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Abstract

Measuring and evaluating geometric errors of an aero-engine blade are a complex research topic. At present, there is not a uniform evaluation criterion and completed strategy in the blade manufacturing industry. This article proposes an effective strategy for measuring and evaluating geometric errors of an aero-engine blade: first, measuring six feature curves and calculating the coordinate transformation value with singular value decomposition to improve the accuracy of blade localization; then, an improved measurement method based on the model offset is introduced to eliminate probe radius compensation errors. Finally, the geometric errors of blade are evaluated using the collected measurement data based on genetic algorithm, and a practical evaluation criterion is provided. The proposed strategy for two aero-engine blades has been performed to demonstrate the effectiveness of the proposed methodology and show that it can prevent false feedback for the underlying manufacturing process for aero-engine blades.

Keywords

Aero-engine blade localization measurement evaluation genetic algorithm

Introduction

The aero-engine blades are designed with extremely strict tolerances in order to ensure efficient energy conversion under the strained operation conditions. Therefore, all manufactured blades must be accurately inspected and evaluated for the sake of conformance to the specified tolerances. Any inaccuracy in evaluating the associated geometric errors may lead to false feedback for the underlying manufacturing process for aero-engine blades. And the geometric errors of blades play an extremely important role in the aerodynamic performance of aircraft engine. So, it is important to develop a correct and effective evaluation method for evaluating correctly geometric errors of aero-engine blades.^1,2

Generally, localization and measurement are two key problems in blade evaluation. The accuracy of measurement data affects directly on the result of blade evaluation. Therefore, a blade must be located accurately before measuring for the purpose of obtaining high-quality measurement data. Nowadays, there are many researches about localization and measurement. Documents of Besl³ apply first the iterative closest point (ICP) algorithm to point cloud registration, which can availably improve the efficiency of registration. And literatures of Jiang⁴ discussed deeply the registration for precision localization of free-form surface. Zhu et al.⁵ discussed various techniques that accelerated the registration process. Amberg et al.⁶ proposed optimal algorithms for surface registration. However, their work about registration and localization concentrated on how to improve the versatility of the algorithm but increased complexity and time cost. And in terms of measurement, the non-contact three-dimensional (3D) scanners and coordinate measuring machines (CMMs) have been widely applied on blade measurement in the industry.^7,8 With the advantage of high speed and the advance on laser technologies, non-contact 3D scanners have been successfully applied on surface data acquisition in reverse engineering. However, laser inspection data are affected by many factors such as part materials, environment, the color of parts, and surface roughness. The measurement data also need to be post-processed before being further used. Sun and Li⁹ presented the application of laser displacement sensor in aero-engine blade measurement; it has the thinner structure and higher efficiency than the CMMs. But because of the improvement of inspection accuracy, more and more purchasers prefer using CMM equipped with touch-trigger probes to measure aero-engine blades. There are many researches concentrated on blade measurement with touch-trigger probes.^10–12 And they discussed some problems about probe radius compensation and measurement path planning.

After accurate localization and measurement, geometric errors of an aero-engine blade can be evaluated correctly. Given the sectional inspection data points, Hsu et al.¹³ proposed to best match the set of discrete data points for each airfoil section onto the corresponding airfoil computer-aided design (CAD) profile. The displacement and rotation errors of an airfoil section were then concurrently evaluated. Li et al.¹⁴ presented a calculation method of twist error of aero-engine blade based on measuring data of CMM. Cheng et al.¹⁵ make a clear analysis of blade blending and torsion deformation, which can become a basis of evaluation. Khameneifar and Feng¹⁶ presented a tolerance evaluation approach based on the reconstruction of the airfoil profile. The position error was isolated from the orientation errors so as to resolve the coupling problem of the existing method. However, these studies above just make local study of measuring and evaluating blade geometry. There is not an efficient evaluation criterion and a completed strategy for measuring and evaluating blade geometric errors.

This article presents a completed strategy for measuring and evaluating blade geometric errors based on genetic algorithm (GA). It aims to provide an effective and correct method of blade evaluation so as to decrease false feedback for correcting the involved blade manufacturing operations. The flowchart of the proposed strategy is illustrated in Figure 1, and it is organized as follows. In the “Blade localization” section, the methodology of blade localization is described, including feature curve measurement and localization results based on singular value decomposition (SVD). The “Improved method of measurement” section presents an improved measurement method, which can eliminate the compensation errors of probe radius. The “Calculation and evaluation” section illustrates a mathematical model of blade evaluation with regional tolerance constraint and provides a solving solution of this model based on GA. The “Experiment results” section illustrates the experimental verification of the proposed strategy. Finally, the “Conclusion and future work” section concludes this article.

Figure 1.

The strategy for measuring and evaluating geometric error of blade.

Blade localization

Inevitably, there are some displacement and rotation errors between measurement points and the corresponding CAD model due to the misalignment of respective coordinate system. It is necessary for blade localization to obtain the displacement and rotation errors before measured. And therefore, the reliable alignment between measurement data of blade and its CAD model is urgent to achieve precise localization.

There are many researches on measurement path planning of blades in literatures of Obeidat and Raman,¹¹ Yu et al.,¹² Li et al.,¹⁷ and Jiang et al.¹⁸ And in this article, six curves specifically are selected as the measurement paths shown in Figure 2. And accordingly, $C_{e}, C'_{e}$ , respectively, represent curves that pass through every cross-sectional leading edge point and trialing edge point on the surface. And $C_{a}, C'_{a}$ pass through two groups of tangent points of maximum thickness circle, and the cross-sectional curves $C_{s}, C'_{s}$ represent the tip cross-sectional curve and the root cross-sectional curve. The position of these six curves can reflect space pose of a blade integrally.

Figure 2.

Measurement paths of blade localization.

Given the pair of point ${p_{i}^{k}, q_{i}^{k}}, i = 1, 2, \dots, n, k = 1, 2, \dots, 6$ obtained by finding the corresponding points $q_{i}^{k}$ on the theory surface of the measurement points $p_{i}^{k}$ , the transformation value $(R, T)$ can be calculated by solving the following least-squares problem, and the mathematical model can be expressed as

F (R, T) = \sum_{k = 1}^{6} \sum_{i = 1}^{N^{k}} {((R \cdot preTran (p_{i}^{k}) + T) - q_{i}^{k})}^{2}

(1)

Mathematically, matrix R represents the angle of rotation around the three coordinate axes and T is the displacement along linear axis. The function $preTran (p_{i}^{k})$ can be described as processing the measurement data, such as weeding out the bad points which have a bad influence on result before solving. The method of SVD can be used to solve this problem, and the detailed proof can be referred in the literatures of Arun et al.¹⁹ and Li and Gu.²⁰

To illustrate the effectiveness of the proposed method for blade localization, a compressor blade machined by grinding is measured by CMM equipped with touch-trigger probes. The deviations of measurement points on six feature curves are shown in Figure 3(a). Localization transformation parameters $([t_{x}, t_{y}, t_{z}, θ_{x}, θ_{y}, θ_{z}]) = [- 0.0095, 0.0293, - 0.0032, - 0.06, - 0.124, 0.031]$ are obtained by the proposed method and the deviations after localization are shown in Figure 3(b). From the comparison of Figure 3, it can conclude that the localization result is accurate and this method can improve the accuracy of blade localization.

Figure 3.

The diagram of deviation comparison: (a) before localization and (b) after localization.

Improved method of measurement

In practice, the surface of a blade is measured section-by-section in engineering. As shown in Figure 4, measurement paths of a blade are cross-sectional curves which provided by designer, and the theoretical sampling points can be generated in the measurement system. However, because of the geometric errors caused by the deformation, there will be an offset between the actual measured points and the theoretical points collected in the measurement system. Furthermore, this deformation of a blade has a bad effect on the normal direction of the blade surface at the contact point. And mistaken normal direction will cause the probe radius compensation errors. To eliminate this compensation error, this article proposed a simple and effective measurement method based on offset model.

Figure 4.

Blade measuring planning paths.

A theoretical offset blade surface $S' (u, v)$ is specified by equation (2)

S' (u, v) = S (u, v) + r \cdot n (u, v)

(2)

where r represents probe radius and $n (u, v)$ represents the normal vector of the blade surface $S (u, v)$ at point $(u, v)$ . The offset model $S' (u, v)$ will be used as the new theoretical model. As shown in Figure 5, $P (u, v)$ represents the actual shape of blade and $P' (u, v)$ represents the trajectory of probe center $p c_{i}$ , which will be collected as the blade actual measurement points. The measurement curve on offset model $S' (u, v)$ and $p c_{i}$ can be used to evaluate geometry of blade. The deviations will be calculated by the minimum distance between $p c_{i}$ and $S' (u, v)$ . This method can thoroughly eliminate probe radius compensation errors.

Figure 5.

Measurement schematic diagram based on offset model.

Generally, the Z coordinate values of sampling points on one cross-sectional curve are invariable theoretically. However, as shown in Figure 6, the geometric deformation of a blade will bring about that the Z coordinate value of the collected probe center $p c_{i}$ is not equal to sampling point $p_{i}$ if the probe moves along the normal vector of a blade surface. In other words, these points collected in the measurement system are not coincided with theoretical points. Therefore, to ensure that the probe center point ${p'_{i}}_{i}$ corresponds to the theoretical point $p_{i}$ , the measurement probe installed on CMM can be planned to move on the section plane parallel to the XY plane instead of moving along the normal vector of a blade surface.

Figure 6.

Deformation analysis for blade measurement.

Calculation and evaluation

Best fitting based on GA

After localization, the measurement points can be obtained based on the method introduced in the “Improved method of measurement” section. And the geometric errors of blades can accurately be evaluated using the measurement points and the corresponding CAD model. Generally, the design tolerance of blade edges is different from the areas of blade body, so the tolerance constraints must be considered in the least-squares problem. It is described as equation (3)

{\begin{matrix} f (x) = \sum_{k = 1}^{M} \sum_{i = 1}^{N^{k}} {‖ d_{i}^{k} (x) ‖}^{2} = \sum_{k = 1}^{M} \sum_{i = 1}^{N^{k}} {((R (x) \cdot \Pr eTran (p_{i}^{k}) + T (x)) - q_{i}^{k})}^{2} \\ s . t . x \in D = {x | μ_{k} \leq d_{i}^{k} (x) \leq ε_{k}, i = 1, \dots, N^{k}} \end{matrix}

(3)

where $N^{k}$ is the number of measurement data and $μ_{k}, ε_{k}$ are different design tolerances in the different feature region $k (k = 1, 2, \dots, M)$ . And $q_{i}^{k}$ is the point on the corresponding CAD model that has the nearest distance to measurement point $p_{i}^{k}$ . Independent variable $x = [Δ x, Δ y, Δ θ]$ represents the rotation angle $Δ θ$ around the normal section plane and displacement $Δ x, Δ y$ along the other two directions.

In this article, because of better favorable and accuracy, the GA is used to solve this problem. And as a global optimization algorithm, GA has been applied in many engineering practices. First, an initial solution $x^{*} = [x_{0}, y_{0}, θ_{0}]$ is obtained by SVD without considering constraint condition, and the feasible solution space is calculated by $Φ (x) = [x_{0} \pm x', y_{0} \pm y', θ_{0} \pm θ']$ . Generally, $x'$ , $y'$ , and $z'$ depend on the accuracy of the solution. The fitness function of GA is defined as equation (4)

fitness F (x) = N + (f (x) / M)

(4)

where N is the number of points beyond tolerance constraint and M represents the total number of measurement points. Obviously, $F (x)$ will rapidly decrease with the decline of N, and $f (x) / M$ will be taken as the evaluation criteria when N is changeless.

The solving process is illustrated in Figure 7. The selection of parameters in GA directly affects the accuracy of the solving result. A set of reasonable parameters are obtained by multiple tests with the MATLAB GA toolbox.

Figure 7.

The flowchart of genetic algorithm.

In order to demonstrate the validity of the proposed methodology, a typical blade is simulated to validate it. The tolerance of blade edge ranges from −0.04 to 0.04 mm, while blade body from −0.04 to 0.07 mm. The number of measurement points is 105. And the theoretical transformation value is $[Δ x, Δ y, Δ θ] = [- 0.05, - 0.0375, 0.05]$ which can ensure that there is no point beyond tolerance. The result using proposed methodology is demonstrated in Figure 8. As shown in Figure 8, the best fitting value approximately converges to zero (actual value: 0.02) when iterations are up to 100 times and the transformation value is $[Δ x, Δ y, Δ θ] = [- 0.0517, - 0.0382, 0.0512]$ .

Figure 8.

Result of solution based on genetic algorithm.

A comparison of ICP without considering constraint condition is listed in Table 1. According to Table 1, the two transformation values $[Δ x, Δ y, Δ θ]$ are basically the same, but the number of points beyond tolerance is zero using the GA and the number of points beyond tolerance is eight using the ICP. Obviously, the accuracy of result using the GA is better than the ICP. However, a limitation that cannot be ignored of GA is the poor calculation efficiency when compared with ICP. It will spend more time for GA to solve registration problems if there are more measuring points and blades. But the correctness of calculation results can be guaranteed using proposed methodology. The ICP algorithm will possibly obtain an untrue result when considering tolerance constraint. Therefore, compared with ICP algorithm, the GA performs more reliable in registration calculation for an aero-engine blade considering tolerance constraint.

Table 1.

The comparison of results between ICP and GA.

Method	Result $(Δ x, Δ y, Δ θ)$	N
ICP	(−0.0498, −0.0379, 0.0422)	8
GA	(−0.0517, −0.0382, 0.0512)	0

ICP: iterative closest point; GA: genetic algorithm.

Evaluation criterion

Actually, profile deviation can be calculated with the distance of point $p_{i}^{k}$ to point $q_{i}^{k}$ after the best fitting. An evaluation criterion of blade geometric errors is provided as equation (5)

{\begin{matrix} μ_{k} < δ_{i}^{k} < ε_{k} \\ S^{k} (δ^{k}) < S_{0} \end{matrix}

(5)

where $δ_{i}^{k}$ represents the directed distance of transformed measurement points to corresponding points on the theory measurement curves and $S^{k} (δ^{k})$ represents the standard deviation of $δ_{i}^{k}$ . $S_{0}$ is threshold value. If entire measurement points meet the design tolerances, the value of $S^{k} (δ^{k})$ will be regarded as an evaluation standard of a blade. Moreover, $x = [Δ x, Δ y, Δ θ]$ acquired in the “Best fitting based on GA” section can be defined as the displacement and rotation errors. The rigid deformation of blade is evaluated by the following equation

{\begin{matrix} Δ Φ = \max (Δ θ j) - \min (Δ θ j) \\ Δ D = \max (\sqrt{Δ x_{j}^{2} + Δ y_{j}^{2}}) - \min (\sqrt{Δ x_{j}^{2} + Δ y_{j}^{2}}) \end{matrix}

(6)

where j represents measurement cross-sectional curves. $Δ Φ$ and $Δ D$ can reflect the blade deformation approximately. Generally, $Δ Φ$ represents the twist errors and $Δ D$ reflects the blending errors.

Experiment results

The developed measurement and evaluation strategy for two aero-engine blades is verified to show its validity compared with the existing methodology in engineering practice.

Example 1

The experimental blade was machined by grinding, and digital model of this blade is shown in Figure 9(a). The blade was measured with three CMMs shown in Figure 10.

Figure 9.

Digital model and measurement model.

Figure 10.

Process of measuring using CMM.

The radius of touch-trigger probe installed on CMM is 1 mm. And the profile tolerance of blade edge ranges from −0.04 to 0.04 mm, while blade body from −0.05 to 0.05 mm. The position tolerance is ±0.2 mm and the orientation tolerance is ±0.3°.

The proposed method will be implemented in accordance with the following process. First, the offset blade model is established in a 3D modeling software (Unigraphics NX), and the measurement path is shown in Figure 9(b). Second, six feature curves are measured, and the result of blade localization is $[0.1219, - 0.023, - 0.0031, 0.009, - 0.013, 0.025]$ which calculated with the method in the “Blade localization” section. Finally, points of probe center on four cross-sectional curves are collected, and the transformation value $[Δ x, Δ y, Δ θ]$ of measurement points on these four curves is calculated with GA considering tolerance constraint. The deviations $δ_{i}^{k}$ and $S^{k} (δ^{k})$ will also be obtained according to the “Evaluation criterion” section. Table 2 shows the evaluation results of the experimental blade using proposed strategy. $S 1$ , $S 2$ , $S 3$ , and $S 4$ represent separately these four cross-sectional curves measured, and Figure 11 shows the deviation between the measurement points and the corresponding section-cross curves after transformation.

Table 2.

The evaluation results using proposed strategy.

	Best fit $[Δ x, Δ y, Δ θ]$	Deviation		Deformation $[Δ Φ, Δ D]$	$S^{k} (δ^{k})$		N
	Best fit $[Δ x, Δ y, Δ θ]$	Maximum	Minimum	Deformation $[Δ Φ, Δ D]$	Edge	Body	Edge	Body
$S 1$	[0.0012, 0.007, 0.015]	0.028	0.002	[0.026, 0.005]	0.0064	0.0041	0	0
$S 2$	[0.0012, 0.009, 0.018]	0.029	0.002		0.0068	0.0044	0	0
$S 3$	[0.0015, 0.010, 0.028]	0.031	0.005		0.0072	0.0039	0	0
$S 4$	[0.0017, 0.012, 0.041]	0.032	0.002		0.0067	0.0042	0	0

Figure 11.

Deviation of section-cross curves.

Obviously, according to Table 2, the number of points beyond tolerance is zero, and both the position and orientation errors are within the given tolerance. From Figure 11, the profile errors of blade also meet the requirement of design tolerance. Therefore, this experiment blade can be evaluated that it is a qualified blade.

However, in engineering practice, this experiment blade is measured and evaluated using the existing methodology, and this methodology is described as follows: (1) blade localization: the traditional 3-2-1 mode, (2) measurement: probe radius compensation based on the theoretical normal of CAD model, and (3) evaluation: using the ICP algorithm without considering the tolerance constraint. The evaluation result is listed in Table 3. From Table 3, there are 10 points beyond tolerance and both the position and orientation errors are evidently greater than the result in proposed method. The evaluation result using the existing methodology shows that the blade is unqualified.

Table 3.

The evaluation result using existing methodology.

	Best fit $[Δ x, Δ y, Δ θ]$	Deviation		Deformation $[Δ Φ, Δ D]$	$S^{k} (δ^{k})$		N
	Best fit $[Δ x, Δ y, Δ θ]$	Maximum	Minimum	Deformation $[Δ Φ, Δ D]$	Edge	Body	Edge	Body
$S 1$	[0.132, −0.027, 0.041]	0.038	−0.012	[0.031, 0.0139]	0.012	0.008	0	0
$S 2$	[0.138, −0.032, 0.048]	0.042	−0.008		0.010	0.008	0	0
$S 3$	[0.141, −0.034, 0.058]	0.050	−0.01		0.011	0.012	0	2
$S 4$	[0.144, −0.034, 0.072]	0.052	−0.008		0.014	0.014	5	3

Example 2

The second experimental blade was machined by computer numeral control (CNC) polishing, and digital model of this blade is shown in Figure 12. The profile tolerance of blade ranges from −0.02 to 0.05 mm. The position tolerance is ±0.1 mm and the orientation tolerance is ±0.17 mm. In this example, two sets of measurement data after polishing this blade are analyzed according to the procedure used in example 1.

Figure 12.

Digital model and measurement model.

For the first set of data, the blade is separately evaluated by the proposed strategy and the existing methodology. Table 4 shows the evaluation results using proposed strategy, and Table 5 shows the evaluation result using existing methodology.

Table 4.

The evaluation results using proposed strategy.

	Best fit $[Δ x, Δ y, Δ θ]$	Deviation		Deformation $[Δ Φ, Δ D]$	$S^{k} (δ^{k})$		N
	Best fit $[Δ x, Δ y, Δ θ]$	Maximum	Minimum	Deformation $[Δ Φ, Δ D]$	Edge	Body	Edge	Body
$S 1$	[–0.0005, −0.0024, 0.0094]	0.0481	0.0085	[0.0991, 0.0055]	0.0033	0.0020	0	0
$S 2$	[0.0019, −0.0022, 0.0381]	0.0472	0.0121		0.0025	0.0051	0	0
$S 3$	[0.0008, −0.0057, −0.0201]	0.0457	0.0125		0.0083	0.0048	0	0
$S 4$	[0.0024, −0.0004, −0.0610]	0.0410	0.0187		0.0077	0.0040	0	0

Table 5.

The evaluation result using existing methodology.

	Best fit $[Δ x, Δ y, Δ θ]$	Deviation		Deformation $[Δ Φ, Δ D]$	$S^{k} (δ^{k})$		N
	Best fit $[Δ x, Δ y, Δ θ]$	Maximum	Minimum	Deformation $[Δ Φ, Δ D]$	Edge	Body	Edge	Body
$S 1$	[−0.0004, −0.0027, 0.0084]	0.0561	0.0095	[0.0981,0.0001]	0.0060	0.0031	0	3
$S 2$	[0.0017, −0.0020, 0.0391]	0.0474	0.0131		0.0030	0.0060	0	0
$S 3$	[0.0003, −0.0047, −0.0171]	0.0537	0.0195		0.0100	0.0052	2	2
$S 4$	[0.0022, −0.0003, −0.0590]	0.0400	0.0137		0.0071	0.0044	0	0

Obviously, from Tables 4 and 5, both the position and orientation errors are within the given tolerance using the two methods. However, there are no points out of tolerance using proposed strategy, and the number of points beyond tolerance is seven using existing methodology. Therefore, this polishing result of experimental blade will be evaluated that it is unqualified using existing methodology due to these points beyond tolerance. But according to the proposed strategy, this blade can be considered qualified.

For the second set of data, the blade is also separately evaluated by the proposed strategy and the existing methodology. The evaluation results of the two methods separately are shown in Tables 6 and 7.

Table 6.

The evaluation results using proposed strategy.

	Best fit $[Δ x, Δ y, Δ θ]$	Deviation		Deformation $[Δ Φ, Δ D]$	$S^{k} (δ^{k})$		N
	Best fit $[Δ x, Δ y, Δ θ]$	Maximum	Minimum	Deformation $[Δ Φ, Δ D]$	Edge	Body	Edge	Body
$S 1$	[0.0033, −0.0038, 0.0166]	0.0504	−0.0009	[0.0260, 0.0033]	0.0060	0.0030	0	1
$S 2$	[0.0035, 0.0020, 0.0010]	0.0494	−0.0082		0.0030	0.0030	0	0
$S 3$	[0.0056, 0.0018, 0.0271]	0.0461	−0.0039		0.0040	0.0020	0	0
$S 4$	[0.0051, −0.0043, 0.0171]	0.0513	−0.0024		0.0060	0.0040	1	0

Table 7.

The evaluation result using existing methodology.

	Best fit $[Δ x, Δ y, Δ θ]$	Deviation		Deformation $[Δ Φ, Δ D]$	$S^{k} (δ^{k})$		N
	Best fit $[Δ x, Δ y, Δ θ]$	Maximum	Minimum	Deformation $[Δ Φ, Δ D]$	Edge	Body	Edge	Body
$S 1$	[0.0030, −0.0036, 0.0146]	0.0544	−0.0008	[0.0260, 0.0035]	0.0080	0.0040	0	3
$S 2$	[0.0036, 0.0021, 0.0010]	0.0495	−0.0082		0.0040	0.0030	0	0
$S 3$	[0.0057, 0.0018, 0.0270]	0.0460	−0.0038		0.0030	0.0020	0	0
$S 4$	[0.0049, −0.0041, 0.0168]	0.0533	−0.0028		0.0070	0.0040	1	2

In Table 6, the number of points beyond tolerance is 2, and in Table 7, the number of points beyond tolerance is 6. By comparing Tables 6 and 7, the number of points beyond tolerance is reduced from 6 to 2 using proposed strategy, and both the position and orientation errors are within the given tolerance.

According to these experiment examples above, obviously, the global profile errors of proposed strategy slightly less than that of existing methodology. The reasons for this situation should include inaccurate localization and probe radius compensation errors in existing methodology. Maybe the transformation value will increase compared with existing methodology, but the position and orientation errors are within the design tolerance. Furthermore, the number of points beyond tolerance mostly is zero or visibly less than that of existing methodology. And the number of points beyond tolerance largely affects evaluation results of blade. Consequently, though the relatively low efficiency, the proposed strategy performs more reliable in evaluating geometric errors of blades considering tolerance constraint when compared with existing methodology. And it can prevent false feedback for the underlying manufacturing process for aero-engine blades.

Conclusion and future work

Measuring and evaluating geometric errors of an aero-engine blade are a complex research topic. At present, there is not an efficient evaluation criterion and a completed strategy for measuring and evaluating blade geometric errors. Therefore, in this article, a systematic strategy for measuring and evaluating geometric errors of aero-engine blades was developed. The main advantage of this strategy is that proposing a systematic procedure supported with precise localization, improved measurement, and effective evaluation, and a practical evaluation criterion was provided in the end. Superior to existing method, the experiment results show that our strategy can effectively evaluate geometric errors of aero-engine blades and prevent false feedback for correcting the involved manufacturing operations.

Under the framework of the proposed strategy, future work will be conducted in the data reduction of measurement points and sections for aero-engine blades. And to establish a more rational evaluation criterion with less measurement data is also an important research topic in the future. The authors plan to concentrate on the measurement data reduction, and try to answer the following two questions:

Which cross-sections should be measured on the profile of blade?

Which points should be measured on each sectional curve?

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work is supported by National Science and Technology Major Project (Grant Number 2018ZX04004001).

References

Khameneifar

Feng

HY.

Airfoil profile reconstruction under the uncertainty of inspection data points. Int J Adv Manuf Tech 2014; 71(1–4): 675–683.

Meng

, et al. Study on the cantilever grinding process of aero-engine blade. Proc IMechE, Part B: J Engineering Manufacture 2014; 228(11): 1393–1400.

Besl

PJ.

A method for registration of 3-D shapes. IEEE Trans Pattern Anal Mach Intell 1992; 14(2): 239–256.

Jiang

LY.

Research on positioning technology of NC machining origin of forging and casting blank and software development. Beijing, China: Beihang University, 2016.

Zhu

Barhak

Srivatsan

, et al. Efficient registration for precision inspection of free-form surfaces. Int J Manuf Technol 2007; 32: 505–515.

Amberg

Romdhani

Vetter

. Optimal step nonrigid ICP algorithms for surface registration. In: IEEE conference on computer vision and pattern recognition, Minneapolis, MN, 17–22 June 2007, p.1491. New York: IEEE.

Zhang

Chen

Ning

Efficient measurement of aero-engine blade considering uncertainties in adaptive machining. Int J Adv Manuf Tech 2015; 86(1): 1–10.

Mahboubkhah

Aliakbari

Burvill

An investigation on measurement accuracy of digitizing methods in turbine blade reverse engineering. Proc IMechE, Part B: J Engineering Manufacture 2018; 232: 1653–1671.

Sun

Laser displacement sensor in the application of aero-engine blade measurement. IEEE Sens J 2016; 16(5): 1377–1384.

10.

Xiao

Huang

Fei

On-machine contact measurement for the main-push propeller blade with belt grinding. Int J Adv Manuf Tech 2016; 87(5–8): 1713–1723.

11.

Obeidat

Raman

An intelligent sampling method for inspecting free-form surfaces. Int J Adv Manuf Technol 2009; 40: 1125–1136.

12.

Zhang

, et al. Adaptive sampling method for inspection planning on CMM for free-form surfaces. Int J Adv Manuf Technol 2013; 67: 1967–1975.

13.

Hsu

T-H

Lai

J-Y

Ueng

W-D.

On the development of airfoil section inspection and analysis technique. Int J Adv Manuf Technol 2006; 30: 129–140.

14.

Huang

. Calculation method of twist error of aero-engine blade based on three-coordinate measuring data. In: Cao

(ed.) AER—advances in engineering research. Amsterdam: Atlantis Press, 2017, pp.843–848.

15.

Cheng

Zhu

Wang

, et al. Blade blending and torsion deformation analysis based on its coordinate measurement data. Adv Mater Res 2013; 715: 1576–1579.

16.

Khameneifar

Feng

HY.

A new methodology for evaluating position and orientation errors of airfoil sections. Int J Adv Manuf Tech 2016; 83(5–8): 1013–1023.

17.

Huang

Research on path planning of aero-engine blade profile measurement based on coordinate measuring machine. In: Cao

Cao

(eds) AER—advances in engineering research. Amsterdam: Atlantis Press, 2017; 849–854.

18.

Jiang

Wang

Zhang

, et al. A practical sampling method for profile measurement of complex blades. Measurement 2016; 81: 57–65.

19.

Arun

Huang

Blostein

SD.

Least-squares fitting of two 3-D point set. IEEE T Pattern Anal 1987; 9(5): 687–700.

20.

PH.

Free-form surface inspection techniques state of the art review. Comput Aided Design 2004; 36(13): 1395–1417.

A methodology for measuring and evaluating geometric errors of aero-engine blades based on genetic algorithm

Abstract

Keywords

Introduction

Blade localization

Improved method of measurement

Calculation and evaluation

Best fitting based on GA

Evaluation criterion

Experiment results

Example 1

Example 2

Conclusion and future work

Footnotes

Declaration of conflicting interests

Funding

References