阅读说明：本技术 一种面向联动轨迹误差预测的五轴机床数字孪生建模方法 (Five-axis machine tool digital twin modeling method for linkage trajectory error prediction ) 是由 吕盾 罗世有 张会杰 刘辉 赵万华 于 2020-12-11 设计创作，主要内容包括：一种面向联动轨迹误差预测的五轴机床数字孪生建模方法,先建立从插补指令位置到刀具中心位置的正运动变换矩阵,将各轴插补指令位置输入得到在工件坐标系下的理想刀具中心位置,并将其合成指令轨迹；再建立各轴从插补指令位置到光栅检测位置的传递函数,将各轴指令位置输入,实现对实际位置的预测；然后建立五轴机床几何误差表征模型；再建立从预测光栅位置到刀具中心位置的正运动变换矩阵,将预测的实际位置和机床几何误差表征模型输入到正运动变换矩阵,得到在工件坐标系下的实际刀具中心位置,并将其合成实际轨迹；集成模型建立五轴数控机床的数字孪生模型,实现五轴联动轨迹误差的预测,保证加工精度、提高加工效率。(A five-axis machine tool digital twin modeling method facing linkage track error prediction is characterized in that a positive motion transformation matrix from an interpolation command position to a cutter center position is established, interpolation command positions of all axes are input to obtain an ideal cutter center position under a workpiece coordinate system, and the ideal cutter center position is synthesized into a command track; then establishing a transfer function of each axis from the interpolation instruction position to the grating detection position, and inputting the instruction position of each axis to realize the prediction of the actual position; then establishing a geometric error representation model of the five-axis machine tool; establishing a positive motion transformation matrix from the predicted grating position to the cutter center position, inputting the predicted actual position and the machine tool geometric error representation model into the positive motion transformation matrix to obtain the actual cutter center position under a workpiece coordinate system, and synthesizing the actual cutter center position into an actual track; the integrated model establishes a digital twin model of the five-axis numerical control machine tool, so that the prediction of five-axis linkage track errors is realized, the machining precision is ensured, and the machining efficiency is improved.)

1. A five-axis machine tool digital twin modeling method for linkage track error prediction is characterized by comprising the following steps:

step 1, establishing a digital twin model of the selected five-axis numerical control machine tool;

step 2, inputting the G code of the machined part into the selected five-axis numerical control machine tool; reading an instruction position interpolated and output by a numerical control system during or before machining, and inputting the instruction position into the digital twin model established in the step 1 to obtain an ideal cutter center position and an actual cutter center position;

and 3, synthesizing the ideal cutter center position into an instruction track, synthesizing the actual cutter center position into an actual track, calculating the deviation of the actual track relative to the instruction track, obtaining the cutter point position track error and the cutter shaft attitude track error, and realizing the prediction of the five-axis linkage track error.

2. The digital twin modeling method for the five-axis machine tool facing the linkage track error prediction as recited in claim 1, wherein the specific method for establishing the digital twin model in step 1 is as follows:

1) establishing a positive motion transformation matrix from the interpolated command position to the tool center positionEstablishing a positive motion transformation matrix according to the kinematic structure of the machine toolInputting interpolation command position of each axis into positive kinematic transformation matrixThen, the axes are instructed in the machine tool coordinate systemConverting the position to a workpiece coordinate system to obtain an ideal cutter center position in the workpiece coordinate system, and synthesizing the ideal cutter center position into an instruction track;

2) establishing a transfer function of each axis from the interpolation command position to the grating detection position: identifying each axis servo feeding system by using an identification method and using a formula (2) to establish a transfer function of each axis servo feeding system, wherein B (z)^-1Feeding back the position for the grating ruler; a (z)^-1Is an interpolation command position; b_iAnd a_jCoefficients of the numerator and denominator, n, respectively, of the discrete transfer function_aAnd n_bThe orders of the numerator and the denominator of the discrete transfer function respectively; inputting the interpolation instruction position of each axis into the established transfer function, and predicting the actual position of raster detection of each axis;

3) establishing a 41-item geometric error characterization model of the five-axis machine tool: characterizing 30-term geometric errors related to the position into a high-order polynomial function with each axis position as a variable, as shown in formula (4), and characterizing 11-term geometric errors related to the position into a constant, as shown in formula (5);

in the formula (f)₁,f₂,…f₃₀A higher order polynomial function of 30 position dependent geometric errors, m representing the different positions of the respective axes, being the shifted position for the translation axis and the rotated angle for the rotation axis; n represents a polynomial order; a is₁₁…a_1nDenotes f₁Coefficient of each order of the function, in the same way, a_30,1…a_30,nDenotes f₃₀Function coefficients of each order; f. of₃₁,f₃₂,…f₄₁For 11 position-independent geometric errors, c₁,c₂,…c₁₁Is an error constant;

4) establishing a positive motion transformation matrix from a raster position to a tool center positionThe positive motion transformation matrix established in step 1) is firstlyOn the basis, geometric error terms of the machine tool are introduced, and a positive motion transformation matrix considering the geometric errors is establishedThen, inputting the actual positions of the raster detection of each axis predicted in the step 2) and the machine tool geometric error characterization model obtained in the step 3) into a positive motion transformation matrixAs shown in formula (7); converting the actual positions of the shafts under the machine tool coordinate system into a workpiece coordinate system to obtain the actual cutter center position considering the influence of geometric errors under the workpiece coordinate system, and synthesizing the actual cutter center position into an actual track;

in the formula: w is a workpiece coordinate system, R is a machine tool coordinate system, S is a main shaft coordinate system, and C, A, X, Y, Z is a machine tool shaft coordinate system respectively; definition ofAfter the influence of geometric errors of the machine tool is considered, a homogeneous transformation matrix of a coordinate system a and a homogeneous transformation matrix of a coordinate system b are obtained;a homogeneous transformation matrix of a workpiece coordinate system and a C-axis coordinate system;a homogeneous transformation matrix of a C-axis coordinate system and an A-axis coordinate system;a homogeneous transformation matrix of an A-axis coordinate system and a machine tool coordinate system;a homogeneous transformation matrix of a machine tool coordinate system and a Y-axis coordinate system;a homogeneous transformation matrix of a Y-axis coordinate system and an X-axis coordinate system;a homogeneous transformation matrix of an X-axis coordinate system and a Z-axis coordinate system;a homogeneous transformation matrix of a Z-axis coordinate system and a main axis coordinate system;a homogeneous transformation matrix of a main shaft coordinate system and a cutter coordinate system;

5) integrating the positive motion transformation matrix, the transfer function and the geometric error representation model established in the steps 1) to 4), establishing a digital twin model of the five-axis numerical control machine tool, and performing error solution on the part instruction track and the actual track obtained through the digital twin model to realize the prediction of the five-axis linkage track error.

Technical Field

The invention belongs to the technical field of numerical control machines, and particularly relates to a five-axis machine tool digital twin modeling method for linkage trajectory error prediction.

Technical Field

In the five-axis machine tool machining research, the control of the contour error of a complex curved surface part is always a difficult problem, and the core for ensuring the contour error of the part is the linkage track error of the five-axis machine tool. The track precision in the part machining process is often unknown before machining, and the machined part is difficult to judge whether the requirement of the profile error can be met, so that the requirement of the precision of the profile error of the part can be met only at an extremely low feeding speed in field machining, and the machining efficiency is greatly influenced.

At present, the research on the track error prediction method at home and abroad is relatively less, and the common method is to realize the estimation of the track error based on a dynamic model and a kinematic model of a numerical control machine. The existing prediction model usually takes the tool position file data of the machine tool as input data, the model needs to continuously carry out forward and inverse kinematics transformation on the tool position file data to realize the transformation between a workpiece coordinate system and a machine tool coordinate system, and the calculation is complex; and the high-precision dynamic model of the numerical control machine tool needs to be established by considering the non-linear parameters such as the rigidity, the damping and the like of the joint part, and the modeling process is complex.

At present, in the field of numerical control machine tool machining, a digital twin model and application mainly face to a geometric layer, and based on languages such as a three-dimensional CAD model and OpenGL, the digital twin model of the numerical control machine tool can mirror the geometric structure of a physical entity in high fidelity to realize synchronous motion of the physical entity. However, at the numerical control machine tool level, the digital twin model still lacks the description of the control mechanism and behavior of deep movements such as precision.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention aims to provide a digital twin modeling method of a five-axis machine tool for linkage track error prediction.

In order to achieve the purpose, the invention adopts the technical scheme that:

a five-axis machine tool digital twin modeling method for linkage track error prediction comprises the following steps:

step 1, establishing a digital twin model of the selected five-axis numerical control machine tool;

step 2, inputting the G code of the machined part into the selected five-axis numerical control machine tool; reading an instruction position interpolated and output by a numerical control system during or before machining, and inputting the instruction position into the digital twin model established in the step 1 to obtain an ideal cutter center position and an actual cutter center position;

and 3, synthesizing the ideal cutter center position into an instruction track, synthesizing the actual cutter center position into an actual track, calculating the deviation of the actual track relative to the instruction track, obtaining the cutter point position track error and the cutter shaft attitude track error, and realizing the prediction of the five-axis linkage track error.

The specific method for establishing the digital twin model in the step 1 is as follows:

1) establishing a positive motion transformation matrix from the interpolated command position to the tool center positionEstablishing a positive motion transformation matrix according to the kinematic structure of the machine toolInputting interpolation command position of each axis into positive kinematic transformation matrixThen, converting the instruction position of each shaft under the machine tool coordinate system into a workpiece coordinate system to obtain the ideal cutter center position under the workpiece coordinate system, and synthesizing the ideal cutter center position into an instruction track;

2) establishing a transfer function of each axis from the interpolation command position to the grating detection position: identifying each axis servo feeding system by using an identification method and using a formula (2) to establish a transfer function of each axis servo feeding system, wherein B (z)^-1Feeding back the position for the grating ruler; a (z)^-1Is an interpolation command position; b_iAnd a_jCoefficients of the numerator and denominator, n, respectively, of the discrete transfer function_aAnd n_bThe orders of the numerator and the denominator of the discrete transfer function respectively; inputting the interpolation instruction position of each axis into the established transfer function, and predicting the actual position of raster detection of each axis;

3) establishing a 41-item geometric error characterization model of the five-axis machine tool: characterizing 30-term geometric errors related to the position into a high-order polynomial function with each axis position as a variable, as shown in formula (4), and characterizing 11-term geometric errors related to the position into a constant, as shown in formula (5);

in the formula (f)₁,f₂,…f₃₀A higher order polynomial function of 30 position dependent geometric errors, m representing the different positions of the respective axes, being the shifted position for the translation axis and the rotated angle for the rotation axis; n represents a polynomial order; a is₁₁…a_1nDenotes f₁Coefficient of each order of the function, in the same way, a_30,1…a_30,nDenotes f₃₀Function coefficients of each order; f. of₃₁,f₃₂,…f₄₁For 11 position-independent geometric errors, c₁,c₂,…c₁₁Is an error constant;

4) establishing a positive motion transformation matrix from a raster position to a tool center positionThe positive motion transformation matrix established in step 1) is firstlyOn the basis, geometric error terms of the machine tool are introduced, and a positive motion transformation matrix considering the geometric errors is establishedThen, inputting the actual positions of the raster detection of each axis predicted in the step 2) and the machine tool geometric error characterization model obtained in the step 3) into a positive motion transformation matrixAs shown in formula (7); converting the actual positions of the shafts under the machine tool coordinate system into a workpiece coordinate system to obtain the actual cutter center position considering the influence of geometric errors under the workpiece coordinate system, and synthesizing the actual cutter center position into an actual track;

in the formula: w is a workpiece coordinate system, R is a machine tool coordinate system, S is a main shaft coordinate system, T is a cutter coordinate system, and C, A, X, Y, Z is machine tool shaft coordinate systems respectively; definition ofAfter the influence of geometric errors of the machine tool is considered, a homogeneous transformation matrix of a coordinate system a and a homogeneous transformation matrix of a coordinate system b are obtained;a homogeneous transformation matrix of a workpiece coordinate system and a C-axis coordinate system;a homogeneous transformation matrix of a C-axis coordinate system and an A-axis coordinate system;a homogeneous transformation matrix of an A-axis coordinate system and a machine tool coordinate system;a homogeneous transformation matrix of a machine tool coordinate system and a Y-axis coordinate system;a homogeneous transformation matrix of a Y-axis coordinate system and an X-axis coordinate system;a homogeneous transformation matrix of an X-axis coordinate system and a Z-axis coordinate system;a homogeneous transformation matrix of a Z-axis coordinate system and a main axis coordinate system;a homogeneous transformation matrix of a main shaft coordinate system and a cutter coordinate system;

5) integrating the positive motion transformation matrix, the transfer function and the geometric error representation model established in the steps 1) to 4), establishing a digital twin model of the five-axis numerical control machine tool, and performing error solution on the part instruction track and the actual track obtained through the digital twin model to realize the prediction of the five-axis linkage track error.

The invention has the following beneficial effects:

the prediction model directly takes interpolation instructions of a numerical control system as input data, only needs to carry out positive motion transformation on the interpolation data, and is relatively simple in calculation; a transfer function identification method is adopted to replace a complex dynamic modeling process, and the identification process is simple; by constructing a digital twin model of the five-axis numerical control machine tool, interpolation instruction data of the numerical control machine tool in part machining is input into the digital twin model in real time, and the track error of the part machined by the five-axis machine tool is predicted, so that the prediction of the part machining track error driven by real-time data of a physical entity (the numerical control machine tool) is realized, a basis is provided for analyzing the cause of the linkage track error, and the method has important significance for ensuring the machining precision and improving the machining efficiency.

Drawings

Fig. 1 is a schematic view of a kinematic structure of a machine tool according to an embodiment of the present invention.

FIG. 2 is a flow chart of the present invention for synthesizing instruction traces.

FIG. 3 is a schematic diagram of the transfer function from the X-axis command position to the raster position according to the present invention.

FIG. 4 is a schematic diagram of the Y-axis position-dependent geometric error of the present invention.

FIG. 5 is a flow chart of synthesizing an actual trajectory according to the present invention.

FIG. 6 is a flow chart of linkage trajectory error prediction in accordance with the present invention.

FIG. 7 is a diagram of a test piece trajectory synthesis in the embodiment of the present invention.

FIG. 8 is a schematic view of the profile error of the present invention.

FIG. 9 (a) shows the trajectory error of the position of the tip according to the embodiment of the present invention; (b) the tool shaft attitude trajectory error is an embodiment of the invention.

Detailed Description

The invention is described in detail below with reference to the figures and examples.

A five-axis machine tool digital twin modeling method for linkage track error prediction comprises the following steps:

step 1, establishing a digital twin model of the selected five-axis numerical control machine tool;

1.1) establishing a positive motion transformation matrix from an interpolation command position to a tool center position

Referring to fig. 1, in the present embodiment, an AC dual-turntable five-axis machine tool is taken as an example, the five-axis machine tool has two open-loop kinematic chains, namely a tool kinematic chain and a workpiece kinematic chain, and the two open-loop kinematic chains form an integral kinematic chain from a workpiece to a tool, wherein the workpiece kinematic chain starts from a machine tool coordinate system and sequentially goes to an axis a and an axis C, and the workpiece is finally fixed on a C-axis workbench; the cutter moving chain starts from a machine tool coordinate system to the Y axis, the X axis and the Z axis, and the cutter is finally fixed on the Z axis; the integral motion chain sequentially goes from the workpiece to the C axis, the A axis, the machine tool coordinate system, the Y axis, the X axis and finally to the Z axis and the cutter;

referring to FIG. 2, a positive motion transformation matrix from the interpolation command position to the tool center position is establishedAccording to the kinematic structure of the AC double-turntable five-axis machine tool shown in the figure 1, a positive motion transformation matrix is established as shown in a formula (1); definition ofFor the homogeneous transformation matrix of a coordinate system and a coordinate system b, the interpolation command position of each axis is input into the positive kinematic transformation matrixConverting the instruction position of each shaft under the machine tool coordinate system into a workpiece coordinate system to obtain the ideal cutter center position under the workpiece coordinate system, and synthesizing the ideal cutter center position into an instruction track;

1.2) establishing a transfer function of each axis from an interpolation command position to a grating detection position:

establishing a transfer function of each shaft from an interpolation instruction position to a grating detection position, taking an X shaft as an example, referring to FIG. 3, and taking the X shaft as a transmission link schematic diagram of the X shaft, wherein an X shaft interpolation instruction controls a motor rotor to rotate through three-loop control of position, speed and current, and drives a lead screw to further drive a mechanical link to move; identifying the X-axis servo feeding system by using an identification method, establishing a transfer function from an interpolation command position of the numerical control system to a grating detection position, and inputting the interpolation command position into the identified transfer function to realize the prediction of the grating detection position;

the specific process is as follows: taking the grating feedback and the instruction position as data drive for the X axis, and identifying a transfer function from the X axis instruction position to the grating feedback position by using an identification method; in order to fully excite the dynamic characteristics of each feed shaft of the machine tool, an excitation signal with a variable amplitude M is selected to generate a G code; inputting the G code into a numerical control system of the machine tool to enable each shaft to do excitation motion; acquiring data such as interpolation instruction positions, grating ruler feedback positions, sampling frequency and the like in excitation motion, identifying each axis servo feeding system by adopting a formula (2), establishing a transfer function of each axis servo feeding system, wherein each axis transfer function identified in the embodiment is shown in a formula (3), and predicting the actual position detected by each axis grating by inputting each axis instruction position into the established transfer function;

1.3) establishing a 41-item geometric error characterization model of the five-axis machine tool:

the five-axis machine tool has 41 items of geometric errors which are divided into position-related geometric errors and position-unrelated geometric errors, referring to fig. 4, taking a Y axis as an example and being a schematic diagram of 6 items of position-related geometric errors, and characterizing 30 items of position-related geometric errors into a high-order polynomial function taking each axis position as a variable, as shown in a formula (4), and characterizing 11 items of position-unrelated geometric errors as a constant, as shown in a formula (5), in the embodiment, taking a C axis as an example, and the high-order polynomial function of the 6 items of position-related geometric errors of the C axis is shown in a formula (6);

in the formulae (4) and (5), f₁,f₂,…f₃₀A higher order polynomial function of 30 position dependent geometric errors, m representing the different positions of the respective axes, being the shifted position for the translation axis and the rotated angle for the rotation axis; n represents a polynomial order; a is₁₁…a_1nDenotes f₁Coefficient of each order of the function, in the same way, a_30,1…a_30,nDenotes f₃₀Function coefficients of each order; f. of₃₁,f₃₂,…f₄₁For 11 position-independent geometric errors, c₁,c₂,…c₁₁Is an error constant; in the formula (6), δ_xc、δ_yc、δ_zc、ε_xc、ε_yc、ε_zcRespectively 6 position-related geometric error functions of the C axis, wherein C is an angle value of the rotating shaft C at different positions;

1.4) establishing a positive motion transformation matrix from the predicted raster position to the tool center position

Referring to FIG. 5, a positive motion transformation matrix from the predicted raster position to the tool center position is establishedThe positive motion transformation matrix established in step 1.1) is firstlyOn the basis, geometric error terms of the machine tool are introduced, and a positive motion transformation matrix considering the geometric errors is establishedAs shown in formula (7): definition ofIn order to consider the influence of the geometric errors of the machine tool, the homogeneous transformation matrix of the coordinate system a and the coordinate system b inputs the actual positions of the raster detection of each axis predicted in the step 1.2) and the geometric error representation model of the machine tool obtained in the step 1.3) into the positive motion transformation matrixObtaining the actual center position of the cutter under a workpiece coordinate system, and synthesizing the actual center position of the cutter into an actual track;

in the formula: w is a workpiece coordinate system, R is a machine tool coordinate system, S is a main shaft coordinate system, and C, A, X, Y, Z is a machine tool shaft coordinate system respectively; definition ofAfter the influence of geometric errors of the machine tool is considered, a homogeneous transformation matrix of a coordinate system a and a homogeneous transformation matrix of a coordinate system b are obtained;a homogeneous transformation matrix of a workpiece coordinate system and a C-axis coordinate system;a homogeneous transformation matrix of a C-axis coordinate system and an A-axis coordinate system;a homogeneous transformation matrix of an A-axis coordinate system and a machine tool coordinate system;a homogeneous transformation matrix of a machine tool coordinate system and a Y-axis coordinate system;a homogeneous transformation matrix of a Y-axis coordinate system and an X-axis coordinate system;a homogeneous transformation matrix of an X-axis coordinate system and a Z-axis coordinate system;a homogeneous transformation matrix of a Z-axis coordinate system and a main axis coordinate system;a homogeneous transformation matrix of a main shaft coordinate system and a cutter coordinate system;

1.5) integrating the positive motion transformation matrix, the transfer function and the geometric error representation model established in the steps 1.1) to 1.4) with reference to FIG. 6, and establishing a digital twin model of the five-axis numerical control machine tool;

step 2, inputting the G code of the machined part into the selected five-axis numerical control machine tool; reading an instruction position interpolated and output by a numerical control system during or before machining, and inputting the instruction position into the digital twin model established in the step 1 to obtain an ideal cutter center position and an actual cutter center position;

and 3, synthesizing the ideal cutter center position into an instruction track, synthesizing the actual cutter center position into an actual track, calculating the deviation of the actual track relative to the instruction track, obtaining the cutter point position track error and the cutter shaft attitude track error, and realizing the prediction of the five-axis linkage track error.

Referring to fig. 7, fig. 7 is an S specimen command trajectory and an actual trajectory obtained by the digital twin model according to the present embodiment; referring to fig. 8, fig. 8 is a schematic diagram of calculating a deviation of an actual trajectory from a commanded trajectory in the present embodiment, where an interlocking trajectory error of part processing includes a tool tip position trajectory error and a tool shaft posture trajectory error, and the tool tip position error ∈_pIs referred to as P_aAnd P_cThe vector between, i.e. the point position P of the knife from the actual track on the calculated command track_aNearest point P_cThe distance of (d); cutter shaft attitude trajectory error epsilon_oIs the actual knife axis direction vector O_aAnd the contour pose vector O closest to the actual tool tip position on the command track_cAngle therebetween, i.e. calculating vector O_aAnd O_cThe included angle between them; referring to fig. 9, fig. 9 shows the results obtained in the present embodiment, which are five-axis linkage tool nose position trajectory error and tool shaft attitude trajectory error, respectively, and the predicted tool nose position trajectory error change range is about (-1.2-1.5) mm and the tool shaft attitude error is displayed according to the error mapThe variation range of the track error is about (-4.5 x 10)^-3～4×10^-3) And rad, thereby realizing the prediction of the five-axis linkage track error.