Design method of additional damping ring for aero thin-webbed gear

Abstract

The application provides a design method of an additional damping ring of an aero thin-webbed gear. The design method comprises the steps of determining initial parameters, obtaining an energy dissipation model of the gear after the additional damping ring, checking the initial parameters and adjusting the design parameters. The method can be used to determine the energy dissipation parameters of the damping ring corresponding to the actual amplitude and frequency of the thin-webbed gear with different numbers of pitch diameters and harmful resonance points, and then determine the contact pressure. By comparing whether the system amplitude ratio and the gear measuring point stress ratio meet the conditions, the damping performance of the damping ring can be effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of damping vibration, in particular to a design method of an additional damping ring of an aviation thin-webbed plate gear. BACKGROUND

[0002] Due to strict weight restrictions on aviation gears, thin-webbed plate structures are widely used in gear design. Aviation thin-webbed plate gears have the characteristics of small weight and high speed, but the problem of vibration fatigue failure is more prominent. When the natural frequency of the thin-webbed plate gear pitch diameter vibration is the same as the excitation frequency, a traveling wave resonance will be excited, and the resonance point produced thereby is harmful, so the thin-webbed plate gears with different pitch diameters and harmful resonance points cannot achieve good vibration reduction effect without parameter design.

[0003] Therefore, it is extremely important to develop an additional damping ring structure parameter to achieve the best vibration reduction effect. SUMMARY

[0004] The purpose of the present application is to provide a design method of an additional damping ring of an aviation thin-webbed plate gear to solve the problems in the prior art.

[0005] The technical solution adopted to achieve the purpose of the present application is as follows: a design method of an additional damping ring of an aviation thin-webbed plate gear, the aviation thin-webbed plate gear comprising a through-hole shaft and a thin-wall web plate. The thin-wall web plate is arranged circumferentially on the outer wall of the through-hole shaft. A gear rim is arranged on the circumference of the thin-wall web plate. An inner wall of the gear rim is provided with a gear slot. The gear slot is an annular groove. A damping ring is installed in the gear slot. The original radius of the damping ring is greater than the installed radius, and the original axial width is greater than the installed axial width. The normal force is provided by the tension generated by compression, so that the damping ring tightly contacts the gear slot. When the gear vibrates, relative movement is generated between the contact joint of the damping ring and the gear slot due to the incoordination relationship, and then damping effect is generated to achieve the purpose of vibration reduction. The design method of the additional damping ring of the aviation thin-webbed plate gear comprises the following steps:

[0006] 1) Determine the initial parameters. According to the influence of the damping ring design and installation parameters on the vibration reduction performance, the initial installation depth d0 of the damping ring, the initial radial thickness h r0 and the axial width h a0 of the damping ring are determined.

[0007] 2) Obtain the energy dissipation model of the gear with the additional damping ring from the initial parameters, and check the initial parameters. If the equivalent amplitude ratio η Amp0 of the energy dissipation model under the initial parameter design does not meet the design requirements, step 3) is entered. If the equivalent amplitude ratio η Amp0 of the energy dissipation model under the initial parameter design meets the design requirements, the design is completed, and the final structure parameters of the additional damping ring are obtained.

[0008] 3) Adjust design parameters. Adjust the axial width h of the damping ring. a If the axial width h a The maximum limit for the axial dimension of the gear has been reached, and the equivalent amplitude ratio η Amp0 If the requirements are still not met, adjust the installation depth and adjust the radial thickness accordingly.

[0009] Furthermore, the damping ring installation depth limit is determined based on the tooth root strength constraint, thereby determining the initial installation depth d0 of the damping ring. In the initial design, the neutral axis of the damping ring is placed within the tooth groove, and the initial radial thickness h of the damping ring is determined based on the initial installation depth d0. r0 .

[0010] Furthermore, determine the initial axial width h. a0 =1.2h r0 .

[0011] Furthermore, in step 2), the initial contact pressure is determined based on the harmful resonance amplitude and frequency.

[0012] Furthermore, in step 2), the dynamics of the gear and the additional damping are analyzed, and the frictional dissipation energy J between the damping ring and the gear is defined as:

[0013] J=||f·Δu|| (1)

[0014] In the formula, f is the gear force acting on the damping ring, and Δu is the mutual sliding trajectory between the gear and the damping ring.

[0015] Without an added damping ring, the dynamic equation of the gear is expressed as:

[0016]

[0017] In the formula, M is the gear's mass matrix, C is the gear's damping matrix, K is the gear's stiffness matrix, and F is the gear's external excitation. f is the amplitude of the time gradient of the gear vibration trajectory. r-g It is the frictional excitation of the gear by the damping ring.

[0018] When the gear is not fitted with a damping ring, the energy conservation equation for the vibration process is expressed as:

[0019]

[0020] In the formula, Q represents the amplitude of the time gradient of the vibration trajectory of the damping ring without the damping ring attached. F This represents the input energy to the gear from an external excitation. Under fixed frequency and amplitude vibration conditions, it is expressed as:

[0021]

[0022] After adding a damping ring, the gear experiences energy dissipation due to dry friction between the gear and the damping ring. The dynamic response equation at a certain time t within one period is extended to:

[0023]

[0024] In the formula, This represents the amplitude of the time gradient of the vibration trajectory of the damping ring after the addition of the damping ring. The time gradient of energy dissipation due to the addition of a damping ring to the gear. Under fixed frequency and amplitude vibration conditions, it is expressed as:

[0025]

[0026] In the formula, u i (t) represents the mode shape without damping. The equation for the relative sliding trajectory after adding a damping ring is expressed as:

[0027]

[0028] Equation (7) yields the energy consumed by the friction between the gear and the additional damping ring.

[0029] Furthermore, regarding the equivalent amplitude ratio η Amp The verification satisfies the following objective function:

[0030]

[0031] In the formula, B int σ represents the initial amplitude of the system without a damping ring. int B represents the initial measuring point stress of the system without a damping ring. new σ is the initial amplitude of the system when a damping ring is added. new The initial stress at the measuring point of the system when the damping ring is added.

[0032] Furthermore, in step 3), if F is obtained based on the contact pressure... c o p -B new / B int Curve and F c o p -σ new / σ int If the curves intersect, the intersection point meets the equivalent amplitude requirement. If the curves do not intersect, the axial width h is used as the reference. a0 The following boundary conditions are determined as variable parameters:

[0033] h a0 ≤h max (9)

[0034] In the formula, hmax is the maximum value of the axial dimension of the gear.

[0035] If the curves intersect under the boundary condition of formula (9), the equivalent amplitude ratio requirement is met. If the curves still do not intersect, the rim thickness SR of the gear is taken as a variable parameter to adjust the installation depth d and the radial thickness h r , and the following boundary condition is determined:

[0036] SR≤SR max (10)

[0037] In the formula, SR max is the maximum value of the rim thickness of the gear.

[0038] If the two curves intersect, the intersection point meets the equivalent amplitude ratio requirement, and the final structural parameters of the additional damping ring are obtained.

[0039] Further, step 3) specifically includes the following sub-steps:

[0040] 3.1) According to the maximum value h max of the axial dimension of the gear, the axial width h a of the additional damping ring is adjusted. It is checked whether the equivalent amplitude ratio η Amp0 meets the requirement. If it meets the requirement, the design is completed, otherwise step 3.2) is entered to continue adjusting the parameters.

[0041] 3.2) By changing the rim thickness SR of the gear, the installation depth d and the radial thickness h r of the additional damping ring are repeatedly adjusted until the equivalent amplitude ratio meets the requirement.

[0042] 3.3) The design is completed, and the final installation depth d, the radial thickness h r , the axial width h a of the additional damping ring and the contact pressure are obtained.

[0043] The technical effects of the present application are self-evident:

[0044] A. The energy dissipation parameters of the damping ring corresponding to the actual amplitude and frequency of the thin-webbed gear with different numbers of pitch diameters and harmful resonance points can be determined, and then the contact pressure can be determined;

[0045] B. The equivalent amplitude ratio is proposed as an evaluation index of the damping ring vibration reduction energy. By comparing whether the system amplitude ratio and the gear stress ratio at the measuring point meet the conditions, the damping ring vibration reduction performance can be effectively improved;

[0046] C. The parameters can be adjusted to make the contact pressure and the equivalent amplitude ratio meet the design requirements, so that the energy dissipation of the damping ring is maximized, the vibration reduction effect is optimal, the stress level is effectively reduced, the harm of the traveling wave vibration to the thin-webbed gear is reduced, and the stability of the gear transmission is improved. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 Dynamics analysis of gear and additional damping;

[0048] Figure 2 Flow chart for designing additional damping ring for gear;

[0049] Figure 3 Schematic diagram of structure size corresponding to each parameter;

[0050] Figure 4 Cross-sectional view of bevel gear;

[0051] Figure 5 Contact pressure of bevel gear shaft under different damping ring design parameters;

[0052] Figure 6 Cross-sectional view of spur gear;

[0053] Figure 7 Contact pressure of spur gear shaft under different damping ring design parameters.

[0054] In the figure: bevel gear damping ring 1, bevel gear 2, spur gear damping ring 3, spur gear 4. DETAILED DESCRIPTION

[0055] The application will be further described below in conjunction with examples, but should not be understood as limiting the above-mentioned subject matter of the application to the following examples. Various substitutions and modifications can be made according to ordinary technical knowledge and conventional means in the art without departing from the above-mentioned technical idea of the application, and all should be included in the protection scope of the application.

[0056] Example 1:

[0057] The embodiment discloses a design method of an additional damping ring for an aviation thin-webbed plate gear, which comprises gear teeth, a rim, and a thin-webbed plate, etc. An annular groove is arranged on the inner wall of the gear rim, and a damping ring is installed in the groove. The original radius of the damping ring is greater than the installed radius, and the original axial width is greater than the installed axial width, and the generated tension provides a normal force to tightly adhere to the gear slot. When the gear vibrates, relative movement is generated by the movement of the contact joint between the damping ring and the gear slot, and then damping effect is generated, so as to achieve the purpose of vibration reduction. Referring to Figure 2 , the design method of the additional damping ring for the aviation thin-webbed plate gear comprises the following steps:

[0058] 1) Determine the initial parameters. According to the influence of the damping ring design and installation parameters on the vibration reduction performance, the initial installation depth d0 of the damping ring, the initial radial thickness h r0 and the axial width h a0 of the damping ring are determined. Referring to Figure 3, the initial installation depth d0 of the damping ring is determined according to the root strength limit, and the initial radial thickness h of the damping ring is determined according to the initial installation depth d0 of the damping ring r0 . The initial axial width h a0 =1.2h r0 .

[0059] 2) The energy dissipation model of the gear with the additional damping ring is obtained from the initial parameters, and the initial parameters are verified. If the equivalent amplitude ratio η Amp0 of the energy dissipation model under the initial parameter design does not meet the design requirements, step 3) is entered. If the equivalent amplitude ratio η Amp0 of the energy dissipation model under the initial parameter design meets the design requirements, the design is completed, and the final structure parameters of the additional damping ring are obtained.

[0060] Referring to Figure 1 , the dynamics of the gear and the additional damping are analyzed, and the frictional energy dissipation J between the damping ring and the gear is defined as:

[0061] J=||f·Δu|| (1)

[0062] In the formula, f is the force acting on the damping ring, and Δu is the mutual sliding track between the gear and the damping ring.

[0063] The dynamics equation of the gear without the additional damping ring is represented as:

[0064]

[0065] In the formula, M is the mass matrix of the gear, C is the damping matrix of the gear, K is the stiffness matrix of the gear, F is the external excitation of the gear, is the amplitude of the time gradient of the vibration track of the gear, and f r-g is the friction excitation of the damping ring to the gear.

[0066] The energy conservation equation of the vibration process of the gear without the additional damping ring is represented as:

[0067]

[0068] In the formula, is the amplitude of the time gradient of the vibration track of the damping ring without the additional damping ring, and Q F is the input energy of the external excitation to the gear. Under the fixed frequency and amplitude vibration working condition, it is represented as:

[0069]

[0070] Gear and damper ring generate energy dissipation by friction. The dynamic response equation at time t in a cycle is expressed as:

[0071]

[0072] where, is the amplitude of time gradient of damper ring vibration trajectory after adding damper ring, is the time gradient of energy dissipation of gear adding damper ring. It is expressed as:

[0073]

[0074] where, u i (t) is the vibration mode without adding damper. The relative sliding trajectory equation after adding damper ring is expressed as:

[0075]

[0076] The energy dissipated by friction between gear and added damper ring is obtained by equation (7).

[0077] The initial contact pressure is determined according to the harmful resonance amplitude and frequency. The equivalent amplitude ratio η Amp The objective function is checked as follows:

[0078]

[0079] where, B int is the initial amplitude of system without adding damper ring, σ int is the initial stress of system at measuring point without adding damper ring, B new is the initial amplitude of system after adding damper ring, σ new is the initial stress of system at measuring point after adding damper ring.

[0080] 3) Adjust the design parameters. Adjust the axial width h a of damper ring. If the axial width h a has reached the maximum limit of gear axial size, the equivalent amplitude ratio η Amp0 still cannot meet the requirements, then adjust the installation depth and the corresponding radial thickness. If the F c o p -B new / B int curve and the F c o p -σ new / σ int curve intersect, the intersection point meets the equivalent amplitude ratio requirement. If the curves do not intersect, the axial width h a0 of damper ring is adjusted.The boundary condition is determined as follows:

[0081] h a0 ≤h max (9)

[0082] where h max is the maximum value of the axial dimension of the gear.

[0083] If the curves intersect under the boundary condition of equation (9), the equivalent amplitude ratio requirement is met. If the curves still do not intersect, the rim thickness SR of the gear is taken as a variable parameter to adjust the installation depth d and the radial thickness h r , and the following boundary condition is determined:

[0084] SR≤SR max (10)

[0085] where SR max is the maximum value of the rim thickness of the gear.

[0086] If the two curves intersect, the intersection point meets the equivalent amplitude ratio requirement, and the final structural parameters of the additional damping ring are obtained.

[0087] Step 3) specifically includes the following sub-steps:

[0088] 3.1) According to the maximum value of the axial dimension of the gear h max , the axial width h a of the additional damping ring is adjusted. It is checked whether the equivalent amplitude ratio η Amp0 meets the requirement. If it does, the design is completed, otherwise, it proceeds to step 3.2) to continue adjusting the parameters.

[0089] 3.2) If necessary, the rim thickness of the gear is increased to provide the required installation depth. By changing the rim thickness SR of the gear, the installation depth d and the radial thickness h r of the additional damping ring are repeatedly adjusted until the equivalent amplitude ratio meets the requirement.

[0090] 3.3) The design is completed, and the final installation depth d, radial thickness h r , axial width h a and contact pressure of the additional damping ring are obtained.

[0091] Example 2:

[0092] The main steps of this example are the same as those of Example 1, wherein the limit of the tooth root strength (the distance from the contact interface to the tooth root is greater than 2.5m n) to determine the damping ring installation depth limit and then reasonably determine the initial installation depth. After determining the initial installation depth, in order to make full use of the tooth groove depth and consider the lightweight of the damping ring, the neutral axis of the damping ring is placed in the tooth groove during initial design, and then the initial radial thickness can be determined according to the initial installation depth. After determining the initial radial thickness, since the damping ring with a "wide rectangular" cross section has better damping performance, while considering the lightweight of the damping structure and minimizing the modification of the gear structure, the initial axial width is determined as 1.2 times the radial thickness.

[0093] Embodiment 3:

[0094] The main steps of this embodiment are the same as those of Embodiment 1. It is determined that the maximum amplitude of the bevel gear 2 during transmission is 11.35 μm, the vibration direction is axial, and the corresponding excitation frequency is 7269 Hz. Since the modulus of the bevel gear 2 is 3, according to the strength limit requirement of the tooth root, the contact interface distance between the damping ring and the tooth root should be greater than 7.5 mm. The structural diagram of the bevel gear 2 is shown in Figure 4 From the structural diagram of the bevel gear 2, it can be seen that the bevel gear damping ring 1 can be installed on the large end face of the bevel gear close to the outer edge portion of the end face. Since the outer edge radius of the large end face of the bevel gear 2 is 59.5 mm, when the axial width of the bevel gear damping ring 1 is designed to be 4 mm, the radial thickness is designed to be 3 mm, and the contact radius is 56 mm, the distance between the damping ring groove and the tooth root circle of the gear is about 8 mm, and the minimum distance between the damping ring groove and the tooth root circle is 8.4 mm, which meets the above strength limit requirement.

[0095] Based on the above analysis, for the bevel gear 2, the installation depth is designed to be 3 mm, the axial width of the bevel gear damping ring 1 is 4 mm, and the initial contact radius is 56 mm. Among them, the gear modulus m n is 3, the maximum amplitude is 11.35 μm, and the corresponding excitation frequency is 7269 Hz. The friction coefficient μ of the bevel gear damping ring 1 is 0.1, the material density is 7860 kg / m 3 , the material elastic modulus is 210 GPa, and the material Poisson's ratio is 0.3.

[0096] Based on the above determination of the central driven bevel gear additional damping ring parameters, the parameter design and determination process of the damping ring is divided into two stages, as shown in Figure 5 The specific implementation process is as follows:

[0097] (1) The first stage, based on the established damping ring energy dissipation model and the proposed final contact pressure determination method, the contact pressure of the initial parameters is 5.49 MPa, as shown in Figure 2 At this time, the equivalent amplitude ratio is 0.61, that is, the amount of amplitude drop at this time is 39%, so it does not meet the requirements;

[0098] (2) The second stage, on the basis of the initial design parameters, the radial thickness of the damping ring is increased to 4 mm while the change of the gear structure is minimized. According to the final contact pressure determination method of the damping ring, the contact pressure at this time is 6.25 MPa, the equivalent amplitude ratio is 0.48, and the amplitude reduction at this time is 52%, thus still meeting the requirements.

[0099] Therefore, based on the above design process, the final installation depth of the gear 1 is determined to be 3 mm, the outer surface radius of the damping ring is 56 mm, the installation axial width is 4 mm, the radial thickness is 4 mm, and the final contact pressure of the damping ring is 6.25 MPa.

[0100] Example 4:

[0101] The main steps of this embodiment are the same as those of Example 1, wherein the amplitude of the spur gear 4 in the transmission process is 1.22 μm, the vibration direction is axial, and the corresponding excitation frequency is 6063 Hz. Since the module of the spur gear 4 is 3, according to the strength limit requirement of the gear tooth root, the distance between the contact interface of the damping ring and the gear tooth root should be greater than 7.5 mm. The structural diagram of the spur gear 4 is shown in Figure 6 From the structural diagram of the spur gear 4, it can be seen that the spur gear damping ring 3 can be installed on the large end face of the spur gear 4 close to the outer edge portion of the end face. When the axial width of the spur gear damping ring 3 is designed to be 3 mm, the radial thickness is designed to be 2 mm, and the contact radius is 50 mm, the distance between the damping ring groove and the gear tooth root circle is about 9.5 mm, which meets the above strength limit requirement.

[0102] Based on the above analysis, for the spur gear 4, the installation depth is designed to be 2 mm, the axial width of the spur gear damping ring 3 is 2 mm, and the initial contact radius is 50 mm. The gear module m n is 3, the maximum amplitude is 1.22 μm, and the corresponding excitation frequency is 6063 Hz. The friction coefficient μ of the spur gear damping ring 3 is 0.1, the material density is 7860 kg / m 3 , the material elastic modulus is 210 GPa, and the material Poisson's ratio is 0.3.

[0103] Based on the above determined parameters of the gear 4 with the additional damping ring, the parameter determination process of the damping ring is divided into three stages, as shown in Figure 7 The specific implementation process is as follows:

[0104] (1) The first stage, based on the established damping ring energy dissipation model and the proposed contact pressure design method, the initial contact pressure at the initial parameters is determined to be 3.61 MPa, as shown in Figure 7 At this time, the equivalent amplitude ratio is 0.65, and the amplitude reduction at this time is 35%, thus not meeting the requirements;

[0105] (2) The second stage, on the basis of the initial design parameters, on the basis of ensuring the minimum change of gear structure, the radial thickness of the damping ring is increased to 3mm, according to the determination method of the final contact pressure of the damping ring, the final contact pressure at this time is 3.67MPa, the equivalent amplitude ratio is 0.60, that is, the amplitude reduction at this time is 40%, so it still does not meet the requirements;

[0106] (3) The third stage, on the basis of the parameters of the second stage, the axial width of the damping ring is expanded to 3mm, and then the contact pressure is obtained as 3.85MPa, the equivalent amplitude ratio at this time is 0.47, the amplitude reduction of the gear after adding the damping ring at this time is 53%, which meets the design requirements.

[0107] Therefore, based on the above parameter design process, the final installation depth of the spur gear 4 is determined as 2mm, the outer surface radius of the damping ring is 50mm, the installation axial width is 3mm, the radial thickness is 3mm, and the final contact pressure of the damping ring is 3.85MPa.

Claims

1. A method for designing an additional damping ring for an aero thin-webbed gear, characterized in that: The aviation thin-webbed gear includes gear teeth, a rim and thin-webbed spokes; an annular groove is arranged on the inner wall of the gear rim; a damping ring is installed in the annular groove; the original radius of the damping ring is greater than the radius after installation, and the original axial width is greater than the axial width after installation; the damping ring is tightly attached to the gear slot by the normal force provided by the tension generated by compression; when the gear vibrates, relative movement is generated by the incoordination between the contact joint surfaces of the damping ring and the gear slot, thereby generating damping effect and achieving the purpose of vibration reduction; The design method of the additional damping ring of the aviation thin-webbed gear comprises the following steps: 1) Determine the initial parameters; according to the influence of the damping ring design and installation parameters on the damping performance, determine the initial installation depth d0 of the damping ring, the initial radial thickness h of the damping ring r0 and the axial width h a0 ; 2) get the energy dissipation model of the gear with the additional damping ring from the initial parameters, check the initial parameters; if the equivalent amplitude ratio η of the energy dissipation model under the initial parameter design does not meet the design requirement, go to step 3); if the equivalent amplitude ratio η of the energy dissipation model under the initial parameter design meets the design requirement, complete the design and get the final structure parameters of the additional damping ring; in step 2), the dynamics of the gear and the additional damping are analyzed, and the frictional energy dissipation J between the damping ring and the gear is defined as: Amp0 does not meet the design requirement, go to step 3); if the equivalent amplitude ratio η of the energy dissipation model under the initial parameter design meets the design requirement, complete the design and get the final structure parameters of the additional damping ring; in step 2), the dynamics of the gear and the additional damping are analyzed, and the frictional energy dissipation J between the damping ring and the gear is defined as: Amp0 does not meet the design requirement, go to step 3); if the equivalent amplitude ratio η of the energy dissipation model under the initial parameter design meets the design requirement, complete the design and get the final structure parameters of the additional damping ring; in step 2), the dynamics of the gear and the additional damping are analyzed, and the frictional J = ||f·Δu|| (1) In the formula, f is the gear force borne by the damping ring, and Δu is the mutual sliding track between the gear and the damping ring; When the gear is not additionally provided with the damping ring, the dynamic equation of the gear is represented as: where M is the mass matrix of the gear, C is the damping matrix of the gear, K is the stiffness matrix of the gear, F is the external excitation of the gear, is the amplitude of the time gradient of the gear vibration trajectory, f r-g is the friction excitation of the damper ring to the gear; When the gear is not additionally provided with the damping ring, the energy conservation equation of the vibration process of the gear is represented as: wherein Q is the amplitude of the time gradient of the vibration trajectory of the damper ring without the addition of the damper ring, Q F is the input energy of the external excitation to the gear; in the fixed frequency and amplitude vibration working condition, it is represented as: After the gear is additionally provided with the damping ring, energy dissipation is generated between the gear and the damping ring due to mutual dry friction; the dynamic response equation at a certain time t in a period is extended and represented as: wherein, is the amplitude of the time gradient of the vibration trajectory of the damping ring after the addition of the damping ring, is the time gradient of the energy dissipation of the gear with the addition of the damping ring; under the condition of fixed frequency and amplitude vibration, it is represented as: wherein u i (t) is the mode shape without added damping; the equation of the relative sliding trajectory after the addition of the damping ring is given by Through equation (7), the energy consumed by the mutual friction between the gear and the additional damping ring is obtained; 3) Adjust design parameters; adjust the axial width h of the damping ring. a If the axial width h a The maximum limit for the axial dimension of the gear has been reached, and the equivalent amplitude ratio η Amp0 If the requirements are still not met, adjust the installation depth and adjust the radial thickness accordingly; if the F is obtained based on the contact pressure... cop -B new / B int Curve and F cop -σ new / σ int If the curves intersect, the intersection point meets the equivalent amplitude requirement; if the curves do not intersect, the axial width h is used as the reference. a0 The following boundary conditions are determined as variable parameters: h a0 ≤h max (9) wherein h max is the maximum value of the gear axial dimension; If the curves intersect under the boundary condition of formula (9), the equivalent amplitude ratio requirement is met; if the curves still do not intersect, the rim thickness SR of the gear is taken as a variable parameter to adjust the installation depth d and the radial thickness h r and the following boundary conditions are determined: SR < SR max (10) wherein SR max is the maximum value of the rim thickness of the gear If the two curves intersect, the intersection point meets the equivalent amplitude ratio requirement, thereby obtaining the final structure parameters of the additional damping ring. Step 3) specifically comprises the following sub-steps: 3.1) According to the maximum value h of the axial dimension of the gear max Adjust the axial width h of the additional damping ring a Check whether the equivalent amplitude ratio η Amp0 meets the requirements; if it does, the design is complete, otherwise go to step 3.2) to continue adjusting the parameters; 3.2) By changing the rim thickness SR of the gear, repeatedly adjust the installation depth d and radial thickness h of the additional damping ring. r until the equivalent amplitude ratio meets the requirements; 3.3) Final installation depth d, radial thickness h and contact pressure of the additional damping ring are determined r axial width h a and contact pressure are determined.

2. The method of designing an additional damping ring for an aero pinion gear as recited in claim 1, wherein: The damping ring installation depth limit value is determined according to the root strength limit, and then the damping ring initial installation depth d0 is determined; the neutral axis of the damping ring is placed in the tooth groove during initial design, and then the damping ring initial radial thickness h is determined according to the damping ring initial installation depth d0 r0 .

3. The method of designing an additional damping ring for an aero pinion gear as recited in claim 1, wherein: determining an initial axial width h a0 = 1.2h r0 .

4. The method of claim 1, wherein: In step 2), the initial contact pressure is determined according to the harmful resonance amplitude and frequency.

5. The method of designing an additional damping ring for an aero thin-plate pinion gear according to claim 1, wherein, Equivalent amplitude ratio η Amp The check satisfies the following objective function: where B int is the initial amplitude of the system without damping ring, σ int is the initial stress at the measuring point of the system without damping ring, B new is the initial amplitude of the system with damping ring, σ new is the initial stress at the measuring point of the system with damping ring.

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