A quasi-static simulation method and system for an asymmetric double-row tapered roller bearing

Abstract

This invention discloses a method comprising: constructing an asymmetric double-row tapered roller bearing numerical model based on user-provided bearing structural and material parameters; solving the nonlinear equations of the model using the homotopy-Newton iterative method based on the asymmetric double-row tapered roller bearing numerical model; and establishing stiffness variation law module and life variation law module to characterize the stiffness and life distribution of the asymmetric double-row tapered roller bearing under load. This invention constructs an asymmetric double-row tapered roller bearing numerical model based on user-provided bearing structural and material parameters, and solves the nonlinear equations of the model using the homotopy-Newton iterative method. The homotopy-Newton method effectively expands the initial value search range and the initial value prediction range of the nonlinear equations.

Description

Technical Field

[0001] This invention belongs to the field of bearing quasi-static simulation technology, and relates to a quasi-static simulation method and system for asymmetric double-row tapered roller bearings. Background Technology

[0002] Double-row tapered roller bearings are widely used in wind power due to their ability to withstand large radial loads, axial loads, and overturning moments. Currently, the main bearings for wind turbine main shafts are primarily double-row tapered roller bearings. Because wind power loads have significant overturning moments, the load on the left bearing of the double-row bearing is much greater than that on the right bearing. This loading condition results in wasted load-bearing capacity on the right bearing and insufficient load-bearing capacity on the left bearing, leading to wasted costs. Currently, there is little analysis of asymmetric double-row tapered roller bearings, and information on their stiffness and life distribution is lacking. Summary of the Invention

[0003] The purpose of this invention is to solve the problem of uneven load distribution on the left and right rows of rollers in existing double-row tapered roller bearings under conditions of large overturning moment, and to provide a quasi-static simulation method and system for asymmetric double-row tapered roller bearings.

[0004] To achieve the above objectives, the present invention employs the following technical solution:

[0005] In a first aspect, the present invention provides a quasi-static simulation method for asymmetric double-row tapered roller bearings, comprising the following steps:

[0006] A numerical calculation model for an asymmetric bearing is established based on the bearing parameters.

[0007] Based on the quasi-static analysis theory of bearings, and combined with the calculation methods of slice force, centrifugal force and gyroscopic torque, the nonlinear equations of the bearing are obtained; then, the homotopy-Newton method is used to solve the nonlinear equations of the bearing to obtain the deformation of the bearing rollers.

[0008] Based on the theory of series and parallel stiffness calculation and combined with the deformation of bearing rollers, a stiffness calculation model for asymmetric double-row tapered roller bearings is established to obtain the stiffness variation law.

[0009] Based on life calculation theory and considering the deformation of bearing rollers, a life calculation model for asymmetric double-row tapered roller bearings is established to obtain the life variation law.

[0010] Secondly, the present invention provides a quasi-static simulation system for asymmetric double-row tapered roller bearings, comprising:

[0011] The bearing model building module is used to build a numerical calculation model of an asymmetric bearing based on the bearing parameters.

[0012] The iterative solution module is used to obtain the bearing nonlinear equations based on the quasi-static analysis theory of bearings, combined with the calculation methods of slice force, centrifugal force and gyroscopic torque; then, the homotopy-Newton method is used to solve the bearing nonlinear equations to obtain the deformation of the bearing rollers.

[0013] The stiffness variation law calculation module is used to establish a stiffness calculation model for asymmetric double-row tapered roller bearings based on the stiffness series and parallel calculation theory and the deformation of the bearing rollers, and to obtain the stiffness variation law.

[0014] The life variation law calculation module is used to establish a life calculation model for asymmetric double-row tapered roller bearings based on life calculation theory and the deformation of bearing rollers, and to obtain the life variation law.

[0015] Thirdly, the present invention provides a computer device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.

[0016] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described above.

[0017] Compared with the prior art, the present invention has the following beneficial effects:

[0018] Based on the bearing structure and material parameters provided by the user, this invention constructs an asymmetric double-row tapered roller bearing numerical model. Based on the asymmetric double-row tapered roller bearing numerical model and combined with the homotopy-Newton iterative method, the nonlinear equations of the model are solved. The homotopy-Newton method can effectively expand the initial value search range of the nonlinear equations and expand the prediction range of the initial values.

[0019] This invention establishes a stiffness variation law module and a life variation law module to characterize the stiffness and life distribution of asymmetric double-row tapered roller bearings under load. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 The flowchart shows the quasi-static simulation method for asymmetric double-row tapered roller bearings provided by this invention.

[0022] Figure 2 This is a flowchart of the stiffness calculation model of the present invention.

[0023] Figure 3 This is a flowchart of the lifetime calculation model of the present invention.

[0024] Figure 4 The image shows the results of the stiffness simulation.

[0025] Figure 5 The simulation results of the overall lifespan are shown in the figure with the increase in the length of the rollers in the left column.

[0026] Figure 6 The simulation results show the overall lifespan of the rollers on the left column with the increased diameter of the small end.

[0027] Figure 7 This is a schematic diagram of a quasi-static simulation system for an asymmetric double-row tapered roller bearing. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0029] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0030] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0031] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0032] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0033] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0034] The present invention will now be described in further detail with reference to the accompanying drawings:

[0035] See Figure 1 This invention discloses a quasi-static simulation method for asymmetric double-row tapered roller bearings, comprising the following steps:

[0036] S1 establishes a numerical calculation model for the asymmetric bearing based on the bearing parameters;

[0037] Based on the quasi-static analysis theory of bearings, and combined with the calculation methods of slice force, centrifugal force and gyroscopic torque, S2 obtains the nonlinear equations of the bearing; then, by combining the homotopy-Newton method, the nonlinear equations of the bearing are solved to obtain the deformation of the bearing rollers.

[0038] Based on the theory of series and parallel stiffness calculation and combined with the deformation of bearing rollers, S3 establishes a stiffness calculation model for asymmetric double-row tapered roller bearings and obtains the stiffness variation law.

[0039] Based on the life calculation theory and combined with the deformation of the bearing rollers, S4 establishes a life calculation model for asymmetric double-row tapered roller bearings and obtains the life variation law.

[0040] Example

[0041] This invention provides a quasi-static simulation method for asymmetric double-row tapered roller bearings, comprising the following steps:

[0042] Step 101: Based on the structural and material parameters of the bearing, establish a three-dimensional numerical model of the asymmetric double-row tapered roller bearing in simulation software. The simulation software is MATLAB; the structural parameters include not only the basic structural parameters of the bearing such as the number of rollers, roller length, roller diameter at both ends, spherical radius at the large end of the roller, pitch circle diameter, tilt angle, and flange angle, but also material parameters such as elastic density, Poisson's ratio, and elastic modulus; the asymmetric double-row tapered roller bearing reflects the difference in roller length and diameter at both ends between the two rows of rollers.

[0043] Step 101 further includes: constructing a contact model between the outer ring and the roller, a contact model between the inner ring and the roller, and a contact model between the inner ring large flange and the roller; extracting model deformation parameters to construct a load balance equation model.

[0044] Taking the outer ring and roller contact model as an example, this article details the process of creating a quasi-static model for an asymmetric double-row tapered roller bearing:

[0045] In the roller coordinate system, the contact point vectors between the roller on the roller and the outer raceway are constructed, and in the raceway coordinate system, the contact point vectors between the roller on the raceway and the outer raceway are constructed. Through Cartesian coordinate transformation, these two vectors are unified into the bearing principal coordinate system. Based on the condition that the contact deformation must be perpendicular to the contact surface, as shown in Formula 1, the contact deformation δ of the outer ring and roller contact model is constructed. o :

[0046] δ o =([r″) ro ] k -[r′ o ] k )[n no ] k (1)

[0047] Among them, [r″ ro ] k The contact point vector between the roller on the main coordinate system and the outer raceway; [r′ o ] k The contact point vector between the rollers on the main coordinate system and the outer raceway; [n no ] k It is the unit normal vector.

[0048] Based on the contact deformation model of the asymmetric double-row tapered roller bearing and the calculation formula for the slice force, such as Formula 2, the load model of the asymmetric double-row tapered roller bearing can be determined:

[0049] q n =δ n / (1.24*10 -5 (nw) 0.11 (2)

[0050] Where, qn For a single slice force of the roller; δ n denoted by , where n is the number of roller slices, and w is the thickness of a single roller slice.

[0051] Step 102: Determine the bearing deformation based on the homotopy-Newton model combined with the bearing model. Construct the homotopy equation of the nonlinear equation, as shown in Formula 3. Solve the nonlinear equilibrium equation based on the growth of the homotopy operator from 0 to 1.

[0052] H(x,t)=F(x)+(t-1)F(x0) (3)

[0053] Where H(x,t) is the constructed homotopy equation; F(x) is the existing nonlinear equation system; t is the homotopy operator; and x0 is the initial vector for iteration.

[0054] Step 103: Based on the bearing deformation and the stiffness calculation model, determine the stiffness variation law.

[0055] like Figure 2 The flowchart shown is for the stiffness calculation model. Combining the bearing's structural parameters and deformation model results, an implicit function differential structure is constructed, as shown in Formula 5, thereby obtaining the bearing stiffness variation law, as shown below. Figure 4 As shown, under fixed preload and rotational speed conditions, the radial stiffness tends to decrease first and then increase as the axial force increases.

[0056] The theoretical formula for calculating the stiffness series and parallel connections is as follows:

[0057]

[0058] Where K is the bearing stiffness matrix; k is the number of bearing columns; and j is the number of rollers.

[0059] The theoretical formula for stiffness calculation is as follows:

[0060]

[0061] Where K is the bearing stiffness matrix; This is the vector of the external load on the bearing; This is the displacement vector of the bearing inner ring.

[0062]

[0063] Among them, F xjk x represents the load in the x-direction on a single roller of the bearing; x represents the radial deformation of the bearing; z represents the axial deformation of the bearing. ξ is the bearing deflection deformation; ζ is the roller radial deformation; ζ is the roller axial deformation; η is the roller deflection deformation.

[0064]

[0065] Among them, F xjk x represents the external force borne by a single roller; z represents the radial deformation of the bearing; z represents the axial deformation of the bearing. ξ is the bearing deflection angle; ζ is the roller radial deformation; ζ is the roller axial deformation; η is the roller deflection angle.

[0066]

[0067]

[0068] Step 104: Based on the bearing deformation and the life calculation model, determine the life change pattern.

[0069] The theoretical formula for calculating lifespan is:

[0070]

[0071] Where L is the bearing life; L i,n,k For the inner raceway life; L o,n,k For the life of the outer raceway; L R,i,n,k For single roller-inner ring contact life; L R,o,n,k is the single roller-outer ring contact life; N is the number of roller revolutions; k is the number of bearing rows; j is the number of bearing rollers.

[0072] like Figure 3 The diagram shows the life calculation model flowchart. Combining the bearing's structural parameters and deformation model results with the life calculation formula, the raceway life and roller-raceway life are constructed respectively. The bearing life variation law is obtained based on the probability product formula, as follows: Figure 5 As shown, it can be seen that the bearing life gradually increases with the increase of the length of the first column. Figure 6 As shown, it can be seen that the bearing life gradually decreases as the diameter of the small end of the first column increases.

[0073] Figure 7 This is a schematic diagram of a quasi-static simulation system for an asymmetric double-row tapered roller bearing. The bearing model construction module is used to construct a numerical model of the asymmetric double-row tapered roller bearing in the simulation software based on the bearing's basic structural and material parameters, obtaining model deformation parameters and constructing a load balance equation model.

[0074] The iterative solution module, in conjunction with the homotopy-Newton iterative model, is used to solve the nonlinear load balance equation model generated by numerical modeling of asymmetric double-row tapered roller bearings.

[0075] The stiffness variation law calculation module combines the bearing's structural parameters and the bearing's deformation model results to construct an implicit function differential structure to determine the bearing's stiffness; the stiffness includes axial stiffness, radial stiffness, and angular stiffness.

[0076] The lifespan variation law calculation module is used to determine the lifespan of the bearings; the lifespan includes the lifespan of the bearings in the left column, the lifespan of the bearings in the right column, and the total lifespan.

[0077] A computer device is provided according to an embodiment of the present invention. This computer device includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0078] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0079] The computer device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The computer device may include, but is not limited to, a processor and memory.

[0080] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0081] The memory can be used to store the computer program and / or module, and the processor implements various functions of the computer device by running or executing the computer program and / or module stored in the memory, and by calling the data stored in the memory.

[0082] If the modules / units integrated into the computer device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0083] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A quasi-static simulation method for asymmetric double-row tapered roller bearings, characterized in that, Includes the following steps: A numerical calculation model for an asymmetric bearing is established based on bearing parameters; the specific method for establishing the numerical calculation model for the asymmetric bearing includes: Construct contact models between the outer ring and rollers, the inner ring and rollers, and the inner ring large flange and rollers; extract the deformation parameters of the contact models between the outer ring and rollers, the inner ring and rollers, and the inner ring large flange and rollers to construct a load balance equation model; The construction of the outer ring and roller contact model includes: In the roller coordinate system, the contact point vectors between the roller on the roller and the outer raceway are constructed, and in the raceway coordinate system, the contact point vectors between the roller on the raceway and the outer raceway are constructed. Through Cartesian coordinate transformation, these two vectors are unified into the bearing principal coordinate system. Based on the condition that the contact deformation must be perpendicular to the contact surface, the contact deformation of the outer ring and roller contact model is constructed. : in, The vector of the contact point between the roller on the main coordinate system and the outer raceway; The vector of the contact points between the rollers on the raceway and the outer raceway in the main coordinate system; It is the unit normal vector; The construction of the inner ring and roller contact model includes: In the roller coordinate system, the contact point vectors between the rollers on the roller and the inner raceway are constructed, and in the raceway coordinate system, the contact point vectors between the rollers on the inner raceway and the inner raceway are constructed. Through Cartesian coordinate transformation, these two vectors are unified into the bearing principal coordinate system. Based on the condition that the contact deformation must be perpendicular to the contact surface, the contact deformation of the inner ring and roller contact model is constructed. : in, The vector of the contact points between the roller and the inner raceway on the roller in the main coordinate system; The vector of the contact points between the rollers on the inner ring and the inner raceway in the main coordinate system; The unit normal vector at the contact point; The inner ring large flange and roller contact model includes: In the roller coordinate system, contact vectors are constructed between the large end of the roller and the large flange of the inner ring, and in the inner ring coordinate system, contact vectors are constructed between the large end of the roller and the large flange of the inner ring. Through Cartesian coordinate transformation, these two vectors are unified into the bearing principal coordinate system. Based on the condition that contact deformation must be perpendicular to the contact surface, the contact deformation of the contact model between the large flange of the inner ring and the large end of the roller is constructed. : in, The contact vector between the large end of the inner roller and the large flange of the inner ring in the main coordinate system; The contact vector between the large end of the roller and the large flange of the inner ring in the main coordinate system; The unit normal vector at the contact point; The deformation parameters of the outer ring and roller contact model, the inner ring and roller contact model, and the inner ring large flange and roller contact model are extracted to construct the load balance equation model, including: in, The radial force borne by the bearing; The number of rollers; For roller phase; For the first column j Contact force of the outer ring of each roller; For the second column j Contact force of the outer ring of each roller; The axial force borne by the bearing; For the first column j Contact force of the inner ring of each roller; For the second column j Contact force of the inner ring of each roller; The torque that the bearing can withstand; For the first column j One roller torque; For the second column j One roller torque; Based on the quasi-static analysis theory of bearings, and combined with the calculation methods of slice force, centrifugal force and gyroscopic torque, the nonlinear equations of the bearing are obtained; then, the homotopy-Newton method is used to solve the nonlinear equations of the bearing to obtain the deformation of the bearing rollers. Based on the theory of series and parallel stiffness calculation and combined with the deformation of bearing rollers, a stiffness calculation model for asymmetric double-row tapered roller bearings is established to obtain the stiffness variation law. Based on life calculation theory and considering the deformation of bearing rollers, a life calculation model for asymmetric double-row tapered roller bearings is established to obtain the life variation law.

2. The quasi-static simulation method for asymmetric double-row tapered roller bearings according to claim 1, characterized in that, The bearing parameters include structural parameters and material parameters; The structural parameters include the number of rollers, roller length, roller diameter at both ends, spherical radius at the large end of the roller, pitch circle diameter, tilt angle, and flange angle. The material parameters include the material's elastic density, Poisson's ratio, and elastic modulus.

3. The quasi-static simulation method for asymmetric double-row tapered roller bearings according to claim 2, characterized in that, Based on the quasi-static analysis theory of bearings, and combined with the calculation methods for slice force, centrifugal force, and gyroscopic torque, a set of nonlinear equations for bearings is obtained, including: Based on the numerical calculation model of the asymmetric double-row tapered roller bearing, and combined with the calculation formulas for slicing force, centrifugal force, and gyroscopic torque, the load model of the asymmetric double-row tapered roller bearing can be determined: The formula for calculating the slicing force is as follows: in, For a single slice of the roller; This is a deformation of the roller slice; The number of roller slices; The thickness of a single roller slice; The formula for calculating centrifugal force is as follows: in, The bearing pitch circle diameter; For roller quality; The angular velocity of the roller's revolution; The formula for calculating the torque of a gyroscope is as follows: in, It is the moment of inertia; The angular velocity of the roller's revolution; The angular velocity of the roller's rotation; The contact angle between the roller and the outer raceway; The contact angle between the roller and the inner raceway.

4. The quasi-static simulation method for asymmetric double-row tapered roller bearings according to claim 2, characterized in that, The deformation of the bearing rollers was obtained using the following method: Homotopy equations for constructing nonlinear equations ; in, This is an existing system of nonlinear equations; For homotopy operators; This is the initial vector for iteration.

5. The quasi-static simulation method for asymmetric double-row tapered roller bearings according to claim 2, characterized in that, The stiffness variation law was obtained using the following method: The theory for stiffness calculation is as follows: in, Here is the bearing stiffness matrix; This is the vector of the external load on the bearing; This is the displacement vector of the bearing inner ring; Based on stiffness calculation theory, the stress on a single roller of the bearing is obtained. x Directional load as follows: in, This refers to the radial deformation of the bearing. This refers to the axial deformation of the bearing. For bearing deflection deformation; The roller deforms radially. The roller deforms along its axial direction; This is due to the deflection deformation of the roller.

6. The quasi-static simulation method for asymmetric double-row tapered roller bearings according to claim 2, characterized in that, The lifespan variation pattern was obtained using the following method: The theory for calculating lifespan is as follows: in, For bearing life; For the life of the inner raceway; For the life of the outer raceway; For single roller-inner ring contact life; For single roller-outer ring contact life; This represents the number of revolutions of the roller. This refers to the number of bearing columns; This represents the number of bearing rollers.

7. A quasi-static simulation system for an asymmetric double-row tapered roller bearing for implementing the method of claim 1, characterized in that, include: The bearing model building module is used to build a numerical calculation model of an asymmetric bearing based on the bearing parameters. The iterative solution module is used to obtain the bearing nonlinear equations based on the quasi-static analysis theory of bearings, combined with the calculation methods of slice force, centrifugal force and gyroscopic torque; then, the homotopy-Newton method is used to solve the bearing nonlinear equations to obtain the deformation of the bearing rollers. The stiffness variation law calculation module is used to establish a stiffness calculation model for asymmetric double-row tapered roller bearings based on the stiffness series and parallel calculation theory and the deformation of the bearing rollers, and to obtain the stiffness variation law. The life variation law calculation module is used to establish a life calculation model for asymmetric double-row tapered roller bearings based on life calculation theory and the deformation of bearing rollers, and to obtain the life variation law.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-6.

Images