Real-time monitoring device and method for thermal elongation of lead screw of machine tool feeding system in machining process

Abstract

The invention discloses a real-time monitoring device for thermal elongation of a screw rod of a machine tool feeding system in a machining process, which is characterized in that axial displacement measurement reference target surfaces are respectively mounted at two ends of a screw rod nut working region on the screw rod of the feeding system, and a displacement sensor substrate is fixedly connected to a machine tool body below the screw rod; displacement sensors are installed on the displacement sensor substrate and located on the inner sides of the two axial displacement measurement reference target surfaces respectively, the displacement sensors are electrically connected with the controller, the structure is simple, installation is convenient, and cost is saved; according to the machine tool feeding system lead screw thermal elongation real-time monitoring method in the machining process, the displacement sensor collects displacement measurement data in real time, the thermal elongation at a certain point of the lead screw at the moment can be calculated by adopting a lead screw thermal elongation distribution density algorithm according to the thermal elongation at the reference target surface, and the thermal elongation of the lead screw at the moment can be calculated. The problem of real-time measurement of the thermal elongation of the lead screw in the machining process of a machine tool is solved.

Description

Technical Field

[0001] This invention belongs to the field of machine tool thermal characteristic measurement technology, specifically relating to a real-time monitoring device for thermal elongation of the lead screw in the machine tool feed system during machining, and also relating to a real-time monitoring method for thermal elongation of the lead screw in the machine tool feed system during machining. Background Technology

[0002] In CNC machine tools, the ball screw assembly is a core component for achieving linear feed motion, and its performance directly affects the machining accuracy and efficiency. During actual operation, the thermal expansion of the screw is affected by various factors. On the one hand, changes in ambient temperature cause thermal expansion and contraction of the screw; on the other hand, during feed axis movement, the friction between multiple moving parts such as bearings and the screw-nut assembly generates a large amount of heat, causing the screw to thermally expand, resulting in thermal errors. This severely affects the positioning accuracy of the feed system, leading to machining errors. Accurately obtaining the thermal expansion of the feed axis in real time is crucial for studying its thermal characteristics and achieving thermal error compensation.

[0003] Currently, monitoring the thermal elongation of lead screws mainly relies on optical grating rulers and laser interferometers. While optical grating rulers offer high measurement accuracy, their high cost, complex installation process, and requirement for precise positioning and adjustment limit their widespread application. Laser interferometers, on the other hand, can only perform measurements under no-load conditions and cannot be used during the manufacturing process.

[0004] Therefore, there is a need for a method to measure the thermal elongation of the lead screw in real time during machine tool operation, which can dynamically monitor and obtain accurate thermal elongation data of the lead screw, be applicable to different application scenarios, provide data for thermal error compensation, and have good economic efficiency. Summary of the Invention

[0005] The purpose of this invention is to provide a real-time monitoring device for thermal expansion of the lead screw in the machine tool feed system during machining, which solves the problems that some existing machine tools do not have grating rulers due to their high cost, and that existing measuring devices cannot measure thermal expansion during machine tool machining.

[0006] Another objective of this invention is to provide a method for real-time monitoring of thermal expansion of the lead screw in a machine tool feed system during machining, thereby providing real-time thermal expansion data for thermal error compensation.

[0007] The technical solution of the present invention is a real-time monitoring device for thermal expansion of the lead screw in the machine tool feed system during processing. The device includes a lead screw, a lead screw nut connected to the lead screw, a worktable fixed to one side of the lead screw nut, the lead screw installed between a fixed-end bearing seat and a motor-end bearing seat, one end of the lead screw passing through the motor-end bearing seat and connected to a motor, axial displacement measuring reference targets installed at both ends of the lead screw within the working range of the lead screw nut, a displacement sensor base plate fixed to the machine tool bed below the lead screw, displacement sensors installed on the displacement sensor base plate inside the two axial displacement measuring reference targets, and the displacement sensors connected to a controller.

[0008] The invention is further characterized in that, The displacement sensor substrate is made of glass substrate, carbon fiber substrate or engineering ceramic substrate.

[0009] The displacement sensor is mounted on a displacement sensor bracket, and the displacement sensor bracket is mounted on a displacement sensor substrate.

[0010] The axial displacement measurement reference target surface adopts a split annular plate structure, which is formed by two symmetrical semi-circular components fixedly connected, and the annular inner hole is assembled with the outer circumference of the lead screw.

[0011] Two semi-circular components are rigidly mounted on the optical axis surfaces at both ends of the lead screw.

[0012] Another technical solution of the present invention is a measurement method for a real-time monitoring device for thermal expansion of the lead screw in a machine tool feed system during machining. The method employs the aforementioned real-time monitoring device for thermal expansion of the lead screw in a machine tool feed system during machining, and the steps are as follows: Step 1: Axial displacement measuring reference targets are installed at both ends of the working range of the lead screw and nut on the feed system lead screw. A displacement sensor base plate is fixed on the machine tool bed below the lead screw. Displacement sensors are installed on the displacement sensor base plate on the inner side of the two axial displacement measuring reference targets. Step 2: During the machine tool processing, the displacement sensor measures the movement of the corresponding axial displacement measurement reference target surface in real time and transmits it to the controller. The controller calculates the thermal elongation of the lead screw based on the thermal elongation distribution density algorithm at the reference target surface.

[0013] Another feature of the present invention is that, In step 2, the algorithm for the thermal elongation distribution density of the lead screw is as follows: Thermal elongation distribution density function The formula is:

[0014] In the formula: This represents the thermal elongation distribution density function; The variables representing the thermal elongation distribution density function and the coordinates of the leadscrew position; The variable representing the thermal elongation distribution density function is the lead screw running time; This indicates the zero position of the reference target surface for measuring the axial displacement at one end of the lead screw's working range. This indicates the termination position of the axial displacement measurement reference target surface at the other end of the lead screw working range.

[0015] The thermally induced positioning error at any position inside the lead screw is expressed as:

[0016] In the formula: express time Positioning error at the location; express Start point of the lead screw Thermal elongation at the point; express End point of the lead screw Thermal elongation at the point.

[0017] The beneficial effects of this invention are: The real-time monitoring device for thermal expansion of the lead screw in the machine tool feed system of the present invention has a simple structure, is easy to install, is highly economical, and is easy to implement; the displacement sensor substrate is made of materials with low thermal expansion coefficients such as glass, carbon fiber, and engineering ceramics, and its structural dimensions are not affected by temperature changes. The present invention discloses a method for real-time monitoring of the thermal elongation of the lead screw in a machine tool feed system during machining. An axial displacement measurement reference target is rigidly clamped onto the optical axis surfaces at both ends of the lead screw, serving as the axial measurement reference for the displacement sensor. A motor drives the lead screw to rotate, causing the lead screw nut to move axially. Heat is generated between the moving parts due to friction. As the heat accumulates, the thermal elongation of the lead screw gradually increases, reflected in the change in distance between the axial displacement measurement reference target and the displacement sensor. The displacement sensor collects displacement measurement data in real time to obtain the thermal elongation at the lead screw reference target. Based on the thermal elongation at the reference target, a lead screw thermal elongation distribution density algorithm is used to calculate the thermal elongation at a specific point on the lead screw at that moment. This method solves the problem of difficulty in real-time measurement of the lead screw's thermal elongation during machine tool machining. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the structure of the real-time monitoring device for thermal elongation of the lead screw in the machine tool feed system during the processing of the present invention; Figure 2This is a schematic diagram of the structure of the motor end bearing seat of the monitoring device of the present invention; Figure 3 This is a schematic diagram of the structure of the fixed end bearing seat of the monitoring device of the present invention; Figure 4 This is a schematic diagram of the lead screw of the monitoring device of the present invention with a reserved reference target surface; Figure 5 This is a schematic diagram illustrating the verification of the real-time monitoring device for lead screw thermal elongation and the measurement method using a laser interferometer. Figure 6 This is a graph showing the thermal deformation curve measured by a laser interferometer in the experiment verifying the effectiveness of the monitoring method of this invention. Figure 7 This is a graph showing the measurement effect of the monitoring method of the present invention and the thermal deformation residual curve measured by the laser interferometer; Figure 8a These are thermal elongation distribution curves obtained at different times using the laser interferometer measurement method. Figure 8b This is a graph showing the thermal elongation distribution at different times obtained by the monitoring method of this invention; Figure 9 This is a graph showing the residual curves of thermal elongation distribution at different times obtained by the monitoring method of this invention and the laser interferometer.

[0019] In the figure, 1. Motor, 2. Motor end bearing housing, 3. Mounting support, 4. Displacement sensor, 5. Axial displacement measurement reference target surface, 6. Lead screw, 7. Worktable, 8. Lead screw nut, 9. Fixed end bearing housing, 10. Displacement sensor substrate, 11. Laser interferometer, 12. Interferometer mirror, 13. Reflector. Detailed Implementation

[0020] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0021] Example 1 The real-time monitoring device for thermal elongation of the lead screw in the machine tool feed system during the machining process of the present invention has the following structure: Figure 1 , Figure 2 and Figure 3As shown, the system includes a lead screw 6, a lead screw nut 8 connected to the lead screw 6, a worktable 7 fixed to one side of the lead screw nut 8, the lead screw 6 being installed between a fixed end bearing seat 9 and a motor end bearing seat 2, one end of the lead screw 6 passing through the motor end bearing seat 2 and connected to a motor 1, axial displacement measuring reference targets 5 being installed at both ends of the lead screw 6 within the working range of the lead screw nut 8, the axial displacement measuring reference targets 5 being thermally expanded or retracted synchronously with the lead screw 6, a displacement sensor base plate 10 being fixed to the machine bed below the lead screw 6, displacement sensors 4 being installed on the displacement sensor base plate 10 on the inner side of the two axial displacement measuring reference targets 5, and the displacement sensors 4 being electrically connected to the controller.

[0022] The displacement sensor 4 is a high-precision displacement sensor that measures the minute movement of the axial displacement measurement reference target surface 5 in real time and transmits it to the controller. The controller calculates the thermal elongation of the lead screw 6 based on the thermal elongation at the reference target surface using the lead screw thermal elongation distribution density algorithm.

[0023] Example 2 Based on Example 1, the displacement sensor substrate 10 is made of materials with low thermal expansion coefficients such as glass substrate, carbon fiber substrate, and engineering ceramic substrate. Its structural dimensions are not affected by temperature changes, and its geometric dimensions remain almost unchanged during the thermal deformation of the lead screw.

[0024] Example 3 Based on embodiment 2, displacement sensor 4 is mounted on displacement sensor bracket 3, and displacement sensor bracket 3 is mounted on displacement sensor substrate 10.

[0025] Example 4 Based on Example 3, such as Figure 4 As shown, the axial displacement measurement reference target surface 5 adopts a split annular plate structure, which is formed by splicing two symmetrical semicircular components, and the annular inner hole is fitted with the outer circumference of the lead screw 6.

[0026] Two semi-circular components are rigidly clamped onto the optical axis surfaces at both ends of the lead screw 6.

[0027] The displacement sensor substrate is fixedly connected to the single feed axis base. During machine tool movement, it is not affected by the movement of other feed axes and can adapt to the measurement of lead screw thermal elongation under any working conditions.

[0028] The present invention relates to a real-time monitoring device for thermal expansion of the lead screw in the machine tool feed system. The displacement sensor substrate 10 is made of a material with a low coefficient of thermal expansion, unaffected by temperature, ensuring that the spatial position of the displacement sensor 4 remains unchanged during the thermal expansion of the feed axis. The axial displacement measuring reference target 5 consists of two annular semicircular parts, installed at the optical axis at both ends of the lead screw's working range. As the lead screw undergoes thermal expansion, the reference target 5 moves synchronously. The displacement sensor 4 measures the movement of the axial displacement measuring reference target 5 in real time, accurately monitoring the thermal expansion of the lead screw. The device is simple in structure, easy to install, economical, and easy to implement.

[0029] Example 5 The measurement method of the real-time monitoring device for thermal expansion of the lead screw in the machine tool feed system during machining, according to the present invention, adopts the real-time monitoring device for thermal expansion of the lead screw in the machine tool feed system during machining as described in Embodiment 4 above, and the steps are as follows: Motor 1 is mounted on motor end bearing seat 2, lead screw 6 is mounted between bearing seat 9 and motor end bearing seat 2, worktable 7 is mounted on lead screw nut 8, and lead screw nut 8 is mounted on lead screw 6, forming a feeding system.

[0030] Step 1, as follows Figure 1 and Figure 5 As shown, axial displacement measuring reference target surfaces 5 are respectively installed at the O and L positions on both ends of the working range of the lead screw 6 of the feed system, and displacement sensor base plate 10 is fixedly connected to the machine tool feed axis base below the lead screw 6. Displacement sensors 4 are respectively installed on the displacement sensor base plate 10 on the inner side of the two axial displacement measuring reference target surfaces 5, and the displacement sensors 4 are electrically connected to the controller. Displacement sensor 4 is installed as follows: Figure 2 , Figure 3 As shown. Δ1 and Δ2 are the distances between the axial displacement measurement reference target surface 5 and the displacement sensor 4, respectively. When the lead screw thermally elongates, it causes a slight movement of the reference target surface, resulting in changes in the values ​​of Δ1 and Δ2. The changes in Δ1 and Δ2 are obtained through the displacement sensor 4, representing the thermal elongation of the reference target surfaces on both sides. and .

[0031] Step 2: During machine tool processing, motor 1 drives the lead screw 6 to rotate, causing the lead screw nut 8 and worktable 7 to move along the lead screw 6. Heat is generated through friction between the lead screw nut 8 and the lead screw 6, as well as between the moving parts of the bearings. The lead screw 6 expands due to heat, causing thermal elongation and moving the reference target surface 5. Because the displacement sensor substrate 10 has a low coefficient of thermal expansion, changes in ambient heat have almost no effect on its geometric dimensions, and the spatial position of the displacement sensor 4 remains unchanged. The distance between the reference target surface 5 and the displacement sensor 4 changes as follows: As the feed system operates, friction generates heat, and the lead screw 6 expands to both sides, increasing both Δ1 and Δ2 distances. When the feed system stops operating, due to convection heat transfer, the temperature of the lead screw 6 decreases, causing it to contract, and decreasing both Δ1 and Δ2 distances. Figure 2 , 3 As shown. The displacement sensor 4 measures the movement of the corresponding axial displacement measuring reference target surface 5 in real time and transmits it to the controller. The controller calculates the thermal elongation of the lead screw 6 based on the thermal elongation at the reference target surface using the lead screw thermal elongation distribution density algorithm.

[0032] The specific algorithm for the thermal elongation distribution density of the lead screw is as follows: According to the principles of thermoelasticity, the thermal elongation of the leadscrew is obtained by integrating the thermal strain caused by the temperature field along the axis, and the thermal elongation distribution density function is given by... The formula is:

[0033] In the formula: This represents the thermal elongation distribution density function; The variables representing the thermal elongation distribution density function and the coordinates of the leadscrew position; The variable representing the thermal elongation distribution density function is the lead screw running time; This indicates the zero position of the reference target surface for measuring the axial displacement at one end of the lead screw's working range. This indicates the termination position of the axial displacement measurement reference target surface at the other end of the lead screw working range.

[0034] The thermally induced positioning error at any position inside the lead screw is expressed as:

[0035] In the formula: express time Positioning error at the location; express Start point of the lead screw Thermal elongation at that point, i.e. Figure 2The change in Δ1.

[0036] express End point of the lead screw Thermal elongation at that point, i.e. Figure 3 The change in Δ2.

[0037] The local thermal elongation and total thermal elongation of the lead screw have a mathematical relationship. Based on the total thermal elongation measured by the machine tool, the thermal elongation at any position can be calculated using the lead screw thermal elongation distribution density algorithm. The real-time thermal elongation measurement method for lead screws proposed in this invention allows for the prefabrication of a reference target surface structure during the manufacturing process for new lead screws, such as... Figure 4 As shown, the installation of the axial displacement measurement reference target surface 5 is omitted.

[0038] Example 6 The measurement method of the real-time monitoring device for thermal expansion of the lead screw in the machine tool feed system of the present invention is applicable to feed systems with different lead screw installation methods, such as fixed at both ends, supported at both ends, and supported at one end and fixed at the other. Compared with traditional thermal expansion measurement methods, the present invention adds measuring target surfaces to both sides of the lead screw working area, which changes the fact that some measurement methods cannot measure the overall thermal expansion of the lead screw. The installation of the reference target surfaces does not affect the operation of the lead screw during machine tool processing, thus solving the problem of difficult monitoring of lead screw thermal expansion in machining processes.

[0039] The present invention discloses a method for real-time monitoring of the thermal elongation of the lead screw in a machine tool feed system during machining. An axial displacement measurement reference target is rigidly clamped onto the optical axis surfaces at both ends of the lead screw, serving as the axial measurement reference for the displacement sensor. A motor drives the lead screw to rotate, causing the lead screw nut to move axially. Heat is generated between the moving parts due to friction. As the heat accumulates, the thermal elongation of the lead screw gradually increases, reflected in the change in distance between the axial displacement measurement reference target and the displacement sensor. The displacement sensor collects displacement measurement data in real time to obtain the thermal elongation at the lead screw reference target. Based on the thermal elongation at the reference target, a lead screw thermal elongation distribution density algorithm is used to calculate the thermal elongation at a specific point on the lead screw at that moment. This solves the problem of real-time measurement of the lead screw's thermal elongation during machine tool machining.

[0040] The measurement method of the real-time monitoring device for thermal elongation of the lead screw in the machine tool feed system during the machining process of the present invention has the following advantages: It can directly measure the actual deformation of the working section of the lead screw caused by thermal effects, and the data source is direct and highly reliable; it can simultaneously monitor the thermal deformation at both ends of the lead screw, fully reflect the overall thermal elongation state of the lead screw, and ensure the comprehensiveness and accuracy of the data. It is suitable for different lead screw installation methods such as fixed at both ends, supported at both ends, and supported at one end and fixed at the other end of the feed system.

[0041] To verify the effectiveness of the method proposed in this invention, the measurement results can be verified. Since the reciprocating movement of the lead screw nut 8 on the lead screw 6 constitutes uniform heating, the resulting thermal deformation is uniformly distributed across the entire lead screw. The thermal elongation distribution function is defined as a constant function and can be expressed as:

[0042] In the formula: This represents the thermal elongation distribution density function under test conditions, i.e., uniform heating. This indicates the installation distance between two axial displacement measurement reference targets.

[0043] Substituting formula (3) into formula (2), the thermal elongation at any point can be simplified as follows:

[0044] In the formula: Indicates the position point of the leadscrew; Indicates the lead screw travel time; This indicates the zero position of the axial displacement measurement reference target surface; This indicates the termination position of the axial displacement measurement reference target surface installation.

[0045] express time Positioning error at the location; express Start point of the lead screw Thermal elongation at the point; express End point of the lead screw Thermal elongation at the point.

[0046] The model requires only one multiplication to obtain thermal elongation, making it easy to implement and highly real-time.

[0047] To verify the effectiveness of the method proposed in this invention, the following was employed: Figure 5The method of measuring thermal elongation using a laser interferometer 11 is shown to verify the effectiveness of the measurement method in Embodiment 5 of the present invention. Specifically, the laser interferometer 11 and the reflector 13 are respectively arranged at both ends of the feed system, and the interferometer 12 is installed on the worktable 7 and moves synchronously with the worktable 7. Several measuring points are set within the movement range of the lead screw 6. When the lead screw 6 moves, the thermal elongation of each measuring point is measured in real time by the laser interferometer 11, thereby reflecting the thermal deformation of the lead screw during the movement. The reference target surface is installed at the positions x1=0 and x2=800mm on the lead screw, and the thermal elongation of the lead screw at several points within the range of [50mm, 750mm] is used as a reference. The lead screw nut is moved back and forth along the lead screw at a feed speed of 3m / min to simulate the working condition. The thermal deformation at different positions x=0, 50, 750 and 800 and the thermal deformation at x=50 and x=750 predicted by the method are measured, as shown. Figure 6 As shown, where x =0 and x A negative value on the thermal deformation curve at 750 indicates that the lead screw elongates in the opposite direction along the specified positive direction. The residuals of the thermal deformation prediction curve of the measurement method in Embodiment 5 of this invention and the thermal deformation curve measured by the laser interferometer 11 are as follows: Figure 7 As shown in the figure, the difference between the thermal elongation at different positions of the lead screw obtained by this method and the measurement data of the laser interferometer 11 is within ±1.5μm, which proves the effectiveness of this method.

[0048] The thermal elongation distribution curves of the lead screw at different times are as follows: Figure 8a and Figure 8b As shown, Figure 8a This is a graph showing the thermal elongation of the lead screw over time within the range of [50mm, 750mm] as measured by a laser interferometer. Figure 8b This is a graph showing the thermal elongation of the lead screw over time in the range [0, 800 mm] as predicted by the measurement method of this invention. Figure 9 The figure shows the residual between the predicted value of the measurement method of this invention and the measured value of the laser interferometer. As can be seen from the figure, the difference between the two data is always kept within ±1.5μm, and has good consistency at any position of the lead screw, which proves that the method maintains high prediction accuracy at different positions.

[0049] The above embodiments of the present invention are merely illustrative examples to clearly illustrate the invention and are not intended to limit the implementation of the invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all possible implementations. The above descriptions are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications based on the technical solutions and concepts of the present invention should fall within the scope of protection of the present invention.

Claims

1. A real-time monitoring device for thermal expansion of the lead screw in the machine tool feed system during machining, characterized in that, The system includes a lead screw (6), a lead screw nut (8) connected to the lead screw (6), a worktable (7) fixed to one side of the lead screw nut (8), the lead screw (6) is installed between the fixed end bearing seat (9) and the motor end bearing seat (2), one end of the lead screw (6) passes through the motor end bearing seat (2) and is connected to the motor (1), axial displacement measuring reference targets (5) are installed at both ends of the working range of the lead screw (6), a displacement sensor base plate (10) is fixed to the machine bed below the lead screw (6), and displacement sensors (4) are installed on the displacement sensor base plate (10) on the inner side of the two axial displacement measuring reference targets (5), and the displacement sensors (4) are connected to the controller.

2. The real-time monitoring device for thermal elongation of the lead screw in the machine tool feed system during processing, as described in claim 1, is characterized in that... The displacement sensor substrate (10) is made of glass substrate, carbon fiber substrate, or engineering ceramic substrate.

3. The real-time monitoring device for thermal elongation of the lead screw in the machine tool feed system during processing, as described in claim 1, is characterized in that... The displacement sensor (4) is mounted on the displacement sensor bracket (3), and the displacement sensor bracket (3) is mounted on the displacement sensor substrate (10).

4. The real-time monitoring device for thermal elongation of the lead screw in the machine tool feed system during processing, as described in claim 1, is characterized in that... The axial displacement measurement reference target surface (5) adopts a split ring plate structure, which is formed by two symmetrical semi-circular components fixedly connected, and the annular inner hole is sleeved and assembled with the outer circumference of the lead screw (6).

5. The real-time monitoring device for thermal elongation of the lead screw in the machine tool feed system during processing, as described in claim 4, is characterized in that... The two semi-circular components are rigidly installed on the optical axis surfaces at both ends of the lead screw (6).

6. The monitoring method of the real-time monitoring device for thermal elongation of the lead screw in the machine tool feed system during machining, as described in any one of claims 1-5, is characterized in that... The steps are as follows: Step 1: Axial displacement measuring reference target surfaces (5) are installed at both ends of the working range of the screw nut (8) on the feed system screw (6). A displacement sensor base plate (10) is fixedly connected to the machine tool bed below the screw (6). Displacement sensors (4) are installed on the inner side of the two axial displacement measuring reference target surfaces (5) on the displacement sensor base plate (10). Step 2: During the machine tool processing, the displacement sensor (4) measures the movement of the corresponding axial displacement measurement reference target surface (5) in real time and transmits it to the controller. The controller uses the lead screw thermal elongation distribution density algorithm based on the thermal elongation at the reference target surface to calculate the thermal elongation of the lead screw (6).

7. The method for real-time monitoring of thermal elongation of the lead screw in the machine tool feed system during machining, as described in claim 6, is characterized in that... In step 2, the algorithm for the thermal elongation distribution density of the lead screw is specifically as follows: Thermal elongation distribution density function The formula is: In the formula: This represents the thermal elongation distribution density function; The variables representing the thermal elongation distribution density function and the coordinates of the leadscrew position; The variable representing the thermal elongation distribution density function is the lead screw running time; This indicates the zero position of the reference target surface for measuring the axial displacement at one end of the lead screw's working range. This indicates the termination position of the axial displacement measurement reference target surface at the other end of the lead screw working range.

8. The method for monitoring the thermal elongation of the lead screw in the machine tool feed system during machining, as described in claim 7, is characterized in that... The thermally induced positioning error at any position within the lead screw is expressed as: In the formula: express time Positioning error at the location; express Start point of the lead screw Thermal elongation at the point; express End point of the lead screw Thermal elongation at the point.

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