A lathe spindle bearing dynamic characteristic analysis method and system considering cutting and electromagnetic coupling

Abstract

The application provides a lathe spindle bearing dynamic characteristic analysis method and system considering cutting and electromagnetic coupling. The dynamic cutting force analytical model is constructed based on tool vibration and cutting mechanism, and the dynamic time-varying load of the cutting end is calculated; the motor electromechanical coupling control model is constructed, the dynamic balance of the motor output torque and the load is solved; the unbalanced magnetic pull analytical model is constructed, and the radial unbalanced magnetic pull response of the motor is obtained; the spindle rotor flexible body model is constructed based on the Timoshenko beam element theory, and the flexible deformation and vibration characteristics of the spindle are represented; the bearing complete dynamics model is constructed based on the Gupta complete dynamics principle, and the microscopic dynamics behavior of each component in the bearing is analyzed; the boundary coupling dynamics model of the spindle system is constructed, and the bearing dynamic characteristic result is solved by using the joint algorithm. The application can truly reflect the dynamics response of each component in the bearing under the multi-field coupling and random fluctuation working condition of the spindle system.

Description

Technical Field

[0001] This invention relates to the field of spindle bearing dynamics technology, specifically to a method and system for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling. Background Technology

[0002] Rolling bearings are the core supporting components of lathe spindle systems, and their dynamic characteristics directly affect spindle rotation accuracy, vibration noise, and overall machine reliability. As high-end lathes develop towards high speed, high precision, and heavy load, spindle bearings simultaneously bear electromagnetic excitation from the motor end, dynamic loads from the cutting end, and centrifugal effects from high-speed rotation, forming complex service conditions with multi-source coupling and time-varying fluctuations, which places higher demands on the accurate analysis of bearing dynamics.

[0003] Existing methods for analyzing spindle bearing dynamics generally suffer from defects such as load simplification, missing coupling, and coarse models. Most studies assume external loads to be constant values ​​or simple time-varying functions, making it difficult to describe the actual cutting loads that fluctuate randomly; moreover, they fail to establish a correlation mechanism between cutting torque and motor electromagnetic parameters, neglect the coupling effect between cutting force and unbalanced magnetic pull, and the system-scale modeling is incomplete.

[0004] Meanwhile, existing methods mostly use simplified bearing models with low degrees of freedom, which cannot accurately analyze the dynamic behavior and contact characteristics of all components such as rolling elements, cages, and races. They also fail to achieve boundary-coordinated solution of the flexible body of the spindle, the bearing, and the electromechanical load, making it difficult to truly reflect the dynamic response of the bearing under combined loads. More comprehensive analysis methods are urgently needed to make up for the above deficiencies. Summary of the Invention

[0005] In order to overcome the defects existing in the prior art, the purpose of this invention is to provide a method and system for analyzing the dynamic characteristics of lathe spindle bearings that takes into account cutting and electromagnetic coupling.

[0006] To achieve the above-mentioned objectives of this invention, this invention provides a method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling, comprising the following steps:

[0007] Obtain the parameters of each component in the spindle-bearing coupling system to be calculated, including the basic materials, structural parameters, and operating condition parameters of the tool, motor, spindle, and bearing;

[0008] A dynamic cutting force analytical model is constructed based on the tool vibration and cutting action mechanism. Based on this model, the dynamic time-varying load at the cutting end is calculated, and the dynamic response of the chip force is obtained.

[0009] A torque balance equation and a current control equation are constructed for the drive motor to form an electromechanical coupling control model. Based on this model and the dynamic response of the chipping force, a dynamic balance equation between the output electromagnetic torque of the motor and the load is constructed, and the real-time electromagnetic torque and current parameters are solved.

[0010] An analytical model of unbalanced magnetic pull force is constructed based on the theory of air gap eccentricity and magnetic permeability Fourier expansion. Combined with the output current of the motor, the radial unbalanced magnetic pull force response of the motor is obtained.

[0011] Combining the dynamic response of chipping force, the output electromagnetic torque of the motor, and the response of radial unbalanced magnetic pull, a flexible body model of the spindle rotor is constructed based on the Timoshenko beam element theory, which includes the dynamic differential equations of all nodes.

[0012] A complete dynamic model of the bearing is constructed based on the Gupta complete dynamics principle, including the dynamic differential equations of the rolling elements, the dynamic differential equations of the cage, and the dynamic differential equations of the bearing rings.

[0013] Based on the installation location of the spindle bearing, the dynamic differential equations of the spindle bearing nodes and the bearing inner ring are integrated to construct a boundary coupled dynamic model of the spindle system. The dynamic characteristics of the bearing are obtained by solving the model using a joint algorithm, and the operating status of the bearing is evaluated.

[0014] Optionally, the tool parameters include: tool mass, triaxial stiffness and damping parameters; the motor parameters include: motor power supply information, stator resistance, permanent magnet flux linkage, stator d-axis and q-axis inductance components, number of pole pairs, and torsional moment of inertia; the spindle parameters include: spindle geometry, material elastic modulus and Poisson's ratio; and the bearing parameters include: bearing rolling element parameters, bearing ring parameters, and lubrication parameters.

[0015] Optionally, the steps for constructing a dynamic cutting force analytical model are as follows:

[0016] The lathe's tooling system is equivalent to a mass-spring-damping system. Tool parameters are mapped to this system to obtain the tool mass m. s And the stiffness of the tool in the x, y, and z directions of spatial coordinates {K} sx ,K sy ,K sz} and damping {C sx C sy C sz};

[0017] Obtain the feed rate s of the cutting tool on the workpiece. s Cutting depth d s Chip force, unit surface equivalent stiffness k s ;

[0018] Calculate the instantaneous resultant force of the chips at time t:

[0019] ,

[0020] Where x(t) and y(t) are the vibration displacements of the tool in the x and y directions, respectively.

[0021] Based on cutting experience coefficients, the instantaneous cutting resultant force is decomposed into components F in the three spatial coordinates x, y, and z. sx F sy F sz :

[0022] Based on Newton's second law, construct the three-degree-of-freedom vibration differential equations for the tool system:

[0023] ,

[0024] Solving the three-degree-of-freedom vibration differential equation yields the dynamic response F of the chipping force in the three spatial coordinates x, y, and z. sx (t), F sy (t), F sz (t).

[0025] Optionally, the steps for constructing the electromechanical coupling control model of the motor are as follows:

[0026] Obtain motor power information, and convert the three-phase AC power in the power information into dq-axis components through Clark transformation and Park transformation;

[0027] Construct the stator current-voltage relationship in a synchronously rotating coordinate system:

[0028] ,

[0029] Among them, i d i q For the stator d-axis and q-axis currents, u d u q For stator d-axis and q-axis voltages, ω E Electric angular velocity is ω, which is mechanical angular velocity. M N p Times, R r For the stator resistance of the motor, φ f For permanent magnet flux, L d and L q These are the stator d-axis and q-axis inductance components;

[0030] Solving the stator current-voltage relationship yields the current i. d i q ;

[0031] Based on the i d i qDrive the output electromagnetic torque of the motor:

[0032] , where N p It is the extreme logarithm;

[0033] Based on the aforementioned relationship between electromagnetic torque and load balance, the differential equation of motor rotational motion is constructed as follows:

[0034] , among which, T M The torque load is formed by the cutting force. C r R is the motor damping coefficient. g J is the workpiece cutting radius. p This represents the torsional inertia of the motor.

[0035] Optionally, the steps for constructing the analytical model of unbalanced magnetic pull are as follows:

[0036] Obtain the motor rotor eccentricity {Δx, Δy} and the initial air gap δ0. At any time t, points O and O' are the centers of the stator and rotor, respectively, and a coordinate system Oxy is established. The radial eccentricity r of the rotor is also determined. r and eccentricity ε r Represented as:

[0037] ,

[0038] ,

[0039] Expanding the air gap permeability of the motor into a Fourier series, the Fourier coefficients Λ n The expression is:

[0040] ,

[0041] Where μ0 is the free permeability and n is the Fourier series;

[0042] The fundamental magnetic flux density amplitude of the rotor permanent magnet is analyzed to be:

[0043] ,

[0044] Among them, B r h is the remanent magnetic flux density. m For the magnetization thickness, α p This is the polar arc coefficient;

[0045] According to motor winding theory, the amplitude of the combined fundamental magnetomotive force of the three-phase stator winding is,

[0046] ,

[0047] Where, Nr I is the number of turns in series per phase. m The amplitude of the alternating current flowing through the stator windings of the motor, y1 is the coil pitch, τ is the pole pitch, and q is the number of slots per pole per phase. Q s m is the total number of stator slots. r This represents the number of phases of the motor.

[0048] The amplitude of the air gap combined magnetomotive force is:

[0049]

[0050] Where φ0 is the internal power factor angle;

[0051] The number of pole pairs N of the motor used in the electromechanical composite drive system p Typically greater than 3, the analytical expression for the amplitude of radial unbalanced magnetic pull is:

[0052]

[0053] Where R is the outer diameter of the rotor core and L is the length of the rotor core;

[0054] Decompose the radial unbalanced magnetic pull into x and y components:

[0055] ,

[0056] The radial coupling excitation at the motor end is obtained.

[0057] Optionally, the steps for constructing the flexible body model of the spindle rotor are as follows:

[0058] The unit is divided according to the stepped structure of the main shaft, with a total number of units of N. se The number of nodes is N sn =N se +1;

[0059] Based on the geometric parameters and material properties of the principal shaft, the transverse shear parameters and radius of inertia are calculated. Introducing the shape factor and shear correction coefficient, the j-th shear parameter is derived and generated. e The mass matrix of each unit containing inertial coupling terms. Gyroscope matrix including rotation effect and the stiffness matrix including shear correction And encapsulate all element matrices according to the corresponding nodes to form the mass matrix M of the entire principal axis. s Gyroscope matrix G s Stiffness matrix K s ;

[0060] Determine the load vector F of the entire spindle s , including the load vector [F] at the motor's working end nodeex ,F ey ,0,0,0,T E ] and the load vector [F] at the cutting end. sx ,F sy ,F sz ,0,0,F sz R g ];

[0061] Based on the quality matrix M s Gyroscope matrix G s Stiffness matrix K s The load vector F of the main shaft s Determine the dynamic differential equations for all nodes of the principal axis:

[0062] Where ω refers to the spindle speed;

[0063] The dynamic differential equations of all nodes of the main shaft are combined to obtain the flexible body model of the main shaft rotor.

[0064] Optionally, the steps for constructing a complete dynamic model of the bearing are as follows:

[0065] The lumped mass method is used to model each component, and the specific steps include the following:

[0066] Based on the relationship between the rolling elements, raceways, and cage, as well as the resistance effect of the lubricating medium, the dynamic equations for the j-th rolling element are derived:

[0067]

[0068] Where r is the radial displacement of the rolling element, a is the axial displacement of the rolling element, and ω x ω y ω z Let ω be the rotational speed of the rolling element about the x, y, and z axes, respectively. m The common rotational speed of the rolling elements is m. b For the mass of the rolling element, C b For rolling element damping, I b J b These are the moments of inertia of the rolling element's rotation and revolution, respectively, in N. i N e These are the contact forces between the rolling element and the inner and outer rings, respectively, in N. cz N cx These represent the z- and x-direction components of the collision contact force between the rolling element and the cage pocket, respectively. The contact force is calculated using Hertzian theory and the penetration relation. ix f iy f ex f eyThese are the frictional force components along the major and minor axes of the contact ellipse between the rolling element and the inner and outer raceways, respectively. The frictional force is obtained by integrating the shear stress, f. cy f ct These are the radial and circumferential friction components of the contact between the rolling element and the cage pocket, respectively, F C For the high-speed centrifugal force of the rolling element, F D G is the resistance to the movement of the rolling element by the lubricating medium. x G y The x and y components of the gyro torque of the rolling body, M i M e These are the spin friction torques of the rolling element and the inner and outer rings, respectively, R. b R is the radius of the rolling element. i R e R represents the circumference radius of the contact point between the rolling element and the inner and outer rings, respectively. m Let α be the bearing pitch circle radius. i α e These are the inner and outer contact angles, β and β, respectively. c The contact angle between the rolling element and the cage pocket;

[0069] Based on the relationships between the cage, guide ring, and all rolling elements, as well as the resistance of the lubricating medium, and considering the translational vibration, polarization, and rotational degrees of freedom of the cage, its dynamic equations are derived:

[0070] Where, x c y c z c These represent the vibrational displacements of the cage in the x, y, and z directions, respectively, ω. cx ω cy These represent the deflection velocities of the cage in the x and y directions, respectively, ω c To maintain the rack speed, m c To maintain the quality of the cage, C c For cage damping, I xy I z The moments of inertia of the cage deflection and rotation, respectively, N b θ is the number of rolling elements. c For the rotational angular displacement of the cage, φ 0j For the initial angular position of the j-th cage pocket, F cx F cy The components of the lubricating fluid dynamic pressure in the x and y directions of the cage and guide ring are respectively, M cz To maintain the frictional torque of the lubricating fluid between the cage and the guide ring;

[0071] Based on the interrelationships between the raceway and all rolling elements, its six-degree-of-freedom dynamic equations are derived:

[0072]

[0073] Where, x i y i z i θ xi θ yi θ zi The translational and rotational vibration displacements of the inner ring in the x, y, and z directions are respectively, m i For inner ring quality, I i I zi These are the moments of inertia of the inner ring deflection and rotation, respectively, φ. bj This is the actual position angle of the rolling element.

[0074] Optionally, the steps for solving the dynamic characteristics of the bearing are as follows:

[0075] Given an initial spindle speed, the rotational speed ω' of the motor connection node around the z-axis is used. M Replaces the mechanical speed ω in the original motor control M ,

[0076] , where N n θ is the motor end node number. z (N n () refers to the rotational vibration displacement in the z-direction of the motor end node;

[0077] The outer ring of the bearing is fixed to the bearing housing, and the inner ring is bound to the node on the main shaft where the bearing is mounted. The degrees of freedom of the dynamic equations of the two are superimposed accordingly. The dynamic differential equations of the rolling elements and cage are retained and combined with the vibration differential equations of all nodes of the main shaft to form a system coupled dynamic equation, resulting in a main shaft system with 6N degrees of freedom. n +6N b +6+3;

[0078] Using the Newmark-beta method and the fourth-order Longokuta method, the degrees of freedom are 6N. n +6N b Solving the +6+3 spindle system yields the bearing dynamic characteristics, including the vibration and mechanical characteristics of each bearing component.

[0079] This invention also proposes a dynamic characteristic analysis system for lathe spindle bearings, including a parameter input module, a processing module, and a storage module.

[0080] The parameter input module is communicatively connected to the processing module. The parameter input module is used to acquire the parameters of each component in the spindle-bearing coupling system to be calculated and send them to the processing module. The processing module is communicatively connected to the storage module. The storage module is used to store at least one executable instruction. The executable instruction causes the processing module to perform the operation corresponding to the above-mentioned lathe spindle bearing dynamic characteristic analysis method considering cutting and electromagnetic coupling, so as to obtain the bearing dynamic characteristic results and evaluate the bearing operating status.

[0081] The beneficial effects of this invention are:

[0082] This invention fully considers the comprehensive influence of dynamic cutting force, motor electromechanical coupling, unbalanced magnetic pull, spindle flexible deformation and bearing full dynamic behavior on the dynamic characteristics of the bearing. It truly reflects the dynamic response of each component inside the bearing under multi-field coupling and random fluctuation conditions of the spindle system, and solves the technical problem that existing methods cannot accurately characterize the dynamic performance of the bearing at the system scale.

[0083] 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

[0084] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0085] Figure 1 This is a schematic diagram of the process of the present invention;

[0086] Figure 2 This is a schematic diagram of the spindle system structure in this invention;

[0087] Figure 3 This is a schematic diagram of the cutting force response modeling at the cutting end in this invention;

[0088] Figure 4 This is a schematic diagram illustrating the modeling of the motor air gap eccentricity and unbalanced magnetic pull at the motor's working end in this invention;

[0089] Figure 5 This is a schematic diagram of the Timoshenko beam structure of the main shaft flexible body in this invention;

[0090] Figure 6 This is a schematic diagram of the lumped mass model of the bearing in this invention. Detailed Implementation

[0091] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown 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 are only used to explain the present invention, and should not be construed as limiting the present invention.

[0092] In the description of this invention, unless otherwise specified and limited, it should be noted that the terms "installation", "connection" and "linking" should be interpreted broadly. For example, they can refer to mechanical or electrical connections, or internal connections between two components. They can be direct connections or indirect connections through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0093] Example 1

[0094] like Figure 1-6 As shown, this invention provides a method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling, specifically including the following steps:

[0095] S1. Obtain the parameters of each component in the spindle-bearing coupling system to be calculated. These parameters include the basic materials, structural parameters, and operating condition parameters of the tool, motor, spindle, and bearings. More specifically, tool parameters include: tool mass, triaxial stiffness, and damping parameters; motor parameters include: stator resistance, permanent magnet flux linkage, d / q-axis inductance, number of pole pairs, and torsional moment of inertia; spindle parameters include: spindle geometry, material elastic modulus, and Poisson's ratio; and bearing parameters include: rolling element parameters, bearing ring parameters, and lubrication parameters.

[0096] S2, such as Figure 3 As shown, a dynamic cutting force analytical model is constructed based on the tool vibration and cutting action mechanism. Based on this model, the dynamic time-varying load at the cutting end is calculated, yielding the dynamic response of the chip force. The specific steps include the following:

[0097] S201, the lathe's tool system is equivalent to a mass-spring-damping system, and the tool parameters are mapped to this system to obtain the tool mass m. s and the stiffness of the tool in the three spatial coordinates x, y, and z {K} sx ,K sy ,K sz} and damping {C sx C sy C sz}

[0098] S202, Obtain the feed rate s of the tool cutting the workpiece. s Cutting depth d s Chip force, unit surface equivalent stiffness k sAmong them, the feed rate s s Cutting depth d s The equivalent stiffness k can be obtained from the part's machining process. s Generally, the data is obtained on-site and calculated using machine tool force sensors in conjunction with process parameters. This is a conventional technique and will not be elaborated upon here.

[0099] S203, Calculate the instantaneous resultant force of the chips at time t:

[0100] ,

[0101] Where x(t) and y(t) are the vibration displacements of the tool in the x and y directions, respectively.

[0102] S204, according to the cutting experience coefficient, the instantaneous cutting resultant force is decomposed into components F in the three spatial coordinates x, y, and z. sx F sy F sz :

[0103] ,

[0104] S205, based on Newton's second law, construct the three-degree-of-freedom vibration differential equations of the tool system:

[0105]

[0106] S206, Solve the three-degree-of-freedom vibration differential equation to obtain the dynamic response F of the chipping force in the three spatial coordinates x, y, and z. sx (t), F sy (t), F sz (t), which gives the dynamic time-varying load at the cutting end.

[0107] S3. Construct an electromechanical coupling control model for the drive motor. Based on this model and the dynamic response of the chipping force obtained in step S1, construct the dynamic balance equation between the motor's output electromagnetic torque and the load, and solve for the real-time electromagnetic torque and current parameters. In this embodiment, the drive motor is a permanent magnet synchronous drive motor, and the electromechanical coupling control model includes torque balance equations and current control equations. Specifically, it includes the following steps:

[0108] S301, acquire motor power information, and convert the three-phase AC power in the power information into dq axis components through Clark transformation and Park transformation;

[0109] S302, the stator current-voltage relationship (i.e., the current control equation) is constructed in the synchronous rotating coordinate system as follows:

[0110] ,

[0111] Among them, i d i q For the stator d-axis and q-axis currents, u d u q For stator d-axis and q-axis voltages, ω E It is the electric angular velocity, which is the mechanical angular velocity ω. M N p Times, R r For the stator resistance of the motor, φ f For permanent magnet flux, L d and L q These are the stator d-axis and q-axis inductance components.

[0112] S303, solve the stator current-voltage relationship equation to obtain the current i d i q This drives the output electromagnetic torque of the motor.

[0113] , where N p It is an extreme logarithm.

[0114] S304, based on the relationship between electromagnetic torque and load balance, only the torque load formed by the cutting force is considered. Construct the differential equation of the motor's rotational motion (i.e., the torque balance equation):

[0115] ,

[0116] Among them, J r C is the torsional inertia of the motor. r R is the motor damping coefficient. g The workpiece cutting radius.

[0117] This step employs an iterative solution. Initial values ​​of the electromagnetic torque and current are first obtained, and then the electromagnetic torque and current values ​​at each time point are continuously updated within the electromechanical coupling control model. Both torque and current change over time. The iteration continues until the motor reaches a stable operating state, obtaining the torque and current values ​​during the steady-state period, which represents the solution to the dynamic balance between the motor's output electromagnetic torque and the load.

[0118] S4. Based on the air gap eccentricity and magnetic permeability Fourier expansion theory, construct an analytical model of unbalanced magnetic pull force. Combine this with the motor output current obtained in step S3 to obtain the maximum radial unbalanced magnetic pull force response of the motor. For example... Figure 4 As shown, considering the direct connection between the motor and the spindle, the vibration displacement at the motor end of the spindle causes rotor eccentricity, resulting in uneven air gap in the motor. Therefore, this step specifically includes the following steps:

[0119] Obtain the motor rotor eccentricity {Δx, Δy} and the initial air gap δ0. At any time t, points O and O' are the centers of the stator and rotor, respectively. Establish a coordinate system Oxy. The radial eccentricity r of the rotor... r and eccentricity ε r It can be represented as:

[0120] ,

[0121] ,

[0122] Expanding the air gap permeability of the motor into a Fourier series, the Fourier coefficients Λ n The expression is:

[0123] ,

[0124] Where μ0 is the free permeability and n is the Fourier series.

[0125] The fundamental magnetic flux density amplitude of the rotor permanent magnet is analyzed to be:

[0126] ,

[0127] Among them, B r h is the remanent magnetic flux density. m For the magnetization thickness, α p This represents the polar arc coefficient.

[0128] According to motor winding theory, the amplitude of the combined fundamental magnetomotive force of the three-phase stator winding is:

[0129]

[0130] Where, N r I is the number of turns in series per phase. m The maximum value of the alternating current flowing through the stator winding is i. d and i q The maximum value of the vector composite current response within a period, where y1 is the coil pitch, τ is the pole pitch, and q is the number of slots per pole per phase. Q s m is the total number of stator slots. r This represents the number of phases of the motor.

[0131] The magnetomotive force (MMF) of a permanent magnet synchronous motor consists of two parts: the fundamental magnetic flux density amplitude of the rotor permanent magnet MMF and the fundamental magnetomotive force amplitude of the stator three-phase windings. The amplitude of the air gap composite MMF is:

[0132]

[0133] Where φ0 is the internal power factor angle.

[0134] The number of pole pairs N of the motor used in the electromechanical composite drive system p Typically greater than 3, the analytical expression for the amplitude of radial unbalanced magnetic pull is:

[0135]

[0136] Among them, f eu R is the maximum radial unbalanced magnetic pull, R is the outer diameter of the rotor core, and L is the length of the rotor core.

[0137] Decompose the radial unbalanced magnetic pull into x and y components:

[0138] ,

[0139] The radial coupling excitation at the motor end is obtained.

[0140] S5. Combining the dynamic response of the chipping force obtained in step S1, the output electromagnetic torque of the motor obtained in step S3, and the radial unbalanced magnetic pull response obtained in step S4, a flexible spindle rotor model is constructed using Timoshenko beam element theory to characterize the flexible deformation and vibration characteristics of the spindle. Specifically, this includes the following steps:

[0141] S501, such as Figure 5 As shown, the main shaft is divided into units based on its stepped structure, with a total number of units of N. se The number of nodes is N sn =N se +1.

[0142] S502, based on the geometric parameters and material properties of the principal shaft, calculate the transverse shear parameters and the radius of rotational inertia. Introduce the shape factor and shear correction coefficient, and derive and generate the j-th... e The 12×12 mass matrix of each element, including inertial coupling terms. A 12×12 gyroscope matrix including rotational effects. and a 12×12 stiffness matrix including shear correction. And encapsulate all element matrices according to the corresponding nodes to form the mass matrix M of the entire principal axis. s Gyroscope matrix G s Stiffness matrix K s The matrix size is 6N. sn ×6N sn .

[0143] Determine the load vector F of the entire spindle s , including the load vector [F] at the motor's working end node ex ,F ey ,0,0,0,T E ] and the load vector [F] at the cutting endsx ,F sy ,F sz ,0,0,F sz R g ].

[0144] Based on the quality matrix M s Gyroscope matrix G s Stiffness matrix K s The load vector F, composed of the load vector at the motor's working end node and the load vector at the cutting end, is... s Determine the dynamic differential equations for all nodes of the principal axis:

[0145] .

[0146] The dynamic differential equations of all nodes of the main shaft are combined to obtain the flexible body model of the main shaft rotor.

[0147] It is an equation matrix, which expands to N. sn The six-degree-of-freedom equations with 1 node can be expanded into 6*Nsn equations, where ω refers to the spindle speed, i.e., the ω mentioned above. M , is a time-varying variable. The spatial 6-DOF vibration displacement vector for all principal axis nodes.

[0148] S6. Construct a complete dynamic model of the bearing based on Gupta's complete dynamics principle, and analyze the microscopic dynamic behavior of each component inside the bearing. Specifically, this step uses the lumped mass method to model each component, including the following steps:

[0149] Based on the relationship between the rolling elements, raceways, and cage, as well as the resistance effect of the lubricating medium, the dynamic equations for the j-th rolling element are derived:

[0150]

[0151] Where r is the radial displacement of the rolling element, a is the axial displacement of the rolling element, and ω x ω y ω z Let ω be the rotational speed of the rolling element about the x, y, and z axes, respectively. m The common rotational speed of the rolling elements is m. b For the mass of the rolling element, C b For rolling element damping, I b J b These are the moments of inertia of the rolling element's rotation and revolution, respectively, in N. i N e These are the contact forces between the rolling element and the inner and outer rings, respectively, in N. cz N cxThese represent the z- and x-direction components of the collision contact force between the rolling element and the cage pocket, respectively. The contact force is calculated using Hertzian theory and the penetration relation. ix f iy f ex f ey These are the frictional force components along the major and minor axes of the contact ellipse between the rolling element and the inner and outer raceways, respectively. The frictional force is obtained by integrating the shear stress, f. cy f ct These are the radial and circumferential friction components of the contact between the rolling element and the cage pocket, respectively, F C For the high-speed centrifugal force of the rolling element, F D G is the resistance to the movement of the rolling element by the lubricating medium. x G y The x and y components of the gyro torque of the rolling body, M i M e These are the spin friction torques of the rolling element and the inner and outer rings, respectively, R. b R is the radius of the rolling element. i R e R represents the circumference radius of the contact point between the rolling element and the inner and outer rings, respectively. m Let α be the bearing pitch circle radius. i α e These are the inner and outer contact angles, β and β, respectively. c The contact angle between the rolling element and the cage pocket.

[0152] Based on the relationships between the cage and guide ring, all rolling elements, and the resistance of the lubricating medium, considering the translational vibration, polarization, and rotational degrees of freedom of the cage, its dynamic equations are derived:

[0153] ,

[0154] Where, x c y c z c These represent the vibrational displacements of the cage in the x, y, and z directions, respectively, ω. cx ω cy These represent the deflection velocities of the cage in the x and y directions, respectively, ω c To maintain the rack speed, m c To maintain the quality of the cage, C c For cage damping, I xy I z The moments of inertia of the cage deflection and rotation, respectively, N b θ is the number of rolling elements. c For the rotational angular displacement of the cage, φ 0j For the initial angular position of the j-th cage pocket, F cx F cyThe components of the lubricating fluid dynamic pressure in the x and y directions of the cage and guide ring are respectively, M cz To maintain the frictional torque of the lubricating fluid between the cage and the guide ring.

[0155] Based on the interrelationships between the raceway and all rolling elements, its six-degree-of-freedom dynamic equations are derived:

[0156]

[0157] Where, x i y i z i θ xi θ yi θ zi The translational and rotational vibration displacements of the inner ring in the x, y, and z directions are respectively, m i For inner ring quality, I i I zi These are the moments of inertia of the inner ring deflection and rotation, respectively, φ. bj This is the actual position angle of the rolling element.

[0158] S7. Based on the spindle bearing installation location, integrate the dynamic differential equations of the spindle bearing nodes and the bearing inner ring to construct a boundary coupled dynamic model of the spindle system. Use a joint algorithm to solve for the bearing's dynamic characteristics and evaluate its operating status. Specifically, this includes the following steps:

[0159] S701, provide the initial spindle speed, using the speed ω' of the motor connection end node around the z-axis. M Replaces the mechanical speed ω in the original motor control M :

[0160] , where N n θ is the motor end node number. z (N n () refers to the rotational vibration displacement in the z-direction of the motor end node.

[0161] In S702, the outer ring of the bearing is fixed to the bearing housing, and the inner ring is bound to the node on the main shaft where the bearing is mounted. The degrees of freedom of the dynamic equations of the two are superimposed accordingly. The dynamic differential equations of the rolling elements and cage are retained and combined with the vibration differential equations of all nodes of the main shaft to form the system coupled dynamic equations, resulting in a main shaft system with 6N degrees of freedom. n +6N b +6+3.

[0162] S703, using the Newmark-beta method and the fourth-order Longokuta method, for a 6N degree of freedom... n +6N bSolving the +6+3 spindle system yields the bearing dynamic characteristics, including the vibration and mechanical characteristics of each bearing component.

[0163] S704 assesses the operating status and health status of the spindle bearing based on the vibration and mechanical characteristics of each component of the bearing.

[0164] Example 2

[0165] The present invention also provides an embodiment of a dynamic characteristic analysis system for lathe spindle bearings. In this embodiment, the system includes a parameter input module, a processing module, and a storage module.

[0166] The parameter input module is communicatively connected to the processing module. The parameter input module is used to acquire the parameters of each component in the spindle-bearing coupling system to be calculated and send them to the processing module. The processing module is communicatively connected to the storage module. The storage module is used to store at least one executable instruction. The executable instruction causes the processing module to perform the operation corresponding to the lathe spindle bearing dynamic characteristic analysis method considering cutting and electromagnetic coupling as described in Embodiment 1, to obtain the bearing dynamic characteristic results and evaluate the bearing operating status.

[0167] In the description of this specification, 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 the invention. 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.

[0168] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling, characterized in that, Includes the following steps: Obtain the parameters of each component in the spindle-bearing coupling system to be calculated, including the basic materials, structural parameters, and operating condition parameters of the tool, motor, spindle, and bearing; A dynamic cutting force analytical model is constructed based on the tool vibration and cutting action mechanism. Based on this model, the dynamic time-varying load at the cutting end is calculated, and the dynamic response of the chip force is obtained. A torque balance equation and a current control equation are constructed for the drive motor to form an electromechanical coupling control model. Based on this model and the dynamic response of the chipping force, a dynamic balance equation between the output electromagnetic torque of the motor and the load is constructed, and the real-time electromagnetic torque and current parameters are solved. An analytical model of unbalanced magnetic pull force is constructed based on the theory of air gap eccentricity and magnetic permeability Fourier expansion. Combined with the output current of the motor, the radial unbalanced magnetic pull force response of the motor is obtained. Combining the dynamic response of chipping force, the output electromagnetic torque of the motor, and the response of radial unbalanced magnetic pull, a flexible body model of the spindle rotor is constructed based on the Timoshenko beam element theory, which includes the dynamic differential equations of all nodes. A complete dynamic model of the bearing is constructed based on the Gupta complete dynamics principle, including the dynamic differential equations of the rolling elements, the dynamic differential equations of the cage, and the dynamic differential equations of the bearing rings. Based on the installation location of the spindle bearing, the dynamic differential equations of the spindle bearing nodes and the bearing inner ring are integrated to construct a boundary coupled dynamic model of the spindle system. The dynamic characteristics of the bearing are obtained by solving the model using a joint algorithm, and the operating status of the bearing is evaluated.

2. The method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling according to claim 1, characterized in that, The tool parameters include: tool mass, triaxial stiffness and damping parameters; the motor parameters include: motor power supply information, stator resistance, permanent magnet flux linkage, stator d-axis and q-axis inductance components, number of pole pairs, and torsional moment of inertia; the spindle parameters include: spindle geometry, material elastic modulus and Poisson's ratio; and the bearing parameters include: bearing rolling element parameters, bearing ring parameters, and lubrication parameters.

3. The method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling according to claim 1, characterized in that, The steps for constructing a dynamic cutting force analytical model are as follows: The lathe's tooling system is equivalent to a mass-spring-damping system. Tool parameters are mapped to this system to obtain the tool mass m. s And the stiffness of the tool in the x, y, and z directions of spatial coordinates {K} sx ,K sy ,K sz } and damping {C sx C sy C sz }; Obtain the feed rate s of the cutting tool on the workpiece. s Cutting depth d s Chip force, unit surface equivalent stiffness k s ; Calculate the instantaneous resultant force of the chips at time t: ， Where x(t) and y(t) are the vibration displacements of the tool in the x and y directions, respectively. Based on cutting experience coefficients, the instantaneous cutting resultant force is decomposed into components F in the three spatial coordinates x, y, and z. sx F sy F sz : Based on Newton's second law, construct the three-degree-of-freedom vibration differential equations for the tool system: ， Solving the three-degree-of-freedom vibration differential equation yields the dynamic response F of the chipping force in the three spatial coordinates x, y, and z. sx (t), F sy (t), F sz (t).

4. The method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling according to claim 1, characterized in that, The steps for constructing a motor electromechanical coupling control model are as follows: Obtain motor power information, and convert the three-phase AC power in the power information into dq-axis components through Clark transformation and Park transformation; Construct the stator current-voltage relationship in a synchronously rotating coordinate system: ， Among them, i d i q For the stator d-axis and q-axis currents, u d u q For stator d-axis and q-axis voltages, ω E Electric angular velocity is ω, which is mechanical angular velocity. M N p Times, R r For the stator resistance of the motor, φ f For permanent magnet flux, L d and L q These are the stator d-axis and q-axis inductance components; Solving the stator current-voltage relationship yields the current i. d i q ; Based on the i d i q Drive the output electromagnetic torque of the motor: , where N p It is the extreme logarithm; Based on the aforementioned relationship between electromagnetic torque and load balance, the differential equation of motor rotational motion is constructed as follows: , among which, T M The torque load is formed by the cutting force. C r R is the motor damping coefficient. g J is the workpiece cutting radius. r This represents the torsional inertia of the motor.

5. The method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling according to claim 1, characterized in that, The steps for constructing an analytical model of unbalanced magnetic pull are as follows: Obtain the motor rotor eccentricity {Δx, Δy} and the initial air gap δ0. At any time t, points O and O' are the centers of the stator and rotor, respectively, and a coordinate system Oxy is established. The radial eccentricity r of the rotor is also determined. r and eccentricity ε r Represented as: ， ， Expanding the air gap permeability of the motor into a Fourier series, the Fourier coefficients Λ n The expression is: ， Where μ0 is the free permeability and n is the Fourier series; The fundamental magnetic flux density amplitude of the rotor permanent magnet is analyzed to be: ， Among them, B r h is the remanent magnetic flux density. m For the magnetization thickness, α p This is the polar arc coefficient; According to motor winding theory, the amplitude of the combined fundamental magnetomotive force of the three-phase stator winding is, ， Where, N r I is the number of turns in series per phase. m The amplitude of the alternating current flowing through the stator windings of the motor, y1 is the coil pitch, τ is the pole pitch, and q is the number of slots per pole per phase. Q s m is the total number of stator slots. r This represents the number of phases of the motor. The amplitude of the air gap combined magnetomotive force is: Where φ0 is the internal power factor angle; The number of pole pairs N of the motor used in the electromechanical composite drive system p Typically greater than 3, the analytical expression for the amplitude of radial unbalanced magnetic pull is: Where R is the outer diameter of the rotor core and L is the length of the rotor core; Decompose the radial unbalanced magnetic pull into x and y components: ， The radial coupling excitation at the motor end is obtained.

6. The method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling according to claim 1, characterized in that, The steps for constructing the flexible body model of the main shaft rotor are as follows: The unit is divided according to the stepped structure of the main shaft, with a total number of units of N. se The number of nodes is N sn =N se +1; Based on the geometric parameters and material properties of the principal shaft, the transverse shear parameters and radius of inertia are calculated. Introducing the shape factor and shear correction coefficient, the j-th shear parameter is derived and generated. e The mass matrix of each unit containing inertial coupling terms. Gyroscope matrix including rotation effect and the stiffness matrix including shear correction And encapsulate all element matrices according to the corresponding nodes to form the mass matrix M of the entire principal axis. s Gyroscope matrix G s Stiffness matrix K s ; Determine the load vector F of the entire spindle s , including the load vector [F] at the motor's working end node ex ,F ey ,0,0,0,T E ] and the load vector [F] at the cutting end. sx ,F sy ,F sz ,0,0,F sz R g ]; Based on the quality matrix M s Gyroscope matrix G s Stiffness matrix K s The load vector F of the main shaft s Determine the dynamic differential equations for all nodes of the principal axis: Where ω is the main spindle speed; The dynamic differential equations of all nodes of the main shaft are combined to obtain the flexible body model of the main shaft rotor.

7. The method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling according to claim 1, characterized in that, The steps to construct a complete dynamic model of a bearing are as follows: The lumped mass method is used to model each component, and the specific steps include the following: Based on the relationship between the rolling elements, raceways, and cage, as well as the resistance effect of the lubricating medium, the dynamic equations for the j-th rolling element are derived: Where r is the radial displacement of the rolling element, a is the axial displacement of the rolling element, and ω x ω y ω z Let ω be the rotational speed of the rolling element about the x, y, and z axes, respectively. m The common rotational speed of the rolling elements is m. b For the mass of the rolling element, C b For rolling element damping, I b J b These are the moments of inertia of the rolling element's rotation and revolution, respectively, in N. i N e These are the contact forces between the rolling element and the inner and outer rings, respectively, in N. cz N cx These represent the z- and x-direction components of the collision contact force between the rolling element and the cage pocket, respectively. The contact force is calculated using Hertzian theory and the penetration relation. ix f iy f ex f ey These are the frictional force components along the major and minor axes of the contact ellipse between the rolling element and the inner and outer raceways, respectively. The frictional force is obtained by integrating the shear stress, f. cy f ct These are the radial and circumferential friction components of the contact between the rolling element and the cage pocket, respectively, F C For the high-speed centrifugal force of the rolling element, F D G is the resistance to the movement of the rolling element by the lubricating medium. x G y The x and y components of the gyro torque of the rolling body, M i M e These are the spin friction torques of the rolling element and the inner and outer rings, respectively, R. b R is the radius of the rolling element. i R e R represents the circumference radius of the contact point between the rolling element and the inner and outer rings, respectively. m Let α be the bearing pitch circle radius. i α e These are the inner and outer contact angles, β and β, respectively. c The contact angle between the rolling element and the cage pocket; Based on the relationships between the cage, guide ring, and all rolling elements, as well as the resistance of the lubricating medium, and considering the translational vibration, polarization, and rotational degrees of freedom of the cage, its dynamic equations are derived: Where, x c y c z c These represent the vibrational displacements of the cage in the x, y, and z directions, respectively, ω. cx ω cy These represent the deflection velocities of the cage in the x and y directions, respectively, ω c To maintain the rack speed, m c To maintain the quality of the cage, C c For cage damping, I xy I z The moments of inertia of the cage deflection and rotation, respectively, N b θ is the number of rolling elements. c For the rotational angular displacement of the cage, φ 0j For the initial angular position of the j-th cage pocket, F cx F cy The components of the lubricating fluid dynamic pressure in the x and y directions of the cage and guide ring are respectively, M cz To maintain the frictional torque of the lubricating fluid between the cage and the guide ring; Based on the interrelationships between the raceway and all rolling elements, its six-degree-of-freedom dynamic equations are derived: Where, x i y i z i θ xi θ yi θ zi The translational and rotational vibration displacements of the inner ring in the x, y, and z directions are respectively, m i For inner ring quality, I i I zi These are the moments of inertia of the inner ring deflection and rotation, respectively, φ. bj This is the actual position angle of the rolling element.

8. The method for analyzing the dynamic characteristics of lathe spindle bearings considering cutting and electromagnetic coupling according to claim 1, characterized in that, The steps to obtain the dynamic characteristics of the bearing are as follows: Given an initial spindle speed, the rotational speed ω' of the motor connection node around the z-axis is used. M Replaces the mechanical speed ω in the original motor control M , , where N n θ is the motor end node number. z (N n () refers to the rotational vibration displacement in the z-direction of the motor end node; The outer ring of the bearing is fixed to the bearing housing, and the inner ring is bound to the node on the main shaft where the bearing is mounted. The degrees of freedom of the dynamic equations of the two are superimposed accordingly. The dynamic differential equations of the rolling elements and cage are retained and combined with the vibration differential equations of all nodes of the main shaft to form a system coupled dynamic equation, resulting in a main shaft system with 6N degrees of freedom. n +6N b +6+3; Using the Newmark-beta method and the fourth-order Longokuta method, the degrees of freedom are 6N. n +6N b Solving the +6+3 spindle system yields the bearing dynamic characteristics, including the vibration and mechanical characteristics of each bearing component.

9. A dynamic characteristic analysis system for lathe spindle bearings, characterized in that, It includes a parameter input module, a processing module, and a storage module. The parameter input module is communicatively connected to the processing module. The parameter input module is used to acquire the parameters of each component in the spindle-bearing coupling system to be calculated and send them to the processing module. The processing module is communicatively connected to the storage module. The storage module is used to store at least one executable instruction. The executable instruction causes the processing module to perform the operation corresponding to the lathe spindle bearing dynamic characteristic analysis method considering cutting and electromagnetic coupling as described in any one of claims 1-8, to obtain the bearing dynamic characteristic results and evaluate the bearing operating status.

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