Gear rigid-elastic coupling dynamics modeling method for equivalent tooth root elastic deformation

Abstract

The invention discloses a gear rigid-elastic coupling dynamics modeling method with equivalent tooth root elastic deformation, and belongs to the field of gear transmission dynamics. According to the rigid-elastic coupling dynamic modeling method, distributed torsion springs serve as connecting force elastic units, and rigid gear teeth and a gear base body are connected to equivalently simulate elastic deformation of gear tooth roots. A novel planetary slewing bearing kinetic model is established for analysis, and a calculation method for the torsional rigidity of an important element torsion spring in a rigid-elastic coupling model is deduced based on a gear meshing rigid-elastic coupling theory. A planetary gear model, a sun gear model and an inner gear ring model of the slewing bearing are established respectively, an equivalent model of tooth root elastic deformation is obtained through a processing mode of elastic unit connection, and the influence rule of torsional rigidity and torsional damping on planetary slewing bearing gear tooth meshing and overall dynamic response is discussed. According to the method, a large amount of product development time and manpower are saved, the cost is low, the precision is high, and the method has important practical value for research and development of high-performance slewing bearing products.

Description

Technical Field

[0001] The present invention belongs to the field of gear transmission dynamics, and specifically is a gear rigid-elastic coupling dynamics modeling method of equivalent tooth root elastic deformation, that is, a processing method of a gear rigid-elastic coupling model connected by a torsion spring. Background Art

[0002] In mechanical transmission systems, gears are core components, and their performance directly affects the stability and efficiency of the entire system. Elastic deformation of the tooth root is an inevitable phenomenon when the gear transmits power and bears loads. It not only affects the meshing accuracy and transmission efficiency of the gear, but may also cause fatigue damage and failure of the gear. However, in the study of gear transmission characteristics, the description and treatment of the elastic deformation of the tooth root are often rough, or even directly ignore its elastic deformation. Therefore, it is necessary to find a common and efficient research method to explore new design schemes and dynamic analysis problems of gear transmission characteristics, which has important theoretical significance and reference value for ensuring the dynamic characteristics and combat performance of military equipment.

[0003] The multi-body dynamics model of the rigid-elastic coupling model consists of a rigid gear tooth, a rigid gear matrix, and an elastic unit, wherein the rigid gear tooth can only undergo relative angular displacement around the central axis of the gear matrix. When the rigid gears are meshed, contact occurs between the rigid gear teeth, and the rigid gear teeth are subjected to contact forces and produce relative angular displacement with the gear matrix. The relative angular displacement is transmitted to the distributed torsion spring, generating a tangential force and torque tangential to the root circle, thereby inhibiting further relative angular displacement between the rigid gear tooth and the gear matrix. Through the above processing method, the relative angular displacement between the rigid gear tooth and the gear matrix is ​​used to replace the bending deformation at the root of the simulated gear tooth.

[0004] Elastic deformation of tooth root refers to the shape change of the tooth root due to the elastic properties of the material when the rigid gear transmits power and bears load. This deformation is temporary, and the tooth root can return to its original shape when the external force is removed. However, long-term elastic deformation and stress concentration may lead to fatigue damage and failure of the tooth root. In order to deeply study the elastic deformation of tooth root and find an effective solution, domestic and foreign scholars have conducted a lot of research work. At present, the main research methods include analytical method, numerical method, experimental method and finite element method. However, the description of the influence of elastic deformation of tooth root on the system in dynamics is insufficient. In addition, among the various calculation standards for gear bending stress calculation, most are based on Lewis formula, which is based on the equal strength cantilever beam assumption of material mechanics, does not consider the sudden change of tooth root section, and ignores the influence of radial load on stress of gear teeth, resulting in the inaccurate reflection of gear bending stress. Summary of the invention

[0005] In order to solve the problems of the prior art, the present invention provides a method for processing a rigid-elastic coupling model of a gear connected by a torsion spring in the rigid-elastic coupling dynamic modeling of a slewing bearing with equivalent elastic deformation of the tooth root, that is, a rigid-elastic coupling dynamic modeling method for equivalently simulating the elastic deformation of the gear tooth root by connecting the rigid gear teeth and the gear matrix through a distributed torsion spring as a connecting force elastic unit. A new planetary slewing bearing dynamic analysis model is established, and the torsional stiffness expression of the distributed torsion spring as the connecting force elastic unit is obtained based on the Ishikawa method. In the modeling software, the planetary gear, sun gear and inner ring gear models of the slewing bearing are respectively established, and the connection between the rigid gear teeth and the gear matrix is ​​disconnected at the tooth root and then connected through an elastic unit to obtain an equivalent model of the elastic deformation of the tooth root. The influence of torsional stiffness and torsional damping on the rigid gear tooth meshing and the overall dynamic response of the planetary slewing bearing is further discussed.

[0006] The technical solution adopted by the present invention is: a gear rigid-elastic coupling dynamic modeling method of equivalent tooth root elastic deformation, disconnecting the connection between the gear tooth and the gear base at the tooth root, so that it is suitable for the situation between the gear rotating base and the elastic teeth, including the following steps:

[0007] 1) Based on the elastic deformation characteristics of the tooth root of the planetary gear train and the motion of the matrix, a rigid-elastic coupling dynamic model of the planetary gear, sun gear and inner gear ring is established;

[0008] 2) According to the actual working conditions, the corresponding constraints and contact settings are made for each component of the slewing bearing, and the penalty function method is used to simulate the four-point contact between the steel ball and the ring raceway and the meshing contact between the gear teeth;

[0009] 3) Based on the gear meshing rigid-elastic coupling theory and the Ishikawa method, the calculation method of the spring-damper stiffness, tooth top thickness, effective tooth root circle radius, rectangle height and equivalent rectangle thickness is further determined;

[0010] 4) A rigid-elastic coupled multi-body dynamic simulation model of a slewing bearing with equivalent tooth root elastic deformation is established to analyze the influence of torsional stiffness and torsional damping on the meshing of planetary slewing bearing teeth and the overall dynamic response.

[0011] Specifically, the specific steps of step 1) are as follows: establish the planetary gear, sun gear and inner ring gear models of the slewing bearing in the modeling software respectively, disconnect the connection between the rigid gear teeth and the gear base at the tooth root respectively, the gear rigid-elastic coupling model is composed of rigid gear teeth, rigid gear base and connection force elastic unit, wherein the rigid gear teeth can only undergo relative angular displacement around the central axis of the gear base, and the distributed torsion spring is used as a connection force elastic unit to connect the rigid gear teeth and the gear base to limit the mutual movement of the rigid gear teeth and the gear base. When the rigid gears are meshed, contact occurs between the rigid gear teeth, generating tangential force and torque tangential to the root circle, thereby inhibiting further relative angular displacement between the rigid gear teeth and the gear base. Through the above processing method, the relative angular displacement between the rigid gear teeth and the gear base is used to replace the bending deformation at the root of the rigid gear teeth.

[0012] Specifically, the specific steps of step 2) are: using the impact function method Impact to calculate the contact force: using the formula: Fn = Kδ e +CV, F in the formula n is the normal contact force; K is the stiffness coefficient; δ is the normal penetration force at the contact point; e is the rigidity index; C is the damping coefficient; V is the normal relative velocity at the contact point.

[0013] Specifically, the specific steps of step 3) are:

[0014] 3.1 In the meshing transmission process of rigid gears, the straight line formed by the meshing points between the gear teeth over time is called the meshing line of the gear. The meshing of the gears occurs on this straight line. First, it is assumed that the rigid-elastic coupling model needs to be based on the meshing point still being located on the meshing line after the gear teeth are deformed in contact. If there is a curved linear spring connection between the gear teeth and the gear base that coincides with the tooth root circle, the tangential force generated by this curved spring is:

[0015]

[0016] Where K e is the bending spring stiffness, D e is the spring damping coefficient, φ is the angle of rotation of the gear base per unit time, Δθ is the angle of rotation of the gear tooth per unit time, r d is the radius of the gear tooth root circle, and ω is the angular velocity of the gear base. The torsional stiffness formula of the torsion spring is:

[0017]

[0018] According to the involute generation formula, (φ-Δθ) can be equivalent to:

[0019]

[0020] Where rb is the base circle radius of the gear;

[0021] The formula for calculating torsional stiffness is:

[0022]

[0023] 3.2 Since the equivalent tooth profile method can consider the gear tooth contact and tooth root bending deformation separately, the gear meshing stiffness calculation is based on the equivalent. The relevant simplified gear tooth geometry is calculated as follows:

[0024] 3.2.1) The auxiliary dimensions are:

[0025]

[0026] Where h i is the tooth height, for external gears

[0027] 3.2.2) Tooth top thickness:

[0028] For standard gears:

[0029]

[0030] Where r a is the radius of the tooth tip circle, α0 is the pressure angle at the pitch circle of the gear tooth, α a is the pressure angle at the tooth tip circle;

[0031] 3.2.3) Effective tooth root circle radius:

[0032] The effective root circle is the radius of the circle where the meshing teeth actually mesh with the gear tooth profile, taking into account the gear center distance error. The empirical formula in practical application is: F =r a -2m;

[0033] 3.2.4) Rectangle height and equivalent rectangle thickness:

[0034] For external gears, when the base circle radius is smaller than the effective root circle radius: Calculation shows that z>33. At this time, the intersection of the effective root circle and the gear tooth profile is set as the intersection of the equivalent trapezoid and the equivalent rectangle, and the following can be deduced based on the geometric relationship:

[0035]

[0036] Considering the nominal tooth root as the actual tooth root, we can get:

[0037]

[0038] When the base circle radius is greater than the effective tooth root circle radius, it can be calculated that z≤33. Similarly, the calculation formula for related parameters is:

[0039]

[0040] At this point, the geometric parameters of all equivalent rectangles and equivalent trapezoids have been derived.

[0041] Specifically, the specific steps of step 4) are: using ADAMS / View to establish and solve a slewing bearing rigid-elastic coupling multi-body dynamics simulation model of equivalent tooth root elastic deformation, using torsional stiffness as a variable to only change the torsional stiffness of the torsion spring at the planetary gear, and based on the results, exploring the influence of torsional stiffness and torsional damping on the planetary slewing bearing tooth meshing and the overall dynamic response. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a dynamic model diagram of the novel planetary slewing bearing of the present invention;

[0043] Figure 2 This is a schematic diagram of the rigid-flexible coupling model of the present invention;

[0044] Figure 3 The contact diagram between the steel ball and the raceway of the ferrule of the present invention;

[0045] Figure 4 A schematic diagram of the steel ball ring raceway coordinate system and force direction vector of the present invention;

[0046] Figure 5 It is a schematic diagram of the meshing force of three pairs of gear teeth of the rigid-elastic coupling model of the planetary slewing bearing of the present invention;

[0047] Figure 6 A schematic diagram showing the contact force comparison of the planetary slewing bearing of the present invention;

[0048] Figure 7 Schematic diagram of the meshing force of gear teeth in Scheme 1 and Scheme 4 in the specific embodiments of the present invention. DETAILED DESCRIPTION

[0049] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0050] Example 1: Figure 1-7 As shown in FIG. 1 , a gear rigid-elastic coupling dynamic modeling method for equivalent tooth root elastic deformation is shown in FIG. 1 . The implementation steps of the method are as follows:

[0051] 1) Based on the elastic deformation characteristics of the tooth root of the planetary gear train and the motion of the matrix, a rigid-elastic coupling dynamic model of the planetary gear, sun gear and inner gear ring is established;

[0052] 2) According to the actual working conditions, the corresponding constraints and contact settings are made for each component of the slewing bearing, and the penalty function method is used to simulate the four-point contact between the steel ball and the ring raceway and the meshing contact between the gear teeth;

[0053] 3) Based on the gear meshing rigid-elastic coupling theory and the Ishikawa method, the calculation method of the spring-damper stiffness, tooth top thickness, effective tooth root circle radius, rectangle height and equivalent rectangle thickness is further determined;

[0054] 4) A rigid-elastic coupled multi-body dynamic simulation model of a slewing bearing with equivalent tooth root elastic deformation is established to analyze the influence of torsional stiffness and torsional damping on the meshing of planetary slewing bearing teeth and the overall dynamic response.

[0055] Furthermore, the specific steps of step 1) are as follows: in the modeling software, the planetary gear, sun gear and inner gear ring models of the slewing bearing are respectively established, and the connection between the rigid gear teeth and the gear base is disconnected at the tooth root. The gear rigid-elastic coupling model is composed of the rigid gear teeth, the rigid gear base and the connection force elastic unit. Figure 2 As shown in the figure, the rigid gear teeth can only undergo relative angular displacement around the central axis of the gear base, and the distributed torsion spring is used as a connecting force elastic unit to connect the rigid gear teeth and the gear base to limit the mutual movement of the rigid gear teeth and the gear base. When the rigid gears are meshing, contact occurs between the rigid gear teeth, generating tangential forces and torques tangential to the root circle, thereby inhibiting further relative angular displacement between the rigid gear teeth and the gear base. Through the above processing method, the relative angular displacement between the rigid gear teeth and the gear base is used to replace the bending deformation at the root of the rigid gear teeth.

[0056] Furthermore, the specific steps of step 2) are: using the impact function method Impact to calculate the contact force: using the formula: Fn = Kδ e +CV, F in the formula n is the normal contact force; K is the stiffness coefficient; δ is the normal penetration force at the contact point; e is the rigidity index; C is the damping coefficient; V is the normal relative velocity at the contact point.

[0057] The structure of planetary slewing bearing is as follows: Figure 1 As shown, 1 is the outer ring, 2 is the inner gear ring, 3 is the planetary gear, 4 is the sun gear, 5 is the gear shaft, and 6 is the steel ball.

[0058] The rigid-elastic coupling model of the gear connected by the torsion spring was established and developed based on the ADAMS platform. The meshing simulation model of the single external meshing pair spur gear and the helical gear was determined by the Ishikawa method, and the results with high accuracy were obtained. The planetary gear, sun gear, and internal gear models were established in Solidworks, and the connection between the gear teeth and the gear base was disconnected at the root of the tooth. The base and the gear teeth were connected with a torsion spring. The rigid-elastic coupling model diagram of the new planetary slewing bearing was obtained.

[0059] The stiffness of the spring-damper can be expressed as:

[0060]

[0061] by Figure 4 Taking the steel ball as an example, determine the coordinate position of the center of curvature of the upper half of the inner ring raceway after load balance in the global coordinate system, as well as the vector direction of the contact force, and establish the equation for solving the coordinate of the center of curvature of the upper half of the inner ring raceway after load balance:

[0062]

[0063] Specifically, the specific steps of step 2 are: using the impact function method Impact to calculate the contact force: using the formula: Fn = Kδ e +CV, F in the formula n is the normal contact force; K is the stiffness coefficient; δ is the normal penetration force at the contact point; e is the rigidity index; C is the damping coefficient; V is the normal relative velocity at the contact point.

[0064] Furthermore, the specific steps of step 3) are:

[0065] 3.1 Ishikawa method is based on the conformal mapping transformation, which maps the curved boundary of the gear to a straight boundary, and then obtains the displacement field of the half-plane by solving the complex function of the concentrated force acting on the half-plane. This method can more accurately describe the elastic deformation behavior of the gear during the meshing process.

[0066] The application of the Ishikawa method in the elastic deformation of rigid tooth roots is mainly reflected in the calculation and analysis of gear meshing stiffness. During the meshing process of gears, the tooth root part will be subjected to large bending stress and contact stress, which will lead to elastic deformation. The Ishikawa method calculates the elastic deformation of the tooth root by considering the geometric parameters, material properties and various deformation factors of the gear during the meshing process, and then evaluates the meshing stiffness and performance of the gear.

[0067] In the meshing transmission process of rigid gears, the straight line formed by the meshing points between the gear teeth over time is called the meshing line of the gear. The meshing of the gears occurs on this straight line. First, it is assumed that the rigid-elastic coupling model needs to be based on the gear teeth after contact deformation, and the meshing points are still located on the meshing line. If there is a curved linear spring connection between the gear teeth and the gear base that coincides with the tooth root circle, the tangential force generated by this curved spring is:

[0068]

[0069] Where K e is the bending spring stiffness, D e is the spring damping coefficient, φ is the angle of rotation of the gear base per unit time, Δθ is the angle of rotation of the gear tooth per unit time, r d is the radius of the gear tooth root circle, and ω is the angular velocity of the gear base. The torsional stiffness formula of the torsion spring is:

[0070]

[0071] According to the involute generation formula, (φ-Δθ) can be equivalent to:

[0072]

[0073] Where r b is the base circle radius of the gear;

[0074] The formula for calculating torsional stiffness is:

[0075]

[0076] 3.2 Since the equivalent tooth profile method can consider the gear tooth contact and tooth root bending deformation separately, the gear meshing stiffness calculation is based on the equivalent. The relevant simplified gear tooth geometry is calculated as follows:

[0077] 3.2.1) The auxiliary dimensions are:

[0078]

[0079] Where h i is the tooth height, for external gears

[0080] 3.2.2) Tooth top thickness:

[0081] For standard gears:

[0082]

[0083] Where r a is the radius of the tooth tip circle, α0 is the pressure angle at the pitch circle of the gear tooth, α a is the pressure angle at the tooth tip circle;

[0084] 3.2.3) Effective tooth root circle radius:

[0085] The effective root circle is the radius of the circle where the meshing teeth actually mesh with the gear tooth profile, taking into account the gear center distance error. The empirical formula in practical application is: F =r a -2m;

[0086] 3.2.4) Rectangle height and equivalent rectangle thickness:

[0087] For external gears, when the base circle radius is smaller than the effective root circle radius: Calculation shows that z>33. At this time, the intersection of the effective root circle and the gear tooth profile is set as the intersection of the equivalent trapezoid and the equivalent rectangle, and the following can be deduced based on the geometric relationship:

[0088]

[0089] Considering the nominal tooth root as the actual tooth root, we can get:

[0090]

[0091] When the base circle radius is greater than the effective tooth root circle radius, it can be calculated that z≤33. Similarly, the calculation formula for related parameters is:

[0092]

[0093] At this point, the geometric parameters of all equivalent rectangles and equivalent trapezoids have been derived.

[0094] Furthermore, the specific steps of step 4) are: using ADAMS / View to establish and solve the slewing bearing rigid-elastic coupling multi-body dynamics simulation model of equivalent tooth root elastic deformation, using torsional stiffness as a variable to only change the torsional stiffness of the torsion spring at the planetary gear, and based on the results, exploring the influence of torsional stiffness and torsional damping on the planetary slewing bearing tooth meshing and the overall dynamic response.

[0095] Figure 6 It is a comparison curve of the dynamic contact force between the rigid-elastic coupling multi-body dynamics model and the gear and all-rigid body split-tooth planetary slewing bearing steel ball and the ring raceway. Analysis shows that the contact impact between the steel ball and the ring raceway in the rigid-elastic coupling model is reduced.

[0096] The boundary condition is set as follows: the output speed of the inner gear ring of the slewing bearing reaches the maximum speed ω in 0.15s i= 374° / s and then keep rotating at a constant speed. At the same time, the center of the inner gear ring (or inner ring) is subjected to a combined load of 1000N·m overturning moment around the y-axis, 6000N axial force along the gravity direction, and 3000N·m load moment around the axis. Keeping this boundary condition unchanged, only changing the torsional stiffness of the torsion spring at the planetary gear, the torsional stiffness setting scheme is shown in the following table.

[0097]

[0098] The results are as follows Figure 7 As shown in the figure, with the decrease of torsional damping, the space for relative displacement between the gear teeth and the gear matrix increases, and the self-engagement adjustment ability between the gear teeth increases, resulting in an increase in the overlap of the gear tooth contact and a smoother gear tooth meshing.

[0099] Based on the rigid-elastic coupled multi-body dynamics simulation model of planetary slewing bearing, the influence of torsional stiffness and torsional damping on the gear meshing and overall dynamic response of the planetary slewing bearing is further explored.

[0100] The present invention proposes a gear rigid-elastic coupling dynamic modeling method for equivalent tooth root elastic deformation, which saves a lot of product development time and manpower, has low cost and high precision, and has important practical value for the research and development of high-performance slewing bearing products.

[0101] The specific implementation modes of the present invention are described in detail above in conjunction with the drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A gear rigid-elastic coupling dynamic modeling method for equivalent tooth root elastic deformation, characterized by: The steps include: 1) Based on the elastic deformation characteristics of the tooth root of the planetary gear train and the motion of the matrix, a rigid-elastic coupling dynamic model of the planetary gear, sun gear and inner gear ring is established; 2) According to the actual working conditions, the corresponding constraints and contact settings are made for each component of the slewing bearing, and the penalty function method is used to simulate the four-point contact between the steel ball and the ring raceway and the meshing contact between the gear teeth; 3) Based on the gear meshing rigid-elastic coupling theory and the Ishikawa method, the calculation method of the spring-damper stiffness, tooth top thickness, effective tooth root circle radius, rectangle height and equivalent rectangle thickness is further determined; 4) A rigid-elastic coupled multi-body dynamic simulation model of a slewing bearing with equivalent tooth root elastic deformation is established to analyze the influence of torsional stiffness and torsional damping on the meshing of planetary slewing bearing teeth and the overall dynamic response.

2. The gear rigid-elastic coupling dynamic modeling method of equivalent tooth root elastic deformation according to claim 1 is characterized by: The specific steps of step 1) are as follows: respectively establishing the planetary gear, sun gear and inner ring gear models of the slewing bearing in the modeling software, respectively disconnecting the connection between the rigid gear teeth and the gear base at the tooth roots, the gear rigid-elastic coupling model is composed of rigid gear teeth, a rigid gear base and a connecting force elastic unit, wherein the rigid gear teeth can only undergo relative angular displacement around the central axis of the gear base, and the distributed torsion spring is used as a connecting force elastic unit to connect the rigid gear teeth and the gear base to limit the mutual movement of the rigid gear teeth and the gear base; when the rigid gears are meshed for transmission, contact occurs between the rigid gear teeth, generating tangential force and torque tangential to the tooth root circle, thereby inhibiting further relative angular displacement between the rigid gear teeth and the gear base, and through the above processing method, the relative angular displacement between the rigid gear teeth and the gear base is used to replace the bending deformation at the tooth root of the simulated rigid gear teeth.

3. The gear rigid-elastic coupling dynamic modeling method of equivalent tooth root elastic deformation according to claim 1 is characterized by: The specific steps of step 2) are: using the impact function method Impact to calculate the contact force: using the formula: F n =Kδ e +CV, F in the formula n is the normal contact force; K is the stiffness coefficient; δ is the normal penetration force at the contact point; e is the rigidity index; C is the damping coefficient; V is the normal relative velocity at the contact point.

4. The gear rigid-elastic coupling dynamic modeling method of equivalent tooth root elastic deformation according to claim 1 is characterized by: The specific steps of step 3) are: 3.1 In the meshing transmission process of rigid gears, the straight line formed by the meshing points between the gear teeth over time is called the meshing line of the gear. The meshing of the gears occurs on this straight line. First, it is assumed that the rigid-elastic coupling model needs to be based on the meshing point still being located on the meshing line after the gear teeth are deformed in contact. If there is a curved linear spring connection between the gear teeth and the gear base that coincides with the tooth root circle, the tangential force generated by this curved spring is: Where K e is the bending spring stiffness, D e is the spring damping coefficient, φ is the angle of rotation of the gear base per unit time, Δθ is the angle of rotation of the gear tooth per unit time, r d is the radius of the gear tooth root circle, ω is the angular velocity of the gear base, and the torsional stiffness formula of the torsion spring is: According to the involute generation formula, (φ-Δθ) can be equivalent to: Where r b is the base circle radius of the gear; The formula for calculating torsional stiffness is: 3.2 Since the equivalent tooth profile method can consider the gear tooth contact and tooth root bending deformation separately, the gear meshing stiffness is calculated based on the equivalent, and the relevant simplified gear tooth geometry is calculated as follows: 3.2.1) The auxiliary dimensions are: Where h is the tooth height. For external gears 3.2.2) Tooth top thickness: For standard gears: Where r a is the radius of the tooth tip circle, α0 is the pressure angle at the pitch circle of the gear tooth, α a is the pressure angle at the tooth tip circle; 3.2.3) Effective tooth root circle radius: The effective root circle is the radius of the circle where the meshing teeth actually mesh with the gear tooth profile, taking into account the gear center distance error. The empirical formula in practical application is: F =r a -2m; 3.2.4) Rectangle height and equivalent rectangle thickness: For external gears, when the base circle radius is smaller than the effective root circle radius: It can be calculated that z>

33. At this time, the intersection of the effective root circle and the gear tooth profile is set as the intersection of the equivalent trapezoid and the equivalent rectangle. According to the geometric relationship, it can be deduced that: Considering the nominal tooth root as the actual tooth root, we can get: When the base circle radius is greater than the effective tooth root circle radius, it can be calculated that z≤33. Similarly, the calculation formula for related parameters is: At this point, the geometric parameters of all equivalent rectangles and equivalent trapezoids have been derived.

5. The gear rigid-elastic coupling dynamic modeling method of equivalent tooth root elastic deformation according to claim 1 is characterized by: The specific steps of step 4) are: using ADAMS / View to establish and solve the slewing bearing rigid-elastic coupling multi-body dynamics simulation model of equivalent tooth root elastic deformation, using torsional stiffness as a variable to only change the torsional stiffness of the torsion spring at the planetary gear, and based on the results, exploring the influence of torsional stiffness and torsional damping on the planetary slewing bearing tooth meshing and the overall dynamic response.

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