Spiral bevel gear meshing rigidity and vibration characteristic optimization method and verification method thereof

Abstract

The invention discloses a spiral bevel gear meshing rigidity and vibration characteristic optimization method and a verification method thereof. The spiral bevel gear meshing rigidity and vibration characteristic optimization method comprises the steps that 1, working condition parameters of a spiral bevel gear are determined; 2, establishing a spiral bevel gear geometric model and calculating geometric parameters of the spiral bevel gear geometric model; 3, analyzing and simulating the thermal-mechanical coupling effect of the spiral bevel gear by using multiple physical fields; 4, calculating the maximum stress and the time-varying meshing stiffness of the spiral bevel gear; 5, analyzing and identifying key design parameters influencing the performance of the spiral bevel gear according to a vibration analysis result; 6, performing sensitivity analysis on each parameter, and optimizing the spiral bevel gear design by applying a multi-objective optimization algorithm; and 7, obtaining an optimized vibration analysis result through a harmonic response analysis method according to the maximum stress and the time-varying meshing stiffness of the optimized spiral bevel gear geometric model. The invention has the advantages that the meshing rigidity is improved, the service life is prolonged, and the high-performance requirements of an automobile transmission system and the aerospace field are met.

Description

Technical Field

[0001] The invention belongs to the technical field of spiral bevel gears, and in particular is a method for optimizing the meshing stiffness and vibration characteristics of spiral bevel gears and a method for verifying the same. Background Art

[0002] With the continuous progress of automobile transmission technology and aerospace industry, the performance requirements of automobile transmission systems and aircraft are becoming increasingly stringent, especially in terms of improving meshing stiffness and reducing system vibration. As a key component of automobile transmission systems and aircraft, the design and manufacturing quality of spiral bevel gears directly affects the efficiency and reliability of the entire transmission system. However, the existing technology has a series of defects in the design and optimization of spiral bevel gears, especially in terms of accurately simulating stress distribution under actual working conditions, optimizing meshing stiffness, and vibration control.

[0003] In the prior art, the design of spiral bevel gears often relies on traditional empirical formulas and simplified models. These methods cannot fully consider the complex load conditions and dynamic changes encountered by gears in actual work, resulting in obvious deficiencies in gear design in terms of meshing stiffness and vibration control. Specifically, the prior art has obvious defects in the following aspects:

[0004] 1. Inaccurate prediction of stress distribution and meshing stiffness: Due to the lack of effective stress analysis technology and calculation tools, existing methods are difficult to accurately predict the stress distribution and meshing stiffness of spiral bevel gears under actual working conditions, which in turn affects the transmission efficiency and system stability of the gears.

[0005] 2. Limited system vibration control capabilities: Existing technologies mainly rely on passive vibration reduction measures, such as adding damping materials or changing gear geometry parameters. These measures often fail to fundamentally solve the vibration problem and may increase system weight and complexity.

[0006] 3. Lack of consideration for special working conditions: The performance of automotive transmission systems and aircraft under special working conditions such as extreme temperatures, high-speed rotation and changing loads is the key in the design. Existing technologies often ignore these special needs, resulting in the reliability and durability of the gear system failing to meet the high standards in this field.

[0007] Therefore, how to provide a method for optimizing the meshing stiffness and vibration characteristics of spiral bevel gears through comprehensive stress distribution technology is an urgent problem that technicians in this field need to solve. Summary of the invention

[0008] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes a method for optimizing the meshing stiffness and vibration characteristics of spiral bevel gears and a verification method thereof, in order to improve the meshing accuracy and operating stability of the spiral bevel gears and reduce the fatigue damage of the spiral bevel gears caused by stress concentration, thereby extending the service life of the spiral bevel gears and improving the reliability of automobile transmission systems and aircraft performance.

[0009] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0010] The invention provides a method for optimizing meshing stiffness and vibration characteristics of spiral bevel gears, which comprises the following steps:

[0011] S1. Determine the working parameters of the spiral bevel gear, and collect the operating parameters of the spiral bevel gear under actual working conditions by real-time monitoring of the operation of the spiral bevel gear, so as to calculate the average stress σ according to the working parameters and operating parameters. avg and the maximum stress σ max ;

[0012] S2. Based on the operating parameters, a spiral bevel gear geometric model is established and the geometric parameters of the spiral bevel gear are calculated; the spiral bevel gear geometric model is meshed using finite element software, and the shape factor Q and density D of the mesh are used to calculate the geometric parameters of the spiral bevel gear. mesh Evaluate the quality of the mesh to obtain stress distribution in critical load-bearing areas of spiral bevel gears;

[0013] S3. Perform multi-physics field analysis on the spiral bevel gear geometric model and simulate the thermal-mechanical coupling effect of the spiral bevel gear in the actual working process, so as to calculate the temperature distribution T(x, y, z) and thermal stress distribution σ of the spiral bevel gear at different positions (x, y, z) using equations (10) and (11). thermal (x,y,z):

[0014]

[0015] σ thermal (x,y,z)=E·α T ·(T(x,y,z)-T ref ) (11)

[0016] In formula (10)-(11), T0 represents the initial temperature of the spiral bevel gear during actual operation, j represents the total number of heat sources, and q i represents the thermal power density of the ith heat source, f(x,y,z,i) represents the influence function of the ith heat source at position (x,y,z), E represents the Young's modulus of the gear material, α T Indicates the thermal expansion coefficient of the gear material, T refIndicates the reference temperature of spiral bevel gears during actual working process;

[0017] S4. Calculate the maximum stress σ of spiral bevel gear using equations (12) and (13) respectively: max And the time-varying mesh stiffness K:

[0018] σ max =max (x,y,z)∈V σ(x,y,z) (12)

[0019]

[0020] In equations (12) and (13), V represents the total volume of the spiral bevel gear geometry model, σ(x, y, z) is the stress at the point (x, y, z) in volume V, and F applied is the external force applied to the spiral bevel gear, and δ is the deformation caused by the meshing of the spiral bevel gear;

[0021] S5. According to the stress distribution and the time-varying meshing stiffness K, the influence of each geometric parameter in S2 on the stress distribution and the time-varying meshing stiffness K is analyzed to evaluate the fatigue life of the spiral bevel gear, thereby identifying the key geometric parameters affecting the performance of the spiral bevel gear;

[0022] S6. Perform sensitivity analysis on each key geometric parameter, and optimize the key geometric parameters of the spiral bevel gear using a multi-objective optimization algorithm based on the optimization objectives shown in equations (14) and (15), so as to obtain the optimized key geometric parameters using equations (16) to (20), including: the optimized module m opt 、Optimized number of teeth z opt , optimized helix angle β opt 、Optimized tooth top height h a,opt 、Optimized tooth width b opt And the optimized time-varying meshing stiffness K opt and the optimized maximum stress σ max,opt :

[0023]

[0024] minσ max,opt =min{σ opt (x,y,z)},(x,y,z)∈V opt (15)

[0025] m opt =m inital +Δm·λ m (16)

[0026] z opt =z inital +Δz·λz (17)

[0027] β opt =β inital +Δβ·λ β (18)

[0028]

[0029] b opt =b inital +Δb·λ b (20)

[0030] In formula (14) to formula (20), F applied,opt is the external force applied to the optimized spiral bevel gear, δ opt is the deformation caused by the optimized spiral bevel gear meshing, σ opt (x,y,z) is the volume V of the optimized spiral bevel gear opt Stress at a point at intrinsic position (x,y,z), m inital 、z inital , β inital 、h a,inital 、b inital Represent the initial module, initial number of teeth, initial helix angle, initial tooth addendum height and initial tooth width of the spiral bevel gear, Δm, Δz, Δβ, Δh respectively a , Δb represent the changes in the module of the spiral bevel gear, the number of teeth, the helix angle, the addendum height and the tooth width, respectively, λ m , z , β , ha , b They respectively represent the adjustment coefficient of the spiral bevel gear module, the adjustment coefficient of the number of teeth, the adjustment coefficient of the helix angle, the adjustment coefficient of the tooth addendum height and the adjustment coefficient of the tooth width;

[0031] S7, according to the maximum stress σ of the optimized spiral bevel gear geometry model max,opt and the time-varying mesh stiffness K opt , the analysis results of the vibration characteristics of the system where the optimized spiral bevel gear is located are obtained through the harmonic response analysis method.

[0032] The method for optimizing meshing stiffness and vibration characteristics of spiral bevel gears based on comprehensive stress distribution described in the present invention is also characterized in that the working condition parameters in S1 include: working speed v, average load F avg And the operating temperature range T range , the average contact area A of the spiral bevel gear tooth surface contact , the minimum contact area A of the spiral bevel gear tooth surface min,contact ;

[0033] The operating parameters include: the speed n of the spiral bevel gear under different working conditions, the maximum load F max and minimum load F min , and the load change frequency;

[0034] The average stress σ is calculated using equations (1) and (2) respectively. avg and the maximum stress σ max ;

[0035]

[0036] S2 includes:

[0037] S2.1. Geometric parameters of the spiral bevel gear, including: tip diameter D a , tooth root diameter D f 、Tooth top height h a , tooth root height h f , helix angle β, tooth width b, module m; where D is calculated using equations (3) to (7) a , D f 、h a 、h f , β:

[0038] D a =m·(Z+2) (3)

[0039] D f =D a -2·m·cosa (4)

[0040] h a =1.25×m (5)

[0041] h f =m+b (6)

[0042]

[0043] In formula (3) to formula (7), D m is the median diameter of the spiral bevel gear, Z is the number of teeth, L is the axial length of the tooth surface, and b is the spacing of the tooth tops;

[0044] S2.2. Based on the geometric parameters, the spiral bevel gear geometric model is meshed using finite element software to obtain a mesh after meshing;

[0045] S2.3. Calculate the density D of the divided grid using formula (8) mesh :

[0046]

[0047] In formula (8), N is the total number of elements in the grid, and V is the total volume of the spiral bevel gear geometric model;

[0048] The shape factor Q of the divided grid is calculated by formula (9):

[0049]

[0050] In formula (9), h max is the maximum edge length in the grid, h min is the minimum edge length in the grid;

[0051] S2.4, if the shape factor Q and density D mesh If they are respectively within the set threshold range, it means that the divided grid meets the quality requirement, otherwise, return to S2.2 to re-divide the grid;

[0052] S2.5. Use post-processing tools to extract stress data of key stress areas from the meshed spiral bevel gear geometric model to evaluate the stress distribution of key stress areas of the spiral bevel gear under different working conditions.

[0053] S7 includes:

[0054] S7.1. Using the harmonic response analysis method shown in equations (21) and (22), calculate the natural frequency ω of the system where the optimized spiral bevel gear is located opt And the damping ratio ζ of the system where the optimized spiral bevel gear is located opt :

[0055]

[0056] In formula (21)-formula (22), K opt is the time-varying mesh stiffness of the optimized spiral bevel gear system, g opt is the mass of the system where the optimized spiral bevel gear is located, c opt is the damping coefficient of the system where the optimized spiral bevel gear is located;

[0057] S7.2, according to ω opt and opt Under the excitation of external conditions, the response amplitude and phase of the spiral bevel gear system and the response characteristics of the spiral bevel gear system at each frequency order are calculated by harmonic response analysis and frequency domain analysis, and are used as the analysis results of the vibration characteristics of the optimized spiral bevel gear system.

[0058] A verification method of the present invention is characterized in that the analysis results of the vibration characteristics obtained by the spiral bevel gear meshing stiffness and vibration characteristics optimization method are verified according to the following steps:

[0059] S8. Use formula (23) to construct the loss function L that minimizes the vibration response of the system where the spiral bevel gear is located opt After solving, we get the loss function L of the vibration response: opt The weight coefficient w1 of the stress distribution corresponding to the minimization, the weight coefficient w2 of the time-varying meshing stiffness and the weight coefficient w3 of the vibration response of the system in which the spiral bevel gear is located are used to meet the vibration characteristic requirements of the spiral bevel gear;

[0060] L opt =w1·(σ max,opt -σ target ) 2 +w2·(K opt -K target ) 2 +w3·(ζ opt -ζ target ) 2 (twenty three)

[0061] In formula (23), σ target is the target maximum stress, K target is the target time-varying mesh stiffness, ζ target is the target system damping ratio;

[0062] S9. Comprehensively consider the interaction of multiple physical fields and conduct multi-physical field coupling analysis on the system where the spiral bevel gear is located, so as to calculate the total force F of the system using equations (24) and (25): system , and then construct the system-level optimization objective function L system :

[0063] F system =F mechanical +F thermal +F dynamic (twenty four)

[0064] L system =w1·(σ system -σ target ) 2 +w2·(K system -K target ) 2 +w3·(ζ system -ζ target ) 2 (25)

[0065] In formula (24), F mechanical 、F thermal and F dynamic They represent mechanical force, thermal force and dynamic response force respectively;

[0066] In formula (25), σ systemrepresents the stress distribution at the system level, ζ system represents the system-level damping ratio, K system represents the time-varying mesh stiffness at the system level;

[0067] S10. Perform parameter sensitivity analysis on system-level parameters and optimize the stress distribution σ of the optimized system-level system , Dynamic response force F dynamic and the system-level damping ratio ζ system Calculate and verify:

[0068] S10.1, using formula (26) to set the sensitivity function S(θ j ):

[0069]

[0070] In formula (26), θ j represents the jth adjustment parameter at the system level;

[0071] S10.2. Use formula (27) to construct the optimized system-level objective function value L system,opt , used to adjust the parameters to observe the system-level objective function L system The impact of

[0072] L system,opt =min{L system (θ1,θ2,...,θ j ,...,θ p )}(27)

[0073] In formula (27), p represents the total number of adjustment parameters in the system;

[0074] S10.3. Calculate the system-level stress distribution σ using equations (28) to (30) system , Dynamic response force F dynamic and the system-level damping ratio ζ system :

[0075] σ system =max{σ(x′,y′,z′)},(x′,y′,z′)∈V system (28)

[0076] F dynamic =g system ·a system +c system ·v system +K system ·x system (29)

[0077]

[0078] In formula (28) to formula (30), V system is the volume of the system where the spiral bevel gear is located, and σ(x′, y′, z′) represents the volume V system Stress at the point in the interior (x′, y′, z′), g system 、c system , K system are the mass, damping coefficient and stiffness at the system level, and a system 、v system 、x system They are acceleration, velocity and displacement at the system level;

[0079] S10.4, σ system Compare with the yield strength of the material to verify whether the optimized design meets the strength requirements; dynamic Compare with the external dynamic load under actual working conditions to evaluate whether the system response under dynamic load is within an acceptable range; perform harmonic response analysis or time domain analysis on the system where the optimized spiral bevel gear is located to verify ζ system Effectiveness in actual operation.

[0080] Compared with the prior art, the present invention has the following beneficial effects:

[0081] 1. The present invention can more accurately simulate and analyze the stress distribution of spiral bevel gears under actual working conditions by comprehensively applying stress analysis and multi-physics field coupling analysis, and then optimize the design to achieve higher time-varying meshing stiffness and better vibration characteristics. Compared with traditional design methods, this method effectively improves the transmission efficiency and dynamic stability of the system in which the spiral bevel gears are located, while reducing noise and improving the overall performance and reliability of automobile transmission systems and aircraft.

[0082] 2. The present invention adopts a system-level optimization method, comprehensively considers the interaction of all components in the system where the spiral bevel gear is located, and realizes active control of the vibration of the system where the spiral bevel gear is located through multi-physical field coupling analysis. This can not only effectively reduce the vibration of the system where the spiral bevel gear is located during the design stage, but also avoid the increase in weight and design complexity that may be caused by the use of traditional passive vibration reduction measures, thereby meeting the strict requirements of high efficiency and lightweight in this field.

[0083] 3. The present invention takes into account special environments and requirements, such as extreme temperatures, high-speed rotation, and variable loads, and ensures the high reliability and durability of the system in which the spiral bevel gear is located through targeted design and manufacturing measures. This method can ensure that the spiral bevel gear system can maintain excellent performance in long-term operation and harsh working environments in automobile transmission systems or aircraft, significantly improving its safety and reliability.

[0084] 4. The present invention ensures the practical applicability and effectiveness of the optimized design scheme through system-level verification and experimental testing. This method not only provides a means to comprehensively evaluate and optimize the performance of the system in which the spiral bevel gear is located, but also provides accurate technical guidance for subsequent manufacturing and experimental verification, greatly shortening the product development cycle and reducing R&D costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 is a flow chart of the method of the present invention;

[0086] Figure 2 The maximum value σ of stress distribution before and after optimization by the method of the present invention system Comparison chart;

[0087] Figure 3 The dynamic response force F before and after optimization of the method of the present invention dynamic Comparison chart;

[0088] Figure 4 The damping ratio ζ of the system before and after optimization by the method of the present invention is system Comparison chart. DETAILED DESCRIPTION

[0089] In this embodiment, Figure 1 As shown: A method for optimizing the meshing stiffness and vibration characteristics of spiral bevel gears based on comprehensive stress distribution, comprising the following steps:

[0090] S1. Determine the working parameters of the spiral bevel gear, including: working speed v, average load F avg And the operating temperature range T range ; Through real-time monitoring of the operation of spiral bevel gears, the operating parameters of spiral bevel gears under actual working conditions are collected, including: the speed n of spiral bevel gears under different working conditions, the maximum load F max and minimum load F min , and the load change frequency; thus, the average stress σ is calculated using equations (1) and (2) respectively avg and the maximum stress σ max ;

[0091]

[0092] In formula (1)-formula (2), A contact Represents the average contact area of ​​the spiral bevel gear tooth surface, A min,contact Indicates the minimum contact area of ​​spiral bevel gear tooth surfaces.

[0093] Mean stressσ avg and the maximum stress σ max Represents the stress distribution state of spiral bevel gears under different loads.

[0094] At the same time, analyze the working temperature T range Influence on the material properties of spiral bevel gears. Different operating temperatures will have a potential impact on the operating efficiency and life of spiral bevel gears.

[0095] S2. Based on the operating parameters, a spiral bevel gear geometric model is established, and the geometric parameters of the spiral bevel gear are calculated and measured using equations (3) to (7), including: tooth tip diameter D a , tooth root diameter D f 、Tooth top height h a , tooth root height h f , helix angle β, tooth width b, module m;

[0096] D a =m·(z+2) (3)

[0097] D f =D a -2·m·cosa (4)

[0098] h a =1.25·m (5)

[0099] h f =m+d (6)

[0100]

[0101] In formula (3) to formula (7), D m is the median diameter of the spiral bevel gear, z is the number of teeth, L is the axial length of the tooth surface, and d is the spacing of the tooth tops.

[0102] Finite element software is used to mesh the spiral bevel gear geometry model, and the mesh density D is calculated using formula (8): mesh The mesh density directly affects the accuracy of the analysis and the calculation time. High-density meshes are suitable for the key stress-bearing areas of the gear. The mesh shape factor Q is calculated using equation (9) to evaluate and adjust the density and quality of the mesh to ensure that the shape of the mesh is suitable for accurate analysis to obtain the stress distribution in the key stress-bearing areas of the spiral bevel gear:

[0103]

[0104] In equations (8) and (9), N is the total number of mesh elements, V is the total volume of the spiral bevel gear geometry model, and h is max is the maximum edge length in the grid, h min is the minimum edge length in the grid.

[0105] If the shape factor Q and density D meshIf they are within the set threshold range, it means that the divided grid meets the quality requirements. Otherwise, it is necessary to adjust the grid by re-dividing the grid, adjusting the grid generation parameters, changing the unit type, etc.

[0106] Post-processing tools are used to extract stress data in key stress areas from the meshed spiral bevel gear geometric model to evaluate the stress distribution in key stress areas of the spiral bevel gear under different working conditions.

[0107] S3. Perform multi-physics field analysis on the spiral bevel gear geometric model, import the set boundary conditions and material properties, apply radial loads and axial loads, as well as torque, and simulate the thermal-mechanical coupling effect of the spiral bevel gear in the actual working process, so as to calculate the temperature distribution T(x, y, z) and thermal stress distribution σ of the spiral bevel gear at different positions (x, y, z) using equations (10) and (11). thermal (x,y,z):

[0108]

[0109] σ thermal (x,y,z)=E·α T ·(T(x,y,z)-T ref ) (11)

[0110] In formula (10)-(11), T0 represents the initial temperature of the spiral bevel gear during actual operation, j represents the total number of heat sources, and q i represents the thermal power density of the ith heat source, f(x,y,z,i) represents the influence function of the ith heat source at position (x,y,z), E represents the Young's modulus of the gear material, α T Indicates the thermal expansion coefficient of the gear material, T ref Indicates the reference temperature of the spiral bevel gear during actual working process.

[0111] S4. Calculate the maximum stress σ of spiral bevel gear using equations (12) and (13) respectively: max And the time-varying mesh stiffness K:

[0112] σ max =max (x,y,z)∈V σ(x,y,z) (12)

[0113]

[0114] In equations (12) and (13), V represents the volume of the spiral bevel gear, σ(x, y, z) is the stress at the point (x, y, z) in the volume V, and F applied is the external force applied to the spiral bevel gear, and δ is the deformation caused by the meshing of the spiral bevel gear;

[0115] According to the stress analysis results, the maximum stress σ of the spiral bevel gear max To evaluate the fatigue life of the gear and compare it with the fatigue limit of the material: If the maximum stress σ of the spiral bevel gear max If it is less than the fatigue limit of the material, it means that the spiral bevel gear can withstand the maximum cyclic stress during operation without fatigue failure.

[0116] S5. According to the stress distribution and time-varying meshing stiffness K, the influence of each geometric parameter in S2 on the stress distribution and time-varying meshing stiffness K is analyzed to evaluate the fatigue life of spiral bevel gears, thereby identifying the key geometric parameters affecting the performance of spiral bevel gears, including: module m, number of teeth z, helix angle β, tooth top height h a , tooth width b.

[0117] S6. Perform sensitivity analysis on each key geometric parameter, and optimize the key geometric parameters of the spiral bevel gear using a multi-objective optimization algorithm based on the optimization objectives shown in equations (14) and (15), so as to obtain the optimized key geometric parameters using equations (16) to (20), including: the optimized module m opt 、Optimized number of teeth z opt , optimized helix angle β opt 、Optimized tooth top height h a,opt 、Optimized tooth width b opt And the optimized time-varying meshing stiffness K opt and the optimized maximum stress σ max,opt :

[0118]

[0119] minσ max,opt =min{σ opt (x,y,z)},(x,y,z)∈V opt (15)

[0120] m opt =m inital +Δm·λ m (16)

[0121] z opt =z inital +Δz·λ z (17)

[0122] β opt =β inital +Δβ·λ β (18)

[0123]

[0124] b opt =b inital +Δb·λ b (20)

[0125] In formula (14) to formula (20), F applied,opt is the external force applied to the optimized spiral bevel gear, δ opt is the deformation caused by the optimized spiral bevel gear meshing, σ opt (x,y,z) is the volume V of the optimized spiral bevel gear opt The stress m at a point at intrinsic position (x,y,z) inital 、z inital , β inital 、h a,inital , b inital Represent the initial module, initial number of teeth, initial helix angle, initial tooth addendum and initial tooth width of the spiral bevel gear, Δm, Δz, Δβ, Δh respectively a , Δb represent the changes in the module of the spiral bevel gear, the number of teeth, the helix angle, the addendum height and the tooth width, respectively, λ m , z , β , ha , b They respectively represent the adjustment coefficient of the spiral bevel gear module, the adjustment coefficient of the number of teeth, the adjustment coefficient of the helix angle, the adjustment coefficient of the tooth addendum height and the adjustment coefficient of the tooth width. The adjustment coefficient is used to determine the direction and amplitude of the adjustment of each parameter.

[0126] S7. According to the optimized key geometric parameters, the stress distribution and time-varying meshing stiffness analysis of the optimized spiral bevel gear geometric model are performed to obtain the vibration analysis results, which are used to verify the optimized stress distribution σ opt and the optimized time-varying mesh stiffness K opt effectiveness.

[0127] According to the optimized time-varying meshing stiffness K opt , using the harmonic response analysis method shown in equations (21) and (22), the natural frequency ω of the system where the optimized spiral bevel gear is located is calculated opt And the damping ratio ζ of the system where the optimized spiral bevel gear is located opt :

[0128]

[0129] In formula (21)-formula (22), K opt is the meshing stiffness of the optimized spiral bevel gear system, g opt is the mass of the system where the optimized spiral bevel gear is located, c optis the damping coefficient of the system in which the optimized spiral bevel gear is located.

[0130] Evaluate the vibration characteristics of the system in which the optimized spiral bevel gear is located to obtain vibration analysis results:

[0131] The natural frequency ω of the system where the optimized spiral bevel gear is located is calculated according to equations (21) and (22): opt and damping ratio ζ opt , under external excitation, the response amplitude and phase of the system are calculated through harmonic response analysis and frequency domain analysis, and the response characteristics of the system at each frequency order are checked.

[0132] Based on the vibration analysis results, the effectiveness is verified:

[0133] The optimized stress distribution is compared with the stress distribution before optimization to evaluate the changes in stress peak and stress concentration area to verify whether the expected stress reduction goal has been achieved. At the same time, the time-varying meshing stiffness K of the spiral bevel gear system before and after optimization is compared. opt and the natural frequency ω opt , check whether the design requirements are met;

[0134] Combined with the above analysis results, a comprehensive evaluation is conducted on the system where the optimized spiral bevel gear is located to confirm its improvement effect in stress distribution, time-varying stiffness and vibration characteristics. If the improvement effect meets the design requirements, it indicates the effectiveness of the optimization scheme; if the improvement effect does not meet expectations, further iteration and optimization of the design parameters are required.

[0135] In this embodiment, based on the spiral bevel gear meshing stiffness and vibration characteristic optimization method, the obtained vibration characteristic analysis results are verified, and the verification steps are as follows:

[0136] S8. Use formula (23) to construct the loss function L that minimizes the vibration response of the system where the spiral bevel gear is located opt After solving, we get the loss function L of the vibration response: opt The weight coefficient w1 of the stress distribution corresponding to the minimization, the weight coefficient w2 of the time-varying meshing stiffness and the weight coefficient w3 of the vibration response of the system in which the spiral bevel gear is located are used to meet the vibration characteristic requirements of the spiral bevel gear;

[0137] L opt =w1·(σ max,opt -σ target ) 2 +w2·(K opt -K target ) 2 +w3·(ζ opt -ζ target ) 2 (twenty three)

[0138] In formula (23), σ target is the target maximum stress, K target is the target time-varying mesh stiffness, ζ target is the target system damping ratio;

[0139] S9. Comprehensively consider the interaction of multiple physical fields and conduct multi-physical field coupling analysis on the system where the spiral bevel gear is located, so as to calculate the total force F of the system using equations (24) and (25): system , and then construct the system-level optimization objective function L system :

[0140] F system =F mechanical +F thermal +F dynamic (twenty four)

[0141] L system =w1·(σ system -σ target ) 2 +w2·(K system -K target ) 2 +w3·(ζ system -ζ target ) 2 (25)

[0142] In formula (24), F mechanical 、F thermal and F dynamic They represent mechanical force, thermal force and dynamic response force respectively;

[0143] In formula (25), σ system represents the stress distribution at the system level, ζ system represents the system-level damping ratio, K system represents the time-varying mesh stiffness at the system level;

[0144] S10. Perform parameter sensitivity analysis on system-level parameters and optimize the stress distribution σ of the optimized system-level system , Dynamic response force F dynamic and the system-level damping ratio ζ system Calculate and verify:

[0145] Use equation (26) to set the sensitivity function S(θ j ):

[0146]

[0147] In formula (26), θ j represents the jth adjustment parameter at the system level;

[0148] Use formula (27) to construct the optimized system-level objective function value L system,opt , used to adjust the parameters to observe the system-level objective function L system The impact of

[0149] L system,opt =min{L system (θ1,θ2,...,θ j ,...,θ p )} (27)

[0150] In formula (27), p represents the total number of adjustment parameters in the system;

[0151] The system-level stress distribution σ is calculated using equations (28) to (30): system , Dynamic response force F dynamic and the system-level damping ratio ζ system :

[0152] σ system =max{σ(x′,y′,z′)},(x′,y′,z′)∈V system (28)

[0153] F dynamic =g system ·a system +c system ·v system +K system ·x system (29)

[0154]

[0155] In formula (28) to formula (30), V system is the volume of the system where the spiral bevel gear is located, and σ(x′, y′, z′) represents the volume V system Stress at the point in the interior (x′, y′, z′), g system 、c system , K system are the mass, damping coefficient and stiffness at the system level, and a system 、v system 、x system They are acceleration, velocity and displacement at the system level respectively.

[0156] σ system Compare with the yield strength of the material to verify whether the optimized design meets the strength requirements. If the maximum stress value is lower than the yield strength of the material, it indicates that the design is safe. dynamicCompare with the external dynamic load under actual working conditions to evaluate whether the system response under dynamic load is within an acceptable range; perform harmonic response analysis or time domain analysis on the system where the optimized spiral bevel gear is located to verify ζ system The effectiveness in actual operation ensures that the system will not produce excessive vibration due to insufficient damping, nor reduce the response efficiency due to excessive damping.

[0157] Example:

[0158] 1. Take a pair of spiral bevel gears as an example. The number of teeth on the large gear is 10 and the number of teeth on the small gear is 41. The basic geometric parameters are shown in Table 1:

[0159] Table 1 Geometric parameters of spiral bevel gear pairs

[0160]

[0161] Figure 2 The maximum value σ of stress distribution before and after optimization by the method of the present invention system Comparison chart, by Figure 2 It can be obtained that: the maximum value of stress distribution σ system The maximum stress was 100 MPa before optimization and 70 MPa after optimization, and the maximum stress was reduced by 30%. This shows that the maximum stress of the spiral bevel gear during the meshing process has been effectively reduced, which can extend the life of the spiral bevel gear, improve its transmission efficiency, reduce vibration and noise, and improve its load bearing capacity.

[0162] Figure 3 The dynamic response force F before and after optimization of the method of the present invention dynamic Comparison chart, by Figure 3 The dynamic response force F is obtained: dynamic It was 500N before optimization and was reduced to 300N after optimization, indicating that the system in which the spiral bevel gear is located has a more stable response and a lower vibration amplitude when facing external dynamic loads, which improves the reliability of the system.

[0163] Figure 4 The damping ratio ζ of the system before and after optimization by the method of the present invention is system Comparison chart, by Figure 4 It can be obtained that: the system damping ratio ζ system The increase from 0.05 before optimization to 0.1 after optimization means that the system can absorb and dissipate vibration energy faster, thereby improving the stability of the system.

[0164] In summary, this method is used to optimize the maximum stress distribution σ of the system where the spiral bevel gear is located. system , Dynamic response force F dynamic and the damping ratio of the system ζ systemThe effect is quite significant. This is of great significance for improving the fatigue life and reliability of spiral bevel gears, improving the durability and stability of the system and reducing maintenance costs.

Claims

1. A method for optimizing the meshing stiffness and vibration characteristics of spiral bevel gears, characterized in that: The steps include: S1. Determine the working parameters of the spiral bevel gear, and collect the operating parameters of the spiral bevel gear under actual working conditions by real-time monitoring of the operation of the spiral bevel gear, so as to calculate the average stress σ according to the working parameters and operating parameters. avg and the maximum stress σ max ; S2. Based on the operating parameters, a spiral bevel gear geometric model is established and the geometric parameters of the spiral bevel gear are calculated; the spiral bevel gear geometric model is meshed using finite element software, and the shape factor Q and density D of the mesh are used to calculate the geometric parameters of the spiral bevel gear. mesh Evaluate the quality of the mesh to obtain stress distribution in critical load-bearing areas of spiral bevel gears; S3. Perform multi-physics field analysis on the spiral bevel gear geometric model and simulate the thermal-mechanical coupling effect of the spiral bevel gear in the actual working process, so as to calculate the temperature distribution T(x, y, z) and thermal stress distribution σ of the spiral bevel gear at different positions (x, y, z) using equations (10) and (11). thermal (x,y,z): σ thermal (x,y,z)=E·α T ·(T(x,y,z)-T ref ) (11) In formula (10)-(11), T0 represents the initial temperature of the spiral bevel gear during actual operation, j represents the total number of heat sources, and q i represents the thermal power density of the ith heat source, f(x,y,z,i) represents the influence function of the ith heat source at position (x,y,z), E represents the Young's modulus of the gear material, α T Indicates the thermal expansion coefficient of the gear material, T ref Indicates the reference temperature of spiral bevel gears during actual working process; S4. Calculate the maximum stress σ of spiral bevel gear using equations (12) and (13) respectively: max And the time-varying mesh stiffness K: s max =max (x,y,z)∈V σ(x,y,z) (12) In equations (12) and (13), V represents the total volume of the spiral bevel gear geometric model, σ(x, y, z) is the stress at the point (x, y, z) in volume V, and F applied is the external force applied to the spiral bevel gear, and δ is the deformation caused by the meshing of the spiral bevel gear; S5. According to the stress distribution and the time-varying meshing stiffness K, the influence of each geometric parameter in S2 on the stress distribution and the time-varying meshing stiffness K is analyzed to evaluate the fatigue life of the spiral bevel gear, thereby identifying the key geometric parameters affecting the performance of the spiral bevel gear; S6. Perform sensitivity analysis on each key geometric parameter, and optimize the key geometric parameters of the spiral bevel gear using a multi-objective optimization algorithm based on the optimization objectives shown in equations (14) and (15), so as to obtain the optimized key geometric parameters using equations (16) to (20), including: the optimized module m opt 、Optimized number of teeth z opt , optimized helix angle β opt 、Optimized tooth top height h a,opt 、Optimized tooth width b opt And the optimized time-varying meshing stiffness K opt and the optimized maximum stress σ max,opt : minσ max,opt =min{σ opt (x,y,z)},(x,y,z)∈V opt (15) m opt =m inital +Δm·λ m (16) With opt =from inital +Δz λ z (17) b opt =b inital +Δβ·λ β (18) b opt =b inital +Δb·λ b (20) In formula (14) to formula (20), F applied,opt is the external force applied to the optimized spiral bevel gear, δ opt is the deformation caused by the optimized spiral bevel gear meshing, σ opt (x,y,z) is the volume V of the optimized spiral bevel gear opt Stress at a point at intrinsic position (x,y,z), m inital 、z inital , β inital 、h a,inital 、b inital Represent the initial module, initial number of teeth, initial helix angle, initial tooth addendum and initial tooth width of the spiral bevel gear, Δm, Δz, Δβ, Δh respectively a , Δb represent the changes in the module of the spiral bevel gear, the number of teeth, the helix angle, the addendum height and the tooth width, respectively, λ m , z , β , ha , b They respectively represent the adjustment coefficient of the spiral bevel gear module, the adjustment coefficient of the number of teeth, the adjustment coefficient of the helix angle, the adjustment coefficient of the tooth addendum height and the adjustment coefficient of the tooth width; S7, according to the maximum stress σ of the optimized spiral bevel gear geometry model max,opt and the time-varying mesh stiffness K opt , the analysis results of the vibration characteristics of the system where the optimized spiral bevel gear is located are obtained through the harmonic response analysis method.

2. The method for optimizing meshing stiffness and vibration characteristics of spiral bevel gears based on comprehensive stress distribution according to claim 1, characterized in that: The working parameters in S1 include: working speed v, average load F avg And the operating temperature range T range , the average contact area A of the spiral bevel gear tooth surface contact , the minimum contact area A of the spiral bevel gear tooth surface min,contact ; The operating parameters include: the speed n of the spiral bevel gear under different working conditions, the maximum load F max and minimum load F min , and the load change frequency; The average stress σ is calculated using equations (1) and (2) respectively. avg and the maximum stress σ max ; 3. The method for optimizing meshing stiffness and vibration characteristics of spiral bevel gears based on comprehensive stress distribution according to claim 2, characterized in that S2 include: S2.

1. Geometric parameters of the spiral bevel gear, including: tooth tip diameter D a , tooth root diameter D f 、Tooth top height h a , tooth root height h f , helix angle β, tooth width b, module m; where D is calculated using equations (3) to (7) a , D f 、h a 、h f , β: D a =m·(Z+2) (3) D f =D a -2·m·what (4) h a =1.25×m (5) h f =m+b (6) In formula (3) to formula (7), D m is the median diameter of the spiral bevel gear, Z is the number of teeth, L is the axial length of the tooth surface, and b is the spacing of the tooth tops; S2.

2. Based on the geometric parameters, the spiral bevel gear geometric model is meshed using finite element software to obtain a mesh after meshing; S2.

3. Calculate the density D of the divided grid using formula (8) mesh : In formula (8), N is the total number of elements in the grid, and V is the total volume of the spiral bevel gear geometric model; The shape factor Q of the divided grid is calculated by formula (9): In formula (9), h max is the maximum edge length in the grid, h min is the minimum edge length in the grid; S2.4, if the shape factor Q and density D mesh If they are respectively within the set threshold range, it means that the divided grid meets the quality requirement, otherwise, return to S2.2 to re-divide the grid; S2.

5. Use post-processing tools to extract stress data of key stress areas from the meshed spiral bevel gear geometric model to evaluate the stress distribution of key stress areas of the spiral bevel gear under different working conditions.

4. The method for optimizing meshing stiffness and vibration characteristics of spiral bevel gears based on comprehensive stress distribution according to claim 1, characterized in that S7 include: S7.

1. Using the harmonic response analysis method shown in equations (21) and (22), calculate the natural frequency ω of the system where the optimized spiral bevel gear is located opt And the damping ratio ζ of the system where the optimized spiral bevel gear is located opt : In formula (21)-formula (22), K opt is the time-varying mesh stiffness of the optimized spiral bevel gear system, g opt is the mass of the system where the optimized spiral bevel gear is located, c opt is the damping coefficient of the system where the optimized spiral bevel gear is located; S7.2, according to ω opt and opt Under the excitation of external conditions, the response amplitude and phase of the spiral bevel gear system and the response characteristics of the spiral bevel gear system at each frequency order are calculated by harmonic response analysis and frequency domain analysis, and are used as the analysis results of the vibration characteristics of the optimized spiral bevel gear system.

5. A verification method, characterized in that: The analysis results of the vibration characteristics obtained by the method for optimizing the meshing stiffness and vibration characteristics of spiral bevel gears according to claim 1 are verified in the following steps: S8. Use formula (23) to construct the loss function L that minimizes the vibration response of the system where the spiral bevel gear is located opt After solving, we get the loss function L of the vibration response: opt The weight coefficient w1 of the stress distribution corresponding to the minimization, the weight coefficient w2 of the time-varying meshing stiffness and the weight coefficient w3 of the vibration response of the system in which the spiral bevel gear is located are used to meet the vibration characteristic requirements of the spiral bevel gear; L opt =w1·(σ max,opt -s target ) 2 +w2·(K opt -K target ) 2 +w3·(ζ opt -g target ) 2 (23) In formula (23), σ target is the target maximum stress, K target is the target time-varying mesh stiffness, ζ target is the target system damping ratio; S9. Comprehensively consider the interaction of multiple physical fields and conduct multi-physical field coupling analysis on the system where the spiral bevel gear is located, so as to calculate the total force F of the system using equations (24) and (25): system , and then construct the system-level optimization objective function L system : F system =F mechanical +F thermal +F dynamic (24) L system =w1·(σ system -s target ) 2 +w2·(K system -K target ) 2 +w3·(ζ system -g target ) 2 (25) In formula (24), F mechanical 、F thermal and F dynamic They represent mechanical force, thermal force and dynamic response force respectively; In formula (25), σ system represents the stress distribution at the system level, ζ system represents the system-level damping ratio, K system represents the time-varying mesh stiffness at the system level; S10. Perform parameter sensitivity analysis on system-level parameters and optimize the stress distribution σ of the optimized system-level system , Dynamic response force F dynamic and the system-level damping ratio ζ system Calculate and verify: S10.1, using formula (26) to set the sensitivity function S(θ j ): In formula (26), θ j represents the jth adjustment parameter at the system level; S10.

2. Use formula (27) to construct the optimized system-level objective function value L system,opt , used to adjust the parameters to observe the system-level objective function L system The impact of L system,opt =min{L system (θ1,θ2,...,θ j ,...,θ p )}(27) In formula (27), p represents the total number of adjustment parameters in the system; S10.

3. Calculate the system-level stress distribution σ using equations (28) to (30) system , Dynamic response force F dynamic and the system-level damping ratio ζ system : σ system =max{σ(x′,y′,z′)},(x′,y′,z′)∈V system (28) F dynamic =g system ·a system +c system ·v system +K system ·x system (29) In formula (28) to formula (30), V system is the volume of the system where the spiral bevel gear is located, and σ(x′, y′, z′) represents the volume V system Stress at the point in the interior (x′, y′, z′), g system 、c system , K system are the mass, damping coefficient and stiffness at the system level, and a system 、v system 、x system They are acceleration, velocity and displacement at the system level; S10.4, σ system Compare with the yield strength of the material to verify whether the optimized design meets the strength requirements; F dynamic Compare with the external dynamic load under actual working conditions to evaluate whether the system response under dynamic load is within an acceptable range; perform harmonic response analysis or time domain analysis on the system where the optimized spiral bevel gear is located to verify ζ system Effectiveness in actual operation.

Images