CN107748539B - Five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition - Google Patents
Five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition Download PDFInfo
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Abstract
本发明公开了一种基于RTCP检测误差特征识别的五轴机床多轴联动误差溯源方法,利用五轴机床RTCP功能测量五轴机床联动时的误差展现形式——刀具刀尖点误差,构建误差图库,再将误差图输入误差与机床联动误差类别映射关系库中,运用特征识别技术溯源出机床联动误差类型,基于轨迹相似度分析准确量化溯源该联动误差值。本发明的优点在于不仅能够评估机床联动性能,而且当机床多轴联动性能不满足要求时,还能明确影响机床多轴联动性能的影响因素,从而给出机床的优化方案,从量值上对影响机床多轴联动性能的因素进行调节,从而达到机床高精度的要求。
The invention discloses a multi-axis linkage error tracing method for five-axis machine tools based on RTCP detection error feature recognition. The RTCP function of five-axis machine tools is used to measure the error presentation form of five-axis machine tools during linkage—tool tip point error, and an error library is constructed. , and then input the error map into the error and machine tool linkage error category mapping library, use feature recognition technology to trace the machine tool linkage error type, and accurately quantify and trace the linkage error value based on trajectory similarity analysis. The advantage of the present invention is that it can not only evaluate the linkage performance of the machine tool, but also can clarify the influencing factors that affect the multi-axis linkage performance of the machine tool when the multi-axis linkage performance of the machine tool does not meet the requirements, so as to give an optimization scheme of the machine tool, and determine the numerical value of the machine tool. The factors affecting the multi-axis linkage performance of the machine tool are adjusted to meet the high precision requirements of the machine tool.
Description
技术领域technical field
本发明属于数控机床技术领域,具体涉及一种基于RTCP误差特征识别的五轴机床多轴联动误差溯源方法。The invention belongs to the technical field of numerical control machine tools, and in particular relates to a method for tracing the source of multi-axis linkage errors of five-axis machine tools based on RTCP error feature recognition.
背景技术Background technique
五轴联动数控机床主要应用于模具、航空航天等复杂型面零件的加工制造。随着零件的精度和物理性能要求的不断提高,对数控机床多轴联动精度提出了更高的要求。数控机床的误差因素可以划分为静态因素和动态因素两大类,其中静态精度是在无切削载荷且机床不运动或运动速度很低的工况下检测的,由于高档数控机床制造装备技术的提升,静态精度只能在有限层面上反映出高档机床的加工精度,联动精度才是影响高档数控机床加工精度的主要因素之一。Five-axis CNC machine tools are mainly used in the processing and manufacturing of complex profile parts such as molds and aerospace. With the continuous improvement of the precision and physical performance requirements of parts, higher requirements are put forward for the multi-axis linkage precision of CNC machine tools. The error factors of CNC machine tools can be divided into two categories: static factors and dynamic factors. The static accuracy is detected under the conditions of no cutting load and the machine tool does not move or the moving speed is very low. Due to the improvement of high-end CNC machine tool manufacturing equipment technology , Static accuracy can only reflect the machining accuracy of high-end machine tools on a limited level, and linkage accuracy is one of the main factors affecting the machining accuracy of high-end CNC machine tools.
目前常用的数控机床联动性能测试仪器主要有球杆仪、R-Test测试仪,球杆仪只能用于两轴或三轴联动性能测试,R-Test可以检测五轴数控机床多个运动轴联动时的机床联动性能。球杆仪和R-Test生产厂商提供了五轴机床联动性能检测仪器及相应的应用软件,利用这些设备及软件可以检测五轴机床多轴联动时机床联动误差,但是所有生产厂商都并未提供引起多轴联动误差的误差因素溯源方法。在国际标准ISO10791-6公布的五轴机床测试标准中,也仅仅提供了五轴机床多轴联动性能检测方法,并没有提出机床联动误差溯源方法。所以,目前国际标准和检测仪器生产商都只能提供检测五轴联动性能的检测仪器和检测方法,仅能指出机床是否存在误差,而当检测结果达不到要求时,并不能给出一个具体的调整机床因素的方案来改善机床加工精度。At present, the commonly used CNC machine tool linkage performance testing instruments mainly include ballbar and R-Test tester. Ballbar can only be used for two-axis or three-axis linkage performance test, while R-Test can detect multiple motion axes of five-axis CNC machine tools. Machine tool linkage performance during linkage. Ballbar and R-Test manufacturers provide five-axis machine tool linkage performance testing instruments and corresponding application software. These equipment and software can be used to detect machine tool linkage errors during multi-axis linkage of five-axis machine tools, but all manufacturers do not provide them. The method of tracing the error factors causing the multi-axis linkage error. In the five-axis machine tool test standard published by the international standard ISO10791-6, only the detection method of the multi-axis linkage performance of five-axis machine tools is provided, and there is no method for the traceability of machine tool linkage errors. Therefore, at present, international standards and testing equipment manufacturers can only provide testing equipment and testing methods for testing the five-axis linkage performance, and can only point out whether there is an error in the machine tool, and when the testing results fail to meet the requirements, they cannot give a specific The scheme of adjusting the machine factor to improve the machining accuracy of the machine tool.
发明内容SUMMARY OF THE INVENTION
本发明的目的是解决上述问题,提出一种步骤简单、可有效溯源的基于RTCP误差特征识别的五轴机床多轴联动误差溯源方法The purpose of the present invention is to solve the above problems, and propose a method for tracing the source of errors of five-axis machine tool multi-axis linkage based on RTCP error feature recognition with simple steps and effective traceability.
为解决上述技术问题,本发明的技术方案是:基于RTCP误差特征识别的五轴机床多轴联动误差溯源方法,包括以下步骤:In order to solve the above-mentioned technical problems, the technical scheme of the present invention is: a five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature identification, comprising the following steps:
S1、依据五轴机床结构类型,通过运动轴误差对五轴机床联动误差的影响程度,分析确定该五轴机床联动误差类别,并检测五轴机床在各联动误差类别情况下的多轴联动误差;S1. According to the structure type of the five-axis machine tool, through the influence of the motion axis error on the linkage error of the five-axis machine tool, analyze and determine the linkage error category of the five-axis machine tool, and detect the multi-axis linkage error of the five-axis machine tool under each linkage error category. ;
S2、建立多轴联动误差与五轴机床联动误差类别间的映射关系数据库,通过刀具刀尖点在X、Y、Z三个方向上的位移误差来体现五轴机床联动误差,并通过三维空间误差图来展现,其中X代表刀具刀尖点在空间刀具坐标系中水平方向轴,Y代表刀具刀尖点在空间刀具坐标系中垂直方向轴,Z代表刀具刀尖点在空间刀具坐标系中竖直方向轴;S2. Establish a mapping relationship database between the multi-axis linkage error and the five-axis machine tool linkage error category. The five-axis machine tool linkage error is reflected by the displacement error of the tool tip point in the three directions of X, Y, and Z, and through the three-dimensional space The error map is displayed, where X represents the horizontal axis of the tool nose point in the space tool coordinate system, Y represents the vertical axis of the tool nose point in the space tool coordinate system, and Z represents the tool nose point in the space tool coordinate system. vertical axis;
S3、依据步骤S2所检测到的刀具刀尖点在X、Y、Z三个方向上误差值的大小,评估五轴机床联动性能;S3. Evaluate the linkage performance of the five-axis machine tool according to the magnitude of the error value of the tool nose point detected in step S2 in the three directions of X, Y, and Z;
S4、若机床联动性能评估结果较差,则利用RTCP检测误差特征识别方法溯源得到影响五轴机床联动性能的误差类别;S4. If the evaluation result of the linkage performance of the machine tool is poor, use the RTCP detection error feature identification method to trace the source to obtain the error category that affects the linkage performance of the five-axis machine tool;
S5、基于轨迹相似性,分析量化溯源步骤S4中得到的机床联动误差影响因数,将检测到的实际误差与误差库中的误差进行相似度的比较,相似度高则认为误差库中的误差代表真实的误差值,即为当前被检测机床的多轴联动误差。S5. Based on the similarity of the trajectory, analyze the influence factor of the machine tool linkage error obtained in the step S4 of quantification and traceability, and compare the similarity between the detected actual error and the error in the error database. If the similarity is high, the error in the error database is considered as representative The real error value is the multi-axis linkage error of the currently detected machine tool.
优选地,所述步骤S4中机床联动性能评估是通过图像特征识别的方法,来进行机床联动性能的评估。Preferably, the evaluation of the linkage performance of the machine tool in the step S4 is performed by means of image feature recognition to evaluate the linkage performance of the machine tool.
优选地,所述步骤S4还包括以下步骤:Preferably, the step S4 further includes the following steps:
S41、刀具刀尖点误差结果图进行归一化处理,形成新的刀具刀尖点误差轨迹图,归一化公式为:S41. The tool nose point error result graph is normalized to form a new tool nose point error trajectory graph. The normalization formula is:
其中,Δ为RTCP检测误差值的集合,Δ(i)为第i个RTCP检测误差,Δ(i)归一化为归一化处理后第i个RTCP检测误差,max(Δ)为误差值集合中的最大值,min(Δ)为误差值集合中的最小值;Among them, Δ is the set of RTCP detection error values, Δ(i) is the ith RTCP detection error, Δ(i) is normalized to the ith RTCP detection error after normalization, and max(Δ) is the error value The maximum value in the set, min(Δ) is the minimum value in the error value set;
S42、将步骤S41归一化后的刀具刀尖点误差轨迹视为一张刀具刀尖点误差轨迹图,将每个刀具刀尖点误差值视为刀具刀尖点误差轨迹图中的一个像素点,提取图像中的轨迹的边界,并用横纵坐标表示;在XOY平面内,这些刀具刀尖点误差轨迹图的边界点坐标点可用点集(x(k),y(k))表示,k为刀具刀尖点误差轨迹图的边界点个数;若将这些坐标点集放置于复数UV坐标系内,uv为复数坐标系的字母代表,横坐标x(k)对应的复数坐标系中的实轴坐标轴,纵坐标y(k)则对应复数坐标系中的虚轴坐标轴,那么XOY平面的坐标点则可用复数表达式(2)来位移表示:S42. The tool nose point error trajectory normalized in step S41 is regarded as a tool nose point error trajectory map, and each tool nose point error value is regarded as a pixel in the tool nose point error track map point, the boundary of the trajectory in the image is extracted, and it is represented by the horizontal and vertical coordinates; in the XOY plane, the boundary point coordinate points of the tool nose point error trajectory map can be represented by the point set (x(k), y(k)), k is the number of boundary points of the tool nose point error trajectory map; if these coordinate point sets are placed in the complex UV coordinate system, uv is the letter representation of the complex coordinate system, and the abscissa x(k) corresponds to the complex coordinate system. The real axis coordinate axis of , and the ordinate y(k) corresponds to the imaginary axis coordinate axis in the complex coordinate system, then the coordinate point of the XOY plane can be represented by the displacement of the complex number expression (2):
s(k)=x(k)+jy(k) (2)s(k)=x(k)+jy(k) (2)
公式(2)中,s(k)代表刀具刀尖点误差轨迹在XOY平面内坐标点的复数表达式,j为常数,x(k)代表刀具刀尖点误差轨迹在XOY平面内对于X轴的坐标值,y(k)代表刀具刀尖点误差轨迹在XOY平面内对于Y轴的坐标值;假设边界的点集(x(k),y(k))共包含N 个点,并设边界的起点为(x(0),y(0)),终点为(x(N-1),y(N-1)),从起点到终点按逆时针方向依次排列,那么采用式(2)所示的复数表达式即为一个周期函数,依据傅里叶变换理论,对s(k)进行离散傅里叶变化如式所示:In formula (2), s(k) represents the complex expression of the coordinate point of the tool nose point error trajectory in the XOY plane, j is a constant, x(k) represents the tool nose point error trajectory in the XOY plane for the X axis The coordinate value of , y(k) represents the coordinate value of the tool nose point error trajectory for the Y axis in the XOY plane; it is assumed that the point set (x(k), y(k)) of the boundary contains N points in total, and set The starting point of the boundary is (x(0), y(0)), and the end point is (x(N-1), y(N-1)), and they are arranged in the counterclockwise direction from the starting point to the end point, then formula (2) The complex expression shown by ) is a periodic function. According to the Fourier transform theory, the discrete Fourier transform of s(k) is shown in the formula:
其中S(u)为傅里叶级数系数,即为傅里叶描述子,e为常数,周期函数傅里叶级数展开后具有唯一的傅里叶描述子,所以将傅里叶描述子作为该刀具刀尖点误差轨迹的特征;where S(u) is the Fourier series coefficient, which is the Fourier descriptor, e is a constant, and the periodic function Fourier series expansion has a unique Fourier descriptor, so the Fourier descriptor As the feature of the tool nose point error trajectory;
S43、溯源五轴机床联动误差类别,提取获得的刀具刀尖点的误差轨迹图里的傅里叶描述子,然后与步骤S42中构建的误差轨迹图库中的傅里叶描述子进行对比,获取差异最小的误差轨迹图;误差轨迹图的傅里叶描述子与误差图库之间的差异可通过累加误差来评价,其公式为:S43, trace the linkage error category of the five-axis machine tool, extract the Fourier descriptor in the obtained error trajectory map of the tool nose point, and then compare it with the Fourier descriptor in the error trajectory library constructed in step S42, and obtain The error trajectory graph with the smallest difference; the difference between the Fourier descriptor of the error trajectory graph and the error gallery can be evaluated by accumulating the error, and the formula is:
公式(4)中,字母E代表误差的累加,Zi代表第i个傅里叶描述子,Zi_图库代表图库中误差轨迹的第i个傅里叶描述子,n为误差轨迹傅里叶描述子个数。In formula (4), the letter E represents the accumulation of errors, Z i represents the i-th Fourier descriptor, Z i_ gallery represents the i-th Fourier descriptor of the error trajectory in the gallery, and n is the error trajectory Fourier The number of leaf descriptors.
优选地,所述步骤S41中归一化是指刀具刀尖点误差轨迹由X、Y和Z三个方向的误差组合而成,以三个方向误差上的最大值归一化为1,最小值归一化为-1,其余误差值按照本身的值除以最大值进行归一化处理。Preferably, the normalization in the step S41 means that the tool nose point error trajectory is formed by combining the errors in the three directions of X, Y and Z, and the maximum value of the errors in the three directions is normalized to 1, and the minimum value is The value is normalized to -1, and the remaining error values are normalized by dividing their own value by the maximum value.
优选地,所述步骤S5中相似度是指通过检测机床测得到的刀具刀尖点误差数列与误差库中的误差数列的相似度。Preferably, the degree of similarity in the step S5 refers to the degree of similarity between the error sequence of the tool nose point obtained by detecting the machine tool and the error sequence in the error library.
优选地,所述相似度是假设检测得到刀具刀尖点误差轨迹数据为T=(t1,…,tN),步骤S3 所得到的误差类型的误差轨迹数据为Rp=(rp1,…,rpM),检测轨迹数据以i=1…N编号,标准轨迹数据以j=1…M编号两个误差数据上任意点之间的动态时间扭曲距离可定义为:Preferably, the similarity is assuming that the tool nose point error trajectory data obtained by detection is T=(t 1 , . . . , t N ), and the error trajectory data of the error type obtained in step S3 is R p =(r p1 , ..., rpM ), the detected trajectory data is numbered with i=1...N, and the standard trajectory data is numbered with j=1...M The dynamic time warp distance between any points on the two error data can be defined as:
公式(5)中min{D(i-1,j-1),D(i,j-1),D(i-1,j)}表示所示三个动态时间扭曲距离中的最小值,对于检测轨迹数据T和标准轨迹数据R,构建一个n×m的矩阵,矩阵中第(i,j)个元素为两段数据点Ti和Rj之间的距离dij;这里采用欧式距离来计算两点之间的距离:In formula (5), min{D(i-1, j-1), D(i, j-1), D(i-1, j)} represents the minimum value among the three dynamic time warp distances shown, For the detection trajectory data T and the standard trajectory data R, an n×m matrix is constructed, and the (i, j)th element in the matrix is the distance d ij between the two data points T i and R j ; the Euclidean distance is used here. to calculate the distance between two points:
两个元素之间的动态扭曲距离为累积距离即D(i,j),是从元素(T1,R1)到(Ti,Ri)之间的最小累积距离,最小累积距离的计算过程如下:在动态扭曲算法中,为了找到两个序列之间的最短距离,需要设置一个扭曲路径W=w1,w2,…,wK;扭曲路径就是一个距离矩阵上某些元素构成的连续集,这个路径定义了时间序列和之间的一个映射,沿着这条路径进行比较,可以得到这两个序列之间的最短距离;在计算两个误差数据之间的距离时,满足上述条件的路径有很多,但是这里的扭曲路径要求满足一个最小的扭曲代价:The dynamic twist distance between two elements is the cumulative distance, namely D(i, j), which is the minimum cumulative distance from the elements (T 1 , R 1 ) to (T i , R i ), and the calculation of the minimum cumulative distance The process is as follows: In the dynamic warping algorithm, in order to find the shortest distance between two sequences, a warped path W=w 1 , w 2 , ..., w K needs to be set; the warped path is composed of some elements on a distance matrix Continuity set, this path defines a mapping between the time series and the time series, and the shortest distance between the two sequences can be obtained by comparing along this path; when calculating the distance between the two error data, the above There are many paths for the condition, but the twisted path here requires a minimum twist cost:
公式(7)中,本实施例中溯源得到各个运动轴的位置环增益参数为: (KppX,KppY,KppZ,KppA,KppB)=(1,0.95,1,1,0.96),KPP为位置环增益参数,DTW(T,R)为DTW 的值,公式(7)中等号右边表示扭曲路径中的最小值。In formula (7), the position loop gain parameters of each motion axis obtained by tracing the source in this embodiment are: (Kpp X , Kpp Y , Kpp Z , Kpp A , Kpp B )=(1, 0.95, 1, 1, 0.96) , KPP is the position loop gain parameter, DTW(T, R) is the value of DTW, and the right side of the equal sign in formula (7) represents the minimum value in the twisted path.
本发明的有益效果是:本发明所提供的基于特征识别的五轴机床多轴联动误差溯源方法不仅能够对机床联动性能进行评估,而且当机床多轴联动性能达不到要求时,还能明确影响机床多轴联动性能的影响因素,从而给出机床的优化方案,从量值上对影响机床多轴联动性能的因素进行调节,从而达到机床高精度的要求。The beneficial effects of the present invention are as follows: the method for tracing the source of errors of five-axis machine tool multi-axis linkage based on feature identification provided by the present invention can not only evaluate the linkage performance of the machine tool, but also can clarify when the multi-axis linkage performance of the machine tool fails to meet the requirements. The factors affecting the multi-axis linkage performance of the machine tool are given, and the optimization scheme of the machine tool is given, and the factors affecting the multi-axis linkage performance of the machine tool are adjusted from the quantitative value, so as to meet the high-precision requirements of the machine tool.
附图说明Description of drawings
图1是本发明基于特征识别的五轴机床多轴联动误差溯源方法的方案流程图;Fig. 1 is the scheme flow chart of the five-axis machine tool multi-axis linkage error tracing method based on feature identification of the present invention;
图2是本发明步骤S4的子步骤图;Fig. 2 is the sub-step diagram of step S4 of the present invention;
图3是本发明的测试示意图;Fig. 3 is the test schematic diagram of the present invention;
图4是本发明的RTCP检测结果图;Fig. 4 is the RTCP detection result figure of the present invention;
图5是本发明联动误差为图4情况下误差80%时RTCP检测结果图;Fig. 5 is the RTCP detection result diagram when the linkage error of the present invention is 80% error under the situation of Fig. 4;
图6是本发明检测结果归一化图;Fig. 6 is the normalization diagram of detection result of the present invention;
图7是本发明检测结果边界提取示意图。FIG. 7 is a schematic diagram of boundary extraction of detection results according to the present invention.
具体实施方式Detailed ways
下面结合附图和具体实施例对本发明做进一步的说明:The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments:
如图1所示,本发明提供的基于RTCP检测特征识别的五轴机床多轴联动误差溯源方法包括以下步骤:As shown in Figure 1, the method for tracing the source of errors of five-axis machine tool multi-axis linkage based on RTCP detection feature identification provided by the present invention comprises the following steps:
S1、依据五轴机床结构类型,分析确定该机床联动误差类别,利用机床RTCP技术检测五轴机床在各联动误差类别情况下的多轴联动误差;S1. According to the structure type of the five-axis machine tool, analyze and determine the linkage error category of the machine tool, and use the machine tool RTCP technology to detect the multi-axis linkage error of the five-axis machine tool under each linkage error category;
在本实施例中某待检测联动性能的五轴联动机床为某国产五轴数控铣床,按照运动轴误差对机床联动误差的影响程度分成多轴联动误差类别,本实施例以各运动轴位置环增益参数的组合为代表来表示机床多轴联动误差。通过利用五轴机床RTCP功能测量五轴机床联动时的误差展现形式——刀具刀尖点误差,RTCP为现有技术,在这里只是做特殊的说明,在不同机床的机床中采用相应的功能模块。利用RTCP功能检测五轴机床联动误差,如图3所示。基于RTCP 的五轴机床联动性能的详细测试方法及测试过程请参见国际标准ISO10791-6。In this embodiment, a five-axis linkage machine tool whose linkage performance is to be tested is a domestic five-axis CNC milling machine, which is divided into multi-axis linkage error categories according to the influence of the motion axis error on the machine tool linkage error. The combination of gain parameters is representative to represent the multi-axis linkage error of the machine tool. By using the RTCP function of the five-axis machine tool to measure the error presentation form of the five-axis machine tool linkage - the tool nose point error, RTCP is the existing technology, only a special description is made here, and the corresponding function modules are used in the machine tools of different machine tools. . Use the RTCP function to detect the linkage error of the five-axis machine tool, as shown in Figure 3. Please refer to the international standard ISO10791-6 for the detailed test method and test process of the linkage performance of the five-axis machine tool based on RTCP.
S2、建立RTCP检测误差与五轴机床联动误差类别间的映射关系数据库;S2. Establish a mapping relationship database between RTCP detection errors and five-axis machine tool linkage error categories;
步骤S1中的基于RTCP的五轴机床多轴联动误差将通过刀具刀尖点在X、Y、Z三个方向上的位移来体现,进而可将三个方向的偏差以三维空间误差图形形式来展示机床多轴联动误差,如图3所示。将刀具刀尖点误差图与五轴机床联动误差类别构建相互映射关系,并构建误差图库。The multi-axis linkage error of the five-axis machine tool based on RTCP in step S1 will be reflected by the displacement of the tool nose point in the three directions of X, Y, and Z, and then the deviation in the three directions can be expressed in the form of a three-dimensional spatial error graph. The multi-axis linkage error of the machine tool is displayed, as shown in Figure 3. The tool nose point error map and the five-axis machine tool linkage error category are mapped to each other, and the error library is constructed.
S3、依据RTCP检测误差,评估五轴机床联动性能;S3. According to the RTCP detection error, evaluate the linkage performance of the five-axis machine tool;
依据在X、Y、Z三个方向上的RTCP检测误差值的大小来评估机床的联动性能。The linkage performance of the machine tool is evaluated according to the magnitude of the RTCP detection error in the three directions of X, Y and Z.
S4、若机床联动性能评估结果较差,利用RTCP检测误差特征识别方法溯源得到影响五轴机床联动性能的误差类别;按照步骤S1的五轴数控机床多轴联动误差测试方法测量得到机床的联动误差,进而可以得到刀具刀尖点误差图,将误差图输入检测误差与机床联动误差类别映射关系库中,运用特征识别技术溯源出机床联动误差类型。本实施例中,采用基于图像的特征识别技术来溯源机床联动误差类型。五轴机床联动误差测量值如图4所示,如图2所示,步骤S4的具体实现包括如下步骤:S4. If the evaluation result of the linkage performance of the machine tool is poor, use the RTCP detection error feature identification method to trace the source to obtain the error category that affects the linkage performance of the five-axis machine tool; measure the linkage error of the machine tool according to the multi-axis linkage error test method of the five-axis CNC machine tool in step S1 , and then the tool nose point error map can be obtained, and the error map can be input into the mapping relationship library between the detection error and the machine tool linkage error category, and the feature recognition technology can be used to trace the machine tool linkage error type. In this embodiment, the image-based feature recognition technology is used to trace the type of linkage error of the machine tool. The measured value of the linkage error of the five-axis machine tool is shown in Figure 4. As shown in Figure 2, the specific implementation of step S4 includes the following steps:
S41、RTCP检测误差结果图预处理;S41, RTCP detection error result map preprocessing;
同一误差类型不同误差值仅会使得误差轨迹的大小产生差别,而不会改变误差轨迹形状。若机床联动误差为图4情况的80%,刀具刀尖点误差图如图5所示,刀具刀尖点误差轨迹在各平面内的形状与图4基本一致,仅仅在形状大小上均存在一定程度的缩小。因此,需对误差轨迹进行归一化处理,形成新的刀具刀尖点误差轨迹图。Different error values of the same error type will only make the size of the error trajectory different, but will not change the shape of the error trajectory. If the linkage error of the machine tool is 80% of the situation in Fig. 4, the tool nose point error diagram is shown in Fig. 5. The shape of the tool nose point error trajectory in each plane is basically the same as that in Fig. 4, except that there is a certain degree of shape and size. degree of reduction. Therefore, the error trajectory needs to be normalized to form a new tool nose point error trajectory.
刀具刀尖点误差轨迹为X、Y和Z三个方向的误差组合而成,以三个方向误差上的最大值归一化为1,最小值归一化为-1,其余误差值按照本身的值除以最大值进行归一化处理,归一化公式为:The tool nose point error trajectory is a combination of errors in the three directions of X, Y and Z. The maximum value of the errors in the three directions is normalized to 1, the minimum value is normalized to -1, and the rest of the error values are based on their own The value of is divided by the maximum value for normalization, and the normalization formula is:
其中Δ为RTCP检测误差值的集合,Δ(i)为第i个RTCP检测误差,Δ(i)归一化为归一化处理后第i个RTCP检测误差。Among them, Δ is the set of RTCP detection error values, Δ(i) is the ith RTCP detection error, and Δ(i) is normalized to the ith RTCP detection error after normalization.
如图4中XOY平面的误差轨迹图通过归一化后的图形如图6所示。The normalized graph of the error trajectory of the XOY plane in Fig. 4 is shown in Fig. 6.
S42、提取检测误差结果图特征;S42, extracting the feature of the detection error result map;
将归一化后的误差轨迹视为一张图像,将每个误差值视为一个像素点,提取图像中的轨迹的边界,并用横纵坐标表示,采用复数描述法可将二维数据降为一维函数。假设轨迹的边界是由如图7所示的k个坐标围成的,在XOY平面内,这些坐标点可用点集(x(k),y(k)) 表示。若将这些坐标点集放置于复数UV坐标系内,横坐标x(k)对应的复数坐标系中的实轴坐标轴,纵坐标y(k)则对应复数坐标系中的虚轴坐标轴,那么XOY平面的坐标点则可用复数表达式(2)来表示。The normalized error trajectory is regarded as an image, and each error value is regarded as a pixel point, and the boundary of the trajectory in the image is extracted and represented by the horizontal and vertical coordinates. The complex number description method can be used to reduce the two-dimensional data to One-dimensional function. Assuming that the boundary of the trajectory is surrounded by k coordinates as shown in Figure 7, in the XOY plane, these coordinate points can be represented by a point set (x(k), y(k)). If these coordinate point sets are placed in the complex UV coordinate system, the abscissa x(k) corresponds to the real axis in the complex coordinate system, and the ordinate y(k) corresponds to the imaginary axis in the complex coordinate system. Then the coordinate point of the XOY plane can be represented by the complex expression (2).
s(k)=x(k)+jy(k) (2)s(k)=x(k)+jy(k) (2)
假设边界的点集(x(k),y(k))共包含N个点,并设边界的起点为(x(0),y(0)),终点为 (x(N-1),y(N-1)),从起点到终点按逆时针方向依次排列,那么采用公式(2)所示的复数表达式即为一个周期函数,依据傅里叶变换理论,对s(k)进行离散傅里叶变化如式所示。Suppose that the point set (x(k), y(k)) of the boundary contains N points in total, and the starting point of the boundary is (x(0), y(0)) and the end point is (x(N-1), y(N-1)), arranged counterclockwise from the starting point to the ending point, then the complex expression shown in formula (2) is a periodic function. According to the Fourier transform theory, s(k) is calculated. The discrete Fourier transform is shown in Eq.
其中S(u)为傅里叶级数系数,即为傅里叶描述子。周期函数傅里叶级数展开后具有唯一的傅里叶描述子,所以将傅里叶描述子作为该刀具刀尖点误差轨迹的特征。Among them, S(u) is the Fourier series coefficient, which is the Fourier descriptor. The Fourier series expansion of the periodic function has a unique Fourier descriptor, so the Fourier descriptor is used as the feature of the tool nose point error trajectory.
S43、基于特征识别溯源五轴机床联动误差类别;S43, based on feature identification and traceability of five-axis machine tool linkage error categories;
当五轴机床RTCP检测获取了刀具刀尖点误差在三个平面上的误差轨迹图后,提取误差轨迹图的傅里叶描述子,将三个平面的傅里叶描述子分别与步骤S42中构建的误差轨迹图库中的傅里叶描述子比对,差异最小的误差轨迹的误差类别即为该五轴机床的检测误差类别。误差轨迹图的傅里叶描述子与误差图库之间的差异可通过累加误差来评价,其公式为:When the five-axis machine tool RTCP detects and obtains the error trajectory map of the tool nose point error on the three planes, extracts the Fourier descriptor of the error trajectory map, and compares the Fourier descriptors of the three planes with those in step S42. The Fourier descriptors in the constructed error trajectory library are compared, and the error category of the error trajectory with the smallest difference is the detection error category of the five-axis machine tool. The difference between the Fourier descriptor of the error locus graph and the error gallery can be evaluated by accumulating the error, and its formula is:
式中Zi代表第i个傅里叶描述子,Zi_图库代表图库中误差轨迹的第i个傅里叶描述子,n 为误差轨迹傅里叶描述子个数。In the formula, Z i represents the ith Fourier descriptor, Z i_ Gallery represents the ith Fourier descriptor of the error trajectory in the gallery, and n is the number of Fourier descriptors of the error trajectory.
本实施例中溯源得到的误差类别为:由运动轴Y轴和B轴的误差大于其余3轴的误差而引起的五轴联动误差。The error category obtained by tracing the source in this embodiment is: the five-axis linkage error caused by the error of the Y-axis and the B-axis of the motion axis being larger than the errors of the other three axes.
S5、运动轨迹相似性分析量化溯源步骤4中得到的机床因素;S5. The machine tool factor obtained in step 4 of the quantification traceability analysis of motion trajectory similarity;
在通过特征识别溯源方法溯源得到五轴机床联动误差类型后,仍需准确分析该误差额准确值,而误差轨迹图像识别显然无法实现精确误差值溯源。刀具刀尖点在X、Y、Z三个方向的原始误差数据包含更为详细的细节信息,可为误差精确溯源提供数据支撑。相似性度量可以清晰准确的表示两组误差数据间的差异,当相似度值较小时,则说明两段数据的差异性较大,若相似度值较大时,则这两段数列的差异性较小。倘若测得刀具刀尖点误差数列与误差库中的误差数列非常相似,则可以认为误差库中的误差数列代表的五轴机床联动误差值即为当前被检机床的多轴联动误差。After the five-axis machine tool linkage error type is traced through the feature identification traceability method, the accurate value of the error amount still needs to be accurately analyzed, and the error trajectory image recognition obviously cannot realize the accurate error value traceability. The original error data of the tool nose point in the three directions of X, Y, and Z contains more detailed information, which can provide data support for the accurate traceability of errors. The similarity measure can clearly and accurately represent the difference between the two sets of error data. When the similarity value is small, it means that the difference between the two pieces of data is large. If the similarity value is large, the difference between the two series of numbers smaller. If the measured tool nose point error sequence is very similar to the error sequence in the error library, it can be considered that the five-axis machine tool linkage error value represented by the error sequence in the error library is the multi-axis linkage error of the currently inspected machine tool.
由于无法保证每一次检测误差的数据长度均一致,可采用DTW距离来表征误差数据间的相似度。Since the data length of each detected error cannot be guaranteed to be consistent, the DTW distance can be used to represent the similarity between error data.
假设检测得到刀具刀尖点误差轨迹数据为T=(t1,…,tN),标准误差库中属于步骤S3得到的误差类型的误差轨迹数据为Rp=(rp1,…,rpM),其中p代表标准误差库中第p个误差轨迹,共有k条误差轨迹。检测轨迹的数据长度为N,标准误差库中误差轨迹数据长度为M。为了下面叙述更为清晰明确,检测轨迹数据以i=1…N编号,标准轨迹数据以j=1…M编号。这两个误差数据上任意点之间的动态时间扭曲距离可定义为:Assuming that the tool nose point error trajectory data obtained by detection is T=(t 1 ,...,t N ), the error trajectory data belonging to the error type obtained in step S3 in the standard error library is R p =(r p1 ,...,r pM ), where p represents the pth error trajectory in the standard error library, and there are k error trajectories in total. The data length of the detection track is N, and the length of the error track data in the standard error library is M. In order to make the following description clearer and clearer, the detected track data is numbered with i=1...N, and the standard track data is numbered with j=1...M. The dynamic time warp distance between arbitrary points on these two error data can be defined as:
对于检测轨迹数据T和标准轨迹数据R,构建一个n×m的矩阵,矩阵中第(i,j)个元素为两段数据点Ti和Rj之间的距离dij。这里采用欧式距离来计算两点之间的距离:For the detection track data T and the standard track data R, an n×m matrix is constructed, and the (i, j)th element in the matrix is the distance d ij between the two data points T i and R j . Here the Euclidean distance is used to calculate the distance between two points:
两个元素之间的动态扭曲距离为累积距离,即D(i,j)是从元素(T1,R1)到(Ti,Rj)之间的最小累积距离。该距离的计算过程如下:在动态扭曲算法中,不再满足两个序列上的各点的一一对应关系,为了找到两个序列之间的最短距离,需要设置一个扭曲路径 W=w1,w2,…,wK。扭曲路径就是一个距离矩阵上某些元素构成的连续集,这个路径定义了时间序列和之间的一个映射,沿着这条路径进行比较,可以得到这两个序列之间的最短距离。The dynamic twist distance between two elements is the cumulative distance, ie D(i,j) is the minimum cumulative distance from the elements (T 1 , R 1 ) to (T i , R j ). The calculation process of the distance is as follows: In the dynamic warping algorithm, the one-to-one correspondence between the points on the two sequences is no longer satisfied. In order to find the shortest distance between the two sequences, a warped path W=w 1 needs to be set, w 2 , ..., w K . A twisted path is a continuum consisting of certain elements on a distance matrix. This path defines a mapping between the time series and . Comparing along this path, the shortest distance between the two sequences can be obtained.
很显然,在计算两个误差数据之间的距离时,满足上述条件的路径有很多,但是这里的扭曲路径要求满足一个最小的扭曲代价。Obviously, when calculating the distance between two error data, there are many paths that meet the above conditions, but the twisted path here requires a minimum twist cost.
公式(7)中,本实施例中溯源得到各个运动轴的位置环增益参数为:In formula (7), the position loop gain parameters of each motion axis obtained by tracing the source in this embodiment are:
(KppX,KppY,KppZ,KppA,KppB)=(1,0.95,1,1,0.96),KPP为位置环增益参数,DTW(T,R) 为DTW的值,公式(7)中等号右边表示扭曲路径中的最小值,进而可依据该误差参数指导机床联动性能的优化调整。(Kpp X , Kpp Y , Kpp Z , Kpp A , Kpp B )=(1, 0.95, 1, 1, 0.96), KPP is the position loop gain parameter, DTW(T, R) is the value of DTW, formula (7 ) The right side of the middle sign indicates the minimum value in the twisted path, and then the optimal adjustment of the linkage performance of the machine tool can be guided according to the error parameter.
本领域的普通技术人员将会意识到,这里所述的实施例是为了帮助读者理解本发明的原理,应被理解为本发明的保护范围并不局限于这样的特别陈述和实施例。本领域的普通技术人员可以根据本发明公开的这些技术启示做出各种不脱离本发明实质的其它各种具体变形和组合,这些变形和组合仍然在本发明的保护范围内。Those of ordinary skill in the art will appreciate that the embodiments described herein are intended to assist readers in understanding the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations without departing from the essence of the present invention according to the technical teaching disclosed in the present invention, and these modifications and combinations still fall within the protection scope of the present invention.
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CN116300691B (en) * | 2023-05-25 | 2023-08-04 | 深圳市正和楚基科技有限公司 | A state monitoring method and system for multi-axis linkage numerical control machining |
CN116449772B (en) * | 2023-06-16 | 2023-10-03 | 成都飞机工业(集团)有限责任公司 | Multi-axis cooperative motion control method, device, equipment and medium |
CN116728158B (en) * | 2023-08-09 | 2023-12-08 | 成都飞机工业(集团)有限责任公司 | Error detection result visualization method for five-axis machine tool R-test detection |
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