A method for real-time monitoring of machine tool lead screw temperature field using CNC motion data

Abstract

This invention belongs to the field of CNC machine tool temperature monitoring, and provides a method for real-time monitoring of the temperature field of a machine tool's lead screw using CNC motion data. This method enables real-time monitoring of the lead screw's temperature field even when the lead screw is obstructed by the machine tool's feed axis structure, during irregular rotational motion, or when the lead screw temperature data cannot be directly measured by instruments. First, the machine tool's feed speed, mechanical coordinates, and feed load are collected from the CNC system. Then, the frictional heat and temperature of the ball bearing pair are deduced. Next, the frictional heat of the rolling bearing and ball screw pair is calculated. Finally, the temperature field of the ball screw is calculated. This invention fully utilizes easily measurable and collectable data during the ball screw's motion, combining the heat source's heat generation mechanism and the structural heat transfer mechanism to calculate the temperature field of the ball screw under complex motion conditions in real time, achieving online monitoring of the lead screw's temperature field. This invention can provide technical support for machine tool thermal optimization design, thermal error compensation, and the construction of machine tool digital twins.

Description

Technical Field

[0001] This invention belongs to the field of virtual sensing for CNC machine tools, and relates to a method for real-time monitoring of the temperature field of a machine tool lead screw using CNC motion data. Background Technology

[0002] Ball screws, as precision transmission components in actuators, are widely used in aerospace, precision instruments, and CNC machining equipment. The advent of CNC machine tools has further broadened their applications, as ball screws are key components for achieving linear motion transmission and positioning in machine tools. Increased screw temperature not only easily leads to thermal expansion and accelerated wear of the ball screw pair, but its radiant heat also affects the accuracy of nearby linear encoders. During service, the complex motion of ball screws greatly complicates direct temperature measurement. Although infrared temperature sensors can measure metal temperature non-contactly, the irregular cylindrical surface of the screw and its irregular rotational motion significantly impact the accuracy of infrared temperature measurements.

[0003] Currently, the commonly used method for obtaining the temperature field of ball screws is to obtain numerical solutions through numerical simulation. The paper "Real-Time Estimation of Temperature Distribution In a Ball-Screw System" uses the finite element method to estimate the temperature distribution of a ball screw system. The paper "Thermal Error Forecast and Performance Evaluation For An Air-cooling Ball Screw System" uses the finite element method to establish a thermal behavior model of the feed shaft, which considers the heat generated by the main heat sources of the ball screw system. The paper "Thermal analysis for the feed drive system of a CNC machine center" analyzes the thermal behavior of a ball screw using the finite element method without considering thermal contact resistance. The paper "Numerical Solution, Simulation and Testing of The Thermal Dynamic Characteristics of Ball-screws" uses a group explicit finite difference method to solve the non-homogeneous heat transfer equations, and then describes the thermal dynamic characteristics of the ball screw by simulating and modeling the temperature field and thermal deformation of the ball screw under the action of a periodic heat source. The paper "Thermo-mechanical Modelling of Ball Screw Preload Force Variation in Different Working Conditions" proposes a numerical modeling strategy that uses a thermodynamically based three-dimensional finite element model of a dual-nut ball screw drive to predict preload changes caused by temperature rise. The paper "Thermal Error Simulation and Compensation In A Jig-boring Machine Equipped with A Dual-drive Servo Feeding System" establishes a thermal structure finite element method to analyze the transient thermal deformation and temperature field of the machine tool under different feed rates. Although numerical simulation methods can more closely approximate the analytical solution of the ball screw's thermal characteristics, their computation time cannot meet the requirements for online monitoring of the ball screw temperature.

[0004] Some studies have employed physics-based modeling methods to analytically calculate the temperature field of the ball screw. The paper "Thermally Induced Positioning Error Modelling and Compensation Based on Thermal Characteristic Analysis" treats the frictional heat generation rate of the ball screw pair as an unknown parameter when calculating the temperature field of the feed system, and then identifies this unknown parameter using experimentally measured temperature data. In effect, this approach treats the frictional heat generation rate of the ball screw pair as a constant. The paper "Piecewise Compensation of Thermal Errors of A Ball Screw Driven CNC Axis" simplifies the frictional heat of the ball screw pair into a piecewise linear function of coordinate position based on the characteristics of the feed system temperature measurement data, and identifies the unknown parameters within it. The above studies, in analyzing the thermal characteristics of ball screw feed systems, have all used this empirical formula or its simplified optimized formula to calculate the frictional heat generation rate of the ball screw pair, or directly used the empirical formula for the frictional heat generation rate of ball bearings to approximate the calculation of the frictional heat generation rate of the ball screw pair. However, the frictional torque in these empirical formulas is still calculated using empirical formulas, and the accuracy of the calculation results has not been verified. Obtaining the frictional heat generation rate of the ball screw pair using parameter identification methods requires obtaining sufficiently reliable experimental data to ensure the accuracy of the identification results. Furthermore, the frictional heat generation mechanism of both ball screw pairs and ball bearing pairs needs to be elucidated. Summary of the Invention

[0005] This invention addresses the challenge of directly measuring and real-time monitoring the temperature of a ball screw during its irregular rotational motion under conditions of obstruction by the machine tool's feed axis structure. By combining virtual sensing technology, it provides a method for real-time monitoring of the ball screw temperature field using CNC motion data. Utilizing machine tool motion data acquired from the CNC system, and considering ambient temperature changes, frictional heating of rolling bearings and ball screw pairs, structural heat transfer, and heat dissipation mechanisms, the method calculates the temperature field of the ball screw under complex motion conditions in real time, enabling online monitoring of the ball screw temperature field. This invention can provide technical support for machine tool thermal optimization design, thermal error compensation, and the construction of machine tool digital twins.

[0006] The technical solution of the present invention:

[0007] A method for real-time monitoring of the temperature field of a machine tool leadscrew using CNC motion data, comprising the following steps:

[0008] Real-time monitoring of the lead screw temperature field is achieved during the irregular rotational motion of the lead screw, even when the machine tool feed axis is obstructed. When the lead screw temperature data cannot be directly measured by instruments, real-time monitoring is achieved through deductive calculation. The calculation of the lead screw temperature field utilizes machine tool motion data collected from the CNC system and is applicable to all CNC systems that provide secondary development protocols. The calculation of the lead screw temperature field considers ambient temperature changes, rolling bearing frictional heating, ball screw pair frictional heating, structural heat transfer, and heat dissipation.

[0009] The first step is to collect the machine tool's feed rate, machine coordinates, and feed load from the CNC system;

[0010] Based on the CNC system's IP address and port number, and in conjunction with the secondary development protocol provided by the CNC system, a connection channel is established with the CNC system via the network port; the secondary development interface functions for reading feed speed, machine coordinates, and feed load are located and read;

[0011] The second step is to calculate the frictional heat of the rolling bearing;

[0012] Apply a rotational motion to the ball bearing that is the same in magnitude and opposite in direction to the angular velocity of the ball center rotating around the inner ring of the bearing, and analyze the motion relationship between the inner and outer rings and the balls of the rolling bearing; the frictional heat of the rotational motion in the contact area of ​​the ball bearing includes the sliding frictional heat between the balls and the inner and outer ring raceways and the rolling frictional heat generated by the balls rolling in the inner and outer ring raceways, as well as the heat generated by the ball bearing due to the applied load and viscous friction.

[0013] The calculation method for the sliding friction heat between the ball and the inner and outer raceways is expressed as follows:

[0014] (1)

[0015] Where, It is the coefficient of sliding friction between the balls and the raceways of the inner and outer rings in a ball bearing. It is the normal force at the contact point between the ball and the inner ring caused by axial load. It is the normal force at the contact point between the ball and the inner ring caused by radial load. It is the normal force at the contact point between the ball and the outer ring caused by axial load. The normal force at the contact point between the ball and the outer ring caused by radial load, S bI S is the sliding stroke that occurs during the movement of the inner ring of the bearing driving the balls. bO This refers to the sliding stroke of the ball as it moves within the outer raceway; i represents the i-th ball in the ball bearing. It refers to the number of balls in a ball bearing;

[0016] The rolling friction heat generated by the balls rolling in the inner and outer raceways is calculated as follows:

[0017] (2)

[0018] In the formula, It is the rolling distance of the balls within the inner ring of the bearing. It is the rolling distance of the balls on the outer ring of the bearing, k is the coefficient of rolling friction between the bearing steels, and r is the rolling distance of the balls on the outer ring of the bearing. b It is the diameter of the ball bearing;

[0019] The heat generated by ball bearings due to applied load and viscous friction is calculated by the following formula:

[0020] (3)

[0021] In the formula, The rotational speed of the leadscrew. It is the torque caused by viscous friction. It is the torque caused by the applied load;

[0022] Therefore, the frictional heat of a rolling bearing is expressed as:

[0023] (4).

[0024] The third step is to calculate the frictional heat of the ball screw assembly;

[0025] The heat generated by the sliding friction of the balls rolling in the screw raceway and nut raceway in a ball screw pair is calculated as follows:

[0026] (5)

[0027] In the formula, It is the coefficient of sliding friction between the ball and the raceway. It is the contact pressure between the ii-th loaded ball in nut A and the raceway of the screw. It is the contact pressure between the ii-th loaded ball in nut A and the raceway of the nut. It is the contact pressure between the jj-th loaded ball in nut B and the raceway of the screw. S is the contact pressure between the jj-th loaded ball in nut B and the nut raceway. bS S is the rolling differential sliding stroke that occurs during the movement of the ball bearings driven by the lead screw. bN This refers to the differential sliding stroke of the balls during the movement of the ball-driven nut; Z n-A Z is the number of balls in nut A. n-B This refers to the number of balls in nut B;

[0028] The rolling friction heat generated by the balls rolling in the lead screw raceway and nut raceway is calculated by the following formula:

[0029] (6)

[0030] In the formula, F a It is the external load borne by the ball screw assembly, F C λ0 is the residual preload of the ball screw pair after applying an external load, α is the helix angle of the raceway, and x is the contact angle between the ball and the raceway. s It is the rolling distance of the ball on the screw raceway, x n It is the rolling distance of the balls on the raceway of the nut;

[0031] The frictional heat between the balls and between the balls and the return mechanism is expressed as a function of time t:

[0032] (7)

[0033] In the formula, q k It is the rate of frictional heat generation between the balls and between the balls and the return mechanism;

[0034] The calculation method for the viscous frictional heat of the lubricant in a ball screw assembly is expressed as follows:

[0035] (8)

[0036] In the formula, f0 is a constant related to the type of ball screw pair and the lubrication method. It is the kinematic viscosity of the lubricant. It is the nominal diameter of the leadscrew. It is the stroke of the lubricant's viscous force, ω S It is the angular velocity of the lead screw rotation;

[0037] The frictional heat of a ball screw pair is expressed as:

[0038] (9).

[0039] The fourth step is to calculate the temperature field of the ball screw;

[0040] Ball screws appear in the form of slender rods. Since the axial temperature change rate is greater than the radial temperature change rate, the heat conduction of ball screws is considered as a one-dimensional heat conduction problem, and its calculation method is as follows:

[0041] (10)

[0042] Where, Let λ be the temperature at position x at time t, λ be the thermal conductivity, ρ be the density of the ball screw material, and c be the specific heat capacity of the ball screw material. The heat source intensity is calculated by dividing the ball screw into M segments, each segment having a length of L.

[0043] (11)

[0044] Where, It is a ball screw The frictional heat generated by the ball screw pair at position x within a time interval, r S Where h is the equivalent radius of the ball screw, and h is the heat dissipation coefficient. It is the ambient temperature around the ball screw at time t. yes The frictional heat generated by the ball bearing pair on the motor side within a certain time period, r fB It is the inner ring radius of the ball bearing on the motor side. yes The frictional heat generated by the ball bearing pair at the support end within a certain time, r bB It is the inner ring radius of the ball bearing at the support end.

[0045] The beneficial effects of this invention are:

[0046] (1) This invention provides a method for real-time monitoring of the lead screw temperature field when the lead screw rotates irregularly due to obstruction by the machine tool feed axis structure, and when the lead screw temperature data cannot be directly measured by a measuring instrument.

[0047] (2) This invention does not require the use of complex and expensive instruments. It directly uses readily available CNC motion data such as mechanical coordinates, feed speed, and feed load to calculate the screw temperature field information that cannot be directly measured in real time.

[0048] (3) The present invention can not only obtain the temperature field information of the lead screw, but also the information of frictional heating of the ball bearing and frictional heating of the ball screw pair. Attached Figure Description

[0049] Figure 1 Flowchart of a method for real-time monitoring of the temperature field of a machine tool leadscrew using CNC motion data;

[0050] Figure 2The graph shows the temperature comparison results of the ball screw pair and the rolling bearing pair; where (a) is the calculated temperature of the nut and bearing at a thermal engine speed of 2000 mm / min; (b) is the measured temperature of the nut and bearing at a thermal engine speed of 2000 mm / min; (c) is the calculated temperature of the nut and bearing at a thermal engine speed of 4000 mm / min; (d) is the measured temperature of the nut and bearing at a thermal engine speed of 4000 mm / min; (e) is the calculated temperature of the nut and bearing at a thermal engine speed of 6000 mm / min; and (f) is the measured temperature of the nut and bearing at a thermal engine speed of 6000 mm / min.

[0051] Figure 3 The figure shows the accuracy assessment results of the lead screw temperature field calculation; where (a) is the measured value of the lead screw thermal expansion at a thermal speed of 2000 mm / min; (b) is the calculated value of the lead screw thermal expansion at a thermal speed of 2000 mm / min; (c) is the measured value of the lead screw thermal expansion at a thermal speed of 4000 mm / min; (d) is the calculated value of the lead screw thermal expansion at a thermal speed of 4000 mm / min; (e) is the measured value of the lead screw thermal expansion at a thermal speed of 6000 mm / min; and (f) is the calculated value of the lead screw thermal expansion at a thermal speed of 6000 mm / min.

[0052] Figure 4 The difference between the calculated and measured thermal expansion of the lead screw is given; where (a) is the difference between the calculated and measured thermal expansion of the lead screw at a thermal speed of 2000 mm / min; (b) is the difference between the calculated and measured thermal expansion of the lead screw at a thermal speed of 4000 mm / min; and (c) is the difference between the calculated and measured thermal expansion of the lead screw at a thermal speed of 6000 mm / min. Detailed Implementation

[0053] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0054] Taking the X-axis lead screw of a VM1050S vertical machining center as an example, the implementation of this invention is described in detail. The CNC system of this vertical machining center is a FANUC system, with an X-axis travel range of -850mm to 0mm. It employs semi-closed-loop control and ball screw drive, with both ends of the lead screw mounted on a saddle via bearing seats. The ball screw is an R40-16T5-FSDC, and the bearings at both ends are angular contact ball bearings, specifically 30TABO6NC1U. The online monitoring process for the lead screw temperature field is as follows: Figure 1 As shown, this includes acquiring machine tool motion information from the CNC system: feed rate, machine coordinates, and feed load; and extrapolating the frictional heat of the ball bearing pair. ; Deducing the frictional heat of the ball screw pair: ; Deducing the temperature field of the bearing, nut, and ball screw: The specific implementation is as follows:

[0055] (1) Collect the machine tool's feed rate, machine coordinates, and feed load from the CNC system;

[0056] The CNC system's IP address is 192.168.1.5, port number is 62973, and the secondary development protocol provided by the FANUC system is FOCAS2. During the ball screw's operation, easily measurable data used for deducing the screw's temperature field include the nut temperature, bearing housing temperature, and initial ambient temperature. Acquired temperature data includes the feed rate, stroke, load, and time fed back from the controller. The basic parameters of the ball screw and ball bearings are shown in Table 1.

[0057] Table 1. Basic Parameters of Ball Screws and Ball Bearings

[0058]

[0059] Before the test, ensure the machine tool is stopped for at least 5 hours to ensure it is in a state of thermal equilibrium. The specific test procedure is as follows:

[0060] 1) Set the temperature sensor acquisition cycle to 10s, read the temperature of the machine tool X-axis nut and bearing housing, and use a laser interferometer to record the thermal expansion of the lead screw at the current temperature;

[0061] 2) The computer is connected to the CNC system via a network cable to read the mechanical coordinate values ​​of the X-axis, feed speed and load data, and to calculate the nut temperature, bearing housing temperature and lead screw temperature in real time;

[0062] 3) The machine tool's X-axis reciprocates for 10 minutes at a feed rate Fx across its entire stroke range;

[0063] 4) Use a laser interferometer to record the thermal expansion of the lead screw under the current state of the machine tool's X-axis;

[0064] 5) Repeat steps 3) and 4) Nh times;

[0065] 6) Stop the X-axis movement and let it stand still for 10 minutes;

[0066] 7) Use a laser interferometer to record the thermal expansion of the lead screw under the current state of the machine tool's X-axis;

[0067] 8) Repeat steps 6) and 7) Nc times.

[0068] The experiment was conducted three times, and the specific experimental information is shown in Table 2.

[0069] Table 2. Test Information

[0070]

[0071] (2) Calculate the frictional heat of the ball bearing and the ball screw pair;

[0072] The heat generated by friction in the ball screw and ball bearing pairs, calculated using a frictional heat generation model, is converted into a temperature change. By actually measuring the temperature changes during the movement of the ball screw and ball bearing pairs and comparing them with the theoretically calculated temperature changes, the accuracy of the frictional heat generation model for the ball screw and ball bearing pairs can be verified. Experimental results are as follows: Figure 2 As shown; (a) is the calculated temperature of the nut and bearing at a thermal engine speed of 2000 mm / min; (b) is the measured temperature of the nut and bearing at a thermal engine speed of 2000 mm / min; (c) is the calculated temperature of the nut and bearing at a thermal engine speed of 4000 mm / min; (d) is the measured temperature of the nut and bearing at a thermal engine speed of 4000 mm / min; (e) is the calculated temperature of the nut and bearing at a thermal engine speed of 6000 mm / min; (f) is the measured temperature of the nut and bearing at a thermal engine speed of 6000 mm / min.

[0073] The experimental results show that the calculated and measured temperatures of the nut and bearing exhibit consistent trends. During X-axis movement, both the calculated and measured temperatures show wave-like fluctuations. This is because, in step 4 of the experimental procedure, when recording the thermal expansion of the lead screw under the current X-axis state using a laser interferometer, there are intermittent pauses in the X-axis, causing a decrease in the temperature of the ball screw and bearing. During the stationary phase of the X-axis movement, the calculated and measured temperatures also show wave-like fluctuations. This is because, in step 7 of the experimental procedure, when recording the thermal expansion of the lead screw under the current X-axis state using a laser interferometer, there are intermittent movements in the X-axis, causing a slight increase in the temperature of the ball screw and bearing.

[0074] The differences between the calculated and measured temperature values ​​at the initial, final, and final moments of the experiment are extracted and shown in Table 3. The difference between the calculated and measured temperature values ​​during the X-axis motion phase is less than 1℃, indicating that the frictional heat calculations for the ball screw and ball bearing pairs are relatively accurate. The difference between the calculated and measured temperature values ​​of the bearing housing near the motor during the X-axis stationary phase is larger, but still within 2℃. This larger difference is because the motor's heat generation worsens the heat dissipation conditions of the bearing housing near the motor, resulting in slower cooling of the bearing housing during the X-axis stationary phase.

[0075] Table 3. Calculated and measured temperature difference (°C)

[0076]

[0077] (3) Calculate the temperature field of the ball screw;

[0078] The ball screw is constantly moving during operation, making it impossible to directly measure its temperature field. However, the expansion caused by temperature changes in the screw can be directly measured. Therefore, a laser interferometer can be used to measure the thermal expansion error of the screw, and this error can be compared with the calculated value of the thermal expansion to evaluate the accuracy of the calculated temperature field of the screw. Experimental results are as follows... Figure 3 As shown; where (a) is the measured value of the thermal expansion of the lead screw at a thermal speed of 2000 mm / min; (b) is the calculated value of the thermal expansion of the lead screw at a thermal speed of 2000 mm / min; (c) is the measured value of the thermal expansion of the lead screw at a thermal speed of 4000 mm / min; (d) is the calculated value of the thermal expansion of the lead screw at a thermal speed of 4000 mm / min; (e) is the measured value of the thermal expansion of the lead screw at a thermal speed of 6000 mm / min; and (f) is the calculated value of the thermal expansion of the lead screw at a thermal speed of 6000 mm / min.

[0079] Obtain the difference between the calculated and measured values ​​of the lead screw's thermal expansion; the result is as follows: Figure 4 As shown in the figures, (a) represents the difference between the calculated and measured thermal expansion of the lead screw at a thermal speed of 2000 mm / min; (b) represents the difference between the calculated and measured thermal expansion of the lead screw at a thermal speed of 4000 mm / min; and (c) represents the difference between the calculated and measured thermal expansion of the lead screw at a thermal speed of 6000 mm / min. The experimental results show that the deviation between the calculated and measured values ​​of thermal expansion during the heating and cooling process of the lead screw throughout its entire stroke can be controlled within 11.8 μm. The deviation in the calculated temperature field of the lead screw, derived in reverse from the lead screw thermal expansion calculation formula, is shown in Table 4. Therefore, the online calculation accuracy of the lead screw temperature field throughout its entire stroke can reach ±1.1℃.

[0080] Table 4. Temperature and thermal expansion difference of the lead screw

[0081]

[0082] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for real-time monitoring of the temperature field of a machine tool lead screw using CNC motion data, characterized in that, The steps are as follows: The first step is to collect the machine tool's feed rate, machine coordinates, and feed load from the CNC system; Based on the CNC system's IP address and port number, and in conjunction with the secondary development protocol provided by the CNC system, a connection channel is established with the CNC system via the network port; the secondary development interface functions for reading feed speed, machine coordinates, and feed load are located and read; The second step is to calculate the frictional heat of the rolling bearing; Apply a rotational motion to the ball bearing that is the same in magnitude and opposite in direction to the angular velocity of the ball center rotating around the inner ring of the bearing, and analyze the motion relationship between the inner and outer rings and the balls of the rolling bearing; the frictional heat of the rotational motion in the contact area of ​​the ball bearing includes the sliding frictional heat between the balls and the inner and outer ring raceways and the rolling frictional heat generated by the balls rolling in the inner and outer ring raceways, as well as the heat generated by the ball bearing due to the applied load and viscous friction. The third step is to calculate the frictional heat of the ball screw assembly; The frictional heat of a ball screw pair includes the sliding frictional heat generated by the rolling of the balls in the screw raceway and nut raceway, the rolling frictional heat generated by the rolling of the balls in the screw raceway and nut raceway, the frictional heat between the balls and between the balls and the return mechanism, and the viscous frictional heat of the ball screw pair lubricant. The fourth step is to calculate the temperature field of the ball screw; Ball screws appear in the form of slender rods. Since the axial temperature change rate is greater than the radial temperature change rate, the heat conduction of ball screws is considered as a one-dimensional heat conduction problem, and its calculation method is as follows: (10) ； In the formula, Let λ be the temperature at position x at time t, λ be the thermal conductivity, ρ be the density of the ball screw material, and c be the specific heat capacity of the ball screw material. The heat source intensity is calculated by dividing the ball screw into M segments, each segment having a length of L. (11) ； Where, It is a ball screw The frictional heat generated by the ball screw pair at position x within a time interval, r S Where h is the equivalent radius of the ball screw, and h is the heat dissipation coefficient. It is the ambient temperature around the ball screw at time t. yes The frictional heat generated by the ball bearing pair on the motor side within a certain time period, r fB It is the inner ring radius of the ball bearing on the motor side. yes The frictional heat generated by the ball bearing pair at the support end within a certain time, r bB It is the inner ring radius of the ball bearing at the support end.

2. The method for real-time monitoring of the temperature field of a machine tool lead screw using CNC motion data according to claim 1, characterized in that, The calculation process for the frictional heat of rolling bearings is as follows: The calculation method for the sliding friction heat between the ball and the inner and outer raceways is expressed as follows: (1) ； Where, It is the coefficient of sliding friction between the balls and the raceways of the inner and outer rings in a ball bearing. It is the normal force at the contact point between the ball and the inner ring caused by axial load. It is the normal force at the contact point between the ball and the inner ring caused by radial load. It is the normal force at the contact point between the ball and the outer ring caused by axial load. The normal force at the contact point between the ball and the outer ring caused by radial load, S bI S is the sliding stroke that occurs during the movement of the inner ring of the bearing driving the balls. bO This refers to the sliding stroke of the ball as it moves within the outer raceway; i represents the i-th ball in the ball bearing. It refers to the number of balls in a ball bearing; The rolling friction heat generated by the balls rolling in the inner and outer raceways is calculated as follows: (2) ； Where, It is the rolling distance of the balls within the inner ring of the bearing. It is the rolling distance of the balls on the outer ring of the bearing, k is the coefficient of rolling friction between the bearing steels, and r is the rolling distance of the balls on the outer ring of the bearing. b It is the diameter of the ball bearing; The heat generated by ball bearings due to applied load and viscous friction is calculated by the following formula: (3) ； Where, The rotational speed of the leadscrew. It is the torque caused by viscous friction. It is the torque caused by the applied load; Therefore, the frictional heat of a rolling bearing is expressed as: (4)。 3. The method for real-time monitoring of the temperature field of a machine tool lead screw using CNC motion data according to claim 1, characterized in that, The frictional heat of a ball screw assembly is calculated as follows: The heat generated by the sliding friction of the balls rolling in the screw raceway and nut raceway in a ball screw pair is calculated as follows: (5) ； Where, It is the coefficient of sliding friction between the ball and the raceway. It is the contact pressure between the ii-th loaded ball in nut A and the raceway of the screw. It is the contact pressure between the ii-th loaded ball in nut A and the raceway of the nut. It is the contact pressure between the jj-th loaded ball in nut B and the raceway of the screw. S is the contact pressure between the jj-th loaded ball in nut B and the nut raceway. bS S is the rolling differential sliding stroke that occurs during the movement of the ball bearings driven by the lead screw. bN This refers to the differential sliding stroke of the balls during the movement of the ball-driven nut; Z n-A Z is the number of balls in nut A. n-B This refers to the number of balls in nut B; The rolling friction heat generated by the balls rolling in the lead screw raceway and nut raceway is calculated by the following formula: (6) ； In the formula, F a It is the external load borne by the ball screw assembly, F C λ0 is the residual preload of the ball screw pair after applying an external load, α is the helix angle of the raceway, and x is the contact angle between the ball and the raceway. s It is the rolling distance of the ball on the screw raceway, x n It is the rolling distance of the balls on the raceway of the nut; The frictional heat between the balls and between the balls and the return mechanism is expressed as a function of time t: (7) ； In the formula, q k It is the rate of frictional heat generation between the balls and between the balls and the return mechanism; The calculation method for the viscous frictional heat of the lubricant in a ball screw assembly is expressed as follows: (8) ； In the formula, f0 is a constant related to the type of ball screw pair and the lubrication method. It is the kinematic viscosity of the lubricant. It is the nominal diameter of the leadscrew. It is the stroke of the lubricant's viscous force, ω S It is the angular velocity of the lead screw rotation; The frictional heat of a ball screw pair is expressed as: (9)。

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