Error compensation method for lead screw of laser cutting machine under plc driving

Abstract

The application discloses a laser cutting machine screw error compensation method under PLC driving and particularly relates to the technical field of laser cutting equipment error compensation, wherein the screw position error is obtained through forward and reverse calibration, the residual error of different reversing strokes is extracted, and a residual error relationship table is established; during the machining process, the PLC determines the comprehensive screw error according to the current target position, the reversing position and the movement direction, performs asymmetric continuous correction on the zero-crossing interval, generates a compensation amount, further takes the corrected position before reversing as a correction anchor point, corrects the current target position through the compensation increment and sends the current target position to a servo driver, realizes continuous compensation of the screw error under the working condition of short-stroke frequent reversing, and improves the laser cutting positioning precision and the contour consistency.

Description

Technical Field

[0001] This invention relates to the field of error compensation technology for laser cutting equipment, specifically to a method for error compensation of the lead screw in a laser cutting machine driven by a PLC. Background Technology

[0002] In PLC-driven laser cutting machines, the positioning accuracy of the cutting head is typically improved by pre-calibrating the lead screw positioning error and establishing a position compensation table. However, when machining minute serrations, dense narrow grooves, or continuous polygonal contours, the feed axis continuously reverses direction within a short stroke. The elastic deformation of the lead screw nut pair generated by the previous reversal is not fully released before the next reversal, causing the actual return error to vary with the running distance after the reversal. Existing methods typically use a fixed reverse clearance value for compensation, which cannot distinguish between long-stroke reversal and short-stroke continuous reversal conditions. This easily leads to overcompensation in the short-stroke region and causes alternating positional shifts between adjacent reversal points, resulting in inconsistent dimensions at the end of narrow grooves and local deformation of minute contours. This limits the positioning accuracy of the laser cutting machine under high-frequency short-stroke reversal conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a method for compensating for lead screw errors in a laser cutting machine driven by a PLC, so as to overcome the shortcomings in the prior art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for compensating for lead screw errors in a laser cutting machine driven by a PLC, comprising: The control screw motion axis passes through the preset calibration position in the forward and reverse directions respectively, and the actual position of each calibration position is obtained. The forward position error and reverse position error are obtained based on the difference between the actual position and the corresponding command position. Perform reversing test strokes of different lengths at each calibration position, obtain the actual displacement at the end of each reversing test stroke, and subtract the position error of the corresponding calibration position from the actual displacement error to obtain the reversing residual error used to characterize the degree of elastic deformation release of the lead screw and nut pair after reversing. A residual error relationship table is established based on the test stroke length of each reversing test and the corresponding reversing residual error, and stored in the PLC. During the laser cutting process, the PLC obtains the position error corresponding to the current position based on the current target position and the direction of movement, and records the reversing position when a change in the direction of movement is detected. The reversing stroke is obtained based on the distance between the current target position and the reversing position. The current reversing residual error is determined from the residual error relationship table based on the reversing stroke. The position error and the current reversing residual error are superimposed to obtain the comprehensive lead screw error, and a compensation amount opposite to the direction of the comprehensive lead screw error is generated. The current target position is corrected according to the compensation amount, and the corrected target position is sent to the servo driver to control the movement of the lead screw of the laser cutting machine.

[0005] Preferably, obtaining the reversing residual error includes: after the lead screw axis reaches a preset calibration position, determining the preset calibration position as the reversing start position, and recording the forward movement direction and the initial actual position; controlling the lead screw axis to change its movement direction and execute reversing test strokes of different lengths, obtaining the actual displacement based on the initial actual position and the final actual position corresponding to each reversing test stroke, and obtaining the command displacement based on the reversing start position and the test end position, and determining the difference between the actual displacement and the command displacement as the actual displacement error; determining the start position error corresponding to the reversing start position based on the forward movement direction, and determining the end position error corresponding to the test end position based on the post-reversing movement direction, and determining the difference between the end position error and the start position error as the basic displacement error; subtracting the basic displacement error from the actual displacement error to obtain the reversing residual error, and associating the reversing residual error with the reversing start position, the reversing direction, and the reversing test stroke length.

[0006] Preferably, establishing a residual error relationship table and determining the current reversing residual error includes: grouping the reversing residual error data according to the reversing start position and the direction of movement after the reversal, and establishing a correspondence between the reversing residual errors within each group according to the reversing test stroke length, forming a residual error relationship table; during the laser cutting process, determining the corresponding residual error data based on the current reversing position and the direction of movement after the reversal; when the current reversing position is located between two adjacent reversing start calibration positions, determining the residual error sequence corresponding to the current reversing position based on the positional relationship between the current reversing position and the two reversing start calibration positions; obtaining the current stroke after the reversal based on the distance between the current target position and the current reversing position, and determining the current reversing residual error from the residual error sequence based on the positional relationship between the current stroke after the reversal and the adjacent reversing test stroke lengths.

[0007] Preferably, the processing of the comprehensive lead screw error includes: algebraically superimposing the basic position error corresponding to the current target position and the current commutation residual error in a unified axial coordinate direction to obtain the current comprehensive lead screw error; determining the first test stroke and the second test stroke surrounding the current commutation stroke based on the current commutation stroke, and converting the first test stroke and the second test stroke into corresponding axial positions starting from the current commutation position; determining the position error of the corresponding axial position respectively, and superimposing it with the commutation residual error corresponding to the corresponding test stroke to obtain the first comprehensive error and the second comprehensive error; when the first comprehensive error and the second comprehensive error have opposite signs, determining the region between the first test stroke and the second test stroke as the zero-crossing transition interval corresponding to the current target position.

[0008] Preferably, the error transition position within the zero-crossing transition interval is determined as follows: The absolute values ​​of the first comprehensive error and the second comprehensive error are obtained; the sum of their absolute values ​​is used to determine the error amplitude ratio of the first comprehensive error and the second comprehensive error within the zero-crossing transition interval; based on the first test stroke, the second test stroke, and the error amplitude ratio corresponding to the first comprehensive error, the error transition stroke corresponding to the change from the direction of the first comprehensive error to the direction of the second comprehensive error is determined; the error transition position is determined based on the error transition stroke, the current reversing position, and the direction of movement after the reversing, so that the error transition position shifts with the relative amplitude of the comprehensive errors on both sides of the zero-crossing.

[0009] Preferably, the comprehensive lead screw error correction within the zero-crossing transition interval includes: determining the distance from the first test stroke to the error transition stroke and the distance from the error transition stroke to the second test stroke as the first-side transition distance and the second-side transition distance, respectively; selecting the corresponding transition distance based on whether the current reversing stroke is located on the first or second side of the error transition stroke, and determining the asymmetric transition ratio based on the ratio of the distance from the current reversing stroke to the error transition stroke to the selected transition distance; determining the error direction based on the sign of the comprehensive error corresponding to the side where the current reversing stroke is located, and continuously scaling the absolute value of the current comprehensive lead screw error using the asymmetric transition ratio to obtain the transition comprehensive error, so that the transition comprehensive error continuously decreases to zero as the current target position approaches the error transition position.

[0010] Preferably, generating the compensation amount includes: determining whether the first comprehensive error and the second comprehensive error corresponding to the current target position have opposite signs; when the two have opposite signs, determining the transition comprehensive error as the error to be compensated; when the two have the same sign, determining the current comprehensive lead screw error as the error to be compensated; determining the lead screw compensation direction opposite to the direction of the error to be compensated under a unified axial coordinate, and determining the lead screw compensation amplitude with the absolute value of the error to be compensated; and forming the current compensation amount for correcting the current target position by the lead screw compensation direction and the lead screw compensation amplitude.

[0011] Preferably, correcting the current target position based on the current compensation amount includes: when a reversal is detected in the lead screw motion axis, determining the correction target position corresponding to the last target position before the reversal as the correction anchor point of the current reversal motion segment; using the current reversal position as the starting position of the stroke after the reversal, and determining the initial compensation amount corresponding to the stroke being zero after the reversal according to the direction of motion after the reversal; obtaining the current compensation amount corresponding to the current target position, determining the difference between the current compensation amount and the initial compensation amount as the compensation increment, and determining the directional position difference between the current target position and the current reversal position as the target displacement after the reversal; performing algebraic superposition of the compensation increment and the target displacement after the reversal to obtain the correction target displacement, and performing position synthesis of the correction target displacement and the correction anchor point to obtain the current correction target position.

[0012] Preferably, the correction anchor point is updated according to the current reversing motion segment, including: keeping the correction anchor point unchanged within the current reversing motion segment, and determining the corresponding current compensation amount and compensation increment for each subsequent target position, generating the corresponding correction target position with the correction anchor point as a common position reference; sending the correction target position to the servo driver to control the lead screw movement; when the next change in motion direction is detected, updating the last correction target position formed before the reversal occurs to the correction anchor point of the next reversing motion segment, and re-determining the corresponding initial compensation amount according to the new reversing position.

[0013] The technical effects and advantages provided by the present invention in the above technical solution are as follows: Compared to existing lead screw compensation methods that use fixed backlash compensation values ​​or single position error compensation tables, the core difference of this invention lies in its approach to the situation where the elastic deformation of the lead screw nut pair is not fully released during short-stroke, high-frequency reversing operations in laser cutting machines. This invention separates the additional positional deviation after reversal from the conventional positional error and establishes a residual error relationship based on the reversal start position, reversal direction, and post-reversal stroke. During actual cutting, the PLC determines the post-reversal stroke in real time based on the current reversal position and target position, and calls upon the reversal residual error corresponding to the current operating condition. This residual error is then superimposed with the basic positional error to form a comprehensive lead screw error. This technique ensures that the compensation amount is no longer solely determined by the lead screw position or a preset fixed return clearance, but continuously varies with the actual running distance after each reversal. This adapts to the gradual release of return errors in dense narrow grooves, small broken lines, and short-stroke reciprocating cutting, reducing over-compensation or under-compensation caused by fixed compensation in the initial reversal stage, and directly improving the positioning consistency and contour dimensional stability of the continuous reversal area.

[0014] Furthermore, this invention does not simply superimpose the basic position error and the reversal residual error and then directly compensate in reverse. Instead, it maps both to the post-reversal travel coordinates starting from the current reversal position. The zero-crossing transition interval is determined based on the sign change of the comprehensive error at adjacent test travel nodes. The error transition position and corresponding asymmetric transition scale are determined based on the actual amplitude of the comprehensive error on both sides of the zero-crossing. This allows the comprehensive error to continuously approach zero and smoothly change the compensation direction when it changes from one direction to the opposite direction after reversal. Simultaneously, the last corrected target position formed before the reversal occurs is used as the correction anchor point for the current reversal segment. Only the change in the current compensation amount relative to the initial compensation amount is transmitted to the subsequent target position. This avoids the abrupt position command jumps caused by the direct switching of absolute compensation amounts near the reversal point in existing technologies. It allows the aforementioned residual error compensation, zero-crossing transition, and subsequent position correction to form a continuous control link, directly reducing the alternating offset and local abrupt error of adjacent contour segments during frequent reversals. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0016] Figure 1 This is a flowchart of the method of the present invention.

[0017] Figure 2 This is a schematic representation of the residual error relationship in this invention.

[0018] Figure 3 This is a schematic diagram of the commutation recognition of the present invention.

[0019] Figure 4 This is a schematic diagram of the overall lead screw error transition of the present invention.

[0020] Figure 5 This is a schematic diagram of the target location for correction according to the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Example 1, please refer to Figures 1 to 5As shown in this embodiment, the laser cutting machine lead screw error compensation method driven by PLC includes: Step S1: Control the lead screw motion axis to pass through the preset calibration position in the forward and reverse directions respectively, obtain the actual position of each calibration position, and obtain the forward position error and reverse position error based on the difference between the actual position and the corresponding command position.

[0023] Specifically, the system controls the lead screw axis to perform a homing operation, using the homing position to determine the axial coordinate reference of the axis, and defines multiple preset calibration positions within the effective stroke of the lead screw. The PLC sends position commands corresponding to each preset calibration position to the servo driver, controlling the lead screw axis to move sequentially to each preset calibration position along the coordinate increasing direction, and then sequentially return to each preset calibration position along the coordinate decreasing direction. The coordinate increasing and decreasing directions are respectively defined as the forward and reverse movement directions. When the lead screw axis reaches each preset calibration position, the actual mechanical position detected by the position detection device is obtained. The actual mechanical position is then converted to the axial coordinate reference so that it has the same position reference as the corresponding command position. For the same preset calibration position, the difference between the actual mechanical position and the corresponding command position is calculated for both forward and reverse movements. The difference between the actual mechanical position and the command position is determined as the forward position error and the reverse position error of the preset calibration position, respectively. According to the axial coordinates of each preset calibration position, the obtained forward position error and reverse position error are used to establish corresponding position error data sequences, which serve as the basis for determining the reversing residual error and calculating the overall error of the lead screw.

[0024] Step S2: Perform reversing test strokes of different lengths at each calibration position, obtain the actual displacement at the end of each reversing test stroke, and subtract the position error of the corresponding calibration position from the actual displacement error to obtain the reversing residual error used to characterize the degree of elastic deformation release of the lead screw and nut pair after reversing.

[0025] Perform a reversal test at each preset calibration position. After the lead screw axis reaches the corresponding preset calibration position along the current motion direction, the preset calibration position is determined as the reversal start position, and the motion direction before reversal and the starting actual position detected by the position detection device are recorded.

[0026] The control screw axis changes its direction of motion and performs multiple reversing test strokes of preset length. At the end of each reversing test stroke, the corresponding actual termination position is obtained. The actual displacement is determined based on the actual starting position and the actual ending position, and the command displacement is determined based on the reversing start position and the corresponding test termination position. The difference between the actual displacement and the command displacement is determined as the actual displacement error. The starting position error corresponding to the reversing start position is obtained from the aforementioned position error data sequence based on the direction of motion before reversing, and the termination position error corresponding to the test termination position is obtained based on the direction of motion after reversing. When the test termination position is located between adjacent preset calibration positions, the termination position error is determined based on the position error corresponding to the adjacent preset calibration positions.

[0027] The difference between the termination position error and the starting position error is determined as the basic displacement error, and the basic displacement error is subtracted from the actual displacement error to obtain the reversing residual error. The reversing residual error represents the additional position deviation caused by the steady-state position error relative to the corresponding motion direction after the direction of the lead screw motion axis changes. The reversing residual error is associated with the corresponding reversing starting position, reversing direction, and reversing test stroke length to form reversing residual error data.

[0028] Step S3: Establish a residual error relationship table based on the test stroke length of each reversing test and the corresponding reversing residual error, and store it in the PLC. During the laser cutting process, the PLC obtains the position error corresponding to the current position based on the current target position and the direction of movement, and records the reversing position when a change in the direction of movement is detected.

[0029] Each commutation residual error obtained in step S2 is associated with its corresponding commutation start position, post-commutation direction, and commutation test stroke length. The residual error data group is determined by the commutation start position and post-commutation direction, and a correspondence between the commutation residual errors within each data group is established according to the commutation test stroke length, forming a residual error relationship table. The residual error relationship table, along with the forward position error data sequence and reverse position error data sequence obtained in step S1, are stored in the PLC.

[0030] During laser cutting, the PLC acquires the target position of the current motion segment, determines the current motion direction based on the direction of position change of the current motion segment, and selects the corresponding positive or negative position error data sequence based on the current motion direction. Based on the positional relationship between the current target position and adjacent preset calibration positions, the basic position error of the current target position is determined from the corresponding position error data. The current motion direction is compared with the saved motion direction of the previous effective motion segment. When the two are opposite, it is determined that the lead screw motion axis has reversed direction. The command position corresponding to the change in motion direction is recorded as the current reversal position, and the motion direction after reversal is recorded, obtaining reversal state data including the current reversal position and the motion direction after reversal. This data is used to subsequently determine the stroke after reversal and to determine the current reversal residual error from the residual error relationship table.

[0031] Step S4: Based on the distance between the current target position and the reversing position, the reversing stroke is obtained. The current reversing residual error is determined from the residual error relationship table according to the reversing stroke. The position error is superimposed with the current reversing residual error to obtain the comprehensive lead screw error, and a compensation amount opposite to the direction of the comprehensive lead screw error is generated.

[0032] Based on the current target position obtained in step S3 Current reversal position And the direction of motion after the reversal, calculate the travel distance of the current target position relative to the current reversal position after the reversal: ;in, This represents the distance traveled from the most recent reversal to the current target position. Indicates the current target location. Indicates the current reversal position.

[0033] Based on the direction of motion after the reversal, the residual error data for the corresponding direction is selected from the residual error relationship table stored in step S3; when the current reversal position... When the position coincides with the starting calibration position of the reversing, select the residual error data set corresponding to that starting calibration position. When the current reversing position... When located between two adjacent reversal start calibration positions, according to Relative to the position ratio of the two reversing initial calibration positions, interpolation is performed on the two sets of residual error data to obtain the residual error sequence corresponding to the current reversing position. Further, based on the stroke after the reversing... Based on the positional relationship between two adjacent commutation test stroke lengths, stroke interpolation is performed on the residual error sequence to obtain the current commutation residual error. .

[0034] Call the basic position error corresponding to the current target position obtained in step S3 According to the positive direction of the axial coordinate uniformly adopted in steps S1 and S2, and By performing algebraic superposition, the overall leadscrew error at the current target position is obtained: ;in, This indicates the positional error of the leadscrew itself in the current direction of motion. This represents the residual commutation error that is added after the commutation. This represents the combined lead screw error formed by the two types of errors at the current target position.

[0035] Based on the travel after the reversal Determine the bounding nodes from the test travel nodes corresponding to the residual error relationship table. Adjacent first test stroke Second test trip Based on the direction of motion after the reversal. Convert the two test strokes into the axial positions corresponding to the current reversal positions: , ,in, This indicates the axial direction of motion after the reversal; the positive direction is taken when the motion increases along the axial coordinate, and the negative direction is taken when the motion decreases along the axial coordinate.

[0036] According to respectively and Determine the first position error and the second position error from the position error data sequence corresponding to the direction of motion, and compare them with... and The corresponding commutation residual errors are algebraically superimposed to obtain the first comprehensive error. Second comprehensive error This unifies the position error data and the reversing residual error data into the post-reversing travel coordinates, starting from the current reversing position.

[0037] judge Whether the above relationship holds true. If the above relationship holds true, the adjacent test stroke interval where the current target position is located is determined to be a zero-crossing transition interval, meaning the combined leadscrew error is within... and The direction changes between them; when the above relationship does not hold, the current comprehensive leadscrew error will be... It is directly used as the error to be compensated.

[0038] For the zero-crossing transition interval, according to the first comprehensive error Second comprehensive error and the corresponding test schedule , Determine the error transition stroke corresponding to zero comprehensive lead screw error. : ;in, This indicates the zero-value travel position when the combined leadscrew error transitions from the first error direction to the second error direction.

[0039] Further determine the total travel distance of the zero-crossing interval: The error ratio on the first side is determined based on the absolute value of the combined error on both sides of the zero-crossing. Second side error ratio : , ;in, Indicates the first test trip To error transition stroke distance, Indicates error transition stroke To the second test trip The distance.

[0040] when At that time, the asymmetric transition ratio is determined based on the distance from the current reverse travel to the error transition travel: ; when At that time, it was determined that: ; when season .

[0041] Therefore, the asymmetric transition ratio The value is 1 at the corresponding test stroke node and continuously decreases to 0 as the current target position approaches the error transition stroke; since the normalized distances on both sides of the zero crossover are respectively... and This is determined so that the transition ratios on both sides are adjusted according to the corresponding comprehensive error amplitudes, instead of using the same distance scale for symmetrical processing.

[0042] The sign of the error is determined based on the position of the current post-commutation travel relative to the error transition travel: when The first comprehensive error is used at that time. The symbol, when The second comprehensive error is used at that time. The symbol; utilizing the asymmetric transition ratio For the current comprehensive lead screw error Scaling the absolute value yields the transition synthesis error. : ;in, The sign of the comprehensive error corresponding to the zero-crossing side where the current target position is located; when season .

[0043] The transition comprehensive error obtained when the current target position is in the zero-crossing transition interval Or, the combined screw error obtained when the current target position is not in the zero-crossing transition interval. The error to be compensated was determined to be... ,Right now: ; Generate a lead screw compensation amount in the opposite direction based on the error to be compensated: ;in, This is the lead screw compensation amount used to correct the current target position, and serves as the input for generating the corrected target position in the next step.

[0044] Step S5: Correct the current target position according to the compensation amount, and send the corrected target position to the servo driver to control the movement of the laser cutting machine lead screw.

[0045] When the PLC detects a reversal in the lead screw axis, it acquires the corrected target position corresponding to the last target position before the reversal, and determines the corrected target position as the corrected anchor point for the current reversal motion segment. The correction anchor point remains unchanged within the current reversing motion segment, serving as a continuous reference for maintaining the forward and backward position control commands before and after the reversal. The uncorrected axial position corresponding to the reversal point is denoted as the reversal position. .

[0046] According to the error compensation method in step S4, the reversing position is... Using the starting position of the current reversing motion segment as the starting position, and the direction of motion after reversal as the error data selection direction, and setting the stroke after reversal to zero, the initial compensation amount corresponding to the direction of motion after reversal at the reversing position is determined. For the current target location Obtain the current compensation amount determined in step S4 based on the current travel after the current reversal. And calculate: ;in, This is the compensation increment generated within the current reversing motion segment relative to the initial reversing state. This serves as the compensation reference for the direction at the reversing position after the reversal. This is the compensation amount corresponding to the current target location.

[0047] Based on the current target location With reversing position The directional position difference under a unified axial coordinate system is used to determine the target displacement after the reversal: The target displacement after the reversal is then algebraically superimposed with the compensation increment to obtain the corrected target displacement relative to the corrected anchor point. ;in, This represents the corrected displacement required to achieve the current target position, starting from the corrected anchor point already established during the reversal; because... Instead of reapplying absolute compensation at the reversing position, the difference between the current compensation amount and the initial compensation amount after the reversing is used. Therefore, the compensation changes caused by the residual error after the reversing and the zero-crossing transition are transmitted incrementally along the current reversing motion segment.

[0048] According to the modified anchor point With correction of target displacement Get the current correction target position : The PLC will specify the current target position for correction. The corresponding position control command is generated and sent to the servo driver, which drives the servo motor and lead screw to execute the current motion. Within the current reversing motion segment, the corrected anchor point is maintained for subsequent target positions. The current compensation increment is calculated based on the corresponding current compensation amount. When a change in motion direction is detected again, the last corrected target position formed before the reversal occurs is updated to the new corrected anchor point, and the starting compensation amount for the next reversal motion segment is determined with the new reversal position.

[0049] To address the problem of the combined effect of conventional lead screw position error and additional residual error after reversal during frequent short-stroke reversals in PLC-driven laser cutting machines, and the potential for abrupt directional changes in compensation error within local intervals, this invention first establishes basic lead screw position error data through forward and reverse calibration. Then, it extracts residual reversal errors through different reversal test strokes and establishes residual error relationships related to reversal position, reversal direction, and post-reversal stroke. During actual processing, the PLC determines the comprehensive lead screw error in real time based on the current target position, reversal position, and motion direction. For intervals where the comprehensive error exhibits zero crossover, it performs asymmetric continuous transition processing to generate corresponding compensation amounts. Using the corrected position established before reversal as the new compensation anchor point, subsequent compensation is continuously transmitted incrementally to the current target position, thereby achieving dynamic and continuous compensation of lead screw errors under short-stroke reversal conditions.

[0050] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for compensating for lead screw errors in a laser cutting machine driven by a PLC, characterized in that, include: The control screw motion axis passes through the preset calibration position in the forward and reverse directions respectively, and the actual position of each calibration position is obtained. The forward position error and reverse position error are obtained based on the difference between the actual position and the corresponding command position. Perform reversing test strokes of different lengths at each calibration position, obtain the actual displacement at the end of each reversing test stroke, and subtract the position error of the corresponding calibration position from the actual displacement error to obtain the reversing residual error used to characterize the degree of elastic deformation release of the lead screw and nut pair after reversing. A residual error relationship table is established based on the test stroke length of each reversing test and the corresponding reversing residual error, and stored in the PLC. During the laser cutting process, the PLC obtains the position error corresponding to the current position based on the current target position and the direction of movement, and records the reversing position when a change in the direction of movement is detected. The reversing stroke is obtained based on the distance between the current target position and the reversing position. The current reversing residual error is determined from the residual error relationship table based on the reversing stroke. The position error and the current reversing residual error are superimposed to obtain the comprehensive lead screw error, and a compensation amount opposite to the direction of the comprehensive lead screw error is generated. The current target position is corrected according to the compensation amount, and the corrected target position is sent to the servo driver to control the movement of the lead screw of the laser cutting machine.

2. The method for compensating for lead screw errors in a laser cutting machine driven by a PLC according to claim 1, characterized in that, Obtaining the reversing residual error includes: after the lead screw axis reaches a preset calibration position, determining the preset calibration position as the reversing start position, and recording the pre-reversing motion direction and the initial actual position; controlling the lead screw axis to change its motion direction and execute reversing test strokes of different lengths, obtaining the actual displacement based on the initial actual position and the final actual position corresponding to each reversing test stroke, and obtaining the command displacement based on the reversing start position and the test end position, and determining the difference between the actual displacement and the command displacement as the actual displacement error; determining the start position error corresponding to the reversing start position based on the pre-reversing motion direction, and determining the end position error corresponding to the test end position based on the post-reversing motion direction, and determining the difference between the end position error and the start position error as the basic displacement error; subtracting the basic displacement error from the actual displacement error to obtain the reversing residual error, and associating the reversing residual error with the reversing start position, the reversing direction, and the reversing test stroke length.

3. The method for compensating for lead screw errors in a laser cutting machine driven by a PLC according to claim 2, characterized in that, Establishing a residual error relationship table and determining the current reversing residual error includes: grouping the reversing residual error data according to the reversing start position and the direction of movement after the reversal, and establishing the correspondence between the reversing residual errors within each group according to the reversing test stroke length, forming a residual error relationship table; during the laser cutting process, determining the corresponding residual error data based on the current reversing position and the direction of movement after the reversal; when the current reversing position is located between two adjacent reversing start calibration positions, determining the residual error sequence corresponding to the current reversing position based on the positional relationship between the current reversing position and the two reversing start calibration positions; obtaining the current stroke after the reversal based on the distance between the current target position and the current reversing position, and determining the current reversing residual error from the residual error sequence based on the positional relationship between the current stroke after the reversal and the adjacent reversing test stroke lengths.

4. The method for compensating for lead screw errors in a laser cutting machine driven by a PLC according to claim 3, characterized in that, The processing of the overall leadscrew error includes: algebraically superimposing the basic position error corresponding to the current target position and the current commutation residual error along a unified axial coordinate direction to obtain the current overall leadscrew error; determining the first test stroke and the second test stroke surrounding the current commutation stroke based on the current commutation stroke, and converting the first test stroke and the second test stroke into corresponding axial positions starting from the current commutation position; determining the position error of the corresponding axial position respectively, and superimposing it with the commutation residual error corresponding to the corresponding test stroke to obtain the first overall error and the second overall error; when the first overall error and the second overall error have opposite signs, determining the region between the first test stroke and the second test stroke as the zero-crossing transition interval corresponding to the current target position.

5. The method for compensating for lead screw errors in a laser cutting machine driven by a PLC according to claim 4, characterized in that, The error transition position within the zero-crossing transition interval is determined as follows: The absolute values ​​of the first and second comprehensive errors are obtained; the sum of their absolute values ​​is used to determine the error amplitude ratio of the first and second comprehensive errors within the zero-crossing transition interval; based on the first test stroke, the second test stroke, and the error amplitude ratio corresponding to the first comprehensive error, the error transition stroke corresponding to the change from the direction of the first comprehensive error to the direction of the second comprehensive error is determined; the error transition position is determined based on the error transition stroke, the current reversing position, and the direction of movement after the reversing, so that the error transition position shifts with the relative amplitude of the comprehensive errors on both sides of the zero-crossing.

6. The method for compensating for lead screw errors in a laser cutting machine driven by a PLC according to claim 5, characterized in that, The comprehensive lead screw error correction within the zero-crossing transition interval includes: determining the distance from the first test stroke to the error transition stroke and the distance from the error transition stroke to the second test stroke as the first-side transition distance and the second-side transition distance, respectively; selecting the corresponding transition distance based on whether the current reversing stroke is located on the first or second side of the error transition stroke, and determining the asymmetric transition ratio based on the ratio of the current reversing stroke to the error transition stroke to the selected transition distance; determining the error direction based on the sign of the comprehensive error corresponding to the side where the current reversing stroke is located, and continuously scaling the absolute value of the current comprehensive lead screw error using the asymmetric transition ratio to obtain the transition comprehensive error, so that the transition comprehensive error continuously decreases to zero as the current target position approaches the error transition position.

7. The method for compensating for lead screw errors in a laser cutting machine driven by a PLC according to claim 6, characterized in that, The process of generating a compensation amount includes: determining whether the first comprehensive error and the second comprehensive error corresponding to the current target position have opposite signs; when they have opposite signs, determining the transition comprehensive error as the error to be compensated; when they have the same sign, determining the current comprehensive lead screw error as the error to be compensated; determining the lead screw compensation direction opposite to the direction of the error to be compensated in a unified axial coordinate system, and determining the lead screw compensation amplitude based on the absolute value of the error to be compensated; and forming the current compensation amount for correcting the current target position by the lead screw compensation direction and the lead screw compensation amplitude.

8. The method for compensating for lead screw errors in a laser cutting machine driven by a PLC according to claim 1, characterized in that, The process of correcting the current target position based on the current compensation amount includes: when a reversal is detected in the lead screw motion axis, determining the corrected target position corresponding to the last target position before the reversal as the corrected anchor point for the current reversal motion segment; using the current reversal position as the starting position of the stroke after the reversal, and determining the initial compensation amount corresponding to the zero stroke after the reversal according to the direction of motion after the reversal; obtaining the current compensation amount corresponding to the current target position, determining the difference between the current compensation amount and the initial compensation amount as the compensation increment, and determining the directional position difference between the current target position and the current reversal position as the target displacement after the reversal; performing algebraic superposition of the compensation increment and the target displacement after the reversal to obtain the corrected target displacement, and combining the corrected target displacement with the correction anchor point to obtain the current corrected target position.

9. The method for compensating for lead screw errors in a laser cutting machine driven by a PLC according to claim 8, characterized in that, The correction anchor point is updated according to the current reversing motion segment, including: keeping the correction anchor point unchanged within the current reversing motion segment, and determining the corresponding current compensation amount and compensation increment for each subsequent target position, generating the corresponding correction target position with the correction anchor point as a common position reference; sending the correction target position to the servo driver to control the lead screw movement; when the next change in motion direction is detected, updating the last correction target position formed before the reversal occurs to the correction anchor point of the next reversing motion segment, and re-determining the corresponding initial compensation amount according to the new reversing position.

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