Method and system for analyzing nonlinear dynamic characteristics of high-speed motorized spindle
Patent Information
- Application Number
- CN202610174630.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-06
- Publication Date
- 2026-06-23
Smart Images
Figure CN122263369A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of high-speed precision machine tool technology, and in particular to a method and system for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle. Background Technology
[0002] Currently, the application of high-end CNC machine tools reflects the overall level of the manufacturing industry and is a crucial guarantee for the machining of precision parts in fields such as aerospace, mold making, and medical applications. Among them, the electric spindle, as a core functional component of high-end CNC machine tools, directly determines the machining accuracy, efficiency, and reliability of the machine tool through its dynamic performance. Therefore, it is necessary to analyze the dynamic characteristics of the electric spindle.
[0003] However, the electric spindle dynamics analysis schemes in related technologies lack unified and standardized process guidance, making it difficult to guarantee the repeatability of analysis results. In particular, when bearing forces are involved, it is impossible to accurately describe and analyze vibration phenomena. Summary of the Invention
[0004] This application aims to at least partially address one of the technical problems in the related art.
[0005] Therefore, the first objective of this application is to propose a nonlinear dynamic characteristic analysis method for high-speed electric spindles. This method considers the nonlinear forces of angular contact ball bearings and linear bearings to analyze the dynamic characteristics of electric spindles, which can solve the problem of low repeatability in current analysis and research, and improve the efficiency of electric spindle dynamic characteristic research and performance optimization.
[0006] The second objective of this application is to propose a system for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle.
[0007] The third objective of this application is to propose an electronic device.
[0008] The fourth objective of this application is to provide a computer-readable storage medium.
[0009] To achieve the above objectives, the first aspect of this application is to propose a method for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle, comprising the following steps:
[0010] The electric spindle rotor system is decomposed and simplified into a shaft system, a bearing system, and a bearing housing system. The shaft system is then discretized and modeled using Timoshenko beam elements to obtain multiple element matrices and node vectors. Based on Hertzian contact theory, nonlinear force models for angular contact ball bearings and linear bearings are established respectively, and the force analysis of the rear bearing housing is performed. The dynamic equation of the bearing housing is established using the various bearing forces acting on the rear bearing housing. Based on Newton's second law, the multiple unit matrices, the node vectors, the nonlinear force model, and the bearing housing dynamic equations are integrated to generate the dynamic equations of the rotor system, wherein the nonlinear bearing force is treated as an external force term in the dynamic equations of the rotor system. The dynamic equations of the rotor system are numerically solved and dynamic response is analyzed to obtain multiple modal parameters and dynamic response results; Using the dynamic response results, sensitivity analysis is performed on various assembly parameters of the rotor system to determine the influence of each assembly parameter on the dynamic characteristics of the electric spindle, and an optimization scheme for the electric spindle structure is generated based on the influence analysis results.
[0011] Optionally, the step of discretizing the rotating shaft system using Timoshenko beam elements includes: discretizing the rotating shaft system into... n Each axis unit and n +1 node, of which, n The integer is positive; calculate the translational and rotational degrees of freedom of each node with respect to the two coordinate axes, and generate the node vector based on the translational and rotational degrees of freedom of the front and rear nodes of the Timoshenko beam element.
[0012] Optionally, the discrete modeling of the rotating shaft system using Timoshenko beam elements includes: calculating correction coefficients for the Timoshenko beam elements based on multiple physical parameters of the rotating shaft system; calculating the mass matrix, inertia matrix, gyroscope matrix, and stiffness matrix of the Timoshenko beam elements based on the correction coefficients and the multiple physical parameters; and characterizing the structural damping matrix of the rotating shaft system using Rayleigh damping.
[0013] Optionally, a nonlinear force model of the angular contact ball bearing is established based on Hertzian contact theory, including: setting the balls of the angular contact ball bearing to be arranged at equal intervals and maintain rolling motion; calculating the rotational speed of the cage based on the radius of the angular contact ball bearing and the rotational speed of the inner ring; calculating the angle through which any ball rotates based on the rotational speed of the cage; calculating the compression of the ball; and combining the angle through which each ball rotates and the compression of the ball to calculate the nonlinear restoring force generated between the balls and the inner and outer rings of the angular contact ball bearing.
[0014] Optionally, a nonlinear force model of the linear bearing is established based on Hertzian contact theory, including: setting the linear bearing to a non-rotating state; calculating the angle of any ball according to the number of balls in the linear bearing; calculating the deformation of any ball according to the gap between the ball and the inner and outer rings of the linear bearing and the angle of any ball; and calculating the nonlinear restoring force generated between the ball and the inner and outer rings of the linear bearing based on the angle and deformation of each ball.
[0015] Optionally, the sensitivity analysis of various assembly parameters of the rotor system to determine the influence of each assembly parameter on the dynamic characteristics of the electric spindle includes: analyzing the preload of the angular contact ball bearing on the influence of inducing chaotic state and subharmonic vibration in the electric spindle system; analyzing the bearing span on the influence of inducing chaotic state in the electric spindle system; and analyzing the influence of changes in linear bearing clearance on the fundamental frequency parameter and subharmonic vibration of the electric spindle system.
[0016] Optionally, the optimization scheme for generating the electric spindle structure based on the influence analysis results includes: adjusting the angle and magnitude of the preload to reduce the vibration amplitude of the electric spindle structure; moving the rear bearing housing inward and eliminating the clearance of the linear bearing to allow the rotor system to avoid nonlinear vibration.
[0017] To achieve the above objectives, a second aspect of this application also proposes a system for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle, comprising the following modules: The decomposition module is used to decompose and simplify the electric spindle rotor system. It decomposes the rotor system into a shaft system, a bearing system, and a bearing housing system. It also uses Timoshenko beam elements to discretize and model the shaft system, obtaining multiple element matrices and node vectors. The modeling module is used to establish nonlinear force models for angular contact ball bearings and linear bearings based on Hertzian contact theory, and to perform force analysis on the rear bearing housing. The dynamic equations of the bearing housing are established using the various bearing forces acting on the rear bearing housing. An integration module is used to integrate the multiple unit matrices, the node vectors, the nonlinear force model, and the bearing housing dynamic equations based on Newton's second law to generate the dynamic equations of the rotor system, wherein the nonlinear bearing force is treated as an external force term in the dynamic equations of the rotor system. The solver module is used to numerically solve the dynamic equations of the rotor system and perform dynamic response analysis to obtain multiple modal parameters and dynamic response results; The analysis module is used to perform sensitivity analysis on various assembly parameters of the rotor system using the dynamic response results, determine the influence of each assembly parameter on the dynamic characteristics of the electric spindle, and generate an optimization scheme for the electric spindle structure based on the influence analysis results.
[0018] To achieve the above objectives, a third aspect of this application also provides an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the high-speed electric spindle nonlinear dynamic characteristic analysis method as described in any one of the first aspects above.
[0019] To achieve the above objectives, the fourth aspect of this application also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle as described in any of the first aspects above.
[0020] The technical solutions provided by the embodiments of this application bring at least the following beneficial effects: This application constructs a standardized analysis system covering the entire process of rotor system decomposition and simplification, nonlinear bearing force modeling, system dynamic equation assembly, numerical solution and dynamic response analysis, parameter sensitivity analysis, and structural optimization suggestion generation. Based on clear physical theories and standardized matrix modeling methods, it can support the reproduction of the analysis process according to the workflow, improve the scientificity and efficiency of electric spindle dynamic characteristic research, and provide a unified analysis paradigm for the industry. Thus, this application establishes a standardized analysis process, improving the repeatability and efficiency of the analysis. Furthermore, this application introduces nonlinear bearing modeling, enabling the model to truly reflect the vibration phenomena caused by bearing nonlinear factors, significantly improving the accuracy of electric spindle dynamic characteristic analysis, and providing reliable data support for subsequent dynamic characteristic evaluation and fault diagnosis. Moreover, this application fully considers the actual working scenarios of electric spindles, incorporating linear bearings into the rotor system modeling scope, taking into account the core function and mechanical characteristics of linear bearings to adapt to rotor thermal expansion. Furthermore, by performing stress analysis on the rear bearing housing and simplifying it into a rigid mass block, a balance was struck between model accuracy and computational efficiency, making it directly applicable to the structural design and performance optimization of actual electric spindles. Several key engineering adjustable parameters were also incorporated into the analysis process, providing clear adjustment directions for subsequent structural optimization and demonstrating strong engineering applicability.
[0021] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description
[0022] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a method for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle, as proposed in an embodiment of this application. Figure 2 This is a schematic diagram of a specific standardized analysis process for the dynamic characteristics of an electric spindle proposed in an embodiment of this application; Figure 3 This is a schematic diagram of the structure of an electric spindle rotor system proposed in an embodiment of this application; Figure 4 This is a schematic diagram of a Timoshenko beam element proposed in an embodiment of this application; Figure 5 This is a schematic diagram of a dynamic model of a rotor-bearing-bearing housing system proposed in an embodiment of this application; Figure 6 This is a schematic diagram of the force on a rear bearing housing according to an embodiment of this application; Figure 7 This is a schematic diagram of the first mode shape of an electric spindle according to an embodiment of this application; Figure 8 This is a schematic diagram of the second-order mode shape of an electric spindle according to an embodiment of this application; Figure 9 This is a schematic diagram of the third mode shape of an electric spindle according to an embodiment of this application; Figure 10 This is a system spectrum diagram showing the variation of preload force according to an embodiment of this application; Figure 11 This is a system spectrum diagram showing how the span varies, as proposed in an embodiment of this application. Figure 12 This is a system spectrum diagram showing the variation of linear bearing clearance as presented in an embodiment of this application; Figure 13 This is a schematic diagram of the structure of a high-speed electric spindle nonlinear dynamic characteristic analysis system proposed in an embodiment of this application. Detailed Implementation
[0023] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.
[0024] The following description, with reference to the accompanying drawings, illustrates a method and system for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle, as proposed in an embodiment of this application.
[0025] Figure 1 This is a flowchart illustrating a method for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle, as proposed in an embodiment of this application. Figure 2 This is a schematic diagram illustrating a specific standardized analysis process for the dynamic characteristics of an electric spindle, as proposed in an embodiment of this application. Figure 1 As shown, the method includes the following steps: Step S101: Decompose and simplify the electric spindle rotor system by decomposing it into a shaft system, a bearing system, and a bearing housing system. Then, use Timoshenko beam elements to discretize and model the shaft system to obtain multiple element matrices and node vectors.
[0026] Specifically, this step first decomposes and simplifies the electric spindle rotor system, dividing it into three subsystems: the shaft system, the bearing system, and the bearing housing system.
[0027] As one possible implementation, such as Figure 3 As shown, the disassembled rotor system includes front bearing 1, front bearing 2, rear bearing 3, rear bearing 4, shaft 5, motor rotor 6, front dynamic balancing disc 7, rear dynamic balancing disc 8, rear bearing housing 9, and linear bearing 10. Based on this, the rotor system can be simplified to consist of a shaft system (including shaft 5, motor rotor 6, and dynamic balancing disc), a bearing system (including bearing assemblies), and a bearing housing system (including rear bearing housing 9 and linear bearing 10).
[0028] Furthermore, Timoshenko beam elements are used to discretize and model the rotating shaft system.
[0029] In one embodiment of this application, the rotating shaft system is discretized using Timoshenko beam elements, including: discretizing the rotating shaft system into... n Each axis unit and n +1 node, of which, n The integer is positive; calculate the translational and rotational degrees of freedom of each node with respect to the two coordinate axes, and generate a node vector based on the translational and rotational degrees of freedom of the front and rear nodes of the Timoshenko beam element.
[0030] Specifically, the Timoshenko beam unit used in this embodiment is as follows: Figure 4 As shown, the rotating shaft system is discretized using Timoshenko beam elements. n Each axis unit and n +1 node. The quantity... n It can be determined based on practical factors such as the required discrete precision, for example, Figure 5 As shown, the axis of rotation is discretized and modeled using Timoshenko beams. The resulting simplified model contains 9 axis elements and 10 nodes.
[0031] For each point, considering its translational degrees of freedom along the Y and Z axes, and its rotational degrees of freedom around the Y and Z axes, we can obtain the nodal degree of freedom vector as shown in the following formula:
[0032] in, y and z This represents the translational degrees of freedom along the corresponding coordinate axis. θ y and θ z Indicates the rotational degrees of freedom about the corresponding coordinate axis, subscript i and i+1 is used to represent the front and back nodes of the beam element, respectively.
[0033] In one embodiment of this application, the discrete modeling of the rotating shaft system using Timoshenko beam elements further includes: calculating correction coefficients for the Timoshenko beam elements based on multiple physical parameters of the rotating shaft system; calculating the mass matrix, inertia matrix, gyroscope matrix, and stiffness matrix of the Timoshenko beam elements based on the correction coefficients and multiple physical parameters; and characterizing the structural damping matrix of the rotating shaft system using Rayleigh damping.
[0034] Specifically, for Timoshenko beam elements, the mass matrix can be calculated using the following formula. :
[0035] The inertia matrix can be calculated using the following formula. :
[0036] The elements of the mass matrix and the inertia matrix can be calculated using the following formulas:
[0037] in, This is the shear compliance coefficient. , To effectively resist shear area, It can be calculated using the following formula:
[0038] in, For the shaft segment density, E and G These are the Young's modulus and shear modulus of the shaft segment material, respectively. Let the moment of inertia of the axis of rotation be . The length of the shaft segment. The cross-sectional area of the shaft segment is... Poisson's ratio of the shaft segment material. D The outer diameter of the shaft. d This is the inner diameter of the shaft.
[0039] Gyroscope Matrix It can be calculated using the following formula:
[0040] in, .
[0041] Stiffness matrix It can be calculated using the following formula:
[0042] in, .
[0043] The structural damping matrix of the rotating shaft system is characterized by Rayleigh damping and can be expressed by the following formula: C= α M+ β K in, , , and This represents the first two natural frequencies of the system. and This indicates the damping ratio of the first two orders. .
[0044] It should be noted that the embodiments of this application accurately quantify the energy loss characteristics of the system through the Rayleigh damping matrix, which can provide a damping model that conforms to engineering practice for the subsequent integrated dynamic equations, supplement the energy loss term in the rotor system dynamic equations, participate in the subsequent numerical integration to solve the steady-state response, and be applied to the subsequent parameter sensitivity analysis.
[0045] Step S102: Based on Hertzian contact theory, nonlinear force models for angular contact ball bearings and linear bearings are established respectively, and the force analysis of the rear bearing housing is performed. The dynamic equation of the bearing housing is established using the various bearing forces acting on the rear bearing housing.
[0046] Specifically, this step involves nonlinear bearing force modeling. First, nonlinear force models are established for angular contact ball bearings and linear bearings in the bearing system, respectively, based on Hertzian contact theory.
[0047] In one embodiment of this application, a nonlinear force model of an angular contact ball bearing is established based on Hertzian contact theory, including: setting the balls of the angular contact ball bearing to be arranged at equal intervals and maintain rolling motion; calculating the rotational speed of the cage based on the radius of the angular contact ball bearing and the rotational speed of the inner ring; calculating the angle through which any ball rotates based on the rotational speed of the cage; calculating the compression of the ball; and combining the angle through which each ball rotates and the compression of the ball to calculate the nonlinear restoring force generated between the balls and the inner and outer rings of the angular contact ball bearing.
[0048] Specifically, this embodiment uses the Hertzian contact model to describe the contact force of the angular contact ball bearing. In practice, assuming the balls are evenly spaced and only undergo rolling motion, the cage rotational speed can be calculated using the following formula:
[0049] in, R jci It is the inner radius. R jcoΩ is the outer radius, Ω is the inner rotation speed, and the outer rotation speed is 0.
[0050] Then, assuming the number of balls in the angular contact ball bearing is... N jc Then the first j The angle through which each ball rotates can be calculated using the following formula:
[0051] Then, based on the axial preload of the angular contact ball bearing... F 0 and contact angle α 0. The compression of the ball bearings can be calculated using the following formula:
[0052]
[0053] in, This refers to the combined Hertzian contact stiffness of the inner and outer rings of an angular contact ball bearing. and These are the Hertzian contact stiffnesses between the inner and outer rings and the balls, respectively. and The specific formula is obtained based on the fitting formula proposed by Brewe and Harmrock, as shown below:
[0054] in, The sum of the principal curvatures of the two contacting objects. , The principal radius of curvature.
[0055] Therefore, the nonlinear restoring force generated between the balls and the inner and outer rings of the angular contact ball bearing and It can be calculated using the following formula:
[0056] in, and These represent the inner circle and the outer circle, respectively.
[0057] In one embodiment of this application, a nonlinear force model of a linear bearing is established based on Hertzian contact theory, including: setting the linear bearing to a non-rotating state; calculating the angle of any ball based on the number of balls in the linear bearing; calculating the deformation of any ball based on the gap between the ball and the inner and outer rings of the linear bearing and the angle of any ball; and calculating the nonlinear restoring force generated between the ball and the inner and outer rings of the linear bearing based on the angle and deformation of each ball.
[0058] Specifically, in this embodiment, the linear bearing is determined to be in an interference fit state, meaning that the assembly relationship between the inner ring of the linear bearing and the shaft, and between the outer ring and the bearing housing, is without clearance and subject to a preset pressure. Assuming the linear bearing is not rotating, then the first... j The angle of each ball can be calculated using the following formula:
[0059] in, N zh It represents the total number of balls in a linear bearing.
[0060] Then, utilizing the gap between the linear bearing balls and the inner and outer rings... pr The ball deformation is calculated using the following formula:
[0061] Therefore, the nonlinear restoring force generated between the balls of a linear bearing and the inner and outer rings can be calculated using the following formula:
[0062] in, .
[0063] Furthermore, a force analysis is performed on the rear bearing housing, and the various bearing forces and external preload forces acting on it are calculated comprehensively to establish the dynamic equation of the bearing housing.
[0064] As one possible implementation, the rear bearing housing is simplified as a rigid mass block, and its translational degrees of freedom in three directions are considered under the action of a linear bearing. The specific force analysis process is as follows: Figure 6 As shown, the rear bearing housing is subjected to the force of the angular contact ball bearing. Linear bearing force and axial preload Therefore, the constructed dynamic equations for the bearing housing are as follows:
[0065] in, m This indicates the concentrated mass of the rear bearing housing. , and These represent the accelerations of the rear bearing housing along the X, Y, and Z axes, respectively.
[0066] Step S103: Based on Newton's second law, integrate multiple unit matrices, node vectors, nonlinear force models and bearing housing dynamic equations to generate the dynamic equations of the rotor system, wherein the nonlinear bearing force is treated as an external force term in the dynamic equations of the rotor system.
[0067] Specifically, this step involves assembling the rotor system dynamics equations. The system equations are assembled based on Newton's second law, integrating the element matrix and node parameters obtained in the previous embodiments, and applying the various nonlinear bearing forces calculated in the previous embodiments as external force terms to the corresponding nodes.
[0068] As an example, the integrated dynamic equations of the rotor system are shown below:
[0069] in, The inertia matrix, , The first derivative of the above node vectors, The second derivative of the above node vectors, The sum of external excitations and nonlinear forces acting on the system. It includes the nonlinear bearing force and rotor system unbalance force calculated in the above embodiments, and the direction of the force matches the direction of each force in the above bearing housing dynamic equation.
[0070] Step S104: Numerical solution and dynamic response analysis of the dynamic equations of the rotor system are performed to obtain multiple modal parameters and dynamic response results.
[0071] Specifically, this step involves numerically solving and dynamically analyzing the dynamic equations of the rotor system established in step S103, including: performing modal analysis to obtain the natural frequencies and mode shapes; and obtaining the steady-state response through numerical integration for subsequent dynamic characteristic analysis or fault diagnosis.
[0072] For example, by solving for the modal and dynamic responses of the above system, the first three mode shapes of the rotating shaft system are obtained as follows: Figures 7 to 9 As shown.
[0073] As one possible approach, modal analysis and dynamic response analysis can be performed following the process of "mathematical modeling → numerical solution → result interpretation." Modal analysis solves for the system's inherent vibration characteristics (e.g., natural frequencies, mode shapes), i.e., the system's free vibration characteristics without external excitation. During modal analysis, the undamped free vibration equation is solved based on the constructed mass and stiffness matrices. When determining eigenvalues through numerical solution, relevant modal solving algorithms (e.g., subspace iteration method, Lanczos method) can be used to solve for the generalized eigenvalues of the assembled M and K. On the other hand, in dynamic response analysis, the steady-state response is obtained through numerical integration. The core of dynamic response analysis is solving the damped forced vibration equation to obtain the vibration response (specific displacement, velocity, and acceleration, etc.) of the rotor system under actual working loads.
[0074] Step S105: Using the dynamic response results, perform sensitivity analysis on various assembly parameters of the rotor system to determine the influence of each assembly parameter on the dynamic characteristics of the electric spindle, and generate an optimization scheme for the electric spindle structure based on the influence analysis results.
[0075] Specifically, this step begins with a parameter sensitivity analysis to examine the impact of key parameters on dynamic characteristics.
[0076] As a possible implementation method, parameter sensitivity analysis specifically includes the following steps: First, determine the key analysis parameters: select the core parameters in the electric spindle rotor system that have a significant impact on the dynamic characteristics. These core parameters include at least the axial preload of the angular contact ball bearing, the bearing span, and the linear bearing clearance, and may also include adjustable engineering parameters such as shaft material properties, bearing contact angle, and shaft segment length. Then, set the parameter variation range and gradient: based on the actual design and working conditions of the electric spindle, determine the reasonable variation range of each key parameter. Next, perform single-parameter variable iterative calculation: keeping other parameters constant, only change the value of a single key parameter, and substitute it into the system dynamic equations in sequence. Obtain the system dynamic response results under each parameter value using the numerical solution method described in step S104. For example, this may include modal characteristics (natural frequency, mode shape), steady-state response spectrum (vibration amplitude, frequency characteristics), and nonlinear vibration state (chaos, subharmonic vibration, etc.). Finally, an analysis of the influence of characteristics is conducted: by comparing the dynamic response results corresponding to different parameter values, the influence of key parameters on the dynamic characteristics of the electric spindle is extracted. For example, the influence of parameter changes on system stability, such as whether insufficient preload or excessive span will cause chaotic vibration; the influence of parameter changes on vibration amplitude, such as the suppression effect of linear bearing clearance on fundamental frequency amplitude under interference fit; and the influence of parameter changes on nonlinear vibration characteristics, such as whether increasing linear bearing clearance under clearance fit will lead to subharmonic vibration.
[0077] In one embodiment of this application, sensitivity analysis is performed on various assembly parameters of the rotor system to determine the influence of each assembly parameter on the dynamic characteristics of the electric spindle, including: analyzing the preload of the angular contact ball bearing on the influence of inducing chaotic state and subharmonic vibration in the electric spindle system; analyzing the bearing span on the influence of inducing chaotic state in the electric spindle system; and analyzing the influence of changes in linear bearing clearance on the fundamental frequency parameter and subharmonic vibration of the electric spindle system.
[0078] Specifically, this embodiment performs a sensitivity analysis of assembly parameters. (The result is...) Figure 10The effect of the preload of the angular contact ball bearing on the dynamic performance of the electric spindle is shown. When the preload increases, the chaotic state of the system disappears and the system gradually stabilizes, but the frequency ratio of subharmonic vibrations changes in stages with the change of preload. Therefore, increasing the preload increases the initial compression of the bearing balls, thereby suppressing the vibration amplitude of the rotor.
[0079] Furthermore, by moving the rear bearing position, the following can be obtained: Figure 11 The effect of changing the bearing span on the dynamic performance of the electric spindle is shown. As the span increases, the system gradually exhibits chaotic phenomena. Furthermore, [the following data was obtained]. Figure 12 The system spectrum diagram shown is illustrated as a function of linear bearing clearance. (From...) Figure 12 It can be seen that when the gap is negative, i.e., under the interference fit condition, only the fundamental frequency exists, and its amplitude is much smaller than that under the gap fit condition. Under the gap fit condition, not only does the peak value of the fundamental frequency increase with the gap, but subharmonic vibration also occurs.
[0080] Furthermore, optimization suggestions for the electric spindle structure are generated to improve its performance. Based on the obtained parameter sensitivity analysis report, this application summarizes the influence patterns of each key parameter, clarifies the sensitive range and optimization direction for parameter adjustment, and provides a quantitative basis for subsequently generating optimization suggestions for the electric spindle structure.
[0081] In one embodiment of this application, an optimization scheme for the electric spindle structure is generated based on the impact analysis results, including: adjusting the angle and magnitude of the preload to reduce the vibration amplitude of the electric spindle structure; moving the rear bearing housing inward and eliminating the clearance of the linear bearing to allow the rotor system to avoid nonlinear vibration.
[0082] Continuing with the example above, and based on the calculation results, optimization suggestions for the electric spindle structure are generated. At the preload angle, increasing the preload can reduce the vibration amplitude of the system; moving the rear bearing housing inward by a certain distance can help the rotor system avoid nonlinear vibration; eliminating the clearance of the linear bearing can also avoid nonlinear vibration; furthermore, interference fit can enhance vibration suppression.
[0083] In summary, the high-speed electric spindle nonlinear dynamic characteristic analysis method of this application constructs a standardized analysis system covering the entire process, including rotor system decomposition and simplification, nonlinear bearing force modeling, system dynamic equation assembly, numerical solution and dynamic response analysis, parameter sensitivity analysis, and structural optimization suggestion generation. Based on clear physical theories and standardized matrix modeling methods, it can support the reproduction of the analysis process according to the workflow, improving the scientificity and efficiency of electric spindle dynamic characteristic research and providing a unified analysis paradigm for the industry. Thus, this method establishes a standardized analysis process, improving the repeatability and efficiency of the analysis. Furthermore, the method introduces nonlinear bearing modeling, enabling the model to realistically reflect the vibration phenomena caused by bearing nonlinear factors, significantly improving the accuracy of electric spindle dynamic characteristic analysis and providing reliable data support for subsequent dynamic characteristic evaluation and fault diagnosis. Moreover, this method fully considers the actual working scenarios of electric spindles, incorporating linear bearings into the rotor system modeling scope, taking into account the core function and mechanical characteristics of linear bearings in adapting to rotor thermal expansion. Furthermore, by performing stress analysis on the rear bearing housing and simplifying it into a rigid mass block, a balance was struck between model accuracy and computational efficiency, making it directly applicable to the structural design and performance optimization of actual electric spindles. Several key engineering adjustable parameters were also incorporated into the analysis process, providing clear adjustment directions for subsequent structural optimization and demonstrating strong engineering applicability.
[0084] To achieve the above embodiments, this application also proposes a system for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle. Figure 13 This is a schematic diagram of the structure of a high-speed electric spindle nonlinear dynamic characteristic analysis system proposed in an embodiment of this application, as shown below. Figure 13 As shown, the system includes: The decomposition module 100 is used to decompose and simplify the electric spindle rotor system, decomposing the rotor system into a shaft system, a bearing system, and a bearing housing system, and discretizing the shaft system using Timoshenko beam elements to obtain multiple element matrices and node vectors.
[0085] Modeling module 200 is used to establish nonlinear force models for angular contact ball bearings and linear bearings based on Hertzian contact theory, and to perform force analysis on the rear bearing housing. The dynamic equations of the bearing housing are established using the various bearing forces acting on the rear bearing housing.
[0086] The integration module 300 is used to integrate multiple unit matrices, node vectors, nonlinear force models and the bearing housing dynamic equations based on Newton's second law to generate the dynamic equations of the rotor system, wherein the nonlinear bearing force is treated as an external force term in the dynamic equations of the rotor system.
[0087] The solver module 400 is used to numerically solve the dynamic equations of the rotor system and perform dynamic response analysis to obtain multiple modal parameters and dynamic response results.
[0088] Analysis module 500 is used to perform sensitivity analysis on various assembly parameters of the rotor system using the dynamic response results, determine the influence of each assembly parameter on the dynamic characteristics of the electric spindle, and generate an optimization scheme for the electric spindle structure based on the influence analysis results.
[0089] It should be noted that the explanation of the aforementioned embodiment of the nonlinear dynamic characteristics analysis method for high-speed electric spindles also applies to the system of this embodiment, and will not be repeated here.
[0090] In summary, the high-speed electric spindle nonlinear dynamic characteristic analysis system of this application analyzes the dynamic characteristics of the electric spindle by considering the nonlinear forces of angular contact ball bearings and linear bearings. This can solve the problem of low repeatability in current analysis and research, and improve the efficiency of electric spindle dynamic characteristic research and performance optimization.
[0091] To implement the above embodiments, this application also proposes an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the high-speed electric spindle nonlinear dynamic characteristic analysis method as described in any of the first aspect embodiments above.
[0092] To implement the above embodiments, this application also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the high-speed electric spindle nonlinear dynamic characteristic analysis method as described in any one of the first aspect embodiments above.
[0093] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0094] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.
[0095] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.
[0096] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.
[0097] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.
[0098] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.
[0099] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.
[0100] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.
Claims
1. A method for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle, characterized in that, Includes the following steps: The electric spindle rotor system is decomposed and simplified into a shaft system, a bearing system, and a bearing housing system. The shaft system is then discretized and modeled using Timoshenko beam elements to obtain multiple element matrices and node vectors. Based on Hertzian contact theory, nonlinear force models for angular contact ball bearings and linear bearings are established respectively, and the force analysis of the rear bearing housing is performed. The dynamic equation of the bearing housing is established using the various bearing forces acting on the rear bearing housing. Based on Newton's second law, the multiple unit matrices, the node vectors, the nonlinear force model, and the bearing housing dynamic equations are integrated to generate the dynamic equations of the rotor system, wherein the nonlinear bearing force is treated as an external force term in the dynamic equations of the rotor system. The dynamic equations of the rotor system are numerically solved and dynamic response is analyzed to obtain multiple modal parameters and dynamic response results; Using the dynamic response results, sensitivity analysis is performed on various assembly parameters of the rotor system to determine the influence of each assembly parameter on the dynamic characteristics of the electric spindle, and an optimization scheme for the electric spindle structure is generated based on the influence analysis results.
2. The method according to claim 1, characterized in that, The discretization modeling of the rotating shaft system using Timoshenko beam elements includes: Discretize the shaft system as follows: n Each axis unit and n +1 node, of which, n It is a positive integer; Calculate the translational and rotational degrees of freedom of each node with respect to the two coordinate axes, and generate the node vector based on the translational and rotational degrees of freedom of the front and rear nodes of the Timoshenko beam element.
3. The method according to claim 1, characterized in that, The discretization modeling of the rotating shaft system using Timoshenko beam elements includes: The correction coefficients for the Timoshenko beam element are calculated based on multiple physical parameters of the rotating shaft system. Based on the correction coefficients and the multiple physical parameters, the mass matrix, inertia matrix, gyroscope matrix, and stiffness matrix of the Timoshenko beam element are calculated respectively. The structural damping matrix of the shaft system is characterized by Rayleigh damping.
4. The method according to claim 1, characterized in that, A nonlinear force model for the angular contact ball bearing is established based on Hertzian contact theory, including: The balls of the angular contact ball bearing are arranged at equal intervals and maintain rolling motion. The rotational speed of the cage is calculated based on the radius of the angular contact ball bearing and the rotational speed of the inner ring. Based on the rotational speed of the cage, calculate the angle through which any ball rotates; The compression of the balls is calculated, and combined with the angle through which each ball rotates and the compression of the balls, the nonlinear restoring force generated between the balls and the inner and outer rings of the angular contact ball bearing is calculated.
5. The method according to claim 1, characterized in that, A nonlinear force model for the linear bearing is established based on Hertzian contact theory, including: Set the linear bearing to a non-rotating state, and calculate the angle of any ball based on the number of balls in the linear bearing; The deformation of any ball is calculated based on the gap between the ball and the inner and outer rings of the linear bearing and the angle of any ball. Based on the angle and deformation of each ball of the linear bearing, the nonlinear restoring force generated between the balls and the inner and outer rings of the linear bearing is calculated.
6. The method according to claim 1, characterized in that, The sensitivity analysis of various assembly parameters of the rotor system is performed to determine the influence of each assembly parameter on the dynamic characteristics of the electric spindle, including: The influence of the preload of the angular contact ball bearing on the induction of chaotic state and subharmonic vibration in the electric spindle system was analyzed. Analyze the impact of bearing span on the induction of chaotic state in the electric spindle system; This study analyzes the impact of changes in linear bearing clearance on the fundamental frequency parameters and subharmonic vibrations of the electric spindle system.
7. The method according to claim 6, characterized in that, The optimization scheme for the electric spindle structure generated based on the impact analysis results includes: Adjust the angle and magnitude of the preload to reduce the vibration amplitude of the electric spindle structure; The rear bearing housing is moved inward and the clearance of the linear bearing is eliminated so that the rotor system avoids nonlinear vibration.
8. A system for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle, characterized in that, Includes the following modules: The decomposition module is used to decompose and simplify the electric spindle rotor system. It decomposes the rotor system into a shaft system, a bearing system, and a bearing housing system. It also uses Timoshenko beam elements to discretize and model the shaft system, obtaining multiple element matrices and node vectors. The modeling module is used to establish nonlinear force models for angular contact ball bearings and linear bearings based on Hertzian contact theory, and to perform force analysis on the rear bearing housing. The dynamic equations of the bearing housing are established using the various bearing forces acting on the rear bearing housing. An integration module is used to integrate the multiple unit matrices, the node vectors, the nonlinear force model, and the bearing housing dynamic equations based on Newton's second law to generate the dynamic equations of the rotor system, wherein the nonlinear bearing force is treated as an external force term in the dynamic equations of the rotor system. The solver module is used to numerically solve the dynamic equations of the rotor system and perform dynamic response analysis to obtain multiple modal parameters and dynamic response results; The analysis module is used to perform sensitivity analysis on various assembly parameters of the rotor system using the dynamic response results, determine the influence of each assembly parameter on the dynamic characteristics of the electric spindle, and generate an optimization scheme for the electric spindle structure based on the influence analysis results.
9. An electronic device, comprising: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the high-speed electric spindle nonlinear dynamic characteristic analysis method as described in any one of claims 1-7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for analyzing the nonlinear dynamic characteristics of a high-speed electric spindle as described in any one of claims 1-7.