Rapid iterative calculation method and system for dynamic meshing stiffness of straight gear of power system

Abstract

The invention discloses a rapid iterative calculation method and system for dynamic meshing stiffness of a straight gear of a power system, and the method comprises the steps: firstly obtaining a rotating shaft parameter and a bearing parameter of the power system, building a flexible shaft model and a bearing model, and building a dynamic digital twin model of the power system in combination with gear parameters; then, the dynamic position, the dynamic attitude angle and the dynamic transmission error of an engaged tooth pair are calculated, then the center distance deviation, the staggered angle misalignment amount and the tooth surface elastic approaching amount of the gear pair are calculated, then a contact tooth surface gap sequence and an influence coefficient matrix are determined, and a gap-deformation equation set in different contact states is established; the dynamic meshing stiffness of the straight gear pair in the power system can be accurately calculated on the basis of the method, the accuracy of the digital twin model is improved, and the dynamic meshing stiffness of the straight gear pair in the power system can be accurately calculated on the basis of the method. And a theoretical basis is provided for state monitoring and health management of the power system.

Description

Technical Field

[0001] The present invention belongs to the technical field of gear measurement, and particularly relates to a fast iterative calculation method and system for the dynamic meshing stiffness of spur gears in a power system. Background Art

[0002] Power systems are usually applied as power conversion devices in equipment such as crawler vehicle engines and wind power transmissions. The main transmission components include gears, rotating shafts, and bearings, etc. And power systems usually serve under harsh working conditions, and transmission components are prone to failure. The condition monitoring and health management of power systems rely on vibration acceleration sensors on the bearing housing or box body. However, there are multiple interfaces and complex coupling paths between the internal source excitation and the sensor measurement points, and the vibration transmission mechanism is unknown. The core of solving the above problems is to accurately evaluate the load transfer at the gear interface, that is, to accurately obtain the gear dynamic meshing stiffness, so as to accurately establish the dynamic digital twin model of the power system and ultimately realize the health management of the power system.

[0003] Existing dynamic digital twin models of power systems generally input the gear meshing stiffness calculated by the energy method into the dynamic digital twin model, and cannot evaluate the gear dynamic meshing stiffness under dynamic misalignment conditions. Existing methods for calculating gear dynamic meshing stiffness mainly include the energy method based on the strain energy formula, the load-related meshing stiffness calculation method considering the elastic deformation of gear teeth, the method considering the comprehensive deformation energy of gears and shafts, and the method combining the potential energy method and the slice theory, etc. However, the above methods cannot simultaneously consider the influence of shaft flexibility and parallelism error on gear dynamic meshing stiffness, and the calculation accuracy of the methods based on the strain energy formula and the comprehensive deformation energy is not high. In addition, although the existing extended influence coefficient method can simultaneously consider shaft flexibility and parallelism error, this method needs to determine the tooth surface contact points through a large number of iterative solutions when performing gear bearing contact analysis, and the number of discrete elements required for solving the tooth surface contact stress distribution is large, resulting in low calculation efficiency and being difficult to be directly applied to the dynamic digital twin model of the power system.

[0004] In the prior art, a Chinese invention patent with the publication number of CN119227420A discloses a method for determining the meshing stiffness of a gear pair, but this method cannot evaluate the meshing stiffness under dynamic misalignment conditions and has low calculation efficiency. A Chinese invention patent with the publication number of CN118657007A discloses a method for determining the meshing stiffness of asymmetric spur gears, but this method only considers the local elastic matrix deformation of the gear and ignores the structural coupling effect of the gear body, resulting in inaccurate calculation results.

[0005] Therefore, it is of great significance to propose a method that can accurately and quickly iterate the calculation of the gear dynamic meshing stiffness of the power system. Summary of the Invention

[0006] To solve the problems existing in the prior art, the present invention provides a fast iterative calculation method and system for the dynamic meshing stiffness of spur gears in a power system, which can accurately calculate the dynamic meshing stiffness of spur gear pairs in the power system.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows: The fast iterative calculation method and system for the dynamic meshing stiffness of spur gears in a power system include the following steps: Establish a flexible shaft model and a lumped parameter bearing model, establish a dynamic digital twin model of the power system dynamics in combination with gear parameters, calculate the dynamic position, dynamic attitude angle and dynamic transmission error of the meshing gear pair, and determine the starting meshing point of the gear; Calculate the center distance deviation of the gear pair based on the dynamic position of the gear pair , calculate the misalignment of the stagger angle based on the dynamic attitude angle of the gear pair , and equivalent the dynamic transmission error of the gear pair to the elastic approach amount of the tooth surface ; Based on the center distance deviation of the gear pair Determine the contact state of the gear pair, calculate the contact tooth surface clearance sequence under the misalignment condition based on the misalignment of the stagger angle , calculate the deformation influence coefficient matrix C of the gear pair based on the gear parameters and tooth profile parameters; Based on the contact state of the gear pair, combined with the deformation influence coefficient matrix C and the clearance sequence under the misalignment condition , establish the clearance-deformation equation set of the gear pair; Based on the clearance-deformation equation set of the gear pair, solve to obtain the gear meshing stiffness ; K ; Feed back the gear meshing stiffness K into the dynamic digital twin model of the power system dynamics to calculate the dynamic meshing force , and update the dynamic position, dynamic attitude angle and dynamic transmission error of the gear pair, and finally iteratively calculate the gear dynamic meshing stiffness .

[0008] Furthermore, when establishing the flexible shaft model and the lumped parameter bearing model, it is based on the shaft parameters and bearing parameters of the power system. The transmission components of the power system include gears, shafts and bearings. The shaft parameters include the length, moment of inertia and mass of the shaft. The bearing parameters include the bearing support stiffness, support damping, number of rolling elements and the mass of the inner and outer rings of the bearing. The gear parameters include the mass, moment of inertia, module, number of teeth, tooth width and center hole radius of the gear.

[0009] Further, the flexible shaft model is established by the rigid body element method; when constructing the lumped parameter bearing model, it is assumed that there are spring-damping structures equal to the number of rollers between the inner ring and the outer ring of the bearing, and it is assumed that there are several spring-damping structures between the outer ring of the bearing and the bearing housing, and the equivalent spring and equivalent damping are calculated based on the bearing parameters.

[0010] Further, when constructing the dynamic digital twin model of the power system, the degrees of freedom of three translational directions and three torsional directions of each rigid body element are defined. Among them, the torsional angle is based on the fixed body coordinate system of the rigid body element and is equivalent to the attitude angle in the inertial coordinate system. The gear meshing force, gear meshing torque, bearing support force and bearing support torque are respectively applied at the corresponding rigid body element positions of the rotating shaft; the Newton's motion equation is established in the translational direction, the Euler's motion equation is established in the torsional direction, the driving torque and the load torque are applied on the rotating shaft, and the initial rotational speed is set for each lumped mass to obtain the dynamic digital twin model of the coupled system.

[0011] Further, the center distance deviation of the gear is obtained by calculating the comprehensive deviation of the meshing gear pair in the horizontal and vertical directions, and is expressed as , where represents the deviation of the meshing tooth pair in the horizontal direction, represents the deviation of the meshing tooth pair in the vertical direction, and the misalignment of the crossing angle is expressed as , where is the rotation angle of the first gear around the radial direction, is the rotation angle of the second gear around the radial direction, and the relationship between the rotation angle and the attitude angle is expressed as , where and are the attitude angles around the horizontal and vertical directions, is the rotational speed, is the time, and the elastic approach amount of the tooth surface is equivalent to the dynamic transmission error of the gear.

[0012] Further, the center distance deviation of the gear pair directly affects the gear contact ratio and indirectly affects the gear contact state. The gear contact state is divided into single-tooth contact, extended-tooth contact and double-tooth contact. The contact state depends on the gear rotation angle and the angular width of the extended area. The angular width of the extended area depends on the gear geometric parameters and the applied load torque. The contact tooth surface clearance sequence under the misalignment condition is expressed as , where represents the vector composed of the distances between all units and the tooth edges in contact, is the clearance sequence under the alignment condition. When only one column of tooth surface discrete units is divided, Denoted as , where n represents the number of discrete tooth surface units divided, and the influence coefficient matrix C includes the Hertz contact, shear, bending, axial compression, and fillet base deformation influence coefficients between each unit. The fillet base deformation influence coefficient refers to the flexible deformation generated in another unit when one unit is loaded. The calculation of each fillet base influence coefficient is based on the cantilever beam deformation theory. The tooth profile parameter refers to the position of the gear meshing point on the tooth profile, and the influence coefficient matrix C is different at different positions.

[0013] Furthermore, before establishing the clearance-deformation equations, first judge the gear contact state. When in the single-tooth contact state, the gear pair clearance-deformation equations are expressed as:

[0014] When in the extended tooth contact state, the gear pair clearance-deformation equations are expressed as:

[0015] When in the double-tooth contact state, the gear pair clearance-deformation equations are expressed as:

[0016] Among them, subscript 1 and subscript 2 respectively represent the first pair of meshing teeth and the second pair of meshing teeth. and respectively represent the influence coefficient matrices of the first pair of meshing teeth and the second pair of meshing teeth. represents the elastic matrix deformation influence coefficient matrix of the second pair of meshing teeth relative to the first pair of meshing teeth. represents the elastic matrix deformation influence coefficient matrix of the first pair of meshing teeth relative to the second pair of meshing teeth. and respectively represent the unit row vector and the unit column vector. represents the gear separation distance, and the tooth surface contact pressure distribution is obtained by solving the above equations and , that is, the contact pressure of each unit is obtained.

[0017] Furthermore, iteratively calculate the solved clearance-deformation equations, including: Before iteration, first judge the clearance value between the discrete units corresponding to the contact tooth profiles whether it is greater than , if it is greater than , then eliminate the corresponding rows and columns of the equations. The convergence condition for iterative solution is that the contact pressure of all units is greater than or equal to 0. The meshing stiffness , where FIt represents the meshing force, that is, the sum of the loads borne by all contact units. The load borne by a contact unit is obtained by multiplying the contact pressure by the unit area.

[0018] Furthermore, calculate the dynamic meshing force including: calculating the meshing damping through the meshing stiffness K , and then calculating the dynamic meshing force based on the meshing stiffness K , meshing damping and dynamic transmission error . Substitute the dynamic meshing force into the dynamic equations of the power system, and numerically solve them by the Runge-Kutta method to calculate the dynamic meshing stiffness of the gear in real time .

[0019] On the other hand, the present invention also provides a fast iterative calculation system for the dynamic meshing stiffness of spur gears in a power system, including a dynamic digital twin model establishment module, a parameter calculation module, an influence coefficient matrix calculation module, a clearance-deformation equation set establishment module, and a solution module; The dynamic digital twin model establishment module of the power system is used to establish a flexible shaft model and a lumped parameter bearing model, establish a dynamic digital twin model of the power system in combination with gear parameters, calculate the dynamic position, dynamic attitude angle and dynamic transmission error of the meshing gear pair, and determine the starting meshing point of the gear; The parameter calculation module is used to calculate the center distance deviation of the gear pair based on the dynamic position of the gear pair , calculate the misalignment of the stagger angle based on the dynamic attitude angle of the gear pair , and equivalent the dynamic transmission error of the gear pair to the elastic approach amount of the tooth surface ; The influence coefficient matrix calculation module is used to determine the contact state of the gear pair based on the center distance deviation of the gear pair , calculate the clearance sequence of the contact tooth surface under the misalignment condition based on the misalignment of the stagger angle , and calculate the deformation influence coefficient matrix C of the gear pair based on the gear parameters and tooth profile parameters; The clearance-deformation equation set establishment module is used to judge the gear contact state, and establish clearance-deformation equation sets for single-tooth contact state, extended tooth contact state and double-tooth contact state respectively in combination with the deformation influence coefficient matrix C and the clearance sequence under the misalignment condition ; The solution module is based on the clearance-deformation equation set of the gear, and obtains the gear meshing stiffness through iterative calculation , and substitute the meshing stiffness K into the dynamic digital twin model of the power system, and numerically solve it by the Runge-Kutta method to obtain the dynamic meshing stiffness of the gear K .

[0020] Compared with the prior art, the present invention has at least the following beneficial effects: The present invention proposes a fast iterative calculation method for the dynamic meshing stiffness of spur gears in a power system. By calculating the dynamic position, dynamic azimuth angle, and dynamic transmission error through the dynamic digital twin model of the power system dynamics, the center distance deviation of the gears, the misalignment of the crossing angle, and the elastic approach amount of the tooth surface are further calculated. A clearance-deformation equation set is established in combination with the gear geometric parameters and contact state, and the gear meshing stiffness is obtained by solving and fed back to the dynamic digital twin model of the power system dynamics, and finally the gear dynamic meshing stiffness is obtained. The present invention fully utilizes the advantages of the fast influence coefficient method to calculate the gear meshing stiffness, and accurately evaluates the influence of the parallelism error caused by the shaft flexibility and bearings on the gear meshing stiffness, and has the advantages of fast calculation speed and high accuracy. Using this method to solve the dynamic meshing stiffness is the basis for accurately evaluating the gear interface load transfer in the power system, and can provide a theoretical basis for the condition monitoring and health management of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is the flowchart of the fast iterative calculation method and system for the dynamic meshing stiffness of spur gears in the power system provided by the present invention.

[0022] Figure 2 is an embodiment disclosed by the present invention, a power system including gears, shafts, and bearings.

[0023] Figure 3 a is a discrete element under the centering condition of the gear contact area, Figure 3 b is a discrete element under the misalignment condition of the gear contact area.

[0024] Figure 4 is the flowchart for judging the gear contact state.

[0025] Figure 5 is the curve of the gear dynamic meshing stiffness obtained by simulation. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] The following will elaborate on the present invention in conjunction with the attached Figures 1 - 5 Although specific embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present invention can be more thoroughly understood and the scope of the present invention can be fully conveyed to those skilled in the art.

[0027] Refer to Figure 1 , the flowchart of the fast iterative calculation method and system for the dynamic meshing stiffness of spur gears in the power system can be calculated by, but not limited to, MATLAB software; Figure 2This is an embodiment disclosed by the present invention. A pair of power systems including gears, rotating shafts and bearings is composed of a pair of spur gears, two rotating shafts and four bearings. Each rotating shaft is respectively divided into seven rigid body units, and each rigid body unit considers the degrees of freedom in three translational and three torsional directions. Gear 1 is located at the position of unit 4, and unit 4 is located in the middle of rotating shaft 1. Gear 2 is located at the position of unit 11, and unit 11 is located in the middle of rotating shaft 2; Figure 3 a and Figure 3 b are schematic diagrams of the discretization of the gear contact area. All discretized units have the same area and are distributed on the common tangent along the axial direction of the gear. When the gears are misaligned, only some units bear the load, as Figure 3 shown in b; Figure 4 is the flowchart for judging the gear contact state. First, determine the contact state rotation angle of the driving gear relative to the starting meshing point, and then judge the current contact state according to the intervals of each contact state rotation angle, calculate the tooth profile parameters of the current contact tooth pair and , and calculate the current influence coefficient matrix according to the tooth profile parameters. By solving, the stress distribution of each contact tooth pair can be obtained, and then the contact load can be solved F ; Figure 5 is the dynamic meshing stiffness curve of the gear pair obtained by simulation.

[0028] Referring to Figure 1 , the present invention provides a fast iterative calculation method and system for the dynamic meshing stiffness of spur gears in a power system, including the following steps: S1. Based on the rotating shaft parameters and bearing parameters of the power system, a flexible shaft model and a lumped parameter bearing model are respectively established. The transmission components of the power system include gears, rotating shafts and bearings. The rotating shaft parameters include the length, moment of inertia and mass of the shaft. The bearing parameters include the bearing support stiffness, support damping, number of rolling elements and the mass of the inner and outer rings of the bearing. The flexible shaft model is established by the rigid body element method. The specific steps are to divide the shaft into several rigid body units, and no elastic deformation occurs within each rigid body unit. Based on the rotating shaft parameters and the theory of mechanics of materials, the equivalent stiffness in three translational and three torsional directions between adjacent rigid body units is calculated. There are translational forces and torsional force moments between any adjacent rigid body units. The lumped parameter bearing model assumes that there are spring-damper structures equal to the number of rollers between the inner and outer rings of the bearing, and assumes that there are several spring-damper structures between the outer ring of the bearing and the bearing housing, and calculates the equivalent spring and equivalent damping based on the bearing parameters. Based on the flexible shaft model and the lumped parameter bearing model, the gear dynamic misalignment caused by the shaft flexibility and the bearing asymmetric support can be analyzed S2. Based on the flexible shaft model and the bearing model, and combined with the gear parameters, establish a dynamic digital twin model of the power system dynamics, calculate the dynamic position, dynamic attitude angle and dynamic transmission error of the meshing gear pair, and determine the starting meshing point of the gear; the dynamic digital twin model of the power system dynamics defines the degrees of freedom of three translational directions and three torsional directions for each rigid body unit, where the torsional angle is based on the fixed body coordinate system of the rigid body unit and is equivalent to the attitude angle in the inertial coordinate system. Apply the gear meshing force and meshing torque on the rigid body unit connected to the gear, and apply the bearing support force and bearing support torque on the rigid body unit connected to the bearing; establish the Newton's equations of motion in the translational direction, establish the Euler's equations of motion in the torsional direction, apply the driving torque and load torque on the rotating shaft, and set the initial rotational speed for each rigid body unit. Finally, obtain the dynamic digital twin model of the coupled system. The dynamic position of the gear pair is the coordinate of the rigid body unit where the gear is located in the inertial coordinate system. The dynamic attitude angle is the transformation angle of the rigid body unit where the gear is located from the inertial coordinate system to the fixed body coordinate system. The dynamic transmission error is the projection of the displacement and rotation angle of the meshing tooth pair along the meshing line direction, which can be calculated according to the azimuth angle of each gear and the dynamic position of the gear. The starting meshing point of the gear is the angular position where the gear enters the double-tooth meshing area; S3. Calculate the center distance deviation of the gear pair based on the dynamic position of the gear pair , calculate the misalignment of the crossing angle based on the dynamic attitude angle of the gear pair , and equivalent the dynamic transmission error of the gear pair to the elastic approach amount of the tooth surface . The center distance deviation of the gear can be expressed as , where represents the deviation of the meshing tooth pair in the horizontal direction, represents the deviation of the meshing tooth pair in the vertical direction. The misalignment of the crossing angle can be expressed as , where is the rotation angle of the first gear around the radial direction, is the rotation angle of the second gear around the radial direction. The relationship between the rotation angle and the attitude angle can be expressed as , where and are the attitude angles around the horizontal and vertical directions, is the rotational speed, is the time. The elastic approach amount of the tooth surface is equivalent to the dynamic transmission error of the gear; S4. Determine the contact state of the gear pair based on the center distance deviation of the gear pair , and calculate the contact tooth surface clearance sequence under the misalignment condition based on the misalignment of the crossing angle ​, calculate the deformation influence coefficient matrix C of the gear pair based on the gear parameters and tooth profile parameters; the gear contact state is divided into single-tooth contact, extended tooth contact, and double-tooth contact, and the contact state depends on the gear rotation angle and the angular width of the extended area. The angular width of the extended area depends on the gear geometric parameters and the applied load torque. The contact tooth surface clearance sequence under the misalignment condition is expressed as , where represents the vector composed of the distances between all elements and the tooth edges in contact, is the clearance sequence under the alignment condition. When only one column of tooth surface discrete elements is divided, can be expressed as , where n represents the number of tooth surface discrete elements divided. The influence coefficient matrix C includes the Hertz contact, shear, bending, axial compression, and fillet base deformation influence coefficients between elements. The fillet base deformation influence coefficient refers to the flexible deformation generated in another element when one element is loaded. The calculation of each fillet base influence coefficient is based on the cantilever beam deformation theory and is related to the gear meshing position and the gear itself parameters. The tooth profile parameters refer to the position of the gear meshing point on the tooth profile, and the influence coefficient matrix C is different at different positions; S5, based on the contact state of the gear pair, and combined with the deformation influence coefficient matrix C and the clearance sequence under the misalignment condition , establish the clearance-deformation equation set of the gear pair; before establishing the clearance-deformation equation set, first judge the gear contact state. When in the single-tooth contact state, the clearance-deformation equation set of the gear pair is expressed as:

[0029] When in the extended tooth contact state, the clearance-deformation equation set of the gear pair is expressed as:

[0030] When in the double-tooth contact state, the clearance-deformation equation set of the gear pair is expressed as

[0031] Among them, subscript 1 and subscript 2 respectively represent the first pair of meshing teeth and the second pair of meshing teeth, and respectively represent the influence coefficient matrices of the first pair of meshing teeth and the second pair of meshing teeth, represents the elastic matrix deformation influence coefficient matrix of the second pair of meshing teeth relative to the first pair of meshing teeth, represents the elastic matrix deformation influence coefficient matrix of the first pair of meshing teeth relative to the second pair of meshing teeth, and respectively represent the unit row vector and the unit column vector, Denote the gear separation distance, which is determined by the angular width of the gear expansion region and the base circle radius, and obtain the tooth surface contact pressure distribution by solving the above equations and , that is, obtain the contact pressure of each unit; S6. Based on the clearance-deformation equations of the gear pair, solve to obtain the gear meshing stiffness K ; Iterative calculation is required to solve the clearance-deformation equations. Before iteration, first judge the clearance value between the discrete units corresponding to the contacting tooth profiles whether it is greater than . If it is greater than , then eliminate the corresponding rows and columns of the equations, thereby reducing the rank of the matrix to achieve the purpose of fast solution. The convergence condition for iterative solution is that the contact pressure of all units is greater than or equal to 0. The meshing stiffness , where F represents the meshing force, that is, the loads borne by all contacting units are added together. The load borne by a contacting unit is obtained by multiplying the contact pressure by the unit area; S7. Based on the gear meshing stiffness K , feedback it to the dynamic digital twin model of the power system to update the dynamic position, dynamic attitude angle and dynamic transmission error of the gear pair, and finally obtain the gear dynamic meshing stiffness through iterative calculation ; After the meshing stiffness K is fed back to the dynamic digital twin model of the power system, first calculate the meshing damping through the meshing stiffness K , and then calculate the dynamic meshing force K based on the meshing stiffness , meshing damping and dynamic transmission error. Substitute the dynamic meshing force into the dynamic equations of the power system and perform numerical solution through the Runge-Kutta method, so as to achieve the purpose of fast and real-time calculation of the gear dynamic meshing stiffness .

[0032] Taking an embodiment disclosed in the present invention shown in Figure 2 as an example for calculation and illustration. Among them, the rotating shaft 1 and the rotating shaft 2 are each evenly divided into 7 rigid body units. The length of each rigid body unit is 30 mm, the diameter is 30 mm, the number of teeth of the gear 1 and the gear 2 is 31, the module is 2, the bearing is a deep groove ball bearing, the number of rolling elements is 9, an input torque of 20 Nm is applied to the unit 1, a load torque of 20 Nm is applied to the unit 8, the input speed of the rotating shaft 1 is 100 r / min, based on this, set the initial speed of each unit around the axial direction, set the simulation time to 1 s, and perform numerical solution in the MATLAB software through the Runge-Kutta method; Figure 3The figure shows a schematic diagram of the discretization of the common tangent plane. Initially, it is assumed that gear 1 and gear 2 are centered, and the clearance of each discrete unit is set to 0 to form a clearance vector H. The tooth profile vectors of each discrete unit are the position angles of the midpoints of the discrete units on the involute tooth profile; Figure 4 The figure shows a flowchart for judging the gear contact state. First, the rotation angle of the driving gear relative to the starting meshing point is determined. Then, according to the rotation angle intervals of each contact state, the current contact state is judged, and the tooth profile parameters of the current contact tooth pair are calculated and , and the current influence coefficient matrix is calculated according to the tooth profile parameters. By solving, the stress distribution of each contact tooth pair can be obtained, and then the contact load can be solved F , and then according to the meshing stiffness at this time is solved, and the meshing stiffness K is fed back to the dynamic digital twin model of the power system. Through the meshing stiffness K the meshing damping is calculated. Then, based on the meshing stiffness K , the meshing damping and the dynamic transmission error, the dynamic meshing force is calculated. The dynamic meshing force is substituted into the dynamic equations of the power system. Finally, while solving the entire dynamic digital twin model, the dynamic meshing stiffness is output; Figure 5 The figure shows the curve of the dynamic meshing stiffness of the gear obtained by simulation. At this time, the gear contact ratio is 1.75, and the average meshing stiffness is 9.91×10 7 N / m. It can be seen that the single and double tooth alternate meshing characteristics of the gear, and there is an extended tooth contact area between the single tooth contact area and the double tooth contact area. In addition, due to the dynamic changes in the position and azimuth angle of the gear, the meshing stiffness is dynamically changing, and fluctuations in the meshing stiffness curve can be seen in both the single tooth meshing area and the double tooth meshing area.

[0033] Embodiment 2. Based on the concept of the above method, the present invention also provides a fast iterative calculation system for the dynamic meshing stiffness of spur gears in a power system, including a dynamic digital twin model establishment module of the power system, a parameter calculation module, an influence coefficient matrix calculation module, a clearance-deformation equation set establishment module, and a solution module; The dynamic digital twin model establishment module of the power system is used to establish a flexible shaft model and a lumped parameter bearing model, combine gear parameters to establish a dynamic digital twin model of the power system, calculate the dynamic position, dynamic attitude angle and dynamic transmission error of the meshing gear pair, and determine the starting meshing point of the gear. Specifically, define the degrees of freedom of three translational directions and three torsional directions for each rigid body unit, and apply gear meshing force, gear meshing torque, bearing support force and bearing support torque at the corresponding rigid body unit positions of the rotating shaft. Establish Newton's equations of motion in the translational direction and Euler's equations of motion in the torsional direction, apply driving torque and load torque on the rotating shaft, and set the initial rotational speed for each lumped mass. Finally, establish a dynamic digital twin model of gear dynamics; The parameter calculation module is used to calculate the center distance deviation of the gear pair based on the dynamic position of the gear pair , calculate the misalignment amount of the crossing angle based on the dynamic attitude angle of the gear pair , and equivalent the dynamic transmission error of the gear pair to the elastic approach amount of the tooth surface ; The influence coefficient matrix calculation module determines the contact state of the gear pair based on the center distance deviation of the gear pair , calculates the contact tooth surface clearance sequence under the misalignment condition based on the misalignment amount of the crossing angle , and calculates the deformation influence coefficient matrix C of the gear pair based on gear parameters and tooth profile parameters; The clearance-deformation equation set establishment module is used to judge the gear contact state and establish clearance-deformation equation sets in single tooth contact state, extended tooth contact state and double tooth contact state respectively; The solution module obtains the gear meshing stiffness through iterative calculation based on the clearance-deformation equation set of the gear , and substitutes the meshing stiffness K into the dynamic digital twin model of the power system, and numerically solves it by the Runge-Kutta method to obtain the dynamic meshing stiffness of the gear K .

[0034] It also includes a flexible shaft calculation module and a bearing calculation module; The flexible shaft calculation module is used to calculate the equivalent stiffness in three translational and three torsional directions between adjacent rigid body units based on shaft parameters and material mechanics theory, and calculate the acting force in the translational direction and the acting torque in the torsional direction between adjacent rigid body units; The bearing calculation module is used to calculate the equivalent spring and equivalent damping between the inner ring and the outer ring of the bearing based on bearing parameters.

[0035] ​The above content is only for explaining the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. Any modification made on the basis of the technical solution in accordance with the technical idea proposed by the present invention falls within the protection scope of the claims of the present invention.

Claims

1. A fast iterative calculation method for the dynamic meshing stiffness of spur gears in a power system, characterized in that, It includes the following steps: Establish a flexible shaft model and a lumped parameter bearing model, establish a dynamic digital twin model of the power system in combination with gear parameters, calculate the dynamic position, dynamic attitude angle and dynamic transmission error of the meshing gear pair, and determine the starting meshing point of the gear; Calculating the center distance deviation of a gear pair based on the dynamic position of the gear pair , calculating the misalignment of the crossing angle based on the dynamic attitude angle of the gear pair , and equivalenting the dynamic transmission error of the gear pair to the elastic approach amount of the tooth surface ; Center distance deviation of gear pair Determine the contact state of the gear pair, based on the misalignment amount of the stagger angle Calculate the contact tooth surface clearance sequence under misalignment conditions , calculate the deformation influence coefficient matrix C of the gear pair based on gear parameters and tooth profile parameters; Based on the contact state of the gear pair, combined with the deformation influence coefficient matrix C and the clearance sequence under misalignment conditions , establish the clearance-deformation equations of the gear pair; Based on the clearance-deformation equations of the gear pair, the gear meshing stiffness is obtained by solving K ; Feed the gear meshing stiffness K back into the dynamic digital twin model of the power system to calculate the dynamic meshing force , and update the dynamic position, dynamic attitude angle, and dynamic transmission error of the gear pair. Finally, iteratively calculate the gear dynamic meshing stiffness .

2. The rapid iterative calculation method for the dynamic meshing stiffness of the spur gear in the power system according to claim 1, characterized in that, When establishing the flexible shaft model and the lumped parameter bearing model, it is based on the shaft parameters and bearing parameters of the power system. The transmission components of the power system include gears, shafts and bearings. The shaft parameters include the length, moment of inertia and mass of the shaft. The bearing parameters include the bearing support stiffness, support damping, number of rolling elements and the mass of the inner and outer rings of the bearing. The gear parameters include the mass, moment of inertia, module, number of teeth, tooth width and center hole radius of the gear.

3. The rapid iterative calculation method for the dynamic meshing stiffness of spur gears in the power system according to claim 1, characterized in that, The flexible shaft model is established by the rigid body element method; when constructing the lumped parameter bearing model, it is assumed that there is a spring-damper structure equal to the number of rollers between the inner and outer rings of the bearing, and it is assumed that there are several spring-damper structures between the outer ring of the bearing and the bearing housing, and the equivalent spring and equivalent damping are calculated based on the bearing parameters.

4. The rapid iterative calculation method for the dynamic meshing stiffness of spur gears in a power system according to claim 1, wherein When constructing the dynamic digital twin model of the power system, define the degrees of freedom of three translational directions and three torsional directions for each rigid body element. Among them, the torsional angle is based on the body-fixed coordinate system of the rigid body element and is equivalent to the attitude angle in the inertial coordinate system. Apply the gear meshing force, gear meshing torque, bearing support force and bearing support torque at the corresponding rigid body element positions of the shaft; establish the Newton's motion equation in the translational direction, establish the Euler's motion equation in the torsional direction, apply the driving torque and load torque on the shaft, and set the initial rotational speed for each lumped mass to obtain the dynamic digital twin model of the coupled system.

5. The rapid iterative calculation method for the dynamic meshing stiffness of spur gears in the power system according to claim 1, characterized in that, The center distance deviation of the gear is obtained by calculating the comprehensive deviation of the meshing gear pair in the horizontal and vertical directions, and is expressed as , where represents the deviation of the meshing gear pair in the horizontal direction, represents the deviation of the meshing gear pair in the vertical direction, and the misalignment of the staggered angle is expressed as , where is the rotation angle of the first gear around the radial direction, is the rotation angle of the second gear around the radial direction, and the relationship between the rotation angle and the attitude angle is expressed as , where and are the attitude angles around the horizontal and vertical directions, is the rotational speed, is the time, and the elastic approach amount of the tooth surface is equivalent to the dynamic transmission error of the gear.

6. The rapid iterative calculation method for the dynamic meshing stiffness of spur gears in a power system according to claim 1, characterized in that, Center distance deviation of the described gear pair directly affects the gear contact ratio and indirectly affects the gear contact state. The described gear contact state is divided into single-tooth contact, extended-tooth contact, and double-tooth contact. The contact state depends on the gear rotation angle and the angular width of the extended zone. The angular width of the extended zone depends on the gear geometric parameters and the applied load torque. The contact tooth surface clearance sequence under the misalignment condition is expressed as , where represents the vector composed of the distances between all cells and the tooth edge where contact occurs, is the clearance sequence under the alignment condition. When only one column of tooth surface discrete cells is divided, is expressed as , where n represents the number of divided tooth surface discrete cells. The influence coefficient matrix C includes the Hertz contact, shear, bending, axial compression, and fillet base deformation influence coefficients between cells. The fillet base deformation influence coefficient refers to the flexible deformation generated in another cell when one cell is loaded. The calculation of each fillet base influence coefficient is based on the cantilever beam deformation theory. The tooth profile parameter refers to the position of the gear meshing point on the tooth profile. The influence coefficient matrix C is different at different positions.

7. The rapid iterative calculation method for the dynamic meshing stiffness of spur gears in a power system according to claim 1, characterized in that, Before establishing the clearance-deformation equation set, first judge the gear contact state. When in the single-tooth contact state, the gear pair clearance-deformation equation set is expressed as: When in the extended tooth contact state, the gear pair clearance-deformation equation set is expressed as: When in the double-tooth contact state, the gear pair clearance-deformation equation set is expressed as: where the subscripts 1 and 2 represent the first pair and the second pair of meshing teeth respectively, and represent the influence coefficient matrices of the first pair and the second pair of meshing teeth respectively, represents the elastic matrix deformation influence coefficient matrix of the second pair of meshing teeth with respect to the first pair of meshing teeth, represents the elastic matrix deformation influence coefficient matrix of the first pair of meshing teeth with respect to the second pair of meshing teeth, and represent the unit row vector and the unit column vector respectively, represents the gear separation distance, and the tooth surface contact pressure distribution is obtained by solving the above equations and , that is, the contact pressure of each element is obtained.

8. The rapid iterative calculation method for the dynamic meshing stiffness of spur gears in a power system according to claim 1, characterized in that, Iteratively calculate the solution of the clearance-deformation equation set, including: Before iteration, first judge whether the clearance value between the discrete units corresponding to the contacting tooth profiles is greater than . If it is greater than , the corresponding rows and columns of the equation set are eliminated. The convergence condition for iterative solution is that the contact pressure of all units is greater than or equal to 0. The meshing stiffness , where F represents the meshing force, that is, the loads borne by all contacting units are added together. The load borne by a contacting unit is obtained by multiplying the contact pressure by the unit area.

9. The rapid iterative calculation method for the dynamic meshing stiffness of spur gears in the power system according to claim 1, characterized in that, Calculating dynamic meshing force including: calculating meshing damping through meshing stiffness K and then calculating the dynamic meshing force based on the meshing stiffness K , meshing damping and dynamic transmission error , substituting the dynamic meshing force into the dynamic equations of the dynamic system, and numerically solving them by the Runge-Kutta method to calculate the dynamic meshing stiffness of the gear in real time .

10. A fast iterative calculation system for the dynamic meshing stiffness of spur gears in a power system, characterized in that, A dynamic digital twin model establishment module of the power system, a parameter calculation module, an influence coefficient matrix calculation module, a clearance-deformation equation set establishment module and a solution module; The dynamic digital twin model establishment module of the power system is used to establish a flexible shaft model and a lumped parameter bearing model, establish a dynamic digital twin model of the power system in combination with gear parameters, calculate the dynamic position, dynamic attitude angle and dynamic transmission error of the meshing gear pair, and determine the starting meshing point of the gear; The parameter calculation module is used to calculate the center distance deviation of the gear pair based on the dynamic position of the gear pair , calculate the stagger angle misalignment based on the dynamic attitude angle of the gear pair , and equivalent the dynamic transmission error of the gear pair to the tooth surface elastic approach ; The influence coefficient matrix calculation module is used to determine the contact state of the gear pair based on the center distance deviation of the gear pair and determine the contact tooth surface clearance sequence under the misalignment condition based on the stagger angle misalignment amount ; calculate the deformation influence coefficient matrix C of the gear pair based on the gear parameters and tooth profile parameters ​ The clearance-deformation equation set establishment module is used to judge the gear contact state, and combines the deformation influence coefficient matrix C and the clearance sequence under the misalignment condition , and respectively establish the clearance-deformation equation sets in the single-tooth contact state, extended-tooth contact state, and double-tooth contact state; The solution module obtains the gear mesh stiffness through iterative calculation based on the clearance-deformation equations of the gears K , and brings the mesh stiffness K into the digital twin model of the dynamic system dynamics, and numerically solves it by the Runge-Kutta method to obtain the dynamic gear mesh stiffness .

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