Method, device, equipment and storage medium for determining meshing stiffness of cracked spur gear

Abstract

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 the meshing stiffness of a cracked spur gear. The method comprises: constructing a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system to confirm coordinate data related to a tooth root crack; and calculating the rotation angle between the two coordinate systems; calculating the tooth pair meshing error based on the coordinate data and the rotation angle to confirm the tooth pair number involved in the meshing and confirm the corresponding tooth pair meshing force; calculating the stiffness parameters of the cracked gear tooth according to the tooth pair meshing force, and calculating the tooth pair meshing stiffness; calculating the comprehensive meshing stiffness of the gear pair according to the tooth pair meshing stiffness, and calculating the gear pair meshing stiffness according to the calculated comprehensive meshing stiffness of the gear pair and the pre-calculated matrix deformation stiffness; the method disclosed in the present application improves the meshing stiffness modeling accuracy of the cracked spur gear pair, and can accurately determine the meshing stiffness of the gear pair during the meshing process of the cracked spur gear pair.

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 the meshing stiffness of a cracked spur gear. Background Art

[0002] Gear mesh stiffness, as a key source of internal excitation in gear transmission systems, has important theoretical value for the verification and prediction of dynamic service performance through in-depth computational research. However, in practical applications, the meshing teeth of spur gear pairs are often affected by multiple factors such as installation errors, changes in operating conditions, and external excitations, resulting in tooth root cracks. This fault significantly weakens the service performance and life of spur gears.

[0003] Current research has revealed that, under the action of external loads, the root cracks of spur gears will induce plastic deformation of the gear teeth, accompanied by a certain angle of plastic deflection; the plastic deformation and deflection phenomena have a significant impact on the meshing state and dynamic performance of cracked spur gear pairs; however, existing research on cracked spur gear pairs often ignores the gear tooth centerline offset caused by plastic deflection, as well as the tooth pair meshing error and meshing stiffness change caused by the gear tooth centerline offset; that is, the existing cracked spur gear meshing stiffness calculation model cannot comprehensively and accurately analyze the meshing stiffness, which limits the scope of application and modeling 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 shortcomings of the prior art, the purpose of the present invention is to provide a method for determining the meshing stiffness of a cracked spur gear, which improves the modeling accuracy of the meshing stiffness of a cracked spur gear pair and can accurately determine the meshing stiffness of the gear pair during the meshing process of the cracked spur gear pair.

[0006] A first aspect of the present invention provides a method for determining the meshing stiffness of a cracked spur gear, comprising: constructing a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system, confirming coordinate data related to a tooth root crack based on the constructed cracked gear tooth plastic deflection analysis model; calculating a rotation angle between the local coordinate system and the global coordinate system based on the confirmed coordinate data, and calculating a tooth pair meshing error based on the coordinate data and the calculated rotation angle; confirming the number of tooth pairs involved in meshing based on the calculated tooth pair meshing error, and confirming the tooth pair meshing force corresponding to the tooth pair number involved in meshing; calculating stiffness parameters of the cracked gear tooth based on the confirmed tooth pair meshing force, and calculating the tooth pair meshing stiffness based on the calculated stiffness parameters; calculating the comprehensive meshing stiffness of the gear pair based on the calculated tooth pair meshing stiffness, and calculating the matrix deformation stiffness, and calculating the gear pair meshing stiffness based on the calculated comprehensive meshing stiffness of the gear pair and the calculated matrix deformation stiffness.

[0007] Optionally, in a first implementation method of the first aspect of the present invention, the cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system is constructed, and coordinate data related to the tooth root crack is confirmed based on the constructed cracked gear tooth plastic deflection analysis model, including: constructing a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system, and the cracked gear tooth plastic deflection analysis model includes a tooth root crack BC; based on the constructed cracked gear tooth plastic deflection analysis model, coordinate data related to the gear crack is confirmed, and the coordinate data include the coordinates of the crack starting point C, the coordinates of the crack end point B, and the coordinates of the symmetrical point D of the crack starting point C with respect to the center line of the cracked gear tooth; the coordinates of the midpoint O of BD are calculated based on the coordinates of the crack end point B and the coordinates of the symmetrical point D.

[0008] Optionally, in a second implementation of the first aspect of the present invention, the rotation angle between the local coordinate system and the global coordinate system is calculated based on the confirmed coordinate data, and the tooth pair meshing error is calculated based on the coordinate data and the calculated rotation angle, including: calculating the rotation angle between the local coordinate system and the global coordinate system based on the coordinates of the crack end point B and the symmetry point D; obtaining the coordinate data of the intersection E2 of the meshing line of the cracked tooth and the tooth profile on the driving side of the normal tooth and the load angle at the intersection E2; based on the obtained load angle of the intersection E2 and the rotation angle, using an iterative algorithm to confirm the coordinates of the actual meshing point E1 of the cracked tooth; and calculating the tooth pair meshing error based on the confirmed coordinate data of the intersection E2 and the confirmed coordinates of the actual meshing point E1.

[0009] Optionally, in a third implementation method of the first aspect of the present invention, the coordinates of the actual meshing point E1 of the cracked tooth are confirmed by an iterative algorithm based on the acquired load angle of the intersection E2 and the rotation angle, including: constructing a first global coordinate expression in the global coordinate system for the corresponding point E3 of the actual meshing point E1 before the plastic deflection of the cracked tooth, and converting the first global coordinate expression into a first local coordinate expression in the local coordinate system according to the rotation angle; constructing a second local coordinate expression of the actual meshing point E1 based on the first local coordinate expression, and converting the second local coordinate expression into a second global coordinate expression in all coordinate systems according to the rotation angle; based on the coordinate data of the intersection E2, the load angle at the intersection E2, and the second global coordinate expression, according to the meshing line equation, confirming the coordinates of the actual meshing point E1 by an iterative algorithm.

[0010] Optionally, in a fourth implementation of the first aspect of the present invention, the tooth pair numbers involved in the meshing are confirmed based on the calculated tooth pair meshing error, and the tooth pair meshing force corresponding to the tooth pair numbers involved in the meshing is confirmed, including: based on the calculated tooth pair meshing error, the tooth pair meshing force of each tooth pair is calculated according to the stiffness load coordination equation; when the calculated tooth pair meshing force is greater than zero, it indicates that the tooth pair corresponding to the tooth pair meshing force is involved in the meshing, and the tooth pair numbers and tooth pair meshing force corresponding to the tooth pair involved in the meshing are recorded.

[0011] Optionally, in a fifth implementation of the first aspect of the present invention, the stiffness parameters of the cracked tooth are calculated according to the confirmed tooth pair meshing force, and the tooth pair meshing stiffness is calculated based on the calculated stiffness parameters, including: calculating the load angle at the actual meshing point E1; calculating the stiffness parameters of the cracked tooth according to the confirmed tooth pair meshing force and the load angle at the actual meshing point E1, the stiffness parameters including bending stiffness, axial compression stiffness, shear stiffness and Hertz contact stiffness.

[0012] Optionally, in a sixth implementation of the first aspect of the present invention, the comprehensive meshing stiffness of the gear pair is calculated based on the calculated tooth pair meshing stiffness, and the matrix deformation stiffness is calculated. The meshing stiffness of the gear pair is calculated based on the calculated comprehensive meshing stiffness of the gear pair and the calculated matrix deformation stiffness, including: calculating the comprehensive meshing stiffness of the gear pair based on the load coordination equation according to the calculated tooth pair meshing stiffness; calculating the matrix deformation stiffness and obtaining the matrix deformation correction coefficient; calculating the meshing stiffness of the gear pair based on the comprehensive meshing stiffness of the gear pair, the matrix deformation stiffness and the matrix deformation correction coefficient.

[0013] The second aspect of the present invention provides a device for determining the meshing stiffness of a cracked spur gear, comprising: a construction module for constructing a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system, and confirming coordinate data related to the tooth root crack based on the constructed cracked gear tooth plastic deflection analysis model; a first calculation module for calculating the rotation angle between the local coordinate system and the global coordinate system based on the confirmed coordinate data, and calculating the tooth pair meshing error based on the coordinate data and the calculated rotation angle; a confirmation module for The calculated tooth pair meshing error confirms the tooth pair number involved in the meshing, and confirms the tooth pair meshing force corresponding to the tooth pair number involved in the meshing; the second calculation module is used to calculate the stiffness parameter of the cracked gear tooth according to the confirmed tooth pair meshing force, and obtain the tooth pair meshing stiffness based on the calculated stiffness parameter; the third calculation module is used to calculate the comprehensive meshing stiffness of the gear pair according to the calculated tooth pair meshing stiffness, and calculate the matrix deformation stiffness, and calculate the gear pair meshing stiffness according to the calculated comprehensive meshing stiffness of the gear pair and the calculated matrix deformation stiffness.

[0014] A third aspect of the present invention provides a device for determining the meshing stiffness of a cracked spur 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 a cracked spur gear performs each step of the method for determining the meshing stiffness of a cracked spur gear described 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 cracked spur gear are implemented.

[0016] In the technical solution of the present invention, a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system is constructed to confirm the coordinate data related to the tooth root crack; and the rotation angle between the two coordinate systems is calculated; the tooth pair meshing error is calculated based on the coordinate data and the rotation angle to confirm the tooth pair number involved in the meshing and the corresponding tooth pair meshing force; the stiffness parameters of the cracked gear tooth are calculated according to the tooth pair meshing force, and the tooth pair meshing stiffness is calculated; the comprehensive meshing stiffness of the gear pair is calculated according to the tooth pair meshing stiffness, and the meshing stiffness of the gear pair is calculated according to the calculated comprehensive meshing stiffness of the gear pair and the pre-calculated matrix deformation stiffness; the method disclosed in the present application improves the modeling accuracy of the meshing stiffness of the cracked spur gear pair, and can accurately determine the meshing stiffness of the gear pair during the meshing process of the cracked spur gear pair. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A first flow chart of a method for determining meshing stiffness provided in an embodiment of the present invention;

[0018] Figure 2 A schematic diagram of a structure of a device for determining meshing stiffness of a cracked spur gear provided by an embodiment of the present invention;

[0019] Figure 3 A schematic diagram of the structure of a device for determining the meshing stiffness of a cracked spur gear provided by an embodiment of the present invention;

[0020] Figure 4 This is the analysis model of plastic deflection of cracked gear teeth;

[0021] Figure 5 The load angle calculation model for the cracked gear tooth after plastic deflection;

[0022] Figure 6 The figure is a comparison of the meshing stiffness calculation results of cracked spur gear pairs and crack-free spur gear pairs;

[0023] Figure 7 Calculation results of mesh stiffness of cracked spur gear pair under different plastic deflection angles. DETAILED DESCRIPTION

[0024] The present invention provides a method, device, equipment and storage medium for determining the meshing stiffness of a cracked spur 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.

[0025] For ease of understanding, the specific process of the embodiment of the present invention is described below. Figures 1 to 6 , an embodiment of a method for determining the meshing stiffness of a cracked spur gear in an embodiment of the present invention includes:

[0026] 101. Construct a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system, and confirm coordinate data related to the tooth root crack based on the constructed cracked gear tooth plastic deflection analysis model;

[0027] In this embodiment, by constructing a cracked gear tooth plastic deflection analysis model, the influence of the crack on the gear tooth performance can be captured and analyzed more accurately, thereby improving the accuracy of the analysis.

[0028] 102. Calculate a rotation angle between a local coordinate system and a global coordinate system based on the confirmed coordinate data, and calculate a tooth pair meshing error based on the coordinate data and the calculated rotation angle;

[0029] 103. Confirm the number of the tooth pair involved in the meshing based on the calculated tooth pair meshing error, and confirm the tooth pair meshing force corresponding to the tooth pair number involved in the meshing;

[0030] 104. Calculate the stiffness parameter of the cracked gear tooth according to the confirmed tooth pair meshing force, and calculate the tooth pair meshing stiffness based on the calculated stiffness parameter;

[0031] 105. Calculate the comprehensive meshing stiffness of the gear pair according to the calculated meshing stiffness of the tooth pair, and calculate the matrix deformation stiffness, and calculate the meshing stiffness of the gear pair according to the calculated comprehensive meshing stiffness of the gear pair and the calculated matrix deformation stiffness;

[0032] The technical solution disclosed in the present application starts with confirming the coordinate data related to the tooth root crack, and gradually derives the tooth pair meshing error, tooth pair meshing force, cracked tooth stiffness parameters, tooth pair meshing stiffness, and the comprehensive meshing stiffness and matrix deformation stiffness of the gear pair. It not only considers the influence of the crack on the local performance of the gear tooth, but also comprehensively evaluates the influence of the crack on the meshing performance of the entire gear pair by calculating the comprehensive meshing stiffness and matrix deformation stiffness of the gear pair, which provides an important basis for the design and optimization of the gear transmission system and helps to improve the reliability and durability of the gear transmission system.

[0033] The present application discloses a method for determining the meshing stiffness of a cracked spur gear, which comprises constructing a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system to confirm coordinate data related to a tooth root crack; and calculating a rotation angle between the two coordinate systems; calculating a tooth pair meshing error based on the coordinate data and the rotation angle to confirm the number of the tooth pair involved in the meshing and the corresponding tooth pair meshing force; calculating the stiffness parameters of the cracked gear tooth according to the tooth pair meshing force, and calculating the tooth pair meshing stiffness; calculating the comprehensive meshing stiffness of the gear pair according to the tooth pair meshing stiffness, and calculating the meshing stiffness of the gear pair according to the calculated comprehensive meshing stiffness of the gear pair and the pre-calculated matrix deformation stiffness; the method disclosed in the present application improves the meshing stiffness modeling accuracy of the cracked spur gear pair, so as to accurately determine the meshing stiffness of the gear pair during the meshing process of the cracked spur gear pair.

[0034] A second embodiment of the method for determining the meshing stiffness of a cracked spur gear in the embodiment of the present invention includes:

[0035] 201. Constructing a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system, wherein the cracked gear tooth plastic deflection analysis model includes a tooth root crack BC;

[0036] 202. Confirming coordinate data related to the gear crack based on the constructed cracked gear tooth plastic deflection analysis model, wherein the coordinate data includes the coordinate of the crack starting point C, the coordinate of the crack end point B, and the coordinate of the symmetric point D of the crack starting point C with respect to the center line of the cracked gear tooth;

[0037] 203. The coordinates of the end point O of BD are calculated based on the coordinates of the crack end point B and the coordinates of the symmetric point D.

[0038] In this embodiment, taking the driving wheel as an example, the cracked gear tooth plastic deflection analysis model is as follows: Figure 4 As shown; Figure 4 In the figure, the dotted line represents the cracked gear tooth profile after plastic deflection, and the solid line represents the normal gear tooth profile; BC is the tooth root crack, q c and α c are the crack depth and crack inclination angle respectively, D is the crack starting point C about the gear tooth center line O pThe symmetrical point of F1; C1 is the crack starting point after the plastic deflection of the cracked gear tooth, E1 is the actual meshing point of the cracked gear tooth, E2 is the intersection of the meshing line A1E1 and the tooth profile on the driving side of the normal gear tooth, and E3 is the corresponding point of point E1 before the plastic deflection of the cracked gear tooth; F1 and F2 are the midpoints of the tooth top of the cracked gear tooth before and after the plastic deflection, respectively.

[0039] According to previous studies, the part above CD of the cracked gear tooth will rotate around the midpoint O of BD under the action of external load by a certain cracked gear tooth plastic deflection angle θ. c , which causes the meshing point of the cracked gear teeth to shift.

[0040] In order to facilitate the subsequent modeling research, the global coordinate system XO of the cracked spur gear pair is established. p -Y and local coordinate system x2-O-y2; where the global coordinate system XO p -Y The positive half axis of the Y axis is from O p Point to the tangent point A1 between the meshing line A1E1 of the spur gear pair and the base circle of the driving wheel. The X-axis is perpendicular to the Y-axis and the origin is at O p ;The positive half axis of the y2 axis of the local coordinate system x2-O-y2 points from O to D, the x2 axis is perpendicular to the y2 axis, and the origin is located at the midpoint O of BD.

[0041] Global coordinate system XO p The coordinate of C under -Y can be determined by the following formula:

[0042] (1)

[0043] In the formula, a1, b1, c1, k r , b r is the crack initiation point related parameter, which can be obtained by the following formula:

[0044] (2)

[0045] In the formula, r i is the tooth root transition curve radius of gear i, and α2 is the angle between the line connecting the starting point of the gear tooth profile and the tooth center line and the gear tooth center line. r and Y r It can be obtained from formula (3):

[0046] (3)

[0047] In the formula, R fi is the root circle radius of gear i, r i is the tooth root transition curve radius of gear i, θ ri is the tooth root crack parameter angle, which can be obtained by the following formula:

[0048] (4)

[0049] Among them, R bi is the base circle radius of gear i.

[0050] Similarly, the global coordinate system XO can be obtained p -The coordinate of B under Y is as follows:

[0051] (5)

[0052] In the formula, a2, b2, c2, k r2 , b r2 is the crack endpoint related parameter, which can be obtained by the following formula:

[0053] (6)

[0054] Since point D and point C are symmetrical about the center line of the gear tooth, the coordinates of point D can be obtained by formula (7):

[0055] (7)

[0056] Therefore, according to the coordinates of the crack end point B and the coordinates of the symmetric point D, the coordinates of the midpoint O of BD can be obtained.

[0057] A third embodiment of the method for determining the meshing stiffness of a cracked spur gear in the embodiment of the present invention includes:

[0058] 301. Calculate the rotation angle between the local coordinate system and the global coordinate system based on the coordinates of the crack endpoint B and the symmetric point D;

[0059] 302. Obtain coordinate data of the intersection point E2 of the meshing line of the cracked gear tooth and the tooth profile of the normal gear tooth driving side and the load angle at the intersection point E2;

[0060] 303. Based on the obtained load angle of the intersection point E2 and the rotation angle, an iterative algorithm is used to confirm the coordinates of the actual meshing point E1 of the cracked gear tooth;

[0061] 304. Calculate the tooth pair meshing error based on the confirmed coordinate data of the intersection point E2 and the confirmed coordinate data of the actual meshing point E1.

[0062] A fourth embodiment of the method for determining the meshing stiffness of a cracked spur gear in the embodiment of the present invention includes:

[0063] 401. Construct a first global coordinate expression of a corresponding point E3 of an actual meshing point E1 before plastic deflection of a cracked gear tooth in a global coordinate system, and convert the first global coordinate expression into a first local coordinate expression in a local coordinate system according to the rotation angle;

[0064] 402. Construct a second local coordinate expression of the actual meshing point E1 based on the first local coordinate expression, and convert the second local coordinate expression into a second global coordinate expression in all coordinate systems according to the rotation angle;

[0065] 403. Based on the coordinate data of the intersection point E2, the load angle at the intersection point E2 and the second global coordinate expression, according to the meshing line equation, an iterative algorithm is used to confirm the coordinates of the actual meshing point E1.

[0066] In this example, see Figure 4 , local coordinate system x2-O-y2 to global coordinate system XO p -Y rotation angle θ0 can be obtained by the following formula:

[0067] (8)

[0068] Point E3 on the involute is in the global coordinate system XO p -Y coordinates are:

[0069] (9)

[0070] In the formula, θ E3 is the load angle of gear i at point E3, and α2 is the angle between the line connecting the starting point of the tooth profile and the tooth center line and the gear tooth center line.

[0071] Convert the coordinates of point E3 from the global coordinate system to the local coordinate system, and we can get:

[0072] (10)

[0073] in, and Represents the horizontal and vertical coordinates of the midpoint O of BD in the global coordinate system.

[0074] As can be seen from the previous text, E1 is the plastic deflection θ of E3 c Therefore, the coordinates of point E1 in the local coordinate system x2-O-y2 are:

[0075] (11)

[0076] Convert the coordinates of E1 in the local coordinate system x2-O-y2 to the global coordinate system XO p -Y coordinates, as shown in formula (12):

[0077] (12)

[0078] Since points E1 and E2 are on the meshing line, the meshing line equation needs to be satisfied, namely:

[0079] (13)

[0080] In the formula, θ E2 is the load angle of gear i at point E2.

[0081] For a certain position of E2, that is, given a θ E2 By using equations (1)-(13), we can search for θ that meets the preset requirements according to the iterative algorithm. E3 ; Specifically, in the first iteration, let θ E3 is equal to the given θ E2 , calculate the coordinates of E1 by using formulas (1)-(12), and then recalculate the ordinate of E1 by using formula (13). Confirm the calculation error based on the recalculated ordinate of E1 and the ordinate of E1 calculated by formula (12), and adjust θ based on the confirmed calculation error. E3 , and then based on the newly adjusted θ E3 The value of is returned when the steps of calculating the coordinates of E1 by formulas (1)-(12) are executed. When the preset number of iterations or the adjusted θ is reached E3 When the preset accuracy requirements are met, the output is based on the latest θ E3 The calculated E1 coordinates are used as the final coordinates; that is, first give an E2 and θ E2 , to obtain the initial iteration process θ E3 , by reverse calculation, the coordinates of point E1 are obtained, and then the calculation error is confirmed based on the new and old coordinates of point E1 to adjust θ E3 , then based on the newly adjusted θ E3 Recalculate the coordinates of point E1; since the θ obtained in one calculation E3 The accuracy may not meet the preset accuracy requirements. Therefore, it is necessary to iteratively adjust θ based on E2 at a given position using an iterative algorithm. E3 , through the iterative algorithm and the θ in each iteration E3 Finally, the coordinates of E1 are determined, and then the equation (12) can be used to determine the coordinates of point E1 in the global coordinate system XO p -Y coordinate.

[0082] Therefore, the distance between point E1 and point E2 can be obtained by formula (14):

[0083] (14)

[0084] Depend on Figure 4 It can be seen that after plastic deflection, the meshing point of the cracked gear moves from E2 to E1, and the displacement is δ E1E2 This displacement will cause a certain tooth pair meshing error in the tooth pair where the cracked tooth is located, so it can also be recorded as S k, and there is S k =δ E1E2 .

[0085] A fifth embodiment of the method for determining the meshing stiffness of a cracked spur gear in the embodiment of the present invention includes:

[0086] 501. Based on the calculated tooth pair meshing error, the tooth pair meshing force of each tooth pair is calculated according to the stiffness load coordination equation;

[0087] 502. When the calculated tooth pair meshing force is greater than zero, it indicates that the tooth pair corresponding to the tooth pair meshing force is involved in meshing, and the tooth pair number corresponding to the tooth pair involved in meshing and the tooth pair meshing force are recorded.

[0088] In this embodiment, according to the gear meshing principle, the meshing stiffness of the meshing tooth pair and the distributed meshing force thereof need to satisfy the stiffness load coordination equation shown in formula (15):

[0089] (15)

[0090] In the formula, R bdp and T p are the base circle radius of the driving side of the active wheel and the torque transmitted, F k , k k and S k (k=1,2,3,…,N) is the meshing force, meshing stiffness and meshing error of tooth pair k, F= , F and S are the meshing force and meshing error of the gear pair respectively, N is the number of tooth pairs, which is a positive integer greater than 1; in this step, K is the comprehensive meshing stiffness of the gear pair without considering the influence of matrix deformation, which is a known value; for the tooth pairs that are not involved in meshing, the meshing error of the tooth pairs can be pre-set or calculated by the existing formula for calculating the separation distance of the tooth pairs.

[0091] It should be noted that in the embodiments of the present application and S are preset; when calculating, the first formula in the stiffness load coordination equation can be rearranged and F k To one side of the equation, the other side is left and , and then rearrange the second equation in the stiffness load coordination equation; for example, when calculating When , the second equation in the stiffness load coordination equation can be used to construct a , , , , , The constructed equation is then used to deduce , and according to this method, other F k The solution equation of is derived in the same way as The related equation will be related to F k Substituting the relevant equations into the first equation after rearrangement in the above load coordination equation, the tooth pair meshing force corresponding to tooth pair 1 can be obtained , and then through the obtained calculate ; F corresponding to other tooth pairs k It can also be obtained in the same way; where k k is the initial tooth pair meshing stiffness of each tooth pair. In the present application, there is no limitation on the method for obtaining the initial tooth pair meshing stiffness of each tooth pair, and it can be obtained by any existing method.

[0092] Formula (15) can be used to determine the number of the sliced ​​gear pairs involved in meshing. The specific method is as follows: first, the initial value of the meshing stiffness of each sliced ​​gear pair, the dynamic meshing torque of the gear pair, and the meshing error of each sliced ​​gear pair are substituted into the stiffness load coordination equation to obtain the meshing force of each meshing tooth pair; when the meshing force F of tooth pair k is k <0, indicating that the tooth pair k is not involved in meshing, that is, the corresponding parameters are removed from the load-deformation coordination equation and the calculation is performed again until the final tooth pair number involved in meshing and its meshing force F are determined. k until.

[0093] A sixth embodiment of the method for determining the meshing stiffness of a cracked spur gear in the embodiment of the present invention includes:

[0094] 601. Calculate the load angle at the actual meshing point E1;

[0095] 602. Calculate the stiffness parameters of the cracked tooth according to the confirmed tooth pair meshing force and the load angle at the actual meshing point E1, wherein the stiffness parameters include bending stiffness, axial compression stiffness, shear stiffness and Hertz contact stiffness.

[0096] In this embodiment, the calculation model of the cracked gear tooth load angle in the cracked spur gear pair after plastic deflection is as follows: Figure 5 As shown in the figure, point C is the intersection of the tooth root crack and the gear tooth profile, point E1 is the actual meshing point of the gear teeth, point F2 is the intersection of the cracked gear tooth centerline and the cracked gear tooth top, point S is the corresponding point of point E1 on the other side of the gear tooth centerline, and α Ep and α2 are the pressure angle at the meshing point E1 and the corresponding center angle of the gear tooth driving side, respectively. Ep is the load angle at the meshing point E1, F k 、F a and F bare the gear meshing force, its horizontal component and its vertical component distributed to the cracked tooth in tooth pair k, respectively, and A1E1 is the meshing line of the spur gear pair. q 、h x and h are the vertical distances from the crack end point, the microelement dx and the meshing point E1 to the center line of the gear tooth, respectively; x and d are the horizontal distances from the microelement dx and the meshing point E1 to point C, respectively.

[0097] According to the energy method, the bending stiffness k of the cracked gear tooth bi,k , axial compression stiffness k ai,k and shear stiffness k si,k It can be obtained from equations (16)-(18):

[0098] (16)

[0099] (17)

[0100] (18)

[0101] In the formula, E i and v i are the elastic modulus and Poisson's ratio of gear i, θ Ei is the load angle of gear i in tooth pair k at the meshing point E1 (where i=p or g, p represents the driving gear, g represents the driving and driven gears), α2 is the angle between the tooth profile starting point-tooth center line and the gear tooth center line, B is the gear tooth width, h q 、h x and h c are the vertical distances from the crack starting point, the microelement dx and point C to the center line of the gear tooth, respectively, c and α c are the crack depth and crack inclination angle respectively, and α is the pressure angle at the microelement dx.

[0102] Hertzian contact stiffness k of meshing tooth pair hk , can be obtained by formula (19):

[0103] (19)

[0104] Where b Ek and ρ Ei are the Hertzian contact half-width of the spur gear pair k at the meshing point E1 and the curvature radius of the gear i in the tooth pair k at the meshing point E1, E i and v i are the elastic modulus and Poisson's ratio of gear i respectively; b Ek It can be obtained by the following formula:

[0105] (20)

[0106] In the formula, F k is the meshing force of tooth pair K.

[0107] Depend on Figure 5 It can be seen that the load angle of the cracked gear at the meshing point E1 at time t is , can be obtained by formula (21):

[0108] (twenty one)

[0109] Where, X A1 and Y A1 Point A1 is in the global coordinate system XO p - Y coordinates, X F2 and Y F2 They are respectively F2 point in the global coordinate system XO p -The horizontal and vertical coordinates under Y.

[0110] Point A1 is in the global coordinate system XO p The horizontal and vertical coordinates under -Y can be obtained by formula (22):

[0111] (twenty two)

[0112] In the formula, R bi is the base circle radius of gear i, α E2 is the pressure angle of gear i at point E2.

[0113] The horizontal and vertical coordinates of point F2 in the local coordinate system x2-O-y2 can be obtained by formula (23):

[0114] (twenty three)

[0115] In the formula, x F1 and F1 are the horizontal and vertical coordinates of point F1 in the local coordinate system x2-O-y2, which can be obtained by formula (24):

[0116] (twenty four)

[0117] Where, X F1 and Y F1 They are respectively F1 point in the global coordinate system XO p -The horizontal and vertical coordinates under Y can be obtained by the following formula:

[0118] (25)

[0119] In the formula, θ i =π / (2z i )-[inv(α ai )-inv(αi )]; inv is the involute equation, and inv(x)=tan(x)-x, α ai is the pressure angle of gear i at the tooth tip circle, α i is the pressure angle of gear i at the pitch circle.

[0120] According to the energy method, the meshing stiffness of each tooth pair is It can be obtained from formula (26):

[0121] (26)

[0122] The parameters in the formula can be determined by formulas (16)-(25).

[0123] A seventh embodiment of the method for determining the meshing stiffness of a cracked spur gear in the embodiment of the present invention includes:

[0124] 701. According to the calculated meshing stiffness of the tooth pair, the comprehensive meshing stiffness of the gear pair is calculated based on the load coordination equation;

[0125] 702. Calculate the deformation stiffness of the matrix and obtain the matrix deformation correction coefficient;

[0126] 703. Calculate the meshing stiffness of the gear pair based on the comprehensive meshing stiffness of the gear pair, the matrix deformation stiffness, and the matrix deformation correction coefficient.

[0127] In this embodiment, according to the gear meshing principle, the meshing stiffness of the meshing tooth pair and the distributed meshing force thereof need to satisfy the stiffness-load coordination equation shown in formula (15):

[0128] (15)

[0129] In the formula, R bdp and T p are the base circle radius of the driving side of the active wheel and the torque transmitted, F k , k k and S k (k=1,2,3,…,N) is the meshing force, meshing stiffness and meshing error of tooth pair k, F and S are the meshing force and meshing error of gear pair respectively, N is the number of tooth pairs, which is a positive integer greater than 1; after confirming the tooth pairs involved in meshing according to the above steps, and according to the F corresponding to the tooth pair k , k k and S k , the comprehensive meshing stiffness K of the gear pair can be recalculated; for the tooth pairs that are not involved in the meshing, the tooth pair meshing error can be preset or calculated using the existing formula for calculating the tooth pair separation distance.

[0130] During the gear meshing process, the gear matrix will also undergo a certain deformation. The stiffness corresponding to this deformation is the matrix stiffness. , can be obtained by the following formula:

[0131] (27)

[0132] In the formula, μ f S is the distance from the meshing line and the focus of the gear tooth symmetry line to the tooth root circle. f is the base circle arc corresponding to the entire gear tooth profile; L * 、M * , P * and Q * The coefficients can be obtained by the following polynomial:

[0133] (28)

[0134] In the formula, X* is L * 、M * , P * and Q * Any one of A, , C, D, and See Table 1 for the values, h f =r f / r int , r f is the tooth root radius, r int is the radius of the gear shaft hole, θ f is the central angle of the gear tooth profile.

[0135] Table 1 A , C, D, and Value

[0136]

[0137] Finally, the gear pair meshing stiffness can be obtained according to the energy method: , as shown in formula (29):

[0138] (29)

[0139] In the formula, ε i is the matrix deformation correction coefficient, which is taken as 1.1 in this application.

[0140] The parameters of the cracked spur gear pair studied in this example are shown in Table 2.

[0141] Table 2 Main parameters of the system

[0142]

[0143] According to the parameters shown in Table 2, the gear pair meshing stiffness is calculated by writing an algorithm program in MATLAB. The calculation results are shown in Figure 6 and Figure 7 shown.

[0144] Depend on Figure 6 It can be seen that the meshing stiffness amplitude of the cracked spur gear pair is smaller than that of the uncracked spur gear pair. The reason is that the root crack reduces the rigidity of the meshing teeth of the gear pair.

[0145] Depend on Figure 7 It can be seen that with the increase of the plastic deflection angle of the cracked gear tooth, the meshing stiffness amplitude of the cracked spur gear pair increases accordingly; this phenomenon emphasizes the necessity of considering the influence of the plastic deflection of the cracked gear tooth on the load angle of the meshing gear tooth under large plastic deflection angles.

[0146] The method disclosed in the present application analyzes the meshing process of a cracked spur gear pair based on the gear meshing principle, establishes a cracked gear tooth plastic deflection analysis model, and analyzes the influence of plastic deformation on the geometric relationship of cracked gear teeth; studies the influence mechanism of the gear tooth centerline deflection caused by the tooth root crack on the tooth pair meshing error and its meshing stiffness, and obtains the meshing stiffness of the cracked spur gear pair by modifying the load-deformation coordination equation of the spur gear pair; the meshing stiffness modeling method of a cracked spur gear pair of an air compressor considering the meshing excitation induced by the plastic deflection angle described in the present application further considers the gear tooth centerline deflection caused by the plastic deflection on the basis of the previous model, as well as the influence of this phenomenon on the tooth pair meshing error, load angle and meshing stiffness. This method improves the modeling accuracy of the meshing stiffness of the cracked spur gear pair, and can provide assistance for improving the understanding of the meshing and dynamic mechanisms of the cracked spur gear pair.

[0147] The above describes the method for determining the meshing stiffness of a cracked spur gear in an embodiment of the present invention. The following describes the device for determining the meshing stiffness of a cracked spur gear in an embodiment of the present invention. Figure 2 , an embodiment of a device for determining meshing stiffness of a cracked spur gear in an embodiment of the present invention comprises:

[0148] A construction module 801 is used to construct a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system, and confirm coordinate data related to a tooth root crack based on the constructed cracked gear tooth plastic deflection analysis model;

[0149] A first calculation module 802, for calculating a rotation angle between a local coordinate system and a global coordinate system based on the confirmed coordinate data, and calculating a tooth pair meshing error based on the coordinate data and the calculated rotation angle;

[0150] A confirmation module 803 is used to confirm the number of the tooth pair involved in the meshing based on the calculated tooth pair meshing error, and to confirm the tooth pair meshing force corresponding to the tooth pair number involved in the meshing;

[0151] A second calculation module 804 is used to calculate the stiffness parameter of the cracked gear tooth according to the confirmed tooth pair meshing force, and calculate the tooth pair meshing stiffness based on the calculated stiffness parameter;

[0152] The third calculation module 805 is used to calculate the comprehensive meshing stiffness of the gear pair according to the calculated tooth pair meshing stiffness, and calculate the matrix deformation stiffness, and calculate the meshing stiffness of the gear pair according to the calculated comprehensive meshing stiffness of the gear pair and the calculated matrix deformation stiffness.

[0153] 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.

[0154] above Figure 2 The meshing stiffness determination device for a cracked spur gear in an embodiment of the present invention is described in detail from the perspective of modular functional entities. The meshing stiffness determination device for a cracked spur gear in an embodiment of the present invention is described in detail from the perspective of hardware processing.

[0155] Figure 3 1 is a schematic diagram of the structure of a device for determining the meshing stiffness of a cracked spur gear provided by an embodiment of the present invention. The device 900 for determining the meshing stiffness of a cracked spur 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 cracked spur 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 cracked spur gear to implement the steps of the method for determining the meshing stiffness of a cracked spur gear provided in the above-mentioned method embodiments.

[0156] The meshing stiffness determination device 900 for a cracked spur 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 3The structure of the device for determining the meshing stiffness of a cracked spur gear shown does not constitute a limitation on the device for determining the meshing stiffness of a cracked spur gear, and may include more or less components than shown in the figure, or combine certain components, or arrange the components differently.

[0157] 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. The computer-readable storage medium stores instructions, which, when executed on a computer, enable the computer to execute the steps of a method for determining the meshing stiffness of a cracked spur gear.

[0158] 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.

[0159] 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.

[0160] 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 cracked spur gear, characterized in that: include: A cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system is constructed. Coordinate data related to the tooth root crack is confirmed based on the constructed cracked gear tooth plastic deflection analysis model. Specifically: Constructing a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system, wherein the cracked gear tooth plastic deflection analysis model includes a tooth root crack BC; Based on the constructed cracked gear tooth plastic deflection analysis model, coordinate data related to the gear crack is confirmed, wherein the coordinate data includes the coordinate of the crack starting point C, the coordinate of the crack end point B, and the coordinate of the symmetric point D of the crack starting point C with respect to the center line of the cracked gear tooth; The coordinates of the midpoint O of BD are calculated based on the coordinates of the crack endpoint B and the coordinates of the symmetric point D; The rotation angle between the local coordinate system and the global coordinate system is calculated based on the confirmed coordinate data, and the tooth pair meshing error is calculated based on the coordinate data and the calculated rotation angle, specifically: The rotation angle between the local coordinate system and the global coordinate system is calculated based on the coordinates of the crack end point B and the symmetric point D; Obtain the coordinate data of the intersection point E2 of the meshing line of the cracked gear tooth and the tooth profile of the normal gear tooth driving side and the load angle at the intersection point E2; Based on the obtained load angle of the intersection point E2 and the rotation angle, an iterative algorithm is used to confirm the coordinates of the actual meshing point E1 of the cracked gear tooth; Calculating the tooth pair meshing error based on the confirmed coordinate data of the intersection point E2 and the confirmed coordinates of the actual meshing point E1; Based on the calculated tooth pair meshing error, the tooth pair numbers involved in the meshing are confirmed, and the tooth pair meshing force corresponding to the tooth pair numbers involved in the meshing is confirmed, specifically: Based on the calculated tooth pair meshing error, the tooth pair meshing force of each tooth pair is calculated according to the stiffness load coordination equation; When the calculated tooth pair meshing force is greater than zero, it indicates that the tooth pair corresponding to the tooth pair meshing force is involved in meshing, and the tooth pair number and the tooth pair meshing force corresponding to the tooth pair involved in meshing are recorded; Calculating the stiffness parameter of the cracked gear tooth according to the confirmed tooth pair meshing force, and calculating the tooth pair meshing stiffness based on the calculated stiffness parameter; The gear pair comprehensive meshing stiffness is calculated based on the calculated tooth pair meshing stiffness, and the matrix deformation stiffness is calculated. The gear pair meshing stiffness is calculated based on the calculated gear pair comprehensive meshing stiffness and the calculated matrix deformation stiffness.

2. The method for determining the meshing stiffness of a cracked spur gear according to claim 1, characterized in that: The method of using an iterative algorithm to confirm the coordinates of the actual meshing point E1 of the cracked gear tooth based on the obtained load angle of the intersection point E2 and the rotation angle includes: Constructing a first global coordinate expression of a corresponding point E3 of the actual meshing point E1 before the cracked gear tooth plastic deflects in the global coordinate system, and converting the first global coordinate expression into a first local coordinate expression in the local coordinate system according to the rotation angle; Constructing a second local coordinate expression of the actual meshing point E1 based on the first local coordinate expression, and converting the second local coordinate expression into a second global coordinate expression in the entire coordinate system according to the rotation angle; Based on the coordinate data of the intersection point E2 and the load angle at the intersection point E2 and the second global coordinate expression, an iterative algorithm is used to confirm the coordinates of the actual meshing point E1 according to the meshing line equation.

3. The method for determining the meshing stiffness of a cracked spur gear according to claim 1, characterized in that: The step of calculating the stiffness parameter of the cracked gear tooth according to the confirmed tooth pair meshing force, and calculating the tooth pair meshing stiffness based on the calculated stiffness parameter, comprises: Calculate the load angle at the actual meshing point E1; According to the confirmed tooth pair meshing force and the load angle at the actual meshing point E1, the stiffness parameters of the cracked tooth are calculated, and the stiffness parameters include bending stiffness, axial compression stiffness, shear stiffness and Hertz contact stiffness.

4. The method for determining the meshing stiffness of a cracked spur gear according to claim 1, characterized in that: The method of calculating the comprehensive meshing stiffness of the gear pair according to the calculated meshing stiffness of the tooth pair and calculating the matrix deformation stiffness, and calculating the meshing stiffness of the gear pair according to the calculated comprehensive meshing stiffness of the gear pair and the calculated matrix deformation stiffness, comprises: According to the calculated meshing stiffness of the tooth pair, the comprehensive meshing stiffness of the gear pair is calculated based on the load coordination equation; Calculate the matrix deformation stiffness and obtain the matrix deformation correction coefficient; The gear pair meshing stiffness is calculated based on the gear pair comprehensive meshing stiffness, the matrix deformation stiffness and the matrix deformation correction coefficient.

5. A device for determining the meshing stiffness of a cracked spur gear, characterized in that: include: A construction module is used to construct a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system, and confirm coordinate data related to the tooth root crack based on the constructed cracked gear tooth plastic deflection analysis model. Specifically: construct a cracked gear tooth plastic deflection analysis model including a local coordinate system and a global coordinate system, and the cracked gear tooth plastic deflection analysis model includes a tooth root crack BC; based on the constructed cracked gear tooth plastic deflection analysis model, confirm coordinate data related to the gear crack, and the coordinate data includes the coordinates of the crack starting point C, the coordinates of the crack end point B, and the coordinates of the symmetric point D of the crack starting point C with respect to the center line of the cracked gear tooth; based on the coordinates of the crack end point B and the coordinates of the symmetric point D, calculate the coordinates of the midpoint O of BD; The first calculation module is used to calculate the rotation angle between the local coordinate system and the global coordinate system based on the confirmed coordinate data, and calculate the tooth pair meshing error based on the coordinate data and the calculated rotation angle, specifically: the rotation angle between the local coordinate system and the global coordinate system is calculated based on the coordinates of the crack end point B and the symmetry point D; the coordinate data of the intersection point E2 of the meshing line of the cracked gear tooth and the tooth profile on the driving side of the normal gear tooth and the load angle at the intersection point E2 are obtained; based on the load angle of the obtained intersection point E2 and the rotation angle, the coordinates of the actual meshing point E1 of the cracked gear tooth are confirmed by an iterative algorithm; the tooth pair meshing error is calculated based on the confirmed coordinate data of the intersection point E2 and the confirmed coordinates of the actual meshing point E1; A confirmation module is used to confirm the number of the tooth pair involved in the meshing based on the calculated tooth pair meshing error, and to confirm the tooth pair meshing force corresponding to the tooth pair number involved in the meshing, specifically: based on the calculated tooth pair meshing error, the tooth pair meshing force of each tooth pair is calculated according to the stiffness load coordination equation; When the calculated tooth pair meshing force is greater than zero, it indicates that the tooth pair corresponding to the tooth pair meshing force is involved in meshing, and the tooth pair number and the tooth pair meshing force corresponding to the tooth pair involved in meshing are recorded; A second calculation module is used to calculate the stiffness parameter of the cracked gear tooth according to the confirmed tooth pair meshing force, and calculate the tooth pair meshing stiffness based on the calculated stiffness parameter; The third calculation module is used to calculate the comprehensive meshing stiffness of the gear pair according to the calculated tooth pair meshing stiffness, and calculate the matrix deformation stiffness, and calculate the meshing stiffness of the gear pair according to the calculated comprehensive meshing stiffness of the gear pair and the calculated matrix deformation stiffness.

6. A device for determining the meshing stiffness of a cracked spur gear, characterized in that: The device for determining meshing stiffness of a cracked spur 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 a cracked spur gear to perform each step of the method for determining the meshing stiffness of a cracked spur gear according to any one of claims 1 to 4.

7. 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 a cracked spur gear as described in any one of claims 1 to 4 are implemented.

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