CN104613897B - The adaptively sampled device of vehicle exterior cladding element mold freedom curved surface and measuring method - Google Patents
The adaptively sampled device of vehicle exterior cladding element mold freedom curved surface and measuring method Download PDFInfo
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Abstract
汽车外覆盖件模具自由曲面自适应采样装置及测量方法。一种汽车外覆盖件模具自由曲面自适应采样装置，其组成包括：测头柄（1），所述的测头柄与激光位移传感器基座（2）连接，所述的激光位移传感器基座与激光位移传感器旋转挡板（3）连接，所述的激光位移传感器旋转挡板分别与左激光位移传感器（6）、右激光位移传感器（8）连接，所述的左激光位移传感器、所述的右激光位移传感器分别与激光位移传感器连接板（4）连接，所述的激光位移传感器连接板上安装有旋钮（5）。本发明应用于数控机床在机测量技术领域。
The self-adaptive sampling device and measurement method of the free-form surface of the mold of the automobile outer cover part. An adaptive sampling device for the free-form surface of an automobile outer cover mold, which comprises: a probe handle (1), the probe handle is connected to a laser displacement sensor base (2), and the laser displacement sensor base It is connected with the laser displacement sensor rotating baffle (3), and the laser displacement sensor rotating baffle is respectively connected with the left laser displacement sensor (6) and the right laser displacement sensor (8), and the left laser displacement sensor, the The right laser displacement sensors are respectively connected with the laser displacement sensor connecting plate (4), and the said laser displacement sensor connecting plate is equipped with a knob (5). The invention is applied to the technical field of on-machine measurement of numerical control machine tools.
Description
技术领域：Technical field:
本发明涉及一种汽车外覆盖件模具自由曲面自适应采样装置及测量方法。属于高精度模具加工技术领域。The invention relates to a self-adaptive sampling device and a measuring method for free-form surface of an automobile outer cover mold. It belongs to the technical field of high-precision mold processing.
背景技术：Background technique:
随着现代加工技术的发展，市场的竞争压力越来越大，在与现代制造技术相关紧密的航空航天、汽车等领域，例如叶轮，汽车覆盖件等自由曲面系列的零件得到了日益广泛的应用，因此零件的加工质量得到了广泛的关注，必须通过对自由曲面进行数字化测量检测其加工精度，曲面数字化测量主要包括接触式测量和非接触式测量两大类，接触式测量利用多种测头实现各种内外表面的测量，采样点的点数与合理分布就成为了一个重要的研究问题，其中等间距等测量方法原理简单且易于实现，在实际测量中应用广泛但也存在很明显的不足；另外如等弧长均匀网格划分技术，一方面通过人机交互实现非均匀网格的划分，另一方面要求已知曲面的边界曲线，也不能实现真正的等弧长。传统的采样方法由于涉及曲面曲率的计算，因此仅局限于对已知数学模型(具体函数表达式)的自由曲面进行采样点规划，但不能解决已知CAD模型的自由曲面采样问题，难以实现CAD 系统与在机检测系统(OMV)的有效对接。针对模具未知自由曲面，通过由3个激光位移传感器组合的无接触测量装置，自适应设置采样点。即基于曲面法向量的变化，在曲面弯曲程度较大区域，采样点密集，反之，曲面的弯曲程度小区域，采样点也比较稀疏；如果被测未知曲面在采样规划方向侧面变化大，可根据需要自适应布置一些偏置点等。本研究采用激光无接触式测量方法对轿车外覆盖件模具的自由曲面进行自适应采样规划。With the development of modern processing technology, the pressure of market competition is increasing. In the fields of aerospace and automobiles closely related to modern manufacturing technology, such as impellers, automotive panels and other free-form surface parts have been increasingly widely used. , so the processing quality of parts has been widely concerned, and the processing accuracy must be detected by digital measurement of free-form surfaces. Digital measurement of curved surfaces mainly includes two categories: contact measurement and non-contact measurement. Contact measurement uses a variety of probes To realize the measurement of various internal and external surfaces, the number and reasonable distribution of sampling points has become an important research problem. Among them, the measurement methods such as equidistant distance are simple in principle and easy to implement. They are widely used in actual measurement, but there are obvious deficiencies; In addition, such as the equal arc length uniform grid division technology, on the one hand, the division of non-uniform grids can be realized through human-computer interaction, and on the other hand, the boundary curve of the surface is required to be known, and the true equal arc length cannot be realized. Because the traditional sampling method involves the calculation of the curvature of the surface, it is limited to the sampling point planning of the free-form surface of the known mathematical model (specific function expression), but it cannot solve the sampling problem of the free-form surface of the known CAD model, and it is difficult to realize CAD Effective connection between the system and the on-machine inspection system (OMV). For the unknown free-form surface of the mold, the sampling point is adaptively set through a non-contact measuring device composed of three laser displacement sensors. That is, based on the change of the normal vector of the surface, the sampling points are dense in the area with a large curvature of the surface, and on the contrary, the sampling points are relatively sparse in the area with a small curvature of the surface; if the measured unknown surface changes greatly in the direction of the sampling plan, according to Some bias points need to be arranged adaptively. In this study, the laser non-contact measurement method is used to carry out adaptive sampling planning for the free-form surface of the car outer panel mold.
发明内容：Invention content:
本发明的目的是提供一种车外覆盖件模具自由曲面自适应采样装置及测量方法。The object of the present invention is to provide a self-adaptive sampling device and measurement method for the free-form surface of a mold of a vehicle exterior panel.
上述的目的通过以下的技术方案实现：Above-mentioned purpose realizes by following technical scheme:
一种汽车外覆盖件模具自由曲面自适应采样装置，其组成包括：测头柄，所述的测头柄与激光位移传感器基座连接，所述的激光位移传感器基座与激光位移传感器旋转挡板连接，所述的激光位移传感器旋转挡板分别与左激光位移传感器、右激光位移传感器连接，所述的左激光位移传感器、所述的右激光位移传感器分别与激光位移传感器连接板连接，所述的激光位移传感器连接板上安装有旋钮。A self-adaptive sampling device for free-form surfaces of automobile outer cover molds, comprising: a probe handle, the probe handle is connected to a base of a laser displacement sensor, and the base of the laser displacement sensor is connected to a rotation stop of the laser displacement sensor plate connection, the laser displacement sensor rotating baffle is connected with the left laser displacement sensor, the right laser displacement sensor respectively, the left laser displacement sensor, the right laser displacement sensor are respectively connected with the laser displacement sensor connecting plate, the A knob is installed on the connecting plate of the laser displacement sensor described above.
所述的汽车外覆盖件模具自由曲面自适应采样装置，所述的激光位移传感器连接板之间安装有前激光位移传感器，所述的前激光位移传感器通过激光位移传感器连接板连接在激光位移传感器基架上。The free-form surface adaptive sampling device of the automobile outer cover part mold, the front laser displacement sensor is installed between the laser displacement sensor connecting plates, and the front laser displacement sensor is connected to the laser displacement sensor through the laser displacement sensor connecting plate on the pedestal.
所述的汽车外覆盖件模具自由曲面自适应采样装置，所述的左激光位移传感器、所述的右激光位移传感器与所述的前激光位移传感器向下发射出三束激光在模具加工表面形成一个三角形小平面测量区域，该区域大小通过旋钮进行调节激光位移传感器射出激光的角度。In the free-form surface adaptive sampling device of the automobile outer cover mold, the left laser displacement sensor, the right laser displacement sensor and the front laser displacement sensor emit three laser beams downward to form on the mold processing surface A triangular facet measuring area, the size of this area is adjusted by the knob to adjust the angle at which the laser displacement sensor emits laser light.
所述的汽车外覆盖件模具自由曲面自适应采样装置，所述的左激光位移传感器为LDL，所述的右激光位移传感器为LDR，所述的前激光位移传感器为LDF。As for the self-adaptive sampling device for the free-form surface of the automobile outer cover mold, the left laser displacement sensor is LDL, the right laser displacement sensor is LDR, and the front laser displacement sensor is LDF.
所述的汽车外覆盖件模具自由曲面自适应采样装置的测量方法，该方法包括如下步骤：The method for measuring the free-form surface adaptive sampling device of the automobile outer cover mold, the method comprises the following steps:
（1）在测量开始前，我们需要建立三个激光位移传感器的测量坐标系，名称分别为LDF、LDL、LDR，并且通过坐标转换将三个坐标系统一到基准坐标系，三个坐标系相连接构成一个边长相等的等边三角形，也可以构成其它形式三角形。(1) Before the measurement starts, we need to establish three measurement coordinate systems of laser displacement sensors, named LDF, LDL, LDR, and transform the three coordinate systems into the reference coordinate system through coordinate transformation, and the three coordinate systems are in phase The connection forms an equilateral triangle with equal side lengths, and other forms of triangles can also be formed.
（2）设机床原点为O，三个坐标轴方向与机床导轨的方向一致，建立机床坐标系Oxyz，建立传感器测量坐标系，当测量机开始工作时LDL 测量值为零的点为原点，建立LDL对应于机床的坐标系，最后在机床上放置圆球建立基准坐标系，每个坐标系对应的坐标轴都与x、y、z轴平行并且方向需要一致。对激光位移传感器进行沿Y轴旋转，所以要建立坐标系自身旋转矩阵T。(2) Set the origin of the machine tool as O, the direction of the three coordinate axes is consistent with the direction of the guide rail of the machine tool, establish the machine tool coordinate system Oxyz, and establish the sensor measurement coordinate system. When the measuring machine starts to work, the point where the LDL measurement value is zero is the origin , establish LDL corresponding to the coordinate system of the machine tool, and finally place a ball on the machine tool to establish the reference coordinate system , the coordinate axes corresponding to each coordinate system are parallel to the x, y, and z axes and the directions need to be consistent. The laser displacement sensor is rotated along the Y axis, so it is necessary to establish the rotation matrix T of the coordinate system itself.
（3）坐标转换完毕后开始沿设定轨迹测量，LDF开始寻边界，移动激光测量装置到起点，开启LDF，其他两个暂不工作。让装置沿某一方向上移动，当测头进入曲面边界R时，输出信号会发生突变，这时测量软件立即记录该突变坐标值，并保存为边界点。(3) After the coordinate conversion is completed, start measuring along the set track, LDF starts to find the boundary, move the laser measuring device to the starting point, turn on the LDF, and the other two do not work temporarily. Let the device move in a certain direction. When the probe enters the boundary R of the surface, the output signal will change suddenly. At this time, the measurement software will immediately record the coordinate value of the change and save it as a boundary point.
（4）LDF探路径，沿曲面测量方向，同时打开三个传感器，移动三点激光测量装置获取三角形小平面的法向量，当前后曲面法向量夹角数值变化时，即超过最小偏转角时，设最小偏转角为阈值，记录测量点，为总体测量时提供数据依据。这样在陡峭明显的区域曲面的前后曲面法向量之间的偏转角越大，所以相邻点之间的间距就越小，测量点就多；在陡峭不明显的区域前后曲面的法向量偏转角越小，则相邻点之间的间距也越大，测量点就小，从而实现采样点的自适应分布；(4) LDF detection path, along the surface measurement direction, open three sensors at the same time, move the three-point laser measurement device to obtain the normal vector of the triangular facet, when the value of the angle between the front and rear surface normal vectors changes, that is, when the minimum deflection angle is exceeded, Set the minimum deflection angle as the threshold, record the measurement points, and provide data basis for the overall measurement. In this way, the larger the deflection angle between the front and rear surface normal vectors of the surface in the steep and obvious area, the smaller the distance between adjacent points, and the more measurement points; The smaller the value, the larger the distance between adjacent points, and the smaller the measurement point, so as to realize the adaptive distribution of sampling points;
特别是测量轨迹的左右方向较为陡峭时，那么三点激光测量装置所计算的法向量会向曲面左右陡峭一侧偏转；此点法向量偏转侧分量与前面法向量的偏转侧分量夹角超过最小偏转角时，设最小偏转角为阈值，沿偏转方向增加采样点。Especially when the left and right direction of the measurement track is relatively steep, the normal vector calculated by the three-point laser measuring device will deflect to the left and right steep side of the surface; the angle between the deflection side component of the normal vector at this point and the deflection side component of the previous normal vector exceeds the minimum For the deflection angle, set the minimum deflection angle as the threshold, and increase the sampling points along the deflection direction.
本发明的有益效果：Beneficial effects of the present invention:
1.该装置及自适应采样方法对分析模具的自由曲面加工精度大有益处，本发明避免由于测量存在接触力，而不能对软质、易碎等物体进行接触测量，避免测量时使工件产生变形，具有很高的测量精度、良好的可靠性与稳定性，所获得的测量数据不需要进行触头半径补偿。1. The device and the self-adaptive sampling method are of great benefit to the analysis of the machining accuracy of the free-form surface of the mold. The present invention avoids contact measurement of soft and fragile objects due to the existence of contact force in the measurement, and avoids the occurrence of workpieces during measurement. Deformation, with high measurement accuracy, good reliability and stability, the obtained measurement data does not require contact radius compensation.
本发明三点激光测量装置是专门针对汽车外覆盖件模具自由曲面，尤其是对模具陡峭面的测量具有很明显的针对性，能够自适应设置采样点，重构曲面的最大拟合误差为0.02mm。The three-point laser measuring device of the present invention is specially aimed at the free-form surface of the mold of the automobile outer cover part, especially the measurement of the steep surface of the mold has obvious pertinence, and the sampling points can be set adaptively, and the maximum fitting error of the reconstructed curved surface is 0.02 mm.
本发明三点激光测量装置测量方法简单，对于长度为100mm左右的曲线，控制点一般在30～40个较为适，可以在满足模具曲面精度要求的前提下，提高工作效率，实验结果证明测量效率比接触式测量高15%，速度提升11%，采样点具有明显的自适应分布。The measurement method of the three-point laser measuring device of the present invention is simple. For a curve with a length of about 100 mm, generally 30 to 40 control points are more suitable, which can improve work efficiency on the premise of meeting the precision requirements of the mold surface. Experimental results prove that the measurement efficiency Compared with contact measurement, it is 15% higher, and the speed is increased by 11%, and the sampling points have obvious adaptive distribution.
附图说明：Description of drawings:
附图1是本发明的结构示意图。Accompanying drawing 1 is a structural representation of the present invention.
附图2是附图1的主视图。Accompanying drawing 2 is the front view of accompanying drawing 1.
附图3是附图1的左视图。Accompanying drawing 3 is the left view of accompanying drawing 1.
附图4是附图1的俯视图。Accompanying drawing 4 is the plan view of accompanying drawing 1.
附图5是本发明的结构与测量示意图。Accompanying drawing 5 is the structure and measurement schematic diagram of the present invention.
附图6是本发明的采样流程示意图。Accompanying drawing 6 is a schematic diagram of the sampling process of the present invention.
附图7是本发明坐标系建立示意图。Accompanying drawing 7 is the schematic diagram of establishing the coordinate system of the present invention.
附图8是本发明测量方向上采样实现过程A图。Accompanying drawing 8 is the diagram A of the implementation process of sampling in the measurement direction in the present invention.
附图9是本发明测量方向上采样实现过程B图。Accompanying drawing 9 is the diagram B of the implementation process of sampling in the measurement direction in the present invention.
附图10是本发明测量方向上采样实现过程C图。Accompanying drawing 10 is a diagram C of the implementation process of sampling in the measurement direction in the present invention.
附图11是本发明测量方向上采样实现过程D图。Accompanying drawing 11 is the diagram D of the implementation process of sampling in the measurement direction in the present invention.
附图12是本发明被测未知小曲面的法向量示意图。Accompanying drawing 12 is the normal vector schematic diagram of the measured unknown small curved surface of the present invention.
附图13是本发明未知小曲面的法向量组示意图。Accompanying drawing 13 is the schematic diagram of the normal vector group of the unknown small curved surface of the present invention.
附图14是本发明两个法向量之间的夹角示意图。Accompanying drawing 14 is the angle diagram between two normal vectors of the present invention.
附图15是本发明采样点的自适应分布示意图。Figure 15 is a schematic diagram of the adaptive distribution of sampling points in the present invention.
附图16是本发明未知曲面陡峭大时法向量向另一侧的摆动示意图。Accompanying drawing 16 is the schematic diagram of the swing of the normal vector to the other side when the unknown curved surface is steep and large according to the present invention.
附图17是本发明偏转法向量的分解示意图。Accompanying drawing 17 is the exploded schematic view of deflection normal vector of the present invention.
具体实施方式：detailed description:
实施例1：Example 1:
一种汽车外覆盖件模具自由曲面自适应采样装置，其组成包括：测头柄1，所述的测头柄与激光位移传感器基座2连接，所述的激光位移传感器基座与激光位移传感器旋转挡板3连接，所述的激光位移传感器旋转挡板分别与左激光位移传感器6、右激光位移传感器8连接，所述的左激光位移传感器、所述的右激光位移传感器分别与激光位移传感器连接板4连接，所述的激光位移传感器连接板上安装有旋钮5。An adaptive sampling device for the free-form surface of an automobile outer cover mold, which consists of: a probe handle 1, the probe handle is connected to a laser displacement sensor base 2, and the laser displacement sensor base is connected to the laser displacement sensor Rotating baffle 3 is connected, and described laser displacement sensor rotating baffle is connected with left laser displacement sensor 6, right laser displacement sensor 8 respectively, and described left laser displacement sensor, described right laser displacement sensor are respectively connected with laser displacement sensor The connecting plate 4 is connected, and a knob 5 is installed on the connecting plate of the laser displacement sensor.
实施例2：Example 2:
根据实施例1所述的汽车外覆盖件模具自由曲面自适应采样装置，所述的激光位移传感器连接板之间安装有前激光位移传感器7，所述的前激光位移传感器通过激光位移传感器连接板连接在激光位移传感器基架上。According to the self-adaptive sampling device for the free-form surface of the automobile outer cover mold described in Embodiment 1, a front laser displacement sensor 7 is installed between the connecting plates of the laser displacement sensor, and the front laser displacement sensor passes through the connecting plate of the laser displacement sensor. Connected to the base frame of the laser displacement sensor.
实施例3：Example 3:
根据实施例1或2所述的汽车外覆盖件模具自由曲面自适应采样装置，所述的左激光位移传感器、所述的右激光位移传感器与所述的前激光位移传感器向下发射出三束激光在模具加工表面形成一个三角形小平面测量区域，该区域大小通过旋钮进行调节激光位移传感器射出激光的角度。According to the self-adaptive sampling device for the free-form surface of the automobile outer cover mold described in embodiment 1 or 2, the left laser displacement sensor, the right laser displacement sensor and the front laser displacement sensor emit three beams downward The laser forms a triangular facet measurement area on the mold processing surface, and the size of this area is adjusted by the knob to adjust the angle at which the laser displacement sensor emits the laser light.
实施例4：Example 4:
根据实施例1或2或3所述的汽车外覆盖件模具自由曲面自适应采样装置，所述的左激光位移传感器为LDL，所述的右激光位移传感器为LDR，所述的前激光位移传感器为LDF。According to the self-adaptive sampling device for the free-form surface of the automobile outer cover mold described in embodiment 1 or 2 or 3, the left laser displacement sensor is LDL, the right laser displacement sensor is LDR, and the front laser displacement sensor is for LDF.
实施例5：Example 5:
一种实施例1-4所述的汽车外覆盖件模具自由曲面自适应采样装置的测量方法，其特征是：该方法包括如下步骤：A method for measuring the free-form surface adaptive sampling device of the automobile outer panel mold described in embodiment 1-4 is characterized in that: the method comprises the following steps:
（1）在测量开始前，我们需要建立三个激光位移传感器的测量坐标系，名称分别为LDF、LDL、LDR，并且通过坐标转换将三个坐标系统一到基准坐标系，三个坐标系相连接构成一个边长相等的等边三角形，也可以构成其它形式三角形。(1) Before the measurement starts, we need to establish three measurement coordinate systems of laser displacement sensors, named LDF, LDL, LDR, and transform the three coordinate systems into the reference coordinate system through coordinate transformation, and the three coordinate systems are in phase The connection forms an equilateral triangle with equal side lengths, and other forms of triangles can also be formed.
（2）设机床原点为O，三个坐标轴方向与机床导轨的方向一致，建立机床坐标系Oxyz，建立传感器测量坐标系，当测量机开始工作时LDL 测量值为零的点为原点，建立LDL对应于机床的坐标系，最后在机床上放置圆球建立基准坐标系，每个坐标系对应的坐标轴都与x、y、z轴平行并且方向需要一致。对激光位移传感器进行沿Y轴旋转，所以要建立坐标系自身旋转矩阵T。(2) Set the origin of the machine tool as O, the direction of the three coordinate axes is consistent with the direction of the guide rail of the machine tool, establish the machine tool coordinate system Oxyz, and establish the sensor measurement coordinate system. When the measuring machine starts to work, the point where the LDL measurement value is zero is the origin , establish LDL corresponding to the coordinate system of the machine tool, and finally place a ball on the machine tool to establish the reference coordinate system , the coordinate axes corresponding to each coordinate system are parallel to the x, y, and z axes and the directions need to be consistent. The laser displacement sensor is rotated along the Y axis, so it is necessary to establish the rotation matrix T of the coordinate system itself.
（3）坐标转换完毕后开始沿设定轨迹测量，LDF开始寻边界，移动激光测量装置到起点，开启LDF，其他两个暂不工作。让装置沿某一方向上移动，当测头进入曲面边界R时，输出信号会发生突变，这时测量软件立即记录该突变坐标值，并保存为边界点。(3) After the coordinate conversion is completed, start measuring along the set track, LDF starts to find the boundary, move the laser measuring device to the starting point, turn on the LDF, and the other two do not work temporarily. Let the device move in a certain direction. When the probe enters the boundary R of the surface, the output signal will change suddenly. At this time, the measurement software will immediately record the coordinate value of the change and save it as a boundary point.
（4）LDF探路径，沿曲面测量方向，同时打开三个传感器，移动三点激光测量装置获取三角形小平面的法向量，当前后曲面法向量夹角数值变化时，即超过最小偏转角时，设最小偏转角为阈值，记录测量点，为总体测量时提供数据依据。这样在陡峭明显的区域曲面的前后曲面法向量之间的偏转角越大，所以相邻点之间的间距就越小，测量点就多；在陡峭不明显的区域前后曲面的法向量偏转角越小，则相邻点之间的间距也越大，测量点就少，从而实现采样点的自适应分布；(4) LDF detection path, along the surface measurement direction, open three sensors at the same time, move the three-point laser measurement device to obtain the normal vector of the triangular facet, when the value of the angle between the front and rear surface normal vectors changes, that is, when the minimum deflection angle is exceeded, Set the minimum deflection angle as the threshold, record the measurement points, and provide data basis for the overall measurement. In this way, the larger the deflection angle between the front and rear surface normal vectors of the surface in the steep and obvious area, the smaller the distance between adjacent points, and the more measurement points; The smaller the , the larger the distance between adjacent points, and the fewer measurement points, so as to realize the adaptive distribution of sampling points;
特别是测量轨迹的左右方向较为陡峭时，那么三点激光测量装置所计算的法向量会向曲面左右陡峭一侧偏转；此点法向量偏转侧分量与前面法向量的偏转侧分量夹角超过最小偏转角时，设最小偏转角为阈值，沿偏转方向增加采样点。Especially when the left and right direction of the measurement track is relatively steep, the normal vector calculated by the three-point laser measuring device will deflect to the left and right steep side of the surface; the angle between the deflection side component of the normal vector at this point and the deflection side component of the previous normal vector exceeds the minimum For the deflection angle, set the minimum deflection angle as the threshold, and increase the sampling points along the deflection direction.
实施例6：Embodiment 6:
坐标系转换Coordinate system conversion
由于我们要对激光位移传感器进行沿Y轴旋转，所以要建立坐标系自身旋转矩阵T。Since we want to rotate the laser displacement sensor along the Y axis, we need to establish the rotation matrix T of the coordinate system itself.
。 .
到的坐标转换可以是，同理到的坐标转换可以是。 arrive The coordinate transformation of can be , the same reason arrive The coordinate transformation of can be .
到坐标转换关系可以表示为： arrive The coordinate transformation relationship can be expressed as:
（1） (1)
式中，W1、K1分别为旋转矩阵和平移矩阵，由于各个坐标系之间平行与方向一致关系，的值可以由机床的位置关系读出，。In the formula, W 1 and K 1 are the rotation matrix and the translation matrix respectively. Due to the parallel and direction consistency relationship between each coordinate system, The value of can be read from the positional relationship of the machine tool, .
如果激光的长度为h，则可以表示为，代入（1）式可得；If the length of the laser is h, it can be expressed as, substituting (1) can be obtained;
（2） (2)
到的转换关系可以表示为 arrive The conversion relationship can be expressed as
（3） (3)
式中，和为 旋转矩阵和平移矩阵，In the formula, with for rotation matrix and translation matrix,
。可以利用LDL对工作台上的标准圆球进行测量，求取拟合中心坐标获得，设求得的中心坐标为，。 . You can use LDL to measure the standard sphere on the workbench and obtain the fitting center coordinates. Let the obtained center coordinates be, .
把上述各值代入式可得Substituting the above values into the formula, we get
（4） (4)
通过上述式子就可以将测量值转化为基准坐标系下，同理LDF，LDR也一样。Through the above formula, the measured value can be converted into the reference coordinate system, and the same is true for LDF and LDR.
实施例7：Embodiment 7:
自适应规划测量点Adaptive planning of measurement points
同时打开三个传感器，激光测量装置开始测量，根据LDF的采样数据，合理分配采样点。Turn on the three sensors at the same time, the laser measuring device starts to measure, and according to the sampling data of LDF, the sampling points are allocated reasonably.
设三角形A，B，C为三角型的顶点分分别为： Let the triangles A, B, and C be triangular vertices respectively:
，他们构成一个平面小区域，在平面足够小的情况下，与被测未知小曲面可以被看成近似处于同一平面上。 , they constitute a small plane area, and when the plane is small enough, it can be regarded as approximately on the same plane as the measured unknown small surface.
设平面某一被测点的法向量为，则：Let the normal vector of a measured point on the plane be ,but:
（5） (5)
则求得m、n、q的值为：Then the values of m, n, and q are obtained as:
（6） (6)
设装置移动到下一小平面对应处一点的法向量为，两个点的法向量尽可能处于同一水平面上，的取值与上面算法一致。Let the device move to the normal vector of a point corresponding to the next small plane as , the normal vectors of the two points are on the same horizontal plane as possible, The value of is consistent with the above algorithm.
设两个法向量之间的夹角为，有如下公式：Assuming that the angle between two normal vectors is , there is the following formula:
（7） (7)
根据上述公式我们可以求得夹角的值为：According to the above formula, we can obtain the value of the included angle as:
（8） (8)
为了合理布置采样点，首先我们设置一个最小偏转角（阈值）。然后根据被测未知曲面的性质，曲面陡峭不平，在陡峭明显的区域曲面的法向量之间的转角越大，所以相邻点之间的间距就越小，测量点就多；在陡峭不明显的区域曲面的法向量转角越小，则相邻点之间的间距也越大，测量点就少，从而实现采样点的自适应分布。In order to arrange the sampling points reasonably, first we set a minimum deflection angle (threshold). Then, according to the nature of the measured unknown surface, the surface is steep and uneven, and the larger the angle between the normal vectors of the surface in the steep and obvious area, the smaller the distance between adjacent points and the more measurement points; The smaller the normal vector angle of the area surface, the larger the distance between adjacent points, and the fewer measurement points, so as to realize the adaptive distribution of sampling points.
实施例8：Embodiment 8:
处理偏转法向量Dealing with deflection normal vectors
在测量过程中，如果所遇到自由曲面非常陡峭，特别是测量轨迹的左右方向较为陡峭，那么三点激光测量装置所计算的法向量会向曲面左右陡峭一侧偏转。法向量“t”，出现向测量轨迹某一侧的摆动，此时被测三角小平面上一点的法向量偏转就不能忽视，这时进行法向量偏转计算。设测量点方向与测量轨迹为同一方向，将此测量点法向量“t”，分解为tx、ty两个分量，且相互垂直，其中tx与t的夹角为，所以tx、ty等于：During the measurement process, if the free-form surface encountered is very steep, especially the left-right direction of the measurement track is relatively steep, the normal vector calculated by the three-point laser measuring device will deflect to the steep left-right side of the surface. The normal vector "t" swings to one side of the measurement track. At this time, the normal vector deflection of a point on the measured triangular facet cannot be ignored. At this time, the normal vector deflection calculation is performed. Assuming that the direction of the measurement point is in the same direction as the measurement track, the normal vector "t" of the measurement point is decomposed into two components t x and t y , which are perpendicular to each other, and the angle between t x and t is , so t x , t y are equal to:
(9) (9)
如果此点与前面法向量的分量夹角超过阈值（设置一个最小偏转角），就沿偏转方向增加采样点，未知曲面陡峭大时法向量向一侧的摆动。If the angle between this point and the component of the previous normal vector exceeds the threshold (set a minimum deflection angle), add sampling points along the deflection direction, and the normal vector swings to one side when the unknown surface is steep.
实施例9：Embodiment 9:
偏转法向量的分解Decomposition of deflection normal vectors
针对被测未知曲面的陡峭，在其偏置方向上设置一些偏置点，主要考虑法向量摇摆方向的法向量分量与前一个法向量的分量夹角，根据其数值大小布置偏置点。布置完偏置点后，再回到原来轨迹。For the steepness of the measured unknown surface, set some offset points in its offset direction, mainly considering the angle between the normal vector component in the normal vector swing direction and the previous normal vector component, and arrange the offset points according to its value. After the offset point is arranged, return to the original track.
曲线测量点布置完，返回起始点，LDF继续寻边界，确定起始点后，沿着边界移动，确定边界，分析边界数据，以另一个采样点为起始点继续进行测量直至测量到整个曲面。各个测量截面是按等间距分布的，这会导致截面分布不合理影响曲面重建精度，所示需要对截面细分；首先根据等间距测量，计算出边界线法向量的偏转，再根据转角大小算出边界上采样点的分布。After the curve measurement point is arranged, return to the starting point, LDF continues to find the boundary, after determining the starting point, move along the boundary, determine the boundary, analyze the boundary data, continue to measure with another sampling point as the starting point until the entire surface is measured. Each measurement section is distributed at equal intervals, which will lead to unreasonable distribution of sections and affect the accuracy of surface reconstruction. As shown, the section needs to be subdivided; first, the deflection of the normal vector of the boundary line is calculated according to the equidistant measurement, and then calculated according to the size of the rotation angle The distribution of sampling points on the boundary.
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