Slice coupling dynamics modeling method for high-speed thin-walled gear transmission system

Abstract

The present invention discloses a slicing coupling dynamic modeling method for a high-speed thin-walled gear transmission system, which divides the dynamic model of the high-speed thin-walled gear transmission system into a meshing force solution model and a finite element condensation model, respectively establishing a meshing force solution model and a finite element condensation model, wherein the finite element condensation model is obtained by coupling a box finite element condensation model with a gear body condensation model, and then coupling the meshing force solution model with the finite element condensation model to obtain a slicing coupling dynamic model of a high-speed thin-walled gear transmission system. The beneficial effect is that by coupling a high-speed thin-walled gear box, the idea of ​​slicing method is introduced to consider the influence of high-speed gear thin-wall flexibility, centrifugal force, inertia force, Coriolis force and box flexibility on the dynamic characteristics of the system in the dynamic system, and the calculation accuracy is higher.

Description

Technical Field

[0001] The invention relates to the technical field of gear transmission system dynamics, and in particular to a slice coupling dynamics modeling method for a high-speed thin-wall gear transmission system. Background Art

[0002] Gear transmission refers to a device that transmits motion and power through a gear pair. It has the advantages of high transmission efficiency, good accuracy, compact structure, and high working reliability. The gear transmission system is the most widely used mechanical transmission method in various modern equipment, such as aviation, wind power, new energy vehicles and other emerging fields.

[0003] At present, with the rapid development of science and technology towards high-precision and high-tech, the stability and reliability of gear transmission systems are becoming more and more important indicators for evaluating mechanical systems. For example: the low reliability of civil aviation aircraft will greatly reduce the safety of aircraft operation; the instability of wind power transmission will not only aggravate the fatigue damage of the transmission system, but also cause frequent wind power accidents; the instability of new energy vehicle transmission will directly affect the comfort experience of drivers and passengers. As a widely used power transmission system, the stability and reliability of the gear transmission system have a huge impact on the entire mechanical system.

[0004] In the prior art, extensive and in-depth research has been carried out in the field of gear dynamics, among which the most widely used research methods are the concentrated parameter method and the finite element method. As high-speed gears develop towards lightweight, the strength of the gear body decreases and the flexibility increases, which leads to irregular deformation of the high-speed thin-walled gear transmission system and triggers a series of dynamic problems in the high-speed thin-walled gear transmission system. The concentrated parameter method and the finite element method cannot conduct in-depth research and analysis on the flexibility of the transmission components under the premise of ensuring the calculation speed. In addition, the structural characteristics of the thin rim and thin web of the high-speed gear itself will cause irregular deformation of the gear body during the meshing process, resulting in different load distribution on the tooth surface of each gear tooth. If only a single gear tooth is studied, the flexible characteristics of the thin-walled structure of the high-speed gear cannot be effectively revealed. On the other hand, during high-speed rotation, centrifugal force, inertia force and Coriolis force are also important factors affecting the flexible deformation of the gear body. Summary of the invention

[0005] In view of the above situation, the present invention provides a slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system, aiming to reflect a series of transmission system dynamic characteristics such as flexible deformation during high-speed thin-walled gear transmission.

[0006] To achieve the above purpose, the technical solution of the present invention is as follows:

[0007] A slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system comprises the following steps:

[0008] S1: Establishing meshing force solution model

[0009] The high-speed thin-walled gear is sliced ​​along the tooth width direction, and the gear teeth and gear tooth slices involved in the meshing are determined through the actual meshing tooth number and the instantaneous contact line. The time-varying meshing stiffness of the corresponding slice is calculated, and the flexible deformation of the dividing surface at the corresponding gear tooth slice position in the finite element polycondensation model is extracted and converted to the actual meshing point of the gear tooth slice. The meshing stiffness of the gear tooth slice and the gear tooth slice is calculated to obtain the dynamic meshing force and meshing torque of the high-speed thin-walled gear transmission system.

[0010] S2: Establishing the finite element polycondensation model

[0011] Firstly, the gear dynamics equation is decoupled to obtain the state equation, the gear body within the tooth root circle is intercepted, the cross-section of each gear tooth is segmented, the number of segments is consistent with the number of gear tooth slices, and concentrated nodes are established on the segmentation surface and the gear shaft journal. Considering the centrifugal force, inertia force and Coriolis force, a finite element shrinkage model of the gear body is established. At the same time, a fixed constraint is imposed on the box body, and concentrated nodes are established at the bearing hole of the box body to establish a finite element shrinkage model of the box body.

[0012] Then, the instantaneous support force and support reaction force of each bearing position are calculated through the deformation of the journal on the gear body and the deformation of the bearing hole of the box body. The support force of the frame can be obtained by the deformation of the bearing hole on the box body, which acts on the journal of the gear shaft to obtain the deformation of the journal. The support reaction force at the bearing end can be calculated and acted on the bearing hole at the corresponding position of the box body, completing the coupling of the finite element shrinkage model of the box body and the shrinkage model of the gear body to obtain the finite element shrinkage model;

[0013] S3: The meshing force solution model is coupled with the finite element shrinkage model to obtain the slice coupling dynamics model of the high-speed thin-walled gear transmission system.

[0014] Preferably, in step S3, the dynamic meshing force and meshing torque of the system calculated in the meshing force solution model are returned to the finite element shrinkage model and act on the dividing surface of the corresponding gear tooth slice, thereby completing the coupling of the high-speed thin-walled gear meshing force solution algorithm and the finite element shrinkage model.

[0015] Preferably, in step S1, the process of establishing the meshing force solution model is as follows:

[0016] The high-speed thin-walled helical gear pair is sliced ​​along the tooth width direction, and the 6-DOF displacement of the small gear and the large gear is considered respectively. The 6-DOF displacement vector of the helical gear pair on the jth slice is defined as:

[0017]

[0018] In the formula, They represent the translation displacement at the jth slice in the pinion and gear coordinate systems respectively; They represent the rotational displacement at the jth slice in the pinion and gear coordinate systems respectively;

[0019] In the meshing model, the meshing of helical gears can be regarded as two frustums in contact, and the meshing point position vector on the jth slice is With the normal unit vector n a (a=p,g) are respectively expressed as:

[0020]

[0021]

[0022] n p =[cosβ b sinα t ,cosβ b cosα t ,sinβ b ]

[0023] n g = -[cosβ b sinα t ,cosβ b cosα t ,sinβ b ]

[0024] In the formula, Rba represents the base circle radius of the pinion and the gear, α t represents the pressure angle, b represents the tooth width, ρtaj represents the projection distance between the meshing point of the small gear and the large gear and the tangent point of the base circle on the jth slice, and L j Indicates that the meshing point is M j The length of the instantaneous meshing line at time ;

[0025] make Then the normal compression deformation of Mj can be expressed as:

[0026]

[0027] Among them, e j It is M j The tooth profile error at the meshing point M j The meshing force and moment of the ith meshing tooth pair can be obtained by calculating the normal compression deformation and the time-varying meshing stiffness at :

[0028]

[0029] In the formula, and are the forces and moments of the i-th meshing tooth pair of the pinion and the gear in the x-axis, y-axis, and z-axis directions, respectively. The total meshing force and meshing moment of the helical gear can be obtained as follows:

[0030]

[0031] Preferably, in the finite element polycondensation model of step S2, the process of establishing the finite element polycondensation model of the gear body is as follows:

[0032] In the ANSYS finite element analysis software, the gear body model is cut off from the part outside the root circle, and the generated cross-section surface is divided into equal-sized dividing surfaces along the tooth width direction. A concentrated node is established on the generated dividing surface and the gear shaft bearing node, and then a python script file is written to complete the fully automated operation of this part of the work.

[0033] Preferably, in the process of establishing the gear body finite element reduction model of the finite element reduction model in step S2, since the gear body finite element model includes movement around the z-axis, it cannot be directly reduced in order, and rotational fixed constraints need to be applied to the input and output ends of the gear body.

[0034] Preferably, in the finite element polycondensation model of step S2, the process of establishing the finite element polycondensation model of the box is as follows:

[0035] Four end covers are installed on the box body and fixedly connected to the box body in the form of bonds. Concentrated nodes are established at the bearing mounting holes inside the four end covers to obtain the displacement and velocity at the bearing holes.

[0036] Preferably, in the process of establishing the finite element polycondensation model of the box of the finite element polycondensation model in step S2, the box is rigidly connected to the ground, and a fixed constraint needs to be applied to the bottom of the box.

[0037] Preferably, in step S3, the coupling of the meshing force solution model and the finite element condensation model further includes: confirming the gear rotation angle through angular displacement, obtaining the actual meshing tooth sequence number, and extracting the deformation of the corresponding gear tooth dividing surface on the corresponding gear body.

[0038] Preferably, in step S3, the coupling of the meshing force solution model and the finite element condensation model also includes: there is an initial intersection difference between the meshing force solution model and the finite element condensation model, and the segmentation surface deformation extracted from the finite element needs to be converted into the meshing force solution coordinate system.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. The slicing coupling dynamic modeling method of high-speed thin-walled gear transmission system proposed in the present invention introduces the idea of ​​slicing method, slices each gear tooth in the meshing force solution model, and divides the root circle surface of each gear tooth of the gear body in the finite element shrinkage model, fully considering the coupling relationship between the slice and the segmentation surface, so as to calculate the stress distribution of each gear tooth surface, gear body deformation, meshing force and other transmission system dynamics problems with higher calculation accuracy.

[0041] 2. The present invention can be used in high-speed gear transmission application scenarios such as aviation, wind power, and new energy vehicles, and can accurately simulate the dynamic characteristics of the gear transmission system under the excitation of spur, helical, and herringbone meshing frequencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A flow chart of the meshing force solution model in the slice coupling dynamics of a high-speed thin-walled gear transmission system;

[0043] Figure 2 It is the schematic diagram of the finite element model of the gear body;

[0044] Figure 3 It is the schematic diagram of the finite element model of the box;

[0045] Figure 4 A flow chart of the finite element polycondensation model in the slice coupling dynamics of a high-speed thin-walled gear transmission system;

[0046] Figure 5 Flowchart for the slice coupling dynamics model of high-speed thin-walled gear transmission system;

[0047] Figure 6 The dynamic meshing force and spectrum diagram in the X direction before and after slicing of a high-speed thin-walled gear transmission system at 30,000 rpm / min;

[0048] Figure 7 This is the stress distribution diagram of the tooth surface before and after slicing of a high-speed thin-walled gear transmission system at 30000rpm / min. DETAILED DESCRIPTION

[0049] The present invention is further described below in conjunction with embodiments and drawings.

[0050] like Figure 5As shown, a slice coupling dynamic modeling method for a high-speed thin-walled gear transmission system is shown. The design concept of this modeling method is to divide the dynamic model of the high-speed thin-walled gear transmission system into a meshing force solution model and a finite element shrinkage model, and establish a meshing force solution model and a finite element shrinkage model respectively. Among them, the finite element shrinkage model is obtained by coupling the finite element shrinkage model of the box body and the gear body shrinkage model, and then the meshing force solution model is coupled with the finite element shrinkage model to obtain the slice coupling dynamic model of the high-speed thin-walled gear transmission system.

[0051] Please refer to Figure 1 As shown in the figure, the process of establishing the meshing force solution model in the slice coupling dynamics of the high-speed thin-walled gear transmission system is as follows:

[0052] First, the high-speed thin-walled helical gear pair is sliced ​​along the tooth width direction, and the 6-DOF displacement of the small gear and the large gear is considered respectively. The 6-DOF displacement vector of the helical gear pair on the jth slice is defined as:

[0053]

[0054] In the formula, Respectively represent the translation displacement at the jth slice in the pinion and gear coordinate systems, They represent the rotational displacement at the jth slice in the pinion and gear coordinate systems respectively.

[0055] In the meshing model, the meshing of helical gears can be regarded as two frustums in contact, and the meshing point position vector on the jth slice is With the normal unit vector n a (a=p,g) are respectively expressed as:

[0056]

[0057]

[0058] n p =[cosβ b sinα t ,cosβ b cosα t ,sinβ b ]

[0059] n g = -[cosβ b sinα t ,cosβ b cosα t ,sinβ b ]

[0060] In the formula, R ba Represents the base circle radius of the pinion and gear, αt represents the pressure angle, b represents the tooth width, ρ taj Represents the projection distance between the meshing point of the small gear and the large gear and the tangent point of the base circle on the jth slice, L j Indicates that the meshing point is M j The length of the instantaneous meshing line.

[0061] make Then M j The normal compression deformation can be expressed as:

[0062]

[0063] Among them, e j It is M j The tooth profile error at the meshing point M j The meshing force and moment of the i-th meshing tooth pair can be obtained by calculating the normal compression deformation and the time-varying meshing stiffness.

[0064] The number of slices involved in the meshing gear is determined by the instantaneous meshing line length, and the time-varying meshing stiffness of each slice is calculated using the potential energy method:

[0065]

[0066] In the formula, and are the forces and moments of the i-th meshing tooth pair of the pinion and the gear in the x-axis, y-axis, and z-axis directions, respectively. The total meshing force and meshing moment of the helical gear can be obtained as follows:

[0067]

[0068] In the finite element polycondensation model, the motion equation of the gear dynamics system can be expressed as follows:

[0069]

[0070] Among them, M, C and K are mass matrix, damping matrix and stiffness matrix respectively, u is the displacement vector, and F is the load vector. According to the orthogonality of modal coordinates, the above equation can be converted into the equation of ndof decoupling:

[0071]

[0072] ndof is the degrees of freedom (DOFs) of the dynamic system, Φ j is the jth mode shape vector, y i is the set of modal coordinates. The influence of higher-order modes is usually limited, so the first n equations in the above formula can solve the system dynamics analysis problem to reduce the amount of calculation. The first n equations are second-order differential equations, which can be converted into the following state equation (25):

[0073]

[0074] in, In particular, w is the displacement vector of the observed degree of freedom; y is the modal coordinate vector; A, B, C, and D are the state equation matrices; F s is the input force vector.

[0075] Gears will generate centrifugal force when operating in a high-speed steady state, and inertial force and Coriolis force when operating in a non-steady state. In order to consider the dynamic characteristics of high-speed gears under the two working conditions, centrifugal force, inertial force and Coriolis force are added to the gear FEM model.

[0076] Please refer to Figure 2 In the gear body finite element shrinkage model, the high-speed thin-walled gear will produce irregular deformation at high speed due to its own flexibility, resulting in uneven load distribution on the tooth surface of each gear. In order to accurately analyze the load distribution on the tooth surface, the gear body within the root circle is intercepted in the finite element, and the cross-section of each gear tooth is divided. The number of divisions is consistent with the number of gear tooth slices, so that the nodes are established on each division surface. The finite element model of the gear body after division is as follows: Figure 2 As shown, in order to couple the gear body and the housing in the finite element shrinkage model, concentrated nodes are established at the bearing end of the gear body, and the establishment order corresponds to the establishment order of the bearing hole nodes on the housing. Since the finite element model of the gear body includes movement around the z-axis, it cannot be directly reduced in order. The finite element shrinkage model of the gear can obtain the flexible deformation of the gear body, and Newton's law can obtain the rigid rotation. In this embodiment, the pinion is the input end and the gear is the output end, so it is necessary to apply rotational fixed constraints to the driving end of the pinion and the load end of the gear in the finite element model of the gear body to obtain the finite element shrinkage model of the gear body. In addition, this process establishes many concentrated nodes on the gear body, and the workload is relatively large. The process can be automated by writing a python script, which has good universality.

[0077] Please refer to Figure 3 In the housing finite element shrinkage model, due to the high speed of the high-speed gear, the existence of installation and manufacturing errors will cause the excitation generated by the gear transmission system during the meshing process to couple between the gear-shaft-bearing, further causing housing vibration. In addition, the wall thickness of the high-speed gear housing is relatively thin, and the supporting structure will deform greatly during the operation of the transmission system, changing the gear meshing state. Therefore, in order to accurately grasp the dynamic characteristics of the high-speed gear transmission system, the high-speed gear box is also condensed. The housing structure targeted by this embodiment is as follows Figure 3As shown, the box is equipped with four end covers, which are fixedly connected to the box in the form of bonds. Concentrated nodes are established at the bearing mounting holes inside the four end covers to obtain the displacement and velocity at the bearing holes. Since the box is rigidly connected to the ground, a fixed constraint needs to be applied to the bottom of the box.

[0078] like Figure 4 As shown in the figure, the process of establishing the finite element polycondensation model in the slice coupling dynamics of the high-speed thin-walled gear transmission system is as follows:

[0079] First, a finite element shrinkage model of the housing is established, and the deformation of the bearing hole is calculated to obtain the support force and torque. At the same time, the rotational motion of the gear is obtained by the inertia of the gear body caused by the drive and load. The rotational angular displacement, angular velocity and angular acceleration of the gear body can be obtained by calculation, so that the centrifugal force, inertia force and Coriolis force can be obtained. Finally, the instantaneous meshing force and meshing torque obtained in the meshing force solution model are used as input, and are imported into the gear body shrinkage model together with the bearing hole support force and torque, the centrifugal force generated by the rotational motion, the inertia force and the Coriolis force to obtain the deformation of the gear body at the next moment, and the deformation at the bearing node is calculated together with the bearing stiffness and damping to obtain the reaction force of the bearing on the frame, which is imported into the housing shrinkage model to form a closed loop.

[0080] Finally, Figure 5 As shown in the figure, the process of establishing the slice coupling dynamics model of the high-speed thin-walled gear transmission system is as follows:

[0081] In the meshing force solution model, the actual contact tooth number of the helical gear pair is first determined. Figure 4 The output part in is used to obtain the instantaneous deformation displacement of the corresponding contact tooth pair from the finite element polycondensation model. The deformation is in the dynamic coordinate system and needs to be converted to the static coordinate system first; secondly, the instantaneous meshing line length is confirmed, and the flexible deformation of the gear body segmentation surface at the corresponding position of each meshing line is extracted and converted to the actual meshing point. Similarly, the time-varying meshing stiffness on the corresponding meshing point slice is extracted and calculated with the deformation at the meshing point to obtain the instantaneous meshing force and meshing torque of the transmission system. Finally, the meshing force and meshing torque are converted to the dynamic coordinate system as an additional Figure 4 The input part in is connected with the transmission system shrinkage model, and acts on the gear body shrinkage model to obtain the deformation of the gear body at the next moment, completing the coupling of the meshing force solution model and the finite element shrinkage model, thereby obtaining the slice coupling dynamics model of the high-speed thin-walled gear transmission system.

[0082] In the coupling process between the meshing force solution model and the finite element condensation model, it is important to ensure that the number of gear tooth slices in the finite element condensation model is consistent with that in the meshing force solution model, so as to more accurately represent the dynamic characteristics of each part of the transmission system.

[0083] Please refer to Figure 6 and 7 As shown in the figure, the dynamic meshing force and spectrum of the high-speed thin-walled gear at 30000rpm / min are compared with the general non-slicing model. Compared with the non-slicing model, the dynamic characteristics of the system after slicing have changed significantly. First, the dynamic meshing force of the transmission system in the X direction at 3000rad / s is shown. Figure 6 As shown in (a) and (b), it can be found that the overall change trend of the two is the same. The dynamic meshing force amplitude of the gear after slicing is increased compared with that before slicing. This is because when the meshing line length is the same, the gear tooth deformation at the thin-walled edge of the gear is larger, and the slicing model can well show this part of the change. Through the corresponding spectrum Figure 6 (c) It can be found that the frequency components before and after slicing are the same, but the amplitude of the meshing frequency increases almost exponentially after slicing, indicating that the slicing model only affects the amplitude of the meshing frequency.

[0084] Please refer to Figure 7 As shown in the figure, the stress distribution of the tooth surface of the high-speed thin-walled gear transmission system before and after slicing at 30000rpm / min is shown. Combined with the arc groove structure of the high-speed thin-walled gear itself, the meshing state of the meshing teeth at three different positions (31 teeth, 35 teeth and 39 teeth) is analyzed. Figure 7 It can be seen that the stress distribution on the gear tooth surface changes greatly before and after slicing. The tooth surface stress before slicing is mainly distributed at the position with less flexibility (31 teeth), and the stress gradually decreases from the tooth top to the tooth root. This phenomenon is particularly obvious on the gear teeth at the arc groove position (39 teeth). After slicing, there will be a non-contact situation on the lower left side of the tooth surface, which will not occur before slicing. This is because the gear teeth on the lower left side are located at the edge of the wheel rim, which are more flexible, and the centrifugal force will cause the deformation of this part to increase, resulting in a non-contact situation. In addition, the gear teeth at the arc groove position are more flexible (such as Figure 7 The stress at the meshing and meshing parts of the tooth surface increases gradually, because the contact line at the meshing and meshing parts is shorter at this time. In addition, the stress decreases at the upper right corner of the tooth surface, and the disengagement phenomenon is more obvious at the lower left corner. The stress gradually concentrates toward the center of the tooth surface, indicating that under high-speed conditions, the deformation of the wheel rims on both sides of the arc groove is large, and the deformation of the middle part is small, so that when the meshing line length reaches the maximum, only the middle part of the gear teeth is fully involved in the meshing.

[0085] Finally, it should be noted that the above description is only a preferred embodiment of the present invention. Under the guidance of the present invention, ordinary technicians in this field can make various similar expressions without violating the purpose and claims of the present invention, and such changes all fall within the scope of protection of the present invention.

Claims

1. A slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system, characterized in that: The following steps are involved: S1: Establishing meshing force solution model The high-speed thin-walled gear is sliced ​​along the tooth width direction, and the gear teeth and gear tooth slices involved in the meshing are determined through the actual meshing tooth number and the instantaneous contact line. The time-varying meshing stiffness of the corresponding slice is calculated, and the flexible deformation of the dividing surface at the corresponding gear tooth slice position in the finite element polycondensation model is extracted and converted to the actual meshing point of the gear tooth slice. The meshing stiffness of the gear tooth slice and the gear tooth slice is calculated to obtain the dynamic meshing force and meshing torque of the high-speed thin-walled gear transmission system. S2: Establishing the finite element polycondensation model Firstly, the gear dynamics equation is decoupled to obtain the state equation, the gear body within the tooth root circle is intercepted, the cross-section of each gear tooth is segmented, the number of segments is consistent with the number of gear tooth slices, and concentrated nodes are established on the segmentation surface and the gear shaft journal. Considering the centrifugal force, inertia force and Coriolis force, a finite element shrinkage model of the gear body is established. At the same time, a fixed constraint is imposed on the box body, and concentrated nodes are established at the bearing hole of the box body to establish a finite element shrinkage model of the box body. Then, the instantaneous support force and support reaction force of each bearing position are calculated through the deformation of the journal on the gear body and the deformation of the bearing hole of the box body. The support force of the frame can be obtained by the deformation of the bearing hole on the box body, which acts on the journal of the gear shaft to obtain the deformation of the journal. The support reaction force at the bearing end can be calculated and acted on the bearing hole at the corresponding position of the box body, completing the coupling of the finite element shrinkage model of the box body and the shrinkage model of the gear body to obtain the finite element shrinkage model; S3: The meshing force solution model is coupled with the finite element shrinkage model to obtain the slice coupling dynamics model of the high-speed thin-walled gear transmission system.

2. The slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system according to claim 1 is characterized in that: In step S3, the dynamic meshing force and meshing torque of the system calculated in the meshing force solution model are returned to the finite element shrinkage model and act on the dividing surface of the corresponding gear tooth slice, thereby completing the coupling of the high-speed thin-walled gear meshing force solution algorithm and the finite element shrinkage model.

3. The slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system according to claim 1 is characterized in that: In step S1, the process of establishing the meshing force solution model is as follows: The high-speed thin-walled helical gear pair is sliced ​​along the tooth width direction, and the 6-DOF displacement of the small gear and the large gear is considered respectively. The 6-DOF displacement vector of the helical gear pair on the jth slice is defined as: In the formula, They represent the translation displacement at the jth slice in the pinion and gear coordinate systems respectively; They represent the rotational displacement at the jth slice in the pinion and gear coordinate systems respectively; In the meshing model, the meshing of helical gears can be regarded as two frustums in contact, and the meshing point position vector on the jth slice is With the normal unit vector n a (a=p,g) are respectively expressed as: n p =[cosβ b sinα t ,cosβ b cosα t ,sinβ b ] n g =-[cosβ b sinα t ,cosβ b cosα t ,sinβ b ] In the formula, Rba represents the base circle radius of the pinion and the gear, α t represents the pressure angle, b represents the tooth width, ρtaj represents the projection distance between the meshing point of the small gear and the large gear and the tangent point of the base circle on the jth slice, and L j Indicates that the meshing point is M j The length of the instantaneous meshing line at time ; make Then M j The normal compression deformation can be expressed as: Among them, e j It is M j The tooth profile error at the meshing point M j The meshing force and moment of the ith meshing tooth pair can be obtained by calculating the normal compression deformation and the time-varying meshing stiffness at : In the formula, and are the forces and moments of the i-th meshing tooth pair of the pinion and the gear in the x-axis, y-axis, and z-axis directions, respectively. The total meshing force and meshing moment of the helical gear can be obtained as follows:

4. The slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system according to claim 1 is characterized in that: In the finite element polycondensation model of step S2, the process of establishing the finite element polycondensation model of the gear body is as follows: In the finite element analysis software, the gear body model is cut off from the part outside the root circle, and the generated cross-section surface is divided into equal-sized dividing surfaces along the tooth width direction. A concentrated node is established on the generated dividing surface and the gear shaft bearing node, and then a python script file is written to complete the fully automated operation of this part of the work.

5. The slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system according to claim 1 or 4, characterized in that: In the process of establishing the finite element polycondensation model of the gear body in step S2, it is necessary to apply rotational fixed constraints to the input end and the output end of the gear body.

6. The slice coupling dynamics modeling method for high-speed thin-walled gear transmission system according to claim 1 is characterized in that: In the finite element polycondensation model of step S2, the process of establishing the finite element polycondensation model of the box is as follows: Four end covers are mounted on the box body and fixedly connected to the box body. Concentrated nodes are respectively established at the bearing mounting holes inside the four end covers to obtain the displacement and velocity at the bearing holes.

7. The slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system according to claim 1 or 6, characterized in that: In the process of establishing the finite element shrinkage model of the box in step S2, the box is rigidly connected to the ground, and a fixed constraint needs to be applied to the bottom of the box.

8. The slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system according to claim 1 is characterized in that: In step S3, the coupling of the meshing force solution model and the finite element polycondensation model further includes: The gear rotation angle is confirmed by angular displacement, the actual meshing tooth number is obtained, and the deformation of the corresponding gear tooth dividing surface on the corresponding gear body is extracted.

9. The slice coupling dynamics modeling method for a high-speed thin-walled gear transmission system according to claim 1 is characterized in that: In step S3, the coupling of the meshing force solution model and the finite element polycondensation model further includes: There is an initial intersection difference between the meshing force solution model and the finite element condensation model. The segmentation surface deformation extracted from the finite element needs to be converted into the meshing force solution coordinate system.

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