Modeling calculation method and system for dynamic stiffness of cutter handle-main shaft combination part

Abstract

The invention belongs to the field of machining, and discloses a modeling calculation method and system for dynamic rigidity of a cutter handle-main shaft combination part, and the method comprises the following steps: S1, modeling a geometric structure and dynamic displacement of the combination part; s2, performing multi-scale modeling on the contact surface morphology and solving the normal spacing variation of the joint part; s3, joint surface micro-convex body contact characteristic modeling is carried out; s4, modeling the non-linear stiffness of the infinitesimal junction surface; and S5, constructing an integral dynamic stiffness matrix of the joint part. According to the modeling calculation method for the dynamic stiffness of the cutter handle-main shaft combination part, high-precision modeling of the dynamic characteristics of the cutter handle-main shaft combination part is achieved through a step Timoshenko straight beam model and a distributed nonlinear spring layer in combination with a slicing method and a fractal contact theory. The method is suitable for high-precision nonlinear dynamic modeling of a numerical control machine tool, a machining center and the like, and vibration, deformation and stability problems in the machining process can be effectively predicted.

Description

Technical Field

[0001] The present invention belongs to the field of machining, and particularly relates to a method and system for modeling and calculating the dynamic stiffness of the tool holder-spindle joint portion. Background Art

[0002] In the field of machining, the dynamic characteristics of the tool holder-spindle joint portion directly affect the stability, machining accuracy and efficiency of the machining system. Especially in complex working conditions such as high-speed cutting, cutting of difficult-to-machine materials and high-precision machining, the influence is particularly significant. The dynamic stiffness characteristics of the joint portion determine the vibration response, cutting force magnitude and tool wear condition during the machining process, and thus affect the quality of the machined surface and the machining efficiency. Therefore, in-depth research on the dynamic characteristics of the joint portion is the key to improving machining performance.

[0003] Existing traditional methods are mainly based on static stiffness models, assuming that the contact characteristics of the joint portion remain unchanged during the machining process, and it is difficult to accurately reflect the dynamic behaviors in actual machining, such as vibration, impact and thermal deformation, etc. This limitation leads to difficulties in further improving the machining quality in high-precision and high-efficiency machining scenarios, and may even cause problems such as chatter and increased tool wear. In addition, the existing methods do not accurately describe the rough surface topography and non-linear contact characteristics of the joint surface, and cannot comprehensively capture the complex behaviors of the joint portion under dynamic loads.

[0004] Therefore, it is necessary to comprehensively consider the rough surface topography, non-linear contact characteristics and dynamic load action of the tool holder-spindle joint portion, and propose a method and system for calculating the dynamic stiffness of the tool holder-spindle joint portion based on the fractal contact theory and the Timoshenko beam model. Summary of the Invention

[0005] To solve the problems existing in the prior art, the present invention provides a method and system for modeling and calculating the dynamic stiffness of the tool holder-spindle joint portion. Through the stepped Timoshenko straight beam model and the non-linear spring layer, combined with the slicing method and the fractal contact theory, high-precision modeling of the dynamic characteristics of the tool holder-spindle joint portion is realized. This method is applicable to high-precision machining scenarios such as CNC machine tools and machining centers, and can effectively predict the vibration, deformation and stability problems during the machining process.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A method for modeling and calculating the dynamic stiffness of the tool holder-spindle joint portion, the method comprising:

[0008] S1. Geometric structure and dynamic displacement modeling of the tool holder-spindle joint portion;

[0009] S2. Based on the established geometric structure and dynamic displacement model of the tool shank-spindle interface, conduct multi-scale modeling of the interface surface topography and solve the variation of the normal spacing;

[0010] S3. According to the established multi-scale model of the surface topography and the solved variation of the normal spacing, conduct modeling of the contact characteristics of the asperities on the interface;

[0011] S4. According to the established model of the contact characteristics of the asperities on the interface, conduct modeling and integration of the non-linear stiffness of the micro-element interface;

[0012] S5. According to the established non-linear stiffness of the micro-element interface and the integration results, construct the overall dynamic stiffness matrix of the tool shank-spindle interface.

[0013] Preferably, the S1 includes:

[0014] Conduct axial segmented dynamic modeling of the tool shank-spindle interface based on the stepped Timoshenko straight beam;

[0015] Use the slicing method to cut the segmented interface into micro-element interfaces at equal angles along the circumferential direction, including:

[0016] ;

[0017] where n sh represents the number of micro-element interfaces, φ shk represents the radial position angle of the k sh th micro-element interface, A shk represents the contact area of the k sh th micro-element interface, r shl and r shs are the radii of the large end and the small end of the segmented interface of the tool shank-spindle interface respectively; ω is the angular velocity of the tool shank; α sh is the taper angle of the tool shank-spindle interface; t is the time variable;

[0018] According to the vibration displacements of the nodes at both ends of the segmented interface and combined with the shape function matrix, deduce the dynamic response at any position of the segmented interface, including:

[0019] ;

[0020] where z, x, and y are the vibration displacements of the tool shank / spindle at any axial position of the segmented interface along the Z, X, and Y directions; θ xi and θ yi are the vibration angular displacements of the tool shank / spindle at any axial position of the segmented interface around the X and Y directions; z i , x i and y iis the translational displacement of the toolholder / spindle node i along the Z, X and Y directions at the segmented interface; θ xi and θ yi is the angular displacement of the toolholder / spindle node i around the X and Y directions at the segmented interface; j 、x j and j is the translational displacement of the toolholder / spindle node j along the Z, X and Y directions at the segmented interface; θ xj and θ yj is the angular displacement of the tool holder / spindle node j around the X and Y directions at the segmented interface; N represents the shape function matrix.

[0021] Preferably, said S2 comprises:

[0022] The fractal dimension and fractal roughness are used to perform multi-scale modeling of the rough surface morphology of the bonding surface;

[0023] According to the geometric relationship between the tool holder and the spindle joint surface, the normal spacing variation of the microelement joint surface is solved;

[0024] Among them, fractal dimension and fractal roughness are used to describe the rough morphology of the bonding surface, including:

[0025] ;

[0026] Where h is the height of the combined surface; x is the horizontal distance; L is the sampling length; γ is the scale parameter, D sh is the fractal dimension, G sh is the fractal roughness; n is the frequency index; is a random phase;

[0027] According to the geometric relationship of the tool holder-spindle joint surface, the kth segment joint surface is sh The solution of the normal spacing variation of the infinitesimal interface includes:

[0028] ;

[0029] In the formula, δ shrk and δ shzk For the kth sh The variation of the spacing between the bonding surfaces of the micro-elements along the radial and axial directions.

[0030] Preferably, the S3 comprises:

[0031] The probability density function of the cross-sectional area of the micro-convex body on the bonding surface is established through the maximum cross-sectional area of the micro-convex body; the correlation model between the locking force and the deformation of the bonding surface, the spacing and the contact force is established, and the simultaneous equations are used to calculate the spacing under the action of the unlocking force;

[0032] The probability density function of the cross-sectional area of the micro-convex body on the combined surface includes:

[0033] The cross-sectional area of the micro-convex body is assumed to be a, and the actual contact area of the micro-convex body is a real , a = 2a real , the radius of the cutoff area of the micro-convex body is r, and the radius of the real contact area of the micro-convex body is r real , the interference between the microconvex body and the rigid plane is δ, and the contact force is P n , the calculation formula of the critical cross-sectional area of the micro-convex body is:

[0034] ;

[0035] Among them, H sh and v sh E is the hardness and Poisson's ratio of the softer material in the toolholder-spindle joint; sh is the equivalent contact elastic modulus of the shank-shank joint, and the calculation formula is:

[0036] ;

[0037] Among them, E s and E h is the elastic modulus of the spindle and tool holder; v s and v h are the Poisson’s ratios of the spindle and tool holder, respectively;

[0038] The probability density function of the cross-sectional area a of the micro-convex body on the tool handle-spindle joint surface is expressed as:

[0039] ;

[0040] Among them, ψ sh is the combined surface expansion factor; a shl is the maximum cross-sectional area of the micro-convex body on the bonding surface, and the calculation formula is:

[0041] ;

[0042] Where erfc(·) represents the error complementary function; s shnp Indicates the locking force F d Normal spacing between the toolholder and spindle interface under action; σ sh It represents the root mean square value of the surface profile of the toolholder-spindle interface;

[0043] Among them, the correlation model between the locking force and the deformation of the joint surface, the spacing and the contact force is established, and the simultaneous equations are used to calculate the initial spacing under the action of the unlocking force, including:

[0044] The locking force F provided by the broaching mechanism of the spindle system dUnder the action, the tool shank-spindle joint surface is pre-tightened and contacted, and the force balance equation of the tool shank is:

[0045] ;

[0046] In the formula, F shnp and F shtp are the normal and tangential contact forces on the contact surface of the tool shank under the action of the locking force F d respectively;

[0047] Under the action of the locking force F d the normal and tangential deformations of the tool shank-spindle joint surface are expressed as:

[0048] ;

[0049] Among them, δ shp is the axial displacement of the tool shank-spindle joint under the action of the locking force F d s shnp is the normal spacing of the tool shank-spindle joint under the action of the locking force F d ;

[0050] When the contact force of the tool shank-spindle joint is 0, the maximum truncated area of the asperities on the joint surface is equal to the critical truncated area, and the initial axial spacing s sh0 of the tool shank-spindle joint is calculated as:

[0051] ;

[0052] Among them, σ sh represents the root mean square value of the surface profile of the tool shank-spindle joint surface, ψ sh is the joint surface domain expansion factor, E sh is the equivalent contact elastic modulus of the tool shank-tool shank joint, and H sh is the hardness of the softer material of the tool shank-spindle joint;

[0053] Based on the fractal contact theory, the normal and tangential contact forces of the tool shank-spindle joint under the action of the locking force F d are:

[0054] ;

[0055] ;

[0056] Among them, a shlp is the maximum truncated area of the asperities of the tool shank-spindle joint under the action of the locking force F d and the calculation formula is:

[0057] ;

[0058] By solving the force equilibrium equations of the tool shank, expressing the normal and tangential deformations of the tool shank-spindle joint surface, the initial axial spacing of the tool shank-spindle joint, the normal and tangential contact forces of the tool shank-spindle joint, and the maximum truncated area of the asperities of the tool shank-spindle joint, the normal spacing of the tool shank-spindle joint under the action of the locking force F d is calculated.

[0059] Preferably, the S4 includes:

[0060] Based on the elastic-plastic fractal contact theory of asperities, the normal / tangential stiffness formulas of the micro-element joint surface are derived;

[0061] By integrating the stiffness of the micro-element joint surface into the total stiffness of the segmented joint surface, the non-linear stiffness modeling from micro to macro is realized;

[0062] Among them, based on the elastic-plastic fractal contact theory of asperities, deriving the normal / tangential stiffness formulas of the micro-element joint surface includes:

[0063] According to the fractal contact theory of the joint surface, the normal and tangential contact stiffnesses of the asperities of the tool shank-tool shank joint surface are calculated as:

[0064] ;

[0065] Among them, k shn (a) represents the normal stiffness of the asperity; k sht (a) represents the tangential stiffness of the asperity;

[0066] By integrating the normal and tangential stiffnesses of the asperities of the k sh th micro-element joint surface of the tool shank-spindle segmented joint surface, the normal and tangential stiffnesses of the micro-element joint surface are calculated. The calculation formulas for the normal and tangential contact stiffnesses of the k sh th micro-element joint surface are:

[0067] ;

[0068] Among them, A shk represents the contact area of the k sh th micro-element joint surface;

[0069] By integrating the stiffness of the micro-element joint surface into the total stiffness of the segmented joint surface, the non-linear stiffness modeling from micro to macro is realized, including:

[0070] After obtaining the normal and tangential contact stiffnesses of all micro-element joint surfaces of the tool shank-spindle joint part, the total stiffnesses of all micro-element joint surfaces in five directions at the axial midpoint of the segmented joint surface are calculated as:

[0071] .

[0072] Preferably, the S5 includes:

[0073] Evenly distribute the total contact stiffness of the segmented joint surface to the non-linear connection springs at both ends to form a local non-linear spring connection model;

[0074] Integrate the stiffness contributions of all segmented joint surfaces to construct the overall stiffness matrix of the tool holder-spindle joint, covering geometric parameters, fractal characteristics, locking force, and vibration displacement factors, and realize the overall modeling of the dynamic stiffness of the tool holder-spindle joint.

[0075] The present invention also provides a dynamic stiffness modeling calculation system for a tool holder-spindle joint. The system is used to implement the foregoing method, and the system includes: a first construction module, a second construction module, a third construction module, a fourth construction module, and a fifth construction module;

[0076] The first construction module is used for modeling the geometric structure and dynamic displacement of the tool holder-spindle joint;

[0077] The second construction module is used to perform multi-scale modeling of the fractal surface topography and solve the normal spacing variation according to the established geometric structure and dynamic displacement model of the tool holder-spindle joint;

[0078] The third construction module is used to perform modeling of the contact characteristics of the asperities on the joint surface according to the established multi-scale model of the fractal surface topography and the solved normal spacing variation;

[0079] The fourth construction module is used to perform non-linear stiffness modeling and integration of the micro-element joint surface according to the established contact characteristic model of the asperities on the joint surface;

[0080] The fifth construction module is used to construct the overall dynamic stiffness matrix according to the established non-linear stiffness of the micro-element joint surface and the integration result.

[0081] Compared with the prior art, the beneficial effects of the present invention are:

[0082] (1) When calculating the stiffness of the tool holder-spindle joint, the present invention considers the rough topography and fractal contact characteristics of the joint surface, and the calculated stiffness is more accurate;

[0083] (2) The present invention solves the normal and tangential contact stiffness of the joint surface through the fractal contact theory and the non-linear spring layer, and the constructed stiffness matrix is more in line with the actual working conditions;

[0084] (3) The present invention has stronger applicability and can adapt to extreme working conditions such as high-speed cutting, heavy-load machining, and complex dynamic loads. Description of the Drawings

[0085] To more clearly illustrate the technical solution of the present invention, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0086] Figure 1 It is a flowchart of a method for modeling and calculating the dynamic stiffness of a tool holder - spindle joint in an embodiment of the present invention;

[0087] Figure 2 It is a schematic diagram of the dynamic modeling of a tool holder - spindle joint in an embodiment of the present invention, where (a) is a structural schematic diagram, (b) is an equivalent dynamic model, (c) is a three - dimensional view of the tool holder taper surface, and (d) is a schematic diagram of a radial section;

[0088] Figure 3 It is a schematic diagram of an equivalent contact model of a micro - element joint surface in an embodiment of the present invention, where (a) is a schematic diagram of the contact between a rigid smooth plane and a rough surface, and (b) is a schematic diagram of the contact deformation of asperities;

[0089] Figure 4 It is a schematic diagram of the force on the tool holder and the contact deformation of the tool holder - spindle joint surface in an embodiment of the present invention. Specific Embodiments

[0090] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0091] To make the above - mentioned objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0092] Embodiment 1

[0093] As Figure 1 shown, the present invention provides a method for modeling and calculating the dynamic stiffness of a tool holder - spindle joint, including the following steps:

[0094] S1. Divide the tool holder - spindle joint along the axial direction into g shThe axial segmentation of the toolholder-spindle joint is dynamically modeled based on the stepped Timoshenko straight beam. The corresponding nodes of the equivalent stepped axis of the spindle and the equivalent stepped axis of the toolholder are connected by nonlinear springs and damping in five directions. The dynamic displacement of any position of the segmented joint surface is derived according to the vibration displacement of the segmented joint surface combined with the shape function matrix, providing a geometric and displacement input basis for stiffness analysis.

[0095] S2, use the slicing method to cut the segmented joint surface into n equal angles along the circumferential direction sh The micro-element bonding surface is obtained, and the normal spacing variation of the micro-element bonding surface of the segmented bonding surface is solved according to the geometric relationship of the tool handle-spindle bonding surface. The rough morphology of the bonding surface is modeled using fractal dimension and fractal roughness.

[0096] S3. By using the maximum cross-sectional area of the micro-convex body on the joint surface, a probability density function of the cross-sectional area of the micro-convex body on the tool handle-spindle joint surface is established, and a correlation model of the normal spacing, contact deformation and contact force of the tool handle-spindle joint surface under the action of the locking force is established, and the initial spacing of the tool handle-spindle joint part is solved by simultaneous equations;

[0097] S4. Based on the elastic-plastic fractal contact theory of micro-convex bodies, the normal and tangential stiffness of the micro-convex bodies of the micro-element bonding surface are established. The normal and tangential stiffness of the micro-element bonding surface are obtained by integrating the normal and tangential stiffness of the micro-convex bodies of the micro-element bonding surface, and all the micro-element bonding surface stiffness of the segmented bonding surface are integrated into the midpoint of the segmented bonding surface, thereby realizing nonlinear stiffness modeling from micro to macro;

[0098] S5. By allocating the total stiffness of the segmented joint surface to the nodes at both ends, the overall stiffness matrix of the tool holder-spindle joint is constructed. The high-precision dynamic stiffness model of the tool-handle is formed by integrating factors such as geometric parameters, fractal characteristics, locking force and vibration displacement.

[0099] In this embodiment of the present invention, S1 includes the following sub-steps:

[0100] S11, geometric parameter definition and step beam model construction;

[0101] S12. Derivation of dynamic displacement of segmented joint surfaces.

[0102] In the embodiment of the present invention, in S11, the steps of defining geometric parameters and constructing the step beam model are as follows:

[0103] The simplified structure of the tool handle-spindle joint is as follows Figure 2 As shown in (a), the taper angle of the joint is α sh= arctan (7 / 48). To consider the influence of the geometric shape of the contact surface of the joint on the dynamic characteristics, a stepped Timoshenko straight beam is used to model the tool holder - spindle joint. The tool holder - spindle joint is axially divided into g sh segmented joint surfaces, and the diameter of the equivalent stepped beam is the average diameter of the segmented conical surface. The corresponding nodes of the spindle equivalent stepped shaft and the tool holder equivalent stepped shaft are connected by non - linear springs and dampers in five directions, as Figure 2 shown in (b).

[0104] During the cutting process, due to the action of dynamic loads, the contact characteristics of the tool holder - spindle joint surface will change with vibration, and the contact characteristics per unit area of the joint surface will also change along the axial and radial contact positions. At the same time, the rough surface topography of the joint surface also has a significant impact on the dynamic characteristics of the tool holder - spindle joint. Therefore, a non - linear stiffness model of the tool holder - spindle joint is established using the fractal contact theory and the slicing method.

[0105] Taking the segmented joint surface ij of the spindle - tool holder joint as an example, the stiffness matrix of the non - linear spring of the distributed layer of the joint surface is deduced. The axial length of the segmented joint surface is represented by l sh as shown in Figure 2 (c). To consider the change of the contact characteristics per unit area of the joint surface along the radial contact position, the slicing method is used to equally divide the segmented joint surface into n sh micro - element joint surfaces along the circumferential direction, as Figure 2 shown in (d). Then, the radial position angle φ sh and the contact area A shk of the k shk th micro - element joint surface of the segmented joint surface can be expressed as:

[0106] (1)

[0107] In the formula, n sh represents the number of micro - element joint surfaces, φ shk represents the radial position angle of the k sh th micro - element joint surface, A shk represents the contact area of the k sh th micro - element joint surface, r shl and r shs are the radii of the large end and the small end of the segmented joint surface of the tool holder - spindle joint respectively; ω is the angular velocity of the tool holder; α sh is the taper angle of the tool holder - spindle joint; t is the time variable.

[0108] In the embodiment of the present invention, in S12, the derivation process of the dynamic displacement of the segmented joint surface is as follows:

[0109] Based on the vibration displacements of the tool shank and the spindle at the two ends of the tool shank-spindle joint surface in the combined section, the vibration displacements of the tool shank and the spindle at any axial position of the segmented joint surface can be calculated as follows:

[0110] (2)

[0111] where z, x, and y are the vibration displacements of the tool shank / spindle at any axial position of the segmented joint surface in the Z, X, and Y directions; θ xi and θ yi are the angular vibration displacements of the tool shank / spindle at any axial position of the segmented joint surface about the X and Y directions; z i , x i and y i are the translational displacements of the tool shank / spindle node i at the segmented joint surface in the Z, X, and Y directions; θ xi and θ yi are the angular displacements of the tool shank / spindle node i at the segmented joint surface about the X and Y directions; z j , x j and y j are the translational displacements of the tool shank / spindle node j at the segmented joint surface in the Z, X, and Y directions; θ xj and θ yj are the angular displacements of the tool shank / spindle node j at the segmented joint surface about the X and Y directions; N represents the shape function matrix.

[0112] After completing the geometric modeling and dynamic displacement derivation of the tool shank-spindle joint, the segmented model based on the stepped Timoshenko straight beam has clarified the geometric characteristics and mechanical simplification rules of the joint, and quantified the distribution law of vibration displacements through the shape function matrix. This step provides key inputs for subsequent analysis: the geometric parameters define the non-uniform distribution characteristics of the contact surface, and the dynamic displacement response provides displacement boundary conditions for the vibration effect in stiffness modeling. Next, it is necessary to combine the fractal theory to perform multi-scale characterization of the surface rough topography to further quantify the statistical characteristics of the contact area and lay a foundation for the modeling of microscopic contact behavior.

[0113] In the embodiment of the present invention, S2 includes the following sub-steps:

[0114] S21. Solving the change amount of the normal spacing of the micro-element joint surface;

[0115] S22. Multi-scale mathematical modeling of the surface rough topography driven by the fractal theory.

[0116] In the embodiment of the present invention, in S21, the steps for solving the change amount of the normal spacing of the micro-element joint surface are as follows:

[0117] Due to the vibration of the tool shank and the spindle at the segmented joint surface, the kth shThe variation of the spacing of each micro - element joint surface in the radial and axial directions can be calculated as follows:

[0118] (3)

[0119] where δ shrk represents the variation of the spacing of the k - th micro - element joint surface in the radial direction; δ sh represents the variation of the spacing of the k - th micro - element joint surface in the axial direction; shzk represents the radial position angle of the micro - element joint surface; z sh shh shh shh shh shh shh shh shhx shhx shhy shhy shs shs shs shs shs shs shsx shsx shsy shsy sh sh is the average radius of the segmented joint surface.

[0120] According to the geometric relationship of the tool - holder - spindle joint surface, the variation of the normal spacing of the k - th micro - element joint surface of the segmented joint surface can be calculated as follows: sh

[0121]

[0121] (4) In the embodiment of the present invention, in S22, the multi - scale mathematical modeling process of the surface rough topography driven by the fractal theory is as follows:

[0122] From a microscopic perspective, the conical surface of the tool - holder - tool - holder joint is composed of many micro - convex bodies, and its contact is formed through the contact deformation of the micro - convex bodies. The actual contact area is smaller than the nominal contact area. The contact surface topography of the tool - holder - tool - holder joint can be represented by the fractal dimension D sh and the fractal roughness G sh as:

[0123]

[0124] (5) where h is the surface height of the joint surface; x is the horizontal distance; L is the sampling length; n is the frequency index;

[0125] is the random phase; γ is the scale parameter, usually taken as 1.5.

[0126] Solve the variation of the normal spacing of the micro-joints of the segmented joint surface according to the vibration displacement, and use the fractal dimension and fractal roughness to perform multi-scale modeling of the rough morphology of the joint surface. This step not only solves the limitation of the traditional model ignoring the influence of surface morphology, but also provides the input conditions of dynamic spacing and fractal parameters for the elastic-plastic contact modeling of the subsequent micro-joint surface stiffness. Next, it is necessary to establish a non-linear correlation model between the contact force and the deformation by combining the contact deformation and spacing analysis of the joint under the action of the locking force, so as to quantify the dynamic regulation mechanism of the pre-tightening state on the contact stiffness.

[0127] In the embodiment of the present invention, S3 includes the following sub-steps:

[0128] S31. Model the contact mechanics model of the micro-convex bodies on the joint surface and the probability density function followed by the truncated area;

[0129] S32. Solve the normal spacing of the joint under the action of the locking force.

[0130] In the embodiment of the present invention, in S31, the modeling of the contact mechanics model of the micro-convex bodies on the joint surface and the probability density function followed by the truncated area is as follows:

[0131] Regard the micro-joint surface of the tool shank-tool shank segmented joint surface as the contact between a rigid ideal smooth plane and a rough surface, as shown in Figure 3 (a). Assume that the top of the micro-convex bodies on the joint surface is spherical, then the contact deformation between the micro-convex bodies and the rigid plane is as shown in Figure 3 (b). The truncated area of the micro-convex body is a, and the actual contact area of the micro-convex body is a real , a = 2a real . The radius of the truncated region of the micro-convex body is r, and the radius of the true contact region of the micro-convex body is r real . The interference amount between the micro-convex body and the rigid plane is δ, and the contact force is P n . When the truncated area of the micro-convex body exceeds the critical truncated area, the contact deformation between the micro-convex body and the rigid plane is elastic deformation; when the truncated area of the micro-convex body is less than the critical truncated area, the contact deformation between the micro-convex body and the rigid plane is plastic deformation. The critical truncated area of the micro-convex body can be calculated by the following formula:

[0132] (6)

[0133] Where, H sh and v sh are the hardness and Poisson's ratio of the softer material of the tool shank-spindle joint; E sh is the equivalent contact elastic modulus of the tool shank-tool shank joint, which can be calculated by the following formula:

[0134] (7)

[0135] Among them, E s and E h are the elastic moduli of the spindle and the tool shank; v s and v h are the Poisson's ratios of the spindle and the tool shank respectively.

[0136] The probability density function that the truncated area a of the asperities on the tool shank-spindle joint surface follows can be expressed as:

[0137] (8)

[0138] Among them, ψ sh is the joint surface domain expansion factor; a shl is the maximum truncated area of the asperities on the joint surface, and the calculation formula is as follows:

[0139] (9)

[0140] Among them, erfc(·) represents the complementary error function; s shnp represents the normal spacing of the tool shank-spindle joint surface under the action of the locking force F d ; σ sh represents the root mean square value of the surface profile of the tool shank-spindle joint surface.

[0141] In the embodiment of the present invention, in S32, the solving process of the normal spacing of the joint part under the action of the locking force is as follows:

[0142] Under the action of the locking force F d provided by the broach mechanism of the spindle system, the tool shank-spindle joint surface is pre-tightly contacted, and the force balance equation of the tool shank is as follows:

[0143] (10)

[0144] In the formula, F shnp and F shtp are respectively the normal and tangential contact forces on the contact surface of the tool shank under the action of the locking force F d .

[0145] Under the action of the locking force F d , the normal and tangential deformations of the tool shank-spindle joint surface can be expressed as:

[0146] (11)

[0147] Among them, δ shp is the axial displacement of the tool shank-spindle joint part under the action of the locking force F d , and is determined by the following formula:

[0148] (12)

[0149] Among them, s sh0 is the initial axial spacing of the tool shank - spindle joint when the contact force is 0; s shp is the axial spacing of the tool shank - spindle joint under the action of the locking force F d ; s shnp is the normal spacing of the tool shank - spindle joint under the action of the locking force F d .

[0150] When the contact force of the tool shank - spindle joint is 0, the maximum truncated area of the asperities on the contact surface is equal to the critical truncated area. Therefore, the initial axial spacing s sh0 of the tool shank - spindle joint can be calculated by the following formula:

[0151] (13)

[0152] Based on the fractal contact theory, the normal and tangential contact forces of the tool shank - spindle joint under the action of the locking force F d are:

[0153] (14)

[0154] (15)

[0155] Among them, a shlp is the maximum truncated area of the asperities of the tool shank - spindle joint under the action of the locking force F d , and can be calculated by the following formula:

[0156] (16)

[0157] By solving the simultaneous equations, the normal spacing of the tool shank - spindle joint under the action of the locking force F d can be calculated.

[0158] Through the correlation model of the locking force with the joint surface deformation, spacing and contact force, the initial spacing of the joint under the action of the locking force has been solved, revealing the non - linear influence law of the pre - tightening force on the contact stiffness. This step clarifies the boundary conditions of the dynamic stiffness of the joint surface under the action of external forces, and provides the initial spacing input data for the modeling of the micro - element joint surface stiffness. Subsequently, based on the elastic - plastic theory of asperities, a stiffness model of the asperities of the micro - element joint surface needs to be established, and the stiffness integration from micro to macro is realized through integration, and finally the stiffness matrix of the segmented joint surface is constructed.

[0159] In the embodiment of the present invention, S4 includes the following sub - steps:

[0160] S41, solving the normal / tangential stiffness of the micro - element joint surface;

[0161] S42. Calculation of the stiffness of the segmented joint surface.

[0162] In the embodiment of the present invention, in S41, the solution process for the normal and tangential stiffnesses of the asperities of the micro-element joint surface is as follows:

[0163] (17)

[0164] Among them, k shn (a) represents the normal stiffness of the asperity; k sht (a) represents the tangential stiffness of the asperity;

[0165] By integrating the normal and tangential stiffnesses of the asperities of the k sh -th micro-element joint surface of the tool shank-spindle segmented joint surface, the normal and tangential stiffnesses of the micro-element joint surface can be calculated. Then, the calculation formulas for the normal and tangential contact stiffnesses of the k sh -th micro-element joint surface are as follows:

[0166] (18)

[0167] Among them, A shk represents the contact area of the k sh -th micro-element joint surface.

[0168] In the embodiment of the present invention, in S42, the total stiffness of the segmented joint surface is:

[0169] After obtaining the normal and tangential contact stiffnesses of all the micro-element joint surfaces of the tool shank-spindle joint part segmented joint surface, the total stiffness in five directions at the axial midpoint of the segmented joint surface of all the micro-element joint surfaces can be calculated as:

[0170] (19)

[0171] Based on the critical truncation area of the asperity and the equivalent elastic modulus, the normal and tangential stiffness formulas of the asperities of the micro-element joint surface are derived. The normal and tangential stiffnesses of the micro-element joint surface are obtained through integration, and the stiffnesses of all the micro-element joint surfaces are integrated into the total stiffness of the segmented joint surface. This step realizes the cross-scale modeling from the microscopic contact behavior to the macroscopic mechanical properties, and reveals the coupling effect between the fractal parameters and the dynamic stiffness. Next, it is necessary to distribute the stiffness of the segmented joint surface to the connecting springs at both ends to provide the stiffness input at the segmented level for the construction of the overall stiffness matrix of the tool shank-spindle joint part.

[0172] Furthermore, S5 includes the following sub-steps:

[0173] S51. Distribution of the stiffness of the segmented joint surface: Distribute the total stiffness of the segmented joint surface to the connecting springs at both ends of the segmented joint surface in a ratio of 1:1.

[0174] S52. Comprehensive construction of the overall stiffness matrix: By comprehensively considering the stiffness contributions of all segmented joint surfaces, the overall stiffness matrix of the tool holder - spindle joint is constructed, covering factors such as geometric parameters, fractal characteristics, locking force, and vibration displacement, realizing the full - link modeling of dynamic stiffness.

[0175] By distributing the stiffness of the segmented joint surface to the corresponding springs at both ends, a local non - linear spring connection model has been formed to ensure the physical equivalence of the segmented stiffness. Finally, all the segmented stiffness contributions are integrated to construct the overall stiffness matrix of the tool holder - spindle joint, comprehensively considering factors such as geometric parameters, fractal characteristics, locking force, and vibration displacement. This step marks the completion of the dynamic stiffness modeling, providing a theoretical tool for the dynamic performance prediction and optimization of the high - precision machine tool spindle system. Subsequent research can carry out experimental verification or parameter sensitivity analysis based on this model to further improve the reliability of engineering applications.

[0176] In the embodiment of the present invention, as Figure 2 shown, considering the contact deformation of the tool holder - spindle joint and the microscopic characteristics of the fractal rough surface, the deformation characteristics of the contact interface are equivalent to the action of non - linear springs and dampers, obtaining the final dynamic stiffness analysis model.

[0177] In the embodiment of the present invention, as Figure 3 shown, considering the microscopic topography of the rough surface of the tool holder - spindle joint surface, the contact interface is equivalent to a contact model between a rigid smooth plane and a rough surface. Through the fractal contact theory, the truncated area and the real contact area of the asperities are calculated, and the elastic and plastic deformation characteristics of the asperities are analyzed. Finally, the contact stiffness model of the joint surface is established.

[0178] In the embodiment of the present invention, as Figure 4 shown, considering the influence of the locking force on the contact characteristics of the tool holder - spindle joint surface, the normal contact force and the tangential contact force are analyzed. By establishing the force balance equation, the contact deformation amount of the joint surface is calculated, and the change in the axial spacing under the action of the locking force is determined. This method can accurately describe the contact characteristics of the joint surface under the action of the pre - tightening force, providing key data support for dynamic stiffness modeling.

[0179] Embodiment Two

[0180] The present invention also provides a dynamic stiffness modeling calculation system for the tool holder - spindle joint. The system is used to implement the foregoing method, and the system includes: a first construction module, a second construction module, a third construction module, a fourth construction module, and a fifth construction module;

[0181] The first construction module is used for the geometric structure and dynamic displacement modeling of the tool holder-spindle joint;

[0182] The second construction module is used for the multi-scale modeling of the fractal surface topography and the solution of the normal spacing variation according to the established geometric structure and dynamic displacement model of the tool holder-spindle joint;

[0183] The third construction module is used for the contact characteristic modeling of the asperities on the joint surface according to the established multi-scale model of the fractal surface topography and the solved normal spacing variation;

[0184] The fourth construction module is used for the non-linear stiffness modeling of the micro-element joint surface according to the established contact characteristic model of the asperities on the joint surface;

[0185] The fifth construction module is used for the construction of the overall dynamic stiffness matrix according to the established non-linear stiffness of the micro-element joint surface.

[0186] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A dynamic stiffness modeling and calculation method for the tool holder - spindle joint, characterized in that, The method comprises: S1, geometric structure and dynamic displacement modeling of the toolholder-spindle joint; S2. Based on the established geometric structure and dynamic displacement model of the tool handle-spindle joint, multi-scale modeling of the joint surface morphology and solution of the normal spacing variation are performed; S3, modeling the contact characteristics of the micro-convex bodies on the bonding surface according to the established multi-scale model of the surface morphology and the solved normal spacing variation; S4. Based on the established contact characteristic model of the micro-convex body of the bonding surface, the nonlinear stiffness modeling and integration of the micro-element bonding surface are performed; S5. Based on the established nonlinear stiffness of the microelement joint surface and the integral results, the overall dynamic stiffness matrix of the tool holder-spindle joint is constructed.

2. The method according to claim 1, wherein Said S1 comprises: Axial segmented dynamic modeling of the toolholder-spindle joint is performed based on the stepped Timoshenko straight beam; The slicing method is used to cut the segmented bonding surface into micro-element bonding surfaces at equal angles along the circumferential direction, including: ； Where n sh represents the number of micro - element joint surfaces, φ shk represents the radial position angle of the k sh -th micro - element joint surface, A shk represents the contact area of the k sh -th micro - element joint surface, r shl and r shs are the radii of the large end and the small end of the joint surface of the tool shank - spindle joint part respectively; ω is the angular velocity of the tool shank; α sh is the taper angle of the tool shank - spindle joint part; t is the time variable; According to the vibration displacement of the nodes at both ends of the segmented joint surface, combined with the shape function matrix, the dynamic response of any position of the segmented joint surface is derived, including: ； where z, x, and y are the vibration displacements of the tool shank / spindle at any axial position of the segmented joint surface in the Z, X, and Y directions; θ xi and θ yi are the angular vibration displacements of the tool shank / spindle at any axial position of the segmented joint surface about the X and Y directions; z i , x i and y i are the translational displacements of the tool shank / spindle node i at the segmented joint surface in the Z, X, and Y directions; θ xi and θ yi are the angular displacements of the tool shank / spindle node i at the segmented joint surface about the X and Y directions; z j , x j and y j are the translational displacements of the tool shank / spindle node j at the segmented joint surface in the Z, X, and Y directions; θ xj and θ yj are the angular displacements of the tool shank / spindle node j at the segmented joint surface about the X and Y directions; N represents the shape function matrix.

3. The method according to claim 2, characterized in that, The S2 comprises: The fractal dimension and fractal roughness are used to perform multi-scale modeling of the rough surface morphology of the bonding surface; According to the geometric relationship between the tool holder and the spindle joint surface, the normal spacing variation of the microelement joint surface is solved; Among them, fractal dimension and fractal roughness are used to describe the rough morphology of the bonding surface, including: ； Among them, h is the surface height of the joint surface; x is the horizontal distance; L is the sampling length; γ is the scale parameter, D sh is the fractal dimension, G sh is the fractal roughness; n is the frequency exponent; is the random phase; According to the geometric relationship of the tool shank-spindle joint surface, solve the variation of the normal spacing of the k-th micro-element joint surface of the segmented joint surface, including: sh ​ ； where δ shrk and δ shzk are the changes in the spacing of the k sh th micro-element bonding surface along the radial and axial directions.

4. The method according to claim 3, wherein The S3 includes: The probability density function of the cross-sectional area of the micro-convex body on the bonding surface is established through the maximum cross-sectional area of the micro-convex body; the correlation model between the locking force and the deformation of the bonding surface, the spacing and the contact force is established, and the initial spacing under the action of the unlocking force is calculated by simultaneous equations; The probability density function of the cross-sectional area of the micro-convex body on the combined surface includes: The truncated area of the preset microconvex body is a, and the actual contact area of the microconvex body is a real , a = 2a real , the radius of the truncated region of the microconvex body is r, and the radius of the true contact region of the microconvex body is r real , the interference amount between the microconvex body and the rigid plane is δ, and the contact force is P n , the calculation formula for the critical truncated area of the microconvex body is: ； Among them, H sh and v sh are the hardness and Poisson's ratio of the softer material at the tool shank - spindle joint; E sh is the equivalent contact elastic modulus of the tool shank - tool shank joint, and the calculation formula is: ； Among them, E s and E h are the elastic moduli of the spindle and the tool shank; v s and v h are the Poisson's ratios of the spindle and the tool shank, respectively; The probability density function of the cross-sectional area a of the micro-convex body on the tool handle-spindle joint surface is expressed as: ； Among them, ψ sh is the joint surface area expansion factor; a shl is the maximum truncated area of the asperities on the joint surface, and the calculation formula is: ； where erfc(·) represents the complementary error function; s shnp represents the normal spacing of the toolholder-spindle joint surface under the action of the locking force F d ; σ sh represents the root mean square value of the surface profile of the toolholder-spindle joint surface; Among them, the correlation model between the locking force and the deformation of the joint surface, the spacing and the contact force is established, and the simultaneous equations are used to calculate the spacing under the action of the unlocking force, including: Under the locking force F provided by the broach mechanism of the spindle system d the tool holder-spindle joint surface is pre-tightened and contacted, and the force balance equation of the tool holder is as follows: ； Where F shnp and F shtp are the normal and tangential contact forces on the contact surface of the tool shank under the action of the locking force F d respectively; Under the locking force F d The normal and tangential deformations of the toolholder-spindle joint surface are expressed as: ； Among them, δ shp is the axial displacement of the tool holder - spindle joint under the action of the locking force F d , and s shnp is the normal spacing of the tool holder - spindle joint under the action of the locking force F d ; When the contact force at the tool shank - spindle joint is 0, the maximum truncated area of the asperities on the joint surface is equal to the critical truncated area, and the initial axial spacing s of the tool shank - spindle joint sh0 The calculation formula is as follows: ； Among them, σ sh represents the root mean square value of the surface profile of the tool shank-spindle joint surface, ψ sh is the joint surface domain expansion factor, E sh is the equivalent contact elastic modulus of the tool shank-tool shank joint, H sh is the hardness of the softer material at the tool shank-spindle joint; Based on the fractal contact theory, under the locking force F d The normal and tangential contact forces at the tool holder-spindle interface are as follows: ； ； where a shlp is the maximum truncated area of the asperities at the tool shank - spindle interface under the action of the locking force F d and the calculation formula is as follows: ； By simultaneously solving the force balance equation of the toolholder, the expressions for the normal and tangential deformations of the toolholder-spindle joint surface, the initial axial spacing of the toolholder-spindle joint, the normal and tangential contact forces of the toolholder-spindle joint, and the maximum truncated area of the asperities of the toolholder-spindle joint, the normal spacing of the toolholder-spindle joint under the action of the locking force F d is calculated.

5. The method according to claim 4, wherein The S4 comprises: Based on the elastic-plastic fractal contact theory of micro-convex bodies, the normal / tangential stiffness formula of the micro-element interface is derived; By integrating the micro-element joint surface stiffness into the total joint surface stiffness of the segmented joint surface, nonlinear stiffness modeling from micro to macro is achieved; Among them, based on the elastic-plastic fractal contact theory of micro-convex bodies, the normal / tangential stiffness formulas of the micro-element interface are derived, including: According to the fractal contact theory of the joint surface, the normal and tangential contact stiffness of the convex body of the handle-handle joint surface is calculated as: ； where k shn (a) represents the normal stiffness of asperities; k sht (a) represents the tangential stiffness of asperities; By integrating the normal and tangential stiffnesses of the micro-convex bodies on the k-th micro-element joint surface of the tool shank-spindle segmented joint surface, the normal and tangential stiffnesses of the micro-element joint surface are calculated. The calculation formulas for the normal and tangential contact stiffnesses of the k-th micro-element joint surface are as follows: sh The normal and tangential stiffnesses of the k-th micro-element joint surface are calculated by integrating the normal and tangential stiffnesses of the micro-convex bodies on the k-th micro-element joint surface of the tool shank-spindle segmented joint surface. The calculation formulas for the normal and tangential contact stiffnesses of the k-th micro-element joint surface are as follows: sh The calculation formulas for the normal and tangential contact stiffnesses of the k-th micro-element joint surface are: ； Among them, A shk represents the contact area of the k sh -th micro-element bonding surface; By integrating the micro-element joint surface stiffness into the total joint surface stiffness of the segmented joint surface, nonlinear stiffness modeling from micro to macro is achieved, including: After obtaining the normal and tangential contact stiffness of all micro-element surfaces of the toolholder-spindle joint segment, the total stiffness of all micro-element surfaces in five directions at the axial midpoint of the segmented joint surface is calculated as: 。 6. The method according to claim 1, characterized in that, The S5 comprises: The total contact stiffness of the segmented joint surface is evenly distributed to the nonlinear connection springs at both ends to form a local nonlinear spring connection model; Combining the stiffness contributions of all segmented joint surfaces, an overall stiffness matrix of the toolholder-spindle joint is constructed, covering geometric parameters, fractal characteristics, locking force, and vibration displacement factors, to achieve the overall modeling of the dynamic stiffness of the toolholder-spindle joint.

7. A dynamic stiffness modeling and calculation system for the tool holder - spindle joint, the system being used to implement the method according to any one of claims 1 - 6, characterized in that, The system includes: a first construction module, a second construction module, a third construction module, a fourth construction module, and a fifth construction module; The first construction module is used for the geometric structure and dynamic displacement modeling of the toolholder-spindle joint; The second construction module is used for the multi-scale modeling of the fractal surface topography and the solution of the normal spacing variation according to the established geometric structure and dynamic displacement model of the toolholder-spindle joint; The third construction module is used for the contact characteristic modeling of the asperities on the joint surface according to the established multi-scale model of the fractal surface topography and the solved normal spacing variation; The fourth construction module is used for the non-linear stiffness modeling and integration of the micro-element joint surface according to the established contact characteristic model of the asperities on the joint surface; The fifth construction module is used for the construction of the overall dynamic stiffness matrix according to the established non-linear stiffness of the micro-element joint surface and the integration results.

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