Aero-gear Dynamic Modeling Method Considering Structural Parameters

Abstract

The present invention belongs to the technical field of gear transmission simulation and relates to a method for dynamic modeling of aircraft gears that considers structural parameters. The method comprises the following steps: 1) obtaining gear structural parameters; 2) calculating the strain energy of the gear structural parameters; 3) treating the gear teeth as cantilever beams fixed to the root circle and calculating the stiffness resulting from the deformation of the meshing teeth; 4) obtaining the composite stiffness of the entire gear pair; 5) introducing the strain energy of the gear structural parameters obtained in step 2) into the composite stiffness of the entire gear pair obtained in step 4) to obtain the gear meshing stiffness with the structural parameters introduced; and 6) establishing a six-degree-of-freedom gear dynamic model that considers the structural parameters based on the results of step 5). The present invention provides a method for dynamic modeling of aircraft gears that considers structural parameters, which can more accurately predict the nonlinear dynamic characteristics of aircraft gear transmissions and provides theoretical support for the lightweight design of gear transmission systems.

Description

Technical Field

[0001] The invention belongs to the technical field of gear transmission simulation, and relates to a gear dynamics modeling method, in particular to an aviation gear dynamics modeling method taking structural parameters into consideration. Background Art

[0002] With the improvement of aviation power transmission performance, the demand for lightweight transmission gears has become increasingly urgent. Currently, the industry focuses on four key aspects of gear weight reduction: web thickness, rim thickness, web aperture, and number of web holes. To ensure the reliability and stability of the gear system during transmission, it is necessary to study and analyze the gear dynamics after changing structural parameters. Accurately and effectively establishing a gear meshing dynamics model is the foundation for coordinated gear weight reduction.

[0003] At present, many scholars at home and abroad have conducted systematic and extensive research on gear meshing stiffness and dynamic modeling, but most of them consider introducing structural parameters as constants into meshing stiffness to establish dynamic models. The lightweight and thin-walled characteristics of aviation gears lead to complex excitation factors, and gear weight reduction will cause mutual coupling of vibration forms such as gear bending and torsion. The weak rigidity of the gear structure causes the vibration to intensify, which ultimately leads to frequent system faults and failures. Summary of the Invention

[0004] In order to solve the above technical problems existing in the background technology, the present invention provides an aviation gear dynamics modeling method considering structural parameters, which can more accurately predict the nonlinear dynamic characteristics of aviation gear transmission and provide theoretical support for the lightweight design of gear transmission systems.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for dynamic modeling of aviation gears considering structural parameters, comprising the following steps:

[0007] 1) Obtain gear structure parameters;

[0008] 2) Calculate the strain energy of gear structural parameters;

[0009] 3) Equivalently treat the gear teeth as cantilever beams fixed to the tooth root circle, and calculate the stiffness caused by the deformation of the meshing gear teeth;

[0010] 4) Obtain the comprehensive composite stiffness of the entire gear pair;

[0011] 5) Introducing the strain energy of the gear structural parameters obtained in step 2) into the comprehensive synthetic stiffness of the entire gear pair obtained in step 4) to obtain the gear meshing stiffness with the structural parameters introduced;

[0012] 6) Based on the results of step 5), a six-degree-of-freedom gear dynamics model considering structural parameters is established.

[0013] Preferably, the gear structural parameters in step 1) include the gear rim, hub and spoke.

[0014] Preferably, the strain energy of the gear structural parameters in step 2) includes the strain energy of the gear rim, the strain energy of the non-perforated spoke plate, the strain energy of the perforated spoke plate, and the strain energy of the hub;

[0015] The strain energy of the gear rim and the strain energy of the non-perforated web are calculated as follows:

[0016]

[0017] in: is the strain energy of the gear rim; is the strain energy of the non-perforated web; is the torque borne by the gear; is the cross-sectional radius; G is the shear modulus of the gear material; is the tooth width of the gear; is the outer diameter of the non-perforated spoke; is the inner diameter of the non-perforated spoke;

[0018] The strain energy of the perforated web is calculated as follows:

[0019]

[0020] in: is the strain energy of the perforated spoke; is the thickness of the perforated web; is the radius of the position of the web hole; is the radius of the web hole; is the outer diameter of the wheel hub; is the arc length of the micro-circular ring that does not pass through the web hole;

[0021] The strain energy of the hub is calculated as:

[0022]

[0023] in: is the strain energy of the hub; is the inner diameter of the wheel hub; is the hub width.

[0024] Preferably, the stiffness generated by the deformation of the meshing gear teeth in step 3) includes Hertzian contact stiffness, bending stiffness, axial compression stiffness, shear stiffness and matrix deformation stiffness;

[0025] The Hertzian contact stiffness is calculated as:

[0026]

[0027] The bending stiffness is calculated as:

[0028]

[0029] The axial compressive stiffness is calculated as:

[0030]

[0031] The shear stiffness is calculated as:

[0032]

[0033] The matrix deformation stiffness is calculated as follows:

[0034]

[0035] in: is the Hertzian contact stiffness; is the bending stiffness; is the axial compressive stiffness; is the shear stiffness; is the matrix deformation stiffness; 、 They are the elastic modulus and Poisson's ratio of the gear material respectively; is the position angle of the integration point; is the position angle of the meshing part; is the center angle corresponding to half a gear tooth; It is the distance from the intersection of the meshing line and the tooth symmetry line to the tooth root circle; It is the arc length corresponding to the entire tooth profile curve of the gear; 、 、 as well as are all fitting parameters.

[0036] Preferably, the specific implementation of step 4) is:

[0037] 4.1) Obtain the stiffness of any pair of meshing teeth in a gear pair caused by deformation when entering mesh and the stiffness caused by deformation when exiting mesh;

[0038] 4.2) Based on the results of step 4.1), the stiffness generated by all meshing teeth in the gear pair during meshing is connected in series to obtain the comprehensive composite stiffness of the entire gear pair.

[0039] Preferably, in step 4.1), the stiffness generated by the deformation of the meshing gear teeth when entering into meshing includes a first bending stiffness , first shear stiffness , first axial compression stiffness and the deformation stiffness of the first gear tooth , the calculation method of each stiffness is:

[0040]

[0041] The stiffness generated by the deformation of the meshing gear teeth when the meshing gear teeth exit the meshing in step 4.1) includes the second bending stiffness , second shear stiffness , Second axial compression stiffness and the deformation stiffness of the second gear tooth , the calculation method of each stiffness is:

[0042]

[0043] in: is the center angle of half a tooth of the driving gear: ; is the meshing angle of the gear; is the logarithm of the driving gear; is the relative angle of the single tooth meshing position of the driving gear, where ; is the center angle of half a tooth of the driven gear: ; is the logarithm of the driving gear; is the relative angle of the single tooth meshing position of the driven gear, where .

[0044] Preferably, the specific implementation of step 4.2) is:

[0045]

[0046] in: is the comprehensive composite stiffness of the entire gear pair, It is the stiffness generated by the deformation of the meshing teeth when they enter meshing; It is the stiffness caused by the deformation of the meshing teeth when they exit meshing.

[0047] Preferably, the specific implementation of step 5) is:

[0048] 5.1) Based on the strain energy of the gear structure parameters obtained in step 2), the total strain of the base part considering the rim and web structure is calculated. :

[0049]

[0050] 5.2) Substitute the total strain obtained in step 5.1) Introduce the comprehensive composite stiffness of the entire gear pair obtained in step 4) to calculate the gear meshing stiffness with the structural parameters introduced ; The gear meshing stiffness of the introduced structural parameters The expression is:

[0051]

[0052] in: is the strain energy of other forms of stiffness; is the matrix stiffness; is the total strain energy of the gear system; is the normal force.

[0053] Preferably, the six degrees of freedom in step 6) include the degree of freedom of the driving gear in the x direction, the degree of freedom of the driving gear in the y direction, the rotational degree of freedom of the driving gear, the degree of freedom of the driven gear in the x direction, the degree of freedom of the driven gear in the y direction, and the rotational degree of freedom of the driven gear;

[0054] The expression of the six-degree-of-freedom gear dynamic model considering the structural parameters is:

[0055]

[0056] in: is the system mass matrix; is the displacement vector; yes The first derivative of ; yes The second derivative of is the meshing damping; is the support damping; is the meshing stiffness matrix of the system, ; is the displacement projection vector; is the support stiffness; is a non-power vector; is the time-varying meshing error of the gear pair.

[0057] Preferably, the time-varying meshing error of the gear pair in step 6) is The expression is:

[0058]

[0059] in: is the base circle helix angle; is the working pressure angle; is the gear pitch deviation; is the gear tooth profile deviation;

[0060] Pitch deviation of the gear and tooth profile deviation The expressions are:

[0061]

[0062]

[0063] in: is the modulus; is the pitch circle diameter; is the meshing frequency; is the initial phase; It's time.

[0064] Beneficial effects:

[0065] The present invention provides a method for modeling aircraft gear dynamics that considers structural parameters, comprising: 1) obtaining gear structural parameters; 2) calculating the strain energy of the gear structural parameters; 3) treating the gear teeth as equivalent to cantilever beams fixed to the root circle, and calculating the stiffness generated by the deformation of the meshing teeth; 4) obtaining the composite stiffness of the entire gear pair; 5) introducing the strain energy of the gear structural parameters obtained in step 2) into the composite stiffness of the entire gear pair obtained in step 4) to obtain the gear mesh stiffness with the structural parameters incorporated; and 6) establishing a six-degree-of-freedom gear dynamic model that considers the structural parameters based on the results of step 5). The present invention incorporates the influence of structural parameters on gear mesh stiffness. Instead of treating the gear as a simple ideal rigid body, the present invention considers the influence of the rim, hub, web, and web hole in the actual gear structure on the gear transmission performance. This method allows for relatively accurate analysis of the actual gear meshing state. Furthermore, the method not only determines the influence of structural parameters on the nonlinear dynamic characteristics of the gear, but also provides a foundation and basis for the lightweight design of aircraft gears. The invention consists of three parts: In the first part, gear structural parameters are incorporated into mesh stiffness, and a formula for synthesizing mesh stiffness is derived. In the second part, leveraging the advantages of vector modeling, a gear mesh dynamics model that considers structural parameters is derived. In the third part, based on the newly established gear dynamics model, dynamic characteristics during gear meshing are simulated, analyzed, and compared using different structural parameters. Vibration acceleration response diagrams are plotted using Matlab. Finally, the proposed method is demonstrated through practical examples. This invention addresses the technical problem that existing aviation gear transmission systems fail to consider the impact of lightweight design on the meshing state of gear pairs, affecting the dynamic behavior of the gear system. Variations in structural parameters such as web thickness, rim thickness, web aperture, and number of web holes can lead to different nonlinear dynamic characteristics of gears. This invention accurately analyzes the impact of web and rim engineering design on gear dynamic behavior, while also reducing the time and cost required for the design phase of aviation power transmission systems. This provides a foundation and basis for improving the design quality and extending the service life of aviation gears during lightweighting. The gear dynamics modeling method proposed in this paper no longer uses structural parameters as fixed values. Instead, it incorporates actual parameters such as the gear rim, hub, and spoke to form a nonlinear gear meshing dynamics model. This gear meshing stiffness model accounts for both deformation during meshing and the impact of structural parameter changes on dynamic behavior. This method can be applied to simulation analysis of gear dynamics, enabling more accurate prediction of the nonlinear dynamic characteristics of aviation gear transmissions and providing theoretical support for the lightweight design of gear transmission systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a flow chart of the overall method provided by the present invention;

[0067] Figure 2This is a diagram of the gear spoke rim structure model for introducing structural parameters in the present invention;

[0068] Figure 3 It is the involute tooth profile and force diagram provided by the present invention;

[0069] Figure 4 This is a schematic diagram of the alternating meshing of single and double teeth in consideration of the change in meshing position of the present invention;

[0070] Figure 5 The invention provides an aviation gear dynamics model taking structural parameters into consideration;

[0071] Figure 6 is a graph of meshing period and meshing stiffness for different web thicknesses;

[0072] Figure 7 It is a graph of meshing period and vibration acceleration for different web thicknesses;

[0073] Figure 8 is a graph of meshing period and meshing stiffness for different rim thicknesses;

[0074] Figure 9 It is a graph of meshing period and vibration acceleration for different rim thicknesses;

[0075] Figure 10 is a graph of meshing period and meshing stiffness for different spoke apertures;

[0076] Figure 11 It is a graph of meshing period and vibration acceleration for different spoke apertures;

[0077] Figure 12 is a graph of meshing period and meshing stiffness for different numbers of spoke holes;

[0078] Figure 13 This is a graph of meshing period and vibration acceleration for different numbers of spoke holes. DETAILED DESCRIPTION

[0079] See Figure 1 The present invention provides an aviation gear dynamics modeling method considering structural parameters, comprising:

[0080] S1: Introduce the structural parameters of the gear rim, hub and spoke; combine Figure 2 As shown, these structural parameters are the tooth width of the gear , thickness of perforated spokes , hub width ;Outer diameter of the non-perforated spoke , inner diameter of the non-perforated spoke , outer diameter of the wheel hub , the inner diameter of the wheel hub ; Radius of the position of the spoke hole , radius of the spoke hole , number of spoke holes .

[0081] S2: Considering the structural differences of gears at different positions, calculate the strain energy of the rim, hub, and spoke. The specific calculation method is:

[0082] The gear rim and the spoke are divided into three parts, and the strain energy of the rim and the non-perforated spoke is calculated by formula (1): 、 :

[0083] (1)

[0084] in: is the strain energy of the gear rim; is the strain energy of the non-perforated web; is the torque borne by the gear; is the cross-sectional radius; G is the shear modulus of the gear material; is the tooth width of the gear; is the outer diameter of the non-perforated spoke; is the inner diameter of the non-perforated spoke;

[0085] The strain energy of the perforated web is calculated by formula (2): :

[0086] (2)

[0087] in: is the strain energy of the perforated spoke; is the thickness of the perforated web; is the radius of the position of the web hole; is the radius of the web hole; is the outer diameter of the wheel hub; is the arc length of the micro-circular ring that does not pass through the web hole;

[0088] The strain energy of the hub is calculated by formula (3): :

[0089] (3)

[0090] in: is the strain energy of the hub; is the inner diameter of the wheel hub; is the hub width.

[0091] S3: Based on the structural parameters of the gear, define the web thickness coefficient and rim thickness coefficient, specifically:

[0092] The web thickness coefficient is defined by formula (4): :

[0093] (4)

[0094] The web thickness coefficient is defined by formula (5): :

[0095] (5)

[0096] S4: Based on the potential energy method, the gear teeth are equivalent to cantilever beams fixed to the root circle. According to the Hertz contact stiffness, bending stiffness, axial compression stiffness, shear stiffness and matrix deformation stiffness generated by the deformation of the meshing gear teeth, and according to the relationship between strain potential energy and deformation stiffness, the calculation formulas for the deformation stiffness of the gears are derived. Specifically,

[0097] The schematic diagram of the variable cross-section cantilever beam of the involute spur gear is shown in Figure 3 Based on the idea of strain potential energy, the gear teeth are transformed into simplified cantilever beams. Under the action of force F, the gear teeth will produce Hertzian contact deformation, bending deformation, axial compression deformation, shear deformation and matrix deformation. In addition, the rim, hub and spoke plate will also deform.

[0098] Due to the corresponding stiffness generated by the deformation of meshing gear teeth, according to the relationship between strain potential energy and deformation stiffness, the calculation formula of each gear deformation stiffness can be derived, namely:

[0099] The Hertz contact stiffness is defined by equation (6): :

[0100] (6)

[0101] in, 、 They are the elastic modulus and Poisson's ratio of the gear material respectively;

[0102] When a pair of gear teeth are meshed, the various deformation potentials stored in each gear tooth are bending deformation U b , compression deformation U a , shear deformation U a ,Right now

[0103] (7)

[0104] (8)

[0105] (9)

[0106] Among them, F a =Fsinα1,Fb =Fcosα1,M=F b xF a h, , A x =2xL gear , M is the bending moment generated by the meshing force, F a 、F b is the decomposition force of the gear meshing force F in the horizontal and vertical directions, h is the horizontal distance from the current contact point to the original point, I x With A x are the area moment of inertia and cross-sectional area of the gear respectively, and x is the ordinate of the integration point at the tooth root transition curve and the involute tooth profile segment; therefore, the axial compression stiffness , bending stiffness and shear stiffness The calculation formula is:

[0107] (10)

[0108] The matrix deformation stiffness is defined by formula (11): :

[0109] (11)

[0110] in, is the position angle of the integration point; is the position angle of the meshing part; is the center angle corresponding to half a gear tooth; It is the distance from the intersection of the meshing line and the tooth symmetry line to the tooth root circle; It is the arc length corresponding to the entire tooth profile curve of the gear; 、 、 as well as are all fitting parameters.

[0111] S5: Considering the change of gear contact position and the transformation from single tooth to double tooth during meshing, the composite meshing stiffness of the superposition of various stiffnesses is calculated. Specifically:

[0112] Considering the situation where the spur gears produce single tooth and double tooth states that transform into each other during the meshing process, the schematic diagram of alternating single and double tooth meshing is shown in Figure 4 , where O1 and O2 are the rotation centers of the driving gear and the driven gear, R a1 and R a2 is the tooth tip circle radius of the driving and driven gears, R b1 and R b2 is the base circle radius of the driving and driven gears, points N1 and N2 are the theoretical engagement points, points A and D are the actual engagement points, and points B and C are the alternating engagement points of single and double teeth.

[0113] From formulas (12) and (13), the calculation formulas for the bending stiffness, shear stiffness, compression stiffness, and deformation stiffness of the gear teeth entering and exiting meshing can be obtained:

[0114] (12)

[0115] (13)

[0116] in: is the center angle of half a tooth of the driving gear: ; is the meshing angle of the gear; is the logarithm of the driving gear; is the relative angle of the single tooth meshing position of the driving gear, where ; is the center angle of half a tooth of the driven gear: ; is the logarithm of the driving gear; is the relative angle of the single tooth meshing position of the driven gear, where .

[0117] According to the rotation angle, the Hertz contact stiffness, bending stiffness, shear stiffness, compression stiffness and tooth deformation stiffness between each pair of meshing teeth are connected in series, and the comprehensive composite stiffness calculation formula of the entire gear pair is finally obtained:

[0118] (14)

[0119] S6: Considering the relationship between gear pitch deviation and tooth profile deviation, the time-varying synthetic error function e of the gear transmission system is defined, and the structural parameters are introduced into the total gear meshing stiffness, specifically:

[0120] The time-varying composite error of the gear reflects the gear's ability to resist deformation in the direction of the meshing line and is a key indicator for evaluating the dynamic performance of the gear system. The gear pitch deviation e p and tooth profile deviation e α Defined as:

[0121] (15)

[0122] (16)

[0123] in, is the modulus; is the pitch circle diameter; is the meshing frequency; is the initial phase; is time; simply transform the gear pitch deviation and tooth profile deviation along the circumferential direction and the meshing line direction to synthesize the gear comprehensive error Defined as:

[0124] (17)

[0125] in, is the base circle helix angle; is the working pressure angle;

[0126] Considering the total strain of the base part under the rim and web structure Defined as:

[0127] (18)

[0128] Introducing gear structural parameters into the total meshing stiffness k of spur gears m Calculation formula:

[0129] (19)

[0130] in, is the strain energy of other forms of stiffness; is the matrix stiffness; is the total strain energy of the gear system; is the normal force.

[0131] S7: Based on the advantages of vector modeling, displacement projection vectors are introduced to achieve the conversion between the deformation of the meshing line and the generalized displacement. The gears are regarded as rigid rotors. Each gear has three degrees of freedom. A gear dynamics model considering structural parameters is established. Specifically:

[0132] In step S7, a six-degree-of-freedom gear dynamics model considering structural parameters is established. The gear meshing stiffness with structural parameters introduced needs to be substituted into the contact model. The gear contact model can be equivalent to the contact between two base cylinders connected by a spring-damper system, such as Figure 5 In the gear contact model, each spur gear is considered to have three degrees of freedom, including two translational degrees of freedom and one rotational degree of freedom, that is, the generalized displacement vector of the system is δ=[x1 y1 w1 x2 y2 w2] T .

[0133] Recombination Figure 5 As shown in the figure, a six-degree-of-freedom gear dynamic model considering structural parameters is established, including:

[0134] The motion differential equation of the gear system considering the structural parameters is:

[0135] (20)

[0136] Where m i is the gear mass, δ i is the displacement vector, k m is the meshing stiffness, q i is the displacement projection vector, k bi is the support stiffness, F is the non-active force vector, e(t) is the time-varying meshing error of the gear pair, and the subscripts i = 1, 2, …, 6 represent the six degrees of freedom of the gear, which are not independent.

[0137] Introducing meshing damping C m and support damping C b ,ξ m ,ξ s are the meshing damping ratio and the support damping ratio, respectively, which can be expressed in matrix form as follows:

[0138] (twenty one)

[0139] in: is the system mass matrix; is the displacement vector; yes The first derivative of ; yes The second derivative of is the meshing damping; is the support damping; is the meshing stiffness matrix of the system, ; is the displacement projection vector; is the support stiffness; is a non-power vector; is the time-varying meshing error of the gear pair.

[0140] S8: Combined with the web thickness coefficient and rim thickness coefficient in S3, Matlab tools are used to simulate and analyze the influence of structural parameters on the dynamic characteristics of aviation gears.

[0141] In step S8, Matlab is used to simulate and analyze the influence of structural parameters on the dynamic characteristics of aviation gears, including:

[0142] According to the aviation gear transmission design manual, the gear module m=3.5, the number of teeth of the driving gear z1=35, the number of teeth of the driven gear z2=34, the rated speed n=8428r / min, the rated meshing frequency f=4916Hz, the input power P=333.55kW, the gear material is 16Cr steel, and the gear density ρ=7.86×10 3 kg / m 3 , Young's modulus E=2.06×10 5MPa, and the parameters were substituted into the aviation gear dynamics model considering the structural parameters established by Matlab tools, and different structural parameters were input to conduct theoretical simulation analysis and comparison of the gear dynamic characteristics.

[0143] Comparison of the dynamic characteristics of aviation gears under different structural parameters obtained based on the modeling method of the present invention Figures 6 to 13 As shown in the figure, changing the gear's web thickness, rim thickness, web aperture, and number of web holes results in a significant nonlinear change in the ratio of the gear mesh stiffness peak-to-peak to the average value, and a significant difference in vibration acceleration. Increasing web thickness, rim thickness, decreasing web aperture, and decreasing web hole number effectively increase the gear's matrix stiffness, thereby increasing its average mesh stiffness and affecting the gear's vibration acceleration response. Comparing the root mean square (RMS) and kurtosis of vibration acceleration under varying structural parameter variations reveals that the RMS value is more sensitive to changes in structural parameters than the kurtosis. The order of influence of each structural parameter on gear vibration is: web thickness > number of web holes > web aperture > rim thickness.

[0144] For aviation gears, the gear meshing stiffness and vibration acceleration under different spoke and rim structural parameters vary greatly. The aviation gear dynamics modeling method proposed in this invention takes into account the influence of changes in gear structural parameters and can more realistically reflect the meshing characteristics of high-speed, lightweight and heavy-loaded gears, thereby obtaining more accurate dynamic behavior and providing support and foundation for gear lightweight design.

Claims

1. A method for dynamic modeling of aviation gears considering structural parameters, characterized by: The following steps are involved: 1) Obtaining gear structural parameters; the gear structural parameters include the gear rim, hub, and spoke; 2) Calculate the strain energy of gear structural parameters; The specific process is: The strain energy of the gear structural parameters includes the strain energy of the gear rim, the strain energy of the non-perforated spoke plate, the strain energy of the perforated spoke plate and the strain energy of the hub; The strain energy of the gear rim and the strain energy of the non-perforated web are calculated as follows: in: is the strain energy of the gear rim; is the strain energy of the non-perforated web; is the torque borne by the gear; is the cross-sectional radius; G is the shear modulus of the gear material; is the tooth width of the gear; is the outer diameter of the non-perforated spoke; is the inner diameter of the non-perforated spoke; The strain energy of the perforated web is calculated as follows: in: is the strain energy of the perforated spoke; is the thickness of the perforated web; is the location radius of the web hole; is the radius of the web hole; is the outer diameter of the wheel hub; is the arc length of the micro-circular ring that does not pass through the web hole; The strain energy of the hub is calculated as: in: is the strain energy of the hub; is the inner diameter of the wheel hub; is the hub width; 3) Equivalently treat the gear teeth as cantilever beams fixed to the tooth root circle, and calculate the stiffness caused by the deformation of the meshing gear teeth; 4) Obtain the comprehensive composite stiffness of the entire gear pair ; 5) The strain energy of the gear structural parameters obtained in step 2) is introduced into the comprehensive synthetic stiffness of the entire gear pair obtained in step 4) to obtain the gear meshing stiffness with the structural parameters introduced. The specific process is as follows: 5.1) Based on the strain energy of the gear structure parameters obtained in step 2), the total strain of the base part considering the rim and web structure is calculated. : 5.2) Substitute the total strain obtained in step 5.1) Introduce the comprehensive composite stiffness of the entire gear pair obtained in step 4) to calculate the gear meshing stiffness with the structural parameters introduced ; The gear meshing stiffness of the introduced structural parameters The expression is: in: is the strain energy of other forms of stiffness; is the matrix stiffness; is the total strain energy of the gear system; is the normal force; 6) Based on the results of step 5), a six-degree-of-freedom gear dynamics model considering structural parameters is established.

2. The aviation gear dynamics modeling method considering structural parameters according to claim 1 is characterized in that: The stiffness generated by the deformation of the meshing gear teeth in step 3) includes Hertzian contact stiffness, bending stiffness, axial compression stiffness, shear stiffness, and matrix deformation stiffness; The Hertzian contact stiffness The calculation method is: The bending stiffness The calculation method is: The axial compression stiffness The calculation method is: The shear stiffness The calculation method is: The matrix deformation stiffness The calculation method is: in: is the Hertzian contact stiffness; is the bending stiffness; is the axial compressive stiffness; is the shear stiffness; is the matrix deformation stiffness; 、 They are the elastic modulus and Poisson's ratio of the gear material respectively; is the position angle of the integration point; is the position angle of the meshing part; is the center angle corresponding to half a gear tooth; It is the distance from the intersection of the meshing line and the tooth symmetry line to the tooth root circle; It is the arc length corresponding to the entire tooth profile curve of the gear; 、 、 as well as are all fitting parameters.

3. The method for dynamic modeling of aviation gears considering structural parameters according to claim 2, characterized in that: The specific implementation of step 4) is: 4.1) Obtain the stiffness of any pair of meshing teeth in a gear pair caused by deformation when entering meshing and the stiffness caused by deformation when exiting meshing; 4.2) Based on the results of step 4.1), the stiffness generated by all meshing teeth in the gear pair during meshing is connected in series to obtain the comprehensive composite stiffness of the entire gear pair.

4. The method for dynamic modeling of aviation gears considering structural parameters according to claim 3, characterized in that: The stiffness generated by the deformation of the meshing gear teeth when entering meshing in step 4.1) includes the first bending stiffness , first shear stiffness , first axial compression stiffness And the deformation stiffness of the first gear tooth , the calculation method of each stiffness is: The stiffness generated by the deformation of the meshing gear teeth when the meshing gear teeth exit the meshing in step 4.1) includes the second bending stiffness , second shear stiffness , Second axial compression stiffness and the deformation stiffness of the second gear teeth , the calculation method of each stiffness is: in: is the center angle of half a tooth of the driving gear: ; is the meshing angle of the gear; is the logarithm of the driving gear; is the relative angle of the single tooth meshing position of the driving gear, where ; is the center angle of half a tooth of the driven gear: ; is the logarithm of the driving gear; is the relative angle of the single tooth meshing position of the driven gear, where .

5. The method for dynamic modeling of aviation gears considering structural parameters according to claim 4, characterized in that: The specific implementation of step 4.2) is: in: is the comprehensive composite stiffness of the entire gear pair, It is the stiffness generated by the deformation of the meshing teeth when they enter meshing; It is the stiffness caused by the deformation of the meshing teeth when they exit meshing.

6. The method for dynamic modeling of aviation gears considering structural parameters according to claim 5, characterized in that: The six degrees of freedom in step 6) include the degree of freedom of the driving gear in the x-direction, the degree of freedom of the driving gear in the y-direction, the rotational degree of freedom of the driving gear, the degree of freedom of the driven gear in the x-direction, the degree of freedom of the driven gear in the y-direction, and the rotational degree of freedom of the driven gear; The expression of the six-degree-of-freedom gear dynamic model considering the structural parameters is: in: is the system mass matrix; is the displacement vector; yes The first derivative of ; yes The second derivative of is the meshing damping; is the support damping; is the meshing stiffness matrix of the system, ; is the displacement projection vector; is the support stiffness; is a non-power vector; is the time-varying meshing error of the gear pair.

7. The method for dynamic modeling of aviation gears considering structural parameters according to claim 6, characterized in that: The time-varying meshing error of the gear pair in step 6) The expression is: in: is the base circle helix angle; is the working pressure angle; is the gear pitch deviation; is the gear tooth profile deviation; Pitch deviation of the gear and tooth profile deviation The expressions are: in: is the modulus; is the pitch circle diameter; is the meshing frequency; is the initial phase; It's time.

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