Numerical control machining error identification and compensation method and device based on machine tool error calibration

Abstract

The present application belongs to the technical field of numerical control processing, and discloses a numerical control processing error identification and compensation method and device based on machine tool error calibration, which comprises the following steps: S1, constructing a machine tool ideal kinematic model of a machine tool, and establishing a machine tool minimum geometric error calibration model based on the machine tool ideal kinematic model, and then calibrating the geometric error of the machine tool based on a ball bar; S2, using the calibrated geometric error to convert the machine tool ideal kinematic model into a machine tool actual kinematic model through a screw pair transformation, and the machine tool actual kinematic model can map the geometric error of the machine tool to the pose error of the tool position point. The present application maps the geometric error of the machine tool to the pose error of the tool position point by establishing the machine tool actual kinematic model, and high-quality error identification and compensation is realized.

Description

Technical Field

[0001] This invention belongs to the field of CNC machining related technology, and more specifically, relates to a method and equipment for CNC machining error identification and compensation based on machine tool error calibration. Background Technology

[0002] Machine tool geometric errors have a significant impact (30%-45%) on the machining accuracy of complex curved surfaces. Machine tool geometric error correction often employs a "measurement-compensation-trial cutting" process. However, due to the lack of a mapping relationship between machine tool geometric errors and tool position pose errors, it is impossible to effectively evaluate machine tool accuracy and compensation effectiveness. This necessitates multiple applications of the correction process to meet machining accuracy requirements, consuming substantial manpower and resources. Therefore, building a model in a virtual environment that reflects the actual motion of the machine tool while considering its geometric errors is of great significance for improving machining accuracy, shortening product production cycles, saving resources, and reducing costs.

[0003] Machine tool geometric error measurement is divided into two methods: direct measurement and indirect measurement. Direct measurement measures the individual errors of each component of the machine tool separately. Due to the large number of error parameters to be calibrated, direct measurement is inefficient and costly. Indirect measurement measures the deviation between the actual and ideal poses along a given measurement path. By establishing an error model, the geometric error parameters of the machine tool can be decoupled, offering significant advantages in efficiency and cost compared to direct measurement. Methods for establishing error models include the DH parameter method, multibody system theory, matrix summation, and the product of exponential functions (POE). The first three methods all use homogeneous transformation matrices for modeling, which can lead to unavoidable singularities. The POE method, due to its mathematical completeness and continuity, has seen increasing application in recent years.

[0004] Error compensation methods are mainly divided into hardware compensation and software compensation. Hardware compensation primarily involves controlling the CNC system of the machine tool to modify the machine tool's servo control system and machining offset. Many CNC manufacturers leverage their technological advantages to integrate error compensation functions into their CNC systems. Software compensation achieves geometric error compensation in machine tool machining by modifying the CNC program. Due to its high flexibility, low cost, and ease of implementation, software compensation is widely used in machine tool error compensation.

[0005] RTCP technology is widely used in CNC machine tool machining. RTCP technology can reduce nonlinear errors during machine tool machining and reduce the programming difficulty for process engineers. Process engineers only need to input the tool position information in the workpiece coordinate system into the control system, and the CNC system will automatically calculate the translational axis displacement and control the machine tool movement based on the rotary axis displacement and the tool position coordinate. Since the RTCP algorithm and parameters are encapsulated inside the control system, the existing kinematic model is difficult to reflect the tool position posture deviation under the RTCP function, and currently the position error of the rotary axis can only be compensated by modifying the RTCP parameters. Therefore, it is urgent to develop a machine tool geometric error simulation compensation system suitable for RTCP function. Summary of the Invention

[0006] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method and device for identifying and compensating CNC machining errors based on machine tool error calibration. By establishing an actual kinematic model of the machine tool, it maps the geometric errors of the machine tool to the positional errors of the tool position. This allows for the assessment of whether the machine tool meets the workpiece machining accuracy requirements without the need for trial cutting, effectively achieving error identification.

[0007] To achieve the above objectives, according to one aspect of the present invention, a method for identifying CNC machining errors based on machine tool error calibration is provided, the method comprising the following steps:

[0008] S1. Construct the ideal kinematic model of the machine tool, and establish a calibration model for minimizing the geometric error of the machine tool based on the ideal kinematic model of the machine tool. Then, calibrate the geometric error of the machine tool based on the ballbar.

[0009] S2, by using the calibrated geometric error and the associated transformation of the screw, the ideal kinematic model of the machine tool is transformed into the actual kinematic model of the machine tool. The actual kinematic model of the machine tool can map the geometric error of the machine tool to the positional error of the tool position, thereby completing the error identification.

[0010] Furthermore, the mathematical expression for the machine tool's minimized geometric error model is:

[0011]

[0012] in, l represents the number of moving joints in the machine tool; ξ i Let be the rotational coordinates of the joint; δ represents the differential form of the variable, η ws η is the error parameter of the workpiece coordinate system. i η is the error parameter of the joint. st θ represents the error parameter of the tool coordinate system. i and θ j The amount of joint movement; This is the homogeneous transformation matrix of the tool coordinate system relative to the workpiece coordinate system; It is the antisymmetric matrix of the joint spinor coordinates.

[0013] Furthermore, when establishing the ideal kinematic model of the machine tool, it is not necessary to consider the joint composition of the tool kinematic chain and the workpiece kinematic chain. It is only necessary to establish the rotation coordinates ξ of each joint sequentially in the order from workpiece to tool on the base coordinate system attached to the machine tool bed. i ; Calculate the initial reference pose g at time zero of the tool kinematic chain and the workpiece kinematic chain. st0 g sw0 Multiply the initial pose of the tool kinematic chain by the matrix exponents of the joint rotations of the tool-to-workpiece kinematic chain, and finally multiply by the inverse of the initial pose of the workpiece kinematic chain to obtain the forward kinematic model g of the machine tool. wt .

[0014] Furthermore, when establishing a machine tool calibration model that minimizes geometric errors based on the ideal kinematic model of the machine tool, the symbol [] is defined. ∨ As arrive The mapping is used to linearize the kinematic parameters of each joint in the POE formula and multiply them by the inverse of the forward kinematic formula on the right. The adjoint transformation is then applied to obtain the geometric error calibration model of the machine tool. Redundant parameters in the geometric error calibration model are then eliminated.

[0015] Furthermore, machine tool rotation error parameters The position-independent geometric error parameter δk i Left-multiply the error coefficient matrix B i This indicates that, for the rotating axis have:

[0016]

[0017] Where ω i ,ω i,1 ,ω i,2 Let p be a set of orthogonal unit vectors. i =ω i ×v i For translational axis have:

[0018]

[0019] Where v i ,v i,1 ,v i,2 It is also a set of orthogonal unit vectors, when measured using a ballbar.

[0020] Furthermore, the actual kinematic model of the machine tool can be used with RTCP instructions, retaining the positional information of the established machine tool forward kinematic equations. Differentiating both sides of the equations yields the deviation of the tool position point in the workpiece coordinate system, influenced by machine tool geometric errors. This deviation is then organized into a matrix, and projecting the matrix along the ball joint direction yields:

[0021]

[0022] in

[0023] A=[Ad0,Ad0-Ad1,Ad1-Ad2,...,Ad l-1 -Ad l Ad l ]

[0024] B = Blockdiag(B ws ,B1,B2,...,B l B st )

[0025] x=[δk ws ,δk1,δk2,...,δk l ,δk st ] T

[0026] Next, the RTCP function is activated, and the ballbar base is placed at any position on the worktable. The center of the workpiece ball is set as the origin of the workpiece coordinate system, and the center of the tool ball is set as the origin of the tool coordinate system. Using the ballbar's built-in measurement mode, the tool ball is made to move in circles relative to the workpiece ball in the XY, YX, and XZ planes, while ensuring that the machine tool's rotating axes rotate synchronously to achieve five-axis linkage. When the machine tool moves to the sampling pose, it is paused to record data to eliminate the influence of machine tool dynamic performance factors. The calibration equations constructed for each sampling pose are arranged in columns to establish a calibration Jacobian matrix for calibrating the machine tool's geometric error parameters. The least squares solution to x is

[0027] Furthermore, constrained by the rigidity and reachable space of the five-axis machine tool, and based on the principle that the translational axis must be located at both ends of the motion chain from the workpiece to the tool, the coordinates of the translational axis can be solved as follows:

[0028]

[0029] The calculated translational axial displacement M t The rotation axis displacement is input into the actual kinematic model of the machine tool to calculate the actual pose of the tool position point under the RTCP function enabled;

[0030] For CNC programs using the RTCP function, the compensated rotational axis displacement is first calculated, and then, based on the aforementioned ideal tool position coordinates P... n Calculate translational axis displacement under actual kinematic parameters Finally The compensated rotational axis displacement is substituted into the ideal kinematic model of the machine tool, which has the same RTCP parameters as the internal RTCP parameters of the control system, to calculate the tool position coordinates P. c P c This refers to the translational axis displacement of the CNC program using the RTCP function after compensation.

[0031] The present invention also provides a CNC machining error compensation method based on machine tool error calibration. The compensation method first uses the CNC machining error identification method based on machine tool error calibration as described above to identify the error, and then compensates for the machine tool error by adjusting the CNC program.

[0032] The present invention also provides a CNC machining error identification system based on machine tool error calibration. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the CNC machining error identification method based on machine tool error calibration as described above.

[0033] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the CNC machining error identification method based on machine tool error calibration as described above, or the CNC machining error compensation method based on machine tool error calibration as described above.

[0034] In summary, compared with the prior art, the CNC machining error identification and compensation method and equipment based on machine tool error calibration provided by the present invention have the following beneficial effects:

[0035] 1. Based on the calibrated machine tool geometric errors, an actual kinematic model of the machine tool that can be used for RTCP commands is established. This model can comprehensively reflect the impact of machine tool geometric errors on tool position posture deviation when RTCP is enabled or disabled. Machine tool accuracy can be effectively evaluated without trial cutting, achieving high-quality error identification, shortening product production cycle, saving resources, and reducing costs.

[0036] 2. This invention analyzes the actual structure of a five-axis machine tool and eliminates redundant geometric error parameters, establishing a minimized machine tool geometric error model suitable for partial pose information measurement methods of ballbar instruments. It calibrates 14 non-redundant minimized geometric error parameters of the five-axis machine tool, thereby improving the compensation quality.

[0037] 3. The machine tool geometric error software compensation method based on the actual inverse kinematics of the machine tool provided by this invention can not only compensate for ordinary CNC programs, but also for CNC programs that enable RTCP, thus expanding the error compensation method of CNC machining RTCP function and improving CNC machining accuracy.

[0038] 4. This invention integrates the two kinematic chains of a machine tool into a generalized serial kinematic chain, eliminating the need to establish separate tool kinematic chains and workpiece kinematic chains, thus simplifying the kinematic modeling process of the machine tool. Attached Figure Description

[0039] Figure 1 This is a flowchart of a CNC machining error compensation method based on error calibration provided by the present invention;

[0040] Figure 2 (a) and (b) in the figure are simplified diagrams and structural schematic diagrams of the five-axis machine tool provided in the embodiments of the present invention, respectively.

[0041] Figure 3 (a) and (b) in the figure are schematic diagrams of position-independent errors of the translational and rotational axes of the five-axis machine tool provided in the embodiments of the present invention;

[0042] Figure 4 This is a flowchart of machine tool geometric error calibration provided in an embodiment of the present invention;

[0043] Figure 5 (a) and (b) in the figure are simulation comparison diagrams of blade finishing error provided in the embodiments of the present invention;

[0044] Figure 6 Figures (a), (b), and (c) in the figure represent the verification results of the machine tool calibration and compensation experiment provided in the embodiments of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0046] Please see Figure 1 This invention provides a CNC machining error compensation method based on machine tool error calibration, the method mainly includes the following steps:

[0047] S1. Construct the ideal kinematic model of the machine tool, and establish a calibration model for minimizing the geometric error of the machine tool based on the ideal kinematic model. Then, calibrate the geometric error of the machine tool based on the ballbar.

[0048] The mathematical expression for the machine tool's minimized geometric error model is:

[0049]

[0050] in, l represents the number of moving joints in the machine tool; ξ i Let be the rotational coordinates of the joint; δ represents the differential form of the variable, η ws η is the error parameter of the workpiece coordinate system. i η is the error parameter of the joint. st θ represents the error parameter of the tool coordinate system. i and θ j The amount of joint movement; This is the homogeneous transformation matrix of the tool coordinate system relative to the workpiece coordinate system; It is the antisymmetric matrix of the joint spinor coordinates.

[0051] The establishment of the ideal kinematic model of the machine tool includes the following sub-steps: Without considering the joint composition of the two kinematic chains, it is only necessary to establish the rotation coordinates ξ of each joint sequentially from the workpiece to the tool on the base coordinate system attached to the machine tool bed. i ; Calculate the initial reference pose g at time zero of the tool kinematic chain and the workpiece kinematic chain. st0 g sw0 Multiplying the initial pose of the tool kinematic chain by the matrix exponents of the joint rotations of the tool-to-workpiece kinematic chain, and finally multiplying by the inverse of the initial pose of the workpiece kinematic chain, yields the forward kinematic model g of a general machine tool. wt .

[0052] The specific sub-steps for establishing a machine tool calibration model that minimizes geometric errors based on the ideal kinematic model of the machine tool are as follows: Define the symbol []. ∨ As arrive The mapping is used to linearize the kinematic parameters of each joint in the POE formula and multiply them by the inverse of the forward kinematic formula on the right. Applying the adjoint transformation, the geometric error model of the machine tool can be obtained:

[0053]

[0054] in l represents the number of moving joints in the machine tool; ξ i Let be the rotational coordinates of the joint; δ represents the differential form of the variable, η ws η is the error parameter of the workpiece coordinate system. iη is the error parameter of the joint. st θ represents the error parameter of the tool coordinate system. i and θ j The amount of joint movement; This is the homogeneous transformation matrix of the tool coordinate system relative to the workpiece coordinate system; It is the antisymmetric matrix of the joint spinor coordinates.

[0055] The first term of the geometric error model represents the tool position deviation caused by workpiece installation error, the second term represents the tool position deviation caused by joint rotation error, the third term represents the tool position deviation caused by tool installation error, and the fourth term represents the tool position deviation caused by joint initial zero position error. This error term benefits from the development of machine tool encoders, and its proportion in machine tool error is relatively small compared to the other three errors, so it is ignored.

[0056] Machine tool rotation error parameters The redundant error parameters, which are not minimized, can affect the stability and efficiency of the iterative identification process. Therefore, it is necessary to eliminate redundant parameters in the geometric error calibration model. The specific steps are as follows:

[0057] Machine tool rotation error parameters It can be determined by the position-independent geometric error parameter δk i Left-multiply the error coefficient matrix B i This indicates that, for the rotating axis have:

[0058]

[0059] Where ω i ,ω i,1 ,ω i,2 Let p be a set of orthogonal unit vectors. i =ω i ×v i For translational axis have:

[0060]

[0061] Where v i ,v i,1 ,v i,2 It is also a set of orthogonal unit vectors, when measured using a ballbar.

[0062] Machine tool geometric error calibration using a ballbar requires further elimination of redundant parameters. Referring to the machine tool coordinate system defined in ISO 230-1:2012 for calibration, 14 minimized five-axis machine tool position-independent error parameters can be obtained for ballbar calibration.

[0063] S2, using the calibrated geometric error, the ideal kinematic model of the machine tool is transformed into the actual kinematic model of the machine tool through the spinor's adjoint transformation. The actual kinematic model of the machine tool can map the geometric error of the machine tool to the positional error of the tool position.

[0064] The actual kinematic model of the machine tool can be used for RTCP commands. Measurements are taken at multiple positions of the machine tool using a ballbar, and a Jacobian matrix for geometric error calibration is constructed based on the measurement data. The actual geometric error of the machine tool is then obtained by solving a least-squares problem, thereby constructing the actual kinematic model of the machine tool.

[0065] In another implementation, after establishing a calibration model that minimizes the machine tool's geometric error, measurements are taken at multiple machine tool poses using a ballbar to construct a Jacobian matrix for geometric error calibration. The actual geometric error of the machine tool is then obtained by solving a least-squares problem. The specific steps are as follows:

[0066] Retaining the positional information of the established machine tool forward kinematics equations, differentiate both sides of the equations to obtain the deviation of the tool position point in the workpiece coordinate system due to machine tool geometric errors. Rearrange this deviation into a matrix and project the matrix along the ball joint direction:

[0067]

[0068] in

[0069] A=[Ad0,Ad0-Ad1,Ad1-Ad2,...,Ad l-1 -Ad l Ad l ]

[0070] B = Blockdiag(B ws ,B1,B2,...,B l B st )

[0071] x=[δk ws ,δk1,δk2,...,δk l ,δk st ] T

[0072] Next, the RTCP function is activated, and the ballbar base is placed at any position on the worktable. The center of the workpiece ball is set as the origin of the workpiece coordinate system, and the center of the tool ball is set as the origin of the tool coordinate system. Using the ballbar's built-in measurement mode, the tool ball is made to perform circular motion relative to the workpiece ball in the XY, YX, and XZ planes, while ensuring synchronous rotation of the machine tool's rotating axes to achieve five-axis linkage. When the machine tool moves to the sampling pose, it is paused to record data to eliminate the influence of machine tool dynamic performance factors. The calibration equations constructed for each sampling pose are arranged in columns to establish a calibration Jacobian matrix for calibrating the machine tool's geometric error parameters. The least squares solution to x is The minimum number of samples m required should satisfy m≥4r+2p+6. Since the calculation of the Jacobian matrix is ​​assumed to be linear approximation, the linear least squares identification process should be repeated until the residuals converge to a certain range.

[0073] In one implementation, obtaining the actual pose of the tool position point includes the following steps:

[0074] First, by using the calibrated geometric error and the associated transformation of the screw, the ideal kinematic model of the machine tool is transformed into the actual kinematic model to calculate the actual pose of the tool position point.

[0075] Secondly, constrained by the rigidity and reachable space of the five-axis machine tool, and based on the principle that the translational axis must be located at both ends of the motion chain from the workpiece to the tool, the coordinates of the translational axis can be solved as follows:

[0076]

[0077] The translational axis displacement M calculated by the control system t By incorporating the rotation axis displacement into the actual kinematic model of the machine tool, the actual pose of the tool position point under RTCP function can be calculated.

[0078] S3, based on the actual kinematic model of the machine tool and the inverse kinematics solution method, compensates for machine tool errors by adjusting the CNC program.

[0079] Step S3 includes the following sub-steps:

[0080] S31, CNC machining error compensation adopts the offline compensation method of directly modifying the CNC program, and uses Paden-Kahan subproblems 2 and 1 in screw theory to solve the machine tool rotation axis displacements θ1, θ2;

[0081] S32, the inverse kinematics solution of the rotation axis adopts the principle of minimizing the rotation amount to ensure that the correction amount of the No. 1 rotation axis closest to the workpiece in the kinematic chain is minimized. By adding or subtracting 2π from the two solutions of the No. 1 rotation axis, six solutions can be obtained. The six solutions are compared with the displacement in the uncompensated CNC program, and the solution with the smallest correction amount is selected as the compensated rotation axis displacement.

[0082] S33, based on the calculated rotational axis displacement and tool position point, and substituting the actual kinematic parameters of the machine tool into the translational axis displacement calculation method, the compensated translational axis displacement can be calculated.

[0083] For CNC programs using the RTCP function, first calculate the compensated rotational axis displacement, and then, based on the aforementioned ideal tool position coordinates P... n Calculate translational axis displacement under actual kinematic parameters Finally The compensated rotational axis displacement is substituted into the ideal kinematic model of the machine tool, which has the same RTCP parameters as the internal RTCP parameters of the control system, to calculate the tool position coordinates P. c P c This refers to the translational axis displacement of the CNC program using the RTCP function after compensation.

[0084] The present invention also provides a method for identifying CNC machining errors based on machine tool error calibration, the method comprising the steps S1-S2 described above.

[0085] The present invention also provides a CNC machining error system based on machine tool error calibration. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the CNC machining error identification method based on machine tool error calibration as described above.

[0086] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the CNC machining error identification system based on machine tool error calibration as described above or the CNC machining error compensation method based on machine tool error calibration as described above.

[0087] The present invention will be further described in detail below with reference to embodiments.

[0088] The CNC machining error compensation method based on error calibration provided in this embodiment of the invention includes operations S1-S3, specifically:

[0089] Operation S1 constructs the ideal kinematic model of the machine tool, and establishes a calibration model for minimizing the geometric error of the machine tool based on the ideal kinematic model. Then, the geometric error of the machine tool is calibrated based on the ballbar.

[0090] Specifically, with Figure 2 Taking the five-axis machine tool shown as an example, an ideal kinematic model of the machine tool is established. Joints 1 to 5 are respectively: C-axis, A-axis, X-axis, Y-axis, and Z-axis.

[0091] The ideal forward kinematic equation of a machine tool can be expressed as:

[0092]

[0093] According to an embodiment of the present invention, a calibration model for minimizing geometric errors of a machine tool is established based on the ideal kinematic model of the machine tool:

[0094]

[0095] in l represents the number of moving joints in the machine tool; ξ i Let be the rotational coordinates of the joint; δ represents the differential form of the variable, η ws η is the error parameter of the workpiece coordinate system. i η is the error parameter of the joint. st θ represents the error parameter of the tool coordinate system. i and θ j The amount of joint movement; This is the homogeneous transformation matrix of the tool coordinate system relative to the workpiece coordinate system; It is the antisymmetric matrix of the joint spinor coordinates.

[0096] According to an embodiment of the present invention, the machine tool rotation error parameter It is not about minimizing; redundant error parameters can affect the stability and efficiency of the iterative identification calculation. Therefore, redundant parameters in the error calibration model need to be eliminated. The specific steps are as follows:

[0097] The rotating shaft has four position-independent geometric error parameters: translational errors in two directions perpendicular to the axis and rotational errors in two directions perpendicular to the axis. The translational axis has two position-independent geometric error parameters for rotational errors about two directions perpendicular to the axis. like Figure 3 As shown. Error parameters It can be determined by the position-independent geometric error parameter δk i Left-multiply the error coefficient matrix B i This indicates that, for the rotating axis have:

[0098]

[0099] Where ω i ,ω i,1 ,ω i,2Let p be a set of orthogonal unit vectors. i =ω i ×v i For translational axis have:

[0100]

[0101] Where v i ,v i,1 ,v i,2 It is also a set of orthogonal unit vectors, taking the rotation axis C as an example, ξ c =[0,0,1,0,0,0] T Taking the translational axis X-axis as an example ξ z =[0,0,0,1,0,0] T have:

[0102]

[0103] The geometric error calibration model measured using a ballbar requires the removal of redundant parameters. Referring to ISO 230-1:2012, the X-axis of the machine tool coordinate system is defined with the actual X-axis of the machine tool as the reference. This eliminates two directional errors related to the X-axis. Projecting the actual Y-axis onto a plane perpendicular to the X-axis of the machine tool coordinate system, and defining the projection line as the Y-axis of the machine tool coordinate system, eliminates one directional error related to the Y-axis. Defining the origin of the machine tool coordinate system on the actual A-axis eliminates two positional errors related to the A-axis. Defining the intersection of the YZ plane of the machine tool coordinate system and the actual A-axis as the origin of the machine tool coordinate system eliminates one positional error related to the C-axis. The 14 minimized geometric errors of the machine tool in this embodiment are shown in Table 1.

[0104] Table 1. 14 Minimized Geometric Errors of Machine Tools

[0105]

[0106]

[0107] Minimizing the geometric error parameters is applied to establish the actual kinematic model of the machine tool for simulation, and a geometric error model of the machine tool for ballbar calibration is constructed:

[0108] δL dbb =J dbb x

[0109] in

[0110]

[0111]

[0112] A=[Ad0,Ad0-Ad1,Ad1-Ad2,...,Ad4-Ad5,Ad5]

[0113] B = Blockdiag(B ws ,B1,B2,...,B5,B st )

[0114] From this, the Jacobian matrix J for identifying the geometric error of a machine tool under any pose can be derived. dbb .

[0115] Enable the RTCP function, place the ballbar base at any position on the worktable, set the center of the workpiece ball as the origin of the workpiece coordinate system, and set the center of the tool ball as the origin of the tool coordinate system. Use the ballbar's built-in measurement mode to make the tool ball move in circles relative to the workpiece ball in the XY, YX, and XZ planes, while ensuring the machine tool's rotating axes rotate synchronously to achieve five-axis linkage during measurement. When the machine tool moves to the sampling pose, it should be paused to record data to eliminate the influence of machine tool dynamic performance factors. A calibration equation can be constructed for each sampling pose. Arranging the calibration equations for each sampling pose in columns can establish a calibration Jacobian matrix for calibrating the machine tool's geometric error parameters.

[0116]

[0117] Where m is the number of sampled poses, and the least squares solution of x is... The minimum number of samples m required should satisfy m≥14. Since the calculation of the Jacobian matrix identification assumes a linear approximation, the linear least squares identification process should be repeated until the residuals converge to a certain range. The flowchart for machine tool geometric error identification is as follows. Figure 4 As shown.

[0118] Operation S2 uses a ballbar to measure the machine tool in multiple poses, and constructs a Jacobian matrix for geometric error calibration based on the measurement data. Then, the actual geometric error of the machine tool is obtained by solving the least squares problem, and the actual kinematic model of the machine tool is constructed.

[0119] Specifically, the ideal kinematic model of the machine tool is transformed into the actual kinematic model of the machine tool by using the calibrated geometric error through the adjoint transformation of the screw. The actual kinematic model of the machine tool can be used for RTCP instructions, which can map the geometric error of the machine tool to the positional error of the tool position.

[0120] Apply adjoint transformation based on the identified machine tool geometric errors. and The actual rotation coordinates of each axis of the computer tool are calculated. From this, the actual kinematic model of the machine tool can be obtained using the forward kinematic model, allowing for the calculation of the actual pose of the tool position point.

[0121] Furthermore, by calculating the actual kinematic model of the machine tool with RTCP enabled, using the displacement of the rotating axis and the tool position information in the workpiece coordinate system, the displacement M of the machine tool's translational axis can be calculated based on the ideal kinematic model of the machine tool using the following formula. t :

[0122]

[0123] By substituting the rotational axis displacement and the calculated translational axis displacement into the actual kinematic model of the machine tool, the actual tool position pose, considering geometric errors and with the RTCP function enabled, can be calculated.

[0124] Operation S3 performs software compensation for machine tool errors based on the actual kinematic model of the machine tool and the inverse kinematics solution method.

[0125] Based on the actual kinematic model of the machine tool, the general inverse kinematics solution method for five-axis machine tools is applied to perform software compensation for machine tool errors. First, the compensated rotational axis displacements are solved using Paden-Kahan subproblems 2 and 1 from screw theory:

[0126]

[0127]

[0128] Where u = r ot Given v = 0 and z = αω1 + βω2 + γ(ω1 × ω2), calculate the three coefficients in z.

[0129]

[0130]

[0131] The solution selection method is applied to ensure that the correction amount of the first rotation axis in the kinematic chain is minimized. By adding or subtracting 2π from the two solutions, a total of six possible solutions are obtained. The six solutions are compared with the displacement in the uncompensated CNC program, and the solution with the smallest correction amount is selected as the compensated rotation axis displacement.

[0132] Furthermore, this method is extended to five-axis machine tool error compensation methods applicable to RTCP. After calculating the compensated rotational axis displacement, the ideal tool position coordinates P are used. n Calculate translational axis displacement under actual kinematic parameters Will The compensated rotational axis displacement is substituted into the ideal kinematic model of the machine tool, which has the same RTCP parameters as the internal RTCP parameters of the control system, to calculate the tool position coordinates P. c P c This refers to the translational axis displacement of the CNC program using the RTCP function after compensation.

[0133] The CNC programs before and after compensation are respectively input into the actual kinematic model of the machine tool to calculate the actual pose of the tool position. The actual pose of each tool position is then imported into the material removal module of the TurboCut CNC machining simulation software. The simulated model is compared with the design model of the part. The point cloud rendering illustrates the impact of machine tool geometric errors on the surface machining errors of the part and the effectiveness of the error compensation method. Figure 5 As shown, from left to right, the diagrams depict the CNC program toolpath trajectory, a comparison of machining errors before and after error compensation, and a comparison of machining errors after error compensation.

[0134] To verify the accuracy of geometric error calibration and the effectiveness of error compensation in the CNC machining error compensation method based on error calibration, the geometric error of the machine tool was calibrated by measuring the trajectory on an actual machine tool. Four points were randomly selected on the surface of a ballbar with the tool ball as the center and the ballbar length as the radius as the tool position point. The RTCP function was enabled to ensure that the tool position point remained unchanged during synchronous rotation of the rotary axis. Nineteen sampling poses were set for each tool position point, and the length change of the ballbar was recorded. Figure 6 As shown, this is to verify the test measurement results.

[0135] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A numerical control machining error identification method based on machine tool error calibration, characterized by, The method comprises the following steps: S1, constructing a machine tool ideal kinematics model of a machine tool, and establishing a machine tool minimum geometric error calibration model based on the machine tool ideal kinematics model, and then calibrating geometric errors of the machine tool based on a ball bar; S2, using the calibrated geometric errors, converting the machine tool ideal kinematics model into a machine tool actual kinematics model through a screw pair transformation, the machine tool actual kinematics model being capable of mapping the geometric errors of the machine tool to a tool position point pose error, and then completing error identification; The mathematical expression of the machine tool minimum geometric error model is: wherein ; is the kinematic chain of the machine tool; is the screw coordinates of the joint; denotes the differential form of a variable, is the error parameter of the workpiece coordinate system, is the error parameter of the joint, is the error parameter of the tool coordinate system; and is the motion of the joint; is the homogeneous transformation matrix of the tool coordinate system with respect to the workpiece coordinate system; is the skew-symmetric matrix of the screw coordinates of the joint; When the minimum geometric error calibration model of machine tool is established based on the ideal kinematic model of machine tool, the symbols are defined As to the mapping, the kinematic parameters of each joint of POE formula are linearized and right multiplied by the inverse of the positive kinematic formula, the geometric error calibration model of machine tool is obtained by applying the adjoint transformation; the redundant parameters in the geometric error calibration model are eliminated; Machine tool screw error parameters From position independent geometric error parameters Left multiplication error coefficient matrix Indicating, for a rotational axis There are: wherein is a set of orthogonal unit vectors, for the translation axes has: wherein is also a set of orthogonal unit vectors, when measured using a protractor .

2. The numerical control machining error identification method based on a machine tool error calibration according to claim 1, characterized by: The establishment of the ideal kinematic model of the machine tool does not need to consider the joint composition of the tool motion chain and the workpiece motion chain, and only needs to sequentially establish the screw coordinates of each joint in the order from the workpiece to the tool on the base coordinate system attached to the machine tool bed ; calculate the initial reference pose of the tool motion chain and the workpiece motion chain at zero time , ; left multiply the matrix index of each joint screw from the tool to the workpiece motion chain by the initial pose of the tool motion chain, and finally left multiply the inverse of the initial pose of the workpiece motion chain to obtain the forward kinematic model of the machine tool .

3. The numerical control machining error identification method based on a machine tool error calibration according to claim 1, characterized by: The machine tool actual kinematics model can be used for RTCP instructions, retains the position information of the established machine tool forward kinematics equation, differentiates both sides of the machine tool forward kinematics equation to obtain a deviation of a tool position point in a workpiece coordinate system affected by machine tool geometric errors, arranges the deviation into a matrix form, and projects the matrix along a ball bar direction to have: Wherein, Then, the RTCP function is started, the ball-bar base is placed at any position on the workbench, the ball center of the workpiece is set as the origin of the workpiece coordinate system, the ball center of the tool is set as the origin of the tool coordinate system, the tool ball is made to move in the X-Y, Y-X and X-Z planes respectively by using the measurement mode of the ball-bar, and the synchronous rotation of the rotating shaft of the machine tool is ensured to realize five-axis linkage. When the machine tool moves to the sampling position, the data is recorded to eliminate the influence of the dynamic performance of the machine tool. The calibration equations constructed by each sampling position are arranged in columns to establish the calibration Jacobian matrix for calibrating the geometric error parameters of the machine tool , x The least square solution of the calibration equations is .

4. The numerical control machining error identification method based on a machine tool error calibration according to claim 1, characterized by: Constrained by the stiffness and reachable space of a five-axis machine tool, according to the principle that a prismatic axis must be located at both ends of a motion chain from a workpiece to a tool, coordinates of the prismatic axis can be solved as: The calculated translational axis displacement and rotational axis displacement are brought into the actual kinematic model of the machine tool to calculate the actual pose of the tool position under the open RTCP function; For CNC programs using the RTCP function, the compensated rotational axis displacement is first calculated, and then the displacement is determined based on the coordinates of the ideal tool position point. Calculate translational axis displacement under actual kinematic parameters Finally The compensated rotational axis displacement is substituted into the ideal kinematic model of the machine tool, which has the same RTCP parameters as the internal RTCP parameters of the control system, to calculate the coordinates of the tool position. , This refers to the translational axis displacement of the CNC program using the RTCP function after compensation.

5. A numerical control machining error compensation method based on machine tool error calibration, characterized by: The compensation method first uses the numerical control machining error identification method based on machine tool error calibration of any one of claims 1-4 to realize error identification, and then adjusts a numerical control program to compensate for machine tool errors.

6. A numerical control machining error identification system based on machine error calibration, characterized by: The system comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the numerical control machining error identification method based on machine tool error calibration of any one of claims 1-4.

7. A computer-readable storage medium, characterized in that: The computer readable storage medium stores machine executable instructions, when the machine executable instructions are called and executed by a processor, the machine executable instructions cause the processor to implement the numerical control machining error identification method based on machine tool error calibration of any one of claims 1-4 or the numerical control machining error compensation method based on machine tool error calibration of claim 5.

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