A design method of an omega-shaped damping ring with adjustable axial-radial contact pressure

Abstract

The invention provides a design method of omega-shaped damping ring with adjustable axial and radial contact pressure. The method fully considers the optimal contact pressure under harmful working conditions of the transmission system, and designs the omega-shaped damping ring profile by optimizing the radial and axial profile coordinates and topological structure, so as to realize the adjustment of the axial and radial contact pressure between the damping ring and the gear, and further realize the efficient suppression of harmful resonance.

Description

Technical Field

[0001] This invention relates to the field of damping and vibration reduction technology, and in particular to a design method for an ω-shaped damping ring with adjustable axial and radial contact pressure. Background Technology

[0002] The demand for lightweight aero-engines has led to the widespread application of thin-spread gears in their transmission systems. Their service conditions are evolving towards high speed, heavy load, and high power density. Under these extreme conditions, thin-spread gears in transmission systems exhibit characteristics such as dense modalities, wide resonant frequency bands, and high resonance peaks, making them highly susceptible to resonance structural damage and high-cycle fatigue failures. Therefore, efficient vibration suppression over a wide frequency range for thin-spread gears in aero-engines is crucial for achieving high reliability and high durability.

[0003] Since the last century, the method of adding damping rings has been widely used for vibration suppression in high-speed gear transmission systems. However, under the requirements of lightweight design, achieving wide-frequency domain and high-power-density vibration suppression of thin-spread gears in aerospace under extreme service conditions remains a key problem that the method of adding damping rings urgently needs to solve.

[0004] In recent years, some progress has been made in the design of additional damping rings, with the emergence of several damping ring design methods that can achieve vibration friction recovery compensation. However, most existing technologies do not consider the service conditions and harmful resonance parameters of thin-spoke gears in their design process, only providing the design process for the damping ring structural parameters, making it difficult to optimize the damping parameters for key resonance conditions. One existing technology considers the harmful resonance parameters of the transmission system, gear modes, and structure, achieving controllable contact pressure design for harmful resonance conditions. However, this damping ring only has radial contact pressure after assembly, making it difficult to achieve efficient suppression of gear vibration under large amplitude, high frequency, and high pitch number conditions.

[0005] Therefore, there is an urgent need to develop a damping ring design method to achieve efficient suppression of vibration of thin-spread gears in aerospace transmission systems under extreme service conditions. Summary of the Invention

[0006] The purpose of this invention is to provide a design method for an ω-shaped damping ring with adjustable axial and radial contact pressure, so as to solve the problems existing in the prior art.

[0007] The technical solution adopted to achieve the purpose of this invention is as follows: a design method for an ω-shaped damping ring with adjustable axial and radial contact pressure. The gear spokes are provided with a gear damping ring groove for mounting the ω-shaped damping ring. The ω-shaped damping ring includes a first end ring, a support ring, and a second end ring connected in sequence. In the free state, the first end ring, support ring, and second end ring are sequentially spirally wound in a directional manner to form two spiral rings. The first end ring extends half a turn. The support ring extends one turn. The second end ring extends half a turn. In the use state, the ω-shaped damping ring is placed in the gear damping ring groove, and the two spiral rings of the ω-shaped damping ring are stacked to form a cylinder. The ω-shaped damping ring and the gear damping ring groove are both interference-fitted in the axial and radial directions. The ω-shaped damping ring is in complete contact with the gear damping ring groove, and the contact pressure is evenly distributed. Based on the size of the gear damping groove, the mode shape of the gear at the harmful resonance point, and the optimal contact pressure and centrifugal force of the gear in the radial and axial directions, the radial and axial profile coordinates and topology of the damping ring are optimized.

[0008] Furthermore, the following steps are included:

[0009] 1) Considering the optimal contact pressure under harmful operating conditions of the transmission system, solve for the radial profile coordinates. From a machining perspective, the radial profile is an open profile formed by cutting off a portion of a circular profile.

[0010] 2) Based on the radial profile coordinates, reconstruct the two radial profiles, keep the radial topology unchanged and stretch them along the axial direction to obtain the axial coordinates, and then obtain the coordinates of the ω-shaped damping ring profile.

[0011] Furthermore, step 1) specifically includes the following sub-steps:

[0012] 1.1) Calculate the optimal radial contact pressure P between the ω-shaped damping ring and the gear, taking into account the harmful resonance amplitude and frequency. r Optimal contact pressure P in the axial direction a And the contact pressure P generated by the centrifugal force of the gear during service. c This leads to the determination of the radial static contact pressure P of the ω-shaped damping ring. r1 and axial static contact pressure P a1 The specific calculation process is as follows:

[0013] 1.1a) Calculate the gear speed when harmful resonance occurs.

[0014]

[0015] Where z is the number of teeth on the gear, and f is the frequency of the harmful resonance point.

[0016] 1.1b) Calculate the contact pressure generated by centrifugal force during gear service.

[0017]

[0018] 1.1c) Radial static contact pressure P of the ω-shaped damping ring r1 and axial static contact pressure P a1 They are respectively

[0019] p r1 =p r -p c (3)

[0020] p a1 =p a (4)

[0021] 1.2) Calculate the radial profile coordinates:

[0022] 1.2a) Using the state after the ω-shaped damping ring is assembled into the gear vibration damping groove as a reference, establish a polar coordinate system with the radial direction as the polar axis and the center of the circle as the pole, and establish polar coordinates in the axial direction.

[0023] 1.2b) After the ω-shaped damping ring is assembled into the gear damping groove, the differential equation of the radial profile's deflection curve is:

[0024] Where m represents the circumferential displacement of the centroid of the annular section containing the radial profile, n represents the radial displacement of the centroid of the annular section containing the radial profile, S represents the cross-sectional area of ​​the annular section containing the radial profile, and c represents the direction passing through the centroid of the section but perpendicular to the section. When m = 0, σ = 0, i.e., the circumferential displacement m boundary condition. When n = 0, ... When σ = 0, that is, the radial displacement n boundary condition.

[0025] Based on the coordinates of the point in the neutral layer after the radial profile ring is assembled into the gear damping groove. Calculate radial profile coordinates

[0026]

[0027]

[0028] Among them, (σ w ,r w ) represents the coordinates of the outer surface profile, (σ) i ,r i ) represents the coordinates of the inner surface profile.

[0029] The present invention also discloses an ω-shaped damping ring, wherein the profile coordinates of the ω-shaped damping ring are designed according to the design method described in any one of the above.

[0030] Furthermore, the material for the ω-shaped damping ring is selected from 60Si2Mn, 60Si2CrV, or 65Mn.

[0031] The present invention also discloses a method for manufacturing any of the above-mentioned ω-shaped damping rings, wherein the ring is integrally formed by pre-pressing and sintering.

[0032] The present invention also discloses a low-noise gear with a damping ring, comprising a gear. The spokes of the gear are provided with gear damping ring grooves for mounting any of the aforementioned ω-shaped damping rings.

[0033] The technical effects of this invention are beyond doubt:

[0034] A. The ω-shaped damping ring and the gear have both radial and axial contact pressures. The profile coordinates of the ω-shaped damping ring are designed according to the actual required radial and axial contact pressures, so as to achieve optimal vibration reduction performance under external excitation.

[0035] B. After the ω-shaped damping ring is assembled with the gear, the axial contact pressure and radial contact pressure are evenly distributed, and the contact rate of the two contact surfaces is high, which greatly improves the vibration reduction effect. Attached Figure Description

[0036] Figure 1 It is a radial profile;

[0037] Figure 2 The axial midline profile of the ω-shaped damping ring;

[0038] Figure 3 The axial profiles of the ω-shaped damping ring are shown at both ends.

[0039] Figure 4 It is an ω-shaped damping ring line;

[0040] Figure 5 Top view of the ω-shaped damping ring profile;

[0041] Figure 6 This is a front view of the ω-shaped damping ring profile.

[0042] Figure 7 The installation position of the ω-shaped damping ring in the bevel gear groove of the thin-spread plate;

[0043] Figure 8 The installation position of the ω-shaped damping ring in the slot of the thin-spread spur gear;

[0044] Figure 9 Flowchart for the design of an ω-shaped damping ring with adjustable axial / radial contact pressure;

[0045] Figure 10 A ω-shaped damping ring in a free state;

[0046] Figure 11 Top view of the ω-shaped damping ring;

[0047] Figure 12 This is a front view of an ω-shaped damping ring;

[0048] Figure 13 This is a cross-sectional view of the ω-shaped damping ring after installation.

[0049] In the figure: 1. Inner surface profile of ω-shaped damping ring; 2. Outer surface profile of ω-shaped damping ring; 3. Gear; 4. ω-shaped damping ring; 401. First end ring; 402. Support ring; 403. Detailed Implementation

[0050] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0051] Example 1:

[0052] This embodiment provides a design method for an ω-shaped damping ring with adjustable axial and radial contact pressure. The spokes of the gear 3 are provided with gear damping ring grooves for mounting the ω-shaped damping ring 4. Figure 10 and Figure 11 The ω-shaped damping ring 4 includes a first end ring 401, a support ring 402, and a second end ring 403 connected in sequence. In the free state, the first end ring 401, the support ring 402, and the second end ring 403 are sequentially and oriented spirally wound to form two spiral rings. The first end ring 401 extends half a turn. The support ring 402 extends one turn. The second end ring 403 extends half a turn. Figure 12 The ω-shaped damping ring 4 is approximately the shape of a spiral ring with an ω-shaped profile. (Participate) Figure 13 In operation, the ω-shaped damping ring 4 is placed in the gear damping ring groove, with two helical rings of the ω-shaped damping ring 4 stacked to form a cylinder. The ω-shaped damping ring 4 and the gear damping ring groove are interference-fitted in both the axial and radial directions. The ω-shaped damping ring 4 is in complete contact with the gear damping ring groove, and the contact pressure is evenly distributed. Based on the dimensions of the gear damping groove, the mode shape of the gear at the harmful resonance point, and the optimal contact pressure and centrifugal force of the gear in the radial and axial directions, the radial and axial profile coordinates and topology of the damping ring are optimized. This embodiment improves vibration reduction performance and provides sufficient design basis for practical engineering applications.

[0053] Example 2:

[0054] The main content of this embodiment is the same as that of Embodiment 1, wherein, see [link / reference]. Figure 1 The design method for an ω-shaped damping ring with adjustable axial and radial contact pressure includes the following steps:

[0055] 1) See Figure 1Considering the optimal contact pressure under harmful operating conditions of the transmission system, the radial profile coordinates are solved. From a manufacturing perspective, the radial profile is an open profile formed by cutting off a portion of a circular profile. Step 1) specifically includes the following sub-steps:

[0056] 1.1) Calculate the optimal radial contact pressure P between the ω-shaped damping ring and the gear, taking into account the harmful resonance amplitude and frequency. r Optimal contact pressure P in the axial direction a And the contact pressure P generated by the centrifugal force of the gear during service. c This leads to the determination of the radial static contact pressure P of the ω-shaped damping ring. r1 and axial static contact pressure P a1 The specific calculation process is as follows:

[0057] 1.1a) Calculate the gear speed when harmful resonance occurs.

[0058]

[0059] Where z is the number of teeth on the gear, and f is the frequency of the harmful resonance point.

[0060] 1.1b) Calculate the contact pressure generated by centrifugal force during gear service.

[0061]

[0062] 1.1c) Radial static contact pressure P of the ω-shaped damping ring r1 and axial static contact pressure P a1 They are respectively

[0063] p r1 =p r -p c (3)

[0064] p a1 =p a (4)

[0065] 1.2) Calculate the radial profile coordinates:

[0066] 1.2a) Using the state after the ω-shaped damping ring is assembled into the gear vibration damping groove as a reference, establish a polar coordinate system with the radial direction as the polar axis and the center of the circle as the pole, and establish polar coordinates in the axial direction.

[0067] 1.2b) After the ω-shaped damping ring is assembled into the gear damping groove, the differential equation of the radial profile's deflection curve is:

[0068]

[0069] Where m represents the circumferential displacement of the centroid of the annular section containing the radial profile, n represents the radial displacement of the centroid of the annular section containing the radial profile, S represents the cross-sectional area of ​​the annular section containing the radial profile, and c represents the direction passing through the centroid of the section but perpendicular to the section. When m = 0, σ = 0, i.e., the circumferential displacement m boundary condition. When n = 0, ... When σ = 0, that is, the radial displacement n boundary condition.

[0070] Based on the coordinates of the point in the neutral layer after the radial profile ring is assembled into the gear damping groove. Calculate the radial profile coordinates:

[0071]

[0072]

[0073] Among them, (σ w ,r w ) represents the coordinates of the outer surface profile, (σ) i ,r i ) represents the coordinates of the inner surface profile.

[0074] 2) Based on the radial profile coordinates, reconstruct the coordinates of the ω-shaped damping ring by reconstructing the two sets of radial profiles. Step 2) specifically includes the following sub-steps:

[0075] 2.1) Import the radial profile into the three-dimensional coordinate system, keeping the topology unchanged, and stretch it axially by Δx / 2 to obtain the coordinates of the support ring 402 profile as shown below. Figure 2 As shown.

[0076] 2.2) Based on the profile coordinates of support ring 402, keeping the topology unchanged, translate Δx / 4 in both the positive and negative axial directions respectively to obtain the profile coordinates of the first end ring 401 and the second end ring 403 as follows: Figure 3 As shown.

[0077] 2.3) Insert the coordinate system of support ring 402 into the coordinate system of the first end ring 401 and the second end ring 403 to obtain the coordinate system of the ω-shaped damping ring with axial and radial contact pressure, as shown below. Figure 4 , Figure 5 and Figure 6 As shown.

[0078] This embodiment proposes a design method for an ω-shaped damping ring with adjustable axial / radial contact pressure. By fully considering the optimal contact pressure under harmful operating conditions of the transmission system, and optimizing the radial and axial profile coordinates and topology of the damping ring, the axial / radial contact pressure between the damping ring and the gear can be adjusted, thereby achieving efficient suppression of harmful resonance.

[0079] Example 3:

[0080] The main content of this embodiment is the same as that of embodiment 1. However, this embodiment takes a thin-spoke bevel gear with an additional ω-shaped damping ring as an example.

[0081] (1) Determine the parameters of the bevel gear and the ω-shaped damping ring. Since the design of the ω-shaped damping ring requires reconstruction of the profile through two sets of radial profiles, the radial profiles are designed first, and the installation depth a of the ω-shaped damping ring is determined based on the structure and dimensions of the bevel gear. a =2mm, radial thickness a = 4.7mm, axial width b = 3.9mm, and the contact surface radius r between the ω-shaped damping ring and the bevel gear r = 50.5mm; to prevent plastic deformation of the damping ring after assembly, material selection is crucial. Materials for this ω-shaped damping ring include, but are not limited to, 60Si2Mn, 60Si2CrV, and 65Mn, with a density ρ = 7860kg / m³. 3 The elastic modulus E = 206 GPa;

[0082] (2) Determine the axial / radial contact pressure. Set the optimal radial contact pressure P between the ω-shaped damping ring and the bevel gear. r =1.8MPa, optimal axial contact pressure P a =0.9MPa, number of teeth z=86, when the gear experiences harmful resonance, considering the harmful resonance frequency of the bevel gear f=9156Hz, calculate the gear speed.

[0083]

[0084] From equation (1), the rotational speed of the bevel gear is n = 668.6 rad / s, and the contact pressure generated by the centrifugal force during the service of the gear is also obtained.

[0085]

[0086] Furthermore, the radial static contact pressure P of the ω-shaped damping ring r1 and axial static contact pressure P a1 They are respectively represented as

[0087] p r1 =p r -p c (3)

[0088] p a1 =p a (4)

[0089] According to equation (2), the contact pressure p generated by centrifugal force is obtained. c =0.8MPa, Equations (3) to (4) yield the radial static contact pressure P. r1 =1.0MPa, axial static contact pressure P a1 =0.9MPa;

[0090] (3) Determine the radial profile coordinates. Using the state after the ω-shaped damping ring is assembled into the bevel gear damping groove as a reference, establish a polar coordinate system. With the radial direction as the polar axis and the center of the circle as the pole, establish polar coordinates in the axial direction to obtain the differential equation of the radial profile deflection curve.

[0091]

[0092] Where m represents the circumferential displacement of the centroid of the annular section containing the radial profile, n represents the radial displacement of the centroid of the annular section containing the radial profile, S represents the cross-sectional area of ​​the annular section containing the radial profile, and c represents the direction passing through the centroid of the section but perpendicular to the section.

[0093] When m = 0 and σ = 0, i.e., the boundary condition for circumferential displacement m;

[0094] When n = 0, When σ = 0, that is, the boundary condition for radial displacement n;

[0095] Based on the coordinates of the point in the neutral layer after the radial profile ring is assembled into the bevel gear damping groove. The coordinates of the outer and inner surface profiles of the annulus containing the radial profile are obtained as follows (σ w ,r w ), (σ i ,r i );

[0096]

[0097]

[0098] In summary, converting the above coordinate points to a Cartesian coordinate system, as follows: Figure 1 As shown;

[0099] (4) Determine the axial tension of the ω-shaped damping ring. Treating the ω-shaped damping ring as an equivalent spring, and according to Hooke's law, obtain the axial tension Δx of the ω-shaped damping ring.

[0100] F=k·Δx (8)

[0101] After the ω-shaped damping ring is assembled into the gear damping groove, the axial contact surface is subjected to the following force:

[0102] F = p a1 ·π·(r 2 -r r 2 (9)

[0103] Where, r r P represents the radius of the inner surface of the bevel gear rim. a1 Indicates axial static contact pressure;

[0104] The axial tensile amount is obtained by combining equations (8) and (9).

[0105]

[0106] It can be seen that the axial tensile amount of the ω-shaped damping ring is also related to the axial static contact pressure. According to Hooke's Law (8) to (10), the axial tensile amount of the ω-shaped damping ring is Δx = 16.1 mm.

[0107] (5) Determine the coordinates of the ω-shaped damping ring profile. Import the radial profile described in (4) into a three-dimensional coordinate system, keeping the topology unchanged, and stretch it Δx / 2 along the axial direction, as shown. Figure 2 As shown; in Figure 2 While maintaining the original topology, we translate the axes by Δx / 4 in both the forward and reverse directions to obtain the following: Figure 3 The coordinates of the shape shown; further, will... Figure 2 Inserting profile coordinates into Figure 3 In the profile coordinate system, the profile coordinates of the ω-shaped damping ring with axial / radial contact pressure are obtained as follows: Figure 4 As shown, the front view of the profile coordinates is as follows: Figure 5 As shown, the top view of the profile coordinates is as follows: Figure 6 As shown, the installation position of the ω-shaped damping ring in the thin-spread bevel gear groove is as follows: Figure 7 As shown.

[0108] Example 4:

[0109] The main content of this embodiment is the same as that of embodiment 1. However, this embodiment takes a thin-spoke spur gear with an additional ω-shaped damping ring as an example.

[0110] (1) Determine the parameters of the spur gear and the ω-shaped damping ring. Since the design of the ω-shaped damping ring requires reconstruction of the radial profile, the radial profile is designed first, and the installation depth 'a' of the ω-shaped damping ring is determined based on the structure and dimensions of the spur gear. a =2mm, radial thickness a = 5.2mm, axial width b / 2 = 2.4mm, and the contact surface radius r between the ω-shaped damping ring and the spur gear = 65mm; to prevent plastic deformation of the damping ring after assembly, material selection is crucial. Materials for this ω-shaped damping ring include, but are not limited to, 60Si2Mn, 60Si2CrV, and 65Mn, with a density ρ = 7860kg / m³. 3 The elastic modulus E = 206 GPa;

[0111] (2) Determine the axial / radial contact pressure. Set the optimal radial contact pressure P between the ω-shaped damping ring and the spur gear. r =1MPa, optimal axial contact pressure P a =0.6MPa, number of teeth z=96, when the gear experiences harmful resonance, considering the harmful resonance frequency of spur gear f=5060Hz, calculate the gear speed.

[0112]

[0113] From equation (1), the rotational speed of the spur gear is obtained as n = 331.01 rad / s, and the contact pressure generated by the centrifugal force during the service of the spur gear is also obtained.

[0114]

[0115] Furthermore, the radial static contact pressure P of the ω-shaped damping ring r1 and axial static contact pressure P a1 They are respectively represented as

[0116] p r1 =p r -p c (3)

[0117] p a1 =p a (4)

[0118] According to equation (2), the contact pressure p generated by centrifugal force is obtained. c =0.3MPa, Equations (3) to (4) yield the radial static contact pressure P. r1 =0.7MPa, axial static contact pressure P a1 =0.6MPa;

[0119] (3) Determine the radial profile coordinates. Using the state after the ω-shaped damping ring is assembled into the spur gear damping groove as a reference, establish a polar coordinate system. With the radial direction as the polar axis and the center of the circle as the pole, establish polar coordinates in the axial direction to obtain the differential equation of the radial profile deflection curve.

[0120]

[0121] Where m represents the circumferential displacement of the centroid of the annular section containing the radial profile, n represents the radial displacement of the centroid of the annular section containing the radial profile, S represents the cross-sectional area of ​​the annular section containing the radial profile, and c represents the direction passing through the centroid of the section but perpendicular to the section.

[0122] When m = 0 and σ = 0, i.e., the boundary condition for circumferential displacement m;

[0123] When n = 0, When σ = 0, that is, the boundary condition for radial displacement n;

[0124] Based on the coordinates of the point in the neutral layer after the radial profile ring is assembled into the spur gear damping groove. The coordinates of the outer and inner surface profiles of the annulus containing the radial profile are obtained as follows (σ w ,r w ), (σ i ,r i);

[0125]

[0126]

[0127] In summary, converting the above coordinate points to a Cartesian coordinate system, as follows: Figure 1 As shown;

[0128] (4) Determine the axial tension of the ω-shaped damping ring. Treating the ω-shaped damping ring as an equivalent spring, and according to Hooke's law, obtain the axial tension Δx of the ω-shaped damping ring.

[0129] F=k·Δx (8)

[0130] After the ω-shaped damping ring is assembled into the vibration damping groove of the spur gear, the axial contact surface is subjected to the following force:

[0131] F = p a1 ·π·(r 2 -r r 2 (9)

[0132] Where, r r P represents the radius of the inner surface of the spur gear rim. a1 Indicates axial static contact pressure;

[0133] The axial tensile amount is obtained by combining equations (8) and (9).

[0134]

[0135] It can be seen that the axial tensile amount of the ω-shaped damping ring is also related to the axial static contact pressure. According to Hooke's Law (8) to (10), the axial tensile amount of the ω-shaped damping ring is Δx = 12.8 mm.

[0136] (5) Determine the radial profile coordinates. Import the radial profile described in (4) into a three-dimensional coordinate system, keeping the topology unchanged, and stretch it Δx / 2 along the axial direction, as shown. Figure 2 As shown; in Figure 2 While maintaining the original topology, we translate the axes by Δx / 4 in both the forward and reverse directions to obtain the following: Figure 3 The coordinates of the shape shown; further, will... Figure 2 Inserting profile coordinates into Figure 3 From the profile coordinates, the profile coordinates of the ω-shaped damping ring with axial / radial contact pressure are obtained. The installation position in the thin-spoke spur gear groove is as follows: Figure 8 As shown.

[0137] In summary, this invention achieves the goal of generating corresponding profile coordinates for any given axial / radial contact pressure, thus completing the design of an ω-shaped damping ring with adjustable axial / radial contact pressure.

[0138] Example 5:

[0139] This embodiment provides an ω-shaped damping ring. The profile coordinates of the ω-shaped damping ring 4 are designed according to the design method described in any one of embodiments 1 to 4. The material of the ω-shaped damping ring 4 is selected from 60Si2Mn, 60Si2CrV, or 65Mn.

[0140] Example 6:

[0141] This embodiment provides a method for manufacturing the ω-shaped damping ring in Embodiment 5, which is integrally formed by pre-pressing and sintering.

[0142] Example 7:

[0143] This embodiment provides a low-noise gear with a damping ring, including gear 3. The spokes of gear 3 are provided with gear damping ring grooves for mounting the ω-shaped damping ring 4 from embodiment 5. Gear 3 is a gear with vibration reduction requirements or exists in a vibrating environment. In actual production, gear 3 is a thin-spoke bevel gear or a thin-spoke spur gear.

Claims

1. A design method for an ω-shaped damping ring with adjustable axial and radial contact pressure, characterized in that: The spokes of the gear (3) are provided with gear damping ring grooves for mounting the ω-shaped damping ring (4); the ω-shaped damping ring (4) includes a first end ring (401), a support ring (402), and a second end ring (403) connected in sequence; in the free state, the first end ring (401), the support ring (402), and the second end ring (403) are sequentially spirally wound in a directional manner to form two spiral rings; the first end ring (401) extends half a turn; the support ring (402) extends one turn; the second end ring (403) extends half a turn; in the use state, ω A ω-shaped damping ring (4) is placed in the gear damping ring groove. The two spiral rings of the ω-shaped damping ring (4) are stacked to form a cylinder. The ω-shaped damping ring (4) and the gear damping ring groove are both interference fit in the axial and radial directions. The ω-shaped damping ring (4) is in complete contact with the gear damping ring groove and the contact pressure is evenly distributed. Based on the size of the gear damping groove, the mode shape of the gear at the harmful resonance point, and the optimal contact pressure and centrifugal force of the gear in the radial and axial directions, the radial and axial profile coordinates and topology of the damping ring are optimized. The design method includes the following steps: 1) Considering the optimal contact pressure under harmful operating conditions of the transmission system, solve for the radial profile coordinates; from a machining perspective, the radial profile is an open profile formed by cutting off a portion of a circular profile; step 1) specifically includes the following sub-steps: 1.1) Calculate the optimal radial contact pressure P between the ω-shaped damping ring and the gear, taking into account the harmful resonance amplitude and frequency. r Optimal contact pressure P in the axial direction a And the contact pressure P generated by the centrifugal force of the gear during service. c This leads to the determination of the radial static contact pressure P of the ω-shaped damping ring. r1 and axial static contact pressure P a1 The specific calculation process is as follows: 1.1a) Calculate the gear speed when harmful resonance occurs. (1) Where z is the number of teeth on the gear, and f is the frequency of the harmful resonance point; 1.1b) Calculate the contact pressure generated by centrifugal force during gear service. (2) 1.1c) Radial static contact pressure P of the ω-shaped damping ring r1 and axial static contact pressure P a1 They are respectively (3) (4) 1.2) Calculate the radial profile coordinates: 1.2a) Using the state after the ω-shaped damping ring is assembled into the gear damping groove as a reference, establish a polar coordinate system with the radial direction as the polar axis and the center of the circle as the pole, and establish polar coordinates in the axial direction; 1.2b) After the ω-shaped damping ring is assembled into the gear damping groove, the differential equation of the radial profile's deflection curve is: (5) Where m represents the circumferential displacement of the centroid of the annular section containing the radial profile, n represents the radial displacement of the centroid of the annular section containing the radial profile, S represents the cross-sectional area of ​​the annular section containing the radial profile, and c represents the direction passing through the centroid of the section but perpendicular to the section. When m = 0 and σ = 0, the boundary condition is circumferential displacement m; when n = 0, ... = 0, σ = 0, i.e., the radial displacement n boundary condition; Based on the coordinates (σ) of the neutral layer point after the radial profile ring is assembled into the gear damping groove, ), Calculate the radial profile coordinates: ， (6) ， (7) Among them, (σ w , r w ) represents the coordinates of the outer surface profile, (σ) i , r i ) represents the coordinates of the inner surface profile; 2) Based on the radial profile coordinates, the two radial profiles are reconstructed to obtain the coordinates of the ω-shaped damping ring.

2. The design method for an ω-shaped damping ring with adjustable axial and radial contact pressure according to claim 1, characterized in that, Step 2) specifically includes the following sub-steps: 2.1) Import the radial profile into the three-dimensional coordinate system, keep the topology unchanged, stretch Δx / 2 along the axial direction to obtain the coordinates of the support ring (402) profile; 2.2) Based on the profile coordinates of the support ring (402), keeping the topology unchanged, translate Δx / 4 in the positive and negative directions along the axial direction respectively to obtain the profile coordinates of the first end ring (401) and the second end ring (403); 2.3) Insert the profile coordinates of the support ring (402) into the profile coordinates of the first end ring (401) and the second end ring (403) to obtain the profile coordinates of the ω-shaped damping ring with axial and radial contact pressure.

3. An ω-shaped damping ring, characterized in that: The profile coordinates of the ω-shaped damping ring (4) are designed according to the design method described in claim 1 or 2.

4. The ω-shaped damping ring according to claim 3, characterized in that: The material of the ω-shaped damping ring (4) is selected as 60Si2Mn, 60Si2CrV or 65Mn.

5. A method for manufacturing the ω-shaped damping ring of claim 3, characterized in that: It is formed into a single piece through pre-pressing and sintering processes.

6. A low-noise gear with a damping ring, characterized in that: Includes a gear (3); the spokes of the gear (3) are provided with a gear damping ring groove for mounting the ω-shaped damping ring (4) of claim 3.

7. A low-noise gear with a damping ring according to claim 6, characterized in that: The gear (3) is a thin-spread bevel gear.

8. A low-noise gear with a damping ring according to claim 6, characterized in that: The gear (3) is a thin-spoke spur gear.

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