Issue |
JNWPU
Volume 37, Number 4, August 2019
|
|
---|---|---|
Page(s) | 767 - 773 | |
DOI | https://doi.org/10.1051/jnwpu/20193740767 | |
Published online | 23 September 2019 |
Research on Influence of CMM Sampling Points on Detection of Feature Parameters for Turbine Blade
CMM采样点对涡轮叶片特征参数检测精度的影响
School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China
Received:
30
September
2018
Sampling plan is an essential part for measuring profile of turbine blade with coordinates measuring machine(CMM), and the detection of feature parameters is a key component of turbine blade inspection. However, the influence of the sampling strategy on the blade feature parameters evaluation has been rarely studied. In order to understand the correlation between the sampling strategy and the accuracy of blade profile feature parameters, firstly, the extraction methods of turbine blade feature parameters were proposed, and these methods were compiled into an executable program TBGeoInspect. Secondly, based on the level principle, the unified mathematical representations of uniform sampling, curvature-based sampling, chord deviation sampling, weighted curvature-based sampling, and curvature-arc length sampling were given. The effect of these five sampling algorithms on the accuracy of turbine blade profile feature parameters was gained through simulation and experiment results of blade sampling. The results validate that the uncertainty of turbine blade feature parameters and sectional curve fitting error are lowest with curvature-arc length sampling method under the same number of sampling points.
摘要
采样点规划是涡轮叶片三坐标测量的必要步骤,特征参数是涡轮叶片的重要检测内容之一。但目前,采样点分布对涡轮叶片特征参数检测精度的影响研究尚处于空白。针对此问题,给出了涡轮叶片特征参数的计算方法并开发了相应软件;基于杠杆平衡原理,研究了适用于自由曲线曲面的均匀采样、曲率采样、弦公差采样、加权曲率采样和曲率-弧长采样算法。通过测量仿真与实验,研究了这5种采样算法对涡轮叶片叶型特征参数计算精度的影响;结果表明:采用曲率-弧长采样算法得到的叶型特征参数的计算误差和叶型曲线拟合误差均小于其他4种采样算法。
Key words: turbine blade / feature parameter / mean camber line / wall thickness / sampling strategy
关键字 : 涡轮叶片 / 特征参数 / 中弧线 / 壁厚 / 采样
© 2019 Journal of Northwestern Polytechnical University. All rights reserved.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
涡轮叶片是涡轮机械的主要组成部分, 是航空发动机最重要的零件之一。新一代航空发动机进气口温度高达1 600~1 900℃, 单晶+复合气膜冷却技术是涡轮叶片的主流结构形式, 采用定向凝固、激光脉冲加工、涂层、超精密磨削等制造工艺, 工序复杂, 变形难以控制[1]。目前, 三坐标测量是涡轮叶片外形尺寸的主要检测方式, 测量精度高、灵活性强, 是目前最可信的涡轮叶片数字化检测方法[2]。
采样点规划是三坐标测量的重要组成部分, 也是自由曲线曲面测量的难点。很多学者对自由曲面曲线采样规划方法做了大量研究, 出现了随机采样[3]、曲率/曲率矩加权采样法[4-6]、细分采样法[7-10]、基于面片曲率的采样法[11]、基于面片大小的采样法[12]、混合采样法[13]、删点采样法[14-15]、二次采样法[16]、弦公差采样法[17-18]等。几乎所有研究都是针对轮廓度误差、弯扭度误差或逆向建模等, 很少研究叶片采样点对叶型参数的影响。而涡轮叶片特征参数是有明确的物理意义的, 是叶片设计制造过程中必须考虑的因素。
涡轮叶片的设计方法可分为2类:①基于控制点, 即按照气动载荷与性能要求, 通过求解微分方程获得叶盆、叶背上关键控制点的坐标, 根据这些控制点, 由分段圆弧、多项式曲线、Bezier曲线或B样条曲线等插值生成叶型线; ②基于叶型特征参数, 由中弧线控制参数及壁厚控制参数生成叶片的中弧线模型及厚度模型, 通过圆心在中弧线上的内切圆构成包络线来生成叶型线。基于叶型特征参数的涡轮叶片设计, 可描述叶片变形与特征参数之间的关系, 能够可靠地设计出高性能的叶型, 越来越受到研究者的重视, 结合叶型参数化设计及计算流体动力学理论出现很多涡轮机械设计软件, 如TURBODesign-1, PropCad, FINE/Design3DTM, BladePro, BladeCAD, AXCAD, T4T等[19]。
涡轮叶片叶型特征参数与其气动性能直接相关, 特征参数检测是叶片尺寸检测的重要内容之一。而三坐标测量点对计算涡轮叶片叶型特征参数的影响尚处于空白。因此, 研究不同三坐标测量点对涡轮叶片叶型特征参数检测精度的影响是非常有意义的。
1 叶型特征参数
涡轮叶片叶型特征参数分为中弧线控制参数:内弦长、安装角、最大挠度、最大挠度位置、前缘几何进气角、后缘几何出气角; 厚度控制参数:最大厚度、最大厚度位置、前缘半径、后缘半径、前缘楔形角、后缘楔形角。如图 1所示, 其中L为弦长, r1为前缘半径, r2为后缘半径, rmax为最大厚度, Fmax为最大挠度, Pmax为最大挠度位置, β为安装角, α1为前缘进气角, α2为后缘出气角, γ1为前缘楔形角, γ2为后缘楔形角。
叶型特征参数提取[20]分为以下几步:
1) 去除噪声点:
a) 手动删除明显噪声点;
b) 删除凸侧噪声:设Pi-1, Pi, Pi+1为3个相邻测量点, ki-1, ki, ki+1分别为点Pi-1, Pi, Pi+1的估算曲率, Vi-1, Vi, Vi+1分别为点Pi-1, Pi, Pi+1指向曲率圆心的矢量。如果ki满足(1)式则Pi为凸侧噪声点, 删除Pi, 并重新计算ki-1, ki+1;
c) 删除凹侧噪声:满足(2)式, 则Pi为凹侧坏点, 删除Pi, 并重新计算Vi-1, Vi+1;
2) 弦线的提取:通过凸包算法, 以叶型测量点凸包多边形最长边为弦线, 其长度为弦长, 其与发动机轴线夹角为安装角。
3) 前后缘半径的提取:通过最小二乘圆弧拟合算法, 选取前(后)缘测量点, 记为(xi, yi) i=1, 2, …, n, 构建矩阵A,B,T, 则前(后)缘圆心为(c1, c2), 前(后)缘半径为。
4) 中弧线的提取:通过叶背(盆)点, 使用三次B样条插值算法, 以前后缘与叶背(盆)分界点作为端点约束, 以分界点切矢作为端点切矢约束, 构建叶背(盆)曲线, 然后采用等半径法求中弧线[21]。在中弧线提取过程中可得到最大厚度、最大厚度位置、最大挠度、最大挠度位置、前缘进气角、后缘出气角、前缘楔形角、后缘楔形角。
结合上述叶型参数提取算法, 采用VC++6.0以及VTK(visualization tool kit)可视化工具包, 开发了涡轮叶片尺寸测量软件TBGeoInspect, 界面如图 2所示。
1 叶型特征参数示意图 |
图2 TBGeoInspect用户界面 |
2 自由曲线采样算法
自由曲线采样方法可以分为3类:①删点法:是在密集均匀采样点的基础上, 以法矢、切矢或相邻采样点连接直线的夹角为判定条件删除不必要的点; ②增点法:在采样关键点的基础上, 以最小采样密度、弦公差或拟合误差为采样准则, 迭代增加采样点;③直接法:直接对曲线按一定准则计算采样点。删点法主要依据曲率相关准则删除点, 与曲率采样结果近似, 对叶型的采样效果并不好[22]; 增点法需要计算叶型关键点, 而且逐步迭代增加采样点, 计算过程复杂。直接法直接针对曲线形状, 几何意义明确, 计算简单, 通过调整采样准则可方便的调整采样点的分布, 在自由曲面测量中应用较广。杠杆平衡原理[5]在自由曲线直接采样中有广泛的应用, 如图 3所示, 杠杆平衡条件满足
式中, mi是点i和点i+1之间曲线段的“质量”。
根据mi的不同计算方式, 可实现不同的采样方法:
1) 均匀采样(包含等参数采样和等弧长采样):
等参数采样以曲线段的参数增量作为曲线段质量, 如(7)式所示
式中, ti和ti+1分别是点i和点i+1的曲线参数。
等弧长采样以曲线段的弧长作为曲线段质量, 可由参数曲线的弧长微分公式表示, 如(8)式所示
式中, , C(t)为曲线方程, ‖·‖2为向量范数。
2) 弦公差采样:
以曲线段的弦高作为曲线段质量, 弦高可由(9)式[17]表示
式中, k(ti)为参数ti曲线的曲率, li为点i和点i+1间弧线的长度。
3) 曲率采样:
以曲线段的曲率积分作为曲线段质量, 如(10)式所示
式中, k(t)为参数t处曲线的曲率。
4) 加权曲率采样[5]:
以曲线段的加权归一化曲率作为曲线段质量, 如(11)式所示
式中, kmax和kmin分别是曲线C(t)的最大曲率和最小曲率, λ为权重系数。
5) 曲率-弧长采样[23]:
以曲线段曲率比重和弧长比重的加权和作为曲线段质量, 如(12)式所示
式中, t为曲线参数, t∈[0, 1];λ为权重系数。
加权曲率采样和曲率-弧长采样算法中, 通过调整权重系数λ的大小, 可调整曲率和弧长的比重。λ值越大, 越接近于等弧长采样, λ值越小, 越接近于曲率采样。
3 自由曲线采样点 |
3 仿真讨论
以某叶型截面线为例, 分别采用均匀采样(等弧长)、弦公差采样、曲率采样、加权曲率采样(λ=0.03)和曲率-弧长采样(λ=0.5)规划测量点, 算例中的权重系数λ是以拟合误差为目标函数的优选值, 采样点分布如图 4所示:
选取前缘半径、后缘半径、弦长、最大厚度、最大挠度点作为叶型的主要特征参数。采用上述5种采样算法分别规划20~200个测量点, 计算特征参数并与理论值比较, 结果如表 1所示, 其中, 最大挠度点误差以最大挠度点的波动半径表示。对测量点进行三次B样条插值并与理论曲线对比, 插值误差如图 5所示。
通过表 1可以看出, 5种采样算法对最大厚度的计算精度都比较高; 均匀采样由于在前后缘点分布密度不够, 导致前后缘识别不是很准确, 从而影响前后缘半径及弦长的计算精度; 曲率采样由于大部分采样点都分布在前后缘, 对前后缘半径的计算精度最高; 曲率-弧长采样对5个关键叶型特征参数的计算精度都比较高, 而且对最大挠度点的计算精度明显高于其他采样方法。从图 5a)最大插值曲线误差和图 5b)平均插值曲线误差可以看出, 采样点数小于100时, 曲率-弧长采样点的曲线插值误差小于加权曲率采样点和弦公差采样点, 明显小于均匀采样点和曲率采样点; 曲率-弧长采样算法能用更少的点表征叶型曲线的曲率形状信息。因此, 曲率-弧长采样更适合叶片采样点规划。
图4 采样点分布 |
叶型参数计算误差
5 采样点插值误差 |
4 测量实验
以涡轮导叶精铸件为例, 如图 6所示, 取A-A截面, 分别采用均匀采样、曲率采样、弦公差采样、曲率-弧长采样、加权曲率采样规划50, 100, 150, 200个采样点。通过专用夹具固定导叶, 使用三坐标测量机(型号型号:GLOBAL D STATUS 121510)触测采样点。对采样点的测量值去噪声处理后进行三次B样条插值, 并导入到TBGeoInspect软件中, 计算A-A截面的叶型参数, 结果如表 2所示。
图 7中, A, B, C, D分别为前缘半径波动范围、后缘半径波动范围、弦长波动范围和最大壁厚波动范围; E为最大挠度点波动半径, 用所求最大挠度点最小外接圆的半径表示。通过表 2和图 7a)~e)可以看出, 弦长和最大厚度的波动误差最小; 前缘半径的波动误差大于后缘半径的波动误差; 曲率-弧长采样计算叶型参数的波动误差明显小于其它4种采样算法。
图6 涡轮导叶三坐标测量实验 |
A-A截面测量数据叶型参数计算结果
7 叶型特征参数误差范围 |
5 结论
本文通过仿真与实验, 研究了均匀采样、曲率采样、弦公差采样、加权曲率采样、曲率-弧长采样点对叶型特征参数及轮廓误差计算精度的影响, 可得出如下结论:
1) 最大厚度和弦长的计算精度受采样点分布的影响较小;
2) 前缘半径受采样点分布的影响大于后缘半径;
3) 曲率-弧长采样对叶型特征参数计算的误差小于均匀采样、曲率采样、弦公差采样和加权曲率采样;
4) 采样点数相同时, 曲率-弧长采样点的插值误差小于加权曲率采样和弦公差采样, 明显小于均匀采样和曲率采样。
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All Tables
All Figures
1 叶型特征参数示意图 |
|
In the text |
图2 TBGeoInspect用户界面 |
|
In the text |
3 自由曲线采样点 |
|
In the text |
图4 采样点分布 |
|
In the text |
5 采样点插值误差 |
|
In the text |
图6 涡轮导叶三坐标测量实验 |
|
In the text |
7 叶型特征参数误差范围 |
|
In the text |
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