Gear pair meshing stiffness determination method, device, equipment and storage medium

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 gear pair. The method comprises: determining initial information of a gear unit, and calculating the meshing force of a tooth pair based on the initial information of the gear unit to calculate the tooth pair parameters of the tooth pair, and calculating the meshing stiffness of the gear pair based on the calculated tooth pair parameters and the pre-calculated matrix deformation stiffness; acquiring deformation information, and calculating updated information of the gear unit according to the deformation information and the meshing stiffness of the gear pair; judging whether the next moment is a preset iteration end time, and if not, using the updated information of the gear unit as the initial information of the gear unit, and returning to execute the calculation of the meshing force of the tooth pair based on the initial information of the gear unit; the method disclosed in the present application improves the modeling accuracy of the meshing stiffness of the gear pair of a helicopter gear transmission system, and can accurately determine the meshing stiffness of the gear pair in the meshing process of the gear pair under the influence of flexible deformation.

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 gear pair. Background Art

[0002] Gear meshing 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. Existing research shows that during the gear meshing process, components supporting the gears, such as bearings, will also deform, which will affect the meshing position of the gear pair and its meshing stiffness.

[0003] Slender shafts play a key role in the aerospace field, such as in mechanical equipment such as helicopter engines and flight control systems. Due to their unique structural characteristics and applications under specific working conditions, slender shafts are prone to elastic deformation, which affects the meshing of gear pairs. However, in existing research on helicopter gear transmission systems, the analysis of gear pair meshing stiffness often ignores the effect of slender shaft deformation inside the transmission system on the meshing performance. In addition, the complex interaction between slender shaft deformation and gear pair meshing has not been fully studied and explored. The lack of such research not only limits the ability to accurately model the meshing stiffness of helicopter gears, thereby limiting the scope of application and modeling accuracy of the model, but also has an adverse effect on the accuracy of the dynamic modeling of the entire helicopter gear transmission system.

[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 gear pair, which improves the modeling accuracy of the meshing stiffness of the gear pair and can accurately determine the meshing stiffness of the gear pair during the meshing process of the gear pair under the influence of flexible deformation.

[0006] A first aspect of the present invention provides a method for determining the meshing stiffness of a gear pair, comprising: obtaining design parameters and operating parameters of a gear transmission system and calculating an initial value of the meshing stiffness of the gear pair, determining matrix information of a shaft unit, initial information of a gear unit and matrix information of a bearing unit based on the obtained design parameters and operating parameters and the calculated initial value of the meshing stiffness of the gear pair; calculating the meshing force of a tooth pair based on the initial information of the gear unit; calculating tooth pair parameters of a tooth pair based on the meshing force of the tooth pair, and calculating the deformation stiffness of a matrix; calculating the meshing stiffness of a gear pair based on the calculated tooth pair parameters and the deformation stiffness of a matrix; obtaining deformation information, and calculating updated information of the gear unit based on the deformation information and the meshing stiffness of the gear pair; judging whether the next moment is a preset iteration end time, and if not, using the updated information of the gear unit as the initial information of the gear unit, and returning to execute the calculation of the meshing force of a tooth pair based on the initial information of the gear unit.

[0007] Optionally, in a first implementation method of the first aspect of the present invention, the matrix information of the shaft unit, the initial information of the gear unit and the matrix information of the bearing unit are determined based on the acquired design parameters and operating parameters and the calculated initial value of the gear pair meshing stiffness, including: determining the matrix information of the shaft unit based on the acquired gear design parameters, the matrix information of the shaft unit including the deformation matrix, stiffness matrix, mass matrix and damping matrix of the shaft unit based on the local coordinate system; determining the matrix information of the bearing unit based on the acquired gear design parameters, the matrix information of the bearing unit including the support stiffness matrix and damping matrix of the bearing unit based on the global coordinate system; calculating the initial value of the gear pair meshing stiffness based on the energy method; the gear design parameters include the initial value of the gear pair side clearance, the initial value of the dynamic transmission error and the initial value of the dynamic transmission error speed, and confirming the initial information of the gear unit based on the initial value of the gear pair side clearance, the initial value of the dynamic transmission error, the initial value of the dynamic transmission error speed and the calculated initial value of the gear pair meshing stiffness.

[0008] Optionally, in a second implementation method of the first aspect of the present invention, the calculation of the tooth pair meshing force based on the initial information of the gear unit includes: obtaining the initial tooth pair meshing stiffness of the tooth pair; based on the obtained design parameters and operating condition parameters, the obtained initial tooth pair meshing stiffness and the initial information of the gear unit, using a pre-constructed load coordination equation to calculate the tooth pair meshing force.

[0009] Optionally, in a third implementation of the first aspect of the present invention, the tooth pair parameters of the tooth pair are calculated based on the tooth pair meshing force, and the matrix deformation stiffness is calculated, including: calculating the potential energy stiffness of the tooth pair based on the tooth pair meshing force, the potential energy stiffness including Hertz contact stiffness, bending stiffness, radial compression stiffness and shear stiffness; calculating the tooth pair meshing stiffness according to the potential energy stiffness, and calculating the comprehensive meshing stiffness of the gear pair according to the tooth pair meshing stiffness and the tooth pair meshing force, the comprehensive meshing stiffness of the gear pair being the tooth pair parameters; calculating the matrix deformation stiffness based on the acquired design parameters and operating condition parameters.

[0010] Optionally, in a fourth implementation method of the first aspect of the present invention, the calculation of the meshing stiffness of the gear pair based on the calculated tooth pair parameters and the matrix deformation stiffness includes: obtaining a 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 obtained matrix deformation correction system.

[0011] Optionally, in a fifth implementation of the first aspect of the present invention, the deformation information is obtained and the update information of the gear unit is calculated based on the deformation information and the gear pair meshing stiffness, including: obtaining the deformation information, calculating the deformation gear pair side clearance, the deformation dynamic transmission error and the deformation dynamic transmission error speed based on the deformation information; calculating the update information of the gear unit based on the deformation gear pair side clearance, the deformation dynamic transmission error, the deformation dynamic transmission error speed and the calculated gear pair meshing stiffness.

[0012] Optionally, in a sixth implementation method of the first aspect of the present invention, the determination of whether the next moment is a preset iteration end time includes: if so, assembling the update information of the gear unit, the confirmed matrix information of the shaft unit, and the matrix information of the bearing unit based on the finite element method to obtain the dynamic equation of the gear transmission system.

[0013] According to a second aspect of the present invention, there is provided a device for determining the meshing stiffness of a gear pair, comprising: a determination module for acquiring design parameters and operating parameters of a gear transmission system and calculating an initial value of the meshing stiffness of a gear pair, and determining matrix information of a shaft unit, initial information of a gear unit and matrix information of a bearing unit based on the acquired design parameters and operating parameters and the calculated initial value of the meshing stiffness of a gear pair; a first calculation module for calculating the meshing force of a tooth pair based on the initial information of the gear unit; a second calculation module for calculating the tooth pair parameters of a tooth pair based on the meshing force of the tooth pair, and calculating the deformation stiffness of a matrix; a third calculation module for calculating the meshing stiffness of a gear pair based on the calculated tooth pair parameters and the deformation stiffness of a matrix; an update module for acquiring deformation information, and calculating the updated information of a gear unit based on the deformation information and the meshing stiffness of a gear pair; an iteration module for determining whether the next moment is a preset iteration end time, and if not, using the updated information of the gear unit as the initial information of the gear unit, and returning to execute the calculation of the meshing force of a tooth pair based on the initial information of the gear unit.

[0014] A third aspect of the present invention provides a gear pair meshing stiffness determination device, the gear pair meshing stiffness determination device comprising: a memory and at least one processor, the memory storing instructions; at least one of the processors calls the instructions in the memory to enable the gear pair meshing stiffness determination device to perform each step of the gear pair meshing stiffness determination method 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 gear pair are implemented.

[0016] In the technical solution of the present invention, the initial information of the gear unit is determined, and the tooth pair meshing force is calculated based on the initial information of the gear unit to calculate the tooth pair parameters of the tooth pair, and the gear pair meshing stiffness is calculated based on the calculated tooth pair parameters and the pre-calculated matrix deformation stiffness; the deformation information is obtained, and the updated information of the gear unit is calculated according to the deformation information and the gear pair meshing stiffness; it is determined whether the next moment is a preset iteration end time, if not, the updated information of the gear unit is used as the initial information of the gear unit, and the calculation of the tooth pair meshing force based on the initial information of the gear unit is returned; the method disclosed in the present application improves the modeling accuracy of the gear pair meshing stiffness of the helicopter gear transmission system, and can accurately determine the gear pair meshing stiffness during the gear pair meshing process under the influence of flexible deformation. 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 the structure of a gear pair meshing stiffness determination device provided by an embodiment of the present invention;

[0019] Figure 3 A schematic diagram of the structure of a gear pair meshing stiffness determination device provided by an embodiment of the present invention;

[0020] Figure 4 It is a schematic diagram of the dynamic model of the spur gear transmission system;

[0021] Figure 5 It is a schematic diagram of the relationship between the local coordinate system of the axis unit and the global coordinate system;

[0022] Figure 6 It is a schematic diagram of the dynamic model of spur gear pair;

[0023] Figure 7 It is a schematic diagram of the geometric relationship of the gear pair before and after the transmission shaft is deformed;

[0024] Figure 8 This is a schematic diagram of the gear tooth load angle calculation model;

[0025] Fig. 9 It is a schematic diagram of the matrix assembly of the spur gear transmission system;

[0026] Fig.10 This is a comparison chart of the calculation results of the meshing stiffness of spur gear pairs;

[0027] Fig.11 This is a comparison chart of the calculation results of the dynamic meshing force of a spur gear pair. DETAILED DESCRIPTION

[0028] The present invention provides a method, device, equipment and storage medium for determining the meshing stiffness of a gear pair. 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.

[0029] 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 gear pair in an embodiment of the present invention includes:

[0030] 101. Acquire design parameters and operating parameters of the gear transmission system and calculate the initial value of the meshing stiffness of the gear pair, and determine the matrix information of the shaft unit, the initial information of the gear unit, and the matrix information of the bearing unit based on the acquired design parameters and operating parameters and the calculated initial value of the meshing stiffness of the gear pair;

[0031] 102. Calculate the meshing force of the gear pair based on the initial information of the gear unit;

[0032] 103. Calculate the tooth pair parameters of the tooth pair based on the tooth pair meshing force, and calculate the matrix deformation stiffness;

[0033] 104. Calculate the meshing stiffness of the gear pair according to the calculated tooth pair parameters and matrix deformation stiffness;

[0034] 105. Obtain deformation information, and calculate update information of the gear unit according to the deformation information and the meshing stiffness of the gear pair;

[0035] 106. Determine whether the next moment is a preset iteration end time. If not, use the updated information of the gear unit as the initial information of the gear unit, and return to calculate the tooth pair meshing force based on the initial information of the gear unit;

[0036] In this embodiment, the update information of the gear unit is used as an iterative update parameter to iteratively simulate the dynamic response of the gear transmission system in actual work, thereby ensuring the accuracy of the calculation results.

[0037] The present application discloses a method for determining the meshing stiffness of a gear pair, which comprises determining the initial information of a gear unit, calculating the meshing force of a tooth pair based on the initial information of the gear unit, calculating the tooth pair parameters of the tooth pair, and calculating the meshing stiffness of the gear pair based on the calculated tooth pair parameters and the pre-calculated matrix deformation stiffness; acquiring deformation information, and calculating the updated information of the gear unit according to the deformation information and the meshing stiffness of the gear pair; judging whether the next moment is a preset iteration end time, and if not, using the updated information of the gear unit as the initial information of the gear unit, and returning to execute the calculation of the meshing force of the tooth pair based on the initial information of the gear unit; the method disclosed in the present application improves the modeling accuracy of the meshing stiffness of the gear pair of a helicopter gear transmission system by studying the coupling effect between the deformation of a slender shaft and the meshing of a gear pair, and can accurately determine the meshing stiffness of the gear pair during the meshing process of the gear pair under the influence of flexible deformation.

[0038] A second embodiment of the method for determining the meshing stiffness of a gear pair in the embodiment of the present invention includes:

[0039] 201. Determine matrix information of the shaft unit based on the acquired gear design parameters, wherein the matrix information of the shaft unit includes a deformation matrix, a stiffness matrix, a mass matrix, and a damping matrix of the shaft unit based on a local coordinate system;

[0040] In this embodiment, the Timoshenko beam unit related theory is used to study the force condition of the shaft unit; Figure 4 It is a schematic diagram of the dynamic model of the spur gear transmission system. In the figure, L is the transmission shaft length, B is the gear tooth width, OXYZ is the global coordinate system, whose origin is located at the left end face of the driving shaft, the X axis is parallel to the meshing line of the gear pair and points to the driven wheel, and the Y axis is perpendicular to the X axis; Figure 5 It is a schematic diagram of the relationship between the local coordinate system of the shaft unit and the global coordinate system. It has two nodes. Since the spur gear does not generate axial force, this scheme ignores the axial deformation, that is, the influence of deformation in the Z-axis direction; therefore, this scheme only considers the lateral deformation of each node of the shaft unit (that is, the deformation in the X-axis and Y-axis directions) and the angular deformation on the XOY plane, that is, each node has three degrees of freedom.

[0041] Establish a local coordinate system on the end face of node i , the deformation matrix of the shaft unit can be obtained, as shown in formula (1):

[0042] (1)

[0043] In the formula, , and are the lateral deformation and angular deformation of node i in the local coordinate system, respectively;

[0044] The stiffness matrix of the shaft unit in the local coordinate system is shown in formula (2):

[0045] (2)

[0046] In the formula, , , and It can be obtained from formula (3)-(6):

[0047] (3)

[0048] (4)

[0049] (5)

[0050] (6)

[0051] Where, E and G are the elastic modulus and shear modulus of the shaft unit respectively; l is the length of the shaft unit; the rectangular cross-sectional area A is the cross-sectional area of ​​the transmission shaft, I is the moment of inertia of the shaft unit section; k is the shear coefficient, and v is the Poisson's ratio;

[0052] The mass matrix of the shaft unit in the local coordinate system is shown in formula (7):

[0053] (7)

[0054] Where ρ is the transmission shaft density.

[0055] The damping matrix of the shaft unit can be calculated using the Rayleigh damping model commonly used in engineering:

[0056] (8)

[0057] In the formula, and is the Rayleigh damping proportionality factor.

[0058] 202. Determine matrix information of a bearing unit based on the acquired gear design parameters, wherein the matrix information of the bearing unit includes a support stiffness matrix and a damping matrix of the bearing unit based on a global coordinate system;

[0059] In this embodiment, this scheme uses a simplified bearing support stiffness model, as shown in formula (9):

[0060] (9)

[0061] In the formula, k bx ,k by and k bθ The bearings are in the global coordinate system x , y and θ Support stiffness in direction;

[0062] The damping matrix of the bearing is shown in formula (10):

[0063] (10)

[0064] In the formula, c bx , c by and c bθ The bearings are in the global coordinate system x , y and θ Directional support damping;

[0065] Since the bearing acts directly on the shaft unit node, its mass matrix is ​​embedded in the mass matrix of the corresponding node, which will not be described here.

[0066] 203. Calculate the initial value of gear pair meshing stiffness based on energy method;

[0067] 204. The gear design parameters include an initial value of a gear pair backlash, an initial value of a dynamic transmission error, and an initial value of a dynamic transmission error speed. The initial information of the gear unit is confirmed based on the initial value of the gear pair backlash, the initial value of the dynamic transmission error, the initial value of the dynamic transmission error speed, and the calculated initial value of the gear pair meshing stiffness.

[0068] In this embodiment, the dynamic model of the spur gear pair is as follows: Figure 6 As shown in the figure, R bj , J j , T j and w j ( j = p or g , p and g Respectively represent the master and slave gears) respectively j Base circle radius, moment of inertia, transmitted torque and speed, θ j For gear j exist θ Deformation in direction, m j For gearj Quality, k m and c m are the mesh stiffness and mesh damping of spur gear pair, x m - O p - y m is the local coordinate system of the gear pair;

[0069] According to the force conditions of the spur gear pair and Newton's second law, the dynamic equations of the spur gear transmission system can be obtained as shown below:

[0070] (11)

[0071] In the formula, , and ( j = p or g , p and g Respectively represent the master and slave gears) respectively j exist x , y and θ Deformation in direction, , and Gear j The velocities in the x, y and theta directions, , and Gear j acceleration in the x, y, and theta directions, is the dynamic meshing force of the spur gear pair ( DMF ), the calculation formula is:

[0072] (12)

[0073] In the formula, k m and c m are the meshing stiffness and meshing damping of the spur gear pair respectively. In formula (12), b is the initial value of the gear pair backlash, δ m is the initial value of the dynamic transfer error, is the initial value of the dynamic transmission error velocity.

[0074] A third embodiment of the method for determining the meshing stiffness of a gear pair in the embodiment of the present invention includes:

[0075] 301. Obtaining the initial tooth pair meshing stiffness of the tooth pair;

[0076] 302. Based on the obtained design parameters and operating parameters, the obtained initial tooth pair meshing stiffness and the initial information of the gear unit, the pre-constructed load coordination equation is used to calculate the tooth pair meshing force;

[0077] 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 load coordination equation shown in formula (13):

[0078] (13)

[0079] In the formula, F k , k k and S k ( k =1,2,3,…, N ) is the tooth pair k Meshing force, meshing stiffness and meshing error, F and S are the meshing force and meshing error of the gear pair respectively, K is the comprehensive meshing stiffness of the gear pair without considering the influence of matrix deformation, N is the number of tooth pairs, which is a positive integer greater than 1. When performing the calculation in this step, k k is the initial tooth pair meshing stiffness calculated based on step 301, F , S and K are all known values, is the initial information of the gear unit calculated based on step 204, that is, the initial dynamic meshing force of the gear pair; when calculating, for example, when calculating When , the second equation in the load coordination equation can be used to construct a , , , , , The constructed equation is then used to deduce Solve the equation, and use this method to convert the other F k The solution equation of is derived in the same way as The related equation will be 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 ; Other tooth pairs corresponding F k It can also be obtained in the same way.

[0080] In this step, equation (13) is used to determine the number of the sliced ​​gear pairs involved in the meshing. The specific method is as follows: first, the initial value of the meshing stiffness of each sliced ​​gear pair, the dynamic meshing force 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 of tooth pair k F k <0, indicating that the tooth pair k does not participate in meshing, that is, remove the corresponding parameters in the load-deformation coordination equation and recalculate until the final tooth pair number and meshing force involved in meshing are determined. F k until.

[0081] A fourth embodiment of the method for determining the meshing stiffness of a gear pair in the embodiment of the present invention includes:

[0082] 401. Calculate the potential energy stiffness of the tooth pair based on the tooth pair meshing force, wherein the potential energy stiffness includes Hertz contact stiffness, bending stiffness, radial compression stiffness and shear stiffness;

[0083] In this embodiment, according to the energy method, the meshing teeth of the spur gear pair can be equivalent to a cantilever beam model with a constant cross section. j As an example, the meshing gear teeth of Figure 8 shown.

[0084] like Figure 8 As shown, is the meshing point of the meshing gear teeth, C Point is the starting point of the tooth profile on the driving side of the meshing gear. R bj are the base circle radius of the gear respectively, A 1 is the meshing line of the gear pair, d Meshing point Tooth height, h Meshing point Half the tooth thickness, e x For microelement dx The tooth height, dx is the microelement width, h x is half of the tooth thickness at the microelement, α 2 for O j C The angle between the center line of the meshing gear teeth, and The meshing teeth are at the meshing point The load angle and pressure angle at Indicates the gear in tooth pair k j At the meshing point The load angle at α x For microelement dx The pressure angle at F k The meshing force assigned to the meshing gear teeth, F a and F b Meshing force F k The vertical and horizontal components of .

[0085] During the meshing process, the gear pair is stored in k Middle gear j The potential energy on the meshing gear teeth consists of four parts: Hertz contact potential energy U hk , bending potential energy U bj,k , radial compression potential energy U aj,k and shear potential U sj,k These four parts of potential energy correspond to the Hertzian contact stiffness k hk , bending stiffness k bj,k , radial compression stiffness k aj,k and shear stiffness k sj,k , can be obtained by equations (14)-(17):

[0086] (14)

[0087] (15)

[0088] (16)

[0089] (17)

[0090] In the formula, E j ( j = p or g, where p and g represent the master and slave gears respectively) and v j Gear j Elastic modulus and Poisson's ratio, R Xj is the radius of curvature at the meshing position, Figure 8 In A 1 , B is the tooth width, b k For tooth pair k The half width of the contact area can be calculated by the following formula:

[0091] (18)

[0092] In the formula, F k is the meshing force borne by the meshing gear teeth, which is the tooth pair meshing force calculated in step 302 .

[0093] Depend on Figure 8 It can be seen that the gear j in the tooth pair k is at the meshing point The load angle at , can be obtained by formula (19):

[0094] (19)

[0095] In the formula, z j , α j and j Gear j The number of teeth and the pitch circle pressure angle and its meshing point If the pressure angle at < R j , formula (19) takes the + sign, if ≥ R j , formula (19) takes - sign, and R j Gear j At the meshing point Tooth center distance and gear j Pitch circle radius.

[0096] 402. Calculate the meshing stiffness of the tooth pair according to the potential energy stiffness, and calculate the comprehensive meshing stiffness of the gear pair according to the meshing stiffness of the tooth pair and the meshing force of the tooth pair, wherein the comprehensive meshing stiffness of the gear pair is a tooth pair parameter;

[0097] In this embodiment, according to the energy method, it can be known that the gear pair k The meshing stiffness can be obtained by formula (20):

[0098] (20)

[0099] The parameters in the formula can be determined by formulas (14)-(19);

[0100] Furthermore, according to formula (20), the tooth pair k The meshing stiffness of the gear pair and the meshing force of the gear pair obtained by formula (13) are used again to obtain the comprehensive meshing stiffness K of the gear pair using the second formula in the load coordination equation shown in formula (13). In the process of solving the comprehensive meshing stiffness K of the gear pair, F , S and S k ( k =1,2,3,…, N ) are all known values.

[0101] 403. Calculate the deformation stiffness of the matrix based on the obtained design parameters and operating condition parameters;

[0102] In this embodiment, during the gear meshing process, the gear base will also undergo a certain deformation, and the stiffness corresponding to this partial deformation is the base deformation stiffness. k fj , can be obtained by the following formula:

[0103] (twenty one)

[0104] 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; L * , M * , P * and Q * The coefficients can be obtained by the following polynomial:

[0105] (twenty two)

[0106] Table 1 A , B '、 C , D , E 'and F 'Value

[0107]

[0108] In the formula, X *for L * , M * , P * and Q* Any one of A , B '、 C , D , E 'and F 'For detailed values, see Table 1. h f = r f / r int , r f is the tooth root circle radius, r int is the radius of the gear shaft hole, θ f is the central angle of the gear tooth profile.

[0109] A fifth embodiment of the method for determining the meshing stiffness of a gear pair in the embodiment of the present invention includes:

[0110] 501. Obtaining a matrix deformation correction coefficient;

[0111] 502. Calculate the meshing stiffness of the gear pair based on the comprehensive meshing stiffness of the gear pair, the matrix deformation stiffness and the acquired matrix deformation correction system;

[0112] In this embodiment, the gear pair meshing stiffness can be obtained according to the energy method: k m , as shown in formula (23):

[0113] (twenty three)

[0114] In the formula, ε j is the matrix deformation correction coefficient, which is taken as 1.1 in the present invention; in this formula, K is the comprehensive meshing stiffness of the gear pair calculated based on step 402, k fj is the deformation stiffness of the substrate calculated based on step 402 .

[0115] A sixth embodiment of the method for determining the meshing stiffness of a gear pair in the embodiment of the present invention includes:

[0116] 601. Obtain deformation information, and calculate deformation gear pair backlash, deformation dynamic transmission error, and deformation dynamic transmission error speed based on the deformation information;

[0117] In this embodiment, each node of the shaft unit is in the process of meshing of the spur gear pair. x , y and θDeformation will occur in all directions; generally, gears cooperate with the transmission shaft through interference fit or other means to achieve the transmission of motion and power, which means that the deformation of the transmission shaft will be transmitted to the gear through the transmission shaft-gear contact pair, which will cause the change of the spatial position of the gear pair, and then affect the meshing of the gear pair.

[0118] The geometric relationship of the gear pair before and after the transmission shaft is deformed is as follows Figure 7 As shown in the figure, δ jh ( j = p or g , h = x or y , respectively represent the driving wheel and the driven wheel) are gears j The corresponding transmission shaft is h Deformation in the axial direction, such as Figure 7 middle, represents the deformation of the transmission shaft corresponding to the driven wheel in the x direction, represents the deformation of the transmission shaft corresponding to the driving wheel in the y direction, and They are the meshing lines of the gear pair under the ideal situation and the influence of the transmission shaft deformation, respectively. O j and O j ' are the gear tooth center installation positions under the ideal situation and the influence of transmission shaft deformation, respectively. and are the meshing point and meshing point of the gear pair under ideal conditions, respectively. and are the meshing points of the gear pair under the influence of the transmission shaft deformation, a and b are the tangent points of the meshing line of the gear pair and the base circle of the driving and driven wheels under the ideal condition, a' and b' are the tangent points of the meshing line of the gear pair and the base circle of the driving and driven wheels under the influence of the transmission shaft deformation, R bj and R aj Gear j Base circle and tip circle radii.

[0119] Depend on Figure 6 The gear pair geometric relationship shown can be used to deduce the gear pair side clearance after bearing deformation, as shown in formula (24):

[0120] (twenty four)

[0121] In the formula, α pg and α pg ' are the pressure angles of the gear pair before and after the bearing deformation,b 0 is the backlash of the gear pair at the previous moment;

[0122] In addition, due to the influence of the transmission shaft node angle deformation, the dynamic transmission error of the gear pair δ m will change, which can be obtained by the following formula:

[0123] (25)

[0124] In the formula, θ shaft_p and θ shaft_g are the angular deformations of the corresponding shaft unit nodes of the driving and driven wheels, and ( j = p or g , p and g Respectively represent the master and slave gears) respectively j exist x and θ Deformation in direction, ( j = p or g , p and g Respectively represent the master and slave gears) are gears j Base circle radius.

[0125] 602. Calculating update information of the gear unit based on the deformation gear pair backlash, the deformation dynamic transmission error, the deformation dynamic transmission error speed and the calculated gear pair meshing stiffness;

[0126] In this embodiment, based on the deformation gear pair backlash and deformation dynamic transmission error calculated in step 601 and the gear pair meshing stiffness calculated in step 502, the update information of the gear unit is calculated using formula (12), formula (26) and formula (27):

[0127] f 1( δ m , b )and f 2( , b ) can be expressed as:

[0128] (26)

[0129] (27)

[0130] in, is the dynamic transmission error speed, ;in, and Gear j The velocities in the x, y and theta directions, and are the angular deformation velocities at the corresponding shaft unit nodes of the master and driven wheels, respectively.

[0131] A seventh embodiment of the method for determining the meshing stiffness of a gear pair in the embodiment of the present invention includes:

[0132] 701. If yes, that is, if the next moment is the preset iteration end time, assembling the update information of the gear unit, the confirmed matrix information of the shaft unit and the matrix information of the bearing unit based on the finite element method to obtain the dynamic equation of the gear transmission system;

[0133] In this embodiment, the gear transmission system is discretized into a series of shaft units using the finite element method, and the Timoshenko beam unit related theory is used to study the stress of the shaft unit; after confirming the update information of the gear unit, the overall matrix of the gear transmission system is assembled based on the assembly method shown in FIG9; due to the local coordinate system of the gear pair and the local coordinate system of the shaft unit x i - O i - y i With the global coordinate system O- X - YZ The directions are the same, so the unit matrices do not need to be transformed when assembling the overall matrix;

[0134] The overall matrix assembly process of the gear transmission system is briefly described as follows: The overall matrix assembly process of the system is exactly the same as the assembly process of the finite element overall stiffness matrix in conventional structural mechanics analysis, that is, according to the correspondence between the local number of each unit node and the overall number of the system node, the sub-matrices of the unit matrix are superimposed on the corresponding positions of the overall matrix according to the degree of freedom position; its overall stiffness matrix is ​​composed of Fig. 9 As shown in the figure, when the block where a node is located is composed of two shadows, it indicates that the node is a coupling node of two types of units, and the degree of freedom element of the node is the algebraic superposition of two different types of unit sub-matrices; when the overall matrix assembly is completed, the dynamic equation of the gear transmission system can be obtained.

[0135] Table 2 Design parameters of gear transmission system

[0136]

[0137] According to the parameters shown in Table 2, the algorithm program is written by Matlab, and the gear pair meshing stiffness is calculated based on the gear pair stiffness determination method disclosed in this embodiment. The calculation results are as follows: Fig.10 and Fig.11 shown.

[0138] Depend on Fig.10 It can be seen that the meshing stiffness obtained by the method of the present invention is quite different from the value calculated by the energy method. This is because dynamic responses such as transmission shaft deformation will affect the meshing of the gear pair. This phenomenon shows that the transmission shaft deformation has a significant effect on the gear meshing, which needs to be considered in subsequent modeling.

[0139] at the same time, Fig.11 The results show that the updated information of the gear unit predicted by the method of the present invention, i.e. the dynamic meshing force of the gear pair, is significantly different from the prediction result of the traditional method (i.e. the gear transmission system dynamics solution method that does not consider the coupling effect of the transmission shaft deformation and the gear pair meshing). This phenomenon indicates that the coupling effect between the shaft deformation and the gear meshing has a significant impact on the dynamic performance of the gear transmission system, which needs to be considered in subsequent modeling.

[0140] The above describes the method for determining the meshing stiffness of a gear pair in an embodiment of the present invention. The following describes the device for determining the meshing stiffness of a gear pair in an embodiment of the present invention. Figure 2 In one embodiment of the present invention, a device for determining the meshing stiffness of a gear pair includes:

[0141] A determination module 801 is used to obtain design parameters and operating parameters of the gear transmission system and calculate the initial value of the meshing stiffness of the gear pair, and determine the matrix information of the shaft unit, the initial information of the gear unit, and the matrix information of the bearing unit based on the obtained design parameters and operating parameters and the calculated initial value of the meshing stiffness of the gear pair;

[0142] A first calculation module 802, configured to calculate the meshing force of a tooth pair based on initial information of the gear unit;

[0143] A second calculation module 803 is used to calculate the tooth pair parameters of the tooth pair based on the tooth pair meshing force, and calculate the matrix deformation stiffness;

[0144] A third calculation module 804 is used to calculate the meshing stiffness of the gear pair according to the calculated tooth pair parameters and the matrix deformation stiffness;

[0145] An updating module 805 is used to obtain deformation information and calculate update information of the gear unit according to the deformation information and the meshing stiffness of the gear pair;

[0146] The iteration module 806 is used to determine whether the next moment is a preset iteration end time. If not, the updated information of the gear unit is used as the initial information of the gear unit, and the calculation of the tooth pair meshing force based on the initial information of the gear unit is returned.

[0147] 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.

[0148] above Figure 2 The gear pair meshing stiffness determination device in the embodiment of the present invention is described in detail from the perspective of modular functional entities, and the gear pair meshing stiffness determination device in the embodiment of the present invention is described in detail from the perspective of hardware processing.

[0149] Figure 3 is a schematic diagram of the structure of a gear pair meshing stiffness determination device provided by an embodiment of the present invention. The gear pair meshing stiffness determination device 900 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 gear pair meshing stiffness determination device 900. 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 gear pair meshing stiffness determination device 900 to implement the steps of the gear pair meshing stiffness determination method provided by the above-mentioned method embodiments.

[0150] The gear pair meshing stiffness determination device 900 may also 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 gear pair meshing stiffness determining device shown does not constitute a limitation on the gear pair meshing stiffness determining device, and may include more or less components than shown in the figure, or combine certain components, or arrange the components differently.

[0151] 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 gear pair.

[0152] 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.

[0153] 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.

[0154] 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 gear pair, characterized in that: include: Acquire design parameters and operating parameters of the gear transmission system and calculate the initial value of the meshing stiffness of the gear pair, and determine the matrix information of the shaft unit, the initial information of the gear unit, and the matrix information of the bearing unit based on the acquired design parameters and operating parameters and the calculated initial value of the meshing stiffness of the gear pair; Calculating the meshing force of the tooth pair based on the initial information of the gear unit; specifically, obtaining the initial meshing stiffness of the tooth pair; calculating the meshing force of the tooth pair using a pre-constructed load coordination equation based on the obtained design parameters and operating condition parameters, the obtained initial meshing stiffness of the tooth pair and the initial information of the gear unit; The tooth pair parameters of the tooth pair are calculated based on the tooth pair meshing force, and the matrix deformation stiffness is calculated; specifically, the potential energy stiffness of the tooth pair is calculated based on the tooth pair meshing force, and the potential energy stiffness includes Hertz contact stiffness, bending stiffness, radial compression stiffness and shear stiffness; the tooth pair meshing stiffness is calculated according to the potential energy stiffness, and the comprehensive meshing stiffness of the gear pair is calculated according to the tooth pair meshing stiffness and the tooth pair meshing force, and the comprehensive meshing stiffness of the gear pair is the tooth pair parameter; the matrix deformation stiffness is calculated based on the obtained design parameters and operating condition parameters; Calculating the meshing stiffness of the gear pair according to the calculated tooth pair parameters and the matrix deformation stiffness; specifically, 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 acquired matrix deformation correction system; Obtain deformation information, and calculate update information of the gear unit according to the deformation information and the meshing stiffness of the gear pair; specifically, obtain deformation information, and calculate the deformation gear pair backlash, deformation dynamic transmission error, and deformation dynamic transmission error speed based on the deformation information; Calculating update information of the gear unit based on the deformation gear pair backlash, the deformation dynamic transmission error, the deformation dynamic transmission error speed, and the calculated gear pair meshing stiffness; It is determined whether the next moment is a preset iteration end time. If not, the updated information of the gear unit is used as the initial information of the gear unit, and the calculation of the tooth pair meshing force based on the initial information of the gear unit is returned.

2. The method for determining the meshing stiffness of a gear pair according to claim 1, characterized in that: The determining of the matrix information of the shaft unit, the initial information of the gear unit and the matrix information of the bearing unit based on the acquired design parameters and operating condition parameters and the calculated initial value of the meshing stiffness of the gear pair comprises: Determine the matrix information of the shaft unit based on the acquired gear design parameters, wherein the matrix information of the shaft unit includes a deformation matrix, a stiffness matrix, a mass matrix, and a damping matrix of the shaft unit based on a local coordinate system; Determining matrix information of the bearing unit based on the acquired gear design parameters, wherein the matrix information of the bearing unit includes a support stiffness matrix and a damping matrix of the bearing unit based on a global coordinate system; Calculate the initial value of gear pair meshing stiffness based on energy method; The gear design parameters include an initial value of the gear pair side clearance, an initial value of the dynamic transmission error and an initial value of the dynamic transmission error speed. The initial information of the gear unit is confirmed based on the initial value of the gear pair side clearance, the initial value of the dynamic transmission error and the initial value of the dynamic transmission error speed and the calculated initial value of the gear pair meshing stiffness.

3. The method for determining the meshing stiffness of a gear pair according to claim 1, characterized in that: The step of determining whether the next moment is a preset iteration end time comprises: If so, the updated information of the gear unit, the confirmed matrix information of the shaft unit and the matrix information of the bearing unit are assembled based on the finite element method to obtain the dynamic equation of the gear transmission system.

4. A device for determining meshing stiffness of a gear pair, characterized in that: include: A determination module is used to obtain design parameters and operating parameters of the gear transmission system and calculate the initial value of the meshing stiffness of the gear pair, and determine the matrix information of the shaft unit, the initial information of the gear unit, and the matrix information of the bearing unit based on the obtained design parameters and operating parameters and the calculated initial value of the meshing stiffness of the gear pair; A first calculation module is used to calculate the meshing force of the tooth pair based on the initial information of the gear unit; specifically, to obtain the initial meshing stiffness of the tooth pair; and to calculate the meshing force of the tooth pair using a pre-constructed load coordination equation based on the obtained design parameters and operating condition parameters, the obtained initial meshing stiffness of the tooth pair and the initial information of the gear unit; The second calculation module is used to calculate the tooth pair parameters of the tooth pair based on the tooth pair meshing force, and calculate the matrix deformation stiffness; specifically, the potential energy stiffness of the tooth pair is calculated based on the tooth pair meshing force, and the potential energy stiffness includes Hertz contact stiffness, bending stiffness, radial compression stiffness and shear stiffness; the tooth pair meshing stiffness is calculated according to the potential energy stiffness, and the gear pair comprehensive meshing stiffness is calculated according to the tooth pair meshing stiffness and the tooth pair meshing force, and the gear pair comprehensive meshing stiffness is the tooth pair parameter; the matrix deformation stiffness is calculated based on the acquired design parameters and operating condition parameters; The third calculation module is used to calculate the meshing stiffness of the gear pair according to the calculated tooth pair parameters and the matrix deformation stiffness; specifically, to obtain 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 acquired matrix deformation correction system; An updating module is used to obtain deformation information, and calculate update information of the gear unit according to the deformation information and the meshing stiffness of the gear pair; specifically, the deformation information is obtained, and the deformation gear pair backlash, deformation dynamic transmission error and deformation dynamic transmission error speed are calculated based on the deformation information; Calculating update information of the gear unit based on the deformation gear pair backlash, the deformation dynamic transmission error, the deformation dynamic transmission error speed, and the calculated gear pair meshing stiffness; The iteration module is used to determine whether the next moment is a preset iteration end time. If not, the updated information of the gear unit is used as the initial information of the gear unit, and returns to calculate the meshing force of the gear pair based on the initial information of the gear unit.

5. A gear pair meshing stiffness determination device, characterized in that: The gear pair meshing stiffness determination device comprises: a memory and at least one processor, wherein the memory stores instructions; At least one of the processors calls the instructions in the memory to enable the gear pair meshing stiffness determination device to perform each step of the gear pair meshing stiffness determination method according to any one of claims 1 to 3.

6. 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 gear pair as described in any one of claims 1 to 3 are implemented.

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