CN111536876A - A method for in-situ measurement of sealing surface of triple eccentric butterfly valve - Google Patents
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Abstract
本发明公开了一种三偏心蝶阀密封面的在位测量方法,包括:获取置于转台上待测工件外部轮廓数据点的坐标信息;对数据点的坐标信息通过最小二乘拟合建立第一空间直线方程;从第一空间直线方程中根据预设锥角选取最优母线方程;通过最优母线方程拟合得到第一圆锥面方程;获取m个拟合的中心点的坐标,将中心点的坐标代入第一圆锥面方程,得到相应的m个第二圆锥面的方程;在数据点到m个第二圆锥面的最小距离值集合中选取误差最小的集合所对应的第二圆锥面为最佳拟合圆锥曲面。通过以上算法,实现了在加工的同时进行测量,随时掌握加工误差,避免离线测量后对工件进行拆卸带来的二次加工误差。
The invention discloses an in-situ measurement method for a sealing surface of a triple eccentric butterfly valve, comprising: acquiring coordinate information of data points on the outer contour of a workpiece to be measured placed on a turntable; The space straight line equation; select the optimal generatrix equation according to the preset cone angle from the first space line equation; obtain the first conical surface equation by fitting the optimal generatrix equation; obtain the coordinates of m fitted center points, The coordinates of are substituted into the equation of the first conical surface, and the corresponding equations of m second conic surfaces are obtained; the second conical surface corresponding to the set with the smallest error is selected from the set of minimum distance values from the data point to the m second conical surfaces: Best fit conic surface. Through the above algorithm, it is possible to measure at the same time of processing, grasp the processing error at any time, and avoid the secondary processing error caused by the disassembly of the workpiece after offline measurement.
Description
技术领域technical field
本发明涉及测量技术领域,具体涉及一种三偏心蝶阀密封面的在位测量方法。The invention relates to the technical field of measurement, in particular to an in-situ measurement method of a sealing surface of a triple eccentric butterfly valve.
背景技术Background technique
目前机械制造过程大多数采用离线测量技术。采用离线测量方法需要加工与测量分别在专业设备上进行,加工完工件需移至测量设备进行检测。这种方法适用于大批量的生产,缺点是不可避免地带来二次装夹误差、加工周期延长和工件周转过程损伤等问题,影响生产进度与效率。At present, most of the mechanical manufacturing process adopts offline measurement technology. Using the offline measurement method requires processing and measurement to be carried out on professional equipment respectively, and the processed parts need to be moved to the measurement equipment for testing. This method is suitable for mass production. The disadvantage is that it will inevitably bring about problems such as secondary clamping error, prolonged processing cycle and workpiece turnover process damage, which will affect the production progress and efficiency.
常用的离线测量方法包括:卡尺测量、三坐标测量仪等。卡尺测量因使用了游标卡尺、千分尺和卡规等标准化的工具,具有价格便宜,使用方便的优点。但是三偏心蝶阀独特的斜锥面结构导致了直边到斜边的最大尺寸只是最大直边和最大斜边上两个点的距离,因此测量常常全凭操作工人的手感,而且测量重复精度很差,不同的工人测量结果也有很大差距。并且三偏心的零泄露密封是需要密封面完全面接触的,尺寸上的误差会导致接触部位只是一条线,因此很难实现零泄露的要求,更不用说实现双向零泄露密封的要求了。此外,目前的三坐标测量仪由于尺寸限制,无法对直径较大的蝶阀进行准确测量;且使用三坐标测量仪就必须将工件从车床加工工作台上拆卸下来,此时测量得到的误差也无法再对工件进行二次的补刀加工。因为测量结束后若要进行二次加工,则必须要重新装夹工件,由于三偏心蝶阀密封面形状的不对称性,二次装夹必然会产生较大的误差,即使重新装夹在车床上也不能进行再次加工,对于仅稍微超过误差允许范围的工件,也只能选择报废处理。Commonly used offline measurement methods include: caliper measurement, three-coordinate measuring instrument, etc. Caliper measurement has the advantages of low price and convenient use due to the use of standardized tools such as vernier calipers, micrometers and calipers. However, the unique inclined cone structure of the triple eccentric butterfly valve leads to the fact that the maximum dimension from the straight edge to the inclined edge is only the distance between the two points on the largest straight edge and the largest oblique edge, so the measurement often depends on the operator's feel, and the measurement repeatability is very high. There are also large differences in the results of different worker measurements. In addition, the triple-eccentric zero-leakage seal requires complete surface contact of the sealing surface, and the dimensional error will cause the contact part to be only a line, so it is difficult to achieve zero-leakage requirements, let alone two-way zero-leakage sealing requirements. In addition, the current three-coordinate measuring instrument cannot accurately measure the butterfly valve with a large diameter due to the size limitation; and the use of the three-coordinate measuring instrument must remove the workpiece from the lathe processing table, and the error obtained at this time cannot be measured. The workpiece is then subjected to secondary tool compensation processing. Because if the secondary processing is to be performed after the measurement, the workpiece must be re-clamped. Due to the asymmetry of the shape of the sealing surface of the triple eccentric butterfly valve, the secondary clamping will inevitably produce a large error, even if it is re-clamped on the lathe Reprocessing is also not possible. For workpieces that only slightly exceed the allowable tolerance range, only scrapping can be selected.
在位测量指的是工件在被加工之后,不对被加工零件进行拆卸,仍然夹持在机床之上,在机床上对被加工零件进行测量,若测量结果不合格,则在机床上直接快速地返修,避免了离线测量后对工件进行拆卸带来的二次加工误差,进一步提高加工精度。In-situ measurement means that the workpiece is not disassembled after being machined, but is still clamped on the machine tool, and the machined part is measured on the machine tool. If the measurement result is unqualified, the machine tool is directly and quickly Rework can avoid the secondary machining error caused by disassembling the workpiece after offline measurement, and further improve the machining accuracy.
因此,如何对工件采用在位测量方法,在加工的同时进行测量,随时掌握加工误差,避免离线测量后对工件进行拆卸带来的二次加工误差,成为亟待解决的问题。Therefore, how to use the in-situ measurement method for the workpiece, measure at the same time as processing, grasp the processing error at any time, and avoid the secondary processing error caused by the disassembly of the workpiece after offline measurement has become an urgent problem to be solved.
发明内容SUMMARY OF THE INVENTION
有鉴于此,本发明实施例提供了一种三偏心蝶阀密封面的在位测量方法,以解决现有技术中采用离线测量对工件进行拆卸带来的二次加工误差问题。In view of this, the embodiment of the present invention provides an in-situ measurement method for the sealing surface of a triple eccentric butterfly valve, so as to solve the problem of secondary processing error caused by the use of offline measurement to disassemble the workpiece in the prior art.
本发明实施例提供了一种三偏心蝶阀密封面的在位测量方法,包括:The embodiment of the present invention provides an in-situ measurement method for the sealing surface of a triple eccentric butterfly valve, including:
获取置于转台上待测工件外部轮廓数据点的坐标信息;Obtain the coordinate information of the external contour data points of the workpiece to be measured placed on the turntable;
对数据点的坐标信息通过最小二乘拟合建立第一空间直线方程;establishing a first space straight line equation by least square fitting to the coordinate information of the data points;
从第一空间直线方程中根据预设锥角选取最优母线方程;Select the optimal busbar equation from the first space straight line equation according to the preset cone angle;
通过最优母线方程拟合得到第一圆锥面方程;The first conical surface equation is obtained by fitting the optimal generatrix equation;
获取m个拟合的中心点的坐标,将中心点的坐标代入第一圆锥面方程,得到相应的m个第二圆锥面的方程;其中,中心点从待测工件的圆锥顶点所在平面中的预设区域内选取,平面与转台的上表面平行,预设区域为包含圆锥顶点的半径为r的圆形区域,或,预设区域为包含圆锥顶点的边长为r的正方形区域,m为大于等于1的自然数;Obtain the coordinates of m fitting center points, and substitute the coordinates of the center points into the first conical surface equation to obtain the corresponding m second conical surface equations; among them, the center point is from the plane where the cone vertex of the workpiece to be measured is located. Select from the preset area, the plane is parallel to the upper surface of the turntable, the preset area is a circular area with a radius r containing the vertices of the cone, or, the preset area is a square area with a side length r containing the vertices of the cone, m is a natural number greater than or equal to 1;
在数据点到m个第二圆锥面的最小距离值集合中选取误差最小的集合所对应的第二圆锥面为最佳拟合圆锥曲面。From the set of minimum distance values from the data point to the m second conical surfaces, the second conical surface corresponding to the set with the smallest error is selected as the best fitting conic surface.
可选地,获取置于转台上待测工件外部轮廓数据点的坐标信息包括:当转台每旋转预定角度后,激光传感器对待测工件进行一次采集操作;当转台旋转一周后,将激光传感器随Z轴下移预定距离以备于下一次采集操作。Optionally, acquiring the coordinate information of the outer contour data points of the workpiece to be measured placed on the turntable includes: when the turntable rotates by a predetermined angle, the laser sensor performs a collection operation on the workpiece to be measured; The axis is moved down a predetermined distance in preparation for the next acquisition operation.
可选地,在对数据点的坐标信息通过最小二乘拟合建立第一空间直线方程之前,还包括:Optionally, before establishing the first space straight line equation by least squares fitting on the coordinate information of the data points, the method further includes:
将数据点中符合要求的最优数据设置为标准点,剩余数据点为待筛选数据点;The optimal data that meets the requirements in the data points is set as the standard point, and the remaining data points are the data points to be screened;
设置相对距离偏差阈值;Set the relative distance deviation threshold;
计算待筛选数据点与标准点之间的相对距离,若相对距离小于等于相对距离偏差阈值,则待筛选数据点为合格数据点。Calculate the relative distance between the data points to be screened and the standard points. If the relative distance is less than or equal to the relative distance deviation threshold, the data points to be screened are qualified data points.
可选地,从第一空间直线方程中根据预设锥角选取最优母线方程包括:Optionally, selecting the optimal generatrix equation from the first space straight line equation according to the preset taper angle includes:
获取第一空间直线方程的方向向量;Obtain the direction vector of the first space straight line equation;
根据方向向量获取获取第一空间直线和标准直线之间的夹角;Obtain the angle between the first space straight line and the standard straight line according to the direction vector;
根据夹角计算得出以第一空间直线为母线的圆锥的锥角;Calculate the cone angle of the cone with the first space straight line as the generatrix according to the included angle;
将锥角范围为18°~23°之间的所有第一空间直线作为第二空间直线;All the first space straight lines whose taper angle ranges from 18° to 23° are used as the second space straight lines;
从第二空间直线中选取出一条直线作为最优母线。A straight line is selected from the second space straight line as the optimal generatrix.
可选地,获取第一空间直线方程的方向向量包括:Optionally, obtaining the direction vector of the first space straight line equation includes:
计算第一空间直线方程的残差平方和;Calculate the residual sum of squares of the first space straight line equation;
对残差残差平方和进行求导得到第一空间直线方程的系数和第一空间直线的方向向量。The coefficient of the first space straight line equation and the direction vector of the first space straight line are obtained by derivation of the residual sum of squared residuals.
可选地,获取m个拟合的中心点的坐标,将中心点的坐标代入第一圆锥面方程,得到相应的m个第二圆锥面方程包括:Optionally, the coordinates of m fitted center points are obtained, and the coordinates of the center points are substituted into the first conical surface equation, and the corresponding m second conic surface equations are obtained, including:
将第二空间直线的方程代入第一圆锥面的一般方程中,获得第二圆锥面的方程,第二圆锥面的方程与第一空间直线方程的系数有关。Substitute the equation of the second space straight line into the general equation of the first conical surface to obtain the equation of the second conical surface, and the equation of the second conical surface is related to the coefficient of the first space straight line equation.
可选地,在数据点到m个第二圆锥面的最小距离值集合中选取误差最小的集合所对应的第二圆锥面为最佳拟合圆锥曲面包括:Optionally, selecting the second conical surface corresponding to the set with the smallest error from the set of minimum distance values from the data point to the m second conical surfaces as the best fitting conic surface includes:
利用多元函数条件极值的拉格朗日乘数法获得数据点到m个第二圆锥面的距离最小值的一般表达式;The general expression for obtaining the minimum distance from the data point to the m second conical surfaces by using the Lagrange multiplier method of the conditional extrema of the multivariate function;
将数据点代入距离最小值的一般表达式,求得数据点到m个第二圆锥面的最小距离值集合;Substitute the data point into the general expression of the minimum distance, and obtain the minimum distance value set from the data point to the m second conical surfaces;
对数据点到m个第二圆锥面的最小距离值集合分别计算误差,选取误差最小的最小距离值集合对应的第二圆锥面为最佳拟合圆锥曲面。Errors are calculated respectively for the minimum distance value set from the data point to the m second conical surfaces, and the second conical surface corresponding to the minimum distance value set with the smallest error is selected as the best fitting conic surface.
可选地,利用多元函数条件极值的拉格朗日乘数法获得数据点到m个第二圆锥面的距离最小值的一般表达式包括:Optionally, the general expression for obtaining the minimum distance from the data point to the m second conical surfaces using the Lagrangian multiplier method of the conditional extrema of the multivariate function includes:
根据数据点的坐标获得拉格朗日函数;Obtain the Lagrangian function according to the coordinates of the data points;
根据三维坐标参数对拉格朗日函数中分别求导,获得同拉格朗日参数相关以及数据点的坐标相关的坐标代数式;Differentiate the Lagrangian functions according to the three-dimensional coordinate parameters, and obtain the coordinate algebraic expressions related to the Lagrangian parameters and the coordinates of the data points;
将坐标代数式代入第二圆锥面的方程,得到与拉格朗日参数相关的第三圆锥面方程;Substitute the coordinate algebra into the equation of the second conical surface to obtain the third conical surface equation related to the Lagrangian parameters;
通过计算第三圆锥面方程的极值,获得拉格朗日参数的具体数值;By calculating the extreme value of the third conical surface equation, the specific value of the Lagrangian parameter is obtained;
通过同拉格朗日参数相关以及数据点的坐标相关的坐标代数式求出数据点到m个第二圆锥面的距离最小值。The minimum distance from the data point to the m second conical surfaces is obtained through the coordinate algebra formula related to the Lagrangian parameter and the coordinate of the data point.
本发明实施例提供了一种三偏心蝶阀密封面的在位测量方法,将待测的三偏心蝶阀工件放置于转台上,通过激光传感器采集待测工件密封面数据点的坐标信息,编码器将激光传感器采集到的数据传到计算机上;通过计算数据点(除拟合空间直线的数据点)到圆锥曲面的距离来判断该数据点是否能够拟合到该圆锥曲面上;不然,寻找下一个平面中心点,继续拟合得到一个圆锥曲面,再计算其余数据点到圆锥曲面的距离来判断该数据点是否能够拟合到该圆锥曲面上;重复以上步骤,拟合误差直到|Δij≤Δ00|,说明该圆锥曲面为最佳拟合面。The embodiment of the present invention provides an in-situ measurement method for the sealing surface of a triple eccentric butterfly valve. The workpiece of the triple eccentric butterfly valve to be measured is placed on a turntable, and the coordinate information of the sealing surface data points of the workpiece to be measured is collected by a laser sensor. The data collected by the laser sensor is transmitted to the computer; by calculating the distance from the data point (except the data point of the fitting space line) to the conic surface, it is judged whether the data point can be fitted to the conical surface; otherwise, find the next The center point of the plane, continue to fit to obtain a conic surface, and then calculate the distance from the remaining data points to the conic surface to judge whether the data point can be fitted to the conic surface; repeat the above steps, the fitting error is until |Δ ij ≤Δ 00 |, indicating that the conic surface is the best fitting surface.
通过以上实施例提供的三偏心蝶阀密封面的在位测量方法,可以获取更为完整的工件的正确测量数据,以提高测量系统测量精度,并对后续的加工起指导作用。实现了在加工的同时进行测量,随时掌握加工误差,避免离线测量后对工件进行拆卸带来的二次加工误差。Through the in-situ measurement method of the sealing surface of the triple eccentric butterfly valve provided in the above embodiment, more complete correct measurement data of the workpiece can be obtained, so as to improve the measurement accuracy of the measurement system and play a guiding role in subsequent processing. It realizes the measurement at the same time of processing, grasps the processing error at any time, and avoids the secondary processing error caused by the disassembly of the workpiece after offline measurement.
附图说明Description of drawings
通过参考附图会更加清楚的理解本发明的特征和优点,附图是示意性的而不应理解为对本发明进行任何限制,在附图中:The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way, in which:
图1示出了本发明实施例中一种三偏心蝶阀密封面的在位测量方法的流程图;1 shows a flow chart of a method for in-situ measurement of a sealing surface of a triple eccentric butterfly valve in an embodiment of the present invention;
图2示出了本发明实施例中一种三偏心蝶阀密封面的采集数据点与合格数据点之间的关系图;Fig. 2 shows the relationship diagram between the collected data points and the qualified data points of the sealing surface of a triple eccentric butterfly valve in an embodiment of the present invention;
图3示出了本发明实施例中另一种三偏心蝶阀密封面在位测量算法的流程图。FIG. 3 shows a flowchart of another in-situ measurement algorithm of the sealing surface of the triple eccentric butterfly valve in the embodiment of the present invention.
具体实施方式Detailed ways
为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域技术人员在没有作出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts shall fall within the protection scope of the present invention.
目前在位测量通过在位测量获得被加工曲面的若干离散数据,根据这些数据,我们希望得到一个连续的曲面与已知数据相吻合,此过程为曲面拟合过程。曲面拟合技术在计算机图形学、数值计算等领域有着广泛的应用。目前常用的曲面拟合方法有:最小二乘法、插值法、缩张算法等。At present, in-situ measurement obtains several discrete data of the processed surface through in-situ measurement. According to these data, we hope to obtain a continuous surface that is consistent with the known data. This process is a surface fitting process. Surface fitting technology has a wide range of applications in computer graphics, numerical computing and other fields. At present, the commonly used surface fitting methods are: least squares method, interpolation method, shrinkage algorithm and so on.
插值法是根据插值原则构造n次多项式Pn(x),使得Pn(x)在各测试点的数据正好通过实测点;虽然插值法能够保留原始数据点,但是,在一般情况下,为了尽可能更大限度地反映实际情况而采集了很多数据点,导致插值多项式Pn(x)的次数很高,这不仅增大了计算量,而且影响了拟合精度,不利于工程实际生产过程中的工件的曲面拟合。缩张算法是一种以收缩、扩张搜索空间为基本特征的直接迭代算法,在基于搜索空间较为简单的条件下,缩张算法无需提供适合的初始值就能实现最优拟合,但是一旦搜索空间复杂化,它的搜索效率就会下降,并且对多参数非线性问题难以实施。最小二乘法是根据已知的数据选取一个近似的函数f(x),使得函数f(x)的均方根误差最小。虽然最小二乘法拟合在保留某些原始数据点的情况下有所不足,但是最小二乘法拟合的最大优点是拟合精度可以调控,可以根据实际使用情况选择不同的拟合精度。最小二乘法线性拟合曲面更是简单直接、便于操作,有利于实际加工过程的反馈。The interpolation method is to construct an n-degree polynomial P n (x) according to the interpolation principle, so that the data of P n (x) at each test point just passes the measured point; although the interpolation method can retain the original data points, but, in general, in order to A lot of data points are collected to reflect the actual situation as much as possible, resulting in a high degree of interpolation polynomial P n (x), which not only increases the amount of calculation, but also affects the fitting accuracy, which is not conducive to the actual production process of the project. Surface fitting of the workpiece in . The shrinkage algorithm is a direct iterative algorithm with the basic characteristics of shrinking and expanding the search space. Under the condition that the search space is relatively simple, the shrinkage algorithm can achieve the best fit without providing suitable initial values. When the space is complicated, its search efficiency will decrease, and it is difficult to implement for multi-parameter nonlinear problems. The least squares method is to select an approximate function f(x) according to the known data, so that the root mean square error of the function f(x) is the smallest. Although the least squares fitting is insufficient in retaining some original data points, the biggest advantage of the least squares fitting is that the fitting accuracy can be regulated, and different fitting accuracies can be selected according to the actual usage. The least squares method of linearly fitting the surface is more simple, direct and easy to operate, which is conducive to the feedback of the actual processing process.
本发明实施例提供了一种三偏心蝶阀密封面的在位测量方法,如图1所示,包括:The embodiment of the present invention provides an in-situ measurement method for the sealing surface of a triple eccentric butterfly valve, as shown in FIG. 1 , including:
步骤S10,获取置于转台上待测工件外部轮廓数据点的坐标信息。In step S10, the coordinate information of the outer contour data points of the workpiece to be measured placed on the turntable is obtained.
在本实施例中,将待测的三偏心蝶阀工件放置于转台上,通过激光传感器采集待测工件密封面数据点的坐标信息,编码器将激光传感器采集到的数据传到计算机上。In this embodiment, the workpiece of the triple eccentric butterfly valve to be tested is placed on the turntable, the coordinate information of the data points of the sealing surface of the workpiece to be tested is collected by the laser sensor, and the encoder transmits the data collected by the laser sensor to the computer.
步骤S20,对数据点的坐标信息通过最小二乘拟合建立第一空间直线方程。Step S20, establishing a first space straight line equation by least squares fitting on the coordinate information of the data points.
在本实施例中,待测的三偏心蝶阀工件随转台转动,激光传感器对待测的三偏心蝶阀工件的密封面进行信息采集,得到待测的三偏心蝶阀工件密封面的三维坐标信息,对数据点进行线性拟合得到多个第一空间直线的方程。In this embodiment, the workpiece of the triple eccentric butterfly valve to be tested rotates with the turntable, and the laser sensor collects information on the sealing surface of the workpiece of the triple eccentric butterfly valve to be tested to obtain the three-dimensional coordinate information of the sealing surface of the workpiece of the triple eccentric butterfly valve to be tested. The points are linearly fitted to obtain a plurality of equations of the first space straight lines.
最小二乘法是根据已知的数据选取一个近似的函数f(x),使得函数f(x)的均方根误差最小。虽然最小二乘法拟合在保留某些原始数据点的情况下有所不足,但是最小二乘法拟合的最大优点是拟合精度可以调控,可以根据实际使用情况选择不同的拟合精度。最小二乘法线性拟合曲面更是简单直接、便于操作,有利于实际加工过程的反馈。The least squares method is to select an approximate function f(x) according to the known data, so that the root mean square error of the function f(x) is the smallest. Although the least squares fitting is insufficient in retaining some original data points, the biggest advantage of the least squares fitting is that the fitting accuracy can be regulated, and different fitting accuracies can be selected according to the actual usage. The least squares method of linearly fitting the surface is more simple, direct and easy to operate, which is conducive to the feedback of the actual processing process.
在本实施方式中,在位测量条件下采用最小二乘法线性拟合曲面可以及时反馈加工误差情况,对后续加工做技术指导,使工件加工精度进一步提高。In this embodiment, using the least squares method to linearly fit the curved surface under the condition of in-situ measurement can timely feedback the machining error, and provide technical guidance for the subsequent machining, so as to further improve the machining accuracy of the workpiece.
步骤S30,从第一空间直线方程中根据预设锥角选取最优母线方程。Step S30, select the optimal busbar equation from the first space straight line equation according to the preset taper angle.
在本实施例中,由于待测的三偏心蝶阀工件的密封面近似圆锥面,因此要从步骤S20中的多个第一空间直线的方程中选取出一条直线来作为拟合圆锥面的最优母线。最优母线根据第一空间直线方程同标准直线之间的锥角大小进行选取。In this embodiment, since the sealing surface of the workpiece of the triple eccentric butterfly valve to be tested is approximately a conical surface, a straight line should be selected from the equations of the plurality of first space straight lines in step S20 as the optimal fitting of the conical surface. busbar. The optimal busbar is selected according to the size of the cone angle between the first space straight line equation and the standard straight line.
步骤S40,通过最优母线方程拟合得到第一圆锥面方程。Step S40, obtaining the first conical surface equation by fitting the optimal generatrix equation.
在本实施例中,在世界坐标系中确定一条线段以及锥角,即可获得多个圆锥面,这些圆锥面顶点未确定。In this embodiment, by determining a line segment and a cone angle in the world coordinate system, a plurality of conical surfaces can be obtained, and the vertices of these conical surfaces are not determined.
步骤S50,获取m个拟合的中心点的坐标,将中心点的坐标代入第一圆锥面方程,得到相应的m个第二圆锥面的方程。其中,中心点从待测工件的圆锥顶点所在平面中的预设区域内选取,平面与转台的上表面平行,预设区域为包含圆锥顶点的半径为r的圆形区域,或,预设区域为包含圆锥顶点的边长为r的正方形区域,m为大于等于1的自然数。In step S50, the coordinates of the m fitted center points are obtained, and the coordinates of the center points are substituted into the first conical surface equation to obtain the corresponding m second conic surface equations. The center point is selected from a preset area in the plane where the cone vertex of the workpiece to be tested is located, the plane is parallel to the upper surface of the turntable, and the preset area is a circular area with a radius r containing the cone vertex, or, the preset area is a square area with side length r containing the vertices of the cone, where m is a natural number greater than or equal to 1.
在本实施例中,激光传感器对待测的三偏心蝶阀工件密封面顶点坐标进行数据采集,在待测工件随转台旋转的过程中,待测工件密封面顶点的x轴坐标和y轴坐标可能发生变化,而待测工件密封面顶点的z轴坐标一般不会发生变化。若待测的三偏心蝶阀工件摆放时,其密封面顶点恰好处于转台中心的正上方,则待测工件密封面顶点的坐标在转台转动过程中不会发生改变。In this embodiment, the laser sensor collects data on the vertex coordinates of the sealing surface of the workpiece of the triple eccentric butterfly valve to be tested. During the rotation of the workpiece to be tested with the turntable, the x-axis and y-axis coordinates of the sealing surface of the workpiece to be tested may occur. changes, and the z-axis coordinate of the apex of the sealing surface of the workpiece to be tested generally does not change. If the workpiece of the triple eccentric butterfly valve to be tested is placed, the vertex of its sealing surface is just above the center of the turntable, the coordinates of the vertex of the sealing surface of the workpiece to be tested will not change during the rotation of the turntable.
以圆形区域为例,在任意一次测量过程中,确定一个以密封面顶点坐标为圆心、r为半径的圆形区域,将该圆形区域按预设大小平均划分为m个单位区域,选取单位区域中心坐标为拟合的中心点,将m个拟合中心点坐标代入步骤S40中的第一圆锥面方程,得到m个第二圆锥面的方程。半径r和m的值可根据实际需要进行设置。Taking a circular area as an example, in any measurement process, determine a circular area with the coordinates of the vertex of the sealing surface as the center and r as the radius, and divide the circular area into m unit areas according to the preset size. The coordinate of the center of the unit area is the center point of the fitting, and the coordinates of the m fitting center points are substituted into the first conical surface equation in step S40 to obtain m equations of the second conical surface. The values of radius r and m can be set according to actual needs.
步骤S60,在数据点到m个第二圆锥面的最小距离值集合中选取误差最小的集合所对应的第二圆锥面为最佳拟合圆锥曲面。Step S60, selecting the second conical surface corresponding to the set with the smallest error from the set of minimum distance values from the data point to the m second conical surfaces as the best fitting conical surface.
在本实施例中,通过计算数据点(除拟合空间直线的数据点)到圆锥曲面的距离来判断该数据点是否能够拟合到该圆锥曲面上;不然,寻找下一个平面中心点,继续拟合得到一个圆锥曲面,再计算其余数据点到圆锥曲面的距离来判断该数据点是否能够拟合到该圆锥曲面上;重复以上步骤,拟合误差直到|Δij≤Δ00|,说明该圆锥曲面为最佳拟合面。In this embodiment, it is determined whether the data point can be fitted to the conic surface by calculating the distance from the data point (except the data point of the fitting space straight line) to the conic surface; otherwise, find the next plane center point, and continue A conic surface is obtained by fitting, and then the distance from the remaining data points to the conic surface is calculated to determine whether the data point can be fitted to the conic surface; repeat the above steps, the fitting error is until |Δ ij ≤Δ 00 |, indicating that the The conic surface is the best fit surface.
通过以上实施例提供的三偏心蝶阀密封面的在位测量方法,可以获取更为完整的工件的正确测量数据,以提高测量系统测量精度,并对后续的加工起指导作用。实现了在加工的同时进行测量,随时掌握加工误差,避免离线测量后对工件进行拆卸带来的二次加工误差。Through the in-situ measurement method of the sealing surface of the triple eccentric butterfly valve provided in the above embodiment, more complete correct measurement data of the workpiece can be obtained, so as to improve the measurement accuracy of the measurement system and play a guiding role in subsequent processing. It realizes the measurement at the same time of processing, grasps the processing error at any time, and avoids the secondary processing error caused by the disassembly of the workpiece after offline measurement.
作为可选的实施方式,获取置于转台上待测工件外部轮廓数据点的坐标信息:当转台每旋转预定角度后,激光传感器对待测工件进行一次采集操作;当转台旋转一周后,将激光传感器随Z轴下移预定距离以备于下一次采集操作。As an optional embodiment, the coordinate information of the outer contour data points of the workpiece to be measured placed on the turntable is obtained: after each rotation of the turntable by a predetermined angle, the laser sensor performs a collection operation on the workpiece to be measured; Move down a predetermined distance along the Z axis for the next acquisition operation.
在本实施例中,待测工件放在转台上,转台带动待测工件匀速旋转,待测工件每转动相同的角度激光测量一次数据,转动一圈之后,激光传感器完成一次测量;之后激光传感器随Z轴向下移动合适的距离,工件每转动相同的角度激光测量一次数据,转动一圈之后,激光传感器完成一次测量。重复上述操作,最终获得全部的数据点。In this embodiment, the workpiece to be measured is placed on the turntable, and the turntable drives the workpiece to rotate at a constant speed. The laser measures data once every time the workpiece to be measured rotates by the same angle. After one rotation, the laser sensor completes one measurement; The Z axis moves downward by a suitable distance, and the laser measures the data every time the workpiece rotates at the same angle. After one rotation, the laser sensor completes one measurement. Repeat the above operation to finally obtain all data points.
所有测定的数据点的特点为:存在一段具有相同数值的数据带以及另一段具有相同数值的数据带。All measured data points are characterized by the presence of one data band with the same value and another data band with the same value.
转台带动工件匀速旋转,可以将数据点按平均旋转角度分成数据点的列。The turntable drives the workpiece to rotate at a constant speed, and the data points can be divided into columns of data points according to the average rotation angle.
作为可选的实施方式,在步骤S20之前,还包括:As an optional implementation manner, before step S20, it also includes:
步骤S11,将数据点中符合要求的最优数据设置为标准点,剩余数据点为待筛选数据点。In step S11, the optimal data that meets the requirements in the data points is set as the standard point, and the remaining data points are the data points to be screened.
步骤S12,设置相对距离偏差阈值。Step S12, setting a relative distance deviation threshold.
步骤S13,计算待筛选数据点与标准点之间的相对距离,若相对距离小于等于相对距离偏差阈值,则待筛选数据点为合格数据点。Step S13: Calculate the relative distance between the data point to be screened and the standard point. If the relative distance is less than or equal to the relative distance deviation threshold, the data point to be screened is a qualified data point.
在本实施例中,利用相对距离偏差去除异常数据点;每次测量完成一圈时,该组数据的数据点会有两段明显差异的数值,此时较小数值的那组数据较为接近标准数值。假定采集到的数据点列中,存在符合要求的最优数据,将其设置为标准点。如图2所示,按照以上方法设置标准点集,计算其他数据点与标准点集之间的相对平均距离D,同时按照需求设置相对距离偏差阈值ε,若D≤ε,则该数据点符合要求,最终求得所有符合要求的数据点。In this embodiment, the relative distance deviation is used to remove abnormal data points; each time the measurement completes a circle, the data points of this group of data will have two values that are significantly different, and the group of data with the smaller value is closer to the standard numerical value. Assuming that there is optimal data that meets the requirements in the collected data point column, set it as the standard point. As shown in Figure 2, set the standard point set according to the above method, calculate the relative average distance D between other data points and the standard point set, and set the relative distance deviation threshold ε according to the requirements. requirements, and finally obtain all the data points that meet the requirements.
作为可选的实施方式,步骤S30包括:As an optional implementation manner, step S30 includes:
步骤S301,获取第一空间直线方程的方向向量。Step S301, obtaining the direction vector of the first space straight line equation.
步骤S302,根据方向向量获取获取第一空间直线和标准直线之间的夹角。Step S302, obtaining the included angle between the first space straight line and the standard straight line according to the direction vector.
步骤S303,根据夹角计算得出以第一空间直线为母线的圆锥的锥角。Step S303: Calculate the taper angle of the cone with the first spatial straight line as the generatrix according to the included angle.
步骤S304,将锥角范围为18°~23°之间的所有第一空间直线作为第二空间直线。In step S304, all the first space straight lines with the taper angle ranging from 18° to 23° are used as the second space straight lines.
步骤S305,从第二空间直线中选取出一条直线作为最优母线。In step S305, a straight line is selected from the second spatial straight line as the optimal generatrix.
在本实施例中,选取锥角为20°的直线作为最优母线。In this embodiment, a straight line with a taper angle of 20° is selected as the optimal bus bar.
作为可选的实施方式,步骤S301包括:As an optional implementation manner, step S301 includes:
计算第一空间直线方程的残差平方和;Calculate the residual sum of squares of the first space straight line equation;
对残差残差平方和进行求导得到第一空间直线方程的系数和第一空间直线的方向向量。The coefficient of the first space straight line equation and the direction vector of the first space straight line are obtained by derivation of the residual sum of squared residuals.
在本实施例中,假设直线方程为: In this embodiment, it is assumed that the equation of the straight line is:
其中为激光传感器采集到的待测三偏心蝶阀工件密封面的数据点坐标。in It is the data point coordinates of the sealing surface of the workpiece of the triple eccentric butterfly valve to be tested collected by the laser sensor.
求得残差平方和为:The residual sum of squares is obtained as:
Qij和Qi,j+1即优化判据,对Qij和Qi,j+1分别求导得:Q ij and Q i, j+1 are the optimization criteria, and the derivation of Q ij and Q i, j+1 is obtained respectively:
第一空间直线方程的系数为:The coefficients of the first space straight line equation are:
由平面垂直法向量可知,标准直线方向向量空间直线的方向向量为 It can be known from the plane vertical normal vector that the standard line direction vector The direction vector of a straight line in space is
则步骤S302中根据方向向量获取获取第一空间直线和标准直线之间的夹角:根据可以计算出第一空间直线lij和标准直线的之间的夹角为 Then in step S302, the angle between the first space straight line and the standard straight line is obtained according to the direction vector: according to The angle between the first space straight line l ij and the standard straight line can be calculated as
步骤S303,根据夹角计算得出以第一空间直线为母线的圆锥的锥角为αij。Step S303, calculating according to the included angle, the taper angle of the cone with the first spatial straight line as the generatrix is α ij .
作为可选的实施方式,步骤S50包括:将第二空间直线的方程代入第一圆锥面的一般方程中,获得第二圆锥面的方程,第二圆锥面的方程与第一空间直线方程的系数有关。As an optional implementation manner, step S50 includes: substituting the equation of the second space straight line into the general equation of the first conical surface to obtain the equation of the second conical surface, the equation of the second conic surface and the coefficients of the equation of the first space straight line related.
在本实施例中,第二空间直线为同标准直线之间锥角αij为20°的第一空间直线,将第二空间直线l2:In this embodiment, the second space straight line is a first space straight line with a taper angle α ij of 20° between the standard straight line and the second space straight line l 2 :
代入圆锥面的方程:G(x,y,z)=a2(x2+y2)-z2,本方程中的系数a根据第二空间直线上的数据点进行拟合计算获得。Substitute into the equation of the conical surface: G(x,y,z)=a 2 (x 2 +y 2 )-z 2 , the coefficient a in this equation is obtained by fitting and calculating according to the data points on the second space straight line.
得到圆锥曲面方程:Get the equation of the conic surface:
确定中心点Cm(x,y,z),将中心点坐标Cm(x,y,z)代入圆锥面的方程得到:Determine the center point C m (x, y, z), and substitute the center point coordinates C m (x, y, z) into the equation of the conical surface to get:
作为可选的实施方式,步骤S60包括:As an optional implementation manner, step S60 includes:
步骤S601,利用多元函数条件极值的拉格朗日乘数法获得数据点到m个第二圆锥面的距离最小值的一般表达式。Step S601 , using the Lagrange multiplier method of the conditional extremum of the multivariate function to obtain a general expression of the minimum distance from the data point to the m second conical surfaces.
具体地,步骤S601包括:Specifically, step S601 includes:
步骤S6011根据数据点的坐标获得拉格朗日函数。Step S6011 obtains the Lagrangian function according to the coordinates of the data points.
列出拉格朗日函数式:List the Lagrange functions:
Lij=(x-xij)2+(y-yij)2+(z-zij)2+λ[a2(x2+y2)-z2] Li ij =(xx ij ) 2 +(yy ij ) 2 +(zz ij ) 2 +λ[a 2 (x 2 +y 2 )-z 2 ]
其中,(x,y,z)为圆锥曲面上的点,(xij,yij,zij)为第二空间直线l2上的点。Wherein, (x, y, z) are points on the conic surface, and (x ij , y ij , z ij ) are points on the second space straight line l 2 .
步骤S6012,根据三维坐标参数对拉格朗日函数中分别求导,获得同拉格朗日参数相关以及数据点的坐标相关的坐标代数式。Step S6012: Differentiate the Lagrangian functions according to the three-dimensional coordinate parameters, and obtain a coordinate algebraic formula related to the Lagrangian parameters and the coordinates of the data points.
对步骤S6011中的拉格朗日函数求导:Derivation of the Lagrangian function in step S6011:
令L'x=0,L'y=0,L'z=0,得到关于λ以及数据点坐标的xyz坐标代数式:Let L' x = 0, L' y = 0, and L' z = 0 to obtain the xyz coordinate algebraic formula for λ and the coordinates of the data points:
步骤S6013,将坐标代数式代入第二圆锥面的方程,得到与拉格朗日参数相关的第三圆锥面方程。Step S6013: Substitute the coordinate algebraic formula into the equation of the second conical surface to obtain the third conical surface equation related to the Lagrangian parameters.
将步骤S6012中的xyz坐标代数式代入圆锥面的方程G(x,y,z)中,得到:Substitute the xyz coordinate algebraic expression in step S6012 into the equation G(x, y, z) of the conical surface to obtain:
步骤S6014,通过计算第三圆锥面方程的极值,获得拉格朗日参数的具体数值。Step S6014, by calculating the extreme value of the third conical surface equation, obtain the specific value of the Lagrangian parameter.
对G(λ)求极值,可以求出λ的值。The value of λ can be obtained by finding the extreme value of G(λ).
步骤S6015,通过同拉格朗日参数相关以及数据点的坐标相关的坐标代数式求出数据点到m个第二圆锥面的距离最小值。Step S6015, obtain the minimum distance from the data point to the m second conical surfaces by using the coordinate algebraic formula related to the Lagrangian parameter and the coordinates of the data point.
已知数据点集合X∈{x=(xij,yij,zij)},计算空间点(xij,yij,zij)到圆锥曲面的距离: Given the set of data points X∈{x=(x ij ,y ij ,z ij )}, calculate the distance from the spatial point (x ij ,y ij ,z ij ) to the conic surface:
步骤S602,将数据点代入距离最小值的一般表达式,求得数据点到m个第二圆锥面的最小距离值集合。Step S602: Substitute the data point into the general expression of the minimum distance, and obtain a set of minimum distance values from the data point to the m second conical surfaces.
由步骤S6012已知,以及步骤S6014中求出的λ的值,代入距离公式dij中,求出数据点到m个第二圆锥面的距离最小值。Known from step S6012, And the value of λ obtained in step S6014 is substituted into the distance formula d ij to obtain the minimum distance from the data point to the m second conical surfaces.
步骤S603,对数据点到m个第二圆锥面的最小距离值集合分别计算误差,选取误差最小的最小距离值集合对应的第二圆锥面为最佳拟合圆锥曲面。Step S603: Calculate errors respectively for the minimum distance value sets from the data point to the m second conical surfaces, and select the second conical surface corresponding to the minimum distance value set with the smallest error as the best fitting conic surface.
令当Δij小于0.2%时,停止迭代,此时,可以找到最佳的拟合圆锥曲面。make When Δij is less than 0.2%, the iteration is stopped, at this time, the best fitting conic surface can be found.
如图3所示,在位测量条件下利用最小二乘线性拟合三偏心蝶阀密封面的算法,包括如下步骤:As shown in Figure 3, the algorithm of using least squares to linearly fit the sealing surface of triple eccentric butterfly valve under the condition of in-situ measurement includes the following steps:
步骤一:激光测量时,工件放在转台上,转台带动工件匀速旋转,工件每转动相同的角度激光测量一次数据,转动一圈之后,激光传感器完成一次测量;之后激光传感器随Z轴向下移动合适的距离,工件每转动相同的角度激光测量一次数据,转动一圈之后,激光传感器完成一次测量。重复上述操作,最终获得全部的数据点。编码器将采集测量得到的数据传到计算机上。Step 1: During the laser measurement, the workpiece is placed on the turntable, and the turntable drives the workpiece to rotate at a constant speed. The laser measures data every time the workpiece rotates at the same angle. After one rotation, the laser sensor completes a measurement; then the laser sensor moves down with the Z axis. For a suitable distance, the laser measures the data every time the workpiece rotates at the same angle. After one rotation, the laser sensor completes one measurement. Repeat the above operation to finally obtain all data points. The encoder transmits the collected and measured data to the computer.
步骤二:利用相对距离偏差去除异常数据点;每次测量完成一圈时,该组数据的数据点会有两段明显差异的数值,此时较小数值的那组数据较为接近标准数值。按照以上方法设置标准点集,计算其他数据点与标准点集之间的相对平均距离D,同时按照需求设置相对距离偏差阈值ε,若D≤ε,则该数据点符合要求,最终求得所有符合要求的数据点。Step 2: Use the relative distance deviation to remove abnormal data points; each time the measurement completes a circle, the data points of this group of data will have two values that are significantly different. At this time, the group of data with the smaller value is closer to the standard value. Set the standard point set according to the above method, calculate the relative average distance D between other data points and the standard point set, and set the relative distance deviation threshold ε according to the requirements. If D≤ε, the data point meets the requirements, and finally all Data points that meet the requirements.
步骤三:通过建立数据点的空间直线方程并进行最小二乘拟合;通过求得“优化判据”——残差平方和,最后得到空间直线lij和该直线的方向向量为 Step 3: By establishing the spatial straight line equation of the data points and performing least squares fitting; by obtaining the "optimization criterion" - the sum of squares of residuals, the spatial straight line l ij and the direction vector of the straight line are finally obtained:
步骤四:根据得到的空间直线计算锥角并进行拟合得到三维曲面约束为圆锥面,得到圆锥曲面的一般方程。Step 4: Calculate the cone angle according to the obtained space straight line and perform fitting to obtain the three-dimensional surface constraint as a conical surface, and obtain the general equation of the conic surface.
步骤五:对于得到的一般圆锥面方程,通过确定中心点Cm(x,y,z)依次得到进一步拟合的圆锥面;利用多元函数条件极值的拉格朗日乘数法,求出数据点集与圆锥面的距离方程dij;通过计算数据点集与圆锥面的距离方程dij的均值Δij,判断最终拟合得到的圆锥曲面为最优解。Step 5: For the obtained general conical surface equation, obtain the further fitted conical surface in turn by determining the center point C m (x, y, z); use the Lagrange multiplier method of the conditional extreme value of the multivariate function to obtain The distance equation d ij between the data point set and the conical surface; by calculating the mean value Δ ij of the distance equation d ij between the data point set and the conical surface, it is judged that the conical surface obtained by the final fitting is the optimal solution.
虽然结合附图描述了本发明的实施例,但是本领域技术人员可以在不脱离本发明的精神和范围的情况下作出各种修改和变型,这样的修改和变型均落入由所附权利要求所限定的范围之内。Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, various modifications and variations can be made by those skilled in the art without departing from the spirit and scope of the present invention, such modifications and variations falling within the scope of the appended claims within the limited range.
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