Equivalent stiffness analysis method and application of double-sleeve-tooth connection structure

Abstract

The invention relates to the technical field of aero-engines, and discloses an equivalent stiffness analysis method and application of a double-sleeve-tooth connection structure, and the analysis method comprises the steps: constructing a mechanical model of the double-sleeve-tooth connection structure; analyzing to obtain normal stiffness brought by meshing of a pair of teeth; the overall meshing rigidity of each sleeve gear is obtained through analysis; and according to the shafting rigidity of each connecting shaft in the double-sleeve-tooth connecting structure and the overall meshing rigidity of each sleeve tooth, the equivalent rigidity of the double-sleeve-tooth connecting structure is obtained through analysis. According to the method, the problem of inaccurate simulation of the connection section of the rotor can be solved, and the modeling efficiency can be improved while the analysis precision during dynamic simulation analysis of the aero-engine rotor containing the double-sleeve-tooth connection structure is ensured. The elastic modulus of the double-sleeve gear shaft is adjusted by taking the obtained equivalent stiffness of the double-sleeve gear connection structure as a target, and the connection stiffness in the rotor dynamic model can be quickly corrected, so that accurate rotor dynamic characteristics can be conveniently obtained, and the real rotor dynamic characteristics can be ensured to be obtained.

Description

Technical Field

[0001] The invention relates to the technical field of aeroengines and discloses an equivalent stiffness analysis method for a double-set gear connection structure and an application thereof. Background Art

[0002] In order to ensure the safe operation of aircraft engine rotors, it is necessary to conduct rotor dynamics simulation analysis on aircraft engine rotor systems. Among them, the accurate simulation of non-continuous connection structures, such as sleeve tooth connection, can provide key data for engine safety research. How to accurately and efficiently construct a double sleeve tooth connection structure is of great significance for obtaining the critical speed characteristics of the rotor.

[0003] In engineering practice, due to the needs of structural functions, the rotor connection parts are connected by two pairs of sleeve teeth at the same time, forming a Figure 1 The double-sleeve gear connection structure shown in the figure is a commonly used rotor connection structure in engines. During the operation of the double-sleeve gear connection structure, the meshing of the tooth surfaces will bring a certain amount of additional stiffness. In order to improve the analysis efficiency in engineering, the sleeve gear structure is often fixed as a whole or connected only at the positioning surface. There is a certain difference between the connection stiffness obtained by these two treatment methods and the connection stiffness formed by the actual sleeve gear tooth surface meshing contact, which may lead to deviations in the dynamic analysis results of the rotor system with the double-sleeve gear connection structure. Summary of the invention

[0004] The purpose of the present invention is to provide an equivalent stiffness analysis method and application of a double-set tooth connection structure, which can avoid the problem of inaccurate simulation of the rotor connection section and ensure the analysis accuracy during the simulation analysis of the rotor dynamics of an aero-engine containing a double-set tooth connection structure. By adjusting the elastic modulus of the double-set tooth shaft with the equivalent stiffness of the double-set tooth connection structure as the goal, the connection stiffness in the rotor dynamics model can be quickly corrected to obtain accurate rotor dynamics characteristics and ensure the acquisition of true rotor dynamics characteristics.

[0005] In order to achieve the above technical effects, the technical solution adopted by the present invention is: An equivalent stiffness analysis method for a double-set tooth connection structure includes: A mechanical model of a double-sleeve gear connection structure is constructed, and the shaft system stiffness of each connecting shaft in the double-sleeve gear connection structure is analyzed and obtained; the double-sleeve gear connection structure comprises a first connecting shaft, a double-sleeve gear shaft, and a second connecting shaft which are coaxially arranged, one end of the first connecting shaft is meshed with the double-sleeve gear shaft through a first set of teeth, and one end of the second connecting shaft is meshed with the double-sleeve gear shaft through a second set of teeth; In the driving system of the first set of teeth or the second set of teeth, the driven shaft is fixed, and torque is applied to the corresponding active shaft, and the normal displacement and normal resultant force of a pair of meshing tooth surfaces in the first set of teeth or the second set of teeth are analyzed and obtained, and the normal stiffness caused by the meshing of a pair of teeth is calculated; Based on the normal stiffness of a pair of teeth meshing obtained by analysis, the overall meshing stiffness of the first set of teeth or the second set of teeth is obtained by analysis; According to the shaft system stiffness of each connecting shaft in the double-set gear connection structure and the overall meshing stiffness of the first set of teeth and the second set of teeth, the equivalent stiffness of the double-set gear connection structure is obtained by analysis.

[0006] Furthermore, in the drive system of the first set of teeth or the second set of teeth, the normal stiffness brought by the meshing of a pair of teeth is ,in is the normal force on a pair of meshing teeth, is the normal displacement of a pair of meshing tooth surfaces.

[0007] Furthermore, the overall meshing stiffness brought about by the meshing contact of the sleeve tooth surface ,in =1 or 2, =1 It represents the overall meshing stiffness brought by the meshing contact of the first set of teeth. =2 hours It represents the overall meshing stiffness brought by the meshing contact of the second set of teeth. , For the The angle between the radial direction of the pitch circle meshing point of the gear and the horizontal direction of the connecting shaft system, is the contact angle, is the number of teeth in the drive train in the first set of teeth or the second set of teeth.

[0008] Furthermore, the series stiffness of the first connecting shaft, the second connecting shaft, the double-set gear shaft, the overall meshing stiffness brought about by the meshing contact of the first set of teeth, and the overall meshing stiffness brought about by the meshing contact of the second set of teeth is used as the equivalent stiffness of the double-set gear connection structure.

[0009] Furthermore, the equivalent stiffness of the double-set tooth connection structure ,in is the stiffness of the first connecting axis, is the stiffness of the second connecting shaft, is the stiffness of the double-set gear shaft, The overall meshing stiffness brought by the meshing contact of the first set of teeth. The overall meshing stiffness brought by the meshing contact of the second set of teeth.

[0010] In order to achieve the above technical effects, the present invention also provides an application of an equivalent stiffness analysis method for a double-set tooth connection structure, including: According to the double-sleeve gear connection structure, a two-dimensional rotor dynamics analysis model based on the double-sleeve gear connection structure is constructed; the double-sleeve gear connection structure includes a first connecting shaft, a double-sleeve gear shaft, and a second connecting shaft that are coaxially arranged, one end of the first connecting shaft is meshed with the double-sleeve gear shaft through a first set of teeth, and one end of the second connecting shaft is meshed with the double-sleeve gear shaft through a second set of teeth; In the two-dimensional rotor dynamics analysis model, the meshing portion between the first connection and the double-set gear shaft is bound and constrained, and the meshing portion between the second connection shaft and the double-set gear shaft is bound and constrained; The stiffness of the binding constraint part is 1×10 9 N / m is set, and the elastic modulus of the double-sleeve gear shaft is adjusted so that the total stiffness of the double-sleeve gear connection structure after adjustment is equal to the equivalent stiffness of the double-sleeve gear connection structure.

[0011] Further, the elastic modulus of the double-set gear shaft is adjusted to ,in ,in is the length of the double-set gear shaft, is the outer diameter of the double-set gear shaft, is the inner diameter of the double-set gear shaft, is the equivalent stiffness of the double-set tooth connection structure, is the stiffness of the first connecting axis, is the stiffness of the second connecting shaft.

[0012] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention can solve the problem of inaccurate simulation of the rotor connection section, and can increase the modeling efficiency while ensuring the analysis accuracy of the simulation analysis of the rotor dynamics of an aero-engine having a double-set gear connection structure.

[0013] 2. The present invention can also adjust the elastic modulus of the double-set gear shaft by taking the equivalent stiffness of the double-set gear connection structure as the goal, and can quickly correct the connection stiffness in the rotor dynamics model to obtain accurate rotor dynamics characteristics and ensure the acquisition of true rotor dynamics characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A schematic diagram of a double-set tooth connection structure in Embodiment 1 or 2; Figure 2 is a flow chart of an equivalent stiffness analysis method for a double-set tooth connection structure in Example 1 or 2; Among them, 1. first connecting shaft; 2. double-set gear shaft; 3. second connecting shaft; 4. first set of gear meshing; 5. second set of gear meshing. DETAILED DESCRIPTION

[0015] The present invention is further described in detail below in conjunction with the embodiments and drawings. However, it should not be understood that the scope of the above subject matter of the present invention is limited to the following embodiments, and all technologies realized based on the content of the present invention belong to the scope of the present invention.

[0016] Example 1 See also Figure 1-Figure 2 , an equivalent stiffness analysis method for a double-set tooth connection structure, comprising: Step 1.1, construct a mechanical model of a double-sleeve gear connection structure, and analyze and obtain the shaft system stiffness of each connecting shaft in the double-sleeve gear connection structure; the double-sleeve gear connection structure includes a first connecting shaft 1, a double-sleeve gear shaft 2, and a second connecting shaft 3 that are coaxially arranged, one end of the first connecting shaft 1 is meshed with the double-sleeve gear shaft 2 through a first set of teeth 4, and one end of the second connecting shaft 3 is meshed with the double-sleeve gear shaft 2 through a second set of teeth 5; Step 1.2: In the driving system of the first set of teeth or the second set of teeth, fix the driven shaft and apply torque to the corresponding active shaft, analyze and obtain the normal displacement and normal resultant force of a pair of meshing tooth surfaces in the first set of teeth or the second set of teeth, and calculate the normal stiffness caused by the meshing of a pair of teeth; Step 1.3, according to the normal stiffness brought by the meshing of a pair of teeth obtained by analysis, the overall meshing stiffness corresponding to the first set of teeth or the second set of teeth is obtained by analysis; Step 1.4: According to the shaft system stiffness of each connecting shaft in the double-set gear connection structure and the overall meshing stiffness of the first set of teeth and the overall meshing stiffness of the second set of teeth, the equivalent stiffness of the double-set gear connection structure is analyzed and obtained.

[0017] In this embodiment, by constructing a mechanical model of a double-sleeve tooth connection structure, the normal displacement and normal resultant force of a pair of tooth surfaces that mesh with each other in the double-sleeve tooth connection structure are analyzed and obtained, and the normal stiffness brought by the meshing of a pair of teeth is calculated, so as to analyze and obtain the overall meshing stiffness of each tooth; finally, according to the shaft system stiffness of each connecting shaft in the double-sleeve tooth connection structure and the overall meshing stiffness of each tooth, the equivalent stiffness of the double-sleeve tooth connection structure is analyzed and obtained; the problem of inaccurate simulation of the rotor connection section can be solved, and the modeling efficiency can be increased while ensuring the analysis accuracy of the simulation analysis of the rotor dynamics of an aeroengine containing a double-sleeve tooth connection structure.

[0018] In step 1.2 of this embodiment, in the driving system of the first set of teeth or the second set of teeth, the normal stiffness brought by the meshing of a pair of teeth is ,in is the normal force on a pair of meshing teeth, is the normal displacement of a pair of meshing tooth surfaces.

[0019] In step 1.3 of this embodiment, the overall meshing stiffness caused by the meshing contact of the sleeve tooth surface is ,in =1 or 2, =1 It represents the overall meshing stiffness brought by the meshing contact of the first set of teeth. =2 hours It represents the overall meshing stiffness brought by the meshing contact of the second set of teeth. , For the The angle between the radial direction of the pitch circle meshing point of the gear and the horizontal direction of the connecting shaft system, is the contact angle, is the number of teeth in the drive train in the first set of teeth or the second set of teeth.

[0020] In step 1.4 of this embodiment, the equivalent stiffness of the double-set tooth connection structure is ,in is the stiffness of the first connecting shaft 1, is the stiffness of the second connecting shaft 3, is the stiffness of the double-set gear shaft 2, The overall meshing stiffness brought by the meshing contact of the first set of teeth. It is the overall meshing stiffness brought by the meshing contact of the second set of teeth. That is, the series stiffness of the first connecting shaft 1, the second connecting shaft 3, the stiffness of the double-set gear shaft 2, the overall meshing stiffness brought by the meshing contact of the first set of teeth, and the overall meshing stiffness brought by the meshing contact of the second set of teeth is used as the equivalent stiffness of the double-set gear connection structure.

[0021] Based on the same inventive concept, this embodiment also provides an application of an equivalent stiffness analysis method for a double-set tooth connection structure, including: Step 2.1, constructing a two-dimensional rotor dynamics analysis model based on a double-sleeve gear connection structure; the double-sleeve gear connection structure comprises a first connecting shaft 1, a double-sleeve gear shaft 2, and a second connecting shaft 3 which are coaxially arranged, one end of the first connecting shaft 1 is meshed with the double-sleeve gear shaft 2 through a first set of teeth 4, and one end of the second connecting shaft 3 is meshed with the double-sleeve gear shaft 2 through a second set of teeth 5; Step 2.2, in the two-dimensional rotor dynamics analysis model, binding and constraining the meshing portion between the first connection and the double-sleeve gear shaft 2, and binding and constraining the meshing portion between the second connection shaft 3 and the double-sleeve gear shaft 2; Step 2.3: The stiffness of the binding constraint part is 1×10 9 N / m is set, and the elastic modulus of the double-sleeve gear shaft 2 is adjusted so that the adjusted total stiffness of the double-sleeve gear connection structure is equal to the equivalent stiffness of the double-sleeve gear connection structure obtained through steps 1.1 to 1.4.

[0022] In this embodiment, after building a two-dimensional rotor dynamics analysis model based on the double-sleeve gear connection structure, the meshing parts between the first connection and the double-sleeve gear shaft 2 and the meshing parts between the second connection shaft 3 and the double-sleeve gear shaft 2 are bound and constrained, and the stiffness of the binding and constrained parts is set according to 1×10 9 N / m is set, and then the elastic modulus of the double-sleeve gear shaft 2 is adjusted with the equivalent stiffness of the double-sleeve gear connection structure as the goal, which can quickly correct the connection stiffness in the rotor dynamics model to obtain accurate rotor dynamics characteristics and ensure the acquisition of true rotor dynamics characteristics.

[0023] In this embodiment, the elastic modulus of the double-sleeve gear shaft 2 is adjusted to ,in ,in is the length of the double-set gear shaft 2, is the outer diameter of the double-set gear shaft 2, is the inner diameter of the double-set gear shaft 2, is the equivalent stiffness of the double-set tooth connection structure, is the stiffness of the first connecting shaft 1, is the stiffness of the second connecting shaft 3, which can make the total stiffness of the double-set tooth connection structure after adjustment equal to the equivalent stiffness of the double-set tooth connection structure obtained through steps 1.1 to 1.4.

[0024] Example 2 See also Figure 1 and Figure 2 This embodiment takes the construction of a dynamic analysis model of a double-set gear connection structure of a main shaft of a certain aircraft engine as an example to explain in detail the equivalent stiffness analysis method and application process of the double-set gear connection structure of the present invention. The specific operation steps are as follows: The first step is to simplify the double-set gear connection structure and establish a mechanical model of the double-set gear connection structure. The double-sleeve gear connection part is taken out from the entire rotor structure, including the first connecting shaft 1, the double-sleeve gear shaft 2, and the second connecting shaft 3. The overall stiffness of the double-sleeve gear connection structure can be obtained by fixing on one side of the first connecting shaft 1 and applying an external load on the second connecting shaft 3. Therefore, the shaft is regarded as a beam with a uniform cross section, and the meshing action of the sleeve gear is regarded as a spring, and a mechanical model is established.

[0025] The second step is to solve the meshing stiffness of the sleeve gear tooth surface A pair of tooth models is taken out from the mechanical model of the double-set tooth connection structure, the shaft body is rigidified, a contact unit is established on the meshing tooth surface, the driven shaft of the model is fixed, a torque is applied to the active shaft, and the displacement in the normal direction of the tooth surface is calculated. The resultant force in the normal direction , according to the formula Get the normal stiffness brought by a pair of tooth surfaces meshing .

[0026] Then each tooth is considered as a separate spring, according to the formula Calculate the overall meshing stiffness caused by the meshing contact of the sleeve gear tooth surface, where =1 or 2, =1 It represents the overall meshing stiffness brought by the meshing contact of the first set of teeth. =2 hours It represents the overall meshing stiffness brought by the meshing contact of the second set of teeth. , For the The angle between the radial direction of the pitch circle meshing point of the gear and the horizontal direction of the connecting shaft system, is the contact angle, is the number of teeth in the driving system of the first set of teeth or the second set of teeth. The calculation results of the overall meshing stiffness brought about by the meshing contact of the tooth surfaces in the first set of teeth and the second set of teeth in this embodiment are shown in Table 1.

[0027] Table 1 Calculation results of sleeve gear meshing stiffness

[0028] The third step is to solve the shaft system stiffness. The cross section of the shaft body is simplified to a regular circle or ring, and the shaft system stiffness can be solved according to the theory of a beam with a fixed equal cross section at one end. The calculation results of the shaft system stiffness of the first connecting shaft 1, the second connecting shaft 3 and the double-sleeve gear shaft 2 in this embodiment are shown in Table 2 Table 2 Calculation results of shafting stiffness

[0029] Step 4: Take the series stiffness of the first connecting shaft 1, the second connecting shaft 3, the double-set gear shaft 2, the overall meshing stiffness brought about by the meshing contact of the first set of gears, and the overall meshing stiffness brought about by the meshing contact of the second set of gears as the equivalent stiffness of the double-set gear connection structure; the equivalent stiffness (series stiffness) of the double-set gear connection structure is N / m, is the stiffness of the first connecting shaft 1, is the stiffness of the second connecting shaft 3, is the stiffness of the double-set gear shaft 2, The overall meshing stiffness brought by the meshing contact of the first set of teeth. The overall meshing stiffness brought by the meshing contact of the second set of teeth.

[0030] The fifth step is to use the material performance parameter correction method in the rotor dynamics model to introduce the double-set gear equivalent stiffness correction.

[0031] In the two-dimensional rotor dynamics analysis model of this embodiment, the meshing part between the first connection and the double-sleeve gear shaft 2 is bound and constrained, and the meshing part between the second connection shaft 3 and the double-sleeve gear shaft 2 is bound and constrained; and the stiffness of the binding and constraining part is set according to 1×10 9 N / m is set. The gear meshing part is not established in the dynamic analysis model. Therefore, to ensure that the double-gear connection stiffness is consistent with the actual situation, the stiffness of the double-gear shaft 2 must be adjusted. By adjusting the elastic modulus of the double-gear shaft 2 to ,in ,in is the length of the double-set gear shaft 2, is the outer diameter of the double-set gear shaft 2, is the inner diameter of the double-set gear shaft 2, is the equivalent stiffness of the double-set tooth connection structure, is the stiffness of the first connecting shaft 1, is the stiffness of the second connecting shaft 3. The elastic modulus of the double-set gear shaft 2 after adjustment Input into the rotor dynamics model to complete the dynamic correction, so that the total stiffness of the double-set tooth connection structure after adjustment is equal to the equivalent stiffness of the double-set tooth connection structure. .

[0032] This embodiment verifies the engine rotor dynamics model through experiments. After the double-set tooth connection structure of the rotor dynamics simulation model is corrected by the method of the present invention, the error between the critical speed obtained by simulation and the experimental critical speed is reduced from 11% to within 2%, which greatly improves the accuracy of the rotor dynamics design.

[0033] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An equivalent stiffness analysis method for a double-set tooth connection structure, characterized in that: include: A mechanical model of a double-sleeve gear connection structure is constructed, and the shaft system stiffness of each connecting shaft in the double-sleeve gear connection structure is analyzed and obtained; the double-sleeve gear connection structure comprises a first connecting shaft, a double-sleeve gear shaft, and a second connecting shaft which are coaxially arranged, one end of the first connecting shaft is meshed with the double-sleeve gear shaft through a first set of teeth, and one end of the second connecting shaft is meshed with the double-sleeve gear shaft through a second set of teeth; In the driving system of the first set of teeth or the second set of teeth, the driven shaft is fixed, and torque is applied to the corresponding active shaft, and the normal displacement and normal resultant force of a pair of meshing tooth surfaces in the first set of teeth or the second set of teeth are analyzed and obtained, and the normal stiffness caused by the meshing of a pair of teeth is calculated; Based on the normal stiffness of a pair of teeth meshing obtained by analysis, the overall meshing stiffness of the first set of teeth or the second set of teeth is obtained by analysis; According to the shaft system stiffness of each connecting shaft in the double-set gear connection structure and the overall meshing stiffness of the first set of teeth and the second set of teeth, the equivalent stiffness of the double-set gear connection structure is obtained by analysis.

2. The equivalent stiffness analysis method of the double-set tooth connection structure according to claim 1 is characterized in that: Normal stiffness of a pair of teeth meshing in the drive system of the first set of teeth or the second set of teeth ,in is the normal force on a pair of meshing teeth, is the normal displacement of a pair of meshing tooth surfaces.

3. The equivalent stiffness analysis method of the double-set tooth connection structure according to claim 1 is characterized in that: Overall meshing stiffness caused by the meshing contact of the sleeve gear tooth surface ,in =1 or 2, =1 It represents the overall meshing stiffness brought by the meshing contact of the first set of teeth. =2 hours It represents the overall meshing stiffness brought by the meshing contact of the second set of teeth. , For the The angle between the radial direction of the pitch circle meshing point of the gear and the horizontal direction of the connecting shaft system, is the contact angle, is the number of teeth in the drive train in the first set of teeth or the second set of teeth.

4. The equivalent stiffness analysis method of the double-set tooth connection structure according to claim 1 is characterized in that: The series stiffness of the first connecting shaft, the second connecting shaft, the double-set gear shaft, the overall meshing stiffness brought about by the meshing contact of the first set of gear surfaces, and the overall meshing stiffness brought about by the meshing contact of the second set of gear surfaces is taken as the equivalent stiffness of the double-set gear connection structure.

5. The equivalent stiffness analysis method of the double-set tooth connection structure according to claim 4 is characterized in that: Equivalent stiffness of double-set tooth connection structure ,in is the stiffness of the first connecting axis, is the stiffness of the second connecting shaft, is the stiffness of the double-set gear shaft, The overall meshing stiffness brought by the meshing contact of the first set of teeth. The overall meshing stiffness brought by the meshing contact of the second set of teeth.

6. An application of an equivalent stiffness analysis method for a double-set tooth connection structure, characterized in that: include: According to the double-sleeve gear connection structure, a two-dimensional rotor dynamics analysis model based on the double-sleeve gear connection structure is constructed; the double-sleeve gear connection structure includes a first connecting shaft, a double-sleeve gear shaft, and a second connecting shaft that are coaxially arranged, one end of the first connecting shaft is meshed with the double-sleeve gear shaft through a first set of teeth, and one end of the second connecting shaft is meshed with the double-sleeve gear shaft through a second set of teeth; In the two-dimensional rotor dynamics analysis model, the meshing portion between the first connection and the double-set gear shaft is bound and constrained, and the meshing portion between the second connection shaft and the double-set gear shaft is bound and constrained; The stiffness of the binding constraint part is 1×10 9 N / m is set, and the elastic modulus of the double-sleeve gear shaft is adjusted so that the total stiffness of the double-sleeve gear connection structure after adjustment is equal to the equivalent stiffness of the double-sleeve gear connection structure described in claim 1.

7. The application of the equivalent stiffness analysis method of the double-set tooth connection structure according to claim 6 is characterized in that: Adjust the elastic modulus of the double-set gear shaft to ,in ,in is the length of the double-set gear shaft, is the outer diameter of the double-set gear shaft, is the inner diameter of the double-set gear shaft, is the equivalent stiffness of the double-set tooth connection structure, is the stiffness of the first connecting axis, is the stiffness of the second connecting shaft.

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