Structural error compensation feedforward control method for swingable cutter machining

Abstract

The invention discloses a structural error compensation feedforward control method for swingable cutter machining, which takes a coordinate vector offset model as a main part, combines a swing angle model of a cutter, adds an anti-backlash compensation factor, and adjusts the anti-backlash compensation factor in real time according to the working conditions of constant speed, acceleration and deceleration in the numerical control machining process. And structural errors such as screw pitch errors, cutting and positioning gaps and the like are compensated in real time, and the machining precision of the numerical control machine tool is improved.

Description

Technical Field

[0001] This invention relates to the field of CNC machining, and more particularly to a feedforward control method for structural error compensation in CNC machining. Background Technology

[0002] In three-axis CNC machining, structural errors arise due to machine tool design and component assembly errors. These structural errors, caused by inherent factors such as machine tool structure and component assembly, directly affect workpiece accuracy. Structural errors can be caused by various factors related to machine tool structure and components; for example, insufficient rigidity of guideways, lead screw backlash, and deformation due to cutting forces during machining can all contribute to structural errors. Furthermore, heat generated by components such as motors and bearings during machining can also contribute to structural errors.

[0003] Common types of structural errors include geometric errors, transmission chain errors, and elastic deformation errors. Geometric errors generally include straightness and perpendicularity errors of the machine tool's axes, such as the X-axis not being perpendicular to the Y-axis, resulting in deviations in side lengths during machining. Transmission chain errors include clearances or wear in components such as lead screws, nuts, and gear transmissions, causing inaccurate feed motion. Elastic deformation errors occur when the machine tool's support structure or cutting tool undergoes elastic deformation under cutting forces, causing the cutting depth to deviate from the set value.

[0004] To reduce structural errors in CNC machining, optimize the structure of CNC machine tools, and ensure precise assembly and debugging, tools such as laser interferometers are used to calibrate the perpendicularity and straightness of each axis.

[0005] Structural errors are one of the core issues in CNC machining accuracy control. Summary of the Invention

[0006] Based on this, the purpose of this invention is to propose a structural error compensation feedforward control method for machining with a swing-out tool. The method is based on a coordinate vector offset model, combined with the tool swing angle model, and adds a backlash compensation factor. The backlash compensation factor is adjusted in real time according to the uniform speed, acceleration and deceleration conditions during CNC machining to compensate for structural errors such as pitch error, cutting and positioning clearance in real time, thereby improving the machining accuracy of CNC machine tools.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a structural error compensation feedforward control method for machining with a wobbly tool, wherein the following conditions are given respectively... The ideal values ​​for the three coordinates, and the actual values ​​for the three coordinates. The deviation values ​​of the three coordinates are compared with the ideal values ​​to obtain the deviation values ​​of the three coordinates. For different working conditions such as constant speed, acceleration and deceleration, the deviation values ​​of the three coordinates are used to adjust the backlash compensation factor of the three coordinates in real time according to the feedback through the swing angle model and vector offset model of each XYZ coordinate direction. The adjusted backlash compensation factor is input to the main controller to finally complete the real-time compensation of the tool. The steps are as follows: S1, Multi-source data synchronous acquisition, using a grating ruler to collect actual coordinates respectively. The actual swing angle is collected using an encoder. , , The motor current is collected using a current sensor to obtain the torque. Determine the motor's operating status; S2, Three-axis decoupling compensation execution. A. Establish the X-axis swing angle model and calculate the X-axis swing angle compensation. The Y-axis and Z-axis swing angle models are similar to the X-axis swing angle model. (1) The X-axis swing angle compensation amount represents the actual swing angle along the X-axis direction. With theoretical pendulum angle The geometric error compensation value in the X-axis direction caused by the difference reflects the offset of the cutting contact point caused by tool tilt; Similarly, we can obtain This is the Y-axis sway angle compensation amount. This is the Z-axis swing angle compensation amount; The tool overhang length in the X-axis direction (mm) is the distance from the tool tip to the center of rotation. The actual swing angle of the tool in the X-axis direction is expressed in radians and is based on the actual data collected by the encoder in S1. The actual swing angle of the tool in the Y-axis direction is expressed in radians and is based on the actual data collected by the encoder in S1. The theoretical tool swing angle in the X-axis direction is expressed in radians; The theoretical tool swing angle in the Y-axis direction is expressed in radians; and These refer to the ideal tool attitude angle set by the program, the geometric constraint of the Y-axis on the X-axis in the theoretical attitude, and the static calibration value. In formula (1), This represents the projection component of the actual tool orientation onto the XY plane. This is the reference projection of the theoretical orientation of the cutting tool; Similarly, we can obtain This is the Y-axis sway angle compensation amount. This is the Z-axis swing angle compensation amount; , ; B. Establish a vector offset model and calculate the vector offset. , (2) These are theoretical coordinate values, representing the position of the CNC program instruction, in mm; These are the actual coordinate values, the positions fed back by the grating ruler, in mm; The rate of change of vector deviation Dynamic response; The damping coefficient; This is the triaxial stiffness matrix, in units of... , represented as , (3) The equivalent stiffness coefficient along the X-axis is... The equivalent stiffness coefficient along the Y-axis is... The Z-axis equivalent stiffness coefficient; C, Vector offset correction, superimposed stiffness compensation term ; D, anti-gap compensation factor Injection, injecting anti-gap compensation factor according to the motion state. ; (4) Uniform gain coefficient, The actual feed rate is in mm / s. Quantify the speed-related frictional resistance. To determine the vector direction of the compensating force; Acceleration gain coefficient, Suppressing cumulative hysteresis caused by mass inertia, This is the jerk suppression coefficient. The impact of accelerometer filtration; Gain coefficient of jerk change It is the change in jerk. The reverse clearance impact coefficient, Gap jump function; In formula (4), the subscript i represents the X-axis, Y-axis and Z-axis labels, and the subscript j represents the jerk label; The X-axis backlash compensation factor is: The Y-axis backlash compensation factor is Z-axis backlash compensation factor ; In practice, a dead zone threshold needs to be set to avoid false triggering due to noise. Let the threshold be... , (5) Provided as required, no special requirements. ; S3, controller output (6), It is a feedforward controller. (7), For time-lookahead The ideal trajectory; generated by the CAM program. For previewing the window; These are position gain, velocity gain, acceleration gain, and jerk gain, respectively. Position gain maps the machine tool transmission ratio; velocity gain compensates for frictional resistance; acceleration gain suppresses inertial lag; and jerk gain reduces impact vibration.

[0008] Preferably, in formula (2), Damping coefficient, unit Suppress high-frequency vibrations (8) βx is the dynamic damping coefficient of the X-axis, βy is the dynamic damping coefficient of the Y-axis, and βz is the dynamic damping coefficient of the Z-axis.

[0009] Preferably, in formula (2), (9) ΔSx is the instantaneous position deviation in the X-axis direction, ΔSy is the instantaneous position deviation in the Y-axis direction, and ΔSz is the instantaneous position deviation in the Z-axis direction, reflecting transmission chain errors and thermal deformation.

[0010] Preferably, in S2, an anti-gap compensation factor is injected according to the motion state. , During the acceleration phase, the integral term compensates for inertial lag. ; Deceleration phase: (10) Eliminate backlash.

[0011] In conventional tool compensation settings, this invention establishes a dual-model structure of swing angle and coordinate vector offset model. Taking coordinate vector offset as the main reference, the invention considers the change of tool swing angle and adds a backlash compensation factor. During constant speed, acceleration and deceleration, the compensation factor is adjusted in real time to compensate for structural errors such as pitch error, cutting and positioning clearance, thereby comprehensively improving machining accuracy. Attached Figure Description

[0012] Figure 1 A schematic diagram of the structure for tool compensation in CNC machining; Figure 2 for Figure 1 A schematic diagram of the structure within the dashed box. Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0014] like Figures 1 to 2 As shown, a structural error compensation feedforward control method for machining with a wobbly tool is provided, respectively. The ideal values ​​for the cutting tool in three coordinates, and the actual values ​​corresponding to the three coordinates. The deviation values ​​of the three coordinates are compared with the ideal values ​​to obtain the deviation values ​​of the three coordinates. For different working conditions such as constant speed, acceleration and deceleration, the deviation values ​​of the three coordinates are used to adjust the backlash compensation factor of the three coordinates in real time according to the feedback through the swing angle model and vector offset model of each XYZ coordinate direction. The adjusted backlash compensation factor is input to the main controller to finally complete the real-time compensation of the tool. The steps are as follows: S1, Multi-source data synchronous acquisition, using a grating ruler to acquire the actual coordinates of the tool. The actual swing angle of the cutting tool is acquired using an encoder. , , The motor current is collected using a current sensor to obtain the torque. Determine the motor's operating status; S2, Three-axis decoupling compensation execution. A. Establish the X-axis swing angle model and calculate the X-axis swing angle compensation amount. (1) The X-axis swing angle compensation amount represents the actual swing angle along the X-axis direction. With theoretical pendulum angle The geometric error compensation value in the X-axis direction caused by the difference reflects the offset of the cutting contact point caused by tool tilt; The tool overhang length in the X-axis direction (mm) is the distance from the tool tip to the center of rotation. is the actual swing angle of the tool in the X-axis direction, expressed in radians, based on the actual data collected by the encoder in S1; is the tool rotation angle around the X-axis as fed back by the real-time sensor. The actual swing angle of the tool in the Y-axis direction, expressed in radians, is based on the actual data collected by the encoder in S1; the projection effect of the swing angle in the Y-axis direction on the X-axis compensation is also shown. The theoretical tool swing angle in the X-axis direction is expressed in radians; The theoretical tool swing angle in the Y-axis direction is expressed in radians; and These refer to the ideal tool attitude angle set by the program, the geometric constraint of the Y-axis on the X-axis in the theoretical attitude, and the static calibration value. In formula (1), This represents the projection component of the actual tool orientation onto the XY plane. This is the reference projection of the theoretical orientation of the cutting tool; Similarly, we can obtain This is the Y-axis sway angle compensation amount. This is the Z-axis swing angle compensation amount; and Calculation and Similarly; , The Y-axis swing angle compensation value is used to correct the angle deviation when the tool swings around the Y-axis, eliminate the difference between the actual swing angle and the commanded swing angle, and ensure the machining angle accuracy. , The Z-axis swing angle compensation value is used to correct the angle deviation when the tool swings around the Z-axis, eliminate the difference between the actual swing angle and the commanded swing angle, ensure the angle accuracy of machining around the Z-axis rotation or swing, and can offset the inherent error of the equipment, thereby improving the accuracy and stability of the swing angle motion. B. Establish a vector offset model, synthesize the X, Y, and Z axes, and calculate the vector offset. , (2) These are theoretical coordinate values, representing the position of the CNC program instruction, in mm; These are the actual coordinate values, the tool position fed back by the grating ruler, in mm; The rate of change of vector deviation Dynamic response; The damping coefficient; This is the triaxial stiffness matrix, in units of... , represented as , (3) The equivalent stiffness coefficient along the X-axis is... The equivalent stiffness coefficient along the Y-axis is... The Z-axis equivalent stiffness coefficient characterizes the machine tool's ability to resist deformation. Damping coefficient, unit Suppress high-frequency vibrations (8) βx is the dynamic damping coefficient of the X-axis, βy is the dynamic damping coefficient of the Y-axis, and βz is the dynamic damping coefficient of the Z-axis.

[0015] (9) ΔSx is the instantaneous position deviation in the X-axis direction, ΔSy is the instantaneous position deviation in the Y-axis direction, and ΔSz is the instantaneous position deviation in the Z-axis direction, reflecting transmission chain errors, thermal deformation, etc.

[0016] C, Vector offset correction, superimposed stiffness compensation term ; D, anti-gap compensation factor Injection, injecting anti-gap compensation factor according to the motion state. ; (4) Uniform gain coefficient, The actual feed rate is in mm / s. Quantify the speed-related frictional resistance. To determine whether the compensating force is increasing or decreasing in vector direction; Acceleration gain coefficient, Suppressing cumulative hysteresis caused by mass inertia, This is the jerk suppression coefficient. The impact of accelerometer filtration; Gain coefficient of jerk change It is the change in jerk; This is the backlash impact coefficient, used to compensate for the fixed backlash in the mechanical transmission chain. Gap jump function; In formula (4), the subscript i represents the X-axis, Y-axis and Z-axis labels, and the subscript j represents the jerk label; The X-axis backlash compensation factor is: The Y-axis backlash compensation factor is Z-axis backlash compensation factor ; In practice, a dead zone threshold needs to be set to avoid false triggering due to noise. Let the threshold be... , (5) Provided as required, no special requirements. ; S3, controller output (6), As a feedforward controller, it generates compensation commands in advance by predicting the dynamic characteristics of the machining trajectory, such as acceleration and jerk, to eliminate modelable deterministic errors, such as lead screw pitch error and tool swing geometric offset. Essentially, it is an open-loop predictive control that does not rely on real-time feedback and has a faster response speed than closed-loop control.

[0017] (7), For time-lookahead The ideal trajectory; generated by the CAM program. For previewing the window; These are position gain, velocity gain, acceleration gain, and jerk gain, respectively; position gain Mapping machine tool transmission ratio; speed gain Compensation for frictional resistance; acceleration gain Suppressing inertial hysteresis; increasing jerk gain Reduce impact vibration.

[0018] In S2, an anti-gap compensation factor is injected according to the motion state. , During the acceleration phase, the integral term compensates for inertial lag. ; Deceleration phase: (10) Eliminate backlash.

Claims

1. A structural error compensation feedforward control method for machining with a wobbly tool, characterized in that... Given x respectively * y * z * The three coordinates of the tool represent the ideal values, and the corresponding actual values ​​are the actual values. The deviation values ​​of the three coordinates are compared with the ideal values ​​to obtain the deviation values ​​of the three coordinates. For different working conditions such as constant speed, acceleration and deceleration, the deviation values ​​of the three coordinates are used to adjust the backlash compensation factors of the three coordinates in real time according to the feedback through the swing angle model and vector offset model of each XYZ coordinate direction. The adjusted backlash compensation factors are input to the main controller to finally complete the real-time compensation of the tool. The steps are as follows: S1, Multi-source data synchronous acquisition: The actual coordinates of the tool in the XYZ region (x1, y1, z1) are acquired using a grating ruler; the actual swing angle θ of the tool is acquired using an encoder. x1 θ y1 θ z1 The motor current is collected using a current sensor to obtain the torque T. m Determine the motor's operating status; S2, Three-axis decoupling compensation is executed, the steps are as follows. A. Establish the X-axis swing angle model and calculate the X-axis swing angle compensation amount; ΔX θ =L x [sin(θ x1 )cos(θ y1 )-sin(θ x0 )cos(θ y0 )] (1) ΔX θ X-axis swing angle compensation amount represents the compensation value for geometric error in the X-axis direction caused by the difference between the actual swing angle and the theoretical swing angle, reflecting the offset of the cutting contact point caused by tool tilt; L x The tool overhang length in the X-axis direction (mm) is the distance from the tool tip to the center of rotation. θ x1 The actual swing angle of the tool in the X-axis direction is expressed in radians and is based on the actual data collected by the encoder in S1. θ y1 The actual swing angle of the tool in the Y-axis direction is expressed in radians and is based on the actual data collected by the encoder in S1. θ x0 θ represents the theoretical tool swing angle in the X-axis direction, expressed in radians. y0 The theoretical tool swing angle in the Y-axis direction is expressed in radians; θ x0 and θ y0 These refer to the ideal tool attitude angle set by the program, the geometric constraint of the Y-axis on the X-axis in the theoretical attitude, and the static calibration value. In formula (1), sin(θ x1 cos(θ) y1 () represents the projection component of the actual tool orientation onto the XY plane; sin(θ x0 cos(θ) y0 () is the reference projection of the theoretical orientation of the cutting tool; Similarly, we obtain ΔY θ The Y-axis sway angle compensation amount, ΔZ θ This is the Z-axis swing angle compensation amount; Y θ =L y [sin(θ y1 )cos(θ z1 )-sin(θ y0 )cos(θ z0 )], ΔZ θ =L z [sin(θ z1 )cos(θ x1 )-sin(θ z0 )cos(θ x0 )]; B. Establish a vector offset model and calculate the vector offset. x, y, and z are theoretical coordinate values, representing the position of the CNC program command, in mm; x1, y1, and z1 are the actual coordinate values, the positions fed back by the grating ruler, in mm; The vector deviation change rate is μm / s, representing the dynamic response; β is the damping coefficient; K s The triaxial stiffness matrix, in units of N / μm, is denoted as K. s =diag(k) sx k sy k sz ),Right now K sx K is the equivalent stiffness coefficient along the X-axis. sy K is the equivalent stiffness coefficient along the Y-axis. sz The Z-axis equivalent stiffness coefficient; C, Vector offset correction, superimposed stiffness compensation term D, anti-gap compensation factor C i (t) Injection, injecting the anti-gap compensation factor C according to the motion state. i (t); k v，i Uniform gain coefficient, |v i | represents the actual feed rate in mm / s, sgn(ΔS) i To determine the vector direction of the compensating force; k α,i Acceleration gain coefficient, To suppress the cumulative hysteresis caused by mass inertia, k j，i k is the jerk suppression coefficient. d，i Gain coefficient of jerk change It represents the change in jerk, k b，i The reverse clearance impact coefficient is δ(ΔS) i (Gap jump function;) The impact of accelerometer filtration; k v，i |v i |Quantify the frictional resistance related to speed; In formula (4), the subscript i represents the X-axis, Y-axis and Z-axis labels, and the subscript j represents the jerk label; The X-axis backlash compensation factor is C. x (t), the Y-axis backlash compensation factor is C. y (t), Z-axis backlash compensation factor C z (t); In practice, a dead zone threshold needs to be set to avoid false triggering due to noise. Let the threshold be ε. ε is given as required; unless otherwise specified, ε = 0.5 μm. S3, controller output G c (t) is the feedforward controller. r(t+τ) is the ideal trajectory with time look-ahead τ; generated by the CAM program, where τ is the look-ahead window; k f k v k α , and k j These are position gain, velocity gain, acceleration gain, and jerk gain, respectively; position gain maps the machine tool transmission ratio; velocity gain compensates for frictional resistance; and acceleration gain suppresses inertial lag. Increase jerk gain to reduce impact vibration.

2. The structural error compensation feedforward control method for machining with a wobbly tool according to claim 1, characterized in that... In formula (2), β is the damping coefficient, with units of N·s / μm, which suppresses high-frequency vibrations. βx is the dynamic damping coefficient of the X-axis, βy is the dynamic damping coefficient of the Y-axis, and βz is the dynamic damping coefficient of the Z-axis.

3. The structural error compensation feedforward control method for machining with a wobbly tool according to claim 1, characterized in that... In formula (2), ΔSx is the instantaneous position deviation in the X-axis direction, ΔSy is the instantaneous position deviation in the Y-axis direction, and ΔSz is the instantaneous position deviation in the Z-axis direction, reflecting transmission chain errors and thermal deformation.

4. The structural error compensation feedforward control method for machining with a wobbly tool according to claim 1, characterized in that... In S2, the anti-gap compensation factor C is injected according to the motion state. i (t), During the acceleration phase, the integral term compensates for the inertial lag k. α,i ·∫ΔS i ; Deceleration phase: Eliminate backlash.

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