Asymmetric spur gear meshing stiffness determination method, device, equipment and storage medium

Abstract

The present invention relates to the field of gear mechanics calculation technology, and discloses a method, device, equipment and storage medium for determining the meshing stiffness of an asymmetric spur gear. The method comprises: calculating an initial value of the meshing stiffness of a gear pair to calculate the dynamic meshing force of the gear pair, and confirming the meshing state of the asymmetric spur gear pair according to the dynamic meshing force of the gear pair; calculating meshing parameters corresponding to the meshing state to calculate the matrix deformation stiffness, obtaining the tooth pair parameters of each tooth pair, and calculating the comprehensive meshing stiffness of the gear pair according to the matrix deformation stiffness and the tooth pair parameters; comparing the comprehensive meshing stiffness of the gear pair with the initial value of the meshing stiffness of the gear pair, and if the comparison result does not meet the threshold condition, using the calculated comprehensive meshing stiffness of the gear pair as the initial value of the meshing stiffness of the gear pair, and returning to execute the calculation of the dynamic meshing force of the gear pair according to the calculated initial value of the meshing stiffness of the gear pair; the method disclosed in the present application can accurately determine the comprehensive meshing stiffness of the gear pair during the dynamic meshing process of the asymmetric 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 an asymmetric spur gear. Background Art

[0002] Gear mesh stiffness is a key source of internal excitation in gear transmission systems, and its computational research has theoretical guiding significance for the verification and prediction of the dynamic service performance of gear transmission systems.

[0003] As a new type of gear design, asymmetric spur gears are characterized by a large pressure angle on the driving side and a small pressure angle on the back side of the tooth. The above design can optimize the tooth root bending strength and tooth surface contact strength; however, during the meshing process of the asymmetric spur gear pair, especially under specific working conditions such as high speed and light load, the asymmetric spur gear pair may experience tooth back meshing, which will significantly change the meshing state of the asymmetric spur gear pair, resulting in unexpected excitation, and may further lead to premature failure of the asymmetric spur gear pair.

[0004] At present, the research on the mesh stiffness of asymmetric spur gear pairs is still insufficient, especially in terms of the influence of tooth back meshing and the coupling effect between the dynamic meshing force of the gear pair and its meshing state. This deficiency limits the scope of application of the mesh stiffness model of asymmetric spur gears.

[0005] It can be seen that the existing technology still needs to be improved and enhanced. Summary of the invention

[0006] In order to overcome the deficiencies of the prior art, the object of the present invention is to provide a method for determining the meshing stiffness of an asymmetric spur gear, which can accurately determine the comprehensive meshing stiffness of the gear pair during the dynamic meshing process of the asymmetric spur gear pair.

[0007] The first aspect of the present invention provides a method for determining the meshing stiffness of an asymmetric spur gear, comprising: calculating the initial meshing stiffness of the gear pair according to the energy method based on the acquired design parameters and operating condition parameters of the asymmetric spur gear; calculating the dynamic meshing force of the gear pair according to the calculated initial meshing stiffness of the gear pair, and confirming the meshing state of the asymmetric spur gear pair according to the numerical value of the dynamic meshing force of the gear pair; calculating the meshing parameters corresponding to the confirmed meshing state, and calculating the matrix deformation stiffness according to the meshing parameters; obtaining the tooth pair parameters of each tooth pair, and calculating the comprehensive meshing stiffness of the gear pair according to the calculated matrix deformation stiffness and the tooth pair parameters; calculating the difference between the comprehensive meshing stiffness of the gear pair and the initial meshing stiffness of the gear pair, and judging whether the calculated difference meets the threshold condition; if the calculated difference does not meet the threshold condition, using the calculated comprehensive meshing stiffness of the gear pair as the initial meshing stiffness of the gear pair, and returning to execute the calculation of the dynamic meshing force of the gear pair according to the calculated initial meshing stiffness of the gear pair.

[0008] Optionally, in a first embodiment of the first aspect of the present invention, the meshing state of the asymmetric spur gear pair is confirmed based on the numerical value of the dynamic meshing force of the gear pair, specifically including: when the calculated dynamic meshing force of the gear pair is less than zero, it indicates that the asymmetric spur gear pair has back-side meshing; when the calculated dynamic meshing force of the gear pair is equal to zero, it indicates that the asymmetric spur gear pair is not meshed; when the calculated dynamic meshing force of the gear pair is greater than zero, it indicates that the asymmetric spur gear pair has drive side meshing.

[0009] Optionally, in a second embodiment of the first aspect of the present invention, the meshing parameters corresponding to the confirmed meshing state are calculated, and the matrix deformation stiffness is calculated based on the meshing parameters, specifically including: when the asymmetric spur gear pair has back-side meshing, determining the back-side meshing position of the tooth, and determining the tooth back meshing parameters at the back-side meshing position of the tooth, the tooth back meshing parameters include the pressure angle at the back-side meshing point of the tooth, and the load angle at the back-side meshing point of the tooth; when the asymmetric spur gear pair has driving side meshing, determining the driving side meshing position, and determining the driving meshing parameters at the driving side meshing position, the driving meshing parameters include the pressure angle at the driving side meshing point and the load angle at the driving side meshing point; calculating the matrix deformation stiffness based on the meshing parameters.

[0010] Optionally, in a third embodiment of the first aspect of the present invention, the obtaining of the tooth pair parameters of each tooth pair specifically includes: obtaining the tooth pair parameters of each tooth pair, and calculating the tooth pair separation distance of each tooth pair according to the obtained tooth pair parameters; calculating the tooth pair meshing force of each tooth pair according to the calculated tooth pair separation distance; calculating the Hertzian contact stiffness, bending stiffness, radial compression stiffness and shear stiffness of each tooth pair according to the calculated tooth pair meshing force, and calculating the tooth pair stiffness of each tooth pair according to the Hertzian contact stiffness, the bending stiffness, the radial compression stiffness and the shear stiffness; calculating the tooth pair meshing stiffness according to the tooth pair stiffness, the tooth pair meshing force and the tooth pair separation distance.

[0011] Optionally, in a fourth embodiment of the first aspect of the present invention, the calculation of the comprehensive meshing stiffness of the gear pair based on the calculated matrix deformation stiffness and the tooth pair parameters specifically includes: obtaining a matrix deformation correction coefficient; calculating the comprehensive meshing stiffness of the gear pair based on the matrix deformation correction coefficient, the tooth pair meshing stiffness and the matrix deformation stiffness.

[0012] Optionally, in a sixth embodiment of the first aspect of the present invention, the step of determining whether the calculated difference satisfies a threshold condition further includes: if the calculated difference satisfies the threshold condition, updating the simulation time; determining whether the updated simulation time is greater than a preset simulation end time; if not, using the calculated comprehensive meshing stiffness of the gear pair as the initial value of the meshing stiffness of the gear pair, and returning to calculate the dynamic meshing force of the gear pair based on the calculated initial value of the meshing stiffness of the gear pair.

[0013] The second aspect of the present invention provides a device for determining the meshing stiffness of an asymmetric spur gear, comprising: a first calculation module, used to calculate the initial meshing stiffness of the gear pair according to the energy method based on the acquired design parameters and operating parameters of the asymmetric spur gear; a confirmation module, used to calculate the dynamic meshing force of the gear pair according to the calculated initial meshing stiffness of the gear pair, and confirm the meshing state of the asymmetric spur gear pair according to the numerical value of the dynamic meshing force of the gear pair; a second calculation module, used to calculate the meshing parameters corresponding to the confirmed meshing state, and calculate the matrix deformation stiffness according to the meshing parameters; a third calculation module , used to obtain the tooth pair parameters of each tooth pair, and calculate the comprehensive meshing stiffness of the gear pair according to the calculated matrix deformation stiffness and the tooth pair parameters; a judgment module, used to calculate the difference between the comprehensive meshing stiffness of the gear pair and the initial value of the meshing stiffness of the gear pair, and judge whether the calculated difference meets the threshold condition; an iteration module, used to use the calculated comprehensive meshing stiffness of the gear pair as the initial value of the meshing stiffness of the gear pair if the calculated difference does not meet the threshold condition, and trigger the confirmation module to return to execute the calculation of the dynamic meshing force of the gear pair according to the calculated initial value of the meshing stiffness of the gear pair.

[0014] A third aspect of the present invention provides an asymmetric spur gear meshing stiffness determination device, the asymmetric spur gear 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 asymmetric spur gear meshing stiffness determination device to perform each step of the asymmetric spur gear 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 an asymmetric spur gear are implemented.

[0016] In the technical solution of the present invention, by obtaining the difference between the comprehensive meshing stiffness of the gear pair and the initial value of the meshing stiffness of the gear pair, when the absolute value of the difference is greater than a preset threshold, the comprehensive meshing stiffness of the gear pair is used as the initial value of the meshing stiffness of the gear pair of the latest round, and the dynamic meshing force of the gear pair of the latest round is returned and recalculated, and then the meshing state is confirmed by the dynamic meshing force of the gear pair of the latest round to confirm the meshing parameters of the latest round, thereby calculating the matrix deformation stiffness of the latest round, and combining the tooth pair parameters of each tooth pair and the matrix deformation stiffness of the latest round to calculate the comprehensive meshing stiffness of the gear pair of the latest round , thereby comparing the latest round of comprehensive meshing stiffness of the gear pair and the initial value of the meshing stiffness of the gear pair, until the absolute value of the target difference is less than or equal to the preset threshold value, then stopping the cyclic calculation, thereby obtaining the latest round of comprehensive meshing stiffness of the gear pair, that is, the most suitable comprehensive meshing stiffness of the gear pair in the dynamic meshing process of the asymmetric spur gear pair, that is, in the technical solution disclosed in the present application, by analyzing the meshing phase relationship between the driving side and the tooth back side of the asymmetric spur gear, and analyzing the coupling effect between the dynamic meshing force of the asymmetric spur gear pair and its meshing state, the comprehensive meshing stiffness of the gear pair in the dynamic meshing process of the asymmetric spur gear pair can be accurately determined. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0018] Figure 2 A second flow chart of a method for determining meshing stiffness of an asymmetric spur gear provided in an embodiment of the present invention;

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

[0020] Figure 4 A schematic diagram of the structure of an asymmetric spur gear meshing stiffness determination device provided by an embodiment of the present invention;

[0021] Figure 5 A schematic diagram of the meshing of the driving side of the asymmetric spur gear pair provided by an embodiment of the present invention;

[0022] Figure 6 A schematic diagram of a calculation model for the load angle of meshing teeth of an asymmetric spur gear provided in an embodiment of the present invention;

[0023] Figure 7 An analysis model for the back-side external meshing of an asymmetric spur gear pair provided in an embodiment of the present invention;

[0024] Figure 8 A schematic diagram of a dynamic model of an asymmetric spur gear transmission provided by an embodiment of the present invention;

[0025] Figure 9a A schematic diagram of the change of meshing stiffness over time provided by an embodiment of the present invention;

[0026] Figure 9b A schematic diagram of the change of the dynamic meshing force of a gear pair over time provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0027] The present invention provides a method, device, equipment and storage medium for determining the meshing stiffness of an asymmetric spur gear. 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.

[0028] For ease of understanding, the specific process of the embodiment of the present invention is described below. Figure 1 and Figure 2 , an embodiment of a method for determining the meshing stiffness of an asymmetric spur gear in an embodiment of the present invention includes:

[0029] 100. Based on the obtained design parameters and operating parameters of the asymmetric spur gear, the initial value of the gear pair meshing stiffness is calculated according to the energy method;

[0030] In this embodiment, the obtained design parameters and operating parameters include the number of teeth, module, elastic modulus, Poisson's ratio, pressure angle, tooth top height coefficient, tooth root height coefficient, tooth root circle radius, gear shaft hole radius, gear tooth profile center angle, etc. of the asymmetric spur gear. For details, please refer to Table 1, which is the design parameters of the gears in this embodiment.

[0031] Table 1 Gear design parameters

[0032]

[0033] In this embodiment, the initial value of the gear pair meshing stiffness is calculated by the energy method. The energy method is an analysis method based on the principle of energy conservation. It derives the dynamic performance parameters of the system by calculating the energy changes of the system under different states. In the gear transmission system, the energy method is mainly used to analyze the meshing process of the gears. By calculating the energy changes of the gears during the meshing process, the initial value of the meshing stiffness of the gear pair is solved. .

[0034] 200. Calculate the dynamic meshing force of the gear pair according to the calculated initial value of the meshing stiffness of the gear pair, and confirm the meshing state of the asymmetric spur gear pair according to the numerical value of the dynamic meshing force of the gear pair;

[0035] The method for determining the meshing stiffness of asymmetric spur gears disclosed in the present application is used to calculate the comprehensive meshing stiffness of the gear pair during the dynamic meshing process of the asymmetric spur gear pair. Affected by dynamic factors, the meshing state of the asymmetric spur gear pair during the dynamic meshing process is random. In order to ensure that the calculated comprehensive meshing stiffness of the gear pair can accurately reflect the actual meshing state, thereby improving the accuracy and reliability of the calculation, the technical solution disclosed in the present application first calculates the dynamic meshing force of the gear pair to confirm the gear meshing state, and then calculates the matrix deformation stiffness, so as to more accurately evaluate the deformation of the asymmetric spur gear pair during the dynamic meshing process.

[0036] Specifically, step 200 specifically includes the steps of:

[0037] 201. Calculate the dynamic meshing force of the gear pair based on the calculated initial value of the meshing stiffness of the gear pair ;

[0038] In this embodiment, based on the six-degree-of-freedom dynamic model of the transmission system, according to the deformation of the driving and driven wheels of the asymmetric spur gear pair in each degree-of-freedom direction and the calculated dynamic meshing force of the gear pair, the transmission dynamic equations of the asymmetric spur gear are constructed; please refer to Figure 8 , Figure 8 It is a schematic diagram of the asymmetric spur gear transmission dynamics model. Specifically, it is a six-degree-of-freedom dynamics model of the transmission system. The transmission dynamics model takes into account the deformation of the master and driven wheels of the asymmetric spur gear pair in the three degrees of freedom directions of x, y and θ. According to the force conditions of the asymmetric spur gear pair and Newton's second law, the dynamics equations of the asymmetric spur gear transmission system can be obtained, as shown in the following formula:

[0039] ;

[0040] In the formula and (i=p or g, p and g represent the master and slave gears of the asymmetric gear pair respectively) are the deformations of gear i in the x and y directions, (i=p or g, p and g represent the master and slave gears of the asymmetric gear pair respectively) is the deformation angle of gear i in the θ direction, , , and are the base circle radius, mass, moment of inertia and transmitted torque of gear i respectively, and (i=p or g) are the transmission shaft support damping of the master and slave gears in the x-direction and y-direction respectively; and (i=p or g) are the transmission shaft support stiffness of the master and slave gears in the x-direction and y-direction respectively; , and are the speeds of gear i in the x, y and θ directions respectively, , and are the accelerations of gear i in the x, y and θ directions respectively.

[0041] In the dynamic equations of the asymmetric spur gear transmission system, is the dynamic meshing force of the gear pair ( DMF ), calculated by the following formula:

[0042] ;

[0043] in, is the initial value of the gear pair meshing stiffness, is the meshing damping of spur gear pair, is the dynamic transmission error of the spur gear pair, is the dynamic transmission error speed of the gear pair, b represents 1 / 2 of the tooth side clearance; f 1( δ m , b )and f 2( , b ) can be expressed as:

[0044] ;

[0045] ;

[0046] is the dynamic transmission error of the spur gear pair, and its calculation formula is:

[0047] ;

[0048] in, and are the deformation angles of gear i in the θ direction, (i=p or g) are the base circle radius of gear i respectively.

[0049] 202. When the calculated dynamic meshing force of the gear pair is less than zero, it indicates that the asymmetric spur gear pair has tooth back meshing;

[0050] 203. When the calculated dynamic meshing force of the gear pair is equal to zero, it indicates that the asymmetric spur gear pair is not meshing, and the iteration is jumped out, that is, the calculation of the matrix deformation stiffness and the comprehensive meshing stiffness of the gear pair is no longer performed;

[0051] 204. When the calculated dynamic meshing force of the gear pair is greater than zero, it indicates that the asymmetric spur gear pair is meshing on the driving side;

[0052] In this embodiment, the relationship between the meshing state of the asymmetric spur gear pair and the numerical value of the dynamic meshing force of the gear pair can be known from the dynamics theory of mechanical systems.

[0053] 300. Calculate meshing parameters corresponding to the confirmed meshing state, and calculate the deformation stiffness of the matrix according to the meshing parameters;

[0054] Specifically, the steps include:

[0055] 301. When the asymmetric spur gear pair has tooth back meshing, determine the tooth back meshing position, and determine the tooth back meshing parameters at the tooth back meshing position, wherein the tooth back meshing parameters include a pressure angle at the tooth back meshing point and a load angle at the tooth back meshing point;

[0056] In this embodiment, it is assumed that When the symmetry line of the gear pair teeth coincides with the tooth center line, please refer to Figure 5 , Figure 5 This is a schematic diagram of the meshing of the drive side of the asymmetric spur gear pair. In the figure, and They are the tooth centers of the driving and driven wheels of the asymmetric spur gear pair, is the meshing line of the asymmetric spur gear pair on the driving side, is the meshing line on the back side of the asymmetric spur gear pair teeth, and They are the actual meshing areas on the drive side and tooth back side of the asymmetric spur gear pair, for and The angle of the positive semi-axis, and They are the global coordinate system and local coordinate system of the asymmetric spur gear pair respectively.

[0057] According to the gear meshing principle, the meshing point on the driving side is Meshing point on the back of the tooth Symmetrical, the axis of symmetry is the center line of the gear pair; At this moment, the driving side and the tooth back side have the same number of meshing teeth and the same meshing stiffness amplitude; according to the gear meshing principle and gear geometry theory, it can be obtained that for:

[0058] ;

[0059] in, Indicates the starting point of gear meshing from the driving side Move to The time required for the point, t represents the meshing moment, yes Figure 5 middle and The angle between is the meshing angle of the asymmetric spur gear pair, , , and are the driving wheel speed, base circle radius, pitch circle pressure angle and displacement coefficient of the driving wheel in the x direction, and m is the gear module.

[0060] According to the gear meshing principle, the driving side meshing line is , the direction of meshing point movement is arrive ; The meshing line on the back of the tooth is , the direction of movement of the meshing line is arrive Therefore, from the above theoretical analysis process, we can know that when When the tooth back side meshing point is , then to move.

[0061] According to the gear meshing principle and gear geometry theory, the asymmetric spur gear pair has a back side meshing starting point. Move to The time required is Therefore, according to The calculation formula and Figure 5 The corresponding derivation process of the back side meshing of the tooth can obtain the local coordinate system Coordinates of meshing position of lower tooth back side ( )for:

[0062] ;

[0063] in, is the back side meshing period of the asymmetric spur gear pair, is the base circle pitch on the back side of the asymmetric spur gear pair teeth, is the base circle radius of the driven wheel, Indicates the speed of the driven wheel, express Point in local coordinate system The vertical coordinate on .

[0064] according to Figure 5 The geometric relationship between the driving and driven wheels shown in the figure can be used to obtain the local coordinate system With global coordinate system The coordinate change relationship is:

[0065] ;

[0066] in, Represents any point in the global coordinate system Specifically, the coordinates of any point in the global coordinate system are expanded into a 4*1 matrix to obtain the homogeneous coordinates corresponding to the two-dimensional coordinates, and the expansion is performed by setting the values ​​of the redundant dimensions to 1; Represents any point in the local coordinate system Specifically, the coordinates of any point in the local coordinate system are expanded into a 4*1 matrix to obtain the homogeneous coordinates corresponding to the two-dimensional coordinates, and the values ​​of the redundant dimensions are set to 1 for expansion; further, each matrix in the above formula can be calculated by the following formulas:

[0067] ;

[0068] ;

[0069] ;

[0070] in, for and The angle of the positive half axis, a is the center distance of the gear pair.

[0071] According to the above formula, the meshing position of the back side of the asymmetric spur gear pair can be obtained in the local coordinate system With global coordinate system The coordinates under the gear ratio, as well as the drive side meshing position corresponding to the tooth back side meshing position.

[0072] In this embodiment, due to the particularity of the tooth profile of the asymmetric spur gear, the method for calculating the meshing parameters at the meshing position on the back side of the tooth cannot directly use the method for calculating the meshing parameters on the driving side.

[0073] Taking the meshing gear teeth of the driving wheel in the asymmetric spur gear pair as an example, the calculation model of the tooth back side load angle is as follows: Figure 6 As shown in the figure, and They are the meshing points on the drive side and tooth back side of the asymmetric spur gear, and They are the tooth tops on the driving side and tooth back side of the asymmetric spur gear, and are the starting points of the involute tooth profile on the drive side and tooth back side of the asymmetric spur gear, and They are the meshing lines of the asymmetric spur gear driving side and tooth back side, and are the tangent points of the meshing lines of the asymmetric spur gear driving side and tooth back side and its base circle, respectively, and They are the meshing points of the asymmetric spur gear pair on the back side of the tooth. The meshing force at , and the vertical and horizontal components of the meshing force.

[0074] According to the gear meshing principle, is the pressure angle of the tooth tip circle on the back side of the asymmetric spur gear tooth , is the pressure angle at the meshing point on the back side of the asymmetric spur gear tooth , is the load angle at the meshing point on the back side of the asymmetric spur gear tooth , can be obtained by the following formula:

[0075] ;

[0076] In the formula, and are the number of teeth of gear i and the pitch circle pressure angle of the tooth back side, is the pressure angle at the meshing point on the back side of the asymmetric spur gear tooth; if , then the above formula takes the + sign, if , then the above formula takes the - sign; and are the meshing points of gear i on the back side of the tooth The tooth center distance and pitch circle radius at; inv(α)=tanα-α is the involute function.

[0077] 302. When the asymmetric spur gear pair is engaged on the driving side, determine the driving side engagement position, and determine the driving engagement parameters at the driving side engagement position, wherein the driving engagement parameters include a pressure angle at the driving side engagement point and a load angle at the driving side engagement point;

[0078] Based on the principle of gear meshing, the global coordinate system The meshing position coordinates of the driving side of the lower asymmetric gear pair ( , )for:

[0079] ;

[0080] in, Indicates the starting point of gear meshing from the driving side Move to The time you need, is the meshing period of the driving side of the asymmetric spur gear pair, is the base circle pitch of the driving side of the asymmetric spur gear pair, is the base circle radius of the driven wheel, is the speed of the driving wheel.

[0081] In this embodiment, the calculation method of the drive meshing parameter may refer to the calculation method of the tooth back meshing parameter.

[0082] 303. Calculate the deformation stiffness of the matrix based on the meshing parameters;

[0083] In this embodiment, the research shows that the gear matrix affects the meshing stiffness of the gear pair, and the matrix deformation stiffness (i=p or g) The calculation formula can be expressed as:

[0084] ;

[0085] In the formula, is the distance from the meshing line and the focus of the gear tooth symmetry line to the tooth root circle, is the base circle arc corresponding to the entire gear tooth profile; , , and The coefficients can be obtained by the following polynomial:

[0086] ;

[0087] In the formula, for , , and Any one of A, , C, D, and See Table 2 for the values. 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.

[0088] Table 2 A , C, D, and Value

[0089]

[0090] 400. Acquire tooth pair parameters of each tooth pair, and calculate the comprehensive meshing stiffness of the gear pair according to the calculated matrix deformation stiffness and the tooth pair parameters;

[0091] Specifically, the steps include:

[0092] 401. Acquire tooth pair parameters of each tooth pair, and calculate the tooth pair separation distance of each tooth pair according to the acquired tooth pair parameters;

[0093] In this embodiment, it can be known from the gear geometry theory that the coordinate system The tooth addendum coordinates under , )for:

[0094] ;

[0095] In the formula, is the radius of the gear tooth tip circle, is the pressure angle of the tooth tip circle on the back side of the asymmetric spur gear tooth , is the pressure angle at the meshing point on the back side of the asymmetric spur gear tooth ; It should be noted that the calculation result of the above formula is a local coordinate system In order to facilitate the subsequent calculation of the separation distance of the gear pairs, the coordinates of the top teeth of the driven gear under the above formula need to be calculated. Convert the driven gear coordinates to the global coordinate system Down.

[0096] Furthermore, the gear pair external meshing analysis model at time t is as follows: Figure 7 As shown in the figure, , , , , as well as are the tooth tops of the driving and driven wheel teeth 1, 2, and 3 respectively; previous studies have shown that under high speed and / or heavy load conditions, the elastic deformation of the meshing gear pairs will cause the tooth pair 1 that theoretically does not participate in the meshing process to enter the meshing process in advance. At this time, the driven wheel tooth 1 rotates angle; therefore, the separation distance of tooth pair 1 at time t is .

[0097] Local Coordinate System Down , , , , as well as The coordinates are:

[0098] , , ;

[0099] , , ;

[0100] The matrix can be calculated by the following formula:

[0101] ;

[0102] in, , Represents the number of teeth of gear i (i=p or g), kk=1,2,3.

[0103] Local coordinate system of driving wheel and the local coordinate system of the driven wheel The coordinate transformation relationship between them is:

[0104] ;

[0105] in, Indicates that any point is in the local coordinate system of the driving wheel Specifically, the coordinates of any point in the local coordinate system of the driving wheel are expanded into a 4*1 matrix to obtain the homogeneous coordinates corresponding to the two-dimensional coordinates, and the expansion is performed by setting the values ​​of the redundant dimensions to 1; Represents any point in the local coordinate system of the driven wheel Specifically, the coordinates of any point in the local coordinate system of the driven wheel are expanded into a 4*1 matrix to obtain the homogeneous coordinates corresponding to the two-dimensional coordinates, and the expansion is performed by setting the values ​​of the redundant dimensions to 1; further, It can be calculated by the following formula:

[0106] ;

[0107] In the formula, is the gear pitch circle pressure angle.

[0108] Combination Figure 7 and gear geometry theory, using , , , , , , , The equal points are in the local coordinate system of the driving wheel The coordinates below can be used to obtain the separation distance of tooth pair 1 at time t:

[0109] ;

[0110] in, and The driven wheel is at point and Point The pressure angle at .

[0111] Similarly, referring to the above modeling process, the separation distances corresponding to tooth pair 2, tooth pair 3, and tooth pair j can be obtained: .

[0112] 402. Calculate the tooth pair meshing force of each tooth pair according to the calculated tooth pair separation distance;

[0113] According to the gear meshing principle, the meshing stiffness of the meshing teeth and the distributed meshing force of the meshing teeth need to satisfy the load coordination equation shown below:

[0114] ;

[0115] In the formula, and are the base circle radius of the driving side of the active wheel and the torque transmitted, , and (j=1, 2, 3, ..., N) is the tooth pair meshing force, tooth pair stiffness and tooth pair separation distance of tooth pair j, F= , is the meshing force of the gear pair; S is the meshing error of the gear pair, K is the meshing stiffness of the gear pair, and N is the number of gear pairs, which is a positive integer greater than 1; It should be noted that in the embodiment of the present application and S are preset; during calculation, the first formula in the load coordination equation can be rearranged to To one side of the equation, the other side is left and , and then rearrange the second equation in the load coordination equation. 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 The solution equation of is derived in the same way as The related equation will be 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 It can also be obtained in the same way.

[0116] Further, in this embodiment, when performing the first iteration, 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. In the second and subsequent iterations, the tooth pair stiffness calculated in step 403 is used. Substitute into the load coordination equation to calculate the tooth pair meshing force for each tooth pair Calculation.

[0117] 403. Calculate the Hertzian contact stiffness, bending stiffness, radial compression stiffness and shear stiffness of each tooth pair according to the calculated tooth pair meshing force, and calculate the tooth pair stiffness of each tooth pair according to the Hertzian contact stiffness, the bending stiffness, the radial compression stiffness and the shear stiffness;

[0118] In this embodiment, research shows that during the meshing process, the potential energy stored on the meshing teeth of the master and driven wheels includes four parts: Hertz contact potential energy , bending potential energy , radial compression potential energy and shear potential ; In gear i, these four parts of potential energy correspond to the Hertzian contact stiffness , bending stiffness , radial compression stiffness and shear stiffness , can be obtained by the following four formulas:

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] In the formula, and are the elastic modulus and Poisson’s ratio of gear i, (i=g or p) is the radius of curvature at the meshing position, which can be obtained from Figure 5 Sure; , , ,in, is the half tooth thickness at the microelement dx, B is the tooth width; d is the meshing point X (X= or , respectively represent the tooth height of the asymmetric spur gear pair at the drive side or tooth back side meshing), x is the microelement dx distance from the meshing point X (X= or , respectively represent the distance of the asymmetric spur gear pair meshing on the drive side or the tooth back side), dx is the microelement width, is the load angle of the meshing teeth of gear i in tooth pair j (j=1, 2, ..., N, N is a positive integer) at the meshing point X, is the Hertzian contact half-width of tooth pair j (j=1, 2, ..., N, N is a positive integer), which can be obtained by the following formula:

[0124] ;

[0125] Through the input gear i(i =p or g ） The parameters of the asymmetric spur gear can be obtained i In the tooth pair j Hertz contact stiffness on (j=1, 2, ..., N, N is a positive integer) k h,j , bending stiffness k bj,i , radial compression stiffness k aj,i , shear stiffness k sj,i and asymmetric spur gears i The matrix deformation stiffness k fi. .

[0126] Furthermore, in this embodiment, according to the energy method, it can be known that the gear pair j ( j =1, 2, …, N , N is a positive integer) It can be obtained by the following formula:

[0127] .

[0128] 404. Calculate the tooth pair meshing stiffness according to the tooth pair stiffness, the tooth pair meshing force and the tooth pair separation distance;

[0129] In this embodiment, according to the gear meshing principle, the meshing stiffness of the meshing tooth pair and the allocated meshing force of the meshing tooth pair need to satisfy the load coordination equation shown below:

[0130] ;

[0131] In the formula, and are the base circle radius of the driving side of the active wheel and the torque transmitted, , and (j=1, 2, 3, ..., N) is the tooth pair meshing force, tooth pair stiffness and tooth pair separation distance of tooth pair j, F= , is the meshing force of the gear pair; S is the meshing error of the gear pair, K is the meshing stiffness of the gear pair, and N is the number of gear pairs, which is a positive integer greater than 1; It should be noted that in the embodiment of the present application and S are preset; , and It has been obtained through steps 401 to 403, and the tooth pair meshing stiffness K can be obtained through the load coordination equation.

[0132] 500. Calculate the comprehensive meshing stiffness of the gear pair according to the calculated matrix deformation stiffness and the tooth pair parameters;

[0133] Specifically, the steps include:

[0134] 501. Obtaining a matrix deformation correction coefficient;

[0135] 502. Calculate the comprehensive meshing stiffness of the gear pair according to the matrix deformation correction coefficient, the meshing stiffness of the tooth pair and the matrix deformation stiffness;

[0136] In this embodiment, the comprehensive meshing stiffness of the asymmetric spur gear pair can be obtained by the following formula:

[0137] ;

[0138] In the formula, (i=p or g), is the base deformation correction coefficient, which is set to 1.1 in this embodiment; K is the tooth pair meshing stiffness, which is obtained through the load equation in step 404.

[0139] 600. Calculate the difference between the comprehensive meshing stiffness of the gear pair and the initial value of the meshing stiffness of the gear pair, and determine whether the calculated difference meets a threshold condition;

[0140] Specifically, judge Whether it is satisfied; among them, is the initial value of the gear pair meshing stiffness, is the comprehensive meshing stiffness of the gear pair, It is a constant and is pre-set by the staff.

[0141] 701. If the calculated difference does not meet the threshold condition, that is, when , the calculated gear pair comprehensive meshing stiffness is used as the initial meshing stiffness value of the gear pair, and the dynamic meshing force of the gear pair is calculated according to the calculated initial meshing stiffness value of the gear pair, so as to iteratively calculate the gear pair comprehensive meshing stiffness obtained in the previous calculation as the initial meshing stiffness value of the gear pair calculated again;

[0142] In this embodiment, when the calculated difference does not meet the threshold condition, the calculated replace , and recalculate the dynamic meshing force of the gear pair and the comprehensive meshing stiffness of the gear pair to gradually correct the calculated comprehensive meshing stiffness of the gear pair until the threshold condition is met until.

[0143] 702. If the calculated difference satisfies the threshold condition, updating the simulation time;

[0144] When When the calculated difference meets the threshold condition, the simulation time is updated; in this embodiment, when the calculated difference meets the threshold condition, it indicates that the comprehensive meshing stiffness of the gear pair corresponding to the current meshing state has been obtained, and then the simulation time is compared with the simulation end time to determine whether to continue the next dynamic meshing simulation of the asymmetric spur gear.

[0145] 703. Determine whether the updated simulation time is greater than the preset simulation end time, that is, determine Whether satisfied.

[0146] 704. If not, then , the calculated gear pair comprehensive meshing stiffness is used as the initial meshing stiffness value of the gear pair, and the process returns to calculate the dynamic meshing force of the gear pair according to the calculated initial meshing stiffness value of the gear pair;

[0147] 705. If so, then When , the iteration is jumped out, that is, the execution of steps 200 to 600 is stopped.

[0148] The present application discloses a method for determining the meshing stiffness of an asymmetric spur gear. By analyzing the meshing phase relationship between the driving side and the tooth back side of the asymmetric spur gear, and analyzing the coupling effect between the dynamic meshing force of the asymmetric spur gear pair and its meshing state, the tooth pair meshing force of the asymmetric spur gear pair and the comprehensive meshing stiffness of the gear pair can be accurately determined, thereby improving the accuracy of mechanical modeling of the asymmetric spur gear transmission system.

[0149] To facilitate the subsequent result presentation, a brief description of the method of the present invention and the traditional models (Model 1 and Model 2) is given, as shown in Table 3.

[0150] Table 3 Model definition

[0151]

[0152] According to the parameters shown in Table 3, the torque transmitted by the driving wheel of the asymmetric gear pair is set to T p =0.1Nm, the driving wheel speed is w p =408.6rad / s; then based on Figure 2 The algorithm of the present invention shown in the figure can be used to obtain the meshing stiffness and dynamic meshing force of the asymmetric spur gear pair through MATLAB, as shown in Figure 9a and Figure 9b shown.

[0153] Depend on Figure 9a and Figure 9b It can be seen that the results predicted by Model 1 and Model 2 are quite different from the predicted values ​​of the method of the present invention, which means that under high-speed and light-load conditions, the coupling effect between the dynamic meshing force of the asymmetric spur gear pair and its meshing state has a significant influence; on the other hand, Figure 9b The results also show that the asymmetric spur gear pair experiences reverse collision, which leads to Figure 9a The singularity of the meshing stiffness of the asymmetric spur gear pair is shown, and these phenomena indicate the rationality of the method of the present invention in considering the coupling effect between the dynamic meshing force of the asymmetric spur gear pair and its meshing state.

[0154] The above describes the method for determining the meshing stiffness of an asymmetric spur gear in an embodiment of the present invention. The following describes the device for determining the meshing stiffness of an asymmetric spur gear in an embodiment of the present invention. Figure 3 , an embodiment of the device for determining the meshing stiffness of an asymmetric spur gear in an embodiment of the present invention comprises:

[0155] The first calculation module 801 is used to calculate the initial value of the meshing stiffness of the gear pair according to the energy method based on the acquired design parameters and operating parameters of the asymmetric spur gear;

[0156] A confirmation module 802 is used to calculate the dynamic meshing force of the gear pair according to the calculated initial value of the meshing stiffness of the gear pair, and to confirm the meshing state of the asymmetric spur gear pair according to the numerical value of the dynamic meshing force of the gear pair;

[0157] The second calculation module 803 is used to calculate the meshing parameters corresponding to the confirmed meshing state, and calculate the deformation stiffness of the substrate according to the meshing parameters;

[0158] The third calculation module 804 is used to obtain the tooth pair parameters of each tooth pair, and calculate the comprehensive meshing stiffness of the gear pair according to the calculated matrix deformation stiffness and the tooth pair parameters;

[0159] A judgment module 805 is used to calculate the difference between the comprehensive meshing stiffness of the gear pair and the initial value of the meshing stiffness of the gear pair, and judge whether the calculated difference meets the threshold condition;

[0160] The iteration module 806 is used to use the calculated comprehensive meshing stiffness of the gear pair as the initial meshing stiffness of the gear pair if the calculated difference does not meet the threshold condition, and trigger the confirmation module to return to calculate the dynamic meshing force of the gear pair based on the calculated initial meshing stiffness of the gear pair.

[0161] above Figure 3 The asymmetric spur gear meshing stiffness determination device in the embodiment of the present invention is described in detail from the perspective of modular functional entities. The asymmetric spur gear meshing stiffness determination device in the embodiment of the present invention is described in detail from the perspective of hardware processing.

[0162] Figure 4 1 is a schematic diagram of the structure of an asymmetric spur gear meshing stiffness determination device provided by an embodiment of the present invention. The asymmetric spur gear 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 asymmetric spur gear 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 asymmetric spur gear meshing stiffness determination device 900 to implement the steps of the asymmetric spur gear meshing stiffness determination method provided by the above-mentioned method embodiments.

[0163] The asymmetric spur gear meshing stiffness determination device 900 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. Those skilled in the art may understand that the asymmetric spur gear meshing stiffness determination device structure shown in the present application does not constitute a limitation on the asymmetric spur gear meshing stiffness determination device, and may include more or less components than shown in the figure, or combine certain components, or arrange components differently.

[0164] 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, cause the computer to execute the steps of the method for determining the meshing stiffness of an asymmetric spur gear.

[0165] 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.

[0166] 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.

[0167] 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 an asymmetric spur gear, characterized in that: include: Based on the obtained design parameters and operating parameters of the asymmetric spur gear, the initial value of the gear pair meshing stiffness is calculated according to the energy method; The dynamic meshing force of the gear pair is calculated according to the calculated initial value of the meshing stiffness of the gear pair, and the meshing state of the asymmetric spur gear pair is confirmed according to the numerical value of the dynamic meshing force of the gear pair; Specifically, when the calculated dynamic meshing force of the gear pair is less than zero, it indicates that the asymmetric spur gear pair has tooth back meshing; When the calculated dynamic meshing force of the gear pair is equal to zero, it indicates that the asymmetric spur gear pair is not meshing; When the calculated dynamic meshing force of the gear pair is greater than zero, it indicates that the asymmetric spur gear pair is meshing on the driving side; Calculating meshing parameters corresponding to the confirmed meshing state; Specifically, when the asymmetric spur gear pair has back-side tooth meshing, the back-side tooth meshing position is determined, and the back-side tooth meshing parameters at the back-side tooth meshing position are determined, wherein the back-side tooth meshing parameters include a pressure angle at the back-side tooth meshing point and a load angle at the back-side tooth meshing point; When the asymmetric spur gear pair is engaged on the driving side, determining the driving side engagement position and the driving engagement parameters at the driving side engagement position, wherein the driving engagement parameters include a pressure angle at the driving side engagement point and a load angle at the driving side engagement point; Calculate the matrix deformation stiffness based on the meshing parameters; Acquire the tooth pair parameters of each tooth pair, and calculate the comprehensive meshing stiffness of the gear pair according to the calculated matrix deformation stiffness and the tooth pair parameters; Calculating the difference between the comprehensive meshing stiffness of the gear pair and the initial value of the meshing stiffness of the gear pair, and determining whether the calculated difference satisfies a threshold condition; If the calculated difference does not meet the threshold condition, the calculated comprehensive meshing stiffness of the gear pair is used as the initial meshing stiffness value of the gear pair, and the process returns to calculate the dynamic meshing force of the gear pair based on the calculated initial meshing stiffness value of the gear pair.

2. A method for determining meshing stiffness of an asymmetric spur gear according to claim 1, characterized in that: The obtaining of the gear pair parameters of each gear pair specifically includes: Acquire tooth pair parameters of each tooth pair, and calculate the tooth pair separation distance of each tooth pair according to the acquired tooth pair parameters; Calculating the tooth pair meshing force of each tooth pair according to the calculated tooth pair separation distance; Calculating the Hertzian contact stiffness, bending stiffness, radial compression stiffness and shear stiffness of each tooth pair according to the calculated tooth pair meshing force, and calculating the tooth pair stiffness of each tooth pair according to the Hertzian contact stiffness, the bending stiffness, the radial compression stiffness and the shear stiffness; The tooth pair meshing stiffness is calculated according to the tooth pair stiffness, the tooth pair meshing force and the tooth pair separation distance.

3. A method for determining meshing stiffness of an asymmetric spur gear according to claim 2, characterized in that: The calculating of the comprehensive meshing stiffness of the gear pair according to the calculated matrix deformation stiffness and the tooth pair parameters specifically includes: Obtaining the matrix deformation correction coefficient; The comprehensive meshing stiffness of the gear pair is calculated according to the matrix deformation correction coefficient, the tooth pair meshing stiffness and the matrix deformation stiffness.

4. The method for determining the meshing stiffness of an asymmetric spur gear according to claim 1, characterized in that: The step of determining whether the calculated difference satisfies a threshold condition further includes: If the calculated difference meets the threshold condition, the simulation time is updated; Determine whether the updated simulation time is greater than the preset simulation end time; If not, the calculated integrated meshing stiffness of the gear pair is used as the initial meshing stiffness value of the gear pair, and the process returns to calculate the dynamic meshing force of the gear pair according to the calculated initial meshing stiffness value of the gear pair.

5. A device for determining the meshing stiffness of an asymmetric spur gear, characterized in that: include: A first calculation module is used to calculate the initial value of the meshing stiffness of the gear pair according to the energy method based on the obtained design parameters and operating condition parameters of the asymmetric spur gear; A confirmation module is used to calculate the dynamic meshing force of the gear pair according to the calculated initial value of the meshing stiffness of the gear pair, and to confirm the meshing state of the asymmetric spur gear pair according to the numerical value of the dynamic meshing force of the gear pair; specifically, when the calculated dynamic meshing force of the gear pair is less than zero, it indicates that the asymmetric spur gear pair has tooth back meshing; When the calculated dynamic meshing force of the gear pair is equal to zero, it indicates that the asymmetric spur gear pair is not meshing; When the calculated dynamic meshing force of the gear pair is greater than zero, it indicates that the asymmetric spur gear pair is meshing on the driving side; The second calculation module is used to calculate the meshing parameters corresponding to the confirmed meshing state. Specifically, when the asymmetric spur gear pair has back-side meshing, the back-side meshing position is determined, and the back-side meshing parameters at the back-side meshing position are determined, and the back-side meshing parameters include the pressure angle at the back-side meshing point and the load angle at the back-side meshing point; when the asymmetric spur gear pair has drive-side meshing, the drive-side meshing position is determined, and the drive meshing parameters at the drive-side meshing position are determined, and the drive meshing parameters include the pressure angle at the drive-side meshing point and the load angle at the drive-side meshing point; Calculate the matrix deformation stiffness based on the meshing parameters; A third calculation module is used to obtain the tooth pair parameters of each tooth pair, and calculate the comprehensive meshing stiffness of the gear pair according to the calculated matrix deformation stiffness and the tooth pair parameters; A judgment module, used for calculating the difference between the comprehensive meshing stiffness of the gear pair and the initial value of the meshing stiffness of the gear pair, and judging whether the calculated difference satisfies a threshold condition; The iteration module is used for adopting the calculated comprehensive meshing stiffness of the gear pair as the initial meshing stiffness of the gear pair if the calculated difference does not meet the threshold condition, and triggering the confirmation module to return to execute the calculation of the dynamic meshing force of the gear pair according to the calculated initial meshing stiffness of the gear pair.

6. An asymmetric spur gear meshing stiffness determination device, characterized in that: The asymmetric spur gear 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 asymmetric spur gear meshing stiffness determination device to perform each step of the asymmetric spur gear meshing stiffness determination method 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 a processor, the various steps of the method for determining the meshing stiffness of an asymmetric spur gear as claimed in any one of claims 1 to 4 are implemented.

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