Turbine Rear Casing Stiffness Measuring Device and Measuring Method

Abstract

The present invention discloses a stiffness measuring device and a measuring method for a turbine rear casing. The stiffness measuring device for the turbine rear casing includes a fixing mechanism, a loading mechanism, and an auxiliary cylinder. Among them, the fixing mechanism is used to connect the turbine rear casing and fix the turbine rear casing. The loading mechanism is used to apply a radial load to the bearing seat of the turbine rear casing. The auxiliary cylinder is configured such that the first end of the auxiliary cylinder can be fixed to the bearing seat of the turbine rear casing, and the second end extends toward the outside of the turbine rear casing. The fixing mechanism fixes the turbine rear casing, and the loading mechanism can apply a load to the fixed turbine rear casing, causing the bearing seat to deform. Accordingly, the second end of the auxiliary cylinder deforms. Since the second end is close to or located on the outside of the turbine rear casing, the deformation of the bearing seat can be calculated by measuring the displacement of the second end. According to the load applied by the loading mechanism, the stiffness of the bearing seat of the turbine rear casing can be obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of aero-engine test, and particularly relates to a turbine rear casing stiffness measurement device and a measurement method. Background Art

[0002] In order to conduct engine dynamics analysis and provide a basis for rotor dynamics analysis, it is necessary to carry out a turbine rear casing stiffness test to obtain the stiffness data of the turbine rear casing. The turbine rear casing stiffness test requires fixing the front mounting edge of the turbine casing as a transition section and radially loading the center section of the bearing seat of the turbine rear casing.

[0003] In order to obtain the stiffness data of the turbine rear casing, it is necessary to take appropriate measuring points on the two mounting edges of the turbine rear casing and measure the axial and radial displacements of the measuring points. The two mounting edges are respectively the bearing seat mounting edge and the front mounting edge of the turbine rear casing. Among them, the bearing seat mounting edge is located inside the center of the turbine rear casing, and it is difficult to arrange displacement dial indicators or lever gauges, and direct contact measurement cannot be achieved.

[0004] Therefore, it is necessary to design an auxiliary measurement device to measure the displacement of the measuring points of the auxiliary measurement device, and indirectly obtain the displacement of the bearing seat mounting edge through the displacement conversion relationship, so as to calculate the stiffness of the turbine rear casing. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the defect that the displacement of the bearing seat mounting edge cannot be directly measured during the measurement of the turbine rear casing stiffness in the prior art, and provide a turbine rear casing stiffness measurement device and a measurement method.

[0006] The present invention solves the above technical problem through the following technical solutions:

[0007] A turbine rear casing stiffness measurement device, the turbine rear casing stiffness measurement device includes:

[0008] A fixing mechanism for connecting the turbine rear casing and fixing the turbine rear casing;

[0009] A loading mechanism for applying a radial load to the bearing seat of the turbine rear casing;

[0010] An auxiliary cylinder, the auxiliary cylinder is configured such that the first end of the auxiliary cylinder can be fixed to the bearing seat of the turbine rear casing, and the second end extends towards the outside of the turbine rear casing.

[0011] In this solution, the fixing mechanism fixes the turbine rear casing. The first end of the auxiliary cylinder is connected to the bearing housing, and the second end extends towards the outside of the turbine rear casing. The loading mechanism can apply a load to the fixed turbine rear casing, causing the bearing housing to deform, and the second end of the auxiliary cylinder will deform accordingly. Since the second end is close to or located outside the turbine rear casing, it is convenient to measure the displacement of the second end. Moreover, the auxiliary cylinder is not directly subjected to the load of the loading mechanism and hardly deforms. Therefore, the relationship between the displacement of the second end and the deformation of the bearing housing is certain. Thus, the deformation of the bearing housing can be calculated by measuring the displacement of the second end, and the stiffness of the bearing housing can be obtained according to the load applied by the loading mechanism.

[0012] Preferably, part of the loading mechanism is inserted into the auxiliary cylinder, and there is a gap between the loading mechanism and the inner wall of the auxiliary cylinder.

[0013] In this solution, the loading mechanism passes through the auxiliary cylinder, so as to ensure that the loading mechanism is connected to the turbine rear casing while not contacting the auxiliary cylinder, avoiding the loading mechanism applying a load to the auxiliary cylinder and causing the auxiliary cylinder to deform. In addition, since there is a gap between the loading mechanism and the inner wall of the auxiliary cylinder, when the auxiliary cylinder is displaced, the loading mechanism will not interfere with the auxiliary cylinder, ensuring the accuracy of the measurement result.

[0014] Preferably, the turbine rear casing stiffness measuring device further includes a bushing, which is used to be inserted into the bearing housing, and the auxiliary cylinder is installed on the bushing.

[0015] In this solution, the auxiliary cylinder is installed on the turbine rear casing through the bushing, without the need to set up a connecting device on the turbine rear casing, avoiding the change of the stiffness at the bearing housing and ensuring that the measurement result can reflect the true stiffness. The loading mechanism can be directly connected to the bushing, so the applied load acts on the bushing rather than on the auxiliary cylinder.

[0016] Preferably, the first end of the auxiliary cylinder is fitted and inserted into the interior of the bushing.

[0017] In this solution, since part of the auxiliary cylinder is fitted and inserted into the bushing, the auxiliary cylinder can be positioned by means of the bushing, and the connection between the auxiliary cylinder and the bushing is more stable.

[0018] Preferably, an installation flange is provided on the outer peripheral part of the auxiliary cylinder near the first end, and the installation flange abuts against the end of the bushing.

[0019] In this solution, the installation flange can realize the axial positioning of the auxiliary cylinder. Combining the cooperation between the first end of the auxiliary cylinder and the bushing, the auxiliary cylinder can be completely positioned. Preferably, through holes are provided on the installation flange, and threaded holes corresponding to the through holes are provided on the bushing. The installation flange can be connected to the bushing by bolts.

[0020] Preferably, the loading mechanism includes a loading shaft having a loading end and an actuating end. The loading end is disposed through the bearing housing, and the actuating end is connected to a driving device that provides a radial load to the loading shaft.

[0021] In this solution, the actuating end of the loading shaft can extend out from the outside of the turbine rear casing, facilitating the connection to the driving device and the loading of the driving device. The loading end is inside the bearing housing, and the radial load applied by the driving device is transmitted through the loading shaft to the bearing housing, causing the bearing housing to deform.

[0022] Preferably, a support rod is pivotally connected to the middle of the loading shaft, and the actuating end is pivotally connected to the driving device. The support rod is perpendicular to the loading shaft.

[0023] In this solution, the loading shaft is pivotally connected to the driving device, and the support rod is pivotally connected to the loading shaft, forming a connection mechanism that makes the loading shaft form a lever. By changing the pivotal connection position between the support rod and the loading shaft, the load output at the loading end can be changed. Additionally, since the support rod is perpendicular to the loading shaft, the support rod can better bear the load from the loading shaft.

[0024] Preferably, the loading end is connected to the bearing housing through a spherical plain bearing on the outside.

[0025] In this solution, the spherical plain bearing of the bearing housing decouples the load output at the loading end, so that when a load is applied at the loading section, no bending moment is output to the bearing housing and only a radial force is applied.

[0026] Preferably, the fixing mechanism includes a turbine casing for connecting the outer duct of the turbine rear casing.

[0027] In this solution, the turbine rear casing is fixed by the turbine casing, so the deformation of the turbine rear casing during the test is closer to the actual situation, thereby improving the measurement accuracy of the stiffness test.

[0028] A method for measuring the stiffness of a turbine rear casing, the method for measuring the stiffness of the turbine rear casing comprising:

[0029] Providing the turbine rear casing stiffness measuring device as described above;

[0030] Fixing the turbine rear casing to the fixing mechanism;

[0031] Installing the first end of the auxiliary cylinder on the bearing housing of the turbine rear casing, installing the loading mechanism on the turbine rear casing, and the loading mechanism applying a radial load to the bearing housing of the turbine rear casing;

[0032] Measuring the displacement of the second end of the auxiliary cylinder;

[0033] Calculate the deformation of the bearing seat according to the displacement of the second end of the auxiliary cylinder, and calculate the stiffness of the bearing seat.

[0034] In this solution, by using the aforementioned turbine rear casing stiffness measuring device, the deformation of the bearing seat inside the turbine rear casing is characterized at a position outside or near the outside of the turbine rear casing, so that the deformation of the bearing seat of the turbine rear casing can be conveniently obtained, and according to the loading condition, the stiffness of the bearing seat area can be calculated.

[0035] Preferably, the displacement of the bearing seat is calculated according to the following formula:

[0036] z0 = z - L·sinθ

[0037] x0 = L·cosθ + x - L

[0038]

[0039] Wherein, z0 is the radial deformation of the bearing seat, x0 is the axial deformation of the bearing seat, θ is the angle of inclination of the auxiliary cylinder after applying the radial load, L is the axial length of the part of the auxiliary cylinder outside the bearing seat, z is the radial displacement at the maximum radial displacement of the second end of the auxiliary cylinder, x is the axial displacement at the maximum axial displacement of the second end of the auxiliary cylinder, and x ′ is the axial displacement of the radial edge opposite to the maximum axial displacement on the second end of the auxiliary cylinder.

[0040] In this solution, by measuring the relevant parameters of the second end of the auxiliary cylinder, according to the above formula, the deformation of the bearing seat in the axial and radial directions can be calculated. Specifically, measuring points can be set at the second end of the auxiliary cylinder, and the displacement at the measuring points can be measured by contacting with a displacement micrometer, and the deformation of the bearing seat can be calculated through the above conversion relationship, and then the stiffness of the turbine rear casing can be obtained.

[0041] The positive and progressive effects of the present invention are as follows: For the turbine rear casing stiffness measuring device of the present invention, the fixing mechanism fixes the turbine rear casing, the first end of the auxiliary cylinder is connected to the bearing seat, and the second end extends towards the outside of the turbine rear casing. The loading mechanism can apply a load to the fixed turbine rear casing, causing the bearing seat to deform, and the second end of the auxiliary cylinder will deform accordingly. Since the second end is close to or located outside the turbine rear casing, it is more convenient to measure the displacement of the second end, and the auxiliary cylinder is not directly subjected to the load of the loading mechanism and hardly deforms. Therefore, the relationship between the displacement of the second end and the deformation of the bearing seat is certain. Therefore, the deformation of the bearing seat can be calculated by measuring the displacement of the second end, and the stiffness of the bearing seat can be obtained according to the load applied by the loading mechanism; the measuring method of the present invention can assist in measuring the displacement of the bearing seat in the turbine rear casing stiffness test, solves the problem of difficult direct measurement, and simplifies the measurement operation and test control. Brief Description of the Drawings

[0042] Figure 1 The figure is a schematic diagram of the usage state of the turbine rear casing stiffness measurement device according to an embodiment of the present invention.

[0043] Figure 2 It is Figure 1 a partially enlarged schematic diagram.

[0044] Figure 3 The figure is a schematic diagram of the structure of the auxiliary cylinder of the turbine rear casing stiffness measurement device according to an embodiment of the present invention.

[0045] Figure 4 The figure is a schematic diagram of the measurement principle of the auxiliary cylinder of the turbine rear casing stiffness measurement device according to an embodiment of the present invention.

[0046] Figure 5 The figure is a flowchart of the turbine rear casing stiffness measurement method according to an embodiment of the present invention.

[0047] Description of the Reference Numerals

[0048] Turbine rear casing 1

[0049] Bearing seat 11

[0050] Loading mechanism 2

[0051] Loading shaft 21

[0052] Loading end 211

[0053] Actuating end 212

[0054] Support rod 22

[0055] Driving device 23

[0056] Auxiliary cylinder 3

[0057] First end 31

[0058] Second end 32

[0059] Mounting flange 33

[0060] Through hole 34

[0061] Turbine casing 4

[0062] Bushing 5

[0063] Flange portion 51

[0064] Spherical plain bearing 6 Detailed Description of the Embodiments

[0065] The present invention will be further described below by way of embodiments, but the present invention is not limited to the scope of the embodiments accordingly.

[0066] This embodiment provides a stiffness measurement device for a turbine rear casing 1, as Figures 1 to 3 shown. The stiffness measurement device for the turbine rear casing 1 includes a fixing mechanism, a loading mechanism 2, and an auxiliary cylinder 3. Among them, the fixing mechanism is used to connect the turbine rear casing 1 and fix the turbine rear casing 1. The loading mechanism 2 is used to apply a radial load to the bearing seat 11 of the turbine rear casing 1. The auxiliary cylinder 3 is configured such that the first end 31 of the auxiliary cylinder 3 can be fixed to the bearing seat 11 of the turbine rear casing 1, and the second end 32 extends towards the outside of the turbine rear casing 1.

[0067] When using the stiffness measurement device for the turbine rear casing 1 of this embodiment, the fixing mechanism fixes the turbine rear casing 1. The first end 31 of the auxiliary cylinder 3 is connected to the bearing seat 11 of the turbine rear casing 1, and the second end 32 extends towards the outside of the turbine rear casing 1. Specifically, in this embodiment, the second end 32 of the auxiliary cylinder 3 is close to the mouth of the turbine rear casing 1 but does not protrude from the turbine rear casing 1, so as to achieve measurement with a relatively compact structure. In other embodiments, the second end 32 of the auxiliary cylinder 3 can also protrude from the turbine rear casing 1, so as to more conveniently measure the displacement of the second end 32.

[0068] The loading mechanism 2 can apply a load to the fixed turbine rear casing 1, causing the bearing seat 11 to deform. The second end 32 of the auxiliary cylinder 3 then deforms accordingly. Since the second end 32 is close to or located outside the turbine rear casing 1, it is more convenient to measure the displacement of the second end 32. Moreover, the auxiliary cylinder 3 is not directly subjected to the load of the loading mechanism 2 and hardly deforms. Therefore, the relationship between the displacement of the second end 32 and the deformation of the bearing seat 11 is certain. Therefore, by measuring the displacement of the second end 32, the deformation of the bearing seat 11 can be calculated, and according to the load applied by the loading mechanism 2, the stiffness of the bearing seat 11 can be calculated.

[0069] As Figure 1 and Figure 2 shown, the loading mechanism 2 of this embodiment includes a loading shaft 21, a support rod 22, and a driving device 23. The loading shaft 21 has a loading end 211 and an actuating end 212. The loading end 211 passes through the bearing seat 11, and the actuating end 212 is connected to the driving device 23. The driving device 23 provides a radial load to the loading shaft 21.

[0070] The actuating end 212 of the loading shaft 21 can protrude from outside the turbine rear casing 1 to facilitate connecting the driving device 23 and the loading of the driving device 23. The loading end 211 is inside the bearing seat 11. The radial load loaded by the driving device 23 is transmitted to the bearing seat 11 through the loading shaft 21, causing the bearing seat 11 to deform.

[0071] The support rod 22 is pivotally connected to the middle of the loading shaft 21. The driving device 23 has a driving shaft that can reciprocate along its own axis. The driving shaft is pivotally connected to the actuating end 212 of the loading shaft 21. The support rod 22 is perpendicular to the loading shaft 21. The loading shaft 21 is pivotally connected to the driving device 23, and the support rod 22 is pivotally connected to the loading shaft 21, forming a connecting mechanism, such that the loading shaft 21 constitutes a lever. By changing the pivotal connection position between the support rod 22 and the loading shaft 21, the load output at the loading end 211 can be changed. Additionally, since the support rod 22 is perpendicular to the loading shaft 21, the support rod 22 can better bear the load from the loading shaft 21. The driving device 23 can be a hydraulic cylinder, an electric cylinder, or other devices.

[0072] As Figure 2 shown, the loading end 211 is connected to the bearing block 11 through the outer spherical bearing 6. The bearing block 11 decouples the load output by the loading end 211, such that when the load is applied to the loading section, no bending moment is output to the bearing block 11, and only a radial force is applied.

[0073] In this embodiment, the fixing mechanism includes a turbine casing 4 for connecting to the outer casing of the rear turbine casing 1. The rear turbine casing 1 is fixed by the turbine casing 4. Therefore, the deformation of the rear turbine casing 1 during the test is closer to the actual situation, thereby improving the measurement accuracy of the stiffness test.

[0074] As Figure 1 and Figure 2 shown, in this embodiment, a part of the loading mechanism 2 is disposed inside the auxiliary cylinder 3. Specifically, the loading shaft 21 is disposed inside the auxiliary cylinder 3, and there is a gap between the loading shaft 21 and the inner wall of the auxiliary cylinder 3. The loading shaft 21 passes through the auxiliary cylinder 3, such that while ensuring the connection of the loading mechanism 2 to the rear turbine casing 1, the loading mechanism 2 does not contact the auxiliary cylinder 3, avoiding the loading mechanism 2 applying a load to the auxiliary cylinder 3 and causing deformation of the auxiliary cylinder 3. Additionally, since there is a gap between the loading shaft 21 and the inner wall of the auxiliary cylinder 3, when the auxiliary cylinder 3 is displaced, the loading shaft 21 will not interfere with the auxiliary cylinder 3, ensuring the accuracy of the measurement result.

[0075] The stiffness measurement device for the rear turbine casing 1 further includes a bushing 5. The bushing 5 is used to be inserted into the bearing block 11, and the auxiliary cylinder 3 is installed on the bushing 5. The auxiliary cylinder 3 is installed on the rear turbine casing 1 through the bushing 5, eliminating the need to provide a connection device on the rear turbine casing 1, avoiding a change in the stiffness at the bearing block 11 and ensuring that the measurement result can reflect the true stiffness. The loading mechanism 2 can be directly connected to the bushing 5. Therefore, the applied load acts on the bushing 5 instead of being applied to the auxiliary cylinder 3.

[0076] The first end 31 of the auxiliary cylinder 3 is fitted and inserted into the interior of the bushing 5. Since a part of the auxiliary cylinder 3 is fitted and inserted into the bushing 5, the auxiliary cylinder 3 can be positioned with the aid of the bushing 5, and the connection between the auxiliary cylinder 3 and the bushing 5 is more stable.

[0077] As Figure 2 and Figure 3 shown, an installation flange 33 is provided on the outer peripheral portion of the auxiliary cylinder 3 near the first end 31, and the installation flange 33 abuts against the end of the bushing 5. Specifically, the bushing 5 has a flange portion 51 at its axial end, and the installation flange 33 of the auxiliary cylinder 3 is fixed to the flange portion 51.

[0078] The installation flange 33 can achieve the axial positioning of the auxiliary cylinder 3. Combining with the fit between the first end 31 of the auxiliary cylinder 3 and the bushing 5, the auxiliary cylinder 3 can be fully positioned. Preferably, through holes 34 are provided on the installation flange 33, and threaded holes (not shown in the figure) corresponding to the through holes 34 one by one are provided on the flange portion 51 of the bushing 5. The installation flange 33 can be connected to the bushing 5 through bolts.

[0079] This embodiment also provides a method for measuring the stiffness of the turbine rear casing 1. As Figure 5 shown, the method for measuring the stiffness of the turbine rear casing 1 includes:

[0080] Providing the stiffness measuring device of the turbine rear casing 1 as described above;

[0081] Fixing the turbine rear casing 1 to the fixing mechanism;

[0082] Installing the first end 31 of the auxiliary cylinder 3 on the bearing seat 11 of the turbine rear casing 1, installing the loading mechanism 2 on the turbine rear casing 1, and the loading mechanism 2 applying a radial load to the bearing seat 11 of the turbine rear casing 1;

[0083] Measuring the displacement of the second end 32 of the auxiliary cylinder 3;

[0084] Calculating the deformation amount of the bearing seat 11 according to the displacement of the second end 32 of the auxiliary cylinder 3, and calculating the stiffness of the bearing seat 11.

[0085] By using the above-mentioned stiffness measuring device of the turbine rear casing 1, the deformation of the internal bearing seat 11 of the turbine rear casing 1 is characterized at a position outside or near the outside of the turbine rear casing 1, so that the deformation amount of the bearing seat 11 of the turbine rear casing 1 can be conveniently obtained, and the stiffness of the bearing seat 11 area can be calculated according to the loading condition.

[0086] The deformation amount of the bearing seat 11 can be calculated according to the following formula:

[0087] z0 = z - L·sinθ

[0088] x0 = L·cosθ + x - L

[0089]

[0090] Among them, z0 is the radial deformation of the bearing housing 11, x0 is the axial deformation of the bearing housing 11, θ is the angle of inclination of the auxiliary cylinder 3 after applying the radial load, L is the axial length of the part of the auxiliary cylinder 3 located outside the bearing housing 11, z is the radial displacement at the maximum radial displacement of the second end 32 of the auxiliary cylinder 3, x is the axial displacement at the maximum axial displacement of the second end 32 of the auxiliary cylinder 3, and x ′ is the axial displacement of the radial edge of the second end 32 of the auxiliary cylinder 3 opposite to the maximum axial displacement. Specifically, reference can be made to Figure 4 , Figure 4 which shows a schematic diagram of the offset of the auxiliary cylinder 3 before and after loading the load.

[0091] By measuring the relevant parameters of the second end 32 of the auxiliary cylinder 3 and according to the above formula, the deformation of the bearing housing 11 in the axial and radial directions can be calculated. Specifically, measuring points can be set at the second end 32 of the auxiliary cylinder 3, and the displacement at the measuring points can be measured by contacting with a displacement micrometer. The deformation of the bearing housing 11 can be calculated through the above conversion relationship, and then the stiffness of the turbine rear casing 1 can be obtained.

[0092] Although the specific embodiments of the present invention have been described above, those skilled in the art should understand that this is only an example. The protection scope of the present invention is defined by the appended claims. Without departing from the principle and essence of the present invention, those skilled in the art can make various changes or modifications to these embodiments, but these changes and modifications all fall within the protection scope of the present invention.

Claims

1. A stiffness measuring device for a turbine rear casing, characterized in that, The turbine rear casing stiffness measuring device includes: A fixing mechanism for connecting the turbine rear casing and fixing the turbine rear casing; A loading mechanism for applying a radial load to the bearing housing of the turbine rear casing; An auxiliary cylinder, the auxiliary cylinder is configured such that the first end of the auxiliary cylinder can be fixed to the bearing housing of the turbine rear casing, and the second end extends toward the outside of the turbine rear casing, and the auxiliary cylinder is not directly subjected to the load of the loading mechanism; Calculate the deformation of the bearing housing by measuring the displacement of the second end of the auxiliary cylinder, and calculate the stiffness of the bearing housing.

2. The turbine rear casing stiffness measuring device according to claim 1, characterized in that, Part of the loading mechanism is inserted into the auxiliary cylinder, and there is a gap between the loading mechanism and the inner wall of the auxiliary cylinder.

3. The turbine rear casing stiffness measurement device according to claim 1, wherein, The turbine rear casing stiffness measuring device further includes a bushing, the bushing is used for inserting into the bearing housing, and the auxiliary cylinder is installed on the bushing.

4. The turbine rear casing stiffness measuring device according to claim 3, wherein, The first end of the auxiliary cylinder is inserted into the inside of the bushing in a matching manner.

5. The turbine rear casing stiffness measuring device according to claim 4, characterized in that, An installation flange is provided on the outer peripheral portion of the auxiliary cylinder near the first end, and the installation flange abuts against the end of the bushing.

6. The turbine rear casing stiffness measurement device according to claim 1, characterized in that The loading mechanism includes a loading shaft, the loading shaft has a loading end and an actuating end, the loading end is inserted into the bearing housing, and the actuating end is connected with a driving device, and the driving device provides a radial load to the loading shaft.

7. The turbine rear casing stiffness measuring device according to claim 6, wherein, A support rod is pivotally connected to the middle of the loading shaft, the actuating end is pivotally connected to the driving device, and the support rod is perpendicular to the loading shaft.

8. The turbine rear casing stiffness measuring device according to claim 6, wherein The loading end is connected to the bearing housing through a joint bearing on the outside.

9. The turbine rear casing stiffness measuring device according to claim 1, characterized in that, The fixing mechanism includes a turbine casing for connecting the outer casing of the turbine rear casing.

10. A method for measuring the stiffness of a turbine rear casing, characterized in that, The turbine rear casing stiffness measuring method includes: Provide the turbine rear casing stiffness measuring device according to any one of claims 1-9; Fix the turbine rear casing to the fixing mechanism; Install the first end of the auxiliary cylinder on the bearing housing of the turbine rear casing, install the loading mechanism on the turbine rear casing, and the loading mechanism applies a radial load to the bearing housing of the turbine rear casing; Measure the displacement of the second end of the auxiliary cylinder; Calculate the deformation of the bearing housing according to the displacement of the second end of the auxiliary cylinder, and calculate the stiffness of the bearing housing.

11. The method for measuring the stiffness of the turbine rear casing according to claim 10, wherein The displacement of the bearing housing is calculated according to the following formula: Among them, is the radial deformation of the bearing housing, is the axial deformation of the bearing housing, θ is the angle of inclination of the auxiliary cylinder after applying the radial load, L is the axial length of the part of the auxiliary cylinder located outside the bearing housing, z is the radial displacement at the maximum radial displacement of the second end of the auxiliary cylinder, x is the axial displacement at the maximum axial displacement of the second end of the auxiliary cylinder, x′ is the axial displacement of the radial edge opposite to the maximum axial displacement on the second end of the auxiliary cylinder, and d is the outer diameter of the auxiliary cylinder.

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