JP2010209956A - Analysis method for squeeze film damper bearing - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an analysis method for a squeeze film damper bearing allowing design of a damper fulfilling target characteristics (a spring constant, maximum stress, etc.) at a high accuracy and considerably shortening a time required for the design. <P>SOLUTION: A simple FEM model with boundary conditions set to a main elastic portion (an intermediate circular arc 16) bearing elastic characteristics out of the damper bearing 10 is prepared. At least one (an open angle θ and a thickness t of the intermediate circular arc part 16) out of the main dimensions of the damper bearing is used as a parameter to change into 2 or higher, and predetermined characteristic values (a spring constant K and maximum stress) of the damper bearing are analyzed by an FEM analysis using a finite element method. An approximate function showing a relationship between the obtained characteristic values and the parameter is set, and the approximate function is used to obtain the characteristic value to the value of the parameter whose FEM analysis is not made. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for analyzing a squeeze film damper bearing that supports a high-speed rotating shaft such as a jet engine and suppresses vibration thereof.

A squeeze film damper bearing is a type of bearing in which a fluid film is formed between a bearing that supports a rotating shaft and a fixed surface, and the bearing is supported by this fluid film pressure, particularly reducing vibration of a high-speed rotating shaft. There are features. Therefore, this bearing has been conventionally used as a bearing for jet engines, turbo compressors, turbochargers and the like.
Hereinafter, in the present application, the squeeze film damper bearing is simply referred to as “damper bearing”.

  Conventional damper bearings are disclosed in Patent Documents 1 to 3, for example.

JP-A-8-261232, “Squeeze film damper bearing” JP 2001-303964 A, “Turbocharger Bearing Structure” Japanese Patent Application Laid-Open No. 2007-56976, “Damper element of bearing, manufacturing method thereof, and gas turbine engine”

  Conventionally, in the structural design of a damper bearing, in order to obtain the required target characteristics (spring constant, maximum stress, etc.), the entire structure (shape, dimensions, material, etc.) of the damper bearing is provisionally set in advance. Based on this, an analysis model (hereinafter referred to as “complete FEM model”) was created, and its characteristics were analyzed by FEM analysis using a finite element method.

  However, in this case, since the complete FEM model covers the entire damper bearing, there is a problem that one FEM analysis requires a long time.

  Further, in the conventional design method, in order to obtain the target characteristics, it is necessary to change a part of the entire structure little by little, and each time a complete FEM model corresponding to the structure needs to be recreated. It took a long time.

  As a result, it is necessary to repeat creation of a complete FEM model and FEM analysis to design the overall structure (shape, dimensions, material, etc. of each part) of the damper bearing that accurately satisfies the target characteristics (spring constant, maximum stress, etc.) As a whole, there was a problem that required a very long time.

On the other hand, the elastic part of the damper bearing can be modeled with a simple beam (hereinafter referred to as “beam model”), and its characteristics can be analyzed using material mechanics with or without a simple FEM analysis. In principle it is possible. In this case, there is an advantage that the characteristic analysis of the damper bearing can be performed in a short time.
However, in this case, there is a great difference from the analysis result of the FEM analysis using the complete FEM model, and there is a problem that the target characteristics (spring constant, maximum stress, etc.) cannot be achieved accurately.

  The present invention has been developed to solve the above-described problems. That is, an object of the present invention is to design a damper bearing that satisfies the target characteristics (spring constant, maximum stress, etc.) with high accuracy, and to significantly reduce the time required for the design. It is to provide an analysis method.

According to the present invention, there is provided an analysis method for an integrated squeeze film damper bearing that is inserted between a cylindrical rotary shaft or radial bearing and a cylindrical fixed surface surrounding the cylindrical rotary shaft or radial bearing, and supports the rotary shaft or radial bearing. ,
A simple FEM model is created by setting boundary conditions in the main elastic portion that bears the elastic characteristics of the damper bearing,
By changing at least one of the main dimensions of the damper bearing as a parameter to a value of 2 or more, a predetermined characteristic value of the damper bearing is obtained by FEM analysis using a finite element method,
Set an approximate function indicating the relationship between the obtained characteristic value and the value of the parameter,
There is provided a method for analyzing a squeeze film damper bearing, wherein the characteristic value with respect to a value of the parameter not subjected to FEM analysis is obtained using the approximate function.

According to a preferred embodiment of the present invention, the damper bearing includes a hollow cylindrical inner ring that slidably supports an outer surface of a rotary shaft or a radial bearing, and a hollow cylindrical shape that is fixed in close contact with the fixed surface. An outer ring and three or more intermediate arc portions that are positioned with a slit between the inner ring and the outer ring and spaced at the same interval in the circumferential direction;
Each of the intermediate arc portions has one circumferential end integrally connected to the outer ring and the other end integrally connected to the inner ring.
A simple FEM model is created using the intermediate arc as the main elastic portion.

The characteristic value is a spring constant or maximum stress,
It is preferable that the approximate function is a common logarithmic approximate curve or a quadratic function whose parameter is the opening angle between the outer ends of the intermediate arc portion or the radial thickness of the intermediate arc portion.

Furthermore, a beam model that simulates at least a part of the simplified FEM model with a beam is created,
It is preferable to modify at least one of the main dimensions of the damper bearing excluding the parameters so that the characteristic value obtained by using this matches the characteristic value obtained by the simple FEM model.

  According to the configuration of the present invention, a simple FEM model in which boundary conditions are set in a main elastic portion that bears the elastic characteristics of an integrated squeeze film damper bearing is created. Therefore, a complete FEM model for the entire damper bearing Compared with the FEM analysis using, the size of the model is significantly smaller (for example, about 1/10), so that the time required for one FEM analysis can be greatly shortened.

  Further, at least one of the major dimensions of the damper bearing (for example, the opening angle between the outer ends of the intermediate arc portion or the thickness of the intermediate arc portion) was changed to a value of 2 or more as a parameter, and the finite element method was used. Analyzing a predetermined characteristic value of the damper bearing by FEM analysis, setting an approximate function indicating a relationship between the obtained characteristic value and the parameter, and using the approximate function, the characteristic with respect to the value of the parameter not subjected to the FEM analysis Since the value is obtained, a damper bearing that satisfies the target characteristics (spring constant, maximum stress, etc.) with high accuracy can be designed, and the time required for the design can be greatly shortened.

Further, a beam model in which at least a part of the simplified FEM model is simulated with a beam is created, and a damper bearing excluding the parameters is used so that a characteristic value obtained by using the beam model matches a characteristic value obtained by the simplified FEM model. By modifying at least one of the main dimensions, the accuracy of the analysis result by the beam model can be improved, and the damper bearing that satisfies the target characteristics (spring constant, maximum stress, etc.) with high accuracy using the beam model Can be designed, and the time required for the design can be further shortened.

It is a functional block diagram of the simulation apparatus which performs the analysis method of the present invention. It is a whole flowchart which shows the analysis method of the squeeze film damper bearing by this invention. 1 is an overall structural diagram of a damper bearing targeted by the present invention. It is a FEM model figure of a damper bearing. 4 is a relationship diagram between a thickness t and a spring constant K. FIG. It is the relationship figure which displayed both the thickness t and the spring constant K by the common logarithm. FIG. 5 is a relationship diagram showing a relationship between an opening angle θ and a common logarithm of a spring constant K. FIG. 6 is a relationship diagram between a thickness t and a spring constant K when the opening angle θ is φ degrees. It is a beam model figure of a damper bearing. It is a comparison figure of the analysis result of a beam model and a simple FEM model. It is a comparison figure of the analysis result of a beam model and a simple FEM model at the time of displaying maximum stress by the quadratic function of thickness t. It is a comparison figure of the FEM analysis result of a beam model, and the analysis result using Formula (6).

  DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, the best mode for carrying out the invention will be described with reference to the drawings. In addition, the same code | symbol is attached | subjected to the common part in each figure, and the overlapping description is abbreviate | omitted.

FIG. 1 is a functional block diagram of a simulation apparatus 1 that executes the analysis method of the present invention. As shown in this figure, a simulation apparatus 1 (for example, a computer) that executes the analysis method of the present invention includes a three-dimensional data input unit 2, a material data storage unit 3, an analysis condition storage unit 4, an FEM analysis unit 5, and an evaluation unit. 6 and a standard storage unit 7.
The three-dimensional data input unit 1 inputs three-dimensional data of an object (damper bearing).
The FEM analysis unit 5 performs FEM analysis using the three-dimensional data, the material data stored in the material data storage unit 3, and the analysis conditions stored in the analysis condition storage unit 4.
The evaluation unit 6 evaluates the object (damper bearing) by comparing the FEM analysis with the standard stored in the standard storage unit 7.

FIG. 2 is an overall flow chart showing a method for analyzing a squeeze film damper bearing according to the present invention.
In this figure, the analysis method of the present invention is for an integrated squeeze film damper bearing that is inserted between a cylindrical rotary shaft or radial bearing and a cylindrical fixed surface surrounding the cylindrical rotary shaft or radial bearing and supports the rotary shaft or radial bearing. This is an analysis method, and includes steps S1 to S4.

In step S1, a simple FEM model is created by setting boundary conditions for the main elastic portion that bears the elastic characteristics of the damper bearing.
The “main elastic part responsible for elastic properties” is, for example, a FEM analysis using a finite element method using a complete FEM model for the entire damper bearing, and selecting a part where a large stress or deflection occurs. It is good. In this simple FEM model, it is preferable to set boundary conditions appropriately.

In step S2, at least one of the major dimensions of the damper bearing is changed to a value of 2 or more as a parameter, and a predetermined characteristic value of the damper bearing is acquired by FEM analysis using a finite element method.
The main dimensions of the damper bearing are, for example, inner diameter, outer diameter, width and length of each part, slit width, material properties (Young's modulus, Poisson's ratio, allowable stress, etc.). The opening angle between the outer ends of the intermediate arc portion) or the radial thickness thereof may be used as a parameter.
The predetermined characteristic value is preferably a spring constant or maximum stress, but may be other characteristic values.

In step S3, an approximation function indicating the relationship between the characteristic value obtained in step S2 and the parameter value is set.
The approximation function is, for example, a common logarithmic approximation curve or a quadratic function whose parameter is the opening angle between the outer ends of the main elastic portion (intermediate arc portion to be described later) or the radial thickness thereof. May be.

  In step S4, the characteristic value for the parameter value that has not been subjected to FEM analysis is obtained using the set approximation function.

  In FIG. 1, the analysis method of the present invention further includes steps S5 to S8.

In step S5, a beam model in which at least a part of the simplified FEM model created in step S1 is simulated with a beam is created.
For example, the main elastic portion (intermediate arc portion to be described later) is simulated with a beam having a constant cross section.

In step S6, at least one of the major dimensions of the damper bearing is changed to a value of 2 or more as a parameter, and a predetermined characteristic value of the damper bearing is obtained by analysis.
This analysis may be FEM analysis using a finite element method, or may be analysis based on material mechanics.

In step S7, an approximation function indicating the relationship between the characteristic value obtained in step S2 and the value of the parameter is set.
This approximate function may be the same as the approximate function set in step S3, or may be a simplified version thereof.

In step S8, at least one of the major dimensions of the damper bearing excluding the parameters is corrected so that the characteristic value obtained using the approximate function set in step S7 matches the characteristic value based on the simple FEM model.
For example, the thickness in the beam model is increased or decreased so that the characteristic values according to the simple FEM model match.

  In step S4, using the approximate function set in step S7, the characteristic value for the parameter value not subjected to FEM analysis is obtained.

  By performing step S4 in detail using the approximate function set in step S7, the number of FEM analyzes in step S2 can be reduced.

FIG. 3 is an overall structural view of a damper bearing targeted by the present invention. FIG. 3A is a diagram of a first embodiment, and FIG. 3B is a diagram of a second embodiment.
3A is a front view of the damper bearing 10 as viewed from the axial direction.

In FIG. 3A, a damper bearing 10 is an integral squeeze film damper bearing and has a hollow cylindrical shape as a whole, and is inserted between a cylindrical rotary shaft 20 and a cylindrical fixed surface 30 surrounding the cylindrical rotary shaft 20. Thus, the rotation of the rotary shaft 20 is supported.
The rotary shaft 20 may be replaced with a normal radial bearing (ball bearing, roller bearing, etc.) to support the radial bearing. That is, the damper bearing may support the “rotary shaft” or the “radial bearing”.
Hereinafter, in this figure, the rotation center of the rotary shaft 20 (or radial bearing) (that is, the center of the cylindrical fixed surface 30) is defined as the origin O, and the x-axis and the y-axis are defined as shown in the figure.

  The damper bearing 10 includes an inner ring 12, an outer ring 14, and four intermediate arc portions 16. The inner ring 12, the outer ring 14, and the intermediate arc portion 16 are partially separated by a slit 18, but are an integral member as a whole. Lubricating oil is supplied to the inner surface of the inner ring 12 and the slit 18, and the vibration of the rotary shaft 20 (or radial bearing) is reduced by the fluid film pressure between the slits 18.

The inner ring 12 is a hollow cylindrical member centered on the origin O, and supports the outer surface of the rotating shaft 20 (or radial bearing) on its inner surface. The clearance between the inner surface of the inner ring 12 and the outer surface of the rotating shaft 20 is set to be as small as possible so that the rotating shaft 20 can rotate at a predetermined high speed around the axis center while the inner ring 12 is fixed.
In the case of a radial bearing, the outer ring of the radial bearing is fixed to the inner ring 12.

  The outer ring 14 is a hollow cylindrical member centered on the origin O, and its outer surface is fixed in close contact with the fixed surface 30. The outer surface of the outer ring 14 is fitted to the fixed surface 30 without a gap, and the rotating shaft 20 can rotate at a predetermined high speed around the axis center without rotating together with the outer ring 14 fixed to the fixed surface 30. It is like that.

The intermediate arc portion 16 is an arc-shaped member whose inner and outer surfaces are arc surfaces centered on the origin O. That is, the intermediate arc portion 16 is a curved beam having a constant radius from the rotation shaft 20 or the rotation center O of the radial bearing and having a constant radial thickness.
Further, the intermediate arc portion 16 is located between the inner ring 12 and the outer ring 14 with a slit 18 having a predetermined width therebetween.
Further, in this example, the four intermediate arc portions 16 are spaced at the same interval in the circumferential direction, and the circumferential angle is 90 degrees.

  Further, each intermediate arc portion 16 has one circumferential end 16 a integrally connected to the outer ring 14 and the other end 16 b integrally connected to the inner ring 12.

The slit 18 includes an outer slit 18 a between the outer ring 14 and an inner slit 18 b between the inner ring 12. Each outer slit 18a is connected to an inner slit 18b of an adjacent intermediate arc portion 16 by an inclined slit 18c inclined in the circumferential direction.
The outer slit 18a, the inner slit 18b, and the inclined slit 18c are preferably through-grooves having the same width in the radial direction and parallel to the axial direction. The width of these slits is such that the slit width does not become zero (ie, does not contact) due to the shaft vibration of the rotary shaft 20 (or radial bearing), and the rotary shaft 20 (or radial bearing) due to the fluid film pressure between the slits 18. It is preferable to set so as to effectively reduce the vibration.

  Further, the outer slit 18a and the inner slit 18b connected by the inclined slit 18c have through holes 19 for stress reduction at both ends thereof. The size of the through hole 19 is set so that the maximum stress generated around the through hole 19 does not exceed the allowable stress of the material.

FIG. 3B is a diagram showing a second embodiment of the damper bearing, and is a front view of the damper bearing 10 as viewed from the axial direction.
The damper bearing 10 includes an inner ring 12, an outer ring 14, and three intermediate arc portions 16. In this example, the three intermediate arc portions 16 are equally spaced in the circumferential direction, and the circumferential angle is 120 degrees.
Other configurations are the same as those of the first embodiment shown in FIG.

In the present invention, the intermediate arc portion of the damper bearing is not limited to 3 or 4, and may be 5 or more.
Further, the damper bearing is not limited to the above-described embodiment, and may be a damper bearing having another configuration.
Hereinafter, the present invention will be described with respect to the damper bearing of FIG.

4A and 4B are FEM model diagrams of the damper bearing. FIG. 4A is a complete FEM model, and FIG. 4B is a simplified FEM model.
4A is a complete FEM model based on FIG. 1A, in which the outer surface of the outer ring 14 of the model is fixed (indicated by a broken line 1), and the inner surface of the inner ring 12 is an integral rigid body (indicated by a broken line 2). As a whole, the characteristics were analyzed by FEM analysis using a finite element method.
In this figure, θ is an opening angle with respect to the axis O between the centers of two adjacent through holes 19.

  In order to create a complete FEM model based on FIG. 3 (A), the inner diameter, outer diameter, width, slit width, material properties (Young's modulus, Poisson's ratio, allowable stress, etc.) of the damper bearing 10 are provisionally provisionally. Must be set to

The inventors of the present invention use a complete FEM model of FIG. 4A as a finite element for the damper bearing 10 having the structure of FIG. 3A with a spring constant satisfying the design specifications as a target characteristic. The characteristics were analyzed by FEM analysis using a method.
As a result, in this model, a large stress is generated around the intermediate arc portion 16 and the through hole 19, but the other stresses generated in the inner ring 12 and the outer ring 14 are sufficiently smaller than the allowable stress. It became clear that it could be ignored.

A simplified FEM model shown in FIG. 4B is a simplified version of the complete FEM model based on this new knowledge.
In this simple FEM model, boundary conditions are appropriately set instead of the outer ring 14 and the inner ring 12, and only the connecting portion of the intermediate arc portion 16, the intermediate arc portion 16, the outer ring 14 and the inner ring 12 (around the through hole 19). The characteristics can be analyzed by FEM analysis using a finite element method.

That is, in this simple FEM model, one end 16a in the circumferential direction of the intermediate arc portion 16 is integrally connected to the peripheral portion 14a of the through hole 19 of the outer ring 14, and this peripheral portion 14a is a rigid body (dashed line) that simulates the fixed surface 30. 3). Further, the other circumferential end 16b of the intermediate arc portion 16 is integrally connected to the peripheral portion 12a of the through hole 19 of the inner ring 12, and this peripheral portion 12a is an integral rigid body that simulates a rotating shaft (or radial bearing). (Indicated by a broken line 4).
Further, the outer end portion (peripheral portion 14a) is completely fixed by a rigid body (dashed line 3), and the inner end portion (peripheral portion 12a) is radially moved along with the movement of the rotating shaft (or radial bearing). Only supported by movable.

By using the simple FEM model described above, the characteristics of the damper bearing 10 are analyzed by the FEM analysis using the finite element method only at the single intermediate arc portion 16 and the ends (peripheral portions 14a and 12a) at both ends thereof. can do.
Accordingly, when compared with FEM analysis using a complete FEM model, the size of the model is significantly smaller (for example, about 1/10), so that the time required for one FEM analysis can be greatly shortened. .

  The inventors of the present invention set the complete constant FEM model in FIG. 4A and FIG. 4B for the damper bearing 10 having the structure in FIG. The characteristics were analyzed by FEM analysis using a finite element method using a simple FEM model.

Table 1 shows the maximum stress and the maximum reaction force RF obtained by this analysis. According to Table 1, the maximum stress is almost the same in both models, and it was confirmed that the maximum stress and the spring constant can be predicted almost accurately (with an error of about 1%) even in the simple FEM model.
In this embodiment, “maximum equivalent stress” is adopted as the “maximum stress”. However, in the invention, the “maximum stress” is not limited to the “maximum equivalent stress”, and may be each stress component.

  In the simple FEM model of FIG. 4B, the spring constant K is changed by changing the opening angle θ of the two through-holes 19 in three ways of α, β, and γ degrees and the thickness t of the intermediate arc portion 16 in five ways. Was determined by FEM analysis. The analysis results are shown in FIGS.

  FIG. 5 is a relationship diagram between the thickness t and the spring constant K. From this figure, it can be seen that the spring constant K increases as the thickness t increases, and the spring constant K increases as the opening angle θ increases.

  FIG. 6 is a relationship diagram in which both the thickness t and the spring constant K are displayed in common logarithm. In this figure, it can be seen that the relationship between the thickness t and the spring constant K is accurately located on a straight line with respect to the three opening angles θ, and can be expressed by the equation (1) in Equation (1).

Incidentally, R _theta ² is a correlation coefficient that displays the accuracy of the approximation, the range of the correlation coefficient is from 0 (low accuracy) to 1 (high accuracy). Therefore, it can be said that Formula (1) is very high precision. In FIG. 4, R _α ² = 0.999, R _β ² = 0.999, and R _γ ² = 0.999.

  FIG. 7 is a relationship diagram showing the relationship between the opening angle θ and the common logarithm of the spring constant K. In this figure, for five thicknesses t, the relationship between the opening angle θ and the spring constant K is precisely located on a straight line, and the common logarithm of the spring constant K is exactly proportional to the opening angle θ. I understand that.

  When equation (1) described above is changed to a common logarithmic type, equation (2) of equation 2 is obtained. Further, the relationship between two angles (for example, θ = γ and θ = α) is given by Equation (3). In the common logarithm, since the common logarithm of the spring constant K is proportional to the opening angle θ, Equation (4) Holds.

Similar to Equation (4), the equation of a straight line satisfying an arbitrary angle θ _n at a certain thickness t is as Equation (5) in Equation 3. Here, a _n , b _n , and C _n are given by Expression (6).
Furthermore, from Equation (5), the approximate function of the beam model is as in Equation (7).

From equations (6) and (7), the spring constant Kn can be obtained for the structure of the damper bearing that has not been subjected to FEM analysis, in this example, the opening angle θ or thickness t that has not been analyzed.
For example, the result when the opening angle θ is φ degrees is shown in FIG. As shown in this figure, with respect to the opening angle θ and thickness t where FEM analysis is not performed, the spring constant Kn is calculated from the two or more data subjected to FEM analysis using the approximate function of the beam model of Equation (7). Can be sought.

Table 2 shows a comparison between the spring constant obtained by FEM analysis and the spring constant obtained by using the approximate function of the beam model of Expression (7).
From this table, it can be seen that the error of the analysis result using the approximate function with respect to the FEM analysis result is about 1% at the maximum, and is so small that it can be ignored in normal design.

FIG. 9 is a beam model diagram of a damper bearing.
In this beam model, one end 16 a in the circumferential direction of the intermediate arc portion 16 is fixed to the rigid body 3 that simulates the fixed surface 30. Further, the other circumferential end 16b of the intermediate arc portion 16 is integrally connected to an integral rigid body 4 that simulates a rotating shaft (or radial bearing).
That is, the one end 16a is supported by the rigid body 3 in a completely fixed manner, and the other end 16b is supported so as to be movable only in the radial direction along with the movement of the rotating shaft (or radial bearing).
In this model, the opening angle θ corresponds to the opening angle between the outer ends of the intermediate arc portion.

  By using this beam model, characteristics can be easily obtained in a short time by simple FEM analysis using the finite element method or by analysis based on material mechanics without performing FEM analysis.

FIG. 10 is a comparison diagram of the analysis results of the beam model and the simple FEM model.
From this figure, it can be seen that the error of the analysis result by the beam model is large. Therefore, when analyzing the damper bearing with the beam model, it is necessary to correct the parameters of the beam model in order to obtain the same result as the simple FEM model. This correction is preferably determined from a relational function between the beam model and the simplified FEM model so that the characteristic value obtained using the beam model matches the characteristic value obtained by the simplified FEM model.

  In the example of the second embodiment, the common logarithmic approximation curve of the formula (1) is used, but other approximations can be used to further improve the accuracy.

In the above example, there are two parameters (opening angle and thickness) of the main elastic portion (intermediate arc portion), but the same method can be applied even under conditions including other parameters.
In the above example, the predetermined characteristic value of the damper bearing is a spring constant, but other characteristic values (for example, maximum stress) can be analyzed by the same process.

FIG. 11 is a comparison diagram of the analysis results of the beam model and the simplified FEM model when the maximum stress is displayed as a quadratic function of the thickness t.
From this figure, the analysis result of the simple FEM model shows that the correlation coefficient is 1 and the accuracy is high when the maximum stress is displayed as a quadratic function of the thickness t. Further, it can be seen that the analysis result of the beam model is lower than that of the simple FEM model.

As described above, assuming a linear relationship with the opening angle θ, the function is a function of two variables (formula (1)). On the other hand, in order to further improve the accuracy, a function of three variables can be used without assuming a linear relationship. For example, when polynomial approximation is used, Expression (1) can be replaced with Expression (8) of Formula 4.
Furthermore, the constants A _θ , B _θ , and C _θ in Expression (8) _depend on the opening angle θ and can be defined by Expression (9). Therefore, the last model is as shown in Equation (10).

FIG. 12 is a comparison diagram between the FEM analysis result of the beam model and the analysis result using Expression (10).
From this figure, it can be seen that since the linear relationship between the angles is not assumed, the accuracy is improved, and the analysis results of the two coincide with each other with high accuracy.

  According to the configuration of the present invention described above, a simple FEM model in which boundary conditions are set in the main elastic portion (intermediate arc portion 16) that bears the elastic characteristics of the integrated squeeze film damper bearing 10 is created. Compared with FEM analysis using a complete FEM model for the entire model, the size of the model is significantly smaller (for example, about 1/10), so the time required for one FEM analysis is greatly reduced. be able to.

  Further, at least one of the main dimensions of the damper bearing (for example, the opening angle θ between the outer ends of the intermediate arc portion or the thickness t of the intermediate arc portion) is changed to a value of 2 or more as a parameter, and the finite element method is performed. A predetermined characteristic value of the damper bearing is analyzed by the used FEM analysis, an approximate function indicating the relationship between the obtained characteristic value and the parameter is set, and the parameter value for which the FEM analysis is not performed using the approximate function is set. Since the characteristic value is obtained, a damper bearing that satisfies the target characteristics (spring constant, maximum stress, etc.) with high accuracy can be designed, and the time required for the design can be greatly shortened.

  Further, a beam model in which at least a part of the simple FEM model is simulated with a beam is created, and the characteristic value obtained by using this is matched with the characteristic value obtained by the simple FEM model. By correcting at least one of the main dimensions, the accuracy of the analysis result by the beam model can be improved, and a damper bearing that satisfies the target characteristics (spring constant, maximum stress, etc.) with high accuracy by using the beam model. The time required for designing can be further shortened.

  Note that the present invention is not limited to the above-described embodiment, and it is needless to say that various modifications can be made without departing from the gist of the present invention.

10 damper bearing,
12 inner ring, 14 outer ring, 16 intermediate arc part,
16a one end, 16b the other end, 18 slits,
18a outer slit, 18b inner slit,
19 Through hole, 20 Rotating shaft, 30 Fixed surface

Claims (4)

An analysis method for an integrated squeeze film damper bearing inserted between a cylindrical rotary shaft or radial bearing and a cylindrical fixed surface surrounding the cylindrical rotary shaft or supporting the rotary shaft or radial bearing,
A simple FEM model is created by setting boundary conditions in the main elastic portion that bears the elastic characteristics of the damper bearing,
By changing at least one of the main dimensions of the damper bearing as a parameter to a value of 2 or more, a predetermined characteristic value of the damper bearing is obtained by FEM analysis using a finite element method,
Set an approximate function indicating the relationship between the obtained characteristic value and the value of the parameter,
A method for analyzing a squeeze film damper bearing, wherein the characteristic value for the value of the parameter not subjected to FEM analysis is obtained using the approximate function. The damper bearing includes a hollow cylindrical inner ring that slidably supports an outer surface of a rotary shaft or a radial bearing, a hollow cylindrical outer ring that is fixed in close contact with the fixed surface, and a space between the inner ring and the outer ring. And three or more intermediate arcs that are spaced apart by the same distance in the circumferential direction.
Each of the intermediate arc portions has one circumferential end integrally connected to the outer ring and the other end integrally connected to the inner ring.
The squeeze film damper bearing analysis method according to claim 1, wherein a simple FEM model is created with the intermediate arc portion as the main elastic portion. The characteristic value is a spring constant or maximum stress,
3. The approximate function is a common logarithmic approximate curve or a quadratic function using the opening angle between the outer ends of the intermediate arc part or the radial thickness of the intermediate arc part as a parameter. Analysis method for squeeze film damper bearing Creating a beam model simulating at least a part of the simplified FEM model with a beam;
The at least one of the main dimensions of the damper bearing excluding the parameter is corrected so that the characteristic value obtained by using this matches the characteristic value by the simple FEM model. Analysis method for squeeze film damper bearings.

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