Method for calculating dynamic load of propeller shaft coupling bolt considering interface friction

Abstract

The present application relates to a kind of propeller shaft coupling bolt dynamic load calculation method considering interface friction, belong to underwater vehicle technical field.The multibody dynamics method is used, considering the geometric structure of shaft system, bolt type and material characteristics, bolt pre-tightening force and shaft system operating condition, the rigid body model is used to establish the geometric model of propeller shaft and universal coupling, the equivalent model of connecting bolt is established using flexible unit, the construction of rigid-flexible coupling multibody dynamics model of universal coupling is completed.The model is simulated using numerical calculation method, thereby the dynamic load calculation of universal coupling connecting bolt is realized.The method simplifies the modeling and analysis process of flange bolt dynamic load, and can consider the effect of friction between coupling flange, compared with the traditional empirical formula calculation method, the method can reflect the dynamic characteristics of universal coupling connecting bolt load, and has guiding role to coupling design, connecting bolt fatigue and life analysis.

Description

Technical Field

[0001] This invention belongs to the field of underwater vehicle technology and relates to a method for calculating the dynamic load of propulsion shaft coupling bolts considering interface friction. Background Technology

[0002] Universal couplings, as torque and power transmission devices, possess advantages such as simple structure, wide power transmission range, high reliability, and ease of maintenance, and have been widely used in vehicles, ships, power generation, and metallurgy. Connecting bolts, as fasteners connecting the universal coupling to the input and output shafts, play a crucial role in the normal operation of the universal coupling and the entire shaft system. Therefore, calculating and analyzing the loads on the connecting bolts of universal couplings is of great significance for the stable and safe operation of the shaft system and even the entire mechanical equipment. Current calculation methods for the loads on the flange connecting bolts of universal couplings mainly focus on static load calculation, preload calculation, connection loosening, bolt fatigue, and fracture. Static load calculation primarily relies on empirical formulas, failing to consider the influence of bolt preload and the frictional characteristics of the flange connection surface, and cannot calculate the dynamic characteristics of the load, thus failing to provide an accurate reference for estimating the bolt connection life. Summary of the Invention

[0003] The technical problem to be solved by this invention is:

[0004] To overcome the shortcomings of existing technologies and considering the influence of bolt preload and flange connection surface friction characteristics on the dynamic load of bolts, this invention provides a method for calculating the dynamic load of flange bolts in universal joints for underwater propulsion shafts, taking into account the friction of the flange connection interface. A flexible connection dynamic model of the universal joint bolts and a multibody dynamic model of the underwater propulsion shaft system are established, enabling the calculation and analysis of the dynamic load of the universal joint bolts under different working conditions. Compared to the rigid connection model, the calculation results of this method more closely approximate the actual condition of the bolts.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating the dynamic load of bolts in a propulsion shaft coupling considering interfacial friction, characterized by the following steps:

[0007] Step 1: Based on the geometric parameters of the propulsion shaft, establish a rigid body dynamics model of the propulsion shaft; the propulsion shaft is an axisymmetric structure, and the center of mass of the propulsion shaft is set to be located on the axis.

[0008]

[0009] In the formula, m is the mass of the propulsion shaft, and j d For the polar moment of inertia of the propulsion shaft, j pFor the polar moment of inertia of the propulsion shaft, a x a y a z Let a be the acceleration of the propulsion shaft in the three translational directions (x, y, z). θx a θy a θz To propel the angular acceleration of the shaft rotating about the x, y, and z axes, F x1 and F x2 For the forces acting on both ends of the propulsion shaft in the x-direction, F y1 and F y2 For the forces acting on both ends of the propulsion shaft in the y direction, F z1 and F z2 M1 and M2 are the forces acting on both ends of the propulsion shaft in the z direction, M1 and M2 are the torques acting on both ends of the propulsion shaft, and l1 and l2 are the axial distances between the center of mass of the propulsion shaft and both ends.

[0010] Step 2: Based on the geometric parameters of the universal joint, establish a mathematical model of the universal joint:

[0011] Transmission ratio from input shaft to intermediate shaft:

[0012]

[0013] Transmission ratio from intermediate shaft to output shaft

[0014]

[0015] Transmission ratio from input shaft to output shaft

[0016]

[0017] Where θ1, θ2, and θ3 are the rotation angles of the input shaft, intermediate shaft, and output shaft, respectively; ω1, ω2, and ω3 are the rotational angular velocities of the input shaft, output shaft, and intermediate shaft, respectively; β1 and β2 are the angles between the input shaft, output shaft, and intermediate shaft and the intermediate shaft, respectively; according to the direction of rotation, the angle between the plane formed by the input shaft and intermediate shaft and the plane formed by the intermediate shaft and output shaft is denoted as γ; and the angle between the two forks at the two ends of the intermediate shaft is denoted as...

[0018] Step 3: Based on the grade, size, and preload of the universal joint connecting bolts, calculate the equivalent stiffness of the connecting bolts in the propulsion shaft system, and establish a dynamic model of the flexible connecting bolts:

[0019]

[0020] In the formula, F x F y F z T x T yAnd T z These represent the components of the force and torque acting on the bolt in the x, y, and z directions, respectively; k 11 k 22 k 33 k represents the stiffness coefficient of the bolt in the three translational directions. 44 k 55 k 66 θ represents the torsional stiffness coefficient of the bolt in the three rotational directions; x, y, and z represent the displacements of adjacent flanges in the three translational directions, i.e., the tensile or bending deformation of the bolt, respectively. x θ y θ z This represents the angular displacement of adjacent flanges in three rotational directions, i.e., the torsional deformation of the bolts; c 11 c 22 c 33 These represent the damping coefficients of the bolt as it deforms in the three translational directions, c and c respectively. 44 c 55 c 66 These represent the damping coefficients of the bolt as it deforms in the three rotational directions; v x v y v z ω x ω y ω z F1, F2, and F3 represent the velocities and angular velocities of adjacent flanges in the three translational and rotational directions, respectively; F1, F2, and F3 represent the preload forces on the bolts in the three translational directions, respectively; T1, T2, and T3 represent the preload moments on the bolts in the three rotational directions, respectively; the bolt stiffness can be calculated using the following formula:

[0021]

[0022] Where E is the elastic modulus of the bolt material, A is the effective cross-sectional area of ​​the bolt, and l is the effective length of the bolt;

[0023]

[0024] Where G is the shear modulus of the bolt material;

[0025]

[0026] Where I is the moment of inertia of the bolt section;

[0027]

[0028] Where R is the effective diameter of the bolt;

[0029] Step 4: Establish a nonlinear friction force model between the flange faces of the universal joint:

[0030] f = μF (10)

[0031]

[0032] Where F represents the normal force between the interfaces, μ represents the coefficient of friction, and μ s v represents the maximum static friction coefficient between the interfaces, and v represents the relative sliding velocity between the interfaces. s μ represents the maximum relative slip velocity under static friction conditions. m The static friction coefficient between interfaces, v m This represents the rate of transition between static and dynamic friction; when the relative sliding velocity v between the interfaces... <v s When the relative sliding velocity reaches v, the coefficient of friction between the two flanges increases linearly; when the relative sliding velocity reaches v... s At this point, the coefficient of friction reaches its maximum static friction coefficient value μ. s As the relative sliding velocity continues to increase, the coefficient of friction decreases linearly; when the relative sliding velocity reaches the velocity v of the transition between dynamic and static friction... m At this point, the frictional state between the two flanges changes to kinetic friction, and the coefficient of friction at this time is the kinetic friction coefficient μ. m ;

[0033] Step 5: Based on the rigid body kinematics equations, combine equations (1) to (11) to form the overall dynamic model of the propulsion shaft system;

[0034] Step 6: Solve the dynamic model of the underwater propulsion shafting system using numerical calculation methods to obtain the dynamic load of the universal joint connecting bolts, i.e., F in Step 3. x F y F z .

[0035] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0036] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0037] The beneficial effects of this invention are as follows:

[0038] This invention provides a method for calculating the dynamic load of flange bolts in a universal joint of an underwater propulsion shaft system, considering the friction at the flange connection interface. Employing multibody dynamics, the method considers the shaft geometry, bolt type and material properties, bolt preload, and shaft operating conditions. A rigid body model is used to establish the geometric model of the propulsion shaft and universal joint, while a flexible element model is used to establish an equivalent model of the connecting bolts, thus constructing a rigid-flexible coupled multibody dynamic model of the universal joint. Numerical simulation is then used to calculate the dynamic load of the universal joint connecting bolts. This method simplifies the modeling and analysis process of the flange bolt dynamic load and can consider the effect of friction between the flange surfaces. Compared to traditional empirical formula calculation methods, this method can reflect the dynamic characteristics of the universal joint connecting bolt load, providing guidance for coupling design, bolt fatigue, and life analysis. Attached Figure Description

[0039] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0040] Figure 1 Rigid body dynamics model of the propulsion shaft;

[0041] Figure 2 Schematic diagram of the kinematic relationship of universal coupling;

[0042] Figure 3 Flexible model of connecting bolts;

[0043] Figure 4 Curve of friction coefficient variation;

[0044] Figure 5 A rigid-flexible coupled multibody dynamics model of a propulsion shaft system including universal joints;

[0045] Figure 6 Rigid body dynamics models of the input shaft, intermediate shaft, and output shaft;

[0046] Figure 7 Bolt location diagram;

[0047] Figure 8 Comparison of bolt dynamic load calculation results: (a) Bolt 1; (b) Bolt 2; (c) Bolt 3; (d) Bolt 4;

[0048] Figure 9 Flowchart of the method of this invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0050] This invention provides a method for calculating the dynamic load of flange bolts in a universal coupling for underwater propulsion shafts, considering flange surface friction. This method addresses the problem in existing technologies regarding the calculation of dynamic loads on the connecting bolts of universal couplings for propulsion shafts, considering bolt preload and flange surface friction. Specifically, it includes the following steps:

[0051] 1) Based on the geometric parameters of the propulsion shaft, establish a rigid body dynamics model of the propulsion shaft. Considering that the propulsion shaft is an axisymmetric structure, set the center of mass of the propulsion shaft to be located on the axis.

[0052]

[0053] In the formula, m is the mass of the propulsion shaft, and j d For the polar moment of inertia of the propulsion shaft, j p For the polar moment of inertia of the propulsion shaft, a x a y a z Let a be the acceleration of the propulsion shaft in the three translational directions (x, y, z). θx a θy a θz To propel the angular acceleration of the shaft rotating about the x, y, and z axes, F x1 and F x2 For the forces acting on both ends of the propulsion shaft in the x-direction, F y1 and F y2 For the forces acting on both ends of the propulsion shaft in the y direction, F z1 and F z2 M1 and M2 are the forces acting on both ends of the propulsion shaft in the z direction, M1 and M2 are the torques acting on both ends of the propulsion shaft, and l1 and l2 are the axial distances between the center of mass of the propulsion shaft and both ends.

[0054] 2) Based on the geometric parameters of the universal joint, establish a mathematical model of the universal joint as follows: Figure 2 As shown, the details are as follows:

[0055] Transmission ratio from input shaft to intermediate shaft:

[0056]

[0057] Transmission ratio from intermediate shaft to output shaft

[0058]

[0059] Transmission ratio from input shaft to output shaft

[0060]

[0061] Where θ1, θ2, and θ3 are the rotation angles of the input shaft, intermediate shaft, and output shaft, respectively; ω1, ω2, and ω3 are the rotational angular velocities of the input shaft, output shaft, and intermediate shaft, respectively; β1 and β2 are the angles between the input shaft, output shaft, and intermediate shaft and the intermediate shaft, respectively; according to the direction of rotation, the angle between the plane formed by the input shaft and intermediate shaft and the plane formed by the intermediate shaft and output shaft is denoted as γ; and the angle between the two forks at the two ends of the intermediate shaft is denoted as...

[0062] 3) Based on the parameters such as the grade, size, and preload of the universal joint connecting bolts, calculate the equivalent stiffness of the connecting bolts in the propulsion shaft system, and establish a dynamic model of the flexible connecting bolts. The local coordinate system of the connecting bolts is as follows: Figure 3 As shown, its dynamic equation can be expressed as:

[0063]

[0064] In the formula, F x F y F z T x T y And T z These represent the components of the force and torque acting on the bolt in the x, y, and z directions, respectively; k 11 k 22 k 33 k represents the stiffness coefficient of the bolt in the three translational directions. 44 k 55 k 66 θ represents the torsional stiffness coefficient of the bolt in the three rotational directions; x, y, and z represent the displacements of adjacent flanges in the three translational directions, i.e., the tensile or bending deformation of the bolt, respectively. x θ y θ z This represents the angular displacement of adjacent flanges in three rotational directions, i.e., the torsional deformation of the bolts; c 11 c 22 c 33 These represent the damping coefficients of the bolt as it deforms in the three translational directions, c and c respectively. 44 c 55 c 66 These represent the damping coefficients of the bolt as it deforms in the three rotational directions; v x v y v z ω x ωy ω z F1, F2, and F3 represent the velocities and angular velocities of adjacent flanges in the three translational and rotational directions, respectively; F1, F2, and F3 represent the preload forces on the bolts in the three translational directions, respectively. T1, T2, and T3 represent the preload moments on the bolts in the three rotational directions, respectively. Bolt stiffness can be calculated using the following formula:

[0065]

[0066] Where E is the elastic modulus of the bolt material, A is the effective cross-sectional area of ​​the bolt, and l is the effective length of the bolt;

[0067]

[0068] Where G is the shear modulus of the bolt material;

[0069]

[0070] Where I is the moment of inertia of the bolt section;

[0071]

[0072] Where R is the effective diameter of the bolt.

[0073] 4) Flange surface friction modeling. A nonlinear friction model is established between the flange surfaces of the universal coupling. The model considers the maximum static friction coefficient, dynamic friction coefficient, and the switching speed between static and dynamic friction at the contact interface, such as... Figure 4 As shown, its formula is specifically expressed as follows:

[0074] f = μF (10)

[0075]

[0076] Where F represents the normal force between the interfaces, μ represents the coefficient of friction, and μ s v represents the maximum static friction coefficient between the interfaces, and v represents the relative sliding velocity between the interfaces. s μ represents the maximum relative slip velocity under static friction conditions. m The static friction coefficient between interfaces, v m This represents the rate of transition between static and dynamic friction. It is the rate at which the relative sliding velocity v between the interfaces changes. <v s When the relative sliding velocity reaches v, the coefficient of friction between the two flanges increases linearly; when the relative sliding velocity reaches v... s At this point, the coefficient of friction reaches its maximum static friction coefficient value μ. s As the relative sliding velocity continues to increase, the coefficient of friction decreases linearly; when the relative sliding velocity reaches the velocity v of the transition between dynamic and static friction... mAt this point, the frictional state between the two flanges changes to kinetic friction, and the coefficient of friction at this time is the kinetic friction coefficient μ. m .

[0077] 5) Based on steps 1-4, establish a dynamic model of the entire propulsion shaft system, such as... Figure 5 As shown.

[0078] 6) Solve the dynamic model of the underwater propulsion shafting system using numerical calculation methods to obtain the dynamic load of the universal joint connecting bolts, i.e., F in step 3). x F y F z .

[0079] Example 1:

[0080] Based on the geometric parameters of the propulsion shaft system, rigid body dynamic models of the input shaft, output shaft, and intermediate shaft are established, such as... Figure 6 As shown, the modeling method is given in equation (1).

[0081]

[0082]

[0083]

[0084] In the formula, m is the mass of the shaft, and j d Let j be the polar moment of inertia of the axis. p For the polar moment of inertia of the propulsion shaft, a x a y a z Let a be the acceleration of the propulsion shaft in the three translational directions (x, y, z). θx a θy a θz To propel the angular acceleration of the shaft rotating about the x, y, and z axes, F x1 and F x2 F represents the force exerted on both ends of the input shaft in the x-direction. y1 Fy2 represents the forces acting on both ends of the input shaft in the y-direction, F z1 and F z2 The values ​​represent the forces acting on the input shaft at both ends in the z-direction. Subscripts i, o, and m represent the input shaft, output shaft, and intermediate shaft, respectively. M1 and M2 represent the torques acting on the input shaft at both ends, and l1 and l2 represent the axial distances of the input shaft's center of mass from its ends. M3 and M4 represent the torques acting on the intermediate shaft at both ends, and l3 and l4 represent the axial distances of the intermediate shaft's center of mass from its ends. M5 and M6 represent the torques acting on the output shaft at both ends, and l5 and l6 represent the axial distances of the output shaft's center of mass from its ends.

[0085] The mechanical relationship between the input shaft, intermediate shaft, and output shaft is as follows (ignoring the influence of the included angle between the shafts):

[0086] F x2 =-F x3 (15)

[0087] F y2 =-F y3 (16)

[0088] F z2 =-F z3 (17)

[0089] F x4 =-F x5 (18)

[0090] F y4 =-F y5 (19)

[0091] F z4 =-F z5 (20)

[0092] The relationship between the forces acting between the shafts, frictional forces, and bolt loads is as follows:

[0093] F x2 =F b1x +μ1F z3 (twenty one)

[0094] F y2 =F b1y +μ1F z3 (twenty two)

[0095] F z2 =F b1z (twenty three)

[0096] F x4 =F b2x +μ2F z4 (twenty four)

[0097] F y4 =F b2y +μ2F z4 (25)

[0098] F z4 =F b2z (26)

[0099] Among them, F b1 For the input shaft flange bolt load, F b2 The output shaft flange bolt load is represented by the subscripts x, y, z, which represent the components in the three directions; μ1 is the friction coefficient of the input shaft flange and μ2 is the friction coefficient of the output shaft flange bolt. The modeling and calculation process is shown in equation (11).

[0100] 2) Based on the geometric parameters of the universal joint, establish a dynamic model of the universal joint and obtain the kinematic relationship expression between the input shaft and the output shaft.

[0101]

[0102] 3) Based on the type and grade of the universal joint connecting bolts, establish its flexibility model. In this case, the bolt type is M20, the bolt grade is 9, and the bolt material is steel. Based on this, the bolt stiffness and damping matrix can be calculated. The bolt preload is determined according to the bolt grade, thereby determining the preload matrix in the equation, thus obtaining the flexible dynamic model of the connecting bolts:

[0103]

[0104] 4) Modeling of frictional force on the flange surfaces of the universal joint. The model considers the effects of the static friction coefficient, dynamic friction coefficient, and interface pre-displacement between the flange surfaces of the coupling. The parameters are as follows: the dynamic friction coefficient is μ d =0.1, static friction coefficient is μ s =0.3, v d =1mm / s, v s =0.1mm / s. Based on the above information, a friction coefficient model for the flange surface of the universal coupling can be established.

[0105]

[0106] 5) Based on the rigid body kinematic equations, equations (12) to (26) are combined to form the overall dynamic model of the propulsion shaft system.

[0107] 6) Solve the propulsion shaft dynamics equations obtained in step 5) using numerical integration. Select four bolts evenly distributed on the input shaft connecting flange as observation points, such as... Figure 7 As shown in the figure, its dynamic load is extracted, and the time-domain waveform is shown in the figure.

[0108] In contrast, the bolt load was calculated using an empirical formula, and the results are as follows: Figure 8 As shown in Table 1, the calculation results show that the bolt load obtained by the empirical formula is a constant and cannot reflect the dynamic time-varying characteristics of the bolt load. However, the RMS value and average value of the dynamic load of the universal joint flange connection bolts calculated by this method are consistent with the empirical formula, demonstrating the correctness of the calculation method. Furthermore, the dynamic load of the connection bolts obtained by this method is a curve that changes periodically with time, reflecting the dynamic time-varying characteristics of the load and more closely approximating the actual situation. In addition, this method can consider the influence of factors such as underwater propulsion shaft speed, torque, and bolt preload on the dynamic load of the bolts.

[0109] Table 1 Comparison of dynamic loads on bolts (N)

[0110]

[0111]

[0112] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for calculating the dynamic load of bolts in a propulsion shaft coupling considering interfacial friction, characterized in that... The steps are as follows: Step 1: Based on the geometric parameters of the propulsion shaft, establish a rigid body dynamics model of the propulsion shaft; the propulsion shaft is an axisymmetric structure, and the center of mass of the propulsion shaft is set to be located on the axis. In the formula, m is the mass of the propulsion shaft, and j d For the polar moment of inertia of the propulsion shaft, j p For the polar moment of inertia of the propulsion shaft, a x a y a z Let a be the acceleration of the propulsion shaft in the three translational directions (x, y, z). θx a θy a θz To propel the angular acceleration of the shaft rotating about the x, y, and z axes, F x1 and F x2 For the forces acting on both ends of the propulsion shaft in the x-direction, F y1 and F y2 For the forces acting on both ends of the propulsion shaft in the y direction, F z1 and F z2 M1 and M2 are the forces acting on both ends of the propulsion shaft in the z direction, M1 and M2 are the torques acting on both ends of the propulsion shaft, and l1 and l2 are the axial distances between the center of mass of the propulsion shaft and both ends. Step 2: Based on the geometric parameters of the universal joint, establish a mathematical model of the universal joint: Transmission ratio from input shaft to intermediate shaft: Transmission ratio from intermediate shaft to output shaft Transmission ratio from input shaft to output shaft Where θ1, θ2, and θ3 are the rotation angles of the input shaft, intermediate shaft, and output shaft, respectively; ω1, ω2, and ω3 are the rotational angular velocities of the input shaft, output shaft, and intermediate shaft, respectively; β1 and β2 are the angles between the input shaft, output shaft, and intermediate shaft and the intermediate shaft, respectively. According to the direction of rotation, the angle between the plane formed by the input shaft and intermediate shaft and the plane formed by the intermediate shaft and output shaft is denoted as γ; the angle between the two forks at the ends of the intermediate shaft is denoted as... Step 3: Based on the grade, size, and preload of the universal joint connecting bolts, calculate the equivalent stiffness of the connecting bolts in the propulsion shaft system, and establish a dynamic model of the flexible connecting bolts: In the formula, F x F y F z T x T y And T z These represent the components of the force and torque acting on the bolt in the x, y, and z directions, respectively; k 11 k 22 k 33 k represents the stiffness coefficient of the bolt in the three translational directions. 44 k 55 k 66 θ represents the torsional stiffness coefficient of the bolt in the three rotational directions; x, y, and z represent the displacements of adjacent flanges in the three translational directions, i.e., the tensile or bending deformation of the bolt, respectively. x θ y θ z This represents the angular displacement of adjacent flanges in three rotational directions, i.e., the torsional deformation of the bolts; c 11 c 22 c 33 These represent the damping coefficients of the bolt as it deforms in the three translational directions, c and c respectively. 44 c 55 c 66 These represent the damping coefficients of the bolt as it deforms in the three rotational directions; v x v y v z ω x ω y ω z F1, F2, and F3 represent the velocities and angular velocities of adjacent flanges in the three translational and rotational directions, respectively; F1, F2, and F3 represent the preload forces on the bolts in the three translational directions, respectively; T1, T2, and T3 represent the preload moments on the bolts in the three rotational directions, respectively; the bolt stiffness can be calculated using the following formula: Where E is the elastic modulus of the bolt material, A is the effective cross-sectional area of ​​the bolt, and l is the effective length of the bolt; Where G is the shear modulus of the bolt material; Where I is the moment of inertia of the bolt section; Where R is the effective diameter of the bolt; Step 4: Establish a nonlinear friction force model between the flange faces of the universal joint: f = μF (10) Where F represents the normal force between the interfaces, μ represents the coefficient of friction, and μ s v represents the maximum static friction coefficient between the interfaces, and v represents the relative sliding velocity between the interfaces. s μ represents the maximum relative slip velocity under static friction conditions. m The static friction coefficient between interfaces, v m This represents the rate of transition between static and dynamic friction; when the relative sliding velocity v between the interfaces... <v s When the relative sliding velocity reaches v, the coefficient of friction between the two flanges increases linearly; when the relative sliding velocity reaches v... s At this point, the coefficient of friction reaches its maximum static friction coefficient value μ. s As the relative sliding velocity continues to increase, the coefficient of friction decreases linearly; when the relative sliding velocity reaches the velocity v of the transition between dynamic and static friction... m At this point, the frictional state between the two flanges changes to kinetic friction, and the coefficient of friction at this time is the kinetic friction coefficient μ. m ; Step 5: Based on the rigid body kinematics equations, combine equations (1) to (11) to form the overall dynamic model of the propulsion shaft system; Step 6: Solve the dynamic model of the underwater propulsion shafting system using numerical calculation methods to obtain the dynamic load of the universal joint connecting bolts, i.e., F in Step 3. x F y F z .

2. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

3. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

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