Deep sea gearbox finite element modeling method based on radial equivalent stiffness

Abstract

The invention discloses a deep sea gearbox finite element modeling method based on radial equivalent stiffness, and relates to the technical field of finite element modeling, and the method comprises the following steps: deducing bending stiffness, shearing stiffness and axial compression stiffness of a meshing gear; the total meshing stiffness of the tooth pairs is obtained by combining the Hertz contact stiffness; establishing a contact stiffness characterization model of the cylindrical roller bearing, the double-row tapered roller bearing and the deep groove ball bearing; establishing a deep sea gearbox model, and performing equivalent simplification based on radial equivalent stiffness to obtain a deep sea gearbox finite element simplified model; and setting boundary conditions to obtain a deep sea gearbox strength checking model. According to the method, the total meshing stiffness of the tooth pair is obtained by deducing the bending stiffness, the shearing stiffness and the axial compression stiffness, the contact stiffness representation model of the three bearings is established to obtain the bearing contact stiffness, equivalent simplification is performed based on the radial equivalent stiffness, and the requirements of deep sea gearbox modeling for high simulation precision and high calculation efficiency are considered.

Description

Technical Field

[0001] The present application relates to the technical field of finite element modeling, and in particular to a finite element modeling method for a deep-sea gearbox based on radial equivalent stiffness. Background Art

[0002] Gear transmission systems are a fundamental component of the powertrain of deep-sea mining equipment and are essential for ensuring efficient, safe, and stable operation. The deformation of deep-sea equipment casings at great depths significantly affects the performance of internal components, making the mechanical performance analysis of gearboxes crucial. This necessitates research into modeling methods for deep-sea gearboxes.

[0003] Currently, the modeling and analysis of deep-sea gearboxes generally adopts the finite element modeling method, which usually relies on full-detail 3D solid modeling.

[0004] While existing finite element modeling methods for deep-sea gearboxes can partially reflect structural characteristics, they suffer from large mesh sizes and low computational efficiency when calculating gear meshing and bearing contact positions, making them difficult to meet engineering design requirements. Furthermore, existing methods lack a systematic and equivalent representation of the radial stiffness coupling mechanism between the bearing, gear, and housing, resulting in insufficient simulation accuracy for dynamic load transfer paths. In summary, existing technologies struggle to balance the high simulation accuracy and computational efficiency required for deep-sea gearbox modeling. Summary of the Invention

[0005] The present application provides a finite element modeling method for deep-sea gearboxes based on radial equivalent stiffness, which is used to solve the problem that the existing technology is difficult to take into account the requirements of high simulation accuracy and high computational efficiency for deep-sea gearbox modeling.

[0006] On the one hand, the present application provides a finite element modeling method for a deep-sea gearbox based on radial equivalent stiffness, comprising the following steps: Step 1: Derived the bending stiffness, shear stiffness and axial compression stiffness of the meshing gears based on the potential energy method.

[0007] Step 2: According to the bending stiffness, the shear stiffness, the axial compression stiffness and the Hertz contact stiffness of the meshing gears, the total meshing stiffness of the gear pair is obtained.

[0008] Step three: Based on Hertz contact theory, a contact stiffness characterization model of cylindrical roller bearings, double-row tapered roller bearings and deep groove ball bearings is established to obtain the bearing contact stiffness.

[0009] Step 4: Establish a deep-sea gearbox model, perform equivalent simplification on the total meshing stiffness of the gear pairs and the contact stiffness of the bearings in the deep-sea gearbox model based on the radial equivalent stiffness, and obtain a simplified finite element model of the deep-sea gearbox.

[0010] Step five: setting boundary conditions for the simplified finite element model of the deep-sea gearbox to obtain a strength verification model of the deep-sea gearbox.

[0011] In a possible implementation, in step 1, the bending stiffness, shear stiffness, and axial compression stiffness of the meshing gears are derived for two cases: when the base circle of the gear is larger than the root circle and when the base circle of the gear is smaller than the root circle.

[0012] In a possible implementation, in step 2, the total meshing stiffness of the tooth pairs when a single tooth pair is meshed and when two tooth pairs are meshed are obtained respectively.

[0013] In a possible implementation, in step three, the contact stiffness characterization model of the cylindrical roller bearing includes the contact stiffness between the roller and the raceway of the cylindrical roller bearing.

[0014] In a possible implementation, in step three, the contact stiffness characterization model of the double-row tapered roller bearing includes the radial stiffness and axial stiffness of the double-row tapered roller bearing.

[0015] In a possible implementation, in step three, the contact stiffness characterization model of the deep groove ball bearing includes the contact stiffness between the roller and raceway of the deep groove ball bearing.

[0016] In a possible implementation, in step 4, a spring unit is used to perform equivalent simplification on the total meshing stiffness of the tooth pairs and the contact stiffness of the bearings in the deep-sea gearbox model.

[0017] In a possible implementation, in step five, the boundary conditions include fixed constraints and pressure.

[0018] The fixed constraints are applied to the sun shaft and the housing end face of the deep-sea gearbox finite element simplified model, and the pressure is applied to the axial direction of the end cover and the radial direction of the housing of the deep-sea gearbox finite element simplified model.

[0019] A finite element modeling method for deep-sea gearboxes based on radial equivalent stiffness in this application has the following advantages: The total meshing stiffness of the tooth pair is obtained by deriving the bending stiffness, shear stiffness and axial compression stiffness. The contact stiffness characterization model of the three bearings is established to obtain the bearing contact stiffness. Equivalent simplification is performed based on the radial equivalent stiffness, taking into account the requirements of deep-sea gearbox modeling for high simulation accuracy and high computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0021] Figure 1 A schematic flow chart of a deep-sea gearbox finite element modeling method based on radial equivalent stiffness provided in an embodiment of the present application; Figure 2 Gear models with base circles and roots of different relative sizes provided in embodiments of the present application; Figure 3 The meshing stiffness of the sun gear of the input planetary gear set provided in the embodiment of the present application; Figure 4 The meshing stiffness of the planetary gears of the input planetary gear set provided in the embodiment of the present application; Figure 5 The meshing stiffness of the sun gear of the output planetary gear set provided in the embodiment of the present application; Figure 6 The meshing stiffness of the planetary gears of the output planetary gear set provided in the embodiment of the present application; Figure 7 A cross-sectional view of a key section of radial stiffness of a deep-sea gearbox model provided in an embodiment of the present application; Figure 8 The gear meshing stiffness equivalent model of the first-stage sun gear, first-stage planetary gear, and inner ring gear provided in the embodiment of the present application; Figure 9 Corresponding to the embodiment of this application Figure 8 The gear meshing stiffness equivalent model of the first-stage planetary gear and the inner ring gear at mark 1; Figure 10 The contact stiffness equivalent model of the cylindrical roller bearing provided in the embodiment of the present application; Figure 11 Schematic diagram of the housing and end cover of the simplified finite element model of the deep-sea gearbox provided in an embodiment of the present application; Figure 12 A schematic diagram of the internal structure of a simplified finite element model of a deep-sea gearbox provided in an embodiment of the present application; Figure 13 A schematic diagram of setting fixed constraints in boundary conditions provided in an embodiment of the present application; Figure 14 A schematic diagram of the pressure setting in the boundary conditions provided in the embodiments of the present application; Figure 15 A schematic diagram of the global displacement of a deep-sea gearbox provided in an embodiment of the present application under an external pressure of 30 MPa; Figure 16 Schematic diagram of radial displacement of the housing of a deep-sea gearbox provided in an embodiment of the present application under an external pressure of 30 MPa; Figure 17 Schematic diagram of radial displacement of the housing of a deep-sea gearbox provided in an embodiment of the present application under an external pressure of 35 MPa; Figure 18 Schematic diagram of radial displacement of the housing of a deep-sea gearbox provided in an embodiment of the present application under an external pressure of 40 MPa; Figure 19 Schematic diagram of radial displacement of the housing of a deep-sea gearbox provided in an embodiment of the present application under an external pressure of 45 MPa; Figure 20 Schematic diagram of radial displacement of the housing of a deep-sea gearbox provided in an embodiment of the present application under an external pressure of 50 MPa; Figure 21 Schematic diagram of the shell stress of the deep-sea gearbox provided in an embodiment of the present application under an external pressure of 30 MPa; Figure 22 Schematic diagram of the stress on the end cover of the deep-sea gearbox provided in an embodiment of the present application under an external pressure of 30 MPa; Figure 23 A schematic diagram of stress concentration locations of an end cover of a deep-sea gearbox provided in an embodiment of the present application; Figure 24 This is a schematic diagram of the end cover structure before structural optimization provided in an embodiment of the present application; Figure 25 A schematic diagram of the end cap structure after structural optimization provided in an embodiment of the present application; Figure 26 Schematic diagram of the stress of the end cover after structural optimization provided in an embodiment of the present application. DETAILED DESCRIPTION

[0022] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0023] like Figure 1 As shown, an embodiment of the present application provides a finite element modeling method for a deep-sea gearbox based on radial equivalent stiffness, comprising the following steps: Step 1: Derived the bending stiffness, shear stiffness and axial compression stiffness of the meshing gears based on the potential energy method.

[0024] Step 2: According to the bending stiffness, the shear stiffness, the axial compression stiffness and the Hertz contact stiffness of the meshing gears, the total meshing stiffness of the gear pair is obtained.

[0025] Step three: Based on Hertz contact theory, a contact stiffness characterization model of cylindrical roller bearings, double-row tapered roller bearings and deep groove ball bearings is established to obtain the bearing contact stiffness.

[0026] Step 4: Establish a deep-sea gearbox model, perform equivalent simplification on the total meshing stiffness of the gear pairs and the contact stiffness of the bearings in the deep-sea gearbox model based on the radial equivalent stiffness, and obtain a simplified finite element model of the deep-sea gearbox.

[0027] Step five: setting boundary conditions for the simplified finite element model of the deep-sea gearbox to obtain a strength verification model of the deep-sea gearbox.

[0028] Exemplarily, in step one, the bending stiffness, shear stiffness, and axial compression stiffness of the meshing gears are derived in two cases: when the base circle of the gear is larger than the root circle and when the base circle of the gear is smaller than the root circle.

[0029] Specifically, the potential energy method can be used to calculate the stiffness of gears during meshing, such as Figure 2 Shown are gear models with base circles and roots of different relative sizes. Figure 2 middle, α 0 represents the pressure angle, α 1 represents the engagement angle, α 2 represents the half angle of tooth thickness, α 3 represents the approximate half-angle of tooth thickness on the tooth root circle, α 4 represents the approximate tooth thickness half angle on the base circle, R r Indicates the tooth root circle radius, R b Indicates the base circle radius, line segments NN' and DD' are used to simplify the curve. h It represents the distance between the gear contact point and the gear centerline, d is the distance from the contact point to the root of the gear, h x The distance from the tooth root is x The height of the cross section.

[0030] Assuming that the meshing gears are two isotropic elastic bodies, the Hertzian contact stiffness of the meshing gears is constant along the line of action and is completely determined by the material of the gears, and has nothing to do with the position of the contact in the line of action and the contact angle. k h It is expressed as follows: .

[0031] in, E represents Young's modulus, L Indicates tooth width,v represents Poisson's ratio.

[0032] When the base circle of the gear is larger than the root circle, the beam model Figure 2 On the right side, when the base circle is smaller than the root circle, the beam model is Figure 2 on the left side.

[0033] According to beam theory, when the base circle of the gear is larger than the root circle, the bending stiffness of the meshing gears is k b , shear stiffness k s and axial compressive stiffness k a It is expressed as follows: .

[0034] .

[0035] .

[0036] in, N Indicates the number of teeth of the external gear, α 0 represents the pressure angle, α 1 represents the engagement angle, α 2 represents the half tooth angle on the base circle, α 3 represents the approximate half tooth angle on the root circle, α It represents the angle between the meshing line and the perpendicular line of the tooth profile symmetry line.

[0037] When the base circle of the gear is smaller than the root circle, the bending stiffness of the meshing gears k b , shear stiffness k s and axial compressive stiffness k a It is expressed as follows: .

[0038] .

[0039] .

[0040] in, α 5 is defined as the force when the distance between the meshing point and the root circle is zero. F and resolution F y The angle between α 5 is represented by the following equation: .

[0041] in, R rrepresents the tooth root circle radius, R b Indicates the base circle radius.

[0042] Exemplarily, in step 2, the total meshing stiffness of the tooth pairs when a single tooth pair is meshed and when a double tooth pair is meshed are obtained respectively.

[0043] Specifically, for a single tooth pair meshing, the total meshing stiffness of the tooth pair is k t It is expressed as follows: .

[0044] in, k b1 、 k s1 、 k a1 They represent the bending stiffness, shear stiffness and axial compression stiffness of the driving gear respectively, k b2 、 k s2 、 k a2 They represent the bending stiffness, shear stiffness and axial compression stiffness of the driven gear respectively.

[0045] For double tooth pairs, the total meshing stiffness of the tooth pairs is k t It is expressed as follows: .

[0046] in, k t1 、 k t2 denote the meshing stiffness of the first pair of meshing teeth and the second pair of meshing teeth, respectively. i Indicates the i For meshing teeth, k h,i Indicates the i The Hertzian contact stiffness of meshing teeth, k b1,i 、 k s1,i 、 k a1,i Respectively represent i The bending stiffness, shear stiffness and axial compression stiffness of the driving gear of the meshing teeth, k b2,i 、 k s2,i 、 k a2,i Respectively represent i Bending stiffness, shear stiffness and axial compression stiffness of the driven gear with respect to the meshing teeth.

[0047] Tables 1 and 2 show the physical parameters of the input and output planetary gearsets of the deep-sea gearbox, respectively. The input and output planetary gearsets share the same ring gear of the gearbox housing.

[0048] Table 1 Physical parameters of input planetary gear sets

[0049] Table 2 Physical parameters of output planetary gear set

[0050] like Figures 3 to 6 As shown, they are the meshing stiffness of the sun gear of the input planetary gear set, the meshing stiffness of the planetary gears of the input planetary gear set, the meshing stiffness of the sun gear of the output planetary gear set, and the meshing stiffness of the planetary gears of the output planetary gear set.

[0051] Exemplarily, in step three, the contact stiffness characterization model of the cylindrical roller bearing includes the contact stiffness between the roller and the raceway of the cylindrical roller bearing.

[0052] Specifically, the contact stiffness between the rollers and raceways of cylindrical roller bearings It is expressed as follows: .

[0053] Among them, the superscript ra represents the inner and outer rings, and the subscript j Indicates the first j A roller, represents the contact stiffness coefficient, represents the film stiffness. 、 The expression is as follows: .

[0054] .

[0055] in, Q represents the external radial load applied to the roller, Indicates the contact deformation between the roller and the inner and outer rings, represents the equivalent elastic modulus, Indicates the effective length of the roller, represents the equivalent radius of the roller and raceway, Indicates the viscosity pressure coefficient of lubricating oil, Indicates the dynamic viscosity coefficient of lubricating oil, Indicates the average speed between the roller and the raceway.

[0056] Exemplarily, in step three, the contact stiffness characterization model of the double-row tapered roller bearing includes the radial stiffness and axial stiffness of the double-row tapered roller bearing.

[0057] Specifically, the radial stiffness of a double row tapered roller bearing The axial stiffness of a double-row tapered roller bearing is obtained by adding the radial stiffness of the first and second row bearings in parallel. The axial stiffness of the first and second row bearings is obtained by adding the parallel values ​​as follows: .

[0058] .

[0059] in, m Indicates the first row of double-row tapered roller bearings m List, Indicates the m The radial stiffness of the bearings, Indicates the m The axial stiffness of the bearing is as follows: .

[0060] .

[0061] in, and They represent the normal contact stiffness between the roller and the inner raceway, and the normal contact stiffness between the roller and the outer raceway, respectively. and They represent the contact angles between the roller and the inner raceway, and the contact angles between the roller and the outer raceway, respectively. Indicates the j The position angle of the rollers, φ j =2 π ( j -1) / Z, where Z represents the number of rollers in each row of bearings.

[0062] and Commonly recorded as , as shown below: .

[0063] in, L e is the effective length of the roller; D w is the average diameter of the roller; Q i(o)j is the effective length of the roller; E 1 and E2 represent the elastic modulus of contact body 1 and contact body 2 respectively, μ 1 and μ 2 represent the Poisson's ratios of contact bodies 1 and 2, k i(o) Indicates the average diameter of the roller ( D w ) and inner and outer raceway diameters ( D ri(o) ) ratio.

[0064] Exemplarily, in step three, the contact stiffness characterization model of the deep groove ball bearing includes the contact stiffness between the roller and raceway of the deep groove ball bearing.

[0065] Specifically, the contact stiffness between the roller and raceway of a deep groove ball bearing K According to Hertz contact deformation theory, it is calculated as follows: .

[0066] in, F be Indicates the force between the roller and raceway of the deep groove ball bearing, Indicates the radial deformation of the contact surface between the roller and raceway of a deep groove ball bearing.

[0067] Exemplarily, in step four, a spring unit is used to perform equivalent simplification on the total meshing stiffness of the tooth pairs and the contact stiffness of the bearings in the deep-sea gearbox model.

[0068] Specifically, deep-sea gearboxes contain complex structures such as numerous gears and bearings. When using finite element software to analyze deep-sea gearbox structures, a large number of nodes and elements are required at key locations such as gear meshing and bearing contact to ensure calculation accuracy. Figure 7 The cross-sectional view of the key sections of radial stiffness of the deep-sea gearbox model is depicted. The radial stiffness is mainly concentrated on three key sections, namely Figure 7 Section 1, Section 2 and Section 3 in the figure. There are non-rigid connections such as gear meshing and bearing contact at these section positions, so the radial stiffness of these sections must be considered to ensure the compressive performance of the gearbox. This application focuses on the radial displacement of the gearbox housing, and simplifies the structure according to the equivalence principle without changing the radial stiffness of the housing. First, based on the total meshing stiffness of the tooth pair calculated in steps one and two, a cylinder with a pitch radius is used to equate the gear, and a spring unit is used to equate the total meshing stiffness of the tooth pair, and an equivalent model of gear meshing stiffness is established. Figure 7 For example, cross section 1 in Figure 8 In the gear meshing stiffness equivalent model of the first-stage sun gear, first-stage planetary gear, and inner ring gear shown in FIG, there are 6 gear meshing positions. Figure 9 Shows the corresponding Figure 8 The gear meshing stiffness equivalent model of the first-stage planetary gear and the inner gear ring at mark 1 is constructed. Then, based on the bearing contact stiffness of the cylindrical roller bearing, double-row tapered roller bearing and deep groove ball bearing calculated in step 3, the spring unit is used to equate the bearing contact stiffness. Figure 10 Taking the contact stiffness equivalent model of the cylindrical roller bearing in as an example, the contact stiffness equivalent models of cylindrical roller bearings, double-row tapered roller bearings and deep groove ball bearings are established.

[0069] In addition, there are many components, including piston baffles, friction plates, skeleton oil seals, etc., which have no direct relationship with the structural strength, as well as a large number of small holes, chamfers and other features that need to be divided into tiny units. These will increase a lot of data processing, so that the mesh division is inappropriate or the quality is too low. And ultimately, the finite element calculation cannot be performed. This application focuses on the radial displacement of the gearbox housing. Without changing the radial stiffness of the housing, the structure is simplified according to the equivalent principle. Under the condition of ensuring high accuracy, the internal structure of the gearbox is simplified, and finally a simplified finite element model of the deep-sea gearbox is obtained. Figure 11 and Figure 12 Shown are schematic diagrams of the outer shell and end cover, and internal structure of the simplified finite element model of the deep-sea gearbox.

[0070] Exemplarily, in step five, the boundary conditions include fixed constraints and pressure.

[0071] The fixed constraints are applied to the sun shaft and the housing end face of the deep-sea gearbox finite element simplified model, and the pressure is applied to the axial direction of the end cover and the radial direction of the housing of the deep-sea gearbox finite element simplified model.

[0072] Specifically, in order to simulate the real working environment of the gearbox, the boundary conditions such as Figure 13 and Figure 14 As shown in the settings. Figure 13 As shown in Figure 1, fixed constraints are applied to the sun shaft and housing end faces of the simplified finite element model of the deep-sea gearbox. Figure 14As shown, pressure is applied in the axial direction of the end cover and the radial direction of the shell of the simplified finite element model of the deep-sea gearbox. Compared with most gearboxes, the special working environment of the deep-sea gearbox brings new challenges and needs to operate at a water depth of 3,000 meters. The shell is actually subjected to a pressure of 30Mpa. The deformation displacement generated by the shell will greatly affect the internal structure, resulting in the gears not being able to mesh properly. For the deep-sea gearbox studied in this application, it is necessary to ensure that the limit radial displacement of the shell for the correct meshing of the gears is 0.5D% (1.4 mm). A cylindrical coordinate system was established to observe its radial displacement, and the axial displacement of the end cover was calculated at the same time to prevent interference with the internal transmission system. In addition, the maximum stress of the gearbox was calibrated to verify its strength. The material of the gearbox is structural alloy steel 42CrMoA with a yield strength of 930MPa.

[0073] The overall displacement of the gearbox housing under an external pressure of 30 MPa is as follows: Figure 15 As shown in the figure, the maximum deformation of the shell occurs at the outer ring of the end cap top block. Due to the lack of support, a displacement of 1.0425 mm occurs compared to the position of the top block when it is subjected to external pressure. A cylindrical coordinate system is established in the cylindrical shell part to more intuitively display the radial displacement of the shell. In order to observe the radial displacement more clearly, the displacement of the cylindrical shell is extracted separately, as shown in the figure. Figure 16 As shown in the figure, under an external pressure of 30 MPa, the maximum radial displacement is only 0.12641 mm, which is less than the 1.4 mm limit displacement required for gear meshing. Figures 17 to 20 The radial displacement of the deep-sea gearbox housing under external pressures of 35 MPa, 40 MPa, 45 MPa, and 50 MPa is shown. The radial displacement at 50 MPa also meets the requirements. According to the current design, the cylindrical housing of the gearbox can withstand higher pressures.

[0074] In addition to the deformation problem, the stress at the key position must also be considered. A solution to the stress concentration caused by the change in section height is proposed. The material used for the deep-sea gearbox is the structural alloy steel 42CrMoA with a yield strength of 930MPa. Figure 21 and Figure 22 As shown, the locations where the yield stress is exceeded are concentrated at the end caps. Figure 23 The stress concentration locations of the end cover are shown, including location 1 and location 2. Location 1 is due to contact with the top block of the transmission shaft, while location 2 is due to the sudden change in section height. The stress concentration at other locations is due to the same reason. In order to avoid damage caused by stress concentration, the structural optimization design of these two locations is carried out, such as Figure 24 and Figure 25The following are schematic diagrams of the end cover structure before and after structural optimization. The inner side of the end cover may interfere with the transmission structure inside the gearbox. Therefore, the stress concentration at position 1 is solved by increasing the thickness of the outer side of the end cover. The thickness t1 of the optimized front end cover is 8.5mm, and the thickness t2 after optimization is 23.5mm. The fillet R1 with a radius of 1mm before optimization is not enough to improve the stress concentration problem because the height of the section at position 2 has changed. Due to the limitation of the structural size, it is impossible to directly increase the fillet R2 to relieve the stress concentration, and it is chosen to expand the fillet R2 with a radius of 5mm downward. The stress of the end cover after structural optimization is as follows Figure 26 Under the same calculation conditions, this stress concentration solution is very effective, with the maximum stress reduced to 594.46 MPa, meeting the yield strength requirements of the gearbox material.

[0075] The embodiment of the present application obtains the total meshing stiffness of the tooth pair by deriving the bending stiffness, shear stiffness and axial compression stiffness, establishes a contact stiffness characterization model for three types of bearings to obtain the bearing contact stiffness, and performs equivalent simplification based on the radial equivalent stiffness, taking into account the requirements of deep-sea gearbox modeling for high simulation accuracy and high computational efficiency.

[0076] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0077] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A finite element modeling method for deep-sea gearbox based on radial equivalent stiffness, characterized in that: The following steps are involved: Step 1: Derivation of the bending stiffness, shear stiffness and axial compression stiffness of the meshing gears based on the potential energy method; Step 2: obtaining the total meshing stiffness of the gear pair according to the bending stiffness, the shear stiffness, the axial compression stiffness and the Hertzian contact stiffness of the meshing gears; Step 3: Based on Hertz contact theory, a contact stiffness characterization model of cylindrical roller bearings, double-row tapered roller bearings, and deep groove ball bearings is established to obtain the bearing contact stiffness; Step 4: Establish a deep-sea gearbox model, perform equivalent simplification on the total meshing stiffness of the gear pairs and the contact stiffness of the bearings in the deep-sea gearbox model based on the radial equivalent stiffness, and obtain a simplified finite element model of the deep-sea gearbox; Step five: setting boundary conditions for the simplified finite element model of the deep-sea gearbox to obtain a strength verification model of the deep-sea gearbox.

2. The finite element modeling method for deep-sea gearbox based on radial equivalent stiffness according to claim 1, characterized in that: In step 1, the bending stiffness, shear stiffness, and axial compression stiffness of the meshing gears are derived in two cases: when the base circle of the gear is larger than the root circle and when the base circle of the gear is smaller than the root circle.

3. The finite element modeling method for deep-sea gearbox based on radial equivalent stiffness according to claim 1, characterized in that: In step 2, the total meshing stiffness of the tooth pairs when a single tooth pair is engaged and when a double tooth pair is engaged are obtained respectively.

4. The finite element modeling method for deep-sea gearbox based on radial equivalent stiffness according to claim 1, characterized in that: In step three, the contact stiffness characterization model of the cylindrical roller bearing includes the contact stiffness between the roller and the raceway of the cylindrical roller bearing.

5. The finite element modeling method for deep-sea gearbox based on radial equivalent stiffness according to claim 1, characterized in that: In step three, the contact stiffness characterization model of the double-row tapered roller bearing includes the radial stiffness and axial stiffness of the double-row tapered roller bearing.

6. The finite element modeling method for deep-sea gearbox based on radial equivalent stiffness according to claim 1, characterized in that: In step three, the contact stiffness characterization model of the deep groove ball bearing includes the contact stiffness between the roller and raceway of the deep groove ball bearing.

7. The finite element modeling method for deep-sea gearbox based on radial equivalent stiffness according to claim 1, characterized in that: In step 4, the spring unit is used to perform equivalent simplification on the total meshing stiffness of the gear pairs and the contact stiffness of the bearings in the deep-sea gearbox model.

8. The finite element modeling method for deep-sea gearbox based on radial equivalent stiffness according to claim 1, characterized in that: In step 5, the boundary conditions include fixed constraints and pressure; The fixed constraints are applied to the sun shaft and the housing end face of the deep-sea gearbox finite element simplified model, and the pressure is applied to the axial direction of the end cover and the radial direction of the housing of the deep-sea gearbox finite element simplified model.

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