A method for dynamic analysis of sliding guide systems considering wear and creep

Abstract

The application provides a sliding guide rail system dynamics analysis method considering wear and creep, and relates to the technical field of numerical control machine tool dynamics analysis. Firstly, a multi-source wear model of the angular contact ball bearing, the screw-nut pair and the sliding guide rail joint surface is established, and a creep degradation model of the bearing end cover bolt is constructed based on the Norton creep law; then, the guide rail system elastic restoring force is corrected in combination with the evolution law of the wear amount and the creep amount, a bidirectional sliding guide rail system dynamics model considering the comprehensive influence of wear and creep is constructed; the bidirectional influence between wear, creep and dynamics response is realized, and finally the dynamics evolution law of the bidirectional sliding guide rail system under the long-term service condition is obtained. The modeling process of the application is clear, has strong universality, high calculation precision, and can truly reflect the degradation process of the dynamics characteristics of the guide rail system with the service time, thereby providing an effective theoretical basis for the service life prediction, structure optimization and operation reliability improvement of the numerical control machine tool.

Description

Technical Field

[0001] This invention relates to the field of CNC machine tool dynamics analysis technology, and in particular to a dynamics analysis method for sliding guide rail systems that takes into account wear and creep. Background Technology

[0002] With the rapid development of modern manufacturing towards higher speed, higher precision, and longer lifespan, the requirements for the machining accuracy and long-term operational reliability of CNC machine tools are constantly increasing. As a key support and guiding unit for CNC machine tools, the bidirectional sliding guide system's dynamic characteristics directly determine the machine tool's motion accuracy, stability, and vibration response, playing an irreplaceable role in precision machining, automated production, and other fields.

[0003] During the long-term service of CNC machine tools, the bidirectional sliding guide system is affected by multiple factors such as friction and wear, and bolt creep, resulting in significant time-varying nonlinear characteristics of the contact forces between its components, which in turn alters the system's dynamic behavior. In this process, the mating surfaces of bearings, nuts, and guideways are the main areas of wear in the bidirectional sliding guide system, and the creep of the bearing end cap bolts also affects the system's dynamics. Therefore, in-depth research into the dynamic evolution of the bidirectional sliding guide system under the influence of wear and creep is of significant theoretical and engineering value for improving the overall performance of CNC machine tools.

[0004] In related research, the Archard wear model provides a theoretical basis for predicting rolling-slip contact wear and has been applied to wear analysis of rolling bearings, rolling guides, etc. Gu et al. studied the influence of wear on the dynamic characteristics of angular contact ball bearings based on the Archard model, finding that increased wear depth exacerbates vibration response. El-Thalji et al. established a dynamic framework for the evolution of rolling bearing wear, revealing the bidirectional coupling relationship between wear and vibration response. Regarding bolt creep research, Xie et al. numerically analyzed the influence of creep on bolt preload, but did not analyze the impact of creep on the dynamic model.

[0005] However, the existing technologies have the following shortcomings: (1) Existing dynamic modeling is mostly focused on ideal conditions or single degradation mechanisms, lacking a systematic analysis of the combined effects of bearing wear, nut wear, guide rail mating surface wear and bolt creep, making it difficult to truly reflect the dynamic behavior of the system under actual service conditions. (2) Wear analysis often treats the wear of each component independently, ignoring the combined effect of wear of multiple components and bolt creep, and does not fully consider the time accumulation effect of wear and creep, resulting in deviations between the dynamic analysis results and reality. (3) When using most finite element analysis methods, it is difficult to quantify the time-varying characteristics such as contact stiffness degradation and preload decay caused by wear and creep, resulting in insufficient computational efficiency and accuracy, and failing to provide reliable support for machine tool life prediction and maintenance strategy formulation. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a dynamic analysis method for sliding guide rail systems that considers wear and creep. This invention establishes a nonlinear dynamic model of a bidirectional sliding guide rail system by comprehensively considering the effects of bearing wear, nut wear, guide rail mating surface wear, and bolt creep on the contact forces of structural components. The modeling method of this invention is highly versatile, accurate, and possesses significant quantitative analysis capabilities. It can comprehensively reflect the time-cumulative effects of wear on multiple components and bolt creep, accurately predicting the dynamic evolution of bidirectional sliding guide rail systems during long-term service, and providing a scientific basis for structural optimization, life prediction, and maintenance strategy formulation for CNC machine tools.

[0007] On the one hand, the present invention provides a dynamic analysis method for a sliding guide system considering wear and creep, comprising the following steps:

[0008] Step 1: Identify the key functional components in the bidirectional sliding guide system of CNC machine tools that cause wear and creep, and analyze the mechanism of action of each influencing factor;

[0009] The key functional components specifically include angular contact ball bearings, lead screw and nut pairs, sliding guide rail mating surfaces, and bearing end cap fixing bolts.

[0010] The specific mechanism of action is as follows: wear affects the system dynamics by changing the deformation and mechanical properties of the contacting components, and creep indirectly changes the contact state of the bearing by attenuating the preload, ultimately changing the dynamic characteristics of the system.

[0011] Step 2: Based on Archard's wear theory, establish a wear calculation model for angular contact ball bearings;

[0012] The specific steps for establishing the wear calculation model for the angular contact ball bearing are: calculating the wear volume W of the angular contact ball bearing. b : In the formula, P b It is the elastic restoring force of the bearing under applied load; K b It is the wear coefficient of the bearing; H b It refers to the Brinell hardness of the material in the soft contact area of ​​the bearing; S b It is the sliding distance;

[0013] The contact ellipse parameters between the ball and the inner raceway are calculated using Hertzian contact theory, and the normal wear depth h of the bearing's inner raceway is calculated using the sliding distance formula. bm : In the formula, A bm This represents the wear area of ​​the inner raceway of the bearing.

[0014] Step 3: Based on Archard's wear theory, establish a wear calculation model for the lead screw and nut pair;

[0015] The specific steps for establishing the wear calculation model for the lead screw and nut pair are: calculating the wear volume W of the lead screw and nut pair. n : In the formula, P n It is the elastic restoring force of the nut under an applied load; K n H is the wear coefficient of the nut; n It is the Brinell hardness of the material in the soft contact area of ​​the nut; S n It is the sliding distance;

[0016] The wear depth of the lead screw and nut pair is specifically as follows: In the formula, A nm This refers to the wear area of ​​the raceway of the lead screw and nut pair;

[0017] Step 4: Based on Archard's wear theory, combined with fractal theory and the slicing method, calculate the wear model of the sliding guide rail mating surface.

[0018] The specific steps for establishing the wear calculation model for the sliding guide rail mating surface are: calculating the wear volume W of the sliding guide rail mating surface. g : In the formula, P g It is the elastic restoring force of the sliding guide surface under external load; K g H is the wear coefficient of the sliding guide rail mating surface; g It refers to the Brinell hardness of the material in the soft contact area of ​​the sliding guide surface; S g It is the sliding distance;

[0019] The sliding mechanism between the mating surfaces of the sliding guide rails differs from that of bearings and lead screw nut pairs, requiring the calculation of the sliding distance S between the mating surfaces. g : In the formula, n g P represents rotational speed. gd t represents the lead of the lead screw, and t represents the running time of the sliding guide.

[0020] The wear depth of the sliding guide rail mating surface is specifically as follows: In the formula, A gm This represents the wear area of ​​the sliding guide rail mating surface.

[0021] Calculate the contact area A of the sliding guide rail mating surface. gm : In the formula, erfc() represents the complementary error function; σ represents the root mean square height; A g0 Z represents the nominal contact area of ​​the mating surfaces being sought; g This represents the actual average plane spacing of the mating surfaces being investigated;

[0022] The total cumulative wear depth h is obtained by summing the wear depth of the horizontal mating surface and the left inclined surface and then adding them to the right inclined mating surface. xg : In the formula, h xg Indicates the cumulative wear depth of the horizontal mating surface of the sliding guide in the X feed direction; h xgl Indicates the cumulative wear depth of the inclined mating surface on the left side of the sliding guide in the X feed direction; h xgr α represents the cumulative wear depth of the inclined mating surface on the right side of the sliding guide in the X-feed direction; α represents the inclination angle of the inclined mating surface of the sliding guide in the X-feed direction.

[0023] The wear depth of the horizontal mating surface and the inclined mating surfaces on each side after wear, under the pre-tightening action of the pressure plate, is accumulated onto the horizontal mating surface, and the wear depth h of the horizontal mating surface after the cumulative wear of each mating surface is calculated. yg : In the formula, h ygh Indicates the cumulative wear depth of the horizontal mating surface of the sliding guide in the Y-feed direction; h yg1 This indicates the cumulative wear depth of the first inclined mating surface of the sliding guide in the Y-feed direction; h yg2 This indicates the cumulative wear depth of the second inclined mating surface of the sliding guide in the Y-feed direction; h yg3 This indicates the cumulative wear depth of the third inclined mating surface of the sliding guide in the Y-feed direction; h yg4 β represents the cumulative wear depth of the fourth inclined mating surface of the sliding guide in the Y-feed direction; β represents the inclination angle of the inclined mating surface of the sliding guide in the Y-feed direction.

[0024] Step 5: Establish a creep model for the bearing end cap bolts;

[0025] Specifically, based on Norton's creep law, the decay law of the bearing end cap bolt preload force over time is described:

[0026] ;

[0027] In the formula, F xdp0 F is the initial preload of a single bolt on the bearing end cap in the X feed direction, unaffected by creep. xdpr E is the preload force of a single bolt on the bearing end cap in the X feed direction after working for a period of time due to creep, where E is the elastic modulus and K and n are the Norton creep coefficients of the material.

[0028] Step 6: Based on Hertzian contact theory, modify the calculation model of elastic restoring force of angular contact ball bearings under the influence of wear and creep;

[0029] Specifically, this involves calculating the normal contact force Q of the left and right bearing balls under external loading and action, which is affected by wear and creep. xbL Q xbR :

[0030] ;

[0031] ;

[0032] In the formula, K xe A is the stiffness coefficient of the angular contact ball bearing. xb0 A is the center distance of curvature between the inner and outer rings without preload. xbpcL A xbpcR The inner and outer ring curvature center distances, α and α, are respectively caused by the combined effects of wear and bolt creep. x0 x represents the initial contact angle of the bearing balls under no preload. xb The displacement of the bearing section in the X-feed direction under external load; x s The displacement of the saddle under external loading and action.

[0033] The axial load F of the left and right bearings in the X feed direction is calculated. xbL F xbR :

[0034] , ;

[0035] In the formula, Z xb α represents the number of balls in the bearing. xL α xR The contact angle of the left and right bearing balls is divided into the contact angle of the left and right bearing balls under external loads, which are affected by wear and creep.

[0036] Calculate the total axial load F of the bearing section in the X feed direction under external load, which is affected by both bearing wear and bolt creep. xb : ;

[0037] Step 7: Based on Hertzian contact theory, modify the calculation model of elastic restoring force of the lead screw and nut pair under the influence of wear;

[0038] Specifically, this involves calculating the normal contact force Q of the left and right nuts under external loading and wear. xnL Q xnR :

[0039] ;

[0040] ;

[0041] In the formula, K xn Let A be the stiffness coefficient of the lead screw and nut pair. xn0 A is the center distance of the groove curvature of the lead screw nut under no preload. xnpcL A xnpcRThese represent the center distance of the groove curvature of the left and right lead screw nut pairs under the influence of wear, β. x0 γ is the initial contact angle of the balls in the lead screw and nut assembly without preload. xn x is the helix angle of the lead screw and nut assembly. w x represents the displacement of the worktable under an applied load. xs The displacement of the leadscrew in the X-feed direction under external loading and action;

[0042] The axial load F of the left and right nuts in the X direction is calculated. xnL F xnR :

[0043] , ;

[0044] In the formula, Z xn β represents the number of balls in the bearing. xL β xR The ball contact angle of the left and right nuts is affected by wear under external load;

[0045] Calculate the total axial load F of the lead screw and nut assembly in the X-feed direction affected by wear under external load. xn :

[0046] ;

[0047] Step 8: Based on fractal contact theory and the slicing method, modify the calculation model of elastic restoring force of the sliding guide joint surface under the influence of wear;

[0048] Specifically, the slicing method is used to divide the mating surface into different small units. The deformation of each small unit is not the same, and the deformation of each small unit is obtained through geometric relationships. The horizontal and inclined mating surfaces of the sliding guide in the X direction are divided into the left front half, the left rear half, the right front half, and the right rear half. The normal elastic restoring force F of the ij-th small unit of the left front half horizontal mating surface is calculated. ijlfhn Tangential elastic restoring force F ijlfhxt and F ijlfhyt :

[0049] ;

[0050] In the formula, a' xlfh a' represents the maximum contact area of ​​the micro-protrusions on the horizontal mating surface of the left front half. c z is the critical contact area of ​​the micro-protrusions on the horizontal mating surface of the left front half. ijlfh δ represents the average planar spacing of the ij-th small unit on the horizontal bonding surface of the left front half. ijlfhxtThe deformation of the horizontal joint surface of the left front half in the X direction is δ. ijlfhyt Let ψ be the deformation of the horizontal bonding surface in the Y direction of the left front half, ψ be the expansion factor, D be the fractal dimension of the bonding surface, G be the fractal roughness of the bonding surface, E be the elastic modulus, and A be the deformation of the horizontal bonding surface in the Y direction. ijlfh γ is the nominal contact area of ​​the small unit, and γ is the scale parameter, which is taken as 1.5.

[0051] Calculate the average planar spacing z of the ij-th small unit on the horizontal bonding surface of the left front half. ijlfh : ;

[0052] In the formula, δ ijlfhn It is the normal deformation of the ij-th small element on the left front half horizontal joint surface under external loading and action, z h0 It is the initial average plane spacing in the normal direction after the horizontal mating surface of the sliding guide rail in the X direction is affected by wear;

[0053] The total normal elastic restoring force F of the horizontal mating surface of the left front half of the sliding guide rail affected by wear in the X direction is obtained by integral calculation. lfhn Tangential elastic restoring force F lfhxt and F lfhyt :

[0054] ;

[0055] In the formula, n xlx This indicates that the left horizontal joint surface is divided into n xlx n xfy This indicates that the left horizontal plane combined with the front half of the plane is divided into n. xfy A lfh This represents the total nominal contact area of ​​the horizontal mating surface in the first half of the left side.

[0056] Step 9: Integrate the mechanical models of each functional component after wear and creep, and establish the dynamic equations of the bidirectional sliding guide rail system considering the effects of wear and creep;

[0057] Specifically, this includes the following dynamic equations for the worktable considering the effects of wear:

[0058] ;

[0059] In the formula, I wx I wy I wz These represent the moments of inertia of the worktable about the X, Y, and Z axes, respectively; c xgx c xgy c xgz c xgθx c xgθy and cxgθz These represent the damping coefficients of the worktable in the six directions; F xn The elastic restoring force of the lead screw and nut pair considering wear effects in the X feed direction; F wxgy With F wxgz The total elastic restoring force of the mating surface in the Y and Z directions after considering the wear effect of the sliding guide in the X feed direction; M wxgx M wxgy and M wxgz These are the total torques of the worktable around the X, Y, and Z axes after wear. wxsn It is the distance between the ball screw shaft in the X direction and the top surface of the worktable.

[0060] The dynamic equations of the ball screw system in the X-feed direction, considering the effects of wear and bearing end cap bolt creep, are as follows:

[0061] ;

[0062] In the formula, c xs and c xb These are the damping of the ball screw in the X-feed direction and the damping of the bearing, respectively; c xn It is the damping of the nut in the X feed direction; F xs and F xb These are the elastic restoring force of the ball screw in the X-feed direction and the elastic restoring force of the bearing considering the effects of wear and creep, respectively.

[0063] The saddle dynamics equations considering wear effects are as follows:

[0064] ;

[0065] In the formula, I sx I sy I sz These represent the moments of inertia of the saddle about the X, Y, and Z axes, respectively; c ygx c ygy c ygz c ygθx c ygθy and c ygθz These represent the damping of the saddle in six directions; F yn It is the elastic restoring force at the ball screw in the Y-feed direction, taking into account the wear effect; F sygx F sygz These represent the total elastic restoring forces of the Y-axis sliding guide mating surface affected by wear in the X and Z directions, respectively; F sxgy F sxgz These represent the total elastic restoring forces in the Y and Z directions of the sliding guide mating surface in the X feed direction, which are affected by wear; M sxgx Msxgy M sxgz These are the total torques around the X, Y, and Z axes under the elastic restoring force of the sliding guide joint surface in the X feed direction after wear; M sygx M sygy M sygz These represent the total torque generated around the X, Y, and Z axes under the elastic restoring force of the sliding guide joint surface in the Y feed direction after wear; sxsn The distance from the ball screw axis in the X-feed direction to the top surface of the saddle; l sysn The distance from the center of the ball screw in the Y-feed direction to the top surface of the saddle is denoted as Y.

[0066] The dynamic equations of the Y-feed ball screw system, considering wear and the creep effects of bearing end cap bolts, are as follows:

[0067] ;

[0068] In the formula, c ys and c yb These represent the damping of the ball screw and the bearing in the Y-feed direction, respectively; c yn F represents the damping of the nut in the Y-feed direction. ys and F yb These represent the elastic restoring force of the ball screw and the elastic restoring force of the bearing in the Y-feed direction after being affected by wear and creep of the bearing end cap bolts, respectively.

[0069] Step 10: Based on the established dynamic equations, calculate and analyze the dynamic response of the bidirectional sliding guide system, analyze the evolution law of the system dynamic characteristics under different wear and creep conditions, and realize the prediction of system degradation characteristics and performance evaluation.

[0070] On the other hand, this application proposes an electronic device comprising: 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 aforementioned dynamic analysis method for a sliding guide system considering wear and creep.

[0071] Thirdly, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the aforementioned dynamic analysis method for a sliding guide system considering wear and creep.

[0072] The beneficial effects of adopting the above technical solution are as follows:

[0073] This invention provides a dynamic analysis method for sliding guide rail systems that considers wear and creep, and has the following beneficial effects:

[0074] (1) This invention integrates multiple degradation factors, such as raceway wear of angular contact ball bearings, wear of lead screw-nut pairs, wear of sliding guide surfaces, and creep of bearing end cover bolt preload structures, into the same dynamic analysis framework, realizing coupled modeling of multiple failure mechanisms of mechanical systems. By constructing wear evolution models of multiple contact pairs and bolt preload creep degradation models, this invention can fully reflect the actual contact geometry evolution, force transmission path changes, and functional degradation processes that occur in the long-term service of CNC machine tool bidirectional sliding guide systems, making up for the limitations of single-factor analysis in existing technologies and making the dynamic response closer to the operating state under actual service conditions.

[0075] (2) Based on the Archard wear model and Norton's creep law, this invention quantifies the time-cumulative effect of wear and creep. By updating physical quantities such as wear depth, contact area evolution, contact angle change, and bolt creep strain, this invention can accurately characterize key time-varying characteristics of the guide rail system, such as contact stiffness attenuation and preload reduction, thereby greatly improving the accuracy and timeliness of dynamic calculations. It provides a scientific and effective technical means for the full life cycle performance evaluation and long-term operational reliability analysis of CNC machine tools.

[0076] (3) The dynamic analysis framework of this invention adopts a highly modular design, with a clear model structure and strong parameter customization capability, which facilitates its application on sliding guide rail structures of CNC machine tools of different models and structural forms. Users can freely adjust key parameters such as wear coefficient and creep coefficient according to the guide rail form, material parameters, working conditions and usage environment of the specific machine tool, which has strong versatility. At the same time, this invention can output wear depth prediction curve, preload attenuation curve and vibration response change trend, which can provide a basis for guide rail structure optimization design, preload strategy optimization, maintenance cycle formulation, health status monitoring, fault diagnosis and accuracy maintenance technology, significantly improving the long-term machining accuracy and operational stability of CNC machine tools. Attached Figure Description

[0077] Figure 1 This is a three-dimensional model of the bidirectional sliding guide rail system for CNC machine tools according to the present invention;

[0078] Figure 2 A schematic diagram showing the change in the position of the curvature center of the inner and outer rings of the bearing in the X-feed direction, considering the effects of wear and bearing end cap bolt creep, provided for an embodiment of the present invention.

[0079] Figure 3 This is a schematic diagram showing the change in the position of the center of curvature of the lead screw and nut pair groove in the X-feed direction, taking into account the wear effect, provided for an embodiment of the present invention.

[0080] Figure 4 This is a schematic diagram of wear analysis of the sliding guide surface in the X-feed direction provided in an embodiment of the present invention;

[0081] Figure 5 This is a schematic diagram of wear analysis of the sliding guide surface in the Y-feed direction provided in an embodiment of the present invention.

[0082] Figure 6 A schematic diagram of the dynamic model of a bidirectional sliding guide rail system considering the effects of wear and creep, provided for an embodiment of the present invention. Detailed Implementation

[0083] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0084] Example 1: On one hand, the present invention provides a dynamic analysis method for a sliding guide system considering wear and creep, comprising the following steps:

[0085] Step 1: Identify the key functional components in the bidirectional sliding guide system of CNC machine tools that cause wear and creep, and analyze the mechanism of action of each influencing factor;

[0086] The key functional components specifically include angular contact ball bearings, lead screw and nut pairs, sliding guide rail mating surfaces, and bearing end cap fixing bolts.

[0087] The specific mechanism of action is as follows: wear affects the system dynamics by changing the deformation and mechanical properties of the contacting components, and creep indirectly changes the contact state of the bearing by attenuating the preload, ultimately changing the dynamic characteristics of the system.

[0088] In this embodiment, the three-dimensional model of the bidirectional sliding guide rail system is as follows: Figure 1 As shown, the core components affected by wear in the system are clearly identified, including: angular contact ball bearings, lead screw and nut pairs, and sliding guide mating surfaces. The impact of bolt creep is determined to be on the bearing end cap fixing bolts, whose creep leads to a decrease in bearing preload, which in turn alters the bearing contact force. The mechanisms of action of each influencing factor are analyzed: wear affects system dynamics by changing the deformation and mechanical properties of contact components, while creep indirectly changes the bearing contact state by decreasing preload, ultimately altering the system's dynamic characteristics. Therefore, this invention incorporates wear and creep factors into the dynamic model of the bidirectional sliding guide system, analyzing their impact on the system's dynamic response.

[0089] Step 2: Based on Archard's wear theory, establish a wear calculation model for angular contact ball bearings;

[0090] The specific steps for establishing the wear calculation model for the angular contact ball bearing are: calculating the wear volume W of the angular contact ball bearing. b : ;

[0091] In the formula, P bIt is the elastic restoring force of the bearing under applied load; K b It is the wear coefficient of the bearing; H b It refers to the Brinell hardness of the material in the soft contact area of ​​the bearing; S b It is the sliding distance;

[0092] In this embodiment, the wear volume W of the angular contact ball bearings in the X and Y feed directions is calculated. xbm W ybm and the wear area A of the bearing xbm A ybm Further calculate the wear depth h of the angular contact ball bearings in the two feed directions. xgbm h ygbm The time-cumulative effect of quantifying wear depth;

[0093] Calculate the wear volume W of the angular contact ball bearings in the two feed directions. xbm W ybm : ;

[0094] In the formula, P xbm It is the elastic restoring force of the bearing in the X feed direction under external load; K xbm H is the wear coefficient of the bearing in the X feed direction; xbm It is the Brinell hardness of the soft contact area material of the X-feed direction bearing; S xbm This is the sliding distance of the bearing in the X feed direction. The subscript m represents the bearing's installation position, including the left side L and the right side R. Since the structure of the angular contact ball bearing in the Y feed direction is exactly the same as that in the X feed direction, the above formula for calculating the wear of the angular contact ball bearing in the X feed direction is completely universal when calculating the wear of the angular contact ball bearing in the Y feed direction. When calculating, the subscript letter x in the above formula needs to be replaced with y to indicate the Y feed direction.

[0095] The contact ellipse parameters between the ball and the inner raceway are calculated using Hertzian contact theory, and the normal wear depth h of the bearing's inner raceway is calculated using the sliding distance formula. bm : In the formula, A bm This represents the wear area of ​​the inner raceway of the bearing.

[0096] In this embodiment, for angular contact ball bearings, the wear of the bearing mainly occurs on the inner raceway during actual operation. The sliding distance S between the bearing balls and the inner raceway in the X feed direction is calculated. xbm : ;

[0097] In the formula, V xbm ω represents the linear velocity of the contact point between the bearing's inner raceway and the balls about the bearing's central axis in the X-feed direction; xbmR represents the rotational angular velocity of the bearing balls in the X feed direction; xbim This indicates the distance between the contact point between the bearing ball and the inner raceway in the X feed direction and the center of the ball; S xbim This indicates the running distance of the inner raceway of the bearing in the X feed direction.

[0098] Then, the normal wear depth h of the inner raceway of the bearing in the X feed direction is calculated. xbm : In the formula, A xbm The wear area of ​​the inner raceway of the X-feed direction bearing.

[0099] Calculate the wear area A of the inner raceway of the bearing in the X feed direction. xbm A xbm =2e xbm πd xim In the formula, e xbm The major semi-axis of the ellipse in which the bearing balls contact the inner raceway in the X-feed direction; d xim The diameter of the bottom of the inner raceway groove of the X-feed direction bearing.

[0100] The semi-major axis e of the contact ellipse between the bearing balls and the inner raceway in the X-feed direction is calculated using Hertz contact theory. xbm： ;

[0101] Due to the external load, the bearing contact force P in the X feed direction is... xbm It is a function of time t, therefore the wear depth is a cumulative calculation process, taking the contact force P at a certain moment as an example. xbm The wear depth h at a certain moment is calculated by substituting it into the wear model. xbm When calculating the wear depth for the next second, the wear depth for the previous second needs to be added, and this process continues until the final wear time is calculated, ultimately yielding the total wear depth h for that wear time. xgbm .

[0102] Step 3: Based on Archard's wear theory, establish a wear calculation model for the lead screw and nut pair;

[0103] The specific steps for establishing the wear calculation model for the lead screw and nut pair are: calculating the wear volume W of the lead screw and nut pair. n : ;

[0104] In the formula, P n It is the elastic restoring force of the nut under an applied load; K n H is the wear coefficient of the nut; n It is the Brinell hardness of the material in the soft contact area of ​​the nut; S n It is the sliding distance;

[0105] In this embodiment, the wear volume W of the lead screw and nut pair in the X and Y feed directions is calculated. xnm W ynm and the wear area A of the lead screw and nut pair xnm A ynm Further calculate the wear depth h of the lead screw and nut pair in both feed directions. xgnm h ygnm The time-cumulative effect of quantifying wear depth;

[0106] Calculate the wear volume W of the lead screw and nut pair in both feed directions. xnm W ynm : ;

[0107] In the formula, P xnm It is the elastic restoring force of the lead screw and nut pair in the X-feed direction under the action of an external load; K xnm It is the wear coefficient of the lead screw and nut pair in the X feed direction; H xnm It is the Brinell hardness of the material in the soft contact area of ​​the lead screw and nut pair in the X feed direction; S xnm This represents the sliding distance of the lead screw and nut pair in the X feed direction. The subscript m represents the installation position of the lead screw and nut pair, including the left side L and the right side R. Since the structure of the lead screw and nut pair in the Y feed direction is exactly the same as that in the X feed direction, the above formula for calculating the wear of the lead screw and nut pair in the X feed direction is completely applicable when calculating the wear of the lead screw and nut pair in the Y feed direction. When calculating, the subscript letter x in the above formula needs to be replaced with y to indicate the Y feed direction.

[0108] The wear depth of the lead screw and nut pair is specifically as follows: In the formula, A nm This refers to the wear area of ​​the raceway of the lead screw and nut pair;

[0109] Calculate the sliding distance S between the balls of the lead screw nut pair and the lead screw raceway in the X feed direction. xnm :

[0110] ;

[0111] In the formula, V xnm ω represents the linear velocity of the contact point between the screw raceway and the ball bearings in the X-feed direction, rotating about the central axis of the screw-nut pair; xnm R represents the rotational angular velocity of the balls in the leadscrew nut pair in the X feed direction; xnim S represents the distance between the contact point of the ball between the lead screw nut pair and the lead screw raceway in the X feed direction, and the center of the ball; xnim This indicates the travel distance of the lead screw raceway in the X feed direction.

[0112] Then, the normal wear depth h of the lead screw and nut pair in the X feed direction is calculated. xnm : In the formula, A xnm The wear area of ​​the raceway of the lead screw nut pair in the X feed direction.

[0113] Calculate the wear area A of the raceway of the lead screw and nut pair in the X feed direction. xnm A xnm =2e xnm πd xsm In the formula, e xnm Let d be the major semi-axis of the ellipse in which the balls of the leadscrew nut pair contact the leadscrew raceway in the X-feed direction; xsm The diameter of the bottom of the raceway groove in the lead screw nut pair in the X feed direction.

[0114] The semi-major axis e of the contact ellipse between the ball bearings and the screw raceway in the X-feed direction is calculated using Hertz contact theory. xnm : ;

[0115] Due to the contact force P of the lead screw and nut pair in the X feed direction under the action of external load. xnm It is a function of time t, therefore the wear depth is a cumulative calculation process, taking the contact force P at a certain moment as an example. xnm The wear depth h at a certain moment is calculated by substituting it into the wear model. xnm When calculating the wear depth for the next second, the wear depth for the previous second needs to be added, and this process continues until the final wear time is calculated, ultimately yielding the total wear depth h for that wear time. xgnm Similarly, the calculation model for the lead screw and nut pair in the Y-feed direction is the same as that in the X-feed direction. When calculating, the subscript x in the formula needs to be replaced with y to represent the Y-feed direction.

[0116] Step 4: Based on Archard's wear theory, combined with fractal theory and the slicing method, calculate the wear model of the sliding guide rail mating surface.

[0117] The specific steps for establishing the wear calculation model for the sliding guide rail mating surface are: calculating the wear volume W of the sliding guide rail mating surface. g : ;

[0118] In the formula, P g It is the elastic restoring force of the sliding guide surface under external load; K g H is the wear coefficient of the sliding guide rail mating surface; g It refers to the Brinell hardness of the material in the soft contact area of ​​the sliding guide surface; S g It is the sliding distance;

[0119] In this embodiment, the wear volume W is calculated based on Archard's wear theory, combined with fractal theory and the slicing method. xgm W ygmand the wear area A in the X and Y feed directions xgm A ygm Further calculate the wear depth h of the sliding guide mating surfaces in the two feed directions. xggm h yggm The time-cumulative effect of quantified wear depth is calculated. In the calculation formula of the wear model for all sliding guide surfaces, the subscript m represents the position of the mating surface (for sliding guides in the X feed direction: m is replaced by h to represent a horizontal mating surface; l to represent a left inclined mating surface; and r to represent a right inclined mating surface. For sliding guides in the Y feed direction: m is replaced by h to represent a horizontal mating surface; l to represent the first inclined mating surface; 2 to represent the second inclined mating surface; 3 to represent the third inclined mating surface; and 4 to represent the fourth inclined mating surface).

[0120] Calculate the wear volume W of the mating surface of the sliding guides in the two feed directions. xgm W ygm : ;

[0121] In the formula, P xgm It is the elastic restoring force of the sliding guide joint surface in the X-feed direction under external load; K xgm H is the wear coefficient of the sliding guide mating surface in the X feed direction; xgm It is the Brinell hardness of the soft contact area material of the sliding guide mating surface in the X-feed direction; S xgm This refers to the sliding distance of the sliding guide mating surface in the X-feed direction. When calculating the wear of the sliding guide mating surface in the Y-feed direction, the above formula for calculating the wear of the sliding guide mating surface in the X-feed direction is completely universal. However, in the calculation, the subscript letter 'x' in the above formula needs to be replaced with 'y' to represent the Y-feed direction.

[0122] The sliding mechanism between the mating surfaces of the sliding guide rails differs from that of bearings and lead screw nut pairs, requiring the calculation of the sliding distance S between the mating surfaces. g : In the formula, n g P represents rotational speed (r / min). gd t represents the lead of the lead screw, and t represents the running time of the sliding guide.

[0123] The wear depth of the sliding guide rail mating surface is specifically as follows: In the formula, A gm This represents the wear area of ​​the sliding guide rail mating surface.

[0124] Calculate the contact area A of the sliding guide rail mating surface. gm : ;

[0125] In the formula, erfc() represents the complementary error function; σ represents the root mean square height; A g0 Z represents the nominal contact area of ​​the mating surfaces being sought; g This represents the actual average plane spacing of the mating surfaces being investigated;

[0126] The wear depth of the sliding guide surface in the X-feed direction is also related to the wear volume W of the guide. xgm Proportional to the wear area A of the guide rail xgm Inversely proportional. When calculating the wear volume of the guide rail, the subscript 'b' in the above formula should be replaced with 'g', representing the sliding guide rail mating surface. Where P... xgm This represents the contact force of the calculated mating surface of the sliding guide in the X-feed direction. In the calculation, this force is the elastic restoring force of the mating surface under vibration. The sliding method between the sliding guide mating surfaces differs from that of bearings and lead screw nut pairs, but the sliding distance between the mating surfaces of each sliding guide in the same feed direction is the same. The sliding distance S between the mating surfaces of the sliding guides in the X-feed direction is calculated. xg : ;

[0127] In the formula, n xg Indicates the screw speed (r / min) in the X feed direction; P xgd represents the lead of the leadscrew in the X feed direction; t represents the travel time of the sliding guide. The sliding distance S between the mating surfaces of the sliding guides in the Y feed direction is calculated. yg When calculating the sliding distance between the sliding guide surfaces in the X-feed direction, replace the subscript x with y in the formula to indicate the Y-feed direction.

[0128] Calculate the actual wear area A of the horizontal mating surface, the left inclined mating surface, and the right inclined mating surface of the sliding guide in the X feed direction. xgh A xgl And A xgr :

[0129] ;

[0130] ;

[0131] ;

[0132] In the formula, A ijlfh A ijlrh A ijrfh A ijrrh These are the wear areas of the horizontal mating surfaces of the left front half, left rear half, right front half, and right rear half of the sliding guide rail in the X direction, respectively; A kjlfs A kjlrsThese are the wear areas of the inclined mating surfaces of the left front half and the left rear half of the inclined mating surfaces of the sliding guide rail in the X direction, respectively; A kjrfs A kjrrs These represent the wear areas of the inclined mating surfaces of the front half and rear half of the right side of the sliding guide rail in the X direction, respectively; z ijlfh z ijlrh z ijrfh z ijrrh These are the actual average planar spacings of the horizontal mating surfaces of the left front half, left rear half, right front half, and right rear half of the sliding guide rail in the X direction, respectively; s kjlfs s kjlrs These are the actual average planar distances between the inclined mating surfaces of the left front half and the left rear half of the inclined mating surfaces of the sliding guide rail in the X direction, respectively; s kjrfs s kjrrs These are the actual average plane spacings of the inclined joint surfaces of the right front half and the right rear half of the inclined joint surfaces of the sliding guide in the X direction, respectively. The specific calculations are detailed in the study of Song et al. (Song G, Li C, Tan Z, et al. Nonlinear dynamics analysis of bi-directional sliding guide system[J]. International Journal of Mechanical Sciences, 2025: 110462.).

[0133] Calculate the contact force P of the horizontal mating surface, the left inclined mating surface, and the right inclined mating surface of the sliding guide in the X-feed direction under the action of an external load. xgh P xgl and P xgr :

[0134] ;

[0135] ;

[0136] ;

[0137] In the formula, F lfhn F lrhn F rfhn F rrhn These represent the contact forces (F) on the front half of the left side horizontal mating surface, the rear half of the left side horizontal mating surface, the front half of the right side horizontal mating surface, and the rear half of the right side horizontal mating surface of the sliding guide rail in the X direction under an applied load; lfsn F lrsnThese represent the contact forces of the inclined mating surfaces of the left front half and the left rear half of the inclined mating surfaces of the sliding guide rail in the X direction under an applied load; F rfsn F rrsn These represent the contact forces of the inclined joint surfaces of the right front half and the right rear half of the sliding guide rail in the X direction under external load. Detailed calculations are described in the study by Song et al.

[0138] Since wear depth primarily affects the magnitude of preload, the preload of the sliding guide in the X-feed direction is mainly applied by the wedge-shaped strips on the inclined mating surface. According to... Figure 4 As can be seen from the provided embodiments of the present invention, the wear depth of the horizontal mating surface and the left inclined surface after wear, under the pre-tightening action of the wedge strip, is accumulated on the right inclined mating surface. Therefore, the wear depth of the horizontal mating surface and the left inclined surface need to be added together and calculated on the right inclined mating surface to obtain the total cumulative wear depth h. xg : ;

[0139] Calculate the actual wear area A of the horizontal mating surface of the sliding guide in the Y-feed direction and the 1st to 4th inclined mating surfaces. ygh A yg1 A yg2 A yg3 And A yg4 :

[0140] ;

[0141] ;

[0142] ;

[0143] ;

[0144] ;

[0145] In the formula, A gmlfh A gmlrh A gmrfh A gmrrh These are the wear areas of the horizontal mating surfaces of the left front half, left rear half, right front half, and right rear half of the sliding guide rail in the Y direction, respectively; A tm1fs A tm1rs These are the wear areas of the first half of the inclined mating surface and the second half of the inclined mating surface of the Y-direction sliding guide, respectively; A tm2fs A tm2rs These are the wear areas of the front half and rear half of the second inclined mating surface of the Y-direction sliding guide, respectively; A tm3fsA tm3rs These are the wear areas of the front half and rear half of the third inclined mating surface of the Y-direction sliding guide, respectively; A tm4fs A tm4rs These are the wear areas of the front half and rear half of the fourth inclined mating surface of the Y-direction sliding guide, respectively; z gmlfh z gmlrh z gmrfh z gmrrh These are the actual average planar spacings of the horizontal mating surfaces of the left front half, left rear half, right front half, and right rear half of the sliding guide rail in the Y direction, respectively; s tm1fn s tm1rn These are the actual average planar distances of the first half of the inclined mating surface and the second half of the inclined mating surface of the Y-direction sliding guide, respectively; s tm2fn s tm2rn These are the actual average planar distances of the front half and rear half of the second inclined mating surface of the Y-direction sliding guide rail, respectively; s tm3fn s tm3rn These are the actual average planar distances of the front half and rear half of the third inclined mating surface of the Y-direction sliding guide rail, respectively; s tm4fn s tm4rn These are the actual average planar distances of the front half and rear half of the fourth inclined joint surface of the Y-direction sliding guide, respectively. The specific calculations are detailed in the study by Song et al.

[0146] Calculate the contact force P of the horizontal mating surface of the sliding guide rail in the Y-feed direction and the 1st to 4th inclined mating surfaces under the action of an external load. ygh P yg1 P yg2 P yg3 and P yg4 :

[0147] ;

[0148] ;

[0149] ;

[0150] ;

[0151] ;

[0152] In the formula, F ylfhn F ylrhn F yrfhn F yrrhnThese represent the contact forces (F) of the left front half, left rear half, right front half, and right rear half horizontal mating surfaces of the Y-direction sliding guide under an applied load; 1fsn F 1rsn These represent the contact forces, respectively, of the front half and rear half of the first inclined mating surface of the Y-direction sliding guide under an applied load; F 2fsn F 2rsn These represent the contact forces, respectively, of the front half and rear half of the second inclined mating surface of the Y-direction sliding guide under an applied load; F 3fsn F 3rsn These represent the contact forces, respectively, of the front half and rear half of the third inclined mating surface of the Y-direction sliding guide under an applied load; F 4fsn F 4rsn The contact forces of the front half of the fourth inclined mating surface and the rear half of the fourth inclined mating surface of the Y-direction sliding guide under the action of external load are respectively calculated in detail in the study of Song et al.

[0153] Since wear depth primarily affects the magnitude of preload, the preload of the sliding guide in the Y-feed direction is mainly applied by the pressure plate of the horizontal mating surface. Therefore, according to... Figure 5 As can be seen from the provided embodiments of the present invention, the wear depth of the horizontal mating surface and each side inclined mating surface after wear is accumulated on the horizontal mating surface under the pre-tightening action of the pressure plate, and the wear depth h of the horizontal mating surface after the wear of each mating surface is calculated. yg : ;

[0154] Step 5: Establish a creep model for the bearing end cap bolts;

[0155] Specifically, based on Norton's creep law, the decay law of the bearing end cap bolt preload force over time is described: ;

[0156] In the formula, F xdp0 F is the initial preload of a single bolt on the bearing end cap in the X feed direction, unaffected by creep. xdpr E is the preload force of a single bolt on the bearing end cap in the X feed direction after working for a period of time due to creep, where E is the elastic modulus and K and n are the Norton creep coefficients of the material.

[0157] According to the force analysis, the bearing end cap is fixed by four bolts. Therefore, the preload F acting on the bearing after creep is... xbp =4F xdpr The decay law of preload force over time after creep of a single bolt on the bearing end cap in the Y-feed direction, and the preload force F on the bearing after creep.ybp Similar to the X feed direction, the subscript x needs to be replaced with y during calculation to indicate the Y feed direction.

[0158] Step 6: Based on Hertzian contact theory, modify the calculation model of elastic restoring force of angular contact ball bearings under the influence of wear and creep;

[0159] Specifically, this involves calculating the normal contact force Q of the left and right bearing balls under external loading and action, which is affected by wear and creep. xbL Q xbR :

[0160] ;

[0161] ;

[0162] In the formula, K xe A is the stiffness coefficient of the angular contact ball bearing. xb0 A is the center distance of curvature between the inner and outer rings without preload. xbpcL A xbpcR The inner and outer ring curvature center distances, α and α, are respectively caused by the combined effects of wear and bolt creep. x0 x represents the initial contact angle of the bearing balls under no preload. xb The displacement of the bearing section in the X-feed direction under external load; x s The displacement of the saddle under external loading and action.

[0163] The axial load F of the left and right bearings in the X feed direction is calculated. xbL F xbR : , In the formula, Z xb α represents the number of balls in the bearing. xL α xR The contact angle of the left and right bearing balls is divided into the contact angle of the left and right bearing balls under external loads, which are affected by wear and creep.

[0164] Calculate the total axial load F of the bearing section in the X feed direction under external load, which is affected by both bearing wear and bolt creep. xb : ;

[0165] In this embodiment, according to Figure 2 According to the provided embodiments of the present invention, the initial distance between the centers of curvature of the inner and outer rings of an angular contact ball bearing when not subjected to preload is A. xb0 Under the action of preload, the center distance of the inner and outer ring curvatures changes from A when there is no preload. xb0 Change to A xbp They can be represented in the following forms:

[0166] ;

[0167] ;

[0168] In the formula, r xi and r xo These are the radii of curvature of the inner and outer rings of the angular contact ball bearing, D. xb δ is the diameter of the bearing balls. xbp f represents the initial deformation of the bearing balls under preload. x0 Let f be the curvature ratio of the raceway. x0 =1.04.

[0169] Calculate the preload F xbp Under the action of the bearing balls, the elastic contact force Q xbp : ;

[0170] In the formula, Z xb This represents the number of balls in a single bearing.

[0171] The bearing is primarily preloaded by the bearing end cap, which in turn is preloaded by bolts. After a period of operation, bolts undergo creep, which alters the bolt force and consequently affects the bearing preload F. xbp The bearing preload F changes. xbp The change will affect the center distance A when the bearing is subjected to preload. xbp The preload F changes due to creep. xbp It is obtained in step 5.

[0172] Calculate the preload F xbp Normal deformation δ of bearing balls in the X-feed direction under action xbp : ;

[0173] In the formula, K xe This represents the normal deformation coefficient of the angular contact ball bearing in the X direction.

[0174] according to Figure 2 As can be seen from the provided embodiments of the present invention, due to the accumulation of wear, the center distance between the left and right bearings during operation is respectively reduced by A. xbp For A xbpcL and A xbpcR Under axial load, the deformation of the bearing in the X direction is x. xb The center distance between the centers of curvature of the inner and outer rings of the left and right bearings is respectively determined by A. xbpcL and A xbpcR They are respectively changed to A xbL A xbR The contact angle is from the initial contact angle αx0 They are respectively transformed into α xL α xR .

[0175] Calculate the center distance A of the left and right bearings after wear. xbpcL and A xbpcR : , ;

[0176] When the system is subjected to an external load, the bearing will deform in the axial direction. xb Calculate the center distance A between the centers of curvature of the inner and outer rings of the left and right bearings in the X feed direction under the applied load, considering the effects of wear and creep. xbL and A xbR :

[0177] ;

[0178] ;

[0179] Calculate the normal contact deformation δ of the left and right bearing balls in the X feed direction under applied load, considering the effects of wear and creep. xbL and δ xbR :

[0180] ;

[0181] ;

[0182] Calculate the normal contact force Q of the left and right bearing balls in the X feed direction under applied load, considering wear and creep effects. xbL and Q xbR :

[0183] ;

[0184] ;

[0185] Calculate the contact angle α of the bearing balls in the left and right bearing directions in the X feed direction under applied load, considering the effects of wear and creep. xL and α xR :

[0186] ;

[0187] ;

[0188] Calculate the axial load F of the left and right bearings in the X feed direction under applied load, considering the effects of wear and creep. xbL and F xbR :

[0189] , ;

[0190] Calculate the total axial load F of the bearing section in the X feed direction under applied load, considering wear and creep effects. xb : ;

[0191] The calculation method for bearing elastic restoring force in the Y-feed direction, considering the effects of wear and creep, is the same as that in the X-feed direction. In the specific calculation, all the letters x in the X-feed direction calculation formula are replaced with y to represent the Y-feed direction.

[0192] Step 7: Based on Hertzian contact theory, modify the calculation model of elastic restoring force of the lead screw and nut pair under the influence of wear;

[0193] Specifically, this involves calculating the normal contact force Q of the left and right nuts under external loading and wear. xnL Q xnR :

[0194] ;

[0195] ;

[0196] In the formula, K xn Let A be the stiffness coefficient of the lead screw and nut pair. xn0 A is the center distance of the groove curvature of the lead screw nut under no preload. xnpcL A xnpcR These represent the center distance of the groove curvature of the left and right lead screw nut pairs under the influence of wear, β. x0 γ is the initial contact angle of the balls in the lead screw and nut assembly without preload. xn x is the helix angle of the lead screw and nut assembly. w x represents the displacement of the worktable under an applied load. xs The displacement of the leadscrew in the X-feed direction under external loading and action;

[0197] The axial load F of the left and right nuts in the X direction is calculated. xnL F xnR : , ;

[0198] In the formula, Z xn β represents the number of balls in the bearing. xL β xR The ball contact angle of the left and right nuts is affected by wear under external load;

[0199] Calculate the total axial load F of the lead screw and nut assembly in the X-feed direction affected by wear under external load. xn : ;

[0200] In this embodiment, the calculation model for the elastic restoring force of the lead screw and nut pair in the X and Y feed directions under the influence of wear is modified; according to Figure 3 As can be seen from the provided embodiments of the present invention, the initial distance between the center of curvature of the nut and the lead screw groove when not subjected to preload is A. xn0 Under preload, the center distance of the curvature of the nut and screw grooves changes from A when there is no preload. xn0 Change to A xnp Among them, A xn0 It can be represented in the following form: ;

[0201] In the formula, r xs r xn These are the radii of curvature of the screw groove and the nut groove that contact the balls, respectively, d xn f is the diameter of the ball bearing at the nut. xn It is the ratio of the radius of curvature of the groove to the curvature of the sphere.

[0202] Calculate the ball bearing under initial preload F xnp The initial deformation δ generated under action xnp : , ;

[0203] In the formula, K xn Q is the contact deformation coefficient at the nut in the X direction. xnp Z is the contact elastic restoring force along the normal direction under the initial preload. xn β represents the number of balls at the nut. x0 It is the contact angle between the ball and the screw groove, or the contact angle between the ball and the nut groove.

[0204] Calculate the center distance A between the centers of curvature of the screw groove and the nut groove under preload in the nut system. xnp : ;

[0205] according to Figure 3 As can be seen from the provided embodiments of the present invention, when the nut assembly is subjected to axial load, the position of the center of curvature changes relatively. The distance between the centers of curvature when no preload is applied is A. xn0 When the preload is applied, the center distance of curvature is A. xnp The center distances of the left and right nuts affected by wear during operation are A and A, respectively. xnpcL and A xnpcR Under axial load, the center distance between the centers of curvature of the left and right nuts changes from A. xnpcL and A xnpcR They are respectively changed to A xnL AxnR The contact angles become β respectively. xL β xR The center distance A of the left and right nuts in the X feed direction after wear is calculated. xnpcL and A xnpcR : , ;

[0206] The center distance A of the left and right nuts after wear under external load is calculated. xnL and A xnR :

[0207] ;

[0208] ;

[0209] The deformation δ of the left and right nut balls along the normal direction in the X feed direction after wear under external load and wear was calculated. xnL and δ xnR :

[0210] ;

[0211] ;

[0212] The contact angle β of the left and right nuts in the X-feed direction after wear under external load and wear effect is calculated. xL and β xR :

[0213] ;

[0214] ;

[0215] The normal contact force Q of the left and right nut balls in the X feed direction after wear is calculated under the action of external load. xnL and Q xnR :

[0216] ;

[0217] ;

[0218] The axial load F of the left and right nuts in the X feed direction after wear under the applied load and the influence of wear is calculated. xnL and F xnR :

[0219] , ;

[0220] The total axial load F of the lead screw and nut assembly in the X feed direction after wear under external load is calculated. xn : ;

[0221] The calculation method for the elastic restoring force of the lead screw and nut pair considering wear in the Y-feed direction is the same as that in the X-feed direction. In the specific calculation, all the letters x in the X-feed direction calculation formula are replaced with y to represent the Y-feed direction.

[0222] Step 8: Based on fractal contact theory and the slicing method, modify the calculation model of elastic restoring force of the sliding guide joint surface under the influence of wear;

[0223] Because the sliding guide rail in the X direction is subjected to external forces F in the X, Y, and Z directions. x0 F y0 F z0 and external torque M x0 M y0 M z0 The effect of the X-direction guide rail causes a corresponding deflection angle between the horizontal and inclined mating surfaces. Therefore, the mating surface is divided into different small units using a slicing method. The deformation of each small unit is different, and the deformation of each small unit is obtained through geometric relationships. The horizontal and inclined mating surfaces of the X-direction sliding guide rail are divided into the left front half, left rear half, right front half, and right rear half. The calculation method for the elastic restoring force of each part is similar. The normal elastic restoring force F of the ij-th small unit of the left front half horizontal mating surface is calculated. ijlfhn Tangential elastic restoring force F ijlfhxt and F ijlfhyt :

[0224] ;

[0225] In the formula, a' xlfh a' represents the maximum contact area of ​​the micro-protrusions on the horizontal mating surface of the left front half. c z is the critical contact area of ​​the micro-protrusions on the horizontal mating surface of the left front half. ijlfh δ represents the average planar spacing of the ij-th small unit on the horizontal bonding surface of the left front half. ijlfhxt The deformation of the horizontal joint surface of the left front half in the X direction is δ. ijlfhyt Let ψ be the deformation of the horizontal bonding surface in the Y direction of the left front half, ψ be the expansion factor, D be the fractal dimension of the bonding surface, G be the fractal roughness of the bonding surface, E be the elastic modulus, and A be the deformation of the horizontal bonding surface in the Y direction. ijlfh γ is the nominal contact area of ​​the small unit, and γ is the scale parameter, which is taken as 1.5.

[0226] Calculate the average planar spacing z of the ij-th small unit on the horizontal bonding surface of the left front half. ijlfh: ;

[0227] In the formula, δ ijlfhn It is the normal deformation of the ij-th small element on the left front half horizontal joint surface under external loading and action, z h0 It is the initial average plane spacing in the normal direction of the horizontal mating surface of the X-direction sliding guide after wear; the comprehensive wear depth h of the inclined mating surface on the right side of the X-feed direction sliding guide after wear. xg The average planar spacing s0 of the inclined mating surfaces after wear was calculated: ;

[0228] Substituting the average planar spacing s0 after wear into the formula for calculating the preload of the lower mating surface and the initial spacing of the mating surface, the preload F of the right-side inclined mating surface after wear is obtained. grsm Due to the principle of structural force balance, the preload on the inclined and horizontal mating surfaces on both sides is the same. The sum of the vertical components of the preload on the inclined mating surfaces after wear is the total preload on the horizontal mating surface after wear. Substituting the total preload on the horizontal mating surface after wear into the formula for calculating the preload on the lower mating surface and the initial distance between the mating surfaces, we can obtain the initial average planar distance z of the horizontal mating surfaces after wear. h0 Finally, the initial average plane spacing of the worn horizontal and inclined mating surfaces is substituted into the formula for calculating the elastic restoring force of the sliding guide system in the X-feed direction to obtain the elastic restoring force of each mating surface of the sliding guide in the X-feed direction after wear.

[0229] Formulas for calculating the preload and initial spacing of the mating surfaces:

[0230] ;

[0231] ;

[0232] In the formula, F g0 A represents the initial preload of the mating surface. g0 This represents the nominal contact area of ​​the mating surfaces being calculated. When F... g0 Given the given information, the initial average planar spacing z of the mating surfaces can be obtained by simultaneously solving the two equations. g0 Given the initial average planar spacing z of the mating surfaces after wear, the solution is to determine this. g0 When the two equations are combined, the initial preload F of the mating surface can be obtained. g0 Given the initial preload F at the mating surface after wear, the calculation is as follows: g0 When the two equations are combined, the initial average planar spacing z of the mating surfaces can be obtained. g0 This step updates the initial average planar spacing of each mating surface after wear.

[0233] The total normal elastic restoring force F of the horizontal mating surface of the left front half of the sliding guide rail affected by wear in the X direction is obtained by integral calculation. lfhn Tangential elastic restoring force F lfhxt and F lfhyt :

[0234] ;

[0235] In the formula, n xlx This indicates that the left horizontal joint surface is divided into n xlx n xfy This indicates that the left horizontal plane combined with the front half of the plane is divided into n. xfy A lfh This represents the total nominal contact area of ​​the horizontal mating surface in the left front half. The calculation method for other mating surfaces of the sliding guide in the X-feed direction is the same as that for the horizontal mating surface in the left front half of the sliding guide in the X-feed direction. Specific expressions are detailed in the research of Song et al. During calculation, simply substitute the initial average plane spacing of each mating surface after wear to obtain the elastic restoring force of each mating surface of the sliding guide in the X-feed direction after wear. The calculation method for the elastic restoring force of the sliding guide mating surface affected by wear in the Y-feed direction is the same as that in the X-feed direction. The wear depth h of the horizontal mating surface in the Y-feed direction after wear is also shown. yg The average planar spacing z of the horizontal mating surfaces in the Y-feed direction after wear can be obtained. s0 : ;

[0236] The average planar spacing z after wear s0 Substituting these values ​​into the formulas for calculating the preload and initial spacing of the mating surfaces, the preload of the horizontal mating surface after wear is obtained. Similarly, the preload of the 1st to 4th inclined mating surfaces is calculated based on force analysis. Substituting the preload of each inclined mating surface after wear into the formulas for calculating the preload and initial spacing of the mating surfaces, the initial average planar spacing of each inclined mating surface after wear is obtained. Finally, substituting the initial average planar spacing of the horizontal and inclined mating surfaces of the Y-feed direction sliding guide after wear into the formulas for calculating the elastic restoring force of each mating surface, the elastic restoring force of each mating surface of the Y-feed direction sliding guide after wear is obtained.

[0237] Step 9: Integrate the mechanical models of each functional component after wear and creep, and establish the dynamic equations of the bidirectional sliding guide rail system considering the effects of wear and creep;

[0238] like Figure 6 As shown, the dynamic equations of the worktable considering the effect of wear are as follows:

[0239] ;

[0240] In the formula, I wx I wy I wz These represent the moments of inertia of the worktable about the X, Y, and Z axes, respectively; c xgx c xgy c xgz c xgθx c xgθy and c xgθz These represent the damping coefficients of the worktable in the six directions; F xn The elastic restoring force of the lead screw and nut pair considering wear effects in the X feed direction; F wxgy With F wxgz The total elastic restoring force of the mating surface in the Y and Z directions after considering the wear effect of the sliding guide in the X feed direction; M wxgx M wxgy and M wxgz These are the total torques of the worktable around the X, Y, and Z axes after wear. wxsn It is the distance between the ball screw shaft in the X direction and the top surface of the worktable.

[0241] The dynamic equations of the ball screw system in the X-feed direction, considering the effects of wear and bearing end cap bolt creep, are as follows:

[0242] ;

[0243] In the formula, c xs and c xb These are the damping of the ball screw in the X-feed direction and the damping of the bearing, respectively; c xn It is the damping of the nut in the X feed direction; F xs and F xb These are the elastic restoring force of the ball screw in the X-feed direction and the elastic restoring force of the bearing considering the effects of wear and creep, respectively.

[0244] The saddle dynamics equations considering wear effects are as follows:

[0245] ;

[0246] In the formula, I sx I sy I sz These represent the moments of inertia of the saddle about the X, Y, and Z axes, respectively; c ygx c ygy c ygz c ygθx c ygθy and c ygθz These represent the damping of the saddle in six directions; F yn It is the elastic restoring force at the ball screw in the Y-feed direction, taking into account the wear effect; F sygx Fsygz These represent the total elastic restoring forces of the Y-axis sliding guide mating surface affected by wear in the X and Z directions, respectively; F sxgy F sxgz These represent the total elastic restoring forces in the Y and Z directions of the sliding guide mating surface in the X feed direction, which are affected by wear; M sxgx M sxgy M sxgz These are the total torques around the X, Y, and Z axes under the elastic restoring force of the sliding guide joint surface in the X feed direction after wear; M sygx M sygy M sygz These represent the total torque generated around the X, Y, and Z axes under the elastic restoring force of the sliding guide joint surface in the Y feed direction after wear; sxsn The distance from the ball screw axis in the X-feed direction to the top surface of the saddle; l sysn The distance from the center of the ball screw in the Y-feed direction to the top surface of the saddle is denoted as Y.

[0247] The dynamic equations of the Y-feed ball screw system, considering wear and the creep effects of bearing end cap bolts, are as follows:

[0248] ;

[0249] In the formula, c ys and c yb These represent the damping of the ball screw and the bearing in the Y-feed direction, respectively; c yn F represents the damping of the nut in the Y-feed direction. ys and F yb These represent the elastic restoring force of the ball screw and the elastic restoring force of the bearing in the Y-feed direction after being affected by wear and creep of the bearing end cap bolts, respectively.

[0250] Step 10: Based on the established dynamic equations, calculate and analyze the dynamic response of the bidirectional sliding guide system, analyze the evolution law of the system dynamic characteristics under different wear and creep conditions, and realize the prediction of system degradation characteristics and performance evaluation.

[0251] This embodiment specifically includes: based on the dynamic equation of the bidirectional sliding guide rail system considering wear and creep effects established in step 9, the displacement response, velocity response, acceleration response and vibration amplitude variation law of the bidirectional sliding guide rail system under given working conditions are calculated by numerical integration or time domain solution method, so as to obtain the variation characteristics of the system dynamic response with service time.

[0252] Furthermore, by substituting the parameters corresponding to different degrees of wear and bolt creep into the aforementioned dynamic equations, the influence of wear and creep on the equivalent stiffness and dynamic stability of the system is analyzed, enabling a quantitative assessment of the dynamic performance degradation process of the bidirectional sliding guide system. By comparing the dynamic response results under different operating times and preload conditions, the trends of vibration amplification, stiffness degradation, and accuracy decline in the long-term service of the CNC machine tool sliding guide system can be predicted, thus providing a basis for guide structure optimization design, preload adjustment strategy formulation, maintenance cycle determination, and life assessment.

[0253] This invention comprehensively considers the wear evolution of multiple key components, such as angular contact ball bearings, lead screw-nut pairs, and sliding guide surfaces, and further introduces the preload attenuation effect caused by bearing end cap bolt creep. Under a unified dynamic modeling framework, it achieves deep coupling of wear, creep, and dynamics. By establishing quantitative relationships between component wear, contact angle changes, actual contact area, contact force degradation, and bolt creep, this invention can accurately reflect the dynamic, nonlinear, and degradation properties of the system during long-term operation in the dynamic solution process. Compared with the commonly used "constant stiffness model" or "single component wear analysis" in existing technologies, this invention has significant advantages in terms of modeling comprehensiveness and result realism. On the one hand, this invention creates a unified modeling framework for multi-source wear and creep, overcoming the limitations of traditional methods that only analyze single influencing factors and are difficult to reflect the true degradation mechanism. Furthermore, the dynamic modeling method of this invention has high modularity and scalability. For sliding guideways of CNC machine tools of different types and structural forms, the corresponding dynamic models can be quickly constructed simply by adjusting the wear coefficient, creep coefficient, contact material parameters, and guideway form according to the actual working conditions, without the need to rebuild the entire structure, thus greatly improving the versatility of the model. 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.

[0254] In summary, the dynamic analysis model of the bidirectional sliding guide system considering the effects of wear and creep established in this invention not only has the advantages of comprehensive modeling, high computational efficiency, accurate results, and strong versatility, but also can realistically and dynamically reflect the performance degradation law of CNC machine tools during long-term service. It provides reliable theoretical support and engineering value for improving the machining accuracy of machine tools, enhancing operational stability, and extending the service life of the entire machine.

[0255] Example 2: This example 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 perform: based on the established dynamic equations of the sliding guide rail system considering the effects of wear and creep, numerically solve and iteratively calculate the bidirectional sliding guide rail system, obtain the displacement response, velocity response, acceleration response and vibration characteristics of the system under different operating times, different wear degrees and different bolt creep states, and analyze the evolution characteristics of the dynamic performance of the sliding guide rail system with service time.

[0256] The electronic device is mainly a computer, including a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements a dynamic analysis method for a sliding guide system considering wear and creep, as described in the embodiment.

[0257] The processor is used to execute all or part of the steps in the dynamic analysis method for a sliding guide system considering wear and creep, 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.

[0258] 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 sliding guide system dynamic analysis method considering wear and creep described in the above embodiments.

[0259] Example 3: This example 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.

[0260] 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 dynamic analysis method for a sliding guide system considering wear and creep described in various embodiments of this application.

[0261] 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, on which computer programs are stored. When the computer program is executed by a processor, it can implement the various steps of the aforementioned dynamic analysis method for a sliding guide system considering wear and creep.

[0262] 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.

[0263] 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.

[0264] 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 dynamic analysis method for a sliding guide system considering wear and creep, characterized in that, Includes the following steps: Step 1: Identify the key functional components in the bidirectional sliding guide system of CNC machine tools that cause wear and creep, and analyze the mechanism of action of each influencing factor; Step 2: Based on Archard's wear theory, establish a wear calculation model for angular contact ball bearings; Step 3: Based on Archard's wear theory, establish a wear calculation model for the lead screw and nut pair; Step 4: Based on Arcard wear theory, and combined with fractal theory and slicing method, establish a wear calculation model for the sliding guide rail mating surface; Step 5: Establish a creep model for the bearing end cap bolts; Step 6: Based on Hertzian contact theory, modify the calculation model of elastic restoring force of angular contact ball bearings under the influence of wear and creep; Step 7: Based on Hertzian contact theory, modify the calculation model of elastic restoring force of the lead screw and nut pair under the influence of wear; Step 8: Based on fractal contact theory and the slicing method, modify the calculation model of elastic restoring force of the sliding guide joint surface under the influence of wear; Step 9: Integrate the mechanical models of the functional components in Steps 2-8 after they are affected by wear and creep, and establish the dynamic equations of the bidirectional sliding guide rail system that take into account the effects of wear and creep; Step 9 specifically includes the following: The dynamic equations of the worktable considering the effects of wear are as follows: ； In the formula, I wx I wy I wz These represent the moments of inertia of the worktable about the X, Y, and Z axes, respectively; c xgx c xgy c xgz c xgθx c xgθy and c xgθz These represent the damping coefficients of the worktable in the six directions; F xn The elastic restoring force of the lead screw and nut pair considering wear effects in the X feed direction; F wxgy With F wxgz The total elastic restoring force of the mating surface in the Y and Z directions after considering the wear effect of the sliding guide in the X feed direction; M wxgx M wxgy and M wxgz These are the total torques of the worktable around the X, Y, and Z axes after wear. wxsn It is the distance between the ball screw shaft in the X direction and the top surface of the worktable; The dynamic equations of the ball screw system in the X-feed direction, considering the effects of wear and bearing end cap bolt creep, are as follows: ； In the formula, c xs and c xb These are the damping of the ball screw in the X-feed direction and the damping of the bearing, respectively; c xn It is the damping of the nut in the X feed direction; F xs and F xb These are the elastic restoring force of the ball screw in the X-feed direction and the elastic restoring force of the bearing considering the effects of wear and creep, respectively. The saddle dynamics equations considering wear effects are as follows: ； In the formula, I sx I sy I sz These represent the moments of inertia of the saddle about the X, Y, and Z axes, respectively; c ygx c ygy c ygz c ygθx c ygθy and c ygθz These represent the damping of the saddle in six directions; F yn It is the elastic restoring force at the ball screw in the Y-feed direction, taking into account the wear effect; F sygx F sygz These represent the total elastic restoring forces of the Y-axis sliding guide mating surface affected by wear in the X and Z directions, respectively; F sxgy F sxgz These represent the total elastic restoring forces in the Y and Z directions of the sliding guide mating surface in the X feed direction, which are affected by wear; M sxgx M sxgy M sxgz These are the total torques around the X, Y, and Z axes under the elastic restoring force of the sliding guide joint surface in the X feed direction after wear; M sygx M sygy M sygz These represent the total torque generated around the X, Y, and Z axes under the elastic restoring force of the sliding guide joint surface in the Y feed direction after wear; sxsn The distance from the ball screw axis in the X-feed direction to the top surface of the saddle; l sysn The distance from the center of the ball screw in the Y-feed direction to the top surface of the saddle; The dynamic equations of the Y-feed ball screw system, considering wear and the creep effects of bearing end cap bolts, are as follows: ； In the formula, c ys and c yb These represent the damping of the ball screw and the bearing in the Y-feed direction, respectively; c yn F represents the damping of the nut in the Y-feed direction. ys and F yb These represent the elastic restoring force of the ball screw and the elastic restoring force of the bearing after being affected by wear and creep of the bearing end cap bolts in the Y feed direction, respectively. Step 10: Based on the established dynamic equations, calculate and analyze the dynamic response of the bidirectional sliding guide system, analyze the evolution law of the system dynamic characteristics under different wear and creep conditions, and realize the prediction of system degradation characteristics and performance evaluation.

2. The dynamic analysis method for a sliding guide rail system considering wear and creep according to claim 1, characterized in that, The key functional components mentioned in step 1 specifically include angular contact ball bearings, lead screw and nut pairs, sliding guide rail mating surfaces, and bearing end cap fixing bolts; The specific mechanism of action is as follows: wear affects the system dynamics by changing the deformation and mechanical properties of the contacting components, and creep indirectly changes the contact state of the bearing by attenuating the preload, ultimately changing the dynamic characteristics of the system.

3. The dynamic analysis method for a sliding guide rail system considering wear and creep according to claim 1, characterized in that, Step 2, establishing the wear calculation model for the angular contact ball bearing, specifically involves calculating the wear volume W of the angular contact ball bearing. b : In the formula, P b It is the elastic restoring force of the bearing under applied load; K b It is the wear coefficient of the bearing; H b It refers to the Brinell hardness of the material in the soft contact area of ​​the bearing; S b It is the sliding distance; The contact ellipse parameters between the ball and the inner raceway are calculated using Hertzian contact theory, and the normal wear depth h of the bearing's inner raceway is calculated using the sliding distance formula. bm : In the formula, A bm This represents the wear area of ​​the inner raceway of the bearing.

4. The dynamic analysis method for a sliding guide rail system considering wear and creep according to claim 3, characterized in that, Step 3, establishing the wear calculation model for the lead screw and nut pair, specifically involves calculating the wear volume W of the lead screw and nut pair. n : In the formula, P n It is the elastic restoring force of the nut under an applied load; K n H is the wear coefficient of the nut; n It is the Brinell hardness of the material in the soft contact area of ​​the nut; S n It is the sliding distance; The wear depth of the lead screw and nut pair is specifically as follows: In the formula, A nm This represents the wear area of ​​the raceway of the lead screw and nut pair.

5. The dynamic analysis method for a sliding guide rail system considering wear and creep according to claim 4, characterized in that, Step 4, establishing the wear calculation model for the sliding guide rail mating surface, specifically involves calculating the wear volume W of the sliding guide rail mating surface. g : In the formula, P g It is the elastic restoring force of the sliding guide surface under external load; K g H is the wear coefficient of the sliding guide rail mating surface; g It refers to the Brinell hardness of the material in the soft contact area of ​​the sliding guide surface; S g It is the sliding distance; The sliding mechanism between the mating surfaces of the sliding guide rails differs from that of bearings and lead screw nut pairs, requiring the calculation of the sliding distance S between the mating surfaces. g : In the formula, n g P represents rotational speed. gd t represents the lead of the lead screw, and t represents the running time of the sliding guide. The wear depth of the sliding guide rail mating surface is specifically as follows: In the formula, A gm This represents the wear area of ​​the sliding guide rail mating surface; Calculate the contact area A of the sliding guide rail mating surface. gm : In the formula, erfc() represents the complementary error function; σ represents the root mean square height; A g0 z represents the nominal contact area of ​​the mating surfaces being calculated; g This represents the actual average plane spacing of the mating surfaces being investigated; The total cumulative wear depth h is obtained by summing the wear depth of the horizontal mating surface and the left inclined surface and then adding them to the right inclined mating surface. xg : In the formula, h xg Indicates the cumulative wear depth of the horizontal mating surface of the sliding guide in the X feed direction; h xgl Indicates the cumulative wear depth of the inclined mating surface on the left side of the sliding guide in the X feed direction; h xgr α represents the cumulative wear depth of the inclined mating surface on the right side of the sliding guide in the X-feed direction; α represents the inclination angle of the inclined mating surface of the sliding guide in the X-feed direction. The wear depth of the horizontal mating surface and the inclined mating surfaces on each side after wear, under the pre-tightening action of the pressure plate, is accumulated onto the horizontal mating surface, and the wear depth h of the horizontal mating surface after the cumulative wear of each mating surface is calculated. yg : In the formula, h ygh Indicates the cumulative wear depth of the horizontal mating surface of the sliding guide in the Y-feed direction; h yg1 This indicates the cumulative wear depth of the first inclined mating surface of the sliding guide in the Y-feed direction; h yg2 This indicates the cumulative wear depth of the second inclined mating surface of the sliding guide in the Y-feed direction; h yg3 This indicates the cumulative wear depth of the third inclined mating surface of the sliding guide in the Y-feed direction; h yg4 β represents the cumulative wear depth of the fourth inclined mating surface of the sliding guide in the Y-feed direction; β represents the inclination angle of the inclined mating surface of the sliding guide in the Y-feed direction.

6. The dynamic analysis method for a sliding guide rail system considering wear and creep according to claim 5, characterized in that, Step 5 specifically involves describing the decay law of the bearing end cap bolt preload over time, based on Norton's creep law: ； In the formula, F xdp0 F is the initial preload of a single bolt on the bearing end cap in the X feed direction, unaffected by creep. xdpr E is the preload force of a single bolt on the bearing end cap in the X feed direction after it has been in operation for a period of time due to creep. K and n are the creep Norton coefficients of the material.

7. The dynamic analysis method for a sliding guide rail system considering wear and creep according to claim 6, characterized in that, Step 6 specifically involves calculating the normal contact force Q of the left and right bearing balls affected by wear and creep under external loading and action. xbL Q xbR : ； ； In the formula, K xe A is the stiffness coefficient of the angular contact ball bearing. xb0 A is the center distance of curvature between the inner and outer rings without preload. xbpcL A xbpcR The inner and outer ring curvature center distances, α and α, are respectively caused by the combined effects of wear and bolt creep. x0 x represents the initial contact angle of the bearing balls under no preload. xb x represents the displacement of the bearing section in the X-feed direction under an applied load; s The displacement of the saddle under external loading and action; The axial load F of the left and right bearings in the X feed direction is calculated. xbL F xbR : ； ； In the formula, Z xb α represents the number of balls in the bearing. xL α xR The contact angles of the left and right bearing balls are divided into those affected by wear and creep under external loads. Calculate the total axial load F of the bearing section in the X feed direction under external load, which is affected by both bearing wear and bolt creep. xb : .

8. The dynamic analysis method for a sliding guide rail system considering wear and creep according to claim 7, characterized in that, Step 7 specifically involves calculating the normal contact force Q of the left and right nuts under external loading and wear. xnL Q xnR : ； ； In the formula, K xn Let A be the stiffness coefficient of the lead screw and nut pair. xn0 A is the center distance of the groove curvature of the lead screw nut under no preload. xnpcL A xnpcR These represent the center distance of the groove curvature of the left and right lead screw nut pairs under the influence of wear, β. x0 γ is the initial contact angle of the balls in the lead screw and nut assembly without preload. xn x is the helix angle of the lead screw and nut assembly. w x represents the displacement of the worktable under an applied load. xs The displacement of the leadscrew in the X-feed direction under external loading and action; The axial load F of the left and right nuts in the X direction is calculated. xnL F xnR : ； ； In the formula, Z xn β represents the number of balls in the bearing. xL β xR The ball contact angle of the left and right nuts is affected by wear under external load; Calculate the total axial load F of the lead screw and nut assembly in the X-feed direction affected by wear under external load. xn : 。 9. A dynamic analysis method for a sliding guide rail system considering wear and creep according to claim 8, characterized in that, Step 8 specifically uses the slicing method to divide the mating surface into different small units. The deformation of each small unit is not the same, and the deformation of each small unit is obtained through geometric relationships. The horizontal and inclined mating surfaces of the sliding guide rail in the X direction are divided into the left front half, left rear half, right front half, and right rear half. The normal elastic restoring force F of the ij-th small unit of the left front half horizontal mating surface is calculated. ijlfhn Tangential elastic restoring force F ijlfhxt and F ijlfhyt : ； In the formula, a' xlfh a' represents the maximum contact area of ​​the micro-protrusions on the horizontal mating surface of the left front half. c z is the critical contact area of ​​the micro-protrusions on the horizontal mating surface of the left front half. ijlfh δ represents the average planar spacing of the ij-th small unit on the horizontal bonding surface of the left front half. ijlfhxt The deformation of the horizontal joint surface of the left front half in the X direction is δ. ijlfhyt Let ψ be the deformation of the horizontal bonding surface in the Y direction of the left front half, ψ be the expansion factor, D be the fractal dimension of the bonding surface, G be the fractal roughness of the bonding surface, E be the elastic modulus, and A be the deformation of the horizontal bonding surface in the Y direction. ijlfh γ is the nominal contact area of ​​the small unit, and γ is the scale parameter, which is taken as 1.5; Calculate the average planar spacing z of the ij-th small unit on the horizontal bonding surface of the left front half. ijlfh : ; In the formula, δ ijlfhn It is the normal deformation of the ij-th small element on the left front half horizontal joint surface under external loading and action, z h0 It is the initial average plane spacing in the normal direction after the horizontal mating surface of the sliding guide rail in the X direction is affected by wear; The total normal elastic restoring force F of the horizontal mating surface of the left front half of the sliding guide rail affected by wear in the X direction is obtained by integral calculation. lfhn Tangential elastic restoring force F lfhxt and F lfhyt : ； In the formula, n xlx This indicates that the left horizontal joint surface is divided into n xlx n xfy This indicates that the left horizontal plane combined with the front half of the plane is divided into n. xfy A lfh This represents the total nominal contact area of ​​the horizontal mating surface in the first half of the left side.

Images