Gear dynamic meshing stiffness calculation method and device

Abstract

The application discloses a kind of gear dynamic engagement stiffness calculation methods, comprising: obtaining the geometric parameters of gear pair, material attribute and gear motion state parameter;Calculate overall stiffness matrix, overall mass matrix, overall damping matrix and overall external load matrix;Establish the dynamic analysis finite element equation when gear engagement, solve the dynamic vibration displacement of engagement point at different time by using average acceleration method;According to dynamic vibration displacement, the dynamic stiffness of two gears in gear pair is calculated, and single-tooth engagement stiffness is obtained;According to the coincidence degree of gear pair, single-tooth engagement stiffness is superimposed to obtain dynamic engagement stiffness;Also disclosed is a kind of device, including motion state module, three-dimensional scanning module and processing module.The application is based on finite element method, not only considers the influence of angular position change on engagement stiffness, but also considers the influence of gear speed on gear engagement stiffness, more truly reflects the dynamic characteristics of gear when transmission, so that the calculation result is more accurate.

Description

Technical Field

[0001] This invention relates to the field of gear testing technology, and in particular to a method and apparatus for calculating the dynamic meshing stiffness of gears. Background Technology

[0002] Among all mechanical transmissions, gear transmissions are widely used due to their accurate transmission ratio, high efficiency, compact structure, and smooth transmission. For gear transmissions with high precision requirements, research on gear dynamic characteristics, fault diagnosis, and gear parameter optimization design is indispensable. Therefore, accurately calculating the meshing stiffness of gears during transmission plays a crucial role in high-speed, high-precision gear transmissions. Based on the above issues, numerical simulation calculations of gear nonlinear dynamics have become an increasingly prominent problem. Currently, simulation methods for gear nonlinear dynamics mostly rely on existing traditional methods, such as: ISO regression formulas, semi-empirical regression formulas, Ishikawa formulas, and finite element methods. ISO regression formulas calculate meshing stiffness through regression equations; semi-empirical regression formulas are obtained by fitting finite element data, providing sufficient accuracy in calculating meshing stiffness within a limited range; while the Ishikawa formula considers the influence of various parameters on tooth deformation and is a calculation method based on mechanics of materials. These numerical calculation methods all consider time-varying meshing stiffness with angular position changes within the statics framework.

[0003] The Chinese patent document "A Method for Measuring and Calculating Time-Varying Gear Meshing Stiffness" (publication number CN108534966B, publication date September 14, 2018) utilizes a distributed fiber optic grating sensor to directly measure the dynamic strain of multiple tooth roots of a rotating gear. The collected tooth root stress-strain signals are converted into tooth root deformation through data processing. The stress at each tooth root is obtained through torque measurement and load distribution calculation, thus yielding the time-varying meshing stiffness of a single tooth. Then, the meshing stiffness of each tooth is interpolated and numerically summed to obtain the overall meshing stiffness of the gear mesh. This invention can measure the strain of multiple tooth roots during gear meshing without affecting the normal operation of the gear, making it suitable for actual dynamic operating conditions. This technology still calculates the time-varying meshing stiffness based on the statics of angular position. However, during transmission, gear pairs are often subjected to additional dynamic excitations caused by rotational speed or other factors affected by rotational speed, which exacerbates the instability of gear transmission. Existing technology ignores the influence of gear meshing speed changes on meshing stiffness under the influence of rotational speed, resulting in an inability to accurately describe the dynamic phenomena of gear systems under the influence of rotational speed. Summary of the Invention

[0004] This invention aims to overcome the problem in existing technologies that neglect the influence of gear meshing speed changes on meshing stiffness, thus failing to accurately describe the dynamic characteristics of gear pairs under the influence of rotational speed. It provides a method and apparatus for calculating gear dynamic meshing stiffness. Based on the finite element method, it not only considers the influence of angular position changes on meshing stiffness but also further considers the influence of rotational speed on gear meshing stiffness, more realistically reflecting the dynamic characteristics of gears during transmission and making the calculation results more accurate.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for calculating the dynamic meshing stiffness of gears includes:

[0007] S1. Obtain the geometric parameters, material properties, and gear motion state parameters of the gear pair;

[0008] S2. Calculate the overall stiffness matrix, overall mass matrix, overall damping matrix, and overall external load matrix;

[0009] S3. Based on the parameters in S2, establish the finite element equation for the dynamic analysis of gear meshing, and use the average acceleration method to solve the dynamic vibration displacement of the meshing point at different times.

[0010] S4. Calculate the dynamic stiffness of the two gears in the gear pair based on the dynamic vibration displacement, and obtain the single-tooth meshing stiffness.

[0011] S5. The dynamic meshing stiffness is obtained by superimposing the single tooth meshing stiffness according to the gear pair overlap ratio.

[0012] In this invention, the overall stiffness matrix and overall mass matrix can be calculated from the geometric parameters and material properties of the gear pair according to existing finite element theory. The overall damping matrix can be calculated from the overall stiffness matrix and overall mass matrix. The overall external load matrix is ​​calculated from the external load data in the gear motion state parameters through the load distribution coefficient relationship. With these quantities known, the average acceleration method is used to solve the finite element equation for the dynamic analysis of gear meshing, thereby obtaining the dynamic vibration displacement of the meshing point at different times. In the average acceleration method, the step size of the average acceleration method considers the meshing speed under the influence of gear rotation speed, making the final calculated single-tooth meshing stiffness more accurate. Therefore, the dynamic meshing stiffness obtained from the single-tooth meshing stiffness based on the gear pair overlap is also more accurate and more in line with the real situation.

[0013] Preferably, in the average acceleration method, the step size dt is... iThe calculation method is as follows: Divide the involute tooth profile of the meshing gear into n nodes, and calculate the time interval of the meshing force from the i-th node to the (i+1)-th node, that is, the distance between the i-th node and the (i+1)-th node divided by the average meshing speed between the two nodes.

[0014] This invention employs the average acceleration method, which incorporates the meshing speed influenced by gear rotation speed into the step size calculation process. The step size is determined by dividing the distance between two adjacent nodes on the involute tooth profile of the meshing gear by the average meshing speed between the two nodes. The step size is smaller when the meshing speed is faster and larger when the meshing speed is slower, thus allowing the calculation of the influence of meshing speed on gear stiffness.

[0015] Preferably, S2 includes the following steps:

[0016] S21. Calculate the element stiffness matrix of each element in the gear and assemble them to obtain the overall stiffness matrix {K}.

[0017] S22. Calculate the unit mass matrix of each unit in the gear, and assemble them to obtain the overall mass matrix {M};

[0018] S23. Calculate the element external load matrix of each unit in the gear, and assemble them to obtain the overall external load matrix {F};

[0019] S24. Calculate the overall damping matrix {C} = α{M} + β{K}, where α is the mass damping coefficient and β is the stiffness damping coefficient.

[0020] In this invention, depending on the selected element of the gear, the final calculated element matrices are also different, and each element matrix has its corresponding geometric position. The element matrix includes the element stiffness matrix, the element mass matrix, and the element external load matrix. The element external load matrix is ​​a column vector with only one column. Only the row element corresponding to the meshing point position is not zero, which represents the magnitude of the external load. All other row elements are zero.

[0021] Preferably, the element stiffness matrix of each element in the gear is calculated based on the geometric parameters and material properties of the gear pair; the assembly stiffness matrix is ​​obtained by accumulating the element stiffness matrices of each element according to their relative positions using the direct assembly method; the fixed inner hole nodes in the gear are extracted, and the stiffness matrices corresponding to all inner hole nodes are deleted from the assembly stiffness matrix to obtain the overall stiffness matrix. Similarly, the element mass matrix of each element in the gear is calculated based on the geometric parameters and material properties of the gear pair; the assembly mass matrix is ​​obtained by accumulating the element mass matrices of each element according to their relative positions using the direct assembly method; the fixed inner hole nodes in the gear are extracted, and the mass matrices corresponding to all inner hole nodes are deleted from the assembly mass matrix to obtain the overall mass matrix.

[0022] In this invention, calculating the element stiffness matrix requires the element's coordinate position, element thickness (gear thickness), element elastic modulus, and element Poisson's ratio; calculating the element mass matrix requires the element's coordinate position, element thickness (gear thickness), and element material density. Then, a direct assembly method is used to assemble and accumulate the element stiffness matrix and element mass matrix according to the coordinate position relationship of the elements to obtain the assembled stiffness matrix and assembled mass matrix. Simultaneously, during the finite element method analysis, the degrees of freedom of all nodes at the gear's inner hole are constrained. Therefore, the mass matrix and stiffness matrix corresponding to the inner hole nodes need to be deleted from the assembled stiffness matrix and assembled mass matrix to obtain the required overall stiffness matrix and overall mass matrix. The calculation method for the overall external load matrix in this invention is also the same as that for the overall stiffness matrix.

[0023] Preferably, the meshing speed v of the i-th node ki It can be determined by the gear rotation speed n j The calculation yielded:

[0024] ;

[0025] Where N xi and N yi Let x and y be the x-coordinates and y-coordinates of the i-th node, respectively; x k and y k These are the x-axis and y-axis coordinates of the gear meshing point, respectively. In this invention, the meshing speed can be calculated from the gear rotation speed in the gear motion state parameters, and it is necessary to consider the meshing speed in two directions simultaneously, namely the speed in the x-axis direction and the speed in the y-axis direction.

[0026] Preferably, the calculation in S4 yields the first gear in the gear pair at t i The dynamic stiffness at time k is gi The second gear at t i The dynamic stiffness at time k is pi The combination of the two results in , where k ci This represents the single-tooth meshing stiffness. In this invention, t... i The dynamic stiffness of the gear meshing point at a given moment is equal to the meshing force at that moment divided by the dynamic vibration displacement at that moment. By applying this dynamic stiffness formula to the finite element models of the first and second gears of the gear pair, the dynamic stiffness of the two gears can be obtained separately, and then combined to obtain the single-tooth meshing stiffness.

[0027] A gear dynamic meshing stiffness calculation device, comprising:

[0028] The motion status module is used to acquire data on the external load and gear speed of the gear pair and input them into the processing module;

[0029] The 3D scanning module is used to acquire the geometric parameters of the gear pair and input them into the processing module to build the gear pair model;

[0030] The processing module calculates the single-tooth meshing stiffness based on the received data, and then superimposes the single-tooth meshing stiffness according to the overlap ratio of the gear pair to obtain the dynamic meshing stiffness.

[0031] The motion state module of this invention includes a torque sensor installed on the input or output shaft corresponding to the gear for measuring torque. The torque data is used to calculate the total external load on the gear and, based on the gear's geometric parameters and load distribution coefficient, the external load data during gear meshing is calculated. The motion state module also includes an angle encoder for measuring the instantaneous angular displacement of the gear during rotation, thereby calculating the gear speed. A three-dimensional scanning module can perform a three-dimensional scan of the gear pair to obtain geometric parameter data, and the processing module establishes a finite element model of the gear pair based on the data. The processing module stores attribute data for gears made of different materials, and can also allow operators to input material attribute data obtained through querying, and calculate and process the dynamic meshing stiffness.

[0032] The present invention has the following beneficial effects: Based on the finite element method, it not only considers the influence of angular position change on meshing stiffness, but also further considers the influence of gear speed on gear meshing stiffness, which more realistically reflects the dynamic characteristics of gears during transmission and makes the calculation results more accurate. Attached Figure Description

[0033] Figure 1 This is a flowchart of the dynamic meshing stiffness calculation method of the present invention;

[0034] Figure 2 This is a schematic diagram of a spur gear pair in an embodiment of the present invention;

[0035] Figure 3 This is a simplified model diagram of the gear pair in an embodiment of the present invention;

[0036] Figure 4 This is a diagram showing the dynamic meshing stiffness of the gear pair according to an embodiment of the present invention. Detailed Implementation

[0037] The present invention will now be further described with reference to the accompanying drawings and specific embodiments.

[0038] like Figure 1 As shown, a method for calculating the dynamic meshing stiffness of gears includes:

[0039] S1. Obtain the geometric parameters, material properties, and gear motion parameters of the gear pair.

[0040] S2. Calculate the overall stiffness matrix, overall mass matrix, overall damping matrix, and overall external load matrix; S2 includes the following steps:

[0041] S21. Calculate the element stiffness matrix of each element in the gear and assemble them to obtain the overall stiffness matrix {K}.

[0042] S22. Calculate the unit mass matrix of each unit in the gear, and assemble them to obtain the overall mass matrix {M};

[0043] S23. Calculate the element external load matrix of each unit in the gear, and assemble them to obtain the overall external load matrix {F};

[0044] S24. Calculate the overall damping matrix {C} = α{M} + β{K}, where α is the mass damping coefficient and β is the stiffness damping coefficient.

[0045] S3. Based on the parameters in S2, establish the finite element equations for the dynamic analysis of gear meshing, and use the average acceleration method to solve the dynamic vibration displacement of the meshing point at different times; in the average acceleration method, the step size dt is... i The calculation method is as follows: Divide the involute tooth profile of the meshing gears into n nodes, and calculate the time interval for the meshing force to move from the i-th node to the (i+1)-th node, which is the distance between the i-th node and the (i+1)-th node divided by the average meshing speed between the two nodes. The meshing speed v at the i-th node is... ki It can be determined by the gear rotation speed n j The calculation yielded:

[0046] ;

[0047] Where N xi and N yi These are the x-axis and y-axis coordinates of the i-th node, respectively.

[0048] S4. Calculate the dynamic stiffness of the two gears in the gear pair based on the dynamic vibration displacement, and obtain the single-tooth meshing stiffness; S4 calculates the first gear in the gear pair at t i The dynamic stiffness at time k is gi The second gear at t i The dynamic stiffness at time k is pi The combination of the two results in , where k ci This indicates the meshing stiffness of a single tooth.

[0049] S5. The dynamic meshing stiffness is obtained by superimposing the single tooth meshing stiffness according to the gear pair overlap ratio.

[0050] Calculate the element stiffness matrix of each element in the gear based on the geometric parameters and material properties of the gear pair. Then, use the direct assembly method to accumulate the element stiffness matrices of each element based on their relative positions to obtain the assembly stiffness matrix. Extract the fixed internal hole nodes in the gear and delete the stiffness matrices corresponding to all internal hole nodes from the assembly stiffness matrix to obtain the overall stiffness matrix. Similarly, calculate the element mass matrix of each element in the gear based on the geometric parameters and material properties of the gear pair. Use the direct assembly method to accumulate the element mass matrices of each element based on their relative positions to obtain the assembly mass matrix. Extract the fixed internal hole nodes in the gear and delete the mass matrices corresponding to all internal hole nodes from the assembly mass matrix to obtain the overall mass matrix.

[0051] In this invention, the overall stiffness matrix and overall mass matrix can be calculated from the geometric parameters and material properties of the gear pair according to existing finite element theory. The overall damping matrix can be calculated from the overall stiffness matrix and overall mass matrix. The overall external load matrix is ​​calculated from the external load data in the gear motion state parameters through the load distribution coefficient relationship. With these quantities known, the average acceleration method is used to solve the finite element equation for the dynamic analysis of gear meshing, thereby obtaining the dynamic vibration displacement of the meshing point at different times. In the average acceleration method, the step size of the average acceleration method considers the meshing speed under the influence of gear rotation speed, making the final calculated single-tooth meshing stiffness more accurate. Therefore, the dynamic meshing stiffness obtained from the single-tooth meshing stiffness based on the gear pair overlap is also more accurate and more in line with the real situation.

[0052] In this invention, the average acceleration method is used, which adds the factor of meshing speed under the influence of gear rotation speed to the step size calculation process of the average acceleration method. The step size is the movement time interval obtained by dividing the distance between two adjacent nodes on the involute tooth profile of the meshing gear by the average meshing speed between the two nodes. When the meshing speed is faster, the step size is smaller, and vice versa, thus calculating the effect of meshing speed on gear stiffness.

[0053] In this invention, depending on the selected element of the gear, the final calculated element matrices are also different, and each element matrix has its corresponding geometric position. The element matrix includes the element stiffness matrix, the element mass matrix, and the element external load matrix. The element external load matrix is ​​a column vector with only one column. Only the row element corresponding to the meshing point position is not zero, which represents the magnitude of the external load. All other row elements are zero.

[0054] In this invention, calculating the element stiffness matrix requires the element's coordinate position, element thickness (gear thickness), element elastic modulus, and element Poisson's ratio; calculating the element mass matrix requires the element's coordinate position, element thickness (gear thickness), and element material density. Then, a direct assembly method is used to assemble and accumulate the element stiffness matrix and element mass matrix according to the coordinate position relationship of the elements to obtain the assembled stiffness matrix and assembled mass matrix. Simultaneously, during the finite element method analysis, the degrees of freedom of all nodes at the gear's inner hole are constrained. Therefore, the mass matrix and stiffness matrix corresponding to the inner hole nodes need to be deleted from the assembled stiffness matrix and assembled mass matrix to obtain the required overall stiffness matrix and overall mass matrix. The calculation method for the overall external load matrix in this invention is also the same as that for the overall stiffness matrix.

[0055] In this invention, the meshing speed can be calculated from the gear rotation speed in the gear motion state parameters. It is necessary to consider the meshing speed in two directions simultaneously, namely the speed in the x-axis direction and the speed in the y-axis direction. In this invention, t... i The dynamic stiffness of the gear meshing point at a given moment is equal to the meshing force at that moment divided by the dynamic vibration displacement at that moment. By applying this dynamic stiffness formula to the finite element models of the first and second gears of the gear pair, the dynamic stiffness of the two gears can be obtained separately, and then combined to obtain the single-tooth meshing stiffness.

[0056] A gear dynamic meshing stiffness calculation device, comprising:

[0057] The motion status module is used to acquire data on the external load and gear speed of the gear pair and input them into the processing module;

[0058] The 3D scanning module is used to acquire the geometric parameters of the gear pair and input them into the processing module to build the gear pair model;

[0059] The processing module calculates the single-tooth meshing stiffness based on the received data, and then superimposes the single-tooth meshing stiffness according to the overlap ratio of the gear pair to obtain the dynamic meshing stiffness.

[0060] The motion state module of this invention includes a torque sensor installed on the input or output shaft corresponding to the gear for measuring torque. The torque data is used to calculate the total external load on the gear and, based on the gear's geometric parameters and load distribution coefficient, the external load data during gear meshing is calculated. The motion state module also includes an angle encoder for measuring the instantaneous angular displacement of the gear during rotation, thereby calculating the gear speed. A three-dimensional scanning module can perform a three-dimensional scan of the gear pair to obtain geometric parameter data, and the processing module establishes a finite element model of the gear pair based on the data. The processing module stores attribute data for gears made of different materials, and can also allow operators to input material attribute data obtained through querying, and calculate and process the dynamic meshing stiffness.

[0061] In embodiments of the present invention, such as Figure 2 The diagram shows a meshing gear pair. In this embodiment, the first gear is the large gear, and the second gear is the small gear. This meshing gear pair can be simplified as follows: Figure 3 The schematic diagram of the single-tooth gear model shown is provided, in which the degrees of freedom of all nodes within the gear are constrained. Figure 2 For the pinion, the starting point of engagement near the tooth root is denoted as B1, and the ending point of engagement near the tooth tip is denoted as B2. For the gear, the opposite is true. b Let r be the base circle radius of the gear. f denoted by ...

[0062] First, calculate the coordinate range from the start of meshing to the end of meshing. For any gear, its base circle half-angle β2 can be expressed as... Where z is the number of teeth on the gear, and α is the pressure angle of the gear. Then, calculate the meshing angle β at the initial meshing point of the pinion. ps Its expression is:

[0063] ;

[0064] Where z1 and z2 represent the number of teeth of the two gears in the gear pair, respectively, the coordinates (x, y) of the starting meshing point of the pinion can be obtained from the meshing angle at the starting meshing point. ps ,y ps )for:

[0065] .

[0066] The above calculation can be obtained from the above public announcement. Figure 2 The coordinates of meshing points B1 and B2 in the single-tooth gear model are given. Point K in the figure represents any meshing point between meshing points B1 and B2. k ,y k () represents the coordinates of point K; therefore, given the coordinates of the meshing point K, the meshing angle β corresponding to that point can be obtained, and its expression is:

[0067] ;

[0068] Then calculate the meshing angle β at the final meshing point of the large gear. gn Its expression is:

[0069] ;

[0070] Where z1 and z2 represent the number of teeth of the two gears in the gear pair, respectively, βgs β represents the meshing angle at the point where the large gear begins to mesh. pn The engagement angle β represents the engagement angle at the pinion's final engagement point. The engagement points of the gear's start and end are known; both are the intersections of the involute curve and the addendum circle. Therefore, β can be calculated using the known coordinates of these intersections and the formula for calculating the engagement angle β. gs and β pn The coordinates (x, y) of the large gear's final meshing point can be obtained from the meshing angle at the final meshing point. gn ,y gn ).

[0071] The external load acting on the large and small gears is F. k The angle between it and the y-axis is the meshing angle β. F kx and F ky F respectively k The components of the force projected onto the x-axis and y-axis can be expressed by the following formula: ;

[0072] Then, for the meshing gear pair, the meshing velocity acting on the pinion moves from left to right from the initial meshing point B1; the meshing velocity acting on the gear moves from right to left from the initial meshing point B2, while considering the meshing velocities in both the x-axis and y-axis directions; the magnitude v of the meshing velocity acting on the gear and pinion... ki It can be determined by the gear rotation speed n j (j=p,g) is expressed as:

[0073] .

[0074] Assuming the involute tooth profile of the meshing gears is divided into n nodes, then for any node, the time interval d for the meshing force to move from the i-th node to the (i+1)-th node is... ti This can be expressed as:

[0075] ;

[0076] Where N xi and N yi Let N be the x-coordinate and y-coordinate of the i-th node, respectively; x(i+1) and N y(i+1) Let x be the x-coordinate and y-coordinate of the (i+1)th node; k and y k These are the x-axis and y-axis coordinates of the gear meshing point, respectively. Here, d... ti It is also the step size in the subsequent average acceleration method.

[0077] According to d'Alembert's principle, after introducing inertial and damping forces into the static analysis finite element equations for gear meshing, the structure remains in equilibrium, resulting in the dynamic analysis finite element equations for gear meshing, which can be expressed as:

[0078] ;

[0079] Where {M} is the global mass matrix, {K} is the global stiffness matrix, {C} is the global damping matrix, and {F} is the nodal time-varying load matrix, i.e., the global external load matrix. Here is the nodal acceleration matrix. Let {X} be the nodal velocity matrix, and {X} be the nodal dynamic vibration displacement matrix. In the embodiments of this invention, all overall matrices are obtained by assembling the element matrices using a direct assembly method. The element stiffness matrix and element mass matrix are assembled using the direct assembly method. The relative positions of the stiffness matrix and mass matrix corresponding to each element are accumulated, and the assembled matrix can be expressed as:

[0080] ;

[0081] Where N is the total number of units in the gear. To extend to the i-th element stiffness matrix required by the global stiffness matrix, To expand to the i-th element mass matrix required for the overall mass matrix, To extend to the overall external load matrix, we need the i-th element external load matrix. Since all node degrees of freedom at the gear's inner hole in the finite element model are constrained, we extract the fixed inner hole node numbers from the finite element model and delete the row and column vectors corresponding to the inner hole nodes in the assembly matrix. This means deleting the mass matrix, stiffness matrix, and external load matrix corresponding to the inner hole nodes to obtain the overall matrix:

[0082] ;

[0083] Where j min N1 is the minimum value among the node numbers in the internal hole, and N2 is the total number of nodes in the gear's internal hole. To extend to the j-th element stiffness matrix required for all fixed nodes, To expand to the j-th element mass matrix required for all fixed nodes, This is the external load matrix of the j-th element required to extend to all fixed nodes. In this embodiment, Rayleigh damping is used to obtain the overall damping matrix {C} = α{M} + β{K}, where α is the mass damping coefficient and β is the stiffness damping coefficient.

[0084] ;

[0085] Where f1 and f2 are the structural frequencies of the large and small gears, respectively, and ξ is the modal viscous damping ratio determined experimentally, typically ranging from 2% to 20%, and from 1% to 2% when the material is in the elastic stage. In this embodiment, the element stiffness matrix, element mass matrix, and element external load matrix are calculated according to existing finite element theory. The data required for the element mass matrix include: the coordinates of the nodes constituting the element, obtained by extracting coordinates from the established finite element model; the element thickness, i.e., the gear thickness parameter; and the element density, obtained by looking up the element's material properties in a table. The data required for the element stiffness matrix include: the coordinates of the nodes constituting the element, obtained by extracting coordinates from the established finite element model; the element thickness, i.e., the gear thickness parameter; and the element's elastic modulus and Poisson's ratio, obtained by looking up tables.

[0086] The dynamic vibration displacement in the finite element equations for the dynamic analysis of gear meshing is solved using the average acceleration method. The specific solution formula is as follows:

[0087] ;

[0088] in In these coefficients, the parameters take the values ​​α = 1 / 4 and δ = 1 / 2. Given the overall mass matrix, overall stiffness matrix, and overall damping matrix, the formula is solved. At the initial state t0, where the gear meshing point is the starting meshing point, the dynamic vibration displacement, velocity, and acceleration at the meshing point are all 0. Then, the known quantities are substituted into the calculation to obtain the acceleration at the first node, i.e., at time t1. ,speed And the dynamic vibration displacement {X1}, and the value at the i-th node, i.e., t, is obtained by iterative calculation using the average acceleration method. i acceleration at any moment ,speed and dynamic vibration displacement {X i}; When the i-th node is the termination point of engagement, the dynamic vibration displacement calculation of all engagement points is completed. When the i-th node is still not the termination point of engagement, the meshing force moves to the (i+1)-th node, and t i+1 =t i +d ti The calculation continues for the (i+1)th node's dynamic vibration displacement until the dynamic vibration displacement calculation for all meshing points from the start to the end of the meshing point is completed. During the calculation, the meshing angle changes accordingly as the meshing point moves, and thus the overall external load matrix also changes accordingly as the meshing point moves. Finally, the meshing force and dynamic vibration displacement corresponding to all moments and meshing points can be obtained.

[0089] In t iThe formula for calculating the dynamic stiffness of the gear meshing point at any given moment can be expressed as K. i =F i / X i F i For t i The meshing force X that acts at the gear meshing point at all times i For t i The dynamic vibration displacement of the gear meshing point at time t. Applying this dynamic stiffness calculation formula to the finite element models of the large gear and the small gear, the dynamic stiffness displacement of the large gear at time t can be obtained respectively. i Dynamic stiffness k at time t gi and the pinion at t i Dynamic stiffness k at time t pi The combination of the two results in single-tooth meshing stiffness. .

[0090] The formula for calculating the overlap ratio in a gear pair is:

[0091] ;

[0092] Where z1 is the number of teeth on the pinion and z2 is the number of teeth on the gear. The pressure angle of the pinion tooth tip circle. Let α be the pressure angle at the addendum circle of the large gear, and alpha be the pressure angle at the pitch circle. The dynamic meshing stiffness of the gear can be calculated by superimposing the meshing stiffness of individual teeth based on the contact ratio, such as... Figure 4 The diagram shown is the dynamic meshing stiffness of the gear calculated in this embodiment.

[0093] The above embodiments are further elaborations and descriptions of the present invention to facilitate understanding, and are not intended to limit the present invention in any way. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method of calculating dynamic mesh stiffness of a gear, characterized by, include: S1. Obtain the geometric parameters, material properties, and gear motion state parameters of the gear pair; S2. Calculate the overall stiffness matrix, overall mass matrix, overall damping matrix, and overall external load matrix; S3. Based on the parameters in S2, establish the finite element equation for the dynamic analysis of gear meshing, and use the average acceleration method to solve the dynamic vibration displacement of the meshing point at different times. S4. Calculate the dynamic stiffness of the two gears in the gear pair based on the dynamic vibration displacement, and obtain the single-tooth meshing stiffness. S5. The dynamic meshing stiffness is obtained by superimposing the single tooth meshing stiffness according to the gear pair overlap ratio. In the average acceleration method, the step size dt is... i The calculation method is as follows: Divide the involute tooth profile of the meshing gear into n nodes, and calculate the time interval of the meshing force from the i-th node to the (i+1)-th node, that is, the distance between the i-th node and the (i+1)-th node divided by the average meshing speed between the two nodes. The meshing speed v at the i-th node ki The gear speed n j The calculation yielded: ； Where N xi and N yi Let x and y be the x-axis coordinates and y-axis coordinates of the i-th node, respectively; j = p, g; symbols related to the large gear have the subscript g, and symbols related to the small gear have the subscript p.

2. The method of claim 1, wherein, S2 includes the following steps: S21. Calculate the element stiffness matrix of each element in the gear and assemble them to obtain the overall stiffness matrix {K}. S22. Calculate the unit mass matrix of each unit in the gear, and assemble them to obtain the overall mass matrix {M}; S23. Calculate the element external load matrix of each unit in the gear, and assemble them to obtain the overall external load matrix {F}; S24. Calculate the overall damping matrix {C} = α{M} + β{K}, where α is the mass damping coefficient and β is the stiffness damping coefficient.

3. The method of claim 2, wherein, The element stiffness matrix of each element in the gear is calculated based on the geometric parameters and material properties of the gear pair. The element stiffness matrix of each element is accumulated by the relative positions using the direct assembly method to obtain the assembly stiffness matrix. The fixed inner hole nodes in the gear are extracted, and the stiffness matrices corresponding to all inner hole nodes are deleted from the assembly stiffness matrix to obtain the overall stiffness matrix.

4. The method of claim 2, wherein, The element mass matrix of each unit in the gear is calculated based on the geometric parameters and material properties of the gear pair. The element mass matrix of each unit is accumulated by the relative positions using the direct assembly method to obtain the assembly mass matrix. The fixed inner hole nodes in the gear are extracted, and the mass matrices corresponding to all inner hole nodes are deleted from the assembly mass matrix to obtain the overall mass matrix.

5. The method of claim 1 or 3 or 4, wherein, The calculation in S4 obtains the first gear in the gear pair at t. i The dynamic stiffness at time k gi The second gear at t i The dynamic stiffness at time k pi The combination of the two yields , where k ci This indicates the meshing stiffness of a single tooth.

6. A device for calculating dynamic mesh stiffness of a gear, adapted to a method for calculating dynamic mesh stiffness of a gear according to claim 1, characterized in that, include: The motion status module is used to acquire data on the external load and gear speed of the gear pair and input them into the processing module; The 3D scanning module is used to acquire the geometric parameters of the gear pair and input them into the processing module to build the gear pair model; The processing module calculates the single-tooth meshing stiffness based on the received data, and then superimposes the single-tooth meshing stiffness according to the overlap ratio of the gear pair to obtain the dynamic meshing stiffness.

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