A statics calculation and analysis method for non-slip working condition of tailstock of numerical control lathe

Abstract

This invention provides a method for static calculation and analysis of the tailstock of a CNC lathe under no-slip conditions, relating to the field of static analysis technology for CNC machine tool structures. First, the maximum static friction force between the sleeve and the tailstock body is calculated based on the mechanical model of the tailstock clamping mechanism. When the applied load is less than this friction force, the no-slip condition is determined. Based on fractal contact theory, nonlinear elastic restoring force models are established for the sleeve-center cone surface joint and the tailstock-bed guide rail joint, respectively. The guide rail joint is discretized using a slicing method to describe its non-uniform contact deformation. Finally, the sub-models are integrated to construct the system static equations under the no-slip condition of the tailstock. The load-displacement response of the system and the bearing characteristics of each joint surface under the no-slip condition are obtained through numerical solution.

Description

Technical Field

[0001] This invention relates to the field of static analysis technology for CNC machine tool structures, and in particular to a method for static calculation and analysis of the tailstock of a CNC lathe under non-slip conditions. Background Technology

[0002] The tailstock of a CNC lathe, as a key functional component, plays a crucial role in supporting the workpiece, especially as a core device for machining slender shaft parts. During machining, the tailstock bears the axial external load generated by the cutting force. The tailstock sleeve relies on the clamping handle to provide axial friction. When the axial external load is less than the axial friction force on the sleeve, there is no relative slippage between the sleeve and the tailstock body. At this time, the external load is transmitted to the tailstock body through the sleeve-center mating surface, and then through the tailstock body to the tailstock body-bed guideway mating surface, forming a force-displacement system under slip-free conditions.

[0003] In existing technologies, traditional static analyses of lathe tailstocks typically simplify the mating surfaces in the system as ideal rigid connections, making it difficult to reflect the actual contact state changes of these surfaces under no-slip conditions. Most existing studies treat the lathe tailstock as a whole for mechanical analysis, failing to consider the complex contact behavior changes between the sleeve-center mating surfaces and the tailstock body-bed guideway mating surfaces within the tailstock system. This results in significant errors in the predicted force-displacement relationships under no-slip conditions, hindering accurate guidance for engineering practice.

[0004] The existing technology has the following shortcomings: (1) It fails to fully consider the complex nonlinear contact behavior between the mating surfaces inside the tailstock system under the combined action of preload and external load; (2) It fails to propose a detailed calculation model for the case where the sleeve does not slip, and cannot accurately identify which working condition the tailstock belongs to; (3) It does not establish a static calculation and analysis model for the lathe tailstock for the specific working condition where the sleeve does not slip, and the general model is difficult to adapt to the load transfer characteristics under this working condition. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a static calculation and analysis method for the tailstock of a CNC lathe under non-slip conditions, which accurately characterizes the mechanical response law of the tailstock system under non-slip conditions, providing a scientific basis for tailstock structure optimization and machining accuracy improvement.

[0006] On the one hand, the present invention provides a method for static calculation and analysis of the tailstock of a CNC lathe under non-slip conditions, including the following steps:

[0007] Step 1: Determine the key functional components, mating surfaces, and load transfer paths of the lathe tailstock system under non-slip conditions;

[0008] The key functional components include the tailstock center, sleeve, clamping mechanism, tailstock body, and bed guide rail;

[0009] The mating surfaces include the sleeve-center mating surface, the horizontal mating surface between the tailstock body and the left side of the bed guide rail, the first inclined mating surface between the tailstock body and the right side of the bed guide rail, and the second inclined mating surface between the tailstock body and the right side of the bed guide rail;

[0010] The load transfer path is: external axial load → center → sleeve - center mating surface → sleeve → tailstock body → tailstock body - bed guide rail mating surface → bed;

[0011] Step 2: Calculate the maximum axial static friction force of the sleeve under the action of the clamping handle to determine the no-slip condition; specifically, based on the thread force transmission principle and friction calculation theory, calculate the force transmission characteristics under the action of the clamping handle, including the radial clamping force and the bolt axial force:

[0012] Calculate the torque T generated by the clamping handle:

[0013] ;

[0014] In the formula, F sb L represents the tightening force of the clamping handle; L represents the handle length of the clamping handle.

[0015] Taking into account the effect of friction, the axial force F of the bolt is obtained. a The parsing expression:

[0016] ;

[0017] In the formula, d2 is the mean diameter of the thread, and ρ' is the equivalent friction angle of the thread in the clamping mechanism.

[0018] Calculate the radial clamping force F on the bushing r :

[0019] ;

[0020] In the formula, N is the normal force on the conical surface of the clamping sleeve; f1 is the coefficient of friction between the clamping sleeve and the conical surface of the sleeve along the axial direction of the clamping sleeve; F a θ represents the axial force on the bolt under the action of the clamping handle; θ is the half-angle of the conical surface between the clamping sleeve and the tailstock.

[0021] Calculate the axial frictional force f acting on the final sleeve. tw :

[0022] ;

[0023] In the formula, f3 is the coefficient of friction between the tailstock and the right side contact surface of the sleeve along the sleeve axis.

[0024] Compare the applied load with the maximum static friction force f tw When the applied load is less than the maximum static friction force, the tailstock is in a non-slip condition.

[0025] Step 3: Establish a static calculation model of the tailstock system of the CNC lathe under non-slip conditions;

[0026] The static calculation model is a nonlinear elastic restoring force coupling of the sleeve-center mating surface and the tailstock-bed guide rail mating surface; the mechanical contributions of the lead screw-nut pair and thrust bearing are ignored, that is, the path does not transmit load when there is no relative slippage, and the boundary conditions of the model are defined: there is no relative displacement between the sleeve and the tailstock, and each mating surface only produces elastic deformation.

[0027] The static calculation model under no-slip condition is as follows:

[0028] ;

[0029] In the formula, F dty F is the axial elastic restoring force at the sleeve-center mating surface. y0 This is the external load applied to the tailstock of the lathe at this moment; P g0d F represents the preload force exerted on the tailstock of the lathe during operation. wgy M is the elastic restoring force along the Y direction at the mating surface of the tailstock body and bed guideways; wgx M is the elastic restoring torque about the X-axis at the tailstock-bed guideway mating surface; dtwx The elastic restoring torque about the X-axis experienced by the tailstock body under the action of the axial elastic restoring force at the sleeve-center mating surface; y d This represents the axial deformation of the center point under an applied load; y w θ represents the axial deformation of the tailstock body under external load; wx The rotation angle of the tailstock body around the X-axis;

[0030] Step 4: Based on fractal contact theory, establish a calculation model for the elastic restoring force of the sleeve-center interface;

[0031] Specifically, based on fractal contact theory, the sleeve-center mating surface is modeled; the initial contact state of the mating surface under preload is calculated, namely the normal spacing and tangential deformation; when the external load causes axial displacement of the sleeve, the deformation of the mating surface is updated, and the total normal elastic restoring force and tangential elastic restoring force of the sleeve-center mating surface are calculated using fractal theory, and then the axial restoring force of the sleeve-center mating surface is synthesized.

[0032] The axial elastic restoring force F at the sleeve-center mating surface under applied load was calculated. dty :

[0033] ;

[0034] In the formula, F nd F is the total normal elastic restoring force at the sleeve-center mating surface. td The total tangential elastic restoring force at the sleeve-center mating surface; α d The cone angle is the cone angle of the sleeve-center cone surface.

[0035] Step 5: Based on fractal theory, calculate the nonlinear elastic restoring force and restoring torque of the tailstock-bed guideway mating surface;

[0036] The guide rail mating surface is discretized into multiple micro-units using a slicing method. The guide rail mating surface includes horizontal and inclined surfaces. The normal and tangential deformations of each micro-unit are determined based on geometric relationships. The elastic restoring force of each micro-unit is calculated based on fractal contact theory. The restoring forces of all micro-units are integrated and summed to obtain the total axial restoring force and the restoring moment about the transverse axis of the guide rail mating surface. Finally, the elastic restoring force of the tailstock-guide rail mating surface in the Y direction and the restoring moment about the X axis are obtained.

[0037] Calculate the nonlinear elastic restoring force F in the Y direction at the tailstock-bed guideway mating surface. wgy :

[0038] ;

[0039] In the formula, F lfthy The elastic restoring force in the Y direction of the front half of the horizontal coupling on the left side of the tailstock-bed guide rail; F lrthy F represents the elastic restoring force in the Y direction of the rear half of the horizontal mating surface on the left side of the tailstock-bed guideway; 1fsy F represents the elastic restoring force in the Y direction of the first inclined coupling front half on the right side of the tailstock-bed guide rail; 1rsy F is the elastic restoring force in the Y direction of the rear half of the first inclined mating surface on the right side of the tailstock-bed guideway; 2fsy F represents the elastic restoring force in the Y direction of the upper half of the second inclined coupling on the right side of the tailstock-bed guide rail; 2rsy The elastic restoring force in the Y direction is the rear half of the second inclined mating surface on the right side of the tailstock-bed guide rail;

[0040] Calculate the restoring torque M of the tailstock-bed guideway mating surface about the X-axis. wgx :

[0041] ;

[0042] In the formula, F ilfthn The normal elastic restoring force of a single micro-protrusion on the upper half of the horizontal joint front section of the tailstock-bed guide rail; F ilrthnThe normal elastic restoring force of a single micro-protrusion on the rear half of the horizontal mating surface on the left side of the tailstock-bed guideway; F i1fsn and F i1fst These are the normal and tangential elastic restoring forces of a single micro-protrusion on the upper half of the first inclined joint on the right side of the tailstock-bed guide rail; F i1rsn and F i1rst These are the normal and tangential elastic restoring forces of a single micro-protrusion on the rear half of the first inclined mating surface on the right side of the tailstock-bed guide rail; F i2fsn and F i2fst These are the normal and tangential elastic restoring forces of a single micro-protrusion on the upper half of the front of the second inclined joint on the right side of the tailstock-bed guide rail; F i2rsn and F i2rst These represent the normal and tangential elastic restoring forces of a single micro-protrusion on the rear half of the second inclined mating surface on the right side of the tailstock-bed guideway; α is the inclination angle of the inclined mating surface on the right side; l tr and l tf These are the lengths of the rear and front halves of the tailstock guide rail, respectively; n tr and n tf These represent the number of slices in the rear and front halves of the tailstock guide rail, respectively; A ilfth and A lfth These are the nominal contact areas of the small unit in the front half of the left horizontal coupling section of the tailstock-bed guide rail, and the nominal contact area of ​​the front half of the left horizontal coupling section, respectively; A ilrth and A lrth These are the nominal contact areas of the small units in the rear half of the left horizontal mating surface of the tailstock-bed guide rail, and the nominal contact areas in the rear half of the left horizontal mating surface, respectively; A i1fs and A 1fs These are the nominal contact areas of the first inclined joint front half of the tailstock body-bed guide rail on the right side and the nominal contact area of ​​the first inclined joint front half on the right side, respectively; A i1rs and A 1rs These are the nominal contact areas of the small unit in the latter half of the first inclined mating surface on the right side of the tailstock-bed guide rail, and the nominal contact area of ​​the latter half of the first inclined mating surface on the right side, respectively; A i2fs and A 2fs These are the nominal contact areas of the small unit in the upper half of the second inclined coupling on the right side of the tailstock-bed guide rail, and the nominal contact area of ​​the upper half of the second inclined coupling on the right side, respectively; A i2rs and A 2rs These are the nominal contact areas of the small unit in the latter half of the second inclined mating surface on the right side of the tailstock-bed guide rail, and the nominal contact area of ​​the latter half of the second inclined mating surface on the right side, respectively.

[0043] Step 6: Solve and analyze the static characteristics of the CNC lathe tailstock system under no-slip conditions;

[0044] Based on the static calculation model under no-slip conditions, the static response of the tailstock is calculated and analyzed. The displacement response, rotation response and load distribution law of each joint surface of the system under different preloads and external loads are analyzed. The stiffness characteristics of the system under no-slip conditions are quantified and the direction of structural optimization is identified.

[0045] On the other hand, this application proposes an electronic device, including: one or more processors, and a memory for storing instructions, which, when executed by the one or more processors, cause the one or more processors to execute the static calculation and analysis method for the tailstock of a CNC lathe without slippage.

[0046] Thirdly, this application proposes a computer-readable storage medium storing executable instructions, which, when executed, cause a processor to perform the described static calculation and analysis method for the tailstock of a CNC lathe without slippage.

[0047] The beneficial effects of adopting the above technical solution are as follows:

[0048] This invention provides a method for static calculation and analysis of the tailstock of a CNC lathe under non-slip conditions, which has the following beneficial effects:

[0049] (1) This invention establishes a dedicated static model for the non-slip working condition where the applied load is less than the maximum static friction of the sleeve, accurately matching the load transmission path of the CNC lathe tailstock system under this working condition, overcoming the problem of poor adaptability of the general model, and making the modeling more targeted.

[0050] (2) Based on fractal contact theory and slicing method, the complex nonlinear behavior of sleeve-top cone surface and non-uniform contact characteristics of tailstock-bed guide rail joint surface are accurately characterized. The nonlinear relationship between elastic restoring force and displacement of each joint surface is quantified, which significantly improves the accuracy of static analysis under no-slip conditions.

[0051] (3) The model has a clear structure and customizable parameters. It can be flexibly adjusted according to the structural dimensions and material properties of different tailstocks. It has strong versatility and can provide a scientific basis for optimizing the preload and designing the mating surface parameters of the tailstock system of CNC lathe under non-slip working conditions. It has important engineering application value. Attached Figure Description

[0052] Figure 1 is a schematic diagram of the tailstock system structure under the non-slip condition of the present invention;

[0053] Figure 2 is a schematic diagram of the force analysis of the tailstock clamping mechanism of the present invention;

[0054] Figure 3 is a schematic diagram of the static model of the non-slip condition of the present invention;

[0055] Figure 4 is a schematic diagram of the sleeve-top cone surface structure and contact of the present invention;

[0056] Figure 5 is a schematic diagram of the structural analysis of the tailstock body-bed guide rail mating surface of the present invention;

[0057] in, Figure 5 (a) - Schematic diagram of the stress analysis of the tailstock body-bed guide rail structure. Figure 5 (b) - Schematic diagram of stress analysis of the joint surface of the tailstock body and bed guide rail. Detailed Implementation

[0058] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0059] Example 1:

[0060] On the one hand, the present invention provides a method for static calculation and analysis of the tailstock of a CNC lathe under non-slip conditions, including the following steps:

[0061] Step 1: Determine the key functional components, mating surfaces, and load transfer paths of the lathe tailstock system under non-slip conditions;

[0062] The key functional components include the tailstock center, sleeve, clamping mechanism, tailstock body, and bed guide rail;

[0063] The mating surfaces include the sleeve-center mating surface, the horizontal mating surface between the tailstock body and the left side of the bed guide rail, the first inclined mating surface between the tailstock body and the right side of the bed guide rail, and the second inclined mating surface between the tailstock body and the right side of the bed guide rail;

[0064] The load transmission path is as follows: external axial load → center → sleeve-center mating surface → sleeve → tailstock body → tailstock body-bed guide rail mating surface → bed; the clamping mechanism generates axial friction force through thread-conical surface force transmission, constraining the relative sliding of the sleeve and tailstock body.

[0065] In this embodiment, according to Figure 1 As shown in the three-dimensional structural diagram of the CNC lathe tailstock, the key functional components of the lathe tailstock under non-slip conditions are the center, sleeve, tailstock body, and clamping mechanism; the mating surfaces of the key load-bearing components include the sleeve-center mating surface and the tailstock body-bed guide rail mating surface (which includes the left horizontal mating surface and two right inclined mating surfaces); the load transmission path is: external axial load → center → sleeve-center mating surface → sleeve → tailstock body → tailstock body-bed guide rail mating surface → bed.

[0066] Step 2: Calculate the maximum axial static friction force of the sleeve under the action of the clamping handle to determine the no-slip condition; specifically, based on the thread force transmission principle and friction calculation theory, calculate the force transmission characteristics under the action of the clamping handle, including the radial clamping force and the bolt axial force:

[0067] The tailstock clamping mechanism of a CNC lathe typically uses a bolt-clamping sleeve connection for force transmission. Its core working mechanism is as follows: the operator applies operating force through the clamping handle, which is converted into the axial thrust of the bolt through the threaded pair of the bolt, and then into the axial clamping force of the clamping sleeve. Subsequently, the clamping sleeve further converts the force into the radial clamping force and axial friction force applied to the sleeve, thereby achieving reliable locking of the tailstock sleeve.

[0068] In this embodiment, as shown... Figure 2 As shown in the force analysis diagram of the clamping mechanism, the tailstock clamping mechanism of a CNC lathe typically adopts a bolt-clamping sleeve connection for force transmission. Its core working mechanism is as follows: the operator applies operating force through the clamping handle, which is converted into the axial thrust of the bolt through the threaded pair of the bolt, and then into the axial clamping force of the clamping sleeve. Subsequently, the clamping sleeve further converts the force into the radial clamping force and axial friction force applied to the sleeve, thereby achieving reliable locking of the tailstock sleeve.

[0069] Calculate the torque T generated by the clamping handle:

[0070] ;

[0071] In the formula, F sb L represents the tightening force of the clamping handle; L represents the handle length of the clamping handle.

[0072] Torque is converted into axial force on the screw through the threaded joint. The thread helix angle φ reflects the geometric transmission characteristics of the thread, while the equivalent friction angle ρ' comprehensively characterizes the frictional effect in the thread contact. Considering the influence of friction, the bolt axial force F is obtained. a The parsing expression:

[0073] ;

[0074] In the formula, d2 is the mean diameter of the thread, and ρ' is the equivalent friction angle of the thread in the clamping mechanism.

[0075] Calculate the thread helix angle φ in the clamping mechanism:

[0076] ;

[0077] In the formula, p is the bolt pitch.

[0078] Calculate the equivalent friction angle ρ' of the thread in the clamping mechanism:

[0079] ;

[0080] In the formula, f2 is the friction coefficient of the thread; β is the thread profile angle.

[0081] In the tailstock clamping mechanism, the axial force of the screw is converted into a radial force F of the clamping sleeve on the sleeve through the conical surface fit. r (Considering conical surface friction), the normal reaction force N of the conical surface satisfies axial force balance (the clamping sleeve moves downwards, and friction hinders the movement):

[0082] ;

[0083] In the formula, N is the normal force on the conical surface of the clamping sleeve; f1 is the coefficient of friction between the clamping sleeve and the conical surface of the sleeve along the axial direction of the clamping sleeve; F a θ is the axial force of the bolt under the action of the clamping handle; θ is the half angle of the conical surface between the clamping sleeve and the tailstock.

[0084] Calculate the radial clamping force F on the bushing r :

[0085] ;

[0086] In the formula, N is the normal force on the conical surface of the clamping sleeve; f1 is the coefficient of friction between the clamping sleeve and the conical surface of the sleeve along the axial direction of the clamping sleeve; F a θ represents the axial force on the bolt under the action of the clamping handle; θ is the half-angle of the conical surface between the clamping sleeve and the tailstock.

[0087] Calculate the axial frictional force f acting on the final sleeve. tw :

[0088] ;

[0089] In the formula, f3 is the coefficient of friction between the tailstock and the right side contact surface of the sleeve along the sleeve axis.

[0090] Compare the applied load with the maximum static friction force f tw When the applied load is less than the maximum static friction force, the tailstock is in a non-slip condition.

[0091] Step 3: Establish a static calculation model of the tailstock system of the CNC lathe under non-slip conditions;

[0092] The static calculation model is a nonlinear elastic restoring force coupling of the sleeve-center mating surface and the tailstock-bed guide rail mating surface. Since the sleeve does not slip, the mechanical contributions of the lead screw-nut pair and the thrust bearing are ignored. That is, the path does not transmit load when there is no relative slip. The boundary conditions of the model are defined as follows: there is no relative displacement between the sleeve and the tailstock, and each mating surface only produces elastic deformation.

[0093] The static calculation model under no-slip condition is as follows:

[0094] ;

[0095] In the formula, F dty F is the axial elastic restoring force at the sleeve-center mating surface. y0 This is the external load applied to the tailstock of the lathe at this moment; P g0d F represents the preload force exerted on the tailstock of the lathe during operation. wgy M is the elastic restoring force along the Y direction at the mating surface of the tailstock body and bed guideways; wgx M is the elastic restoring torque about the X-axis at the tailstock-bed guideway mating surface; dtwx The elastic restoring torque about the X-axis experienced by the tailstock body under the action of the axial elastic restoring force at the sleeve-center mating surface; y d This represents the axial deformation of the center point under an applied load; y w θ represents the axial deformation of the tailstock body under external load; wx The rotation angle of the tailstock body around the X-axis;

[0096] In this embodiment, as shown... Figure 3 The CNC lathe tailstock structure model is shown in the diagram. The core of the model is the nonlinear elastic restoring force coupling between the sleeve-center mating surface and the tailstock body-bed guide rail mating surface. Since the sleeve does not slip, the mechanical contributions of the lead screw-nut pair and thrust bearing are ignored (this path does not transmit load when there is no relative slippage). The boundary conditions of the model are defined as follows: there is no relative displacement between the sleeve and the tailstock body, and each mating surface only undergoes elastic deformation. According to the analysis in step 1, the load transmission path is: external axial load → center → sleeve-center mating surface → sleeve → tailstock body → tailstock body-bed guide rail mating surface → bed.

[0097] Step 4: Based on fractal contact theory, establish a calculation model for the elastic restoring force of the sleeve-center interface;

[0098] Specifically, based on fractal contact theory, the sleeve-center mating surface is modeled; the initial contact state of the mating surface under preload is calculated, namely the normal spacing and tangential deformation; when the external load causes axial displacement of the sleeve, the deformation of the mating surface is updated, and the total normal elastic restoring force and tangential elastic restoring force of the sleeve-center mating surface are calculated using fractal theory, and then the axial restoring force of the sleeve-center mating surface is synthesized.

[0099] The axial elastic restoring force F at the sleeve-center mating surface under applied load was calculated. dty :

[0100] ;

[0101] In the formula, Fnd F is the total normal elastic restoring force at the sleeve-center mating surface. td The total tangential elastic restoring force at the sleeve-center mating surface; α d The cone angle is the cone angle of the sleeve-center cone surface.

[0102] In this embodiment Figure 4 The sleeve-center mating surface is shown, with an initial preload of P applied to the contact surface. 0d Due to the preload, the normal elastic restoring force on the sleeve-center surface is P. n0d The tangential elastic restoring force is P t0d The initial axial preload on the sleeve-center mating surface can be obtained by the following formula:

[0103] ;

[0104] In the formula, α d P is the cone angle of the sleeve-center cone surface; n0d and P t0d These are the normal elastic restoring force and the tangential elastic restoring force of the sleeve-center mating surface, respectively.

[0105] pass Figure 4 The total nominal contact area A of the sleeve-center mating surface can be calculated. d :

[0106] ;

[0107] In the formula, r a r is the radius of the smaller end of the part where the center contacts the sleeve; b The radius of the larger end of the contact area between the center and the sleeve; l d The height of the part where the tip contacts the sleeve.

[0108] according to Figure 4 The analysis can calculate the normal distance s between the sleeve and the center joint surface under the action of preload. n0d :

[0109] ;

[0110] Where, δ n0d The normal deformation of the sleeve-center mating surface under preload; s cd The initial normal distance when the contact force at the sleeve-center mating surface is zero can be calculated using the following formula:

[0111] ;

[0112] In the formula, the left side is the critical cut-off area a of the micro-protrusion on the sleeve-center mating surface. 'cd In the above formula, b d =(πq d / 2) 2 , q d =0.454+0.41v d , v d and H d These represent the Poisson's ratio and hardness of the material, respectively; G d D represents the fractal roughness parameter of the mating surface of the sleeve tip; d ψ is the fractal dimension of the mating surface of the sleeve tip; d E is the expansion factor. d 'A' is the elastic modulus. d σ represents the nominal contact area of ​​the mating surfaces; γ is a scale parameter, taken as 1.5; d is the root mean square height; erfc() is the complementary error function.

[0113] according to Figure 4 The analysis shows that the tangential deformation δ on the sleeve-center mating surface under the preload can be calculated. t0d :

[0114] ;

[0115] Further calculations can yield the normal elastic restoring force P at the sleeve-center mating surface under preload. n0d and tangential elastic restoring force P t0d :

[0116] ;

[0117] In the formula, a' l0d a' represents the maximum contact area of ​​the micro-protrusions on the sleeve-center mating surface; cd This refers to the critical contact area of ​​the micro-protrusions on the sleeve-center mating surface.

[0118] By combining the above formulas, the preload P can be calculated. g0d The initial normal spacing s of the sleeve-center mating surface under action n0d and initial tangential deformation δ t0d .

[0119] Based on this, the axial elastic restoring force F at the sleeve-center joint surface under external load is further calculated. dty :

[0120] The normal elastic restoring force F at the sleeve-center mating surface under applied load was calculated. nd and tangential elastic restoring force F td :

[0121] ;

[0122] In the formula, a ' ld a is the maximum cross-sectional area of ​​the micro-protrusion on the sleeve-center mating surface under external load; ' cd The critical contact area of ​​the micro-protrusions on the sleeve-center mating surface; s nd The normal distance between the sleeve and center mating surfaces under applied load; s td This represents the tangential deformation of the sleeve-center mating surface under an applied load. The normal spacing s between the mating surfaces. nd and tangential deformation s td These can be represented as follows:

[0123] ;

[0124] ;

[0125] In the formula, α d The cone angle is the cone angle of the sleeve-center cone surface.

[0126] Finally, by combining the above equations, we can obtain the axial elastic restoring force F at the sleeve-center mating surface under external load. dty With the axial displacement y of the top d and the axial displacement y of the sleeve t The relationship between them.

[0127] Step 5: Based on fractal theory, calculate the nonlinear elastic restoring force and restoring torque of the tailstock-bed guideway mating surface;

[0128] The guide rail mating surface is discretized into multiple micro-elements using a slicing method. These micro-elements include both horizontal and inclined surfaces. The axial displacement and minute rotation that the tailstock as a whole may experience under axial load are considered. The normal and tangential deformations of each micro-element are determined based on geometric relationships. The elastic restoring force of each micro-element is calculated based on fractal contact theory. The restoring forces of all micro-elements are integrated and summed to obtain the total axial restoring force and the restoring moment about the transverse axis of the guide rail mating surface. Finally, the elastic restoring force of the tailstock body-guide rail mating surface in the Y-direction and the restoring moment about the X-axis are obtained.

[0129] Calculate the nonlinear elastic restoring force F in the Y direction at the tailstock-bed guideway mating surface. wgy :

[0130] ;

[0131] In the formula, combined Figure 5 (a) A schematic diagram of the stress analysis of the bed-tailstock guide rail structure shows that F lfthyThe elastic restoring force in the Y direction of the front half of the horizontal coupling on the left side of the tailstock-bed guide rail; F lrthy F represents the elastic restoring force in the Y direction of the rear half of the horizontal mating surface on the left side of the tailstock-bed guideway; 1fsy F represents the elastic restoring force in the Y direction of the first inclined coupling front half on the right side of the tailstock-bed guide rail; 1rsy F is the elastic restoring force in the Y direction of the rear half of the first inclined mating surface on the right side of the tailstock-bed guideway; 2fsy F represents the elastic restoring force in the Y direction of the upper half of the second inclined coupling on the right side of the tailstock-bed guide rail; 2rsy The elastic restoring force in the Y direction is the rear half of the second inclined mating surface on the right side of the tailstock-bed guide rail;

[0132] Calculate the restoring torque M of the tailstock-bed guideway mating surface about the X-axis. wgx :

[0133] ;

[0134] In the formula, F ilfthn The normal elastic restoring force of a single micro-protrusion on the upper half of the horizontal joint front section of the tailstock-bed guide rail; F ilrthn The normal elastic restoring force of a single micro-protrusion on the rear half of the horizontal mating surface on the left side of the tailstock-bed guideway; F i1fsn and F i1fst These are the normal and tangential elastic restoring forces of a single micro-protrusion on the upper half of the first inclined joint on the right side of the tailstock-bed guide rail; F i1rsn and F i1rst These are the normal and tangential elastic restoring forces of a single micro-protrusion on the rear half of the first inclined mating surface on the right side of the tailstock-bed guide rail; F i2fsn and F i2fst These are the normal and tangential elastic restoring forces of a single micro-protrusion on the upper half of the front of the second inclined joint on the right side of the tailstock-bed guide rail; F i2rsn and F i2rst These represent the normal and tangential elastic restoring forces of a single micro-protrusion on the rear half of the second inclined mating surface on the right side of the tailstock-bed guideway; α is the inclination angle of the inclined mating surface on the right side; l tr and l tf These are the lengths of the rear and front halves of the tailstock guide rail, respectively; n tr and n tf These represent the number of slices in the rear and front halves of the tailstock guide rail, respectively; A ilfth and A lfth These are the nominal contact areas of the small unit in the front half of the left horizontal coupling section of the tailstock-bed guide rail, and the nominal contact area of ​​the front half of the left horizontal coupling section, respectively; A ilrthand A lrth These are the nominal contact areas of the small units in the rear half of the left horizontal mating surface of the tailstock-bed guide rail, and the nominal contact areas in the rear half of the left horizontal mating surface, respectively; A i1fs and A 1fs These are the nominal contact areas of the first inclined joint front half of the tailstock body-bed guide rail on the right side and the nominal contact area of ​​the first inclined joint front half on the right side, respectively; A i1rs and A 1rs These are the nominal contact areas of the small unit in the latter half of the first inclined mating surface on the right side of the tailstock-bed guide rail, and the nominal contact area of ​​the latter half of the first inclined mating surface on the right side, respectively; A i2fs and A 2fs These are the nominal contact areas of the small unit in the upper half of the second inclined coupling on the right side of the tailstock-bed guide rail, and the nominal contact area of ​​the upper half of the second inclined coupling on the right side, respectively; A i2rs and A 2rs These are the nominal contact areas of the small unit in the latter half of the second inclined mating surface on the right side of the tailstock-bed guide rail, and the nominal contact area of ​​the latter half of the second inclined mating surface on the right side, respectively.

[0135] In this embodiment, since the deformation amounts on the horizontal mating surfaces are not uniform, we need to use the slicing method to divide the surface and calculate the elastic restoring force of each small unit mating surface separately. Finally, we calculate the total elastic restoring force of the entire mating surface by integrating the elastic restoring forces of each small unit mating surface. Figure 5 (b) A schematic diagram of the cross-section analysis of the bed-tailstock guideway mating surface shows that the guideway is divided into two parts, front and rear, with the middle position of the tailstock guideway as the boundary. The rear half of the tailstock guideway is further divided into n... tr Divide the first half into n small units. tf Small units.

[0136] pass Figure 5 We can determine the total nominal contact area A of the horizontal mating surface of the front half of the left tailstock guide rail. lfth and the nominal contact area A of each unit ilfth They are as follows:

[0137] ;

[0138] ;

[0139] In the formula, l tf The length of the front half of the guide rail; l bl This refers to the contact width of the horizontal mating surface of the guide rail.

[0140] The normal deformation δ of the i-th small element on the horizontal plane of the front half of the left tailstock guide rail is calculated.ilfthn and the tangential deformation δ in the Y direction ilfthy :

[0141] ;

[0142] ;

[0143] In the formula, y w θ represents the displacement of the tailstock in the Y direction; wx The angle of deflection of the tailstock around the X-axis is given.

[0144] Therefore, by using the method for calculating the elastic restoring force of the mating surface and the calculated deformation, we can obtain the normal elastic restoring force F of the i-th small unit on the horizontal plane of the front half of the left tailstock guide rail. ilfthn and tangential elastic restoring force F ilfthy :

[0145] ;

[0146] In the formula, a ' cg a is the critical cutoff area of ​​the micro-protrusion on the mating surface; ' lft v represents the maximum cross-sectional area of ​​a single micro-protrusion on the upper half of the front of the horizontal coupling on the left side of the tailstock-bed guide rail; g and H g These represent the Poisson's ratio and hardness of the material, respectively; G g D represents the fractal roughness parameter of the mating surface between the tailstock and the bed guideways. g ψ is the fractal dimension of the tailstock-bed guideway mating surface; g E is the expansion factor. g 'A' is the elastic modulus. ilfth γ is the nominal contact area of ​​a single micro-protrusion on the upper half of the horizontal joint front section on the left side of the tailstock-bed guideway; γ is a dimensional parameter, taken as 1.5; σ g is the root mean square height; erfc() is the complementary error function.

[0147] Calculate the average planar spacing z of the i-th small unit on the horizontal mating surface of the front half of the left tailstock guide rail. ilfth :

[0148] ;

[0149] In the formula, z lfth0 This indicates the initial average planar distance between the front half of the left horizontal joint of the tailstock-bed guide rail under the action of initial preload.

[0150] By summing the restoring forces of each small unit, we can obtain the total elastic restoring force F in the Y direction of the front half of the left horizontal coupling of the tailstock-bed guideway. lfthy :

[0151] ;

[0152] In the formula, A lfth The total nominal contact area of ​​the front half of the horizontal joint on the left side of the tailstock body-bed guide rail.

[0153] pass Figure 5 We can determine the total nominal contact area A of the rear half of the horizontal mating surface on the left side of the tailstock-bed guide rail. lrth and the nominal contact area A of each unit ilrth :

[0154] ;

[0155] ;

[0156] In the formula, l tr This is the length of the rear half of the guide rail.

[0157] The normal deformation δ of the i-th small element on the horizontal plane of the rear half of the left tailstock guide rail is calculated. ilrthn and the tangential deformation δ in the Y direction ilrthy :

[0158] ;

[0159] ;

[0160] By using the elastic restoring force calculation method of the bonding surface and the calculated deformation, we can obtain the normal elastic restoring force F of the i-th small element on the horizontal plane of the rear half of the left tailstock guide rail. ilrthn and tangential elastic restoring force F ilrthy :

[0161] ;

[0162] In the formula, a ' lrt The maximum cross-sectional area of ​​a single micro-protrusion on the rear half of the horizontal mating surface on the left side of the tailstock-bed guide rail.

[0163] Calculate the average planar spacing z of the i-th small unit on the horizontal mating surface of the rear half of the left tailstock guide rail. ilfth :

[0164] ;

[0165] In the formula, zlrth0 This indicates the initial average planar spacing of the rear half of the left horizontal mating surface of the tailstock-bed guideway under the action of initial preload.

[0166] By summing the restoring forces of each small unit, we can obtain the total elastic restoring force F in the Y direction for the rear half of the horizontal mating surface on the left side of the tailstock-bed guideway. lrthy :

[0167] ;

[0168] In the formula, A lrth This refers to the total nominal contact area of ​​the rear half of the horizontal mating surface on the left side of the tailstock body-bed guide rail.

[0169] pass Figure 5 The total nominal contact area A of the first inclined joint front half on the right side of the tailstock-bed guide rail can be calculated. 1fs and the nominal contact area A of each unit i1fs :

[0170] ;

[0171] ;

[0172] In the formula, l sl This refers to the contact width of the inclined mating surface of the guide rail.

[0173] The deformation δ in the Y direction of the i-th small unit in the front half of the first inclined joint on the right side of the tailstock-bed guide rail is calculated. i1fy and tangential deformation δ i1fs :

[0174] ;

[0175] ;

[0176] In the formula, s lt This represents the tangential displacement of the first inclined joint surface under the action of preload.

[0177] By using the method for calculating the elastic restoring force of the mating surface and the calculated deformation, we can obtain the normal elastic restoring force F of the i-th small unit in the front half of the first inclined mating surface on the right side of the tailstock-bed guide rail. i1fsn Tangential elastic restoring force F i1fst And the elastic restoring force F in the Y direction i1fsy :

[0178] ;

[0179] In the formula, a ' 1fsThe maximum cross-sectional area of ​​a single micro-protrusion on the upper half of the first inclined joint on the right side of the tailstock-bed guide rail;

[0180] The average planar spacing s of the i-th small unit in the front half of the first inclined joint on the right side of the tailstock body-bed guide rail ilfn The initial distance s between the inclined mating surfaces of the right tailstock guide rail and the initial preload under the action of the initial preload. ilfn0 same.

[0181] The sum of the restoring forces of each small unit yields the total elastic restoring force F in the Y direction of the first inclined connecting section on the right side of the tailstock-bed guideway. 1fsy :

[0182] ;

[0183] In the formula, A 1fs This refers to the total nominal contact area of ​​the first inclined joint front half on the right side of the tailstock body-bed guide rail.

[0184] pass Figure 5 The total nominal contact area A of the rear half of the first inclined mating surface on the right side of the tailstock-bed guideway can be calculated. 1rs and the nominal contact area A of each unit i1rs :

[0185] ;

[0186] ;

[0187] The deformation δ in the Y direction of the i-th small element in the rear half of the first inclined joint surface on the right side of the tailstock-bed guide rail is calculated. i1ry and tangential deformation δ i1rs :

[0188] ;

[0189] ;

[0190] By using the calculation method of elastic restoring force of the mating surface and the calculated deformation, we can obtain the normal elastic restoring force F of the i-th small unit in the rear half of the first inclined mating surface on the right side of the tailstock-bed guide rail. i1rsn Tangential elastic restoring force F i1rst And the elastic restoring force F in the Y direction i1rsy :

[0191] ;

[0192] In the formula, a ' 1rsThe maximum cross-sectional area of ​​a single micro-protrusion on the rear half of the first inclined mating surface on the right side of the tailstock-bed guide rail;

[0193] The average planar spacing s of the i-th small unit in the rear half of the first inclined mating surface on the right side of the tailstock body-bed guide rail ilrn The initial distance s between the inclined mating surfaces of the right tailstock guide rail and the initial preload under the action of the initial preload. ilfn0 same.

[0194] The sum of the restoring forces of each small unit yields the total elastic restoring force F in the Y direction for the rear half of the first inclined mating surface on the right side of the tailstock-bed guideway. 1rsy :

[0195] ;

[0196] In the formula, A 1rs This refers to the total nominal contact area of ​​the rear half of the first inclined mating surface on the right side of the tailstock-bed guide rail.

[0197] pass Figure 5 The total nominal contact area A of the upper half of the second inclined joint on the right side of the tailstock-bed guide rail can be calculated. 2fs and the nominal contact area A of each unit i2fs :

[0198] ;

[0199] ;

[0200] The deformation δ in the Y direction of the i-th small element in the front half of the second inclined joint on the right side of the tailstock-bed guide rail is calculated. i2fy and tangential deformation δ i2fs :

[0201] ;

[0202] ;

[0203] In the formula, s 2t This represents the tangential displacement of the second inclined joint surface under the action of preload.

[0204] By using the method for calculating the elastic restoring force of the mating surface and the calculated deformation, we can obtain the normal elastic restoring force F of the i-th small unit in the front half of the second inclined mating surface on the right side of the tailstock-bed guide rail. i2fsn Tangential elastic restoring force F i2fst And the elastic restoring force F in the Y direction i2fsy :

[0205] ;

[0206] In the formula, a ' 2fs The maximum cross-sectional area of ​​a single micro-protrusion on the upper half of the front of the second inclined joint on the right side of the tailstock-bed guide rail;

[0207] The average planar spacing s of the i-th small unit in the front half of the second inclined joint on the right side of the tailstock body-bed guide rail i2fn The initial distance s between the inclined mating surfaces of the right tailstock guide rail and the initial preload under the action of the initial preload. ilfn0 same.

[0208] The sum of the restoring forces of each small unit yields the total elastic restoring force F in the Y direction of the upper half of the second inclined coupling on the right side of the tailstock-bed guideway. 2fsy :

[0209] ;

[0210] In the formula, A 2fs This refers to the total nominal contact area of ​​the front half of the second inclined joint on the right side of the tailstock body-bed guide rail.

[0211] pass Figure 5 The total nominal contact area A of the rear half of the second inclined mating surface on the right side of the tailstock-bed guideway can be calculated. 2rs and the nominal contact area A of each unit i2rs :

[0212] ;

[0213] ;

[0214] The deformation δ in the Y direction of the i-th small element in the rear half of the second inclined joint surface on the right side of the tailstock-bed guide rail is calculated. i2ry and tangential deformation δ i2rs :

[0215] ;

[0216] ;

[0217] By calculating the elastic restoring force of the mating surface and the calculated deformation, we can obtain the normal elastic restoring force F of the i-th small unit in the rear half of the second inclined mating surface on the right side of the tailstock-bed guide rail. i2rsn Tangential elastic restoring force F i2rst And the elastic restoring force F in the Y direction i2rsy :

[0218] ;

[0219] In the formula, a ' 2rs The maximum cross-sectional area of ​​a single micro-protrusion on the rear half of the second inclined mating surface on the right side of the tailstock-bed guide rail;

[0220] The average planar spacing s of the i-th small unit in the rear half of the second inclined mating surface on the right side of the tailstock body-bed guide rail i2rn The initial distance s between the inclined mating surfaces of the right tailstock guide rail and the initial preload under the action of the initial preload. ilfn0 same.

[0221] By summing the restoring forces of each small unit, we can obtain the total elastic restoring force F in the Y direction of the rear half of the second inclined mating surface on the right side of the tailstock-bed guideway. 2rsy :

[0222] ;

[0223] In the formula, A 2rs This refers to the total nominal contact area of ​​the rear half of the second inclined mating surface on the right side of the tailstock-bed guide rail.

[0224] The total elastic restoring force F in the Y direction of the tailstock-bed guideway mating surface is calculated. wgy :

[0225] ;

[0226] The total elastic restoring torque M of the tailstock-bed guideway mating surface about the X-axis was calculated. wgx :

[0227] ;

[0228] Step 6: Solve and analyze the static characteristics of the CNC lathe tailstock system under no-slip conditions;

[0229] Based on the static calculation model under no-slip conditions, the static response of the tailstock is calculated and analyzed. The displacement response, rotation response and load distribution law of each joint surface of the system under different preloads and external loads are analyzed. The stiffness characteristics of the system under no-slip conditions are quantified and the direction of structural optimization is identified.

[0230] This embodiment specifically includes: based on the static equation of the CNC lathe tailstock system under no-slip condition established in step 3, the displacement response of the CNC lathe tailstock system under no-slip condition is calculated by Newton's iteration method to obtain the variation characteristics of the system's static response with service time.

[0231] Furthermore, by substituting different external loads and structural parameters into the static equations, the influence of different external loads and structural parameters on the static characteristics of the system is analyzed, thereby achieving a quantitative evaluation of the performance of the tailstock of the CNC lathe.

[0232] This invention, by comprehensively considering the contact behavior of key components such as the sleeve-center mating surface and the tailstock-bed guideway mating surface, establishes a quantitative relationship between the actual contact area, actual deformation, and elastic restoring force of the mating surfaces. This invention can accurately reflect the displacement response of the system during long-term operation in the static solution process. Compared with the "constant deformation model" commonly used in existing technologies, this invention has significant advantages in terms of modeling comprehensiveness and result realism. On the one hand, this invention creates a static modeling framework for tailstocks under no-slip conditions, overcoming the limitation of traditional general models that cannot reflect the true static characteristics of tailstocks under no-slip conditions. Furthermore, the static modeling method of this invention has high modularity and scalability. For tailstocks of different types and structural forms of CNC lathes, only the structural parameters need to be adjusted according to the actual working conditions to quickly construct the corresponding static model, without the need to rebuild the entire structure, greatly improving the model's versatility. Simultaneously, this invention can provide a scientific basis for CNC machine tool life prediction, accuracy maintenance, structural optimization design, maintenance cycle formulation, early degradation diagnosis, and health monitoring strategies.

[0233] In summary, the static analysis model of the CNC lathe tailstock system under non-slip conditions established in this invention not only has the advantages of comprehensive modeling, high computational efficiency, accurate results, and strong versatility, but also can truly reflect the static performance law of the CNC lathe tailstock under non-slip conditions during long-term service, providing reliable theoretical support and engineering value for improving machining accuracy, enhancing operational stability, and extending the service life of the entire machine.

[0234] Example 2:

[0235] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the described method for static calculation and analysis of the tailstock of a CNC lathe without slippage.

[0236] The electronic device can be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements a static calculation and analysis method for the tailstock of a CNC lathe under non-slip conditions, as described in the embodiment. It is understood that the electronic device may also include input / output (I / O) interfaces and communication components.

[0237] The processor is used to execute all or part of the steps in the static calculation and analysis method for the tailstock of a CNC lathe without slippage, as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in an electronic device, as well as application-related data.

[0238] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the static calculation and analysis method for the tailstock of a CNC lathe without slippage described in the above embodiments.

[0239] Example 3:

[0240] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0241] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the static calculation and analysis method for the tailstock of a CNC lathe without slippage described in the various embodiments of this application.

[0242] The aforementioned storage media include: flash memory, hard disk, multimedia card, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory, random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, server, APP (Application) application store, and other media capable of storing program verification codes. These media store computer programs, and when executed by a processor, they can implement the various steps of the aforementioned method for static calculation and analysis of the tailstock of a CNC lathe without slippage.

[0243] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0244] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0245] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of the methods disclosed herein and their equivalents, then the intent of this disclosure also includes such modifications and variations.

Claims

1. A method for static calculation and analysis of the tailstock of a CNC lathe under non-slip conditions, characterized in that, Includes the following steps: Step 1: Determine the key functional components, mating surfaces, and load transfer paths of the lathe tailstock system under non-slip conditions; Step 2: Calculate the maximum axial static friction force of the sleeve under the action of the clamping handle to determine the non-slip condition; specifically, based on the principle of thread force transmission and the theory of friction calculation, calculate the force transmission characteristics under the action of the clamping handle. The force transmission characteristics described in step 2 include radial clamping force and bolt axial force: Calculate the torque T generated by the clamping handle: ； In the formula, F sb L represents the tightening force of the clamping handle; L represents the handle length of the clamping handle. Taking into account the effect of friction, the axial force F of the bolt is obtained. a The parsing expression: ； In the formula, d2 is the pitch diameter of the thread, ρ' is the equivalent friction angle of the thread in the clamping mechanism, and φ is the thread helix angle; Calculate the radial clamping force F on the bushing r : ； In the formula, N is the normal force on the conical surface of the clamping sleeve; f1 is the coefficient of friction between the clamping sleeve and the conical surface of the sleeve along the axial direction of the clamping sleeve; F a θ represents the axial force on the bolt under the action of the clamping handle; θ is the half-angle of the conical surface between the clamping sleeve and the tailstock. Calculate the axial frictional force f acting on the final sleeve. tw : ； In the formula, f3 is the coefficient of friction between the tailstock body and the right side contact surface of the sleeve along the sleeve axis; Compare the applied load with the maximum static friction force f tw When the applied load is less than the maximum static friction force, the tailstock is in a non-slip condition. Step 3: Establish a static calculation model of the tailstock system of the CNC lathe under non-slip conditions; The static calculation model is a nonlinear elastic restoring force coupling of the sleeve-center mating surface and the tailstock-bed guide rail mating surface; the mechanical contributions of the lead screw shaft-nut pair and thrust bearing are ignored, that is, the path does not transmit load when there is no relative slippage, and the boundary conditions of the model are defined: there is no relative displacement between the sleeve and the tailstock, and each mating surface only produces elastic deformation. The static calculation model of the CNC lathe tailstock system under no-slip condition established in step 3 is as follows: ； In the formula, F dty F is the axial elastic restoring force at the sleeve-center mating surface. y0 This is the external load applied to the tailstock of the lathe at this moment; P g0d F represents the preload force exerted on the tailstock of the lathe during operation. wgy M is the elastic restoring force along the Y direction at the mating surface of the tailstock body and bed guideways; wgx M is the elastic restoring torque about the X-axis at the tailstock-bed guideway mating surface; dtwx The elastic restoring torque about the X-axis experienced by the tailstock body under the action of the axial elastic restoring force at the sleeve-center mating surface; y d This represents the axial deformation of the center point under an applied load; y w θ represents the axial deformation of the tailstock body under external load; wx The rotation angle of the tailstock body around the X-axis; Step 4: Based on fractal contact theory, establish a calculation model for the elastic restoring force of the sleeve-center interface; Specifically, based on fractal contact theory, the sleeve-center mating surface is modeled; the initial contact state of the mating surface under preload is calculated, namely the normal spacing and tangential deformation; when the external load causes axial displacement of the sleeve, the deformation of the mating surface is updated, and the total normal elastic restoring force and tangential elastic restoring force of the sleeve-center mating surface are calculated using fractal theory, and then the axial restoring force of the sleeve-center mating surface is synthesized. Step 5: Based on fractal theory, calculate the nonlinear elastic restoring force and restoring torque of the tailstock-bed guideway mating surface; The guide rail mating surface is discretized into multiple micro-units using a slicing method. The mating surface includes both horizontal and inclined surfaces. The normal and tangential deformations of each micro-unit are determined based on geometric relationships. The elastic restoring force of each micro-unit is calculated based on fractal contact theory. The restoring forces of all micro-units are integrated and summed to obtain the total axial restoring force and the restoring moment about the transverse axis of the guide rail mating surface. Finally, the elastic restoring force of the tailstock-guide rail mating surface in the Y direction and the restoring moment about the X-axis are obtained. Step 6: Solve and analyze the static characteristics of the CNC lathe tailstock system under no-slip conditions; Based on the static calculation model under no-slip conditions, the static response of the tailstock is calculated and analyzed. The displacement response, rotation response and load distribution law of each joint surface of the system under different preloads and external loads are analyzed. The stiffness characteristics of the system under no-slip conditions are quantified and the direction of structural optimization is identified.

2. The method for static calculation and analysis of the tailstock of a CNC lathe under non-slip conditions according to claim 1, characterized in that, The key functional components mentioned in step 1 include the tailstock center, sleeve, clamping mechanism, tailstock body, and bed guide rail; The mating surfaces include the sleeve-center mating surface, the horizontal mating surface between the tailstock body and the left side of the bed guide rail, the first inclined mating surface between the tailstock body and the right side of the bed guide rail, and the second inclined mating surface between the tailstock body and the right side of the bed guide rail; The load transfer path is as follows: external axial load → center → sleeve - center mating surface → sleeve → tailstock body → tailstock body - bed guide rail mating surface → bed.

3. The method for static calculation and analysis of the tailstock of a CNC lathe under non-slip working conditions according to claim 1, characterized in that, The axial elastic restoring force F at the sleeve-center mating surface calculated in step 4 under the applied load. dty : ； In the formula, F nd F is the total normal elastic restoring force at the sleeve-center mating surface. td The total tangential elastic restoring force at the sleeve-center mating surface; α d The cone angle is the cone angle of the sleeve-center cone surface.

4. The method for static calculation and analysis of the tailstock of a CNC lathe under non-slip working conditions according to claim 1, characterized in that, The nonlinear elastic restoring force F in the Y direction of the tailstock-bed guideway mating surface calculated in step 5. wgy : ； In the formula, F lfthy The elastic restoring force in the Y direction of the front half of the horizontal coupling on the left side of the tailstock-bed guide rail; F lrthy F represents the elastic restoring force in the Y direction of the rear half of the horizontal mating surface on the left side of the tailstock-bed guideway; 1fsy F represents the elastic restoring force in the Y direction of the first inclined coupling front half on the right side of the tailstock-bed guide rail; 1rsy F is the elastic restoring force in the Y direction of the rear half of the first inclined mating surface on the right side of the tailstock-bed guideway; 2fsy F represents the elastic restoring force in the Y direction of the upper half of the second inclined coupling on the right side of the tailstock-bed guide rail; 2rsy The elastic restoring force in the Y direction is the rear half of the second inclined mating surface on the right side of the tailstock-bed guide rail; Calculated restoring torque M of the tailstock-bed guideway mating surface about the X-axis wgx : ； In the formula, F ilfthn The normal elastic restoring force of a single micro-protrusion on the upper half of the horizontal joint front section of the tailstock-bed guide rail; F ilrthn The normal elastic restoring force of a single micro-protrusion on the rear half of the horizontal mating surface on the left side of the tailstock-bed guideway; F i1fsn and F i1fst These are the normal and tangential elastic restoring forces of a single micro-protrusion on the upper half of the first inclined joint on the right side of the tailstock-bed guide rail; F i1rsn and F i1rst These are the normal and tangential elastic restoring forces of a single micro-protrusion on the rear half of the first inclined mating surface on the right side of the tailstock-bed guide rail; F i2fsn and F i2fst These are the normal and tangential elastic restoring forces of a single micro-protrusion on the upper half of the front of the second inclined joint on the right side of the tailstock-bed guide rail; F i2rsn and F i2rst These represent the normal and tangential elastic restoring forces of a single micro-protrusion on the rear half of the second inclined mating surface on the right side of the tailstock-bed guideway; α is the inclination angle of the inclined mating surface on the right side; l tr and l tf These are the lengths of the rear and front halves of the tailstock guide rail, respectively; n tr and n tf These represent the number of slices in the rear and front halves of the tailstock guide rail, respectively; A ilfth and A lfth These are the nominal contact areas of the small unit in the front half of the left horizontal coupling section of the tailstock-bed guide rail, and the nominal contact area of ​​the front half of the left horizontal coupling section, respectively; A ilrth and A lrth These are the nominal contact areas of the small units in the rear half of the left horizontal mating surface of the tailstock-bed guide rail, and the nominal contact areas in the rear half of the left horizontal mating surface, respectively; A i1fs and A 1fs These are the nominal contact areas of the first inclined joint front half of the tailstock body-bed guide rail on the right side and the nominal contact area of ​​the first inclined joint front half on the right side, respectively; A i1rs and A 1rs These are the nominal contact areas of the small unit in the latter half of the first inclined mating surface on the right side of the tailstock-bed guide rail, and the nominal contact area of ​​the latter half of the first inclined mating surface on the right side, respectively; A i2fs and A 2fs These are the nominal contact areas of the small unit in the upper half of the second inclined coupling on the right side of the tailstock-bed guide rail, and the nominal contact area of ​​the upper half of the second inclined coupling on the right side, respectively; A i2rs and A 2rs These are the nominal contact areas of the small unit in the latter half of the second inclined mating surface on the right side of the tailstock-bed guide rail, and the nominal contact area of ​​the latter half of the second inclined mating surface on the right side, respectively.

5. An electronic device, characterized in that, include: One or more processors, and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to perform the static calculation and analysis method for the tailstock of a CNC lathe without slippage, as described in any one of claims 1-4.

6. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed, cause the processor to perform the static calculation and analysis method for the tailstock of a CNC lathe without slippage, as described in any one of claims 1-4.

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