone gear pair; this finding emphasizes the significant influence of load distribution on the meshing mechanism and dynamic response of the herringbone gears, suggesting that it must be considered in the subsequent modeling of the meshing stiffness of the herringbone gears.

[0052] The present application discloses a method for determining the meshing stiffness of a shifted herringbone gear pair. Firstly, based on the structural characteristics of the herringbone gear, it is decomposed into left-handed and right-handed helical gears, and the corresponding meshing analysis model of the shifted helical gear pair is constructed by using the gear meshing principle; secondly, by analyzing the influence of the displacement on the meshing condition of the helical gear pair and drawing on the idea of ​​the "slicing method", the meshing stiffness of the shifted helical gear pair is derived; then, the load distribution relationship between the meshing points of the helical gear pair and between the left-handed and right-handed helical gears is studied by means of a group of load coordination equations, and the meshing stiffness of the shifted herringbone gear pair is calculated based on the proposed iterative algorithm; the method disclosed in the present application makes it possible to study the load distribution relationship between the left-handed and right-handed helical gears and the influencing mechanism of the displacement design, thereby significantly improving the prediction accuracy of the time-varying meshing stiffness model of the herringbone gear pair, that is, improving the accuracy and reliability of the output meshing stiffness of the gear pair.

[0053] The above describes the method for determining the meshing stiffness of the shifted herringbone gear in the embodiment of the present invention. The following describes the device for determining the meshing stiffness of the shifted herringbone gear in the embodiment of the present invention. Figure 2 In one embodiment of the present invention, a device for determining the meshing stiffness of a herringbone gear comprises: Initialization module 801, used to discretize the herringbone gear pair to obtain slice information, and confirm the initial load distribution information of the herringbone gear pair based on the obtained design parameters and working condition parameters of the herringbone gear and the slice information; A confirmation module 802 is used to determine the meshing point coordinate information of each sliced ​​gear obtained by discretization processing based on the slice information, and confirm the load angle of the herringbone gear pair based on the meshing point coordinate information; A calculation module 803 is used to confirm the tooth meshing stiffness based on the initial load distribution information, calculate the matrix deformation stiffness based on the confirmed load angle, and then calculate the gear pair meshing stiffness based on the tooth meshing stiffness and the matrix deformation stiffness; A judgment module 804 is used to judge whether a preset iteration stop condition is met based on the meshing stiffness of the gear pair, and if not, to calculate and confirm the modified load distribution information based on the initial load distribution information and the calculated meshing stiffness of the gear pair; The iteration module 805 is used to use the modified load distribution information as the initial load distribution information and return to execute the confirmation of the tooth body meshing stiffness based on the initial load distribution information.

[0054] Based on the same idea as the method in the above embodiment, the device provided by the present application can implement the method in the above embodiment.

[0055] above Figure 2 The meshing stiffness determination device of the modified herringbone gear in the embodiment of the present invention is described in detail from the perspective of modular functional entity. The meshing stiffness determination device of the modified herringbone gear in the embodiment of the present invention is described in detail from the perspective of hardware processing.

[0056] Figure 31 is a schematic diagram of the structure of a device for determining the meshing stiffness of a shifted herringbone gear provided by an embodiment of the present invention. The device 900 for determining the meshing stiffness of a shifted herringbone gear may have relatively large differences due to different configurations or performances, and may include one or more processors (central processing units, CPU) 910 (for example, one or more processors) and a memory 920, and one or more storage media 930 (for example, one or more mass storage devices) storing application programs 933 or data 932. Among them, the memory 920 and the storage medium 930 may be temporary storage or permanent storage. The program stored in the storage medium 930 may include one or more modules (not shown in the figure), and each module may include a series of instruction operations in the device 900 for determining the meshing stiffness of a shifted herringbone gear. Furthermore, the processor 910 may be configured to communicate with the storage medium 930, and execute a series of instruction operations in the storage medium 930 on the device 900 for determining the meshing stiffness of a shifted herringbone gear, so as to implement the steps of the method for determining the meshing stiffness of a shifted herringbone gear provided in the above-mentioned method embodiments.

[0057] The device 900 for determining the meshing stiffness of the herringbone gear may further include one or more power supplies 940, one or more wired or wireless network interfaces 950, one or more input and output interfaces 960, and / or one or more operating systems 931, such as Windows Serve, Mac OS X, Unix, Linux, FreeBSD, etc. It will be appreciated by those skilled in the art that Figure 3 The structure of the device for determining the meshing stiffness of the shifted herringbone gears shown does not constitute a limitation on the device for determining the meshing stiffness of the shifted herringbone gears, and may include more or less components than shown in the figure, or combine certain components, or arrange the components differently.

[0058] The present invention also provides a computer-readable storage medium, which may be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium. Instructions are stored in the computer-readable storage medium. When the instructions are executed on a computer, the computer executes the steps of the method for determining the meshing stiffness of a shifted herringbone gear.

[0059] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the above-described system, device, or unit can refer to the corresponding process in the aforementioned method embodiment and will not be repeated here.

[0060] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the whole or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk and other media that can store program code.

[0061] Finally, it should be noted that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for determining the meshing stiffness of a modified herringbone gear, characterized in that: include: Discretize the herringbone gear pair to obtain slice information, and confirm the initial load distribution information of the herringbone gear pair based on the obtained design parameters and operating parameters of the herringbone gear and the slice information; Determine meshing point coordinate information of each slice gear obtained by discretization processing based on the slice information, and confirm the load angle of the herringbone gear pair based on the meshing point coordinate information; The meshing stiffness of the gear body is determined based on the initial load distribution information, and the deformation stiffness of the matrix is ​​calculated based on the determined load angle, and the meshing stiffness of the gear pair is calculated based on the meshing stiffness of the gear body and the deformation stiffness of the matrix; Determining whether a preset iteration stop condition is satisfied based on the meshing stiffness of the gear pair, and if not, confirming the modified load distribution information based on the initial load distribution information and the calculated meshing stiffness of the gear pair; The modified load distribution information is used as the initial load distribution information, and the process returns to confirm the tooth meshing stiffness based on the initial load distribution information.

2. The method for determining meshing stiffness of a modified herringbone gear according to claim 1, characterized in that: The discretization process is performed on the herringbone gear pair to obtain slice information, and based on the obtained design parameters and operating parameters of the herringbone gear and the slice information, the initial load distribution information of the herringbone gear pair is confirmed, including: Discretize the herringbone gear pair along the tooth width direction to obtain a plurality of left-handed helical gear slices, a plurality of right-handed helical gear slices, and slice information, wherein the slice information includes the number of slices; Acquire design parameters and operating parameters of the herringbone gear, wherein the design parameters include the normal pressure angle and the helix angle of the left-handed helical gear and the normal pressure angle and the helix angle of the right-handed helical gear, and the operating parameters include the torque transmitted by the herringbone gear pair driving wheel; Based on the acquired design parameters and operating parameters of the herringbone gear, slicing information and pre-constructed load equation, the initial load distribution information of the herringbone gear pair is confirmed.

3. The method for determining meshing stiffness of a modified herringbone gear according to claim 1, characterized in that: The meshing point coordinate information of each sliced ​​gear obtained by discretization processing based on the slice information includes: Constructing a local coordinate system, and establishing a reference line parallel to the tooth width direction of the herringbone gear pair in the constructed local coordinate system; Based on the constructed local coordinate system and reference line, the meshing point coordinate information of each left-handed helical gear slice and each right-handed helical gear slice obtained by discretization processing is determined.

4. The method for determining meshing stiffness of a modified herringbone gear according to claim 1, characterized in that: The step of confirming the load angle of the herringbone gear pair based on the meshing point coordinate information includes: Confirm the pressure angle and tooth center distance at the meshing point based on the meshing point coordinate information; Calculate the pitch circle radius at the meshing point based on the design parameters and operating parameters of the herringbone gear; Based on the confirmed pressure angle and tooth center distance at the meshing point and the calculated pitch circle radius, the load angle of the herringbone gear pair is calculated.

5. The method for determining meshing stiffness of a modified herringbone gear according to claim 1, characterized in that: The step of confirming the tooth meshing stiffness based on the initial load distribution information comprises: According to the obtained design parameters and working condition parameters of the herringbone gear, combined with the initial load distribution information, the force information of the herringbone gear pair is confirmed, wherein the force information includes a radial component of meshing force, a tangential component of meshing force, and an axial component of meshing force; The deformation stiffness of each sliced ​​gear is calculated based on the design parameters and working condition parameters of the herringbone gear, the calculated initial load distribution information and the confirmed force information, wherein the deformation stiffness includes Hertz contact stiffness, tangential bending stiffness, tangential shear stiffness, radial compression stiffness, axial bending stiffness, axial shear stiffness and axial torsional stiffness; The tooth meshing stiffness is calculated based on the calculated deformation stiffness of each slice gear.

6. The method for determining meshing stiffness of a modified herringbone gear according to claim 5, characterized in that: The step of calculating the matrix deformation stiffness based on the confirmed load angle, and then calculating the gear pair meshing stiffness based on the tooth body meshing stiffness and the matrix deformation stiffness, comprises: The matrix deformation stiffness is calculated based on the design parameters and operating parameters of the herringbone gear and the confirmed load angle; Obtaining a matrix deformation correction coefficient, and calculating the meshing stiffness of a left-handed sliced ​​helical gear pair and the meshing stiffness of a right-handed sliced ​​helical gear pair based on the meshing stiffness of the tooth body, the matrix deformation stiffness and the matrix deformation correction coefficient; The mesh stiffness of the gear pair is calculated based on the mesh stiffness of the left-handed sliced ​​helical gear pair and the mesh stiffness of the right-handed sliced ​​helical gear pair.

7. The method for determining meshing stiffness of a modified herringbone gear according to claim 1, characterized in that: The determining whether a preset iteration stop condition is satisfied based on the meshing stiffness of the gear pair, and if not, confirming the modified load distribution information based on the initial load distribution information and the calculated meshing stiffness of the gear pair, comprises: If the calculated meshing stiffness of the gear pair does not meet the preset convergence accuracy and the current number of iterations is less than the preset maximum number of iterations, the preset iteration stop condition is not met; Obtaining preset constraints and pre-built objective functions, and confirming meshing number information based on preset constraints, initial load distribution information, and gear pair meshing stiffness; The pre-constructed objective function is modified based on the meshing number information, and the modified objective function is solved by genetic algorithm to obtain the modified load distribution information.

8. A device for determining the meshing stiffness of a herringbone gear, characterized in that: include: An initialization module is used to discretize the herringbone gear pair to obtain slice information, and to confirm the initial load distribution information of the herringbone gear pair based on the obtained design parameters and working condition parameters of the herringbone gear and the slice information; A confirmation module, used to determine the meshing point coordinate information of each sliced ​​gear obtained by discretization processing based on the slice information, and confirm the load angle of the herringbone gear pair based on the meshing point coordinate information; A calculation module, used to confirm the tooth meshing stiffness based on the initial load distribution information, calculate the matrix deformation stiffness based on the confirmed load angle, and then calculate the gear pair meshing stiffness based on the tooth meshing stiffness and the matrix deformation stiffness; A judgment module, used for judging whether a preset iteration stop condition is satisfied based on the meshing stiffness of the gear pair, and if not, confirming the modified load distribution information based on the initial load distribution information and the calculated meshing stiffness of the gear pair; The iterative module is used to use the modified load distribution information as the initial load distribution information and return to execute the confirmation of the tooth body meshing stiffness based on the initial load distribution information.

9. A device for determining the meshing stiffness of a herringbone gear, characterized in that: The device for determining meshing stiffness of a shifted herringbone gear comprises: a memory and at least one processor, wherein instructions are stored in the memory; At least one of the processors calls the instructions in the memory to enable the device for determining the meshing stiffness of the shifted herringbone gears to perform each step of the method for determining the meshing stiffness of the shifted herringbone gears according to any one of claims 1 to 7.

10. A computer-readable storage medium having instructions stored thereon, characterized in that: When the instructions are executed by the processor, the various steps of the method for determining the meshing stiffness of the shifted herringbone gears as described in any one of claims 1 to 7 are implemented.

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