CN110399628B - Constant-pressure pre-tightening angular contact bearing rigidity value correction method considering vibration influence - Google Patents
Constant-pressure pre-tightening angular contact bearing rigidity value correction method considering vibration influence Download PDFInfo
- Publication number
- CN110399628B CN110399628B CN201910410138.1A CN201910410138A CN110399628B CN 110399628 B CN110399628 B CN 110399628B CN 201910410138 A CN201910410138 A CN 201910410138A CN 110399628 B CN110399628 B CN 110399628B
- Authority
- CN
- China
- Prior art keywords
- bearing
- axial
- radial
- stiffness
- rigidity
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 26
- 238000012937 correction Methods 0.000 title claims abstract description 23
- 238000004364 calculation method Methods 0.000 claims abstract description 37
- 238000004458 analytical method Methods 0.000 claims abstract description 32
- 238000006073 displacement reaction Methods 0.000 claims description 50
- 230000004044 response Effects 0.000 claims description 26
- 238000005096 rolling process Methods 0.000 claims description 21
- 238000005452 bending Methods 0.000 claims description 17
- 230000014509 gene expression Effects 0.000 claims description 13
- 230000009471 action Effects 0.000 claims description 12
- 230000008569 process Effects 0.000 claims description 12
- 239000011159 matrix material Substances 0.000 claims description 10
- 230000008859 change Effects 0.000 claims description 9
- 238000006243 chemical reaction Methods 0.000 claims description 9
- 229910000831 Steel Inorganic materials 0.000 claims description 5
- 230000005284 excitation Effects 0.000 claims description 5
- 238000009434 installation Methods 0.000 claims description 5
- 239000010959 steel Substances 0.000 claims description 5
- 238000010276 construction Methods 0.000 claims description 4
- 238000013016 damping Methods 0.000 claims description 4
- 238000013461 design Methods 0.000 claims description 3
- 238000011161 development Methods 0.000 claims description 3
- 238000013519 translation Methods 0.000 claims description 3
- 230000007423 decrease Effects 0.000 claims description 2
- 239000000463 material Substances 0.000 claims description 2
- 238000003825 pressing Methods 0.000 claims description 2
- 239000013598 vector Substances 0.000 claims description 2
- 238000004088 simulation Methods 0.000 abstract description 9
- 238000012360 testing method Methods 0.000 description 9
- 238000010586 diagram Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- 238000011835 investigation Methods 0.000 description 2
- 230000036316 preload Effects 0.000 description 2
- 238000005299 abrasion Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
Images
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Support Of The Bearing (AREA)
- Rolling Contact Bearings (AREA)
Abstract
A method for correcting rigidity numerical values of constant-pressure pre-tightening angular contact bearings considering vibration influence comprises the following steps: 1. constructing a finite element model of the rotor system; 2. constructing a simplified model of the angular contact bearing; 3. solving a bearing load-rigidity curve to give an initial value for rigidity; 4. performing modal shape trial calculation on a rotor system comprising a bearing equivalent spring model; 5. and carrying out iterative correction of the bearing rigidity by considering the vibration load. A two-dimensional equivalent spring model is constructed by using Matrix27 in ANSYS software, so that the calculation amount for carrying out the whole numerical simulation of the rotor system is reduced on the premise of ensuring the calculation accuracy. When the rigidity of the spring is corrected, the main factors influencing the rigidity of the bearing are comprehensively considered by combining the vibration mode characteristics of a target structure, and the influence of steady-state vibration and pretightening force on the rigidity of the bearing is repeatedly considered. The model can effectively communicate a macroscopic rotor system with a microscopic bearing mechanical analysis model, and has a large application demand in actual work.
Description
Technical Field
The invention belongs to the technical field of vibration reliability of a rotor structure, and particularly relates to an iterative angular contact bearing rigidity correction method capable of considering vibration load action under a constant-pressure pre-tightening condition.
Background
Structural damage caused by resonance is a common fault of a rotor structure, and avoiding resonance of the rotor structure under actual working conditions is an important concern when designing the rotor structure. The angular contact bearing is used as a common connecting piece of a rotor structure and a bearing frame, has important influence on the integral resonance frequency of the rotor system, and the stress condition of the angular contact bearing under the resonance condition is also focused.
When a rotor system resonates, the bearing serving as a connecting piece of the rotor and the stator is subjected to load change, and the contact state of the rolling body and the raceway is changed, so that the rigidity of the bearing is changed, and further the resonant frequency of the rotor system is shifted. In general, due to the complex configuration of an actual rotor system, the working state of a bearing when the system resonates cannot be directly measured through tests, and only a numerical simulation technology can be relied on. In most simulation practices, the connection position of the rotor structure and the bearing is usually set as a fixed connection. The setting mode is feasible when structural static force analysis is carried out, but in modal analysis, the axial rigidity of the original system is changed, and therefore large precision deviation is brought to a calculation result. A plurality of researchers develop a great deal of special research by taking the bearing as an object, provide a mechanical analysis model considering the contact action of the rolling body and the raceway, improve the simulation precision, make the local model of the bearing too complex, greatly improve the calculated amount, and cause that the dynamic simulation aiming at the whole complex rotor system is difficult to develop. Therefore, up to now, a bearing numerical simulation model which can not only consider the influence of the vibration of the whole machine on the working state of the bearing and provide the precision meeting the modal analysis result of the whole machine, but also can carry out the dynamic analysis of the whole machine on a complex rotor system is not provided, and the model which can effectively communicate the macroscopic rotor system with the microscopic bearing mechanical analysis has a great demand in the actual work.
The invention provides an equivalent spring model of an angular contact bearing and a rigidity iterative correction method considering the vibration load effect. A two-dimensional equivalent spring model is constructed by using Matrix27 provided in ANSYS software, so that the calculation amount of numerical simulation is greatly reduced on the premise of ensuring the calculation accuracy. In addition, when the rigidity of the spring is corrected, the main factors influencing the rigidity of the bearing are comprehensively considered by combining the vibration mode characteristics of the target structure, and the influence of steady-state vibration and pretightening force on the rigidity of the bearing is considered. The existing research shows that through the iterative correction of the rigidity, the modal frequency of the structure is closer to the test result, which also shows that the stress of the bearing is closer to the real situation in the vibration process.
Disclosure of Invention
The invention takes the angular contact bearing as an object (particularly, the 7000C type angular contact bearing is taken as an example), and provides the angular contact bearing rigidity correction method which not only meets the requirement of the overall modal analysis precision, but also can analyze the stress condition of the bearing during resonance. Because the frequency values of the umbrella-shaped vibration mode and the pitch diameter vibration mode of the rotor structure are usually lower, the low-frequency excitation force can excite resonance, and the concrete process of bearing rigidity analysis is given by taking the pitch circle and the pitch diameter of the vibration rotor as examples.
The specific steps implemented are given below in combination with the following calculation:
step 1: constructing a finite element model of a rotor system
And establishing a finite element model of the target rotor system in CAE preprocessing software aiming at the given entity model, then importing the established finite element model into finite element software ANSYS, and defining corresponding material parameters, given rotating speed and displacement constraint conditions.
Step 2: construction of simplified model of angular contact bearing
(1) Selection spring unit
Matrix unit Matrix27 in ANSYS software is selected as a basic unit for constructing a bearing equivalent model. Matrix27 is a Matrix element with arbitrary geometry, which is composed of two nodes, each node has six degrees of freedom, and comprises three directions of translation and three directions of rotation (as shown in fig. 1). It is a versatile unit that can be represented in matrix form as stiffness, damping and mass. In the bearing simplification model, matrix27 is used to represent stiffness. For a bearing, the main stiffness is axial and radial, and the circumferential stiffness is zero, so that the Matrix27 needs to convert the node coordinate system from a cartesian coordinate system to a local cylindrical coordinate system and set the circumferential stiffness (Y direction) to 0 when in use.
(2) Constructing an equivalent bearing model
The bearing is equivalent to a spring mass model formed by a bearing outer ring, n spring-bearing inner rings (as shown in figure 2).
Axial and radial stiffness K of primary interest for bearings a 、K r It should be established and simplified as well as the axial stiffness k of the spring a And radial stiffness k r The conversion relationship of (1). Along the axial direction, the bearing uses n springs in parallel to represent the axial stiffness, K is known easily a ＝n·k a . For radial stiffness, the finite element model shown in fig. 3a and 3b can be used to obtain the conversion K r ＝n’·k r (wherein n' is the radial stiffness of the bearing and the simplified radial stiffness k r The scaling factor of (c). In fig. 3a and 3b, the free end of the middle spring is fully constrained, and meanwhile, the circumferential displacement of a node on the inner side of the rotor model is constrained to be 0, so that the rotor is limitedAnd (4) rotating in the circumferential direction. Then applying different radial forces F in the direction of the arrows r And the displacement of the far end node of the acting force along the radial force direction is used for representing the radial rigid body displacement of the rotor, so that the spring stiffness k is obtained r Radial stiffness K of equivalent model of time-response r 。
When the bearing stress is calculated, because the Matrix27 unit only comprises two nodes and is set to have axial stiffness and radial stiffness, the stress of the spring can be obtained by multiplying the relative displacement of the two nodes by the stiffness in the corresponding direction.
And step 3: solving the bearing load-rigidity curve and giving an initial value to the rigidity
(1) Solving bearing axial load-stiffness curve
It is known from the analysis of rolling bearings (Mo Changsen) that under the action of pure axial load, if the rolling elements of an all-steel angular contact bearing are uniformly stressed and the contact angle does not change during the loading process, the calculation formula of the axial elastic contact deformation can be written as
In the formula delta a Axial deflection (in mm); f a Axial force (in N); z is the number of rolling bodies; d is the diameter of the rolling body (unit is mm), and alpha is the contact angle of the bearing (unit is DEG).
For simplicity of presentation, let
Then the formula (1) is changed into
Namely, it is
The bearing rigidity refers to the ratio of the variation of the external load on the bearing in a certain state to the variation of the relative displacement between the inner ring and the outer ring, i.e. the bearing rigidity is
According to the definition can be obtained
Substituting the specification of the bearing into the formulas (2) and (5) to obtain a relation curve of the axial force, the axial displacement and the axial rigidity of the bearing.
(2) Solving radial load-stiffness curve of bearing
The calculation formula of the radial elastic contact deformation under the action of single radial force is as follows:
in the formula of r Radial deformation (in mm); f r Is the radial force (in N).
For simplicity of presentation, let
Can obtain the product
Substituting the specification of the bearing into the formulas (6) and (7) to obtain a relation curve of the radial force of the bearing, the radial displacement and the radial rigidity.
For the 7000C bearing example, the specification is given in Table 1.
TABLE 1 7000C angular contact bearing specification table
| Model number | 7000C type angular contact bearing |
| Outer diameter D (mm) | 26 |
| Inner diameter d (mm) | 10 |
| Width B (mm) | 8 |
| Roller diameter D w (mm) | 4.763 |
| Radius of curvature R of inner ring groove i (mm) | 2.620 |
| Outer ring groove curvature radius R e (mm) | 2.620 |
| Contact angle alpha (°) | 13 to 17 (for example, 15) |
| Number of rollers n | 9 |
Solving according to the formulas (2), (5), (6) and (7) can obtain the relationship between the relative displacement and the rigidity of the inner rail and the outer rail of the bearing and the magnitude of the acting force of the 7000C bearing under the action of axial and radial loads (see fig. 4 and 5).
And 4, step 4: carrying out modal shape trial calculation on rotor system comprising bearing equivalent spring model
Firstly, reasonably setting boundary conditions of a finite element model according to the actual connection mode of a rotator, a bearing and a bearing frame. For the force-bearing frame, applying displacement full constraint at the position of the response displacement constraint according to the installation mode under the actual working condition to ensure that the displacement of each direction node is 0; for the bearing, the connection mode of the bearing and a bearing frame in an actual structure is combined to determine that the displacement constraint is applied to the inner ring or the outer ring of the bearing, and the inner ring or the outer ring of the bearing is fixed; the rotating body and the bearing are constrained by the spring unit, and only one point needs to be constrained by axial displacement, so that the rotating body has no free mode.
And then, according to the requirements of working conditions, carrying out modal analysis in a given frequency range to obtain modal frequency and a corresponding modal vibration mode. Typically, the frequency range in which modal analysis is required will be given in conjunction with the operating conditions, and the modal frequency is the point of resonance frequency present within the frequency band. It is further noted that the initial value of the bearing stiffness is given in terms of the nominal pretension.
And 5: iterative correction of bearing stiffness taking into account vibration load
And combining the bearing load-rigidity curve and the influence of constant-pressure pre-tightening on the bearing force to form a bearing rigidity iterative correction flow shown in a dotted line block diagram of fig. 6. The purpose of development and the main results of each sub-step are explained below:
(1) Modal calculation
The correction of the bearing stiffness influences the main response frequency of the rotor structure, so modal calculation needs to be carried out after the bearing stiffness is adjusted every time, the main response frequency value is refreshed, and the main response frequency value is used as the reference frequency f of harmonic response analysis (the specific implementation process of the modal calculation can refer to modal analysis content in an ANSYS help document).
(2) Harmonic response analysis of a given magnitude
The reference frequency F is used as the reference of the sweep frequency range, harmonic response analysis of a given excitation magnitude is carried out in combination with actual design, relative displacement of nodes at two ends of the spring in the bearing simplified model is utilized, acting force on each spring is obtained through solving, vectors of the acting force are summed, and then acting force F applied to the bearing when a rotor system resonates is obtained.
(3) Paired bearing stress distribution under condition of considering constant-pressure pre-tightening
Because the stiffness-load curve of the bearing is a convex function in a rated load range, iteration of the bearing by using the load obtained by the finite element has a steady state solution, and the stiffness of the equivalent spring model can be corrected by using the point.
1) Establishing bearing stress distribution relation when rotor structure generates umbrella-shaped vibration
Typically, angular contact bearings are mounted in a centered manner (for ease of discussion, the individual bearings of a pair are numbered as bearing I and bearing II, respectively). Under the condition of constant-pressure pre-tightening, the pre-tightening force applied to the bearing is kept unchanged in use, the pre-tightening force is 200N, 7000C type ball bearings installed in pairs are taken as an example, an axial load-displacement curve is given by combining the graph shown in FIG. 4, and a relation graph of acting force and deformation of the bearing I and the bearing II is obtained (see FIG. 7).
The abscissa in the figure is the axial deformation δ a And the ordinate indicates the axial load. The curve I and the curve II are axial load-displacement curves of the bearing I and the bearing II respectively. The intersection O of the two curves represents the axial pretension force F a0 = axial deformation under the action of 200N, if the axial force borne by the bearing is F a While the deformation of the bearing I increases by delta a Bearing II then decreases delta a . Since the displacement of the bearing is not directly calculated in the calculation process, delta a For the unknowns,. DELTA.F cannot be found using only force balance aI And Δ F aII (ΔF aI 、ΔF aII Representing the amount of change in the axial force experienced by bearing I and bearing II, respectively). Given that the axial force varies nearly linearly with axial displacement over the range of investigation shown in FIG. 7, it is believed that Δ F is approximated in the following studies aI ＝ΔF aII ＝F a /2. Therefore, the stress expressions of the bearing I and the bearing II are respectively
F aI ＝F a0 +F a /2 (8)
F aII ＝F a0 -F a /2 (9)
It should be noted that the core F is now removed au ＝2F a0 (F aI = 0), ratio empirical formula F au ＝2.83F a0 And is low.
2) Establishing bearing stress distribution relation when pitch diameter vibration of rotor structure occurs
When the pitch diameter vibration of the rotor structure occurs, the bearing has axial force and radial force. The bearing stress is drawn as figure 8a along the section perpendicular to the pitch line, and it can be known that the pitch diameter vibration causes the bearing to be respectively subjected to bending moment M caused by the axial force of the spring axial And bending moment M caused by radial force radial . The bending moments of the bearings I, II caused by the axial force of the spring are different and are respectively M axial_I 、M axial_II And (4) showing. M is a group of radial It is caused by a component of the radial force in a direction perpendicular to the pitch line.
The calculation expression for the above-mentioned moment is given below:
M sum ＝M radial +M axial ＝M radial +M axial_I +M axial_II (10)
wherein M is sum Is a resultant moment.
Wherein N is the number of the spring units,
is the axial force on the i-th spring unit>
Is the moment arm value corresponding to the force, and the calculation formula is->
Wherein R is the turning radius of the outer ring spring node of the rolling bearing, theta i In the angular position in which the i-th cell is present>
The angular position of the pitch line.
The bending moment borne by the bearing II can be obtained in the same way
Since the radial forces of bearing I and bearing II have the same component in the direction perpendicular to the pitch line, M radial Can be expressed as follows:
wherein L is the axial installation distance (the distance between the ball centers of the rolling elements) of the two groups of bearings,
the radial force applied to the bearing for the ith spring unit.
Further, the stress condition of the spring is further equivalent to that the bearing I and the bearing II are subjected to single radial acting loads F with the same magnitude and opposite directions xeq (as shown in FIG. 8 b), the expression is:
F xeq ＝M radial /L (14)
(4) Substituting bearing load-rigidity curve to correct bearing rigidity
Subjecting the above-mentioned F aI 、F aII Respectively substituting the obtained numerical solutions into F in a bearing axial load-rigidity curve expression (5) a Respectively obtaining updated bearing axial rigidity I and II according to K a ＝n·k a Reassigns the axial stiffness of the single spring according to the conversion relation; the adjustment of the radial stiffness of the bearing is similar to the axial adjustment, i.e. F xeq F substituting solving result into bearing load-rigidity curve expression (7) r Respectively obtaining updated radial rigidity of bearings I and II, and then pressing K r ＝n’·k r The radial stiffness of the individual springs is reassigned. Is at the end ofAnd after the axial stiffness and the radial stiffness of the spring are updated, returning to the first sub-step of the step 5, carrying out a new round of modal analysis, and stopping iteration when the stiffness change of the spring is lower than a threshold value. Fig. 9 shows a data control flow of the entire correction process, taking the bearing stiffness iteration under the umbrella-shaped vibration condition as an example. The data control flow is similar when nodal diameter vibration occurs, and is not described in detail.
The invention has the advantages and beneficial effects that: the invention utilizes Matrix27 provided in ANSYS software to construct a two-dimensional equivalent spring model, and greatly reduces the calculation amount for carrying out the whole numerical simulation of the rotor system on the premise of ensuring the calculation precision. In addition, when the spring stiffness is corrected, the method provided by the invention combines the vibration mode characteristics of the target structure, more comprehensively considers the main factors influencing the bearing stiffness, and repeatedly inspects the influence of steady-state vibration and pretightening force on the bearing stiffness. The invention can effectively communicate the macroscopic rotor system with the model for the mechanical analysis of the microscopic bearing, and has a great deal of application requirements in the actual work. The existing research shows that through the iterative correction of the rigidity, the modal frequency of the structure is closer to the test result, which also shows that the stress of the bearing is closer to the real situation in the vibration process.
Drawings
Fig. 1 shows a Matrix unit Matrix27.
FIG. 2 is a bearing equivalent spring mass model.
Fig. 3a and 3b are finite element models for calculating the conversion relationship between the radial stiffness of the bearing and the radial stiffness of the spring.
Fig. 4 is a load-displacement curve under axial and radial loads.
FIG. 5 is a load-stiffness curve under axial and radial loads.
Fig. 6 is a bearing stiffness correction flow.
FIG. 7 shows preload force F a0 And 200N, the axial load-displacement curve of a bearing I and a bearing II in a 7000C type ball bearing installed in pair.
Fig. 8a and 8b are schematic diagrams of the pitch diameter vibration bearing force and a simplified model thereof.
FIG. 9 is a flow chart of iterative data control of axial stiffness.
Fig. 10 is an axial position schematic of the spring unit.
FIG. 11 is a rotor system finite element model with an equivalent spring model.
FIG. 12 is a boundary condition of a finite element model.
FIG. 13 shows the radial stiffness K of the bearing r Radial stiffness k with spring r The change of (c) is fitted to a curve.
FIG. 14 shows the radial stiffness K of the bearing r Radial stiffness k with spring r The fitted residual of the variation curve.
Fig. 15a, 15b, 15c, and 15d show natural mode shapes in the range of 0 to 1000 Hz.
Fig. 16a and 16b show the distribution of the amount of deformation of the spring unit in two main vibration modes.
Detailed Description
The following provides embodiments of the present invention in combination with specific examples. The rotor structure involved in the case is a gyro rotor prototype, the system resonance test frequency value measured in the test is lower than the numerical simulation result, and the single-side bearing is found to be seriously worn when the bearing is disassembled after the test. The case is combined with the rigidity correction scheme provided by the invention, the resonance frequency simulation value obtained by solving is closer to the test result, and the phenomenon that the bearing is stressed unevenly is found in the iteration process, so that a reasonable explanation is provided for the abrasion phenomenon observed in the test.
Step 1: building a rotor structure model
And carrying out finite element modeling according to the actual structure of the rotor by using ANSYS software.
Step 2: construction of simplified model of angular contact bearing
(1) Selection spring unit
Matrix unit Matrix27 in ANSYS software is selected as a basic unit for constructing a bearing equivalent model. Matrix27 is a Matrix element with arbitrary geometry, which is composed of two nodes, each node has six degrees of freedom, and comprises three directions of translation and three directions of rotation (as shown in fig. 1). It is a versatile unit that can be represented in matrix form as stiffness, damping and mass. In the bearing simplified model, matrix27 is used to represent stiffness. For a bearing, the main stiffness is axial and radial, and the circumferential stiffness is zero, so that the Matrix27 needs to convert the node coordinate system from a cartesian coordinate system to a local cylindrical coordinate system and set the circumferential stiffness (Y direction) to 0 when in use.
(2) Constructing an equivalent bearing model
The bearing is equivalent to a spring mass model formed by a bearing outer ring, n spring-bearing inner rings (as shown in figure 2) by canceling bearing balls, equally dividing the bearing inner ring and the bearing outer ring into n equal parts along the circumferential direction, connecting the n pairs of nodes one by using n Matrix27 units, and adding ball mass to the nodes of the spring outer ring.
Axial and radial stiffness K of primary interest for bearings a 、K r It should be established and simplified as well as the axial stiffness k of the spring a And radial stiffness k r The conversion relationship of (1). Along the axial direction, the bearing uses n springs in parallel to represent the axial stiffness, K is known easily a ＝n·k a . For radial stiffness, the finite element model shown in fig. 3a and 3b can be used to obtain the conversion relation K r ＝n’·k r . In fig. 3a and 3b, the free end of the middle spring is fully constrained, and meanwhile, the circumferential displacement of a node on the inner side of the rotor model is constrained to be 0, so that the circumferential rotation of the rotor is limited. Then applying different radial forces F in the direction of the arrows r And the displacement of the far end node of the acting force along the radial force direction is used for representing the radial rigid body displacement of the rotor, so that the spring stiffness k is obtained r Radial stiffness K of equivalent model of time-response r 。
When the bearing stress is calculated, because the Matrix27 unit only comprises two nodes and is set to have axial stiffness and radial stiffness, the stress of the spring can be obtained by multiplying the relative displacement of the two nodes by the stiffness in the corresponding direction.
And step 3: solving the bearing load-rigidity curve and giving an initial value to the rigidity
(1) Solving bearing axial load-stiffness curve
It is known from the analysis of rolling bearings (Mo Changsen) that under the action of pure axial load, if the rolling elements of an all-steel angular contact bearing are uniformly stressed and the contact angle does not change during the loading process, the calculation formula of the axial elastic contact deformation can be written as
In the formula of a Axial deformation (in mm); f a Axial force (in N); z is the number of rolling bodies; d is the diameter (in mm) of the rolling body, and alpha is the contact angle (in DEG) of the bearing.
Order to
Then the formula (1) becomes
Namely that
The rigidity of the bearing refers to the ratio of the variation of the external load borne by the bearing in a certain state to the variation of the relative displacement between the inner ring and the outer ring of the bearing, namely
According to the definition can be obtained
Substituting the specification of the bearing into the formulas (2) and (5) to obtain a relation curve of the axial force, the axial displacement and the axial rigidity of the bearing.
(2) Solving radial load-stiffness curve of bearing
The calculation formula of the radial elastic contact deformation under the action of single radial force is as follows:
in the formula delta r Radial deformation (in mm); f r Is the radial force (in N).
Order to
Can obtain
Substituting the specification of the bearing into the formulas (6) and (7) to obtain a relation curve of the radial force of the bearing with the radial displacement and the radial rigidity.
For 7000C bearings, the specifications are given in table 1.
TABLE 1 7000C angular contact bearing specification table
| Model number | 7000C type angular contact bearing |
| Outer diameter D (mm) | 26 |
| Inner diameter d (mm) | 10 |
| Width B (mm) | 8 |
| Roller diameter D w (mm) | 4.763 |
| Radius of curvature R of inner ring groove i (mm) | 2.620 |
| Outer ring groove curvature radius R e (mm) | 2.620 |
| Contact angle alpha (°) | 13 to 17 (for calculation example 15) |
| Number of rollers n | 9 |
Solving according to the formulas (2), (5), (6) and (7) can obtain the relationship between the relative displacement and the rigidity of the inner rail and the outer rail of the bearing and the magnitude of the acting force of the 7000C bearing under the action of axial and radial loads (see fig. 4 and 5).
And 4, step 4: carrying out modal shape trial calculation on rotor comprising bearing equivalent spring model
And reasonably setting boundary conditions of the finite element model according to the actual connection mode of the rotor, the bearing and the bearing frame, and carrying out modal analysis in a given frequency range to obtain the main response frequency and the response modal vibration mode. Note that the initial value of the bearing stiffness is given in terms of the nominal pretension.
And combining the bearing load-rigidity curve and the influence of constant-pressure pre-tightening on the bearing force to form a bearing rigidity iterative correction flow shown in a dotted line block diagram of fig. 6. The purpose of development and the main results of each sub-step are set forth below:
(1) Modal calculation
The correction of the bearing stiffness can affect the main response frequency of the rotor structure, so modal calculation needs to be carried out after the bearing stiffness is adjusted every time, the main response frequency value is refreshed, and the main response frequency value is used as the reference frequency f of harmonic response analysis.
(2) Harmonic response analysis of a given magnitude
And (3) taking the modal frequency point F as a sweep frequency range reference, and combining with the actual design to carry out harmonic response analysis of a given excitation magnitude to obtain the acting force F applied to the bearing by the rotor system when the rotor system resonates.
(3) Paired bearing stress distribution under condition of considering constant-pressure pre-tightening
Because the stiffness-load curve of the bearing is a convex function in a rated load range, iteration of the bearing by utilizing the load obtained by the finite element has a steady state solution, and the stiffness of the equivalent spring model can be corrected by utilizing the point.
3) Establishing bearing stress distribution relation when rotor structure generates umbrella-shaped vibration
Typically, angular contact bearings are mounted in a centered manner (for ease of discussion, the individual bearings of a pair of bearings are numbered bearing I and bearing II, respectively). Under the condition of constant-pressure pre-tightening, the pre-tightening force applied to the bearing is kept unchanged in use, the pre-tightening force is 200N, 7000C type ball bearings installed in pairs are taken as an example, an axial load-displacement curve is given by combining the graph shown in FIG. 4, and a relation graph of acting force and deformation of the bearing I and the bearing II is obtained (see FIG. 7).
The abscissa in the figure is the axial deformation δ a And the ordinate indicates the axial direction under load. And the curve I and the curve II are axial load-displacement curves of the bearing I and the bearing II respectively. The intersection O of the two curves represents the axial pretension force F a0 Axial deformation under 200N, if external load F acts on the shaft a While, the deformation of the bearing I increases by delta a Bearing II then reduces delta a . Since the displacement of the bearing is not directly calculated in the calculation process, δ a For the unknowns,. DELTA.F cannot be found using only force balance aI And Δ F aII . Given that the axial force varies nearly linearly with axial displacement over the range of investigation shown in FIG. 7, it is believed that Δ F is approximated in the following studies aI ＝ΔF aII ＝F a /2. Therefore, the stress expressions of the bearing I and the bearing II are respectively
F aI ＝F a0 +F a /2 (8)
F aII ＝F a0 -F a /2 (9)
It should be noted that the core F is now removed au ＝2 F a0 (F aI = 0), ratio empirical formula F au ＝2.83 F a0 And is low.
4) Establishing bearing stress distribution relation when pitch diameter vibration of rotor structure occurs
When the pitch diameter vibration of the rotor structure occurs, the bearing has axial force and radial force. The bearing stress is drawn as figure 8a along the section perpendicular to the pitch line, and it can be known that the pitch diameter vibration causes the bearing to be respectively subjected to bending moment M caused by the axial force of the spring axial And bending moment M caused by radial force radial . The bending moments of the bearings I, II caused by the axial force of the spring are different and are respectively M axial_I 、M axial_II And (4) showing. M radial It is caused by a component of the radial force in a direction perpendicular to the pitch line.
The calculation expression for the above moment is given below:
M sum ＝M radial +M axial ＝M radial +M axial_I +M axial_II (10)
wherein M is sum Is a resultant moment.
Wherein N is the number of the spring units,
is the axial force on the i-th spring unit>
The force arm value corresponding to the force is calculated as ^>
Wherein R = D/2, θ i In the angular position in which the i-th cell is present>
The angular position of the pitch line.
The bending moment borne by the bearing II can be obtained in the same way
Since the radial forces of bearing I and bearing II have the same component in the direction perpendicular to the pitch line, M radial Can be expressed as follows:
wherein L is the axial installation distance (the distance between the ball centers of the rolling elements) of the two groups of bearings,
the radial force applied to the bearing for the ith spring unit.
Further, the stress condition of the spring is further equivalent to that the bearing I and the bearing II are subjected to single radial acting loads F with the same magnitude and opposite directions xeq (as shown in fig. 8 b).
(4) Substituting the load-rigidity curve of the bearing to correct the rigidity of the bearing
In the above-mentioned F aI 、F aII 、F xeq Substituting the solution result into a bearing load-stiffness curve, updating the stiffness of the bearing, returning to the first step of modal analysis, and stopping iteration when the stiffness change of the spring is lower than a threshold value. Fig. 9 shows a data control flow of the whole calibration process, taking the bearing stiffness iteration under the umbrella-shaped vibration condition as an example. The data control flow is similar when nodal diameter vibration occurs, and details are not repeated.
The present invention will be described in further detail with reference to examples.
(1) Construction of rotor system model
Fig. 10 shows a section of a typical rotating system consisting of three parts, namely a rotating shaft, a bearing and a rotating body, wherein a 7000C angular contact bearing (specification shown in table 1) is installed at the position shown in the figure, and the axial pre-load is set to be 200N. A finite element model of the entire rotor system is shown in fig. 11.
The base bottom and the rotating shaft top are subjected to full constraint of shaft, diameter and Zhou Sanxiang (see fig. 12).
In this model, the bearing is equivalent to 90 springs equally circumferentially spaced, i.e. n =90. Along the axis, the bearing uses 90 springs in parallel to represent the axial stiffness, known as K a ＝90·k a . For radial stiffness, the model shown in fig. 3a and 3b is used for solving. FIG. 13 shows the radial stiffness K of the integral model r Following the radial stiffness k of the spring r The curve of the change, equation (16), gives an expression for the fitted curve.
K r ＝A 2 +(A 1 -A 2 )/[1+(k r /A 3 ) p ] (14)
Wherein A is 1 ＝20.69676，A 2 ＝538426.591，A 3 ＝5985.99667，p＝1.00124。
Negation function of the above equation
k r ＝A 3 [(A 1 -A 2 )/(K r -A 2 )-1] 1/p (15)
According to formula (1), according to a pre-tightening force F a0 =200N preset axial stiffness of the bearing (ideally, the rolling elements are stressed the same): k a ＝1.540×10 4 N/mm, then k a ＝1.711×10 2 N/mm。
When the bearing is mounted on a main shaft to work, the radial deformation amount is small, and the axial deformation amount is large. Combining the displacement coordination relationship after the bearing positioning and pre-tightening, and according to a pre-tightening clearance angle contact ball bearing rigidity formula given by researchers of collecting from the chen, wearing from the dawn and the like (see Xing Jishou, dai Shu. Calculating the rigidity of the pre-tightening clearance angle contact ball bearing [ J]Machine tool, 1990 (5): 8-10.) calculation yields K r ＝1.105×10 5 N/mm, then k r ＝1.547×10 3 N/mm。
(2) Trial calculation of modal shape
After modeling of the rotor system is completed, modal solution is carried out, and two resonance frequency points exist in the range of 1000Hz, one resonance frequency point is 604.58Hz, the rotor generates 1 pitch diameter (1 ND) vibration, the other resonance frequency point is 898.50Hz, the rotor generates umbrella-shaped (0 ND) vibration, and the vibration mode is shown in fig. 15a, 15b, 15c and 15 d.
The wheel system is then subjected to harmonic response analysis under axial and radial excitation, respectively. In the range of 0-1000 Hz, the resonance is excited at 898.50Hz in the axial frequency sweep, and the resonance is excited at 604.58Hz in the radial frequency sweep. Fig. 16a and 16b show the deformation distribution of the spring unit under the two vibration modes, and it can be seen that under the umbrella-shaped vibration condition, the bearing is only subjected to axial force, and under the pitch diameter vibration condition, the bearing is relatively complicated in stress.
(3) Iterative correction of bearing stiffness taking into account vibration load
1) Iteration of spring stiffness during umbrella vibration
The modal damping ratio ζ of the structure was set to 0.01, and spring stiffness correction iterations were performed, with the main calculation results shown in table 2. The 869.1Hz provided by the comparison test result reduces the modal frequency error after stiffness correction by about 2%, and in addition, when the rotor generates steady umbrella-shaped vibration, the axial stiffness on a pair of 7000C bearings actually differs by 76.6%, the bearing load with larger stress is improved by 68.9%, and the axial stiffness is improved to 1.835 × 10 4 N/mm, which is 19.15% higher than the initial state.
TABLE 2 axial stiffness iteration results with pretension of 200N
2) Iteration of spring stiffness at nodal diameter vibration
M can be obtained by calculation according to the formulas (10) to (13) axial_II ＝-16.05N·mm，M axial_I ＝-20.86N·mm，M radial ＝-592.08N·mm，M sum = 628.98N · mm (minus)The value representing a counterclockwise direction along a cross section perpendicular to the pitch line). It can be seen that the bending moment caused by the radial force accounts for 91.7% of the total bending moment. The stress condition of the spring is further equivalent to that the bearing I and the bearing II are subjected to single radial acting load F with the same magnitude and opposite directions xeq Is known as F xeq ＝16.52N。
As can be seen from the formula (7), K r ＝1.105×10 5 N/mm, single radial force F x0 2643.19N, F obtained xeq To F x0 At this time, the radial stiffness of the bearing is only improved by 0.2%, so in this example, the influence of the pitch diameter vibration of the rotor on the radial stiffness of the bearing can be ignored. However, it should be noted that the rotating shaft of the present embodiment has good rigidity, and bending vibration on the rotating shaft does not occur, and it is necessary to examine the influence of bending moment on the radial rigidity of the bearing if the bending vibration pattern on the rotating shaft is excited.
Claims (5)
1. A method for correcting rigidity numerical values of constant-pressure pre-tightening angular contact bearings considering vibration influence is characterized by comprising the following steps of:
step 1: constructing a finite element model of a rotor system
Establishing a finite element model of a target rotor system in CAE preprocessing software aiming at a given entity model, then importing the established finite element model into finite element software ANSYS, and defining corresponding material parameters, a given rotating speed and displacement constraint conditions;
and 2, step: construction of simplified model of angular contact bearing
(1) Selection spring unit
Selecting a Matrix unit Matrix27 in ANSYS software as a basic unit for constructing a bearing equivalent model;
(2) Constructing an equivalent bearing model
A bearing rolling body is cancelled, the inner ring and the outer ring of the bearing are equally divided into n equal parts along the circumferential direction, then n pairs of nodes are connected one by using n Matrix27 units, and the ball mass is attached to the nodes of the outer ring of the spring, so that the bearing is equivalent to a spring mass model formed by the outer ring of the bearing and n spring-bearing inner rings;
and step 3: solving the bearing load-rigidity curve and giving an initial value to the rigidity
(1) Solving bearing axial load-stiffness curve
As known from the analysis method of rolling bearing (Mo Changsen), the calculation formula of the axial elastic contact deformation of the all-steel angular contact bearing is written as follows if the rolling elements of the all-steel angular contact bearing are uniformly stressed and the contact angle of the all-steel angular contact bearing is not changed in the loading process under the action of pure axial load
In the formula delta a Is the axial deflection, in mm; f a Is axial force in units of N; z is the number of rolling bodies; d is the diameter of the rolling body, and the unit is mm, and alpha is the contact angle of the bearing, and the unit is degree;
to simplify the presentation, let
Then the formula (1) becomes
Namely that
The rigidity of the bearing refers to the ratio of the variation of the external load borne by the bearing in a certain state to the variation of the relative displacement between the inner ring and the outer ring of the bearing, namely
According to the definition can be obtained
Substituting the specification of the bearing into formulas (2) and (5) to obtain a relation curve of the axial force, the axial displacement and the axial rigidity of the bearing;
(2) Solving radial load-stiffness curve of bearing
The calculation formula of the radial elastic contact deformation under the action of single radial force is as follows:
in the formula of r Radial deformation in mm; f r Is radial force, in units of N;
for simplicity of presentation, let
Can obtain the product
Substituting the specification of the bearing into formulas (6) and (7) to obtain a relation curve of the radial force of the bearing, the radial displacement and the radial rigidity;
and 4, step 4: carrying out modal shape trial calculation on rotor system comprising bearing equivalent spring model
Firstly, reasonably setting boundary conditions of a finite element model according to an actual connection mode of a rotator, a bearing and a bearing frame; for the force-bearing frame, applying displacement full constraint at the position of the response displacement constraint according to the installation mode under the actual working condition to ensure that the displacement of each direction node is 0; for the bearing, the displacement constraint is determined to be applied to the inner ring or the outer ring of the bearing by combining the connection mode of the bearing and the bearing frame in the actual structure, and the bearing is fixed; the rotating body and the bearing are constrained by the spring unit, and only one point of the spring unit needs to be constrained by axial displacement, so that the rotating body has no free mode;
and 5: iterative correction of bearing stiffness taking into account vibration load
Combining a bearing load-rigidity curve and the influence of constant-pressure pre-tightening on bearing stress to form a bearing rigidity iterative correction flow; the purpose of development and the results of each sub-step are explained below:
(1) Modal calculation
The correction of the bearing stiffness can influence the main response frequency of the rotor structure, so modal calculation needs to be carried out after the bearing stiffness is adjusted every time, the main response frequency value is refreshed, and the main response frequency value is used as the reference frequency f of harmonic response analysis;
(2) Harmonic response analysis of a given magnitude
The method comprises the steps of taking a reference frequency F as a sweep frequency range reference, carrying out harmonic response analysis of a given excitation magnitude in combination with actual design, utilizing relative displacement of nodes at two ends of springs in a bearing simplified model to solve to obtain acting force on each spring, summing vectors of the acting force on each spring, and further obtaining acting force F applied to a bearing when a rotor system resonates;
(3) Paired bearing stress distribution under condition of considering constant-pressure pre-tightening
Because the stiffness-load curve of the bearing is a convex function in a rated load range, the iteration of the bearing by utilizing the load obtained by the finite element has a steady state solution, and the stiffness of the equivalent spring model is corrected by utilizing the point;
1) Establishing bearing stress distribution relation when rotor structure generates umbrella-shaped vibration
The angular contact bearings are installed in a centering mode, and a single bearing in a pair of bearings is respectively numbered as a bearing I and a bearing II; under the condition of constant-pressure pre-tightening, the pre-tightening force applied to the bearing is kept unchanged in use, the pre-tightening force is 200N,
the abscissa is the axial deflection delta a The ordinate represents the axial load; the curve I and the curve II are axial load-displacement curves of the bearing I and the bearing II respectively; the intersection O of the two curves represents the axial pretension force F a0 Axial deformation under the action of =200N, if the axial force applied to the bearing is F a While, the deformation of the bearing I increases by delta a Bearing II then decreases delta a (ii) a Because the position of the bearing is not directly aligned in the calculation processShift is calculated, thus delta a For the unknowns,. DELTA.F cannot be found using only force balance aI And Δ F aII ；ΔF aI 、ΔF aII Respectively representing the variation of the axial force borne by the bearing I and the bearing II; the axial force varies nearly linearly with axial displacement, so in the following study, Δ F is considered approximately aI ＝ΔF aII ＝F a 2; therefore, the stress expressions of the bearing I and the bearing II are respectively
F aI ＝F a0 +F a /2 (8)
F aII ＝F a0 -F a /2 (9)
Note that at this time, the check F is loosened au ＝2F a0 ，F aI Ratio of 0 to empirical formula F au ＝2.83F a0 Low;
2) Establishing bearing stress distribution relation when pitch diameter vibration of rotor structure occurs
When the pitch diameter vibration of the rotor structure occurs, the bearing has axial force and radial force; bending moment M caused by axial force of spring on bearing due to pitch diameter vibration axial And bending moment M caused by radial force radial (ii) a The bending moments of the bearings I, II caused by the axial force of the spring are different and are respectively M axial_I 、M axial_II Represents; m radial Caused by the component of the radial force in the direction perpendicular to the pitch line;
the computational expression for resultant moment is given below:
M sum ＝M radial +M axial ＝M radial +M axial_I +M axial_II (10)
wherein M is sum Is the resultant moment;
wherein N is the number of the spring units,
is the axial force on the i-th spring unit>
Is the moment arm value corresponding to the force, and the calculation formula is->
Wherein R is the turning radius of the outer ring spring node of the rolling bearing, theta i In the angular position in which the i-th cell is present>
The angle position of the pitch line;
the bending moment borne by the bearing II can be obtained in the same way
Since the radial forces of bearing I and bearing II have the same component in the direction perpendicular to the pitch line, M radial Can be expressed as follows:
wherein L is the axial installation distance of the two groups of bearings, namely the distance between the ball centers of the rolling bodies,
a radial force applied to the bearing for the ith spring unit;
further, the stress condition of the spring is further equivalent to that the bearing I and the bearing II are subjected to single radial acting loads F with the same magnitude and opposite directions xeq The expression is as follows:
F xeq ＝M radial /L (14)
(4) Substituting the load-rigidity curve of the bearing to correct the rigidity of the bearing
Subjecting the above F to aI 、F aII Respectively substituting the obtained numerical solutions into F in a bearing axial load-rigidity curve expression (5) a Respectively obtaining the updated axial rigidity of the bearings I and II according to K a ＝n·k a The conversion relation of (2) reassigns the axial stiffness of the single spring; the adjustment of the radial stiffness of the bearing is similar to the axial adjustment, i.e. F xeq Substituting the solution result into F in a bearing load-rigidity curve expression (7) r Respectively obtaining updated radial rigidity of bearings I and II, and then pressing K r ＝n’·k r Reassigning the radial stiffness of the individual springs; and after the axial stiffness and the radial stiffness of the spring are updated, returning to the first sub-step of the step 5, performing a new round of modal analysis, and stopping iteration when the stiffness change of the spring is lower than a threshold value.
2. The method for correcting the rigidity value of the constant-pressure pre-tightening angular contact bearing considering the influence of vibration according to claim 1, wherein: matrix27 is a Matrix unit with any geometric shape, which is composed of two nodes, each node has six degrees of freedom and comprises translation in three directions and rotation in three directions; it is a versatile unit that can be represented in matrix form as stiffness, damping and mass; in the bearing simplification model, matrix27 is used to represent stiffness; for the bearing, the main rigidity is axial and radial, and the circumferential rigidity is zero, so the Matrix27 needs to convert the node coordinate system from a cartesian coordinate system to a local cylindrical coordinate system and set the circumferential rigidity to 0 when in use.
3. The method for correcting the rigidity value of the constant-pressure pre-tightening angular contact bearing considering the influence of vibration according to claim 2, wherein: when the bearing stress is calculated, because the Matrix27 unit only comprises two nodes and is set to have axial stiffness and radial stiffness, the stress of the spring can be obtained by multiplying the relative displacement of the two nodes by the stiffness in the corresponding direction.
4. The method for correcting the rigidity value of the constant-pressure pre-tightening angular contact bearing considering the influence of vibration according to claim 1, wherein: axial and radial stiffness K of interest for bearings a 、K r It should be established and simplified as well as the axial stiffness k of the spring a And radial stiffness k r The conversion relation of (1); along the axial direction, the bearing uses n springs in parallel to represent the axial stiffness, K is known easily a ＝n·k a (ii) a And for radial rigidity, obtaining a conversion relation K of the radial rigidity by adopting a finite element model r ＝n’·k r And n' is the radial stiffness k of the whole bearing and the radial stiffness k of the simplified spring r A conversion factor of (d); the free end of the middle spring is fully constrained, and meanwhile, the circumferential displacement of a node on the inner side of the rotor model is constrained to be 0, so that the circumferential rotation of the rotor is limited; then applying different radial forces F in the direction of the arrows r And the displacement of the far end node of the acting force along the radial force direction is used for representing the radial rigid body displacement of the rotor, so that the spring stiffness k is obtained r Radial stiffness K of equivalent model of time-response r 。
5. The method for correcting the rigidity value of the constant-pressure pre-stressed angular contact bearing considering the influence of vibration according to claim 1, wherein the method comprises the following steps: carrying out modal analysis in a given frequency range to obtain modal frequency and a corresponding modal shape; the frequency range needing modal analysis is given by combining working conditions, and the modal frequency is a resonance frequency point existing in the frequency band; it is further noted that the initial value of the bearing stiffness is given in terms of the nominal pretension.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910410138.1A CN110399628B (en) | 2019-05-17 | 2019-05-17 | Constant-pressure pre-tightening angular contact bearing rigidity value correction method considering vibration influence |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910410138.1A CN110399628B (en) | 2019-05-17 | 2019-05-17 | Constant-pressure pre-tightening angular contact bearing rigidity value correction method considering vibration influence |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110399628A CN110399628A (en) | 2019-11-01 |
| CN110399628B true CN110399628B (en) | 2023-04-18 |
Family
ID=68323637
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910410138.1A Active CN110399628B (en) | 2019-05-17 | 2019-05-17 | Constant-pressure pre-tightening angular contact bearing rigidity value correction method considering vibration influence |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110399628B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111460714B (en) * | 2020-03-31 | 2022-11-29 | 上海机电工程研究所 | Auxiliary stiffness approximation calculation method and system suitable for multi-body static contact problem |
| CN113239430B (en) * | 2021-04-29 | 2022-12-09 | 西安交通大学 | Calculation method for acting force of three-ring-plate node ring plate for power transmission steel pipe tower |
| CN114091306B (en) * | 2021-11-18 | 2024-04-26 | 大连华锐重工集团股份有限公司 | Method for analyzing deflection of installation plane of slewing bearing based on finite element simulation |
| CN117807735B (en) * | 2024-03-01 | 2024-06-11 | 盛瑞传动股份有限公司 | Method, device, equipment and storage medium for determining thickness of adjusting gasket |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006317394A (en) * | 2005-05-16 | 2006-11-24 | Tokyo Institute Of Technology | Rigidity identifying system of elastic support |
| CN106528903A (en) * | 2015-09-15 | 2017-03-22 | 利弗莫尔软件技术公司 | Systems and methods of conducting numerical simulation of an underwater explosion |
| CN106560816A (en) * | 2016-02-02 | 2017-04-12 | 梁明轩 | Antifriction bearing dynamic stiffness influence factor analysis method |
-
2019
- 2019-05-17 CN CN201910410138.1A patent/CN110399628B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2006317394A (en) * | 2005-05-16 | 2006-11-24 | Tokyo Institute Of Technology | Rigidity identifying system of elastic support |
| CN106528903A (en) * | 2015-09-15 | 2017-03-22 | 利弗莫尔软件技术公司 | Systems and methods of conducting numerical simulation of an underwater explosion |
| CN106560816A (en) * | 2016-02-02 | 2017-04-12 | 梁明轩 | Antifriction bearing dynamic stiffness influence factor analysis method |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110399628A (en) | 2019-11-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110399628B (en) | Constant-pressure pre-tightening angular contact bearing rigidity value correction method considering vibration influence | |
| WO2023035582A1 (en) | Method for simulating contact dynamic characteristics of high-speed heavy-load ball bearings in liquid rocket engine | |
| Liu et al. | Load distribution calculation of a four-point-contact slewing bearing and its experimental verification | |
| JP5506420B2 (en) | Torque calculation method, calculation device, and calculation program for 4-point contact ball bearings | |
| CN107989818B (en) | A kind of W2B type water pump shaft connecting bearings and its durability analysis method | |
| CN112364463B (en) | Squirrel-cage elastic support rigidity and stress analysis method | |
| CN110348168A (en) | Consider the aeroplane engine mainshaft bearing calculation of the rating life method of changed play | |
| Wang et al. | Improvement of location and orientation tolerances propagation control in cylindrical components assembly using stack-build assembly technique | |
| Graßmann et al. | Validation of a finite-element model of a wind turbine blade bearing | |
| Deng et al. | Life calculation of angular contact ball bearings for industrial robot RV reducer | |
| Cheng et al. | Research on the effect of structural and material parameters on vibrations based on quasi-static model of bearings | |
| US20100064801A1 (en) | Method for balancing supercritical shafts | |
| CN111563342A (en) | Strain gauge measuring point layout optimization method for rotor blade | |
| Cheng et al. | Research on mechanical characteristics of fault-free bearings based on centrifugal force and gyroscopic moment | |
| Mutra et al. | Parametric design of turbocharger rotor system under exhaust emission loads via surrogate model | |
| CN109960870B (en) | Large-scale high-speed rotation equipment multi-stage part rigidity prediction method based on contact area maximization measurement and adjustment | |
| CN112685831B (en) | Optimization method for suspension and auxiliary frame part structures | |
| CN110532732B (en) | Method for determining rubbing relationship between blade and casing | |
| CN107563041A (en) | A kind of big part static strength fast evaluation method of Wind turbines | |
| CN114936483A (en) | Finite element equivalent modeling method for statics simulation analysis of large bearing | |
| Jin et al. | Reliability coupling mechanism analyses of T-rotation-type CMA with frame deformation in CNC machine tools | |
| CN107451374A (en) | A kind of computational methods in thin wall flexible bearing support life-span | |
| Lin et al. | Dynamic modeling and parameter identification of a gun saddle ring | |
| CN116754134A (en) | Rotor imbalance state identification method based on test and simulation data fusion | |
| Liu et al. | An efficient dynamic modeling technique for a central tie rod rotor |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |