阅读说明：本技术 一种严格定义下切削加工的零件轮廓误差预测方法和系统 (Part contour error prediction method and system for cutting under strict definition ) 是由 张俊 吴浩宇 尹佳 张会杰 赵万华 于 2021-08-06 设计创作，主要内容包括：本发明公开了一种严格定义下切削加工的零件轮廓误差预测方法和系统,属于数控加工技术领域。首先给出轮廓误差的严格定义,避免了在大曲率零件计算过程中定义失效的问题；其次采用系统辨识的方法代替复杂的坐标变换,建立进给伺服系统模型；接下来采用局部搜索的方法确定目标插补点,同时采用局部直线插补的方式拟合加工轨迹,并且根据理论插补点与实际插补点的位置关系分别求解轮廓误差,提高了计算效率,适用于复杂零件轮廓误差的预测。本发明方法同时考虑了轮廓误差的预测效率与计算准确性,适用于大曲率零件轮廓误差的预测。(The invention discloses a part contour error prediction method and system for cutting under strict definition, and belongs to the technical field of numerical control machining. Firstly, the strict definition of the contour error is given, so that the problem of definition failure in the calculation process of the large-curvature part is avoided; secondly, a system identification method is adopted to replace complex coordinate transformation, and a feeding servo system model is established; and then, a target interpolation point is determined by adopting a local search method, a processing track is fitted by adopting a local linear interpolation mode, and the contour error is respectively solved according to the position relation of the theoretical interpolation point and the actual interpolation point, so that the calculation efficiency is improved, and the method is suitable for predicting the contour error of the complex part. The method simultaneously considers the prediction efficiency and the calculation accuracy of the contour error, and is suitable for predicting the contour error of the large-curvature part.)

1. A part contour error prediction method for strictly defining under-cutting machining is characterized by comprising the following steps:

step 1) obtaining a machine tool transfer function, and obtaining an actual interpolation instruction position of the part machining based on a theoretical interpolation instruction position of the part machining;

step 2) strictly defining the profile error based on the part processing characteristics, and acquiring a theoretical interpolation instruction position closest to the actual interpolation instruction position based on the strictly defined profile error;

under the premise that the profile error after strict definition is the minimum time span, actually interpolating the normal distance from the command position to the ideal processing track;

step 3) calculating to obtain an ideal machining track of the part based on the theoretical interpolation command position in the step 2), and obtaining a theoretical interpolation command position required by part contour error calculation based on the ideal machining track;

step 4) calculating a required theoretical interpolation instruction position based on the actual interpolation instruction position and the part contour error, and acquiring a contour error corresponding to the actual interpolation instruction position;

and 5) repeating the steps 1) to 4) to obtain the contour error at each actual interpolation command position.

2. The method for predicting the part profile error in the cutting process under strict definition according to claim 1, wherein the machine tool transfer function in the step 1) is obtained by identifying a servo system of the machine tool through a system identification method.

3. The method for predicting the part profile error in the cutting process under strict definition according to claim 1, wherein the machine transfer function is established by:

firstly, acquiring an excitation signal capable of exciting the movement of each feed shaft of a machine tool;

then converting the excitation signal into an excitation code and inputting the excitation code into a numerical control system of the machine tool to enable each feed shaft of the machine tool to carry out excitation movement;

acquiring data of a theoretical interpolation instruction position and a grating detection position in the process of exciting movement of each feed shaft of the machine tool;

and establishing a machine tool transfer function based on the theoretical interpolation instruction position and the grating detection position data through system identification.

4. The method of predicting part contour error in a cutting process under strict definition according to claim 1, wherein in the step 2), the theoretical interpolation command position closest to the actual interpolation command position is obtained by a center window method or a system traversal method.

5. The method for predicting part profile errors in cutting machining under strict definition according to claim 4, wherein in the step 2), when the theoretical interpolation command position closest to the actual interpolation command position is obtained by a center window method, the specific operation process is as follows:

a moving window is designated at each interpolation point, and the distance between the actual interpolation command position and each interpolation point in the window is calculated respectively, so that the theoretical interpolation command position closest to the actual interpolation command position is determined.

6. The method for predicting part profile errors in a strictly defined undercut machining process of claim 1, wherein in step 3), the ideal machining path is obtained by a linear interpolation method.

7. The method for predicting the profile error of a part subjected to cutting under strict definition according to claim 1, wherein in the step 4), the specific calculation process of the profile error is as follows:

firstly, a theoretical interpolation instruction position closest to an actual interpolation instruction position is obtained, and a direction vector of the theoretical interpolation instruction position and a direction vector of a connecting line of the actual interpolation instruction position and the theoretical interpolation instruction position are calculated;

determining the specific calculation condition of the contour error according to the sign of the product of the quantity of the two direction vectors;

making a perpendicular line from the actual instruction position to the direction vector of the theoretical interpolation instruction point to obtain the position coordinate of the foot;

and obtaining a contour error vector based on the contour error definition, and further calculating to obtain a contour error.

8. The method for predicting the profile error of a part subjected to cutting under strict definition according to claim 7, wherein the specific calculation conditions of the profile error in the step 4) comprise the following three conditions:

case 1: when in useCalculating P_aToAs a contour error value;

case 2: when in useCalculating P_aToAs a contour error value;

case 3: when in useCalculating P_aTo P_rAs a contour error value;

wherein, P_aActual interpolation command positions; p_rA theoretical interpolation command position closest to the actual interpolation command position; p_r+1Is P_rThe next theoretical interpolation command position; p_r-1Is P_rPrevious theoretical interpolation of instruction bitsAnd (4) placing.

9. A system for predicting part profile errors for a strictly defined undercut operation, comprising:

the transfer function module is used for obtaining a machine tool transfer function and obtaining an actual interpolation instruction position of part machining based on the machine tool transfer function and a theoretical interpolation instruction position of machining;

the ideal processing track module is interacted with the transfer function module and used for obtaining a theoretical interpolation instruction position closest to the actual interpolation instruction position based on the strictly defined contour error and further calculating to obtain an ideal processing track of the part;

and the contour error calculation module is interacted with the ideal processing track module and used for calculating the normal distance from the actual interpolation command position to the ideal processing track.

Technical Field

The invention belongs to the technical field of numerical control machining, and relates to a part contour error prediction method and system for cutting machining under strict definition.

Background

In recent years, in the fields of aerospace, automobiles, ships and the like, a large number of high-speed and high-precision numerical control machining centers are gradually used for machining and manufacturing precise and complex parts. Particularly, some key parts gradually develop towards complex profiles, light structures and precise manufacturing, the geometrical configuration of the parts is complex and difficult to process, the requirement on the appearance coordination is high, and new higher requirements are provided for the working performance of the multi-axis linkage numerical control machine tool. In the numerical control machining process, due to the fact that a machine tool feed shaft servo system lags, the multi-shaft dynamic characteristics are not matched and external disturbance factors exist, deviation between an actual machining track and a theoretical track is caused, namely, a profile error. Therefore, the research on the contour error prediction method has important significance for improving the tracking precision of the numerical control system and realizing high-precision numerical control machining.

In the aspect of profile error research, patent number CN108803487A discloses a point location profile error prediction method for a side milling surface of a part, which reconstructs a processing surface, calculates the distance from an actual tool location point to an ideal processing surface, and obtains a point location profile error; the patent number CN109240214A discloses a contour error estimation and visualization method facing multi-axis numerical control machining, which divides a machining track into a straight line and a curve, the curve track adopts linear spline interpolation as the straight line, and the distance between each tool location point and an ideal track is calculated; the patent number CN106843146A discloses a self-adaptive variable gain contour error compensation method, which utilizes a tangential error inverse push strategy to quickly find a foot point on a curve contour, which is closest to an actual knife location point, according to a geometric position relation between a free curve generated by a numerical control parameter curve interpolator and the actual knife location point, thereby realizing high-precision estimation of a contour error vector; patent number CN110262394A discloses a method for compensating contour error in numerical control machining, which estimates the contour error at the current moment by collecting the command contour and the real-time response contour in real time; li academic Wei et al (Li academic Wei, Zhao Wanhua, Lu grasp constant. track error modeling multi-axis linkage machine tool contour error compensation technology [ J ]. Western Ann university of transportation academic, 2012,46(03):47-52.) calculate the shortest distance between the actual point and two straight lines consisting of the three nearest points on the theoretical curve, and select the minimum value as the contour error.

In summary, the basic idea of the present research on contour error prediction is as follows: and generating a processing track according to the ideal interpolation point data, calculating the actual position point coordinates corresponding to the ideal interpolation points, and solving the distance from the actual position points to the ideal processing track to be used as a contour error. The disadvantage of this method is that the profile error definition is not strict, and when the curvature of the processing track changes greatly, a large deviation is generated. Meanwhile, in the aspect of contour error prediction algorithm, most researches focus on improving prediction accuracy and neglecting the problems of complex algorithm calculation and long calculation time, and are difficult to be specifically applied to the task of real-time contour error calculation, especially under the condition of relatively complex parts. Therefore, it is desirable to develop a new method for calculating the contour error to solve the above problems.

Disclosure of Invention

The invention aims to overcome the defects that in the prior art, the error definition of a contour error measuring method is not strict, the algorithm calculation process is complex, and the consumed time is long, and provides a part contour error prediction method and a part contour error prediction system for cutting under strict definition.

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

a part contour error prediction method for strictly defining lower cutting machining comprises the following steps:

step 1) obtaining a machine tool transfer function, and obtaining an actual interpolation instruction position of the part machining based on a theoretical interpolation instruction position of the part machining;

step 2) strictly defining the profile error based on the part processing characteristics, and acquiring a theoretical interpolation instruction position closest to the actual interpolation instruction position based on the strictly defined profile error;

under the premise that the profile error after strict definition is the minimum time span, actually interpolating the normal distance from the command position to the ideal processing track;

step 3) calculating to obtain an ideal machining track of the part based on the theoretical interpolation command position in the step 2), and obtaining a theoretical interpolation command position required by part contour error calculation based on the ideal machining track;

step 4) calculating a required theoretical interpolation instruction position based on the actual interpolation instruction position and the part contour error, and acquiring a contour error corresponding to the actual interpolation instruction position;

and 5) repeating the steps 1) to 4) to obtain the contour error at each actual interpolation command position.

Preferably, the machine tool transfer function in step 1) is obtained by identifying a machine tool servo system through a system identification method.

Preferably, the process of establishing the transfer function of the machine tool is specifically as follows:

firstly, acquiring an excitation signal capable of exciting the movement of each feed shaft of a machine tool;

then converting the excitation signal into an excitation code and inputting the excitation code into a numerical control system of the machine tool to enable each feed shaft of the machine tool to carry out excitation movement;

acquiring data of a theoretical interpolation instruction position and a grating detection position in the process of exciting movement of each feed shaft of the machine tool;

and establishing a machine tool transfer function based on the theoretical interpolation instruction position and the grating detection position data through system identification.

Preferably, in step 2), the theoretical interpolation command position closest to the actual interpolation command position is obtained by a center window method or a system traversal method.

Preferably, in step 2), when the theoretical interpolation command position closest to the actual interpolation command position is obtained by the center window method, the specific operation process is as follows:

a moving window is designated at each interpolation point, and the distance between the actual interpolation command position and each interpolation point in the window is calculated respectively, so that the theoretical interpolation command position closest to the actual interpolation command position is determined.

Preferably, in step 3), the ideal processing track is obtained by a method of linear interpolation.

Preferably, in step 4), the specific calculation process of the contour error is as follows:

firstly, a theoretical interpolation instruction position closest to an actual interpolation instruction position is obtained, and a direction vector of the theoretical interpolation instruction position and a direction vector of a connecting line of the actual interpolation instruction position and the theoretical interpolation instruction position are calculated;

determining the specific calculation condition of the contour error according to the sign of the product of the quantity of the two direction vectors;

making a perpendicular line from the actual instruction position to the direction vector of the theoretical interpolation instruction point to obtain the position coordinate of the foot;

and obtaining a contour error vector based on the contour error definition, and further calculating to obtain a contour error.

Further preferably, in step 4), the specific calculation conditions of the contour error include the following three conditions:

case 1: when in useCalculating P_aToAs a contour error value;

case 2: when in useCalculating P_aToAs a contour error value;

case 3: when in useCalculating P_aTo P_rAs a contour error value;

wherein, P_aActual interpolation command positions; p_rA theoretical interpolation command position closest to the actual interpolation command position; p_r+1Is P_rThe next theoretical interpolation command position; p_r-1Is P_rThe previous theoretical interpolation command position.

A part profile error prediction system for a well-defined undercut process, comprising:

the transfer function module is used for obtaining a machine tool transfer function and obtaining an actual interpolation instruction position of part machining based on the machine tool transfer function and a theoretical interpolation instruction position of machining;

the ideal processing track module is interacted with the transfer function module and used for obtaining a theoretical interpolation instruction position closest to the actual interpolation instruction position based on the strictly defined contour error and further calculating to obtain an ideal processing track of the part;

and the contour error calculation module is interacted with the ideal processing track module and used for calculating the normal distance from the actual interpolation command position to the ideal processing track.

Compared with the prior art, the invention has the following beneficial effects:

the invention discloses a part contour error prediction method for cutting under strict definition, which firstly gives out strict definition of contour error and avoids the problem of definition failure in the calculation process of a large-curvature part; secondly, a system identification method is adopted to replace complex coordinate transformation, and a feeding servo system model is established; and then, a target interpolation point is determined by adopting a local search method, a processing track is fitted by adopting a local linear interpolation mode, and the contour error is respectively solved according to the position relation of the theoretical interpolation point and the actual interpolation point, so that the calculation efficiency is improved, and the method is suitable for predicting the contour error of the complex part. The method simultaneously considers the prediction efficiency and the calculation accuracy of the contour error, and is suitable for predicting the contour error of the large-curvature part.

The invention also discloses a part contour error prediction system for strictly defining the lower cutting process, which is established based on the method and comprises three modules, wherein the three modules are respectively as follows: the transfer function module is used for obtaining a machine tool transfer function and obtaining an actual interpolation instruction position of part machining based on the machine tool transfer function and a theoretical interpolation instruction position of machining; the ideal processing track module is interacted with the transfer function module and used for obtaining a theoretical interpolation instruction position closest to the actual interpolation instruction position based on the strictly defined contour error and further calculating to obtain an ideal processing track of the part; and the contour error calculation module is interacted with the ideal processing track module and used for calculating the normal distance from the actual interpolation command position to the ideal processing track.

Drawings

FIG. 1 is a flow chart of a part profile error prediction method of the present invention;

FIG. 2 is a model of the servo feeding system of the machine tool of the present invention;

FIG. 3 is a schematic diagram of the strict definition of profile error according to the present invention;

FIG. 4 is a theoretical interpolation point solution principle of the present invention closest to the actual command position;

FIG. 5 is a schematic diagram of theoretical interpolation points required for determining profile errors in accordance with the present invention;

FIG. 6 is a schematic diagram of the profile error calculation according to the present invention.

Detailed Description

The invention is described in further detail below with reference to the accompanying drawings:

example 1

A part contour error prediction method for strictly defining lower cutting machining comprises the following steps:

step 1) obtaining a machine tool transfer function, and obtaining an actual interpolation instruction position of the part machining based on a theoretical interpolation instruction position of the part machining;

step 2) strictly defining the profile error based on the part processing characteristics; under the premise that the profile error after strict definition is the minimum time span, actually interpolating the normal distance from the command position to the ideal processing track;

acquiring a theoretical interpolation instruction position closest to the actual interpolation instruction position based on the strictly defined contour error;

step 3) calculating to obtain an ideal machining track of the part based on the theoretical interpolation command position in the step 2), and obtaining a theoretical interpolation command position required by part contour error calculation based on the ideal machining track;

step 4) acquiring a corresponding contour error at the position of the actual interpolation instruction based on the position of the actual interpolation instruction and the position of the theoretical interpolation instruction;

step 5) repeat steps 1) to 4) to obtain the contour error at each actual interpolation command position in the embodiment 2

A part contour error prediction method for strictly defining lower cutting machining comprises the following steps:

step 1: identifying the transfer function of each feed shaft of the machine tool, inputting a theoretical interpolation command of part machining into the transfer function, and obtaining an actual interpolation command position. The transfer function of the machine tool servo system is identified by adopting a system identification method, and the identification steps are as follows: firstly, acquiring an excitation signal to fully excite the movement of each feed shaft of the machine tool; secondly, converting the excitation signal into an excitation G code, inputting the excitation G code into a numerical control system of the machine tool, enabling each feed shaft of the machine tool to perform excitation motion, and collecting data of a theoretical interpolation instruction position and a grating detection position; and finally, establishing a transfer function of the machine tool feeding system through system identification.

Next, an actual interpolation command position for the machining of the part is obtained. Firstly, a theoretical interpolation instruction position of part machining is obtained, and the theoretical interpolation instruction position is input to a machine tool transfer function, so that a corresponding actual interpolation instruction position can be obtained.

Step 2: according to the part machining characteristics, a strict definition of the profile error is given. The profile error is generally defined as a deviation of an actual interpolation command position from an ideal machining track, and there are two common definitions, namely, a normal distance (definition 1) from the actual interpolation command position to the ideal track and a shortest distance (definition 2) from the actual interpolation command position to the ideal track. When the curvature of the part is large, a plurality of contour error results may be generated by calculating according to definition 1, and an over-cut may be generated at a position where the curvature of the machining trajectory is large by calculating according to definition 2, so that the contour error cannot be accurately calculated by the above definitions. Based on this, a strict definition of the profile error is given herein: the contour error is the normal distance from the actual interpolation command position to the ideal processing track, the time span is minimum, and under strict definition, the problem of the previous definition can be avoided when the contour error is calculated.

And step 3: solving the actual interpolation command position P_aNearest theoretical interpolation command position P_r. For the subsequent contour error calculation, the distance actual interpolation command position P on the ideal processing track needs to be obtained_aNearest theoretical interpolated command bitPut P_r. Suppose (P)_i,O_i) Representing the tool pose, P, of any point on the command trajectory_iIndicating the position of the reference nose point, O_iShowing the direction of the cutter shaft; (P)_a,O_a) Representing the sum of P on the actual track_iCorresponding interpolation point poses; p_c、P_c1Are respectively P_aA drop on an ideal trajectory; p_rFor a given interpolation period, the distance P_aThe nearest interpolation point; mu.s_pDescribing the position deviation of the actual blade tip position from the reference trajectory of the blade tip position, and_othe angular deviation from the actual arbor direction to the arbor direction reference trajectory is described.

By local point-by-point comparison, i.e. each interpolation point P_iSpecifying a moving window k, and calculating the actual interpolation command positions P_aThe distance from each interpolation point in the window is determined, thereby determining the actual interpolation command position P_aNearest theoretical interpolation command position P_r。

And 4, step 4: and generating an ideal processing track, and determining interpolation points required by contour error calculation. The key to calculating the contour error is to calculate the actual interpolation command position P_aThe method adopts a linear interpolation mode to generate an ideal processing track and uses a line segment P to calculate the normal distance to the ideal track in consideration of the calculation efficiency_r-1P_rAs P_r-1And P_rIdeal locus therebetween, line segment P_rP_r+1As P_rAnd P_r+1The ideal trajectory therebetween. While according to the actual interpolated commanded position P_aAnd P_r-1、P_r、P_r+1Determining the theoretical interpolation instruction position and the ideal track required by the subsequent contour error calculation according to the relative distance condition.

According to the actual interpolation command position P_aAnd P_r-1、P_r、P_r+1The relative distance of (2) can be classified into the following three cases:

case 1: at this timeCalculating Pa toAs a contour error value.

Case 2: at this timeCalculating Pa toAs a contour error value.

Case 3: at this timeAnd calculating the distance between Pa and Pr to serve as a contour error value.

And 5: according to the actual interpolation command position P_aSolving P with theoretical interpolation command position information_aDistance from the ideal machining trajectory.

Taking case 1 in step 4 as an example, the contour error calculation steps are as follows:

and setting the coordinates of each interpolation command point as follows: p_r-1(x_r-1,y_r-1,z_r-1)，P_r(x_r,y_r,z_r)，P_r+1(x_r+1,y_r+1,z_r+1) (ii) a Actual interpolation command position point coordinates: pa (x)_a,y_a,z_a) The direction vector of the theoretical interpolation command position is:

wherein: x ═ X_r-x_r-1，Y＝y_r-y_r-1，Z＝z_r-z_r-1；

Make point P_aTo a straight linePerpendicular line of (1), foot of which is P_r'(x_r',y_r',z_r') thenStraight lineDirection vector of (2):

wherein: x ═ X_a-x_r',Y＝y_a-y_r',Z＝z_a-z_r'

By vectorsSum vectorThe vertical availability is:

X·X′+Y·Y′+Z·Z＝0

and point P_rIn a straight line P_r-1P_rTo find P_i'(x_i',y_i',z_i') coordinates are as follows:

wherein Ex ═ x_a-x_r,Ey＝y_a-y_r,Ez＝z_a-z_r。

According to the definition of the profile error, the profile error vector of the tool nose position can be obtained as follows:

further, it is possible to obtain:

at this time, the die length of the nose profile error is:

step 6: and (5) repeating the steps 1-5 to obtain the contour error of each actual interpolation instruction position.

Example 3

A method for predicting part profile error in a strictly defined undercut machining, as shown in fig. 1, includes the following steps:

step 1: and identifying the transfer function of each feed shaft of the machine tool, and predicting the actual interpolation command position according to the theoretical interpolation command position.

In the machining process of the machine tool, due to the influences of machine tool structure errors, cutting processes and dynamic characteristics of a driving system, following errors exist between the actual positions and the command positions of all feeding systems, profile errors are generated during multi-axis linkage, and the positions refer to tool location point information, so that in order to predict the profile errors, ideal tool location point information and actual tool location point information of part machining commands need to be obtained firstly. Referring to fig. 2, the machining command outputs actual tool position information via a servo control system of the machine tool. Based on this, the transfer function of the machine tool servo system is identified by adopting a system identification method, and the identification steps are as follows: firstly, acquiring an excitation signal, wherein the M sequence has better autocorrelation and pseudo-randomness and is easy to generate and copy, so that the amplitude-variable M sequence signal is selected to fully excite the movement of each feed axis of the machine tool; secondly, converting the excitation signal into an excitation G code, inputting the excitation G code into a numerical control system of the machine tool, enabling each feed shaft of the machine tool to perform excitation motion, and collecting data of a theoretical interpolation instruction position and a grating detection position; finally, through system identification, establishing a transfer function of each feeding shaft, wherein the discrete expression form is as follows:

wherein: b (z)^-1) Detecting a position for the grating; a (z)^-1) Is an interpolation command position; b_iAnd a_jCoefficients of the numerator and denominator, n, respectively, of the discrete transfer function_aAnd n_bRespectively the order of the numerator and denominator of the discrete transfer function. According to the characteristics of a machine tool servo system, the transfer function is simplified into a second-order model, and the transfer function of each feeding shaft can be obtained by utilizing a Matlab system to identify a tool box. The machine tool used for the identification experiment is a five-axis numerical control machining center DMU50, and the model of the knife handle is BT 50; the cutter is an integral hard alloy cutter with the diameter of 20mm, 4 teeth, the helical angle of 30 degrees and the cutter suspension length of 78 mm. The transfer functions of the x-axis and the y-axis are obtained by identification as follows:

the actual interpolation command position is then acquired. Firstly, a theoretical interpolation instruction position of part machining is obtained, and the theoretical interpolation instruction position is input into a machine tool transfer function, so that an actual interpolation instruction position can be obtained.

Step 2: a strict definition of the profile error is given according to the machined part characteristics. Contour error is generally defined as the deviation of the actual interpolated command position from the ideal machining trajectory,there are two common definitions, namely, the normal distance from the actual interpolation command position to the ideal trajectory (definition 1) and the shortest distance from the actual interpolation command position to the ideal trajectory (definition 2). Referring to FIG. 3, (P)_i,O_i) Representing the tool pose, P, of any point on the command trajectory_iIndicating the position of the reference nose point, O_iShowing the direction of the cutter shaft; (P)_a，O_a) Representing the sum of P on the actual track_iCorresponding interpolation point poses; p_c、P_c1Are respectively P_aA drop on an ideal trajectory; p_rFor a given interpolation period, the distance P_aThe nearest interpolation point; mu.s_pDescribing the position deviation of the actual blade tip position from the reference trajectory of the blade tip position, and_othe angular deviation from the actual arbor direction to the arbor direction reference trajectory is described.

At the moment, the curvature of the processing track is larger, if the processing track is calculated according to definition 1, two normal distances | P exist_aP_cI and P_aP_c1| |, the value of the contour error cannot be judged; if calculated according to definition 2, the profile error at this time is | | | P_a P_c1If | then the interpolation point P_iAnd P_c1The traces in between are cut away, resulting in failure of the workpiece. Neither of the above definitions can accurately calculate the contour error. Based on this, a strict definition of the profile error is given herein: the contour error is the normal distance from the actual interpolation command position to the ideal processing track, and the time span is minimum. Under strict definition, P_aThe contour error of the point is P_aP_cIn this case, the problem of the above-mentioned definition being not strict is avoided.

And step 3: solving the actual interpolation command position P_aNearest theoretical interpolation command position P_r. Strict definition of profile error according to step 2, P_aThe contour error of a point is the normal distance from the point to the nearest interpolation point track, so that the distance from the actual interpolation command position P needs to be acquired first_aNearest theoretical interpolation command position P_r。

Referring to FIG. 4, a local point-by-point comparison method is adopted, i.e. each interpolation point P is obtained_iAssigning a moving window k, minCalculating the actual interpolation command position P_aThe distance between the theoretical interpolation command position P and each interpolation point in the window is determined so as to determine the theoretical interpolation command position P closest to the actual interpolation command position_r。

And 4, step 4: and generating an ideal processing track, and determining interpolation points required by contour error calculation. The key to calculating the contour error is to calculate the actual interpolation command position P_aThe ideal machining trajectory is generated by linear interpolation in consideration of calculation efficiency, and the normal distance to the ideal trajectory is calculated by using a line segment P, see fig. 6_r-1P_rAs P_r-1And P_rIdeal locus therebetween, line segment P_rP_r+1As P_rAnd P_r+1The ideal trajectory therebetween.

While according to the actual interpolated commanded position P_aAnd P_r-1、P_r、P_r+1The ideal trajectory required for subsequent profile error calculations is determined.

Referring to FIG. 5, the actual interpolation command position P is determined_aAnd P_r-1、P_r、P_r+1The relative distance of (2) can be classified into the following three cases:

case 1: at this timeCalculating Pa toAs a contour error value.

Case 2: at this timeCalculating Pa toAs a contour error value.

Case 3: at this timeCalculating the distance from Pa to Pr as a contour errorThe difference value.

And 5: according to the actual command position P_aSolving for P based on the position information of the interpolation command_aDistance from the ideal machining trajectory.

Taking case 1 in step 4 as an example, the contour error calculation steps are as follows:

and setting the coordinates of each interpolation command point as follows: p_r-1(x_r-1，y_r-1，z_r-1)，P_r(x_r，y_r，z_r)，P_r+1(x_r+1，y_r+1，z_r+1) (ii) a Actual command position point coordinates: p_a(x_a，y_a，z_a) The direction vector of the interpolation instruction point is:

wherein: x ═ X_r-x_r-1，Y＝y_r-y_r-1，Z＝z_r-z_r-1；

Make point P_aTo a straight linePerpendicular line of (1), foot of which is P_r'(x_r'，y_r'，z_r') then a straight lineDirection vector of (2):

wherein: x ═ X_a-x_r'，Y＝y_a-y_r'，Z＝z_a-z_r'

By vectorsSum vectorThe vertical availability is:

X·X′+Y·Y′+Z·Z＝0

and point P_rIn a straight line P_r-1P_rTo find P_i'(x_i'，y_i'，z_i') coordinates are as follows:

wherein Ex ═ x_a-x_r，Ey＝y_a-y_r，Ez＝z_a-z_r。

According to the definition of the profile error, the profile error vector of the tool nose position can be obtained as follows:

further, it is possible to obtain:

at this time, the die length of the nose profile error is:

step 6: and (5) repeating the steps 1-5 to obtain the contour error of each actual interpolation instruction position.

Example 4

A part profile error prediction system for a well-defined undercut process, comprising:

the transfer function module is used for obtaining a machine tool transfer function and obtaining an actual interpolation instruction position of part machining based on the machine tool transfer function and a theoretical interpolation instruction position of machining;

the ideal processing track module is interacted with the transfer function module and used for obtaining a theoretical interpolation instruction position closest to the actual interpolation instruction position based on the strictly defined contour error and further calculating to obtain an ideal processing track of the part;

and the contour error calculation module is interacted with the ideal processing track module and used for calculating the normal distance from the actual interpolation command position to the ideal processing track.

In summary, in the method for predicting the profile error of the part of the present invention, the transfer function of each feed axis of the machine tool is identified, and the theoretical interpolation command position of the part processing is input to the transfer function to obtain the actual interpolation command position; then, strictly defining the contour error, and solving a theoretical interpolation instruction position closest to the actual interpolation instruction position by using a central window method; and fitting according to the theoretical interpolation command position to obtain an ideal processing track, and calculating the deviation of the actual interpolation command position from the ideal processing track to obtain the profile error of each actual interpolation command position. The method simultaneously considers the calculation accuracy and the prediction efficiency of the profile error, can realize the accurate and rapid prediction of the profile error of the part, and can provide theoretical basis for optimizing processing parameters and ensuring the profile precision of the part.

The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.