Method for calculating tooth surface contact stress of multistage parallel shaft gear transmission system

Abstract

The invention relates to the technical field of mechanical engineering, and discloses a tooth surface contact stress calculation method for a multistage parallel shaft gear transmission system. Compared with the prior art that the gear surface contact stress is calculated only according to the gear structure, the influence of the system structure flexibility on the gear meshing characteristic is neglected, and consequently the calculation of the gear surface contact stress is inaccurate, the technical scheme is combined with the structural characteristics of the system, and the multi-stage parallel shaft gear transmission system is dispersed into a plurality of basic units; a stiffness matrix of a system is established by calculating a stiffness matrix of each basic unit, then a statics equilibrium equation set of the system is established according to working condition information and a load vector, the meshing misalignment amount of a gear pair is obtained by solving the statics equilibrium equation set of the system, and the tooth surface contact stress is calculated according to the meshing misalignment amount. According to the technical scheme, the influence of a flexible structure on the system is comprehensively considered, and more accurate calculation of the tooth surface contact stress of the multistage parallel shaft gear transmission system, which is more suitable for practical application, is realized.

Description

Technical Field

[0001] This invention relates to the field of mechanical engineering technology, and in particular to a method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system. Background Technology

[0002] Multi-stage parallel shaft gear transmission systems are transmission systems formed by sequentially connecting the output gear of the first stage and the input gear of the next stage of multiple gear pairs. As a core component of modern mechanical transmission, they are widely used in wind power, shipbuilding, metallurgy and rail transportation. They achieve large reduction ratios and high torque transmission through multi-stage gear series connection, meeting the high efficiency and reliability requirements of heavy equipment for power distribution.

[0003] Tooth surface contact stress is a key indicator for evaluating the load-bearing capacity and durability of gears, directly affecting their fatigue strength and wear performance. It is typically calculated based on Hertzian contact theory. The calculation of tooth surface contact stress is crucial data for ensuring the efficient and stable operation of multi-stage parallel shaft gear transmission systems.

[0004] Current technology calculates tooth surface contact stress based solely on gear structure. However, the flexibility of the system structure (including shaft deformation, gear elastic deformation, and housing deformation) can significantly alter gear meshing characteristics, causing the tooth surface contact stress distribution to deviate from the ideal state. The axial misalignment or tooth surface misalignment caused by flexibility can result in a significant difference between the actual contact state and the ideal contact state.

[0005] Therefore, how to achieve more accurate calculation of tooth surface contact stress in multi-stage parallel shaft gear transmission systems that better fits practical applications is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to solve the problem that the influence of structural flexibility on the system is ignored when calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system in the current technology. Therefore, this invention provides a method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system, so as to achieve a more practical and accurate calculation of the tooth surface contact stress of a multi-stage parallel shaft gear transmission system.

[0007] To address the aforementioned technical problems, this invention provides a method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system, comprising:

[0008] Based on the structural information of the multi-stage parallel shaft gear transmission system, the multi-stage parallel shaft gear transmission system is discretized into multiple basic units;

[0009] Each of the basic units is modeled to establish the corresponding stiffness matrix;

[0010] Based on the stiffness matrix of each basic unit and the working condition information of the multi-stage parallel shaft gear transmission system, a set of static equilibrium equations for the system is established.

[0011] The static equilibrium equations of the system are solved to obtain the meshing misalignment of the gear pair, and the tooth surface contact stress is calculated based on the meshing misalignment.

[0012] Preferably, the basic unit includes: a shaft segment unit, a bearing unit, a housing unit, and a gear meshing unit group.

[0013] Preferably, the step of modeling each of the basic units to establish the corresponding stiffness matrix includes:

[0014] The shaft segment element is modeled using Timoshenko beam elements, and the corresponding stiffness matrix is ​​established.

[0015] The bearing unit is modeled as a spring-damped unit, and a corresponding stiffness matrix is ​​established.

[0016] A three-dimensional finite element model is established for the box-shaped unit, and the corresponding stiffness matrix is ​​established using the finite element substructure method.

[0017] The gear meshing unit group is modeled as a group of parallel spring-damping units, and the corresponding stiffness matrix is ​​established.

[0018] Preferably, the establishment of the stiffness matrix of the gear meshing unit group includes:

[0019] The gear pair in the gear meshing unit group is discretized into multiple gear slices along the tooth width direction;

[0020] Establish the stiffness matrix of the gear meshing unit group based on the stiffness calculation formula of each gear slice;

[0021] No. The formula for calculating the stiffness of a gear slice is:

[0022] ;

[0023] In the formula, For the first The number of contact points on each gear slice For the first Stiffness at each contact point For the first The stiffness of each gear slice.

[0024] Preferably, the step of solving the static equilibrium equations of the system to obtain the meshing misalignment of the gear pair, and calculating the tooth surface contact stress based on the meshing misalignment, includes:

[0025] The stiffness matrix of each gear slice is substituted into the static equilibrium equations of the system in sequence to obtain the generalized transmission error, and the meshing misalignment is calculated based on the generalized transmission error; the generalized transmission error is the relative displacement of the gear slice along the tooth width direction along the normal meshing line direction.

[0026] The meshing misalignment is introduced into the tooth surface bearing contact equation and the tooth surface load distribution is obtained by solving the equation.

[0027] The tooth surface contact stress is obtained by incorporating the tooth surface load distribution into the Hertzian contact stress calculation formula.

[0028] Preferably, the formula for calculating the meshing misalignment amount is:

[0029] , ;

[0030] in, This is the amount of meshing misalignment. For the first The relative displacement of each gear slice along the normal meshing line direction This refers to the generalized propagation error.

[0031] Preferably, the matrix form of the tooth surface bearing contact equation is:

[0032] ;

[0033] The bending deformation compliance matrix at the contact point. The Hertzian contact deformation at the contact point. For gear pair transmission error, This refers to the remaining gap between contact points after loading. For the set of meshing misalignment quantities, For contact point The load, It is an n-dimensional unit vector. This is the load distribution vector on the tooth surface. For the normal meshing force of the gear pair, For the first The gap between the contact points.

[0034] Preferably, the formula for calculating Hertzian contact stress is:

[0035] ;

[0036] For tooth surface contact stress, The radius of curvature of the contact point on the drive wheel. Let be the radius of curvature of the contact point on the driven wheel. The Young's modulus of the drive wheel. The Young's modulus of the driven wheel. The Poisson's ratio of the driving wheel and the driven wheel. Let Poisson's ratio be the driven wheel. This is the equivalent contact line length at the contact point.

[0037] Preferred options also include:

[0038] Determine whether the relative error between the two generalized transmission errors calculated is less than the convergence tolerance; if yes, proceed to the step of calculating the meshing misalignment based on the generalized transmission error; if no, return to the step of establishing the stiffness matrix of the gear meshing unit group based on the stiffness calculation formula of each gear slice to reconstruct the stiffness matrix of each gear slice.

[0039] Preferably, the system's static equilibrium equations are as follows:

[0040] ;

[0041] Here is the system stiffness matrix; This is the static displacement vector of the system obtained based on the meshing misalignment. This is the system load vector.

[0042] This invention provides a method for calculating tooth surface contact stress in a multi-stage parallel shaft gear transmission system. Compared to current technologies that calculate tooth surface contact stress solely based on the gear structure while neglecting the influence of system structural flexibility on gear meshing characteristics, leading to inaccurate calculations, this method discretizes the multi-stage parallel shaft gear transmission system into multiple basic units, calculates the stiffness matrix of each basic unit to construct the system's stiffness matrix, and then establishes the system's static equilibrium equations based on load vectors using operating condition information. Solving these equations yields the meshing misalignment of the gear pair, and the tooth surface contact stress is calculated based on this misalignment. By dividing the flexible structure of the multi-stage parallel shaft gear transmission system into basic units and analyzing the stress conditions of each basic unit during tooth surface contact stress calculation, this method achieves a more practical and accurate calculation of tooth surface contact stress in multi-stage parallel shaft gear transmission systems. Attached Figure Description

[0043] To more clearly illustrate the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1A flowchart illustrating a method for calculating tooth surface contact stress in a multi-stage parallel shaft gear transmission system, provided as an embodiment of the present invention;

[0045] Figure 2 This is a schematic diagram of the finite element substructure method for a multi-stage gear transmission system housing unit, provided in an embodiment of the present invention.

[0046] Figure 3 A mechanical model diagram of a gear meshing unit assembly provided in an embodiment of the present invention;

[0047] Figure 4 The first embodiment provided by the present invention A schematic diagram of a slice model;

[0048] Figure 5 This is a comparison diagram of the relative displacement and meshing misalignment of a meshing pair along the normal meshing line direction, provided for an embodiment of this application. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0050] The core of this invention is to provide a method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system, so as to achieve a more practical and accurate calculation of the tooth surface contact stress of the multi-stage parallel shaft gear transmission system.

[0051] To enable those skilled in the art to better understand the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] Figure 1 A flowchart illustrating a method for calculating tooth surface contact stress in a multi-stage parallel shaft gear transmission system, as provided in this embodiment of the invention, is shown below. Figure 1 As shown, the method includes:

[0053] S10: Based on the structural information of the multi-stage parallel shaft gear transmission system, the multi-stage parallel shaft gear transmission system is discretized into multiple basic units;

[0054] S11: Model each basic element to establish the corresponding stiffness matrix;

[0055] S12: Establish the system static equilibrium equations based on the stiffness matrix of each basic unit and the working condition information of the multi-stage parallel shaft gear transmission system.

[0056] S13: Solve the static equilibrium equations of the system to obtain the meshing misalignment of the gear pair, and calculate the tooth surface contact stress based on the meshing misalignment.

[0057] The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system provided in this application is used to calculate the tooth surface contact stress of the multi-stage parallel shaft gear transmission system. Considering structural flexibility, it can calculate the tooth surface contact stress of each gear pair in the multi-stage parallel shaft gear transmission system under different working conditions. The execution subject of this method can be a multi-stage parallel shaft gear transmission system tooth surface contact stress calculation device. This device may specifically include a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the multi-stage parallel shaft gear transmission system tooth surface contact stress calculation method provided in the above embodiments. In some embodiments, the multi-stage parallel shaft gear transmission system tooth surface contact stress calculation device may also include a display, touch screen, or other human-computer interaction device. In specific implementations, the multi-stage parallel shaft gear transmission system tooth surface contact stress calculation device provided in this embodiment may include, but is not limited to, smartphones, tablets, laptops, or desktop computers.

[0058] Of course, it is understood that if the methods in the above embodiments are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the technical solutions of this application can be embodied in the form of a software product, which is stored in a storage medium and executes all or part of the steps of the methods described in the various embodiments of this application.

[0059] Firstly, in step S10, by reading information about the multi-stage parallel shaft gear transmission system, mainly including specific structural information and system operating condition information, the multi-stage parallel shaft gear transmission system is discretized into a series of nodes and basic units based on the structural characteristics of each component. Based on structural characteristics, it is mainly divided into four basic units: shaft segment unit, bearing unit, housing unit, and gear meshing unit group. These four basic units are the main components involved in the operation of the multi-stage parallel shaft gear transmission system, and their flexibility affects the calculation of tooth surface contact stress. Therefore, this application achieves a more accurate tooth surface contact stress calculation by dividing the system into basic units. Of course, in other embodiments, depending on the specific structure of the multi-stage parallel shaft gear transmission system and the components included in the four basic units, the multi-stage parallel shaft gear transmission system can be divided into more or fewer basic units. The four basic units in this embodiment are applicable to most multi-stage parallel shaft gear transmission systems.

[0060] In step S11, each basic element is modeled, and the stiffness matrix of each basic element is calculated based on the modeling. This application provides a method for calculating the stiffness matrix for cases containing four basic elements. This includes: modeling the shaft segment element using Timoshenko beam elements and establishing the corresponding stiffness matrix; modeling the bearing element as a spring-damped element and establishing the corresponding stiffness matrix; establishing a three-dimensional finite element model for the box element and establishing the corresponding stiffness matrix using the finite element substructure method; and modeling the gear meshing element group as a group of parallel spring-damped elements and establishing the corresponding stiffness matrix. Figure 2 This is a schematic diagram of the finite element substructure method for a multi-stage gear transmission system housing unit provided in an embodiment of the present invention, as shown below. Figure 2 As shown, the box is regarded as a basic unit, a three-dimensional finite element model of the box is established, the nodes of the inner holes of each bolt are coupled as corresponding central coupling nodes and all degrees of freedom are constrained, the nodes of the inner holes of each bearing seat are coupled as corresponding central coupling nodes, and the stiffness matrix is ​​extracted by the finite element substructure method. Figure 3 A mechanical model diagram of a gear meshing unit assembly provided in an embodiment of the present invention is shown below. Figure 3 As shown, each gear pair is discretized into a series of slices along the tooth width direction. The meshing process of the meshing pairs after axial discretization is as follows: Figure 3 As shown, where, where and The radii of the base circles of the master and driven gears. and It is the rotational speed of the driving and driven gears. and It is the rotation center of the driving and driven gears. It is the theoretical line of engagement. It is the meshing plane. It is the helix angle of the base circle. Figure 4 The first embodiment provided by the present invention A schematic diagram of a model of slices, in which and These are the installation angle and the engagement angle. and It is the first The rotation center of each slice. It is the first The meshing stiffness of each slice, Indicates the meshing clearance.

[0061] Therefore, it can be concluded that establishing the stiffness matrix of the gear meshing unit group includes: discretizing the gear pair in the gear meshing unit group into multiple gear slices along the tooth width direction; establishing the stiffness matrix of the gear meshing unit group based on the stiffness calculation formula of each gear slice; the... The formula for calculating the stiffness of a gear slice is:

[0062] ;

[0063] For the first The number of contact points on each gear slice For the first Stiffness at each contact point For the first The stiffness of each gear slice.

[0064] After establishing the models of each basic unit and calculating the stiffness matrix of each unit, the stiffness matrix of the multi-stage parallel shaft gear transmission system can be obtained by assembling it using the finite element method in step S12. Based on the power input / output positions and the load vector determined according to the operating condition information, the system's static equilibrium equations can be established. The system's static equilibrium equations can be expressed as:

[0065] ;

[0066] Here is the system stiffness matrix; This is the static displacement vector of the system obtained based on the meshing misalignment. This is the system load vector.

[0067] Finally, in step S13, the meshing misalignment of the gear pair is obtained by solving the static equilibrium equations of the multi-stage parallel shaft gear transmission system, and the tooth surface contact stress is calculated based on the meshing misalignment.

[0068] The tooth surface contact stress calculation method for multi-stage parallel shaft gear transmission systems provided in this application addresses the problem of inaccurate tooth surface contact stress calculations caused by current technologies that only calculate tooth surface contact stress based on gear structure while neglecting the influence of system structural flexibility on gear meshing characteristics. This technical solution discretizes the multi-stage parallel shaft gear transmission system into multiple basic units based on the system's structural characteristics. The system's stiffness matrix is ​​constructed by calculating the stiffness matrix of each basic unit. Then, based on operating condition information and load vectors, a set of static equilibrium equations for the system is established. Solving these equations yields the meshing misalignment of the gear pair, and the tooth surface contact stress is calculated based on this misalignment. By dividing the flexible structure of the multi-stage parallel shaft gear transmission system into basic units and analyzing the stress conditions of each basic unit when calculating tooth surface contact stress, this method achieves a more practical and accurate calculation of tooth surface contact stress for multi-stage parallel shaft gear transmission systems.

[0069] Based on the above embodiments, this embodiment also provides a specific method for calculating tooth surface contact stress, including: substituting the stiffness matrix of each gear slice into the system static equilibrium equations in sequence to obtain the generalized transmission error, and calculating the meshing misalignment based on the generalized transmission error; the generalized transmission error is the relative displacement of the gear slice along the normal meshing line direction along the tooth width direction; introducing the meshing misalignment into the tooth surface bearing contact equation and solving it to obtain the tooth surface load distribution; introducing the tooth surface load distribution into the Hertzian contact stress calculation formula to obtain the tooth surface contact stress.

[0070] Figure 5 This application provides a comparison diagram of the relative displacement and meshing misalignment of a meshing pair along the normal meshing line direction. It is understood that, considering the influence of structural flexibility on gear meshing, the relative displacement of the gear slices along the tooth width direction along the normal meshing line direction after loading is different, and this is defined as the generalized transmission error. The difference in the relative displacement of the gear slices along the tooth width direction is the meshing misalignment of the gear pair. Therefore, the formula for calculating the meshing misalignment is:

[0071] , ;

[0072] in, This is the amount of meshing misalignment. For the first The relative displacement of each gear slice along the normal meshing line direction This refers to the generalized propagation error.

[0073] in, ; ;

[0074] ;

[0075] ;

[0076] The first in the gear meshing unit group The generalized coordinates of a slice, For projection vectors, For installation angle, The engagement angle, Let be the radius of the base circle of the driving gear. Let be the radius of the base circle of the driven gear. The helix angle of the base circle. For lateral displacement about each axis, The symbol "" represents the rotation angle about each axis. “ in "and symbol" “ in "Indicates that the drive wheel rotates counterclockwise, symbol " “ in "and symbol" “ in "" indicates that the drive wheel rotates clockwise.

[0077] When the When the generalized transmission error of the first gear slice is greater than zero, it indicates that the gear slice participates in meshing. When the generalized transmission error of a slice is less than zero, it indicates that the slice did not participate in meshing under the influence of structural flexibility, and disengagement occurred. Therefore, the gear pair meshing misalignment is introduced into the tooth surface bearing contact equation, and the tooth surface load distribution can be obtained through iterative solution.

[0078] During iteration, to ensure the rationality of the system, this application pre-sets a convergence tolerance based on the system structure. When calculating the generalized transmission error, it determines whether the relative error between the two calculated generalized transmission errors is less than the convergence tolerance. If so, it proceeds to the step of calculating the meshing misalignment based on the generalized transmission error. If not, it returns to the step of establishing the stiffness matrix of the gear meshing unit group based on the stiffness calculation formula of each gear slice to reconstruct the stiffness matrix of each gear slice.

[0079] This application also provides specific tooth surface bearing contact equations, the matrix form of which is as follows:

[0080] ;

[0081] The bending deformation compliance matrix at the contact point. The Hertzian contact deformation at the contact point. For gear pair transmission error, This refers to the remaining gap between contact points after loading. For the set of meshing misalignment quantities, For contact point The load, It is an n-dimensional unit vector. This is the load distribution vector on the tooth surface. For the normal meshing force of the gear pair, For the first The gap between the contact points.

[0082] When calculating contact stress using Hertzian contact stress, the formula for calculating Hertzian contact stress is:

[0083] ;

[0084] For tooth surface contact stress, The radius of curvature of the contact point on the drive wheel. Let be the radius of curvature of the contact point on the driven wheel. The Young's modulus of the drive wheel. The Young's modulus of the driven wheel. The Poisson's ratio of the driving wheel and the driven wheel. Let Poisson's ratio be the driven wheel. This is the equivalent contact line length at the contact point.

[0085] The foregoing has provided a detailed description of the method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system provided by this invention. The various embodiments in the specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system, characterized in that, include: Based on the structural information of the multi-stage parallel shaft gear transmission system, the multi-stage parallel shaft gear transmission system is discretized into multiple basic units; Each of the basic units is modeled to establish the corresponding stiffness matrix; Based on the stiffness matrix of each basic unit and the working condition information of the multi-stage parallel shaft gear transmission system, a set of static equilibrium equations for the system is established. The static equilibrium equations of the system are solved to obtain the meshing misalignment of the gear pair, and the tooth surface contact stress is calculated based on the meshing misalignment.

2. The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system according to claim 1, characterized in that, The basic unit includes: shaft segment unit, bearing unit, housing unit and gear meshing unit group.

3. The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system according to claim 2, characterized in that, The process of modeling each of the basic units to establish the corresponding stiffness matrix includes: The shaft segment element is modeled using Timoshenko beam elements, and the corresponding stiffness matrix is ​​established. The bearing unit is modeled as a spring-damped unit, and a corresponding stiffness matrix is ​​established. A three-dimensional finite element model is established for the box-shaped unit, and the corresponding stiffness matrix is ​​established using the finite element substructure method. The gear meshing unit group is modeled as a group of parallel spring-damping units, and the corresponding stiffness matrix is ​​established.

4. The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system according to claim 3, characterized in that, The establishment of the stiffness matrix of the gear meshing unit group includes: The gear pair in the gear meshing unit group is discretized into multiple gear slices along the tooth width direction; Establish the stiffness matrix of the gear meshing unit group based on the stiffness calculation formula of each gear slice; No. The formula for calculating the stiffness of a gear slice is: ； In the formula, For the first The number of contact points on each gear slice For the first Stiffness at each contact point For the first The stiffness of each gear slice.

5. The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system according to claim 4, characterized in that, Solving the static equilibrium equations of the system to obtain the meshing misalignment of the gear pair, and calculating the tooth surface contact stress based on the meshing misalignment, includes: The stiffness matrix of each gear slice is substituted into the static equilibrium equations of the system in sequence to obtain the generalized transmission error, and the meshing misalignment is calculated based on the generalized transmission error; the generalized transmission error is the relative displacement of the gear slice along the tooth width direction along the normal meshing line direction. The meshing misalignment is introduced into the tooth surface bearing contact equation and the tooth surface load distribution is obtained by solving the equation. The tooth surface contact stress is obtained by incorporating the tooth surface load distribution into the Hertzian contact stress calculation formula.

6. The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system according to claim 5, characterized in that, The formula for calculating the meshing misalignment amount is: ， ； in, This is the amount of meshing misalignment. For the first The relative displacement of each gear slice along the normal meshing line direction This refers to the generalized propagation error.

7. The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system according to claim 6, characterized in that, The matrix form of the tooth surface bearing contact equation is as follows: ； The bending deformation compliance matrix at the contact point. The Hertzian contact deformation at the contact point. For gear pair transmission error, This refers to the remaining gap between contact points after loading. For the set of meshing misalignment quantities, For contact point The load, It is an n-dimensional unit vector. This is the load distribution vector on the tooth surface. For the normal meshing force of the gear pair, For the first The gap between the contact points.

8. The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system according to claim 7, characterized in that, The formula for calculating Hertzian contact stress is: ； For tooth surface contact stress, The radius of curvature of the contact point on the drive wheel. Let be the radius of curvature of the contact point on the driven wheel. The Young's modulus of the drive wheel. The Young's modulus of the driven wheel. The Poisson's ratio of the driving wheel and the driven wheel. Let Poisson's ratio be the driven wheel. This is the equivalent contact line length at the contact point.

9. The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system according to claim 5, characterized in that, Also includes: Determine whether the relative error between the two calculated generalized propagation errors is less than the convergence tolerance; If so, proceed to the step of calculating the meshing misalignment based on the generalized transmission error; If not, return to the step of establishing the stiffness matrix of the gear meshing unit group based on the stiffness calculation formula of each gear slice to reconstruct the stiffness matrix of each gear slice.

10. The method for calculating the tooth surface contact stress of a multi-stage parallel shaft gear transmission system according to any one of claims 1 to 9, characterized in that, The system's static equilibrium equations are as follows: ； Here is the system stiffness matrix; This is the static displacement vector of the system obtained based on the meshing misalignment. This is the system load vector.

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