A method for modeling contact stiffness of a ball bearing under coupling of assembly load and connection load

Abstract

The application provides a kind of load and connection load coupling ball bearing contact stiffness modeling method for assembling load, comprising the following steps: establishing the three-dimensional entity model of angular contact ball bearing;Establish bearing-rotor system model;Obtain different connection load;The three-dimensional entity model implanted with connection load is imported into ANSYS, and the three-dimensional entity model is meshed;Bearing elements and shaft adopt hexahedral mesh, set a layer of shell unit in bearing inner ring, couple the nodes of bearing inner ring with the nodes of shaft, realize rigid motion;By applying axial force to the centroid of bearing inner ring rigid surface to implant assembling load, change the axial force, obtain different assembling load;The ANSYS finite element statics analysis module implanted with connection load and assembling load is imported into finite element dynamics analysis module, and the finite element model of angular contact bearing contact stiffness is established.The application is convenient for studying the contact characteristics of angular contact ball bearing under complex working conditions, and can accurately calculate the contact stiffness.

Description

Technical Field

[0001] This invention relates to the field of bearing technology, and more specifically, to a method for modeling the contact stiffness of ball bearings under the coupling of assembly load and connection load. Background Technology

[0002] Angular contact ball bearings are essential support components in modern industrial rotating equipment, and they require adjustment during installation. The adjustment process (such as adjustment loads and connection loads) significantly impacts the service performance of the bearing body and the rotor system. The service performance of the rotor system can be obtained through rotor system dynamics modeling and analysis. In rotor system dynamics modeling, rolling bearings are generally simplified to stiffness, and the impact of the adjustment process on the rotor system's service performance is often reflected in its effect on the bearing contact stiffness.

[0003] Contact stiffness serves as a bridge between the rolling bearing assembly and adjustment process and the service performance of the rotor system. Accurate calculation of contact stiffness is crucial for studying the impact of rolling bearing assembly and adjustment process parameters on the rotor system's service performance. Therefore, it is necessary to develop a method for modeling ball bearing contact stiffness under the coupling of assembly and adjustment loads and connection loads. Summary of the Invention

[0004] Based on this, in order to accurately calculate the contact stiffness, the present invention provides a method for modeling the contact stiffness of ball bearings under the coupling of assembly load and connection load, the specific technical solution of which is as follows: A method for modeling the contact stiffness of a ball bearing under coupled assembly and connection loads includes the following steps: S1. Establish a three-dimensional solid model of the angular contact ball bearing and insert the initial clearance; S2. Based on the inner and outer ring diameters of the angular contact ball bearing, establish a bearing-rotor system model that includes the shaft and bearing housing and is interference-fitted with the inner and outer rings. S3, change the interference fit between the shaft and the inner ring of the bearing, and between the bearing housing and the outer ring of the bearing to obtain different connection loads; S4. Import the 3D solid model with the connected load into ANSYS. In the ANSYS finite element static analysis module, set the parameters and material properties of the 3D solid model and perform mesh generation on the 3D solid model. S5, the bearing components and shaft adopt a hexahedral mesh, and a layer of shell elements is set in the inner ring of the bearing to couple the nodes of the inner ring of the bearing with the nodes of the shaft to achieve rigid motion; S6, by applying an axial force to the center of mass of the rigid surface of the bearing inner ring to implant the adjustment load, and by changing the axial force, different adjustment loads can be obtained; S7. Import the ANSYS finite element statics analysis module containing the connection load and the adjustment load into the finite element dynamics analysis module, insert boundary conditions, and establish a finite element model of the contact stiffness of the angular contact bearing.

[0005] The proposed ball bearing contact stiffness modeling method under the coupling of assembly load and connection load establishes a finite element model of angular contact bearing contact stiffness to address the dual load coupling effect of assembly load and connection load. This facilitates the study of the contact characteristics of angular contact ball bearings under complex working conditions and can reasonably and accurately simulate the contact characteristics of the bearing-shaft joint and accurately calculate the contact stiffness.

[0006] Further, in step S3, according to the formula Calculate the connection load ; in This indicates the Poisson's ratio of the bearing inner ring. Indicates the axial Poisson's ratio. This indicates the elastic modulus of the bearing inner ring. Indicates the elastic modulus of the shaft. Indicates the outer diameter of the bearing inner ring. Indicates the inner diameter of the bearing inner ring. Indicates the outer diameter of the shaft.

[0007] Furthermore, the method for modeling the contact stiffness of ball bearings under the coupling of assembly load and connection load also includes the following steps: Calculate the radial stiffness of the bearing and axial stiffness ; in, , , , , Indicates the first Normal contact stiffness between the ball and the inner ring groove of the bearing Indicates the first Normal contact stiffness between the ball and the outer ring groove of the bearing Indicates the first The contact angle between the ball and the inner ring of the bearing. The first The contact angle between the ball and the outer ring of the bearing. Indicates the number of balls. Indicates the position angle of the ball.

[0008] Furthermore, the method for modeling the contact stiffness of ball bearings under the coupling of assembly load and connection load also includes the following steps: According to the formula Calculate the normal contact deformation of an angular contact ball bearing ; Deformation of normal contact Taking the derivative, we obtain the normal contact stiffness as... ; in, This represents the contact load between two contacting objects. This represents the equivalent elastic modulus of two contacting objects. Represents the ellipticity coefficient. It represents the sum of the curvatures of the two contacting objects on the principal plane of the contact point. 、 This represents the first and second type of complete elliptic integrals.

[0009] Furthermore, the boundary conditions include rotational speed conditions and constraint conditions. Attached Figure Description

[0010] The invention will be further understood from the following description taken in conjunction with the accompanying drawings. The components in the drawings are not necessarily drawn to scale, but rather the emphasis is on illustrating the principles of the embodiments. In different views, the same reference numerals designate corresponding parts.

[0011] Figure 1 This is a schematic diagram of the overall process of a ball bearing contact stiffness modeling method under the coupling of assembly load and connection load in one embodiment of the present invention; Figure 2 This is a theoretical analytical diagram of a thick-walled circular ring according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the inner ring interference fit in one embodiment of the present invention; Figure 4 This is a schematic diagram of the interference fit of the outer ring in one embodiment of the present invention; Figure 5 This is a connection load assembly diagram according to an embodiment of the present invention; Figure 6 This is a schematic diagram of finite element mesh generation in one embodiment of the present invention; Figure 7 This is a schematic diagram of finite element load application in one embodiment of the present invention; Figure 8 This is the result of the installation load-contact stiffness in one embodiment of the present invention. Figure 1 ; Figure 9 This is the connection load-contact stiffness result in one embodiment of the present invention. Figure 2 . Detailed Implementation

[0012] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to its embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of protection of the invention.

[0013] It should be noted that when an element is referred to as being "fixed to" another element, it can be directly attached to the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0014] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0015] In this invention, "first" and "second" do not represent a specific quantity or order, but are merely used to distinguish names.

[0016] like Figure 1 As shown, a method for modeling the contact stiffness of a ball bearing under coupled assembly load and connection load in one embodiment of the present invention includes the following steps: S1. Establish a three-dimensional solid model of the angular contact ball bearing and insert the initial clearance.

[0017] S2. Based on the inner and outer ring diameters of the angular contact ball bearing, establish a bearing-rotor system model that includes the shaft and bearing housing and has an interference fit with the inner and outer rings.

[0018] Here, the shaft with an interference fit to the inner ring is established based on the inner ring diameter of the angular contact ball bearing. The interference fit between the bearing inner ring and the shaft, as well as the interference fit between the outer ring and the bearing housing, are set according to the national standard "Limits and Fits".

[0019] S3 allows for different connection loads by changing the interference fit between the shaft and the inner ring of the bearing, and between the bearing housing and the outer ring of the bearing.

[0020] like Figure 5 As shown, the connecting load is the load between the contact surface of the shaft and the inner ring. By giving different deviation values ​​to the shaft through the three-dimensional solid model, different interference fits between the shaft and the inner ring can be achieved. Therefore, by changing the interference fit between the shaft and the inner ring of the bearing, and between the bearing housing and the outer ring of the bearing, different connecting loads can be obtained.

[0021] An interference fit between the inner ring and the shaft, and an interference fit between the outer ring and the bearing housing, will cause contact between the rolling elements and the inner and outer raceways.

[0022] S4. Import the 3D solid model with the embedded connecting loads into ANSYS. In the ANSYS finite element statics analysis module, set the parameters and material properties of the 3D solid model, and mesh the 3D solid model, such as... Figure 6 As shown. Here, ANSYS refers to general-purpose finite element analysis software, and the method described uses ANSYS to convert the geometric model into a finite element module.

[0023] A three-dimensional solid model of the interference fit between the shaft and the angular contact ball bearing was established, which considers continuous loads. The parameters of the three-dimensional solid model include the elastic modulus. Poisson's ratio

[0024] S5, the bearing components and shaft adopt a hexahedral mesh, and a layer of shell elements is set in the inner ring of the bearing to couple the nodes of the inner ring of the bearing with the nodes of the shaft to achieve rigid motion.

[0025] By coupling the nodes of the shaft and the inner ring, the shaft and the bearing have the same degree of freedom, thus achieving coupled motion between the shaft and the bearing.

[0026] The bearing, with its interference fit with the inner ring, exhibits high rigidity during operation. By incorporating a shell element within the bearing's inner ring, the nodes of the inner ring are coupled to the nodes of the shaft, achieving rigid motion and simulating real-world operating conditions.

[0027] S6 involves applying an axial force to the centroid of the rigid surface of the bearing inner ring to implant an adjustment load, thereby changing the axial force to obtain different adjustment loads. In step S6, a finite element model of the adjustment load is obtained by acquiring different adjustment loads, such as... Figure 7 As shown.

[0028] S7. Import the ANSYS finite element statics analysis module containing the connection load and the adjustment load into the finite element dynamics analysis module, insert boundary conditions, and establish a finite element model of the contact stiffness of the angular contact bearing.

[0029] The boundary conditions include rotational speed conditions and constraint conditions. Based on the established finite element model of the contact stiffness of the angular contact bearing, the contact stiffness of the angular contact ball bearing is calculated.

[0030] The proposed ball bearing contact stiffness modeling method under the coupling of assembly load and connection load establishes a finite element model of angular contact bearing contact stiffness to address the dual load coupling effect of assembly load and connection load. This facilitates the study of the contact characteristics of angular contact ball bearings under complex working conditions and can reasonably and accurately simulate the contact characteristics of the bearing-shaft joint and accurately calculate the contact stiffness.

[0031] In one embodiment, in step S3, according to the formula Calculate the connection load .

[0032] in, This indicates the Poisson's ratio of the bearing inner ring. Indicates the axial Poisson's ratio. This indicates the elastic modulus of the bearing inner ring. Indicates the elastic modulus of the shaft. Indicates the outer diameter of the bearing inner ring. Indicates the inner diameter of the bearing inner ring. Indicates the outer diameter of the shaft.

[0033] Specifically, the connection loads are calculated using theories of mechanics of materials and elasticity. The calculation of connection loads can be solved using the theory of elastic wall thickness circular rings. For example... Figure 2 As shown, assume the ring experiences a pressure of p per unit length, and the inner radius of the ring is... The outer radius is Then the formula is as follows:

[0034] .

[0035] The above formula is the general solution for a thick circular ring, applicable to cases where internal and external pressures range from zero to arbitrary values ​​and act alone.

[0036] If an elastic modulus is The outer diameter is An inner diameter ring of D is interference-fitted onto another ring with an elastic modulus of D. The outer diameter is D, and the inner diameter is On the ring, the diameter interference is Then a common pressure P is generated between the two rings, and the radial interference is the sum of the radial displacements caused by the pressure P on each ring.

[0037] The fit between the bearing inner ring and the shaft is as follows: Figure 3 As shown, where, The inner diameter of the bearing inner ring is the common diameter of the interference fit interface between the bearing and the shaft. The inner diameter of the shaft is the diameter of the inner diameter of the shaft. Under normal operating conditions, the shaft is a solid shaft. This refers to the diameter of the bearing's inner raceway. , , , These are the elastic modulus of the shaft, the elastic modulus of the bearing inner ring, the Poisson's ratio of the shaft, and the elastic Poisson's ratio of the bearing inner ring, respectively.

[0038] The fit between the bearing outer ring and the bearing housing is as follows: Figure 4 As shown, where, The outer diameter of the bearing outer ring is the interference fit interface and common diameter between the bearing and the bearing housing. The outer raceway diameter of the bearing is given. Under normal operating conditions, the bearing is a solid shaft. The inner and outer diameters of the bearing housing are generally assumed to be infinite during calculations. , , , These are the elastic modulus of the shaft, the elastic modulus of the bearing inner ring, the Poisson's ratio of the shaft, and the elastic Poisson's ratio of the bearing inner ring, respectively.

[0039] Based on the deformation of the inner and outer rings at the interference fit position, the interference amount of the interference fit can be determined as follows: The formula for calculating the connection load is: .

[0040] In one embodiment, the angular contact bearing contact stiffness modeling method further includes the following steps: Calculate the radial stiffness of the bearing and axial stiffness .

[0041] in, , , , , Indicates the first Normal contact stiffness between the ball and the inner ring groove of the bearing Indicates the first Normal contact stiffness between the ball and the outer ring groove of the bearing Indicates the first The contact angle between the ball and the inner ring of the bearing. The first The contact angle between the ball and the outer ring of the bearing. Indicates the number of balls. Indicates the position angle of the ball.

[0042] If the contact angle and contact load between the ball and the inner and outer grooves are known, the following can be calculated: The normal contact stiffness between the ball and the inner ring groove of the bearing and the first The normal contact stiffness between the ball and the outer ring raceway of the bearing. The radial component of the contact stiffness between the ball and the inner ring raceway is... The axial component of the contact stiffness between the ball and the inner groove is The radial component of the contact stiffness between the ball and the outer groove is The axial component of the contact stiffness between the ball and the outer groove is .

[0043] From the principle of series and parallel connections of springs, we can obtain the first... Radial stiffness at the contact point between the ball and the inner and outer grooves and axial stiffness They are respectively as well as .

[0044] radial stiffness of bearing and axial stiffness They are respectively as well as Radial stiffness and axial stiffness These are the calculation expressions for the contact stiffness of high-speed angular contact ball bearings, taking into account the influence of assembly and adjustment loads.

[0045] like Figure 8 as well as Figure 9 As shown, through the formula as well as The radial stiffness of the bearing can be calculated accurately. and axial stiffness .

[0046] In one embodiment, the method for modeling the contact stiffness of a ball bearing under the coupling of assembly load and connection load further includes the following steps: According to the formula Calculate the normal contact deformation of an angular contact ball bearing ; Deformation of normal contact Taking the derivative, we obtain the normal contact stiffness as... ; in, This represents the contact load between two contacting objects. This represents the equivalent elastic modulus of two contacting objects. Represents the ellipticity coefficient. It represents the sum of the curvatures of the two contacting objects on the principal plane of the contact point. 、 This represents the first and second type of complete elliptic integrals.

[0047] The ball bearing contact stiffness modeling method under the coupling of assembly load and connection load is based on the classical Hertz theory of bearings. It uses the theories of mechanics of materials and elasticity to establish a theoretical model of the connection load on the bearing stiffness. It couples two load conditions, assembly load and connection load, which is convenient for studying the contact characteristics of bearings under complex working conditions. It can reasonably and accurately simulate the contact characteristics of the bearing and shaft joint and accurately calculate the contact stiffness.

[0048] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0049] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for modeling the contact stiffness of a ball bearing under coupled assembly and connection loads, characterized in that, The method for modeling the contact stiffness of ball bearings under the coupling of assembly load and connection load includes the following steps: S1. Establish a three-dimensional solid model of the angular contact ball bearing and insert the initial clearance; S2. Based on the inner and outer ring diameters of the angular contact ball bearing, establish a bearing-rotor system model that includes the shaft and bearing housing and is interference-fitted with the inner and outer rings. S3, change the interference fit between the shaft and the inner ring of the bearing, and between the bearing housing and the outer ring of the bearing to obtain different connection loads; S4. Import the 3D solid model with the connected load into ANSYS. In the ANSYS finite element static analysis module, set the parameters and material properties of the 3D solid model and perform mesh generation on the 3D solid model. S5, the bearing components and shaft adopt a hexahedral mesh, and a layer of shell elements is set in the inner ring of the bearing to couple the nodes of the inner ring of the bearing with the nodes of the shaft to achieve rigid motion; S6, by applying an axial force to the center of mass of the rigid surface of the bearing inner ring to implant the adjustment load, and by changing the axial force, different adjustment loads can be obtained; S7. Import the ANSYS finite element statics analysis module containing the connection load and the assembly load into the finite element dynamics analysis module, insert boundary conditions, and establish a finite element model of the contact stiffness of the angular contact bearing; In step S3, according to the formula Calculate the connection load ; in, This indicates the Poisson's ratio of the bearing inner ring. Indicates the axial Poisson's ratio. This indicates the elastic modulus of the bearing inner ring. Indicates the elastic modulus of the shaft. Indicates the outer diameter of the bearing inner ring. Indicates the inner diameter of the bearing inner ring. Indicates the outer diameter of the shaft. This indicates the amount of interference in an over-interference pair. The deformation of the inner and outer rings at the interference fit positions, respectively.

2. The method for modeling the contact stiffness of a ball bearing under the coupling of assembly load and connection load as described in claim 1, characterized in that, The method for modeling the contact stiffness of ball bearings under the coupling of assembly load and connection load also includes the following steps: Calculate the radial stiffness of the bearing and axial stiffness ; in, , , , , Indicates the first Normal contact stiffness between the ball and the inner ring groove of the bearing Indicates the first Normal contact stiffness between the ball and the outer ring groove of the bearing Indicates the first The contact angle between the ball and the inner ring of the bearing. The first The contact angle between the ball and the outer ring of the bearing. Indicates the number of balls. Indicates the position angle of the ball.

3. The method for modeling the contact stiffness of a ball bearing under the coupling of assembly load and connection load as described in claim 2, characterized in that, The method for modeling the contact stiffness of ball bearings under the coupling of assembly load and connection load also includes the following steps: According to the formula Calculate the normal contact deformation of an angular contact ball bearing ; Deformation of normal contact Taking the derivative, we obtain the normal contact stiffness as... ; in, This represents the contact load between two contacting objects. This represents the equivalent elastic modulus of two contacting objects. Represents the ellipticity coefficient. It represents the sum of the curvatures of the two contacting objects on the principal plane of the contact point. 、 This represents the first and second type of complete elliptic integrals.

4. The method for modeling the contact stiffness of a ball bearing under the coupling of assembly load and connection load as described in claim 3, characterized in that, The boundary conditions include rotational speed conditions and constraint conditions.

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