Geometric Inspection of Film-cooling Holes Via Light-field Imaging*

Sheng-ming Xu Sheng-xian Shi Fei Zeng Ming-yu Gan Yang Li

(1.Shanghai Jiao Tong University；2.AECC Hunan Aviation Powerplant Research Institute)

Abstract：In a high thrust-weight-ratio aero-engine,turbine blades are exposed to extremely high temperature and pressure which sets higher demands in the blade cooling technology.To boost film-cooling effectiveness,an accurate,efficient,and all-sided inspection of film cooling holes is urgently requested to ensure the quality of turbine blades.The tiny size of film-cooling holes adds to extreme difficulties in the inspection process both by contact and non-contact measurement.This paper proposed a non-contact measuring technique to cope with the inspection of turbine blades.A specially designed light-field camera with a small field of view and proper depth of field is applied to resolve a 3D geometry of film cooling holes.The technique uses one light field camera to capture images of the blade surface.3D lightfield reconstruction algoritm is applied and point cloud of the blade is generated.Due to the compactness of the non-contact single light-field imaging system,information inside the holes becomes attainable.By precisely controlling the relative pose of the camera to the blade surface,the device can obtain hole diamter and outlet angle with an accuracy of±0.03mmand±1°17’respectively.The average time consumed forreconstructing one film cooling hole is a bout5 seconds.

Keywords：Film-cooling Hole Inspection；Light-field Imaging；3D Reconstruction

1 Introduction

With the rising demand for a longer lifespan and higher performance of aero-engines,more sophisticated film-cooling holes(FCHs) are being employed in hot end components such as combustor and turbine to ensure the safe running and the long lifetime of the engine.Cooling techniques for highpressure turbine blade is a combination of internal cooling and film cooling [1].Various advanced cooling techniques have made it possible to expose turbine blades to a higher gas temperature.Many studies have found that the design of FCHs,especially by using shaped holes,will help boost cooling efficiency significantly [2-5].The widely used FCHs nowadays are round and fan shaped ones subject to structural strength and limitations in the machining process.Non-traditional machining process,namely laser drilling [6],electrodischarge machining(EDM),and electrochemical machining(ECM)[7-8],are facing challenges in guaranteeing consistency and reliability of FCHs.The main procedures of the commonly used EDM are drilling,coating,and expanding.These operations will have an impact on the stability of machining quality.Comparatively,laser drilling,particularly femtosecond laser,can improve the quality of FCHs effectively but is susceptible to machining environment and laser parameter.Moreover,the polarization of light tends to deform the shaped holes [9].Other studies [10-11] have suggested that machining errors of FCHs will lead to local blockage during operation and thus cause changes in the geometric parameters (cross-sectional area,equivalent diameter,outlet angle)upon which cooling efficiency is dependent.

A highly efficient and high-precision inspection technique for massive FCHs on hot end components in an aeroengine is urgently demanded to ensure machining quality and to prolong lifespan of the components.There are a few proven techniques that address inspection and at least meet the industrial requirement.

These techniques include a coordinate measuring machine (CMM) that applies a probe in detecting the profile of a blade.The probe is moved according to a planned path along the blade surface.The size of the spheric probe is taken into consideration by an algorithm to resolve 3D coordinates of the sampled points.CMM can barely be employed in a measurement task of FCHs as the diameter of probes with even the smallest size is still larger than that of the hole exit section.Some researchers have investigated the usage of micro-probes whose diameter is around 50μm.They use fiber deflection probes to reconstruct the inner morphology and depth of FCHs [11-12].Though being highly accurate,the point by point scanning approach falls behind in terms of efficiency.

Measurement based on 2D imaging is a non-contact one that is aimed at improving accuracy and efficiency.Imaging devices and a turbine blade are mounted on a high-precision translational and rotational platform for the acquisition of information.Image recognition algorithms are then applied to obtain hole diameter and shape.Though being convenient and fast in its implementation,this technique fails to detect depth information and thus is insufficient in obtaining comprehensive hole parameters.

The focus of FCHs inspection is the measurement of diameter and outlet angle of round FCHs whereas few methods have been dedicated for measuring section area,equivalent diameter,outlet angle of shaped holes.This problem belongs in nature to 3D geometric measurement.Laser beam scanning [13-14] and acoustic emission touch testing [14-16] are proposed for measuring 3D information of micro-holes,yet they are facing certain limitaions and challenges when it comes to productization.Laser beams tend to reflect several times on the inner surface of micro-holes,resulting in difficulties in image capture.Acoustic ways are less efficient than a production line requires.Methodology that addresses fast and robust FCHs inspection should be the research focus of the coming stage.This paper is based on previous researches of 3D reconstruction via light-field imaging[17-18]and it describes the exploration of fast light-field imaging technique in the inspection of FCHs.

2 Principle of Light-field Imaging

2.1 Concept

It is possible to describe light propagation by assigning a plenoptic function for each light ray.An arbitrary point on a light ray can be represented by a 5-dimensional plenoptic function,i.e.light-field function,L(x,y,z,θ,φ)[19-20].(x,y,z)are spatial coordinates and(θ,φ)are azimuth and elevation angles as shown in Fig.1.In the case of measuring FCHs,light is considered to propagate in a uniform media without any blockage.The 5D representation can be thus simplified to a 4D one asL(u,v,s,t).As indicated by Fig.1(b),an object can be reconstructed by back-propagating a completely recorded 4D light-field.

Fig.1 Two representations of light-field

Unfortunately,to obtain clear images,the traditional 2D imaging technique uses image sensors to gather focused light rays that propagate from an object,go through the camera lens system,and reach some pixels on the sensor plane.This kind of imaging process records only intensity and spatial information of incident rays while missing the angular information of light rays.As suggested by Fig.2,the principle of light-field imaging is different from the traditional 2D imaging.A micro-lens array (MLA) is mounted in front of the image sensor in a light-field camera to split light rays.The split rays are then recorded by the image sensor as angular information.This kind of camera architecture allows 4D plenoptic functions to be recorded and enables 3D object reconstruction.

Fig.2 A comparision between(a)

The whole imaging process demonstrated in Fig.2(b)can be described as light rays from an object,a representation of a FCH,in this case,going through the camera main lens system and reaching the MLA plane.Each micro-lens will split rays with different orientations and project them onto different pixels on the image sensor,meaning there is a connection between one object point and a couple of pixels even if the camera is ideally focused on the object.The images recorded by a light-field camera are called raw light-field images here.According to the light-field imaging principle,each pixel beneath a micro-lens corresponds to a unique incident angle.The number of pixels one micro-lens covers is thus a measure of angular resolution of a recorded light-field[21].By rendering a raw light-field image,sub-aperture image array can be obtained which represents images resulted from different viewing angles.In this way,a light-field camera can be treated as a virtual array of small cameras.The 3D reconstructing algorithm is based on converting images with parallax into a point cloud of the recorded objects.

Fig.3 displays the flow chart of the FCHs inspection method based on light-field imaging.The centers of each micro-lens must be measured before any further operations can be performed.This step is called the MLA calibration.There are two feasible ways of MLA calibration.One way is to take an image of a whiteboard with diffuse reflection.The other way which is adopted in this paper is to adjust the camera aperture to its minimum and record the image of such a whiteboard.By locating micro-lens centers on the image,coordinates of each micro-lens are calculated.After MLA calibration,perspective shift is performed to extract sub-aperture images.A camera metric calibration is implemented before the 3D reconstruction takes place.These two procedures produce a point cloud of the measured area.Finally,feature extraction is carried out for extracting FCH parameters.

Fig.3 Flow chart of the methodology

2.2 Reconstruction Principle

2.2.1 Extracting Sub-aperture Images

After obtaining centers of each micro-lens,an area of Nby-N pixels is identified beneath each micro-lens.By taking out a specific pixel with the same local coordinates from each micro-lens and rearranging them,a sub-aperture image of a certain viewing angle is generated.From the perspective of light-field imaging,the intersection of a light ray with the camera main lens is regarded as(u,v),then the intersection of the same ray with the MLA plane is (s,t).When performing the just-stated operation,we are equivalently keeping (u,v)fixed and counting every(s,t)value.

As indicated by Fig.4,perspective A means viewing the object from the uppermost part of the main lens aperture.Light rays that pass perspective A will propagate to the same local pixels beneath the micro-lenses.The sub-aperture image A is obtained by aligning those pixels in a way that they are distributed on the MLA plane.The steps hold the same for perspective B to E.The total number of possible perspectives is equal to the number of pixels under a micro-lens,which is,in this case,represented as N-by-N.In practice,micro-lenses are circular,leading to a vignetting phenomenon that reduces the total number of usable perspectives.In conclusion,by applying rendering algorithms,multiple sub-aperture images can be obtained from one raw light-field image.It is worth noting that,there exists parallax between every two different sub-aperture images which will be taken advantage of in the later 3D reconstruction process.

2.2.2 3D reconstruction based on parallax

Epipolar constraint is applicable in the sub-aperture images extracted from a raw light-field image.By taking one certain row (or column) of pixels from sub-aperture images of the same row (or column) and stacking these rows of pixels,an epipolar plane image (EPI) is formed.Fig.5(a) shows one certain row (or column) of pixels and the corresponding EPI.In the EPI,slope values imply information about the depth of each sampled point.To give an intuitive explanation between EPI slopes and object depths,Fig.5(b)uses multiple traditional cameras aiming at the targeted object to signify multiple sub-aperture images.The images from each camera are given below.In the example EPIs,the red circle holds a positive slope value while the blue one has a negative slope.This can be interpreted as: the red circle is within the plane of focus(PoF)while the blue one is outside the PoF.The yellow circle is set right at the PoF that leads to a zero slope.Therefore,parallax can be quantified by calculating slopes on an EPI.

Fig.5 (a)An example EPI;(b)relation between EPI slope and object depth metric calibration

2.2.3 Metric Calibration

The camera metric calibration converts the magnitude of parallax to real physical depth.The way light propagates inside the camera system is shown in Fig.6.A bunch of rays emitting from point sourcePare refracted by the main lens and converge at pointQ.They propagate forward and form a circle of confusion on the MLA plane.The center is denoted asClfand its diameter isDlf.Then the light rays go across the MLA and eventually reach different pixels on the sensor plane,forming a projected circle of confusion.The center is denoted asCdfand its diameter isDdf.Characteristics of a confusion circle(Cdf,Ddf)are solvable out of the scattered patterns on the image plane[22].

Fig.6 Propagation model of light inside a light-field camera

Wherelpjandpciare micro-lens center and center of its scattered pattern respectively.siis the image distance.flis the focal length of the micro-lens.In this case,metric calibration is performed through building a deterministic relation between the characteristics of the confusion circle and the point object.

Without loss of generality,the center of the main lens is set as the origin in this paper.Thez-axis is set as the main lens axis that points outside the camera.In the light-field projection model,the main lens is regarded as a thin lens while the MLA is viewed as a pin-hole array model for simplicity.By applying Gaussian optics,a relation between the depthPzof object pointP(Px,Py,Pz)and its confusion circle diameterDdfcan be derived as:

Wherepmis the effective main lens aperture andfmis the main lens focal length.sois the object distance.ppis the pixel pitch.PointP,O,andQare on the same line and the projected confusion circle centerCdfis on the extension line ofPOQ.Equations can be derived according to rules of similar triangles:

3 Experimental Practices

3.1 Test Rigs and Procedures

This paper includes a measurement test of some turbine blades to validate the proposed technique.As Fig.7 demonstrates,the measurement system consists of a monochrome industrial grade light field camera (VOMMA VA4300-MCL,7192×5432px),a composite main lens (AF Micro-Nikkor 200mm f/4D IF-ED and AF Nikkor 50mm f/1.4D mounted together by a 50～62 adapter ring),and a testing platform.The measurement procedures are:

Fig.7 FCHs measurement system based on:(a)light-feld imaging;(b)confocal microscopy

1) Metric calibration.This investigation applied a volumetric calibration for a light-field camera[24].A calibration board with a 0.4mm dot array on it is placed on a high-precision translational stage(Thorlabs LNR50S/M,0.1μm).The translation range covers 300μm in front of and behind the PoF.The translation step size is 20μm.There are a total of 31 positions where images are recorded.Relations between object points and their confusion circle characteristics are built out of raw calibration images.

2) Raw image capture.In Fig.7,the camera is placed downwards to capture images of the illuminated turbine blade (illumination omitted in Fig.7).The illumination is optimized by applying tiny bulbs or optical fiber according to the actual situation.Raw images are rendered and sub-aperture images are extracted.Parallax is quantified using EPI.

3)Parallax to depth conversion.The parameter obtained in step (1) is used to convert parallax (obtained in step 2) into real physical depth.

The whole process is accelerated by GPU.A point cloud with 436000 points can be calculated with 5 seconds.The robustness of the measurement is only subject to different illumination strategies,which is rather an engeneering problem that will not be included here.

3.2 Result and Analysis

To validate the system accuracy,a blade with roughly 50 film cooling holes are tested both with light-field imaging and confocal microscopy.The metrology equipment of the latter is AliconaμCMM with has an accuracy of less than 1μm.The accuracy is high enough for its results to be considered as gound truth.The blade is scanned and measured by the device automatically and a point cloud is generated.Fig.8(a)and(c)displays results generated by the AliconaμCMM.Parameters such as hole diameterdand outlet angleαis calculated.

Limited by magnification,field of view,and current resolution of the light-field camera,the experiment only focuses on a local area with FCHs on it.

The measured data is shown in Fig.8(b).It is in the format of a colored point cloud from which FCH parameters are extracted.Though fitting the point cloud of one FCH to the shape of a cylinder,αanddcan be calculated.Tab.1 shows the comparision between the results.The parameters of FCHs measured by light-field imaging is valid.Moreover,the time consumed is greatly reduced.

Tab.1 Data acquired by light-field imaging and confocal microscopy

4 Conclusions

This paper proposed a method for geometric measurement and inspection of film cooling holes using light field imaging.The technique uses one light field camera and highly efficient algorithms to reconstruct 3D geometry of filmcooling holes.Point coulds from confocal microscopy and light field imaing are compared to validate measurement precision,revealing an averaged system precision of 1°17’and 0.03mm in terms of FCH outlet angle and hole diameter.The time consumed per FCH is reduced from 30min to 5s.The future work is to further raise the accuracy,to reduce data fluctuation and to be robust under different conditions.