Spindle rotation accuracy prediction method based on grease deterioration

Abstract

This invention discloses a method for predicting spindle rotational accuracy based on grease degradation, belonging to the field of spindle accuracy prediction technology. The method includes: determining the equivalent shear rate and equivalent temperature required for accelerated grease degradation testing based on the actual operating conditions of the spindle bearing; conducting accelerated degradation tests on the grease under these conditions; sampling at preset intervals to obtain grease samples at different degradation stages; measuring the oil separation rate and cone penetration of each grease sample to establish a time-varying model; and conducting friction tests on the grease samples at different degradation stages under preset normal load, entrainment speed, and sliding-rolling ratio conditions to establish a dynamic friction coefficient model. This invention achieves quantitative characterization of the dynamic degradation law of grease performance by accelerating the measurement of oil separation rate and cone penetration changes of grease under the coupled effects of temperature, shear rate, and time, and establishing a time-varying model.

Description

Technical Field

[0001] This invention relates to the field of spindle accuracy prediction technology, and in particular to a method for predicting spindle rotation accuracy based on grease deterioration. Background Technology

[0002] The long-term accuracy retention of CNC machine tool spindles is a core characteristic of their service performance and reliability. Current research on long-term accuracy degradation modeling of CNC machine tool spindles mainly relies on the framework of macroscopic mechanical wear theory, predicting accuracy evolution trends by simulating the material loss process of key kinematic pairs. Existing modeling methods typically simplify lubrication conditions, assuming the lubrication state to be constant or using empirical static parameters. In fact, the physicochemical properties of grease, the core medium of spindle bearings, such as oil separation rate and cone penetration, undergo significant dynamic performance degradation under the coupled effects of long-term temperature field, shear force field, and time history. This degradation alters the lubrication mechanism and contact characteristics of the friction interface, affecting the wear process and dynamic response of the system.

[0003] However, existing methods have some shortcomings. Most of them fail to effectively integrate the dynamic degradation process of grease, lack experimental methods to systematically quantify the dynamic decay law of grease performance parameters with temperature, shear rate and time, and lack a general modeling method to effectively correlate time-varying degradation parameters with tribological interface behavior. Most studies still regard the influence of grease as a fixed background condition or approximate it with constants, and fail to construct a physical correlation chain from "evolution of medium performance" to "change of interface friction characteristics" and then to "deterioration of system accuracy". Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a method for predicting spindle rotation accuracy based on grease degradation, which solves the problems of difficulty in quantifying dynamic grease degradation and the lack of correlation chains for spindle accuracy decline.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: This invention provides a method for predicting spindle rotation accuracy based on grease degradation, comprising: determining the equivalent shear rate and equivalent temperature required for accelerated grease degradation testing according to the actual operating conditions of the spindle bearing; conducting accelerated degradation testing on the grease under the equivalent shear rate and equivalent temperature conditions; sampling at a preset cycle to obtain grease samples at different degradation stages; measuring the oil separation rate and cone penetration of each grease sample to establish a time-varying model; conducting friction tests on grease samples at different degradation stages under preset normal load, entrainment speed, and sliding-rolling ratio conditions to establish a dynamic friction coefficient model; embedding the time-varying model and the dynamic friction coefficient model into the bearing mechanical model and wear model to calculate the normal contact load, contact stress, and wear depth of each rolling element under different speed and load conditions, and updating the actual clearance according to the wear depth; calculating the spindle rotation center offset and radial runout caused by a single bearing based on the updated actual clearance, and calculating the total radial runout of the spindle shaft end in combination with the geometric relationship of the front and rear bearing supports.

[0007] As a preferred embodiment of the spindle rotation accuracy prediction method based on grease degradation described in this invention, the specific steps for determining the equivalent shear rate and equivalent temperature required for the accelerated degradation test of the grease based on the actual operating conditions of the spindle bearing are as follows: The characteristic shear rate is calculated based on the pitch circle diameter, operating speed, and bearing clearance of the spindle bearing. Based on the acceleration factor of the grease deterioration acceleration test, the characteristic shear rate is converted into the equivalent shear rate of the external grease deterioration acceleration test device. Obtain the stable temperature of the bearing outer ring after the spindle reaches thermal equilibrium; A bearing thermal network model is established. The steady-state temperature is substituted into the bearing thermal network model as a known value to solve for the steady-state ambient temperature inside the cavity. The steady-state ambient temperature inside the cavity is then used as the equivalent temperature.

[0008] As a preferred embodiment of the spindle rotation accuracy prediction method based on grease deterioration described in this invention, the bearing thermal network model is established based on the thermal balance equation and includes at least the bearing housing outer surface nodes, bearing outer ring body nodes, outer ring raceway contact surface nodes, rolling element nodes, inner ring raceway contact surface nodes, bearing inner ring body nodes, journal nodes, and oil-gas mixture nodes in the cavity. The thermal resistance between thermal nodes in the bearing thermal network model includes at least one of conductive thermal resistance, convective thermal resistance, radiative thermal resistance, and contact thermal resistance.

[0009] As a preferred embodiment of the spindle rotation accuracy prediction method based on grease deterioration described in this invention, the specific steps for establishing the time-varying model are as follows: Oil separation rate and cone penetration were measured for grease samples at different stages of deterioration. A time-varying basic model was established with the cumulative shear-thermal aging time as the independent variable, and a time-varying model was then established based on the time-varying basic model. The time-varying fundamental model is a saturated model that includes an exponential decay term. The overall degradation rate in the time-varying fundamental model is determined by both shear and thermal effects.

[0010] As a preferred embodiment of the spindle rotation accuracy prediction method based on grease degradation described in this invention, the comprehensive degradation rate refers to the coupling function of equivalent shear rate and equivalent temperature. The overall degradation rate is constructed based on the shear power law and Arrhenius's law.

[0011] As a preferred embodiment of the spindle rotation accuracy prediction method based on grease deterioration described in this invention, the specific steps of conducting the friction test are as follows: The ball-disc friction tester was used for testing, with the friction pair consisting of bearing steel balls and bearing steel discs. Repeated tests were conducted for each set of normal load, entrainment speed, and slip-roll ratio conditions. After the friction coefficient reaches a steady state, the average friction coefficient in the steady state is taken as the steady-state friction coefficient under the corresponding working condition.

[0012] As a preferred embodiment of the spindle rotation accuracy prediction method based on grease deterioration described in this invention, the specific steps for establishing the dynamic friction coefficient model are as follows: The Gupta four-parameter exponential model serves as the basic constitutive framework; By introducing oil separation rate and cone penetration as state variables into the model parameters, the model parameters are expanded from constants to functions of oil separation rate, cone penetration, roll ratio, and normal load. Based on the steady-state friction coefficient, the parameters of the basic constitutive framework are fitted to establish a dynamic friction coefficient model.

[0013] As a preferred embodiment of the spindle rotation accuracy prediction method based on grease deterioration described in this invention, the specific steps of embedding the time-varying model and dynamic friction coefficient model into the bearing mechanical model and wear model are as follows: Based on discrete time, the oil separation rate and cone penetration at each discrete time are determined using a time-varying model. Based on the actual clearance, and combined with the force balance and deformation compatibility equations of the bearing, the normal contact load of each rolling element is solved. Based on Hertzian contact theory, the contact stress is calculated from the normal contact load, and the slip-roll ratio of each rolling element is calculated based on the bearing kinematics. Substituting the oil separation rate, cone penetration, normal load, and sliding-rolling ratio at each discrete time into the dynamic friction coefficient model, we obtain the friction coefficient under the corresponding working conditions. By combining the friction coefficient, contact stress, and the micro-slip distance between the rolling element and the raceway in the contact area, the wear depth is calculated using a wear model, and the actual clearance is updated based on the wear depth. The actual clearance refers to the sum of the bearing's initial clearance at the factory and the total wear depth.

[0014] As a preferred embodiment of the spindle rotation accuracy prediction method based on grease deterioration described in this invention, the specific steps for calculating the spindle rotation center offset and the radial runout caused by a single bearing based on the updated actual clearance are as follows: Calculate the spindle center offset when the major axis of the bearing inner ring is in the vertical direction, and the spindle center offset when the minor axis of the bearing inner ring is in the vertical direction, respectively. Calculate the radial runout caused by a single bearing based on the offset between the two spindle centers.

[0015] As a preferred embodiment of the spindle rotation accuracy prediction method based on grease deterioration described in this invention, the calculation of the total radial runout of the spindle end in combination with the geometric relationship of the front and rear bearing supports refers to calculating the total radial runout of the spindle end based on the geometric relationship of the front and rear bearing supports and the radial runout of the front and rear bearings respectively.

[0016] The beneficial effects of this invention are as follows: By accelerating the experimental determination of the changes in oil separation rate and cone penetration of grease under the coupled effects of temperature, shear rate, and time, and establishing a time-varying model, a quantitative characterization of the dynamic decay law of grease performance is achieved. This compensates for the shortcomings of existing methods in systematically characterizing the grease degradation process, and improves the authenticity and reliability of spindle rotation accuracy prediction. By coupling the grease degradation state with the dynamic friction coefficient model, bearing mechanics model, and wear model, a predictive relationship is established from the evolution of grease performance to the total radial runout of the spindle end. This compensates for the lack of physical correlation chains in existing methods, improves the physical authenticity and interpretability of spindle rotation accuracy prediction, and provides a quantitative basis for grease selection, maintenance cycle optimization, and spindle reliability design. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a method for predicting spindle rotation accuracy based on grease deterioration.

[0019] Figure 2 This is a simplified diagram of bearing heat transfer.

[0020] Figure 3 This is a flowchart for obtaining parameters and constructing a model for grease degradation.

[0021] Figure 4 This is a flowchart for calculating the total radial runout. Detailed Implementation

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0023] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0024] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0025] Reference Figures 1-4 This is one embodiment of the present invention, which provides a method for predicting spindle rotation accuracy based on grease deterioration, comprising the following steps: S1. Determine the equivalent shear rate and equivalent temperature required for the accelerated deterioration test of the grease based on the actual operating conditions of the spindle bearing, and conduct an accelerated deterioration test on the grease under the equivalent shear rate and equivalent temperature conditions. Take samples according to the preset cycle to obtain grease samples at different deterioration stages.

[0026] It should be noted that in high-speed rolling bearings, the fibrous thickener network of grease breaks, orients, and collapses under the repeated rolling, squeezing, and high-speed shearing of the raceway and rolling elements, resulting in increased oil separation rate, changes in consistency, and decreased oil holding capacity.

[0027] The shear field distribution inside a bearing is non-uniform and difficult to measure directly. This method uses the principle of engineering eigenvalue mapping. Although it cannot simulate the precise shear rate at every point, it can calculate the characteristic shear rate that characterizes the average shear intensity level of the internal lubricating grease by using the overall kinematic parameters of the bearing. .

[0028] The classical formula for calculating the shear rate is: ; in, Represents the classical shear rate; Indicates relative sliding speed; This indicates the thickness of the lubricating film or gap.

[0029] The shear within the bearing primarily originates from spin sliding and differential sliding between the rolling elements and the raceway, as well as the drag flow of grease between the raceway and the cage guide surfaces. Characteristic shear rates can be derived by correlating internal kinematics with operating parameters and key structural dimensions. The estimation formula is used to select the bearing clearance. As a lubricating film or gap thickness Since bearing clearance is the main space that holds most of the grease and determines the overall flow resistance, the classical formula for calculating the shear rate can be extended to: ; in, Indicates the characteristic shear rate; This represents a dimensionless parameter used to correct for the additional shear contribution caused by the complex motion inside the bearing. This indicates the bearing pitch circle diameter, in meters (m). This indicates the bearing's operating speed, expressed in r / min. This indicates the bearing clearance.

[0030] Complex motions mainly include the spinning of the rolling elements, differential sliding, and drag flow at the cage guide surfaces; The theoretical value is between 0 and 1, where 0 represents pure rolling and 1 corresponds to complete sliding; in engineering practice, The specific value depends on the bearing's geometric parameters and operating conditions, and is usually in the range of 0.3 to 1.0. It can be calibrated through finite element simulation or comparative experiments. In this scheme, in order to simplify the modeling process while ensuring the equivalence of the dominant degradation mechanism, a value of 0.5 is preferred.

[0031] Based on characteristic shear rate Ultimately used to control the equivalent shear rate of the external grease degradation test device. It is determined by the following formula: ; in, Indicates the equivalent shear rate; This indicates the acceleration factor in the grease degradation acceleration test.

[0032] The acceleration factor in the accelerated grease degradation test aims to shorten the test cycle by increasing the shear rate. The value must ensure that the microstructure evolution mechanism of the grease under accelerated conditions is consistent with the actual working conditions. The specific value needs to be calibrated through a step shear rate pre-test based on the shear sensitivity of the grease to determine the upper limit of the linear response region.

[0033] In this embodiment, the equivalent thermal environment specifically refers to the steady-state temperature of the cavity where the lubricating grease is located during the bearing's service life, denoted as . The steady-state ambient temperature inside the cavity serves as a true representation of the thermal load borne by the grease phase over a long period, distinct from the instantaneous flash temperature of the rolling contact area, and serves as the basis for setting the ambient temperature of the subsequent grease accelerated degradation test device.

[0034] The temperature of the bearing outer ring surface is directly measured by a temperature sensor, and the measured value is used as the reference temperature. For spindle structures that are difficult to measure directly, the temperature of the front bearing housing can be measured, and a correction relationship between the housing temperature and the outer ring temperature can be established through pre-tests or finite element thermal analysis, converting the housing temperature into an equivalent value of the outer ring temperature. There is a steady-state temperature difference between the outer ring temperature of the bearing and the ambient temperature inside the cavity. The quantitative relationship between the two is determined by the thermal network method. The theoretical basis of the thermal network method is to compare the temperature field problem with a circuit problem and establish the heat balance equation of each node based on Kirchhoff's heat flow law.

[0035] like Figure 2 As shown in the simplified diagram of bearing heat transfer, the heat transfer path of the bearing thermal network model mainly includes three basic heat transfer modes: heat conduction between solids, heat convection between solids and fluids, and heat radiation between separated solid surfaces.

[0036] Based on the heat transfer characteristics of the bearing, the bearing thermal network model is divided into several thermal nodes. Figure 2 In this diagram, L1 and L2 represent the contact heat conduction between the rolling element and the inner and outer raceways, corresponding to the thermal resistance between the rolling element node and the contact surface node of the inner and outer raceways; L3 and L4 represent the heat convection between the rolling element and the surrounding grease, corresponding to the thermal resistance between the rolling element node and the node of the oil-air mixture in the cavity; L5 and L6 represent the contact heat conduction between the inner and outer rings and the bearing housing and journal, corresponding to the thermal resistance between the inner and outer ring body nodes and the bearing housing and journal nodes; L7 and L8 represent the heat convection between the grease in the grease chamber and the bearing housing, corresponding to the thermal resistance between the node of the oil-air mixture in the cavity and the node of the bearing housing; L9 represents the heat exchange between the outer surface of the bearing housing and the ambient air, including both convection and radiation, corresponding to the thermal resistance between the node of the outer surface of the bearing housing and the ambient air.

[0037] The bearing thermal network model includes at least the following thermal nodes: bearing housing outer surface nodes, bearing outer ring body nodes, outer ring raceway contact surface nodes, rolling element nodes, inner ring raceway contact surface nodes, bearing inner ring body nodes, journal nodes, and intracavity oil-gas mixture nodes; wherein, the intracavity oil-gas mixture nodes correspond to the steady-state ambient temperature of the grease within the cavity. , which is the quantity to be determined in this step.

[0038] The fineness of the thermal node division can be adjusted according to the calculation accuracy requirements. For high-speed precision spindle bearings, thermal nodes are set separately from the inner and outer ring raceway contact surfaces and the main body. Hertz diffusion thermal resistance is introduced to describe the heat transfer between the contact area and the main body, so as to more accurately reflect the local thermal characteristics of the contact area.

[0039] For any number For a hot node, the heat balance equation can be expressed as: ; in, This represents the total number of hot nodes; Indicates the first The total number of adjacent hot nodes of a hot node; Indicates the first The temperature of each thermal node, in K; Indicates the first The temperature of each thermal node, in K; Indicates the first The hot node and the first Thermal resistance between hot nodes, in K / W; These represent the specific heat capacity, density, and nodal volume of the material, respectively. and These represent the hot node indexes; It indicates a specific time.

[0040] The thermal resistance between thermal nodes in the bearing thermal network model includes at least one of the following: conductive thermal resistance, convective thermal resistance, radiative thermal resistance, and contact thermal resistance. The specific calculation of the thermal resistance between thermal nodes is based on the classical formulas of heat transfer.

[0041] Conductive thermal resistance, derived from Fourier's law of thermal conductivity, is classified into two types: axial and radial. Its expression is: ; in, Indicates axial thermal resistance; This indicates the thermal conductivity of the material, expressed in W / (m·K). Indicates the length of the axial heat conduction path, in meters (m). Indicates the radial heat conduction path length; This indicates the thermally conductive cross-sectional area, in m². and These represent the outer radius and the inner radius, respectively, in meters (m). This indicates radial thermal resistance.

[0042] Convection thermal resistance, obtained according to Newton's law of cooling, is expressed as follows: ; In the formula, Indicates convective thermal resistance; This represents the convective heat transfer coefficient, with units of W / (m²·K); This indicates the heat exchange area, in m².

[0043] convective heat transfer coefficient It depends on the fluid properties, flow state, and surface geometry; for different types of heat transfer surfaces, such as Figure 2 The convection components of L3, L4, L7, L8 and L9 in the middle.

[0044] Radiation thermal resistance, according to the Stefan-Boltzmann law, is expressed as follows: ; in, Indicates radiative thermal resistance; This represents the Stefan-Boltzmann constant, with a value of [value missing]. ; Indicates surface emissivity; This represents the radiative surface area, with the unit being m². These represent the absolute temperatures of the two surfaces, in Kelvin (K). Indicates the radiative heat transfer coefficient. .

[0045] Radiative heat transfer mainly occurs at the boundary surface between the bearing thermal network model and the external environment (e.g., Figure 2 The radiation portion of L9 in the middle), and the solid surface with a large temperature difference that is visible.

[0046] Contact thermal resistance exists at the mating surfaces between the bearing ring and the bearing housing / journal (e.g., Figure 2 The expressions for L5 and L6 in the text are as follows: ; in, Indicates contact thermal resistance; Indicates the contact heat transfer coefficient; Indicates the contact area.

[0047] The heat source in the bearing thermal network model mainly comes from the frictional heat generated by the frictional torque. According to the Palmgren empirical formula, the total bearing frictional torque consists of a torque term related to lubricant viscosity and a torque term related to the load, expressed as follows: ; in, This indicates the total frictional torque of the bearing; The torque term represents the force related to the viscosity of the lubricant; This represents the torque term related to the load.

[0048] For high-speed angular contact ball bearings, the contribution of spin friction torque must also be considered. The expression for the bearing frictional heat power is as follows: ; in, This indicates the power of heat generated by bearing friction.

[0049] Substituting the thermal resistances and heat generation rates into the heat balance equation, equations are listed for each thermal node. These equations are then combined to obtain a system of linear equations concerning the temperatures of each thermal node. The reference temperature is then used as the reference temperature. Substituting the known values ​​of the main nodes of the bearing outer ring, we solve the linear equations to obtain the steady-state temperature inside the cavity. That is, the equivalent temperature.

[0050] After determining the equivalent shear rate and equivalent temperature, an accelerated grease degradation test was conducted using a temperature-controlled rheometer or a customized shear aging test bench. The test setup should meet the following requirements: temperature control range of current room temperature to 150℃, with a temperature control accuracy of ±1℃; shear rate control range of 0 to 5000 s. -1 .

[0051] Using a certain brand of high-speed spindle bearing grease as the subject, a sufficient sample of no less than 500g was placed in the test apparatus, and a continuous shear test was carried out under the conditions of (equivalent shear rate, equivalent temperature). The shear decay of the grease is typically rapid in the initial stage and slow in the later stage. Logarithmic distribution sampling was used, with each sample being no less than 50g. After sampling, the oil separation rate was determined according to industry standards. With cone penetration Oil separation rate and cone penetration This is the degradation index.

[0052] To establish a complete degradation database, at least three combined tests of equivalent shear rate and three equivalent temperature were conducted, with each group repeated three times and the average value taken to obtain grease samples at different degradation stages.

[0053] S2. The oil separation rate and cone penetration of each grease sample were measured, and a time-varying model was established.

[0054] It should be noted that this step aims to transform discrete experimental data into a mathematical constitutive model that can continuously and dynamically predict the performance state of the grease, providing input for subsequent precision simulations.

[0055] The time-varying fundamental model is a saturated model containing an exponentially decaying term, expressed as follows: ; in, Indicates the degradation index at shear-thermal aging time Actual measured values ​​at the time (e.g., oil separation rate) or cone penetration (The unit is the unit of the corresponding physical quantity). This represents the measured value of the degradation index at the initial moment; This represents the steady-state saturation value that the degradation index approaches after a theoretically infinite time. This represents the overall degradation rate related to external load conditions; This represents the cumulative shear-thermal aging time.

[0056] Overall degradation rate This characterizes the rate of performance degradation of grease under specific external load conditions; and establishes a comprehensive degradation rate. The quantitative relationship with controllable experimental parameters is established by constructing the following load-rate correlation function, expressed as follows: ; in, This indicates a proportionality factor related to the brand and type of lubricating grease. This represents the load intensity function, used to integrate and quantify the coupling effect of shear and thermal effects.

[0057] Load strength function The specific form is constructed based on the shear power law and Arrhenius's law, and the expression is: ; in, Indicates a dimensionless reference; The shear effect index, obtained through data fitting, reflects the sensitivity of the degradation process to mechanical shear. It represents the apparent activation energy, obtained through data fitting, and reflects the thermal sensitivity of the degradation process to temperature, conforming to Arrhenius's law. This represents the ideal gas constant (8.314 J·mol⁻¹). -1 ·K -1 ).

[0058] The global material parameters obtained from the solution Local parameters obtained under any working condition Substituting into the time-varying basic model, we obtain the final time-varying model that predicts the time-varying state of the lubricating grease performance.

[0059] S3. Based on grease samples at different deterioration stages, friction tests were conducted under preset normal load, entrainment speed and sliding-rolling ratio conditions to establish a dynamic friction coefficient model.

[0060] It should be noted that a ball-disc friction testing machine is used for friction testing, and the friction pair consists of GCr15 bearing steel balls and a bearing steel disc (the surface roughness of the bearing steel disc is determined based on the actual bearing material). Before each friction test, approximately 2g of grease is evenly applied to the surface of the bearing steel disc. The friction test conditions must cover the actual service conditions of the spindle bearing contact area, including normal load, entrainment speed, and sliding-rolling ratio. In this embodiment, the normal load is selected. The entrainment speed is 10~100N (corresponding to Hertzian contact stress of 0.5~2.0GPa). The speed range is 0.1~5 m / s, and the slip-roll ratio is... It ranges from 0 to 1.0.

[0061] Suppose there are X types of degradation states, Z types of normal loads, and O types of entrainment velocities. For the test conditions (x=1, ..., X; z=1, ..., Z; o=1, ..., O) under the x-th degradation state, z-th load, and o-th entrainment velocity, repeat the test 3 times, and take the average value as the steady-state friction coefficient dataset under the current working condition. }

[0062] To characterize the steady-state friction coefficient Depending on the working conditions and deterioration indicators The dynamic change law is based on the classical mechanism model describing elastohydrodynamic friction, and the state variables are introduced for extension; oil separation rate and cone penetration are both indicators of the deterioration state of grease.

[0063] Using the Gupta four-parameter exponential model, widely applied in point contact elastohydrolubrication friction analysis, as the basic constitutive framework, dynamic friction model coupling and fitting are performed to obtain the drag equation model, in the form of, ; in, This represents the point contact drag coefficient, i.e., the steady-state friction coefficient; Indicates sliding speed With entrainment speed The ratio of the two values, i.e., the slip-roll ratio; , , and This represents an undetermined parameter, considered a constant related to a specific lubricant-material pair, and cannot reflect the time-varying characteristics of the lubricant's own performance.

[0064] Indicators characterizing the deterioration of lubricating grease performance Introducing it as an independent variable into the drag equation model expands the model parameters from constants to... For continuous functions, construct a dynamic constitutive relation, expressed as follows: ; in, Indicates the slip-roll ratio Normal load and degradation indicators Point contact drag coefficient under combined action.

[0065] The point contact drag equation model is the dynamic friction coefficient model, which clarifies that the friction coefficient is simultaneously controlled by both the instantaneous operating conditions and the state of the lubricating grease.

[0066] S4. Embed the time-varying model and dynamic friction coefficient model into the bearing mechanical model and wear model to calculate the normal contact load, contact stress and wear depth of each rolling element under different speed and load conditions, and update the actual clearance according to the wear depth.

[0067] At each calculation time t, assuming the spindle is in static equilibrium, and considering the current time-varying clearance c(t), the normal contact load W(t) of the v-th rolling element is calculated by solving the force balance and deformation compatibility equations of the bearing; for an angular contact ball bearing subjected to combined loads, the nonlinear equations are as follows: ; in, Indicates axial load; Indicates radial load; Indicates the bearing load-displacement coefficient; Indicates the contact angle; Indicates the number of rolling elements; Indicates the azimuth angle of the rolling element; This indicates the axial and radial deformation of the bearing inner ring relative to the outer ring, and the current time-varying clearance. Related; This represents the v-th rolling element.

[0068] For angular contact ball bearings, the slip ratio S of the vth rolling element is defined as the ratio of the sliding speed to the entrainment speed, where the sliding speed is... Determined by the relative motion between the rolling elements and the raceway: ; Among them, the entrainment speed The average velocity of the two contact surfaces: ; in, Indicates the first The sliding speed of each rolling element; Indicates the first The entrainment speed of each rolling element; The cage angular velocity (rad / s) is obtained from the bearing kinematics equations. The inner angular velocity (rad / s) is determined by the spindle speed. Indicates the first The radius of gyration (mm) of the contact point between the rolling element and the raceway; Indicates the first The radius of gyration (mm) of the contact point between the rolling element and the inner ring.

[0069] It should be noted that the slip-roll ratio varies with the azimuth angle of the rolling element. and normal contact load The sliding ratio varies depending on the rolling element.

[0070] Solve The normal contact load of each rolling element can then be obtained. .

[0071] According to Hertzian contact theory, by Calculate the maximum contact stress in the contact elliptical region. The expression is, ; in, This indicates the maximum contact stress in the elliptical contact region; and This indicates the major and minor semi-axis of the contact ellipse.

[0072] Based on bearing kinematics, the microscopic slip distance between the rolling elements and the raceway in the contact area is calculated. .

[0073] For angular contact ball bearings, the first The microscopic sliding distance of each rolling element in the contact area is determined by the roll-slip ratio and the major semi-axis of the contact ellipse. The decision, expressed as: ; in, Indicates the first The microscopic slip distance of each rolling element; This represents an empirical correction factor, determined by the creep characteristics of the contact area. An exemplary value range is 0.1 to 0.5, which can be obtained through a single wear test.

[0074] Construct a basic wear model, selecting the Archard wear formula, the expression of which is: ; in, Indicates the amount of wear; Indicates the wear coefficient; Indicates the Brinell hardness of the bearing material; This represents the contact stress index (preferably 1.3).

[0075] The expression for the wear coefficient is, ; in, This represents the geometric transformation factor, which is determined by the inherent geometric dimensions of the bearing. Dimensionless coefficients relating to material pair and lubrication condition.

[0076] The expression for the geometric transformation coefficient is, ; in, Indicates the diameter of the rolling element.

[0077] Extending the Archard wear formula, the complete wear model is as follows. ; in, Indicates the amount of wear.

[0078] Wear inside the bearing directly manifests as increased clearance. Actual gap at time The sum of the initial clearance and the cumulative wear depth is expressed as follows: ; in, express The actual time gap; This indicates the initial clearance of the bearing when it leaves the factory; Indicates the depth of wear.

[0079] S5. Calculate the spindle rotation center offset and radial runout caused by a single bearing based on the updated actual clearance, and calculate the total radial runout of the spindle end in combination with the geometric relationship of the front and rear bearing supports.

[0080] It should be noted that the calculation of spindle rotation center offset caused by a single bearing is due to wear leading to uneven clearance, which causes a change in the trajectory of the spindle axis during rotation. Considering the two most unfavorable extreme positions, when the long axis of the bearing inner ring is in the vertical direction, the spindle center offset is... ; When the short axis of the bearing inner ring is in the vertical direction, the spindle center offset is: ; in, This indicates the spindle center offset when the long axis of the bearing inner ring is in the vertical direction. This indicates the spindle center offset when the short axis of the bearing inner ring is in the vertical direction. This indicates the outer diameter of the bearing.

[0081] The radial runout contributed by a single bearing is calculated as follows: the radial runout caused by a single bearing is twice the amplitude of the spindle center offset at its two extreme positions. The expression is: ; in, This indicates the radial runout caused by a single bearing.

[0082] The spindle of a CNC machine tool is usually supported by a pair of angular contact ball bearings. The runout error of the front and rear bearings will be transmitted and amplified to the machining point (spindle end) at the end of the spindle through the leverage effect.

[0083] The expression for the total radial runout at the spindle end is as follows: ; in, This indicates the total radial runout at the spindle end; These represent the radial runout caused by the clearance of the front and rear bearings (bearings 1 and 2), respectively. Indicates the span between the front and rear bearing support points; This indicates the overhang from the front bearing support point to the tool mounting point on the spindle end.

[0084] In summary, this invention achieves a quantitative characterization of the dynamic degradation law of grease performance by accelerating the determination of the oil separation rate and cone penetration changes of grease under the coupled effects of temperature, shear rate, and time, and establishing a time-varying model. This overcomes the shortcomings of existing methods in systematically characterizing the grease degradation process and improves the authenticity and reliability of spindle rotation accuracy prediction. Furthermore, by coupling the grease degradation state with the dynamic friction coefficient model, bearing mechanics model, and wear model, a predictive relationship is established from the evolution of grease performance to the total radial runout of the spindle end. This overcomes the shortcomings of existing methods in lacking a physical correlation chain, improves the physical authenticity and interpretability of spindle rotation accuracy prediction, and provides a quantitative basis for grease selection, maintenance cycle optimization, and spindle reliability design.

[0085] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting spindle rotation accuracy based on grease degradation, characterized in that: include: The equivalent shear rate and equivalent temperature required for the accelerated deterioration test of the grease are determined based on the actual operating conditions of the spindle bearing. The accelerated deterioration test of the grease is carried out under the equivalent shear rate and equivalent temperature conditions. Samples are taken at a preset cycle to obtain grease samples at different deterioration stages. The oil separation rate and cone penetration of each grease sample were measured, and a time-varying model was established. Based on grease samples at different stages of deterioration, friction tests were conducted under preset normal load, entrainment speed and sliding-rolling ratio conditions to establish a dynamic friction coefficient model. The time-varying model and dynamic friction coefficient model are embedded into the bearing mechanical model and wear model to calculate the normal contact load, contact stress and wear depth of each rolling element under different speed and load conditions, and update the actual clearance according to the wear depth. The spindle rotation center offset and radial runout caused by a single bearing are calculated based on the updated actual clearance, and the total radial runout at the spindle end is calculated in combination with the geometric relationship of the front and rear bearing supports.

2. The spindle rotation accuracy prediction method based on grease degradation as described in claim 1, characterized in that, The specific steps for determining the equivalent shear rate and equivalent temperature required for the accelerated deterioration test of the lubricating grease based on the actual operating conditions of the spindle bearing are as follows: The characteristic shear rate is calculated based on the pitch circle diameter, operating speed, and bearing clearance of the spindle bearing. Based on the acceleration factor of the grease deterioration acceleration test, the characteristic shear rate is converted into the equivalent shear rate of the external grease deterioration acceleration test device. Obtain the stable temperature of the bearing outer ring after the spindle reaches thermal equilibrium; A bearing thermal network model is established. The steady-state temperature is substituted into the bearing thermal network model as a known value to solve for the steady-state ambient temperature inside the cavity. The steady-state ambient temperature inside the cavity is then used as the equivalent temperature.

3. The spindle rotation accuracy prediction method based on grease degradation as described in claim 2, characterized in that, The bearing thermal network model is based on the thermal balance equation and includes at least the nodes on the outer surface of the bearing housing, the main body nodes of the outer ring of the bearing, the contact surface nodes of the outer ring raceway, the rolling element nodes, the contact surface nodes of the inner ring raceway, the main body nodes of the inner ring of the bearing, the journal nodes, and the nodes of the oil-gas mixture in the cavity. The thermal resistance between thermal nodes in the bearing thermal network model includes at least one of conductive thermal resistance, convective thermal resistance, radiative thermal resistance, and contact thermal resistance.

4. The spindle rotation accuracy prediction method based on grease degradation as described in claim 1, characterized in that, The specific steps for establishing the time-varying model are as follows: Oil separation rate and cone penetration were measured for grease samples at different stages of deterioration. A time-varying basic model was established with the cumulative shear-thermal aging time as the independent variable, and a time-varying model was then established based on the time-varying basic model. The time-varying fundamental model is a saturated model that includes an exponential decay term. The overall degradation rate in the time-varying fundamental model is determined by both shear and thermal effects.

5. The spindle rotation accuracy prediction method based on grease degradation as described in claim 4, characterized in that, The overall degradation rate refers to the coupling function of the equivalent shear rate and the equivalent temperature. The overall degradation rate is constructed based on the shear power law and Arrhenius's law.

6. The spindle rotation accuracy prediction method based on grease degradation as described in claim 1, characterized in that, The specific steps for conducting the friction test are as follows: The ball-disc friction tester was used for testing, with the friction pair consisting of bearing steel balls and bearing steel discs. Repeated tests were conducted for each set of normal load, entrainment speed, and slip-roll ratio conditions. After the friction coefficient reaches a steady state, the average friction coefficient in the steady state is taken as the steady-state friction coefficient under the corresponding working condition.

7. The spindle rotation accuracy prediction method based on grease degradation as described in claim 6, characterized in that, The specific steps for establishing the dynamic friction coefficient model are as follows: The Gupta four-parameter exponential model serves as the basic constitutive framework; By introducing oil separation rate and cone penetration as state variables into the model parameters, the model parameters are expanded from constants to functions of oil separation rate, cone penetration, roll ratio, and normal load. Based on the steady-state friction coefficient, the parameters of the basic constitutive framework are fitted to establish a dynamic friction coefficient model.

8. The spindle rotation accuracy prediction method based on grease degradation as described in claim 1, characterized in that, The specific steps for embedding the time-varying model and dynamic friction coefficient model into the bearing mechanics model and wear model are as follows: Based on discrete time, the oil separation rate and cone penetration at each discrete time are determined using a time-varying model. Based on the actual clearance, and combined with the force balance and deformation compatibility equations of the bearing, the normal contact load of each rolling element is solved. According to Hertzian contact theory, the contact stress is calculated from the normal load. Substituting the oil separation rate, cone penetration, normal load, and sliding-rolling ratio at each discrete time into the dynamic friction coefficient model, we obtain the friction coefficient under the corresponding working conditions. By combining the friction coefficient, contact stress, and the micro-slip distance between the rolling element and the raceway in the contact area, the wear depth is calculated using a wear model, and the actual clearance is updated based on the wear depth. The actual clearance refers to the sum of the bearing's initial clearance at the factory and the total wear depth.

9. The spindle rotation accuracy prediction method based on grease degradation as described in claim 1, characterized in that, The specific steps for calculating the spindle rotation center offset and radial runout caused by a single bearing based on the updated actual clearance are as follows: Calculate the spindle center offset when the major axis of the bearing inner ring is in the vertical direction, and the spindle center offset when the minor axis of the bearing inner ring is in the vertical direction, respectively. Calculate the radial runout caused by a single bearing based on the offset between the two spindle centers.

10. The spindle rotation accuracy prediction method based on grease degradation as described in claim 9, characterized in that, The calculation of the total radial runout at the spindle end based on the geometric relationship of the front and rear bearing supports refers to calculating the total radial runout at the spindle end based on the geometric relationship of the front and rear bearing supports and the corresponding radial runout of each bearing.

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