Yu Jinhu,Chen Zhitong,Jing Zepeng

aSchool of Mechanical Engineering and Automation,Beihang University,Beijing 100083,China

bAVIC Commercial Aircraft Engine Manufacturing Co.,Ltd.,Shanghai 201306,China

cCo-Innovation Center for Advanced Aero-Engine,Beijing 100083,China

An approach for machining distortion measurements and evaluation of thin-walled blades with small datum

Yu Jianhuaa,b,c,*,Chen Zhitonga,c,Jiang Zepenga

aSchool of Mechanical Engineering and Automation,Beihang University,Beijing 100083,China

bAVIC Commercial Aircraft Engine Manufacturing Co.,Ltd.,Shanghai 201306,China

cCo-Innovation Center for Advanced Aero-Engine,Beijing 100083,China

Inspection techniques for aero-engine blades are a hot topic in industry.Since these blades have a sculptured surface and a small datum,measurement results may deviate from an actual position.There are few proper approaches compensating for non-uniform distribution errors that are within specified tolerance ranges.This study aimed to develop a meshing structure measuring approach for the distortion of blades via non-contact optical 3D scanning.A rough measurement and a registration procedure are initially adopted to rectify the coordinate system of a blade,which avoids the initial coordinate system errors caused by the small datum.A measurement path with meshing structure is then unfolded on the blade surface.For non-uniform distribution errors,the meshing structure measurement is more visual and clear than the traditional constant height curves method.All measuring points take only 7 min to complete,and the distribution of error is directly and accurately presented by the meshing structure.This study provides a basis for future research on distortion control and error compensation.

1.Introduction

The surface curvature of blades is becoming increasingly complex with the development of high bypass turbofan engines.Such engines require thin blades with high thrust-to-weight ratios to improve sustained performance.1,2Inspecting and analyzing machining distortions are indispensable for evaluating processing methods for two reasons:(1)The quality of a machined blade can be judged against its accuracy requirement;and(2)Distortion analysis may provide reasons for blade non-conformity and suggestions for quality improve-ment.Since blades constitute a high proportion of an aeroengine and significantly affect its aerodynamic efficiency,rapid measurement and accurate evaluation of machining distortions is critical.3–5

Hsu et al.6attempted to apply coordinate measurement techniques to a blade section measurement method in order to evaluate blade dimensions and geometric tolerance.They initially determined the coordinate system of a blade and proposed a two-step measurement procedure.An analysis process for blade parameters was discussed and an algorithm related to the optimal positioning of measurement data was then developed.Mansour7provided a small number of points for a simulation method via contact 3D scanning while remaining within the allowable deviation.Fu et al.8proposed a 3D pro file measurement method based on multi-value coding.Their paper mainly discussed the principle of a non-contact 3D profile and generalized a measurement system for blades.A machining distortion is frequently evaluated by investigating bending and torsion deviations between a nominal machined surface and an actual machined surface.9–11However,such an evaluation fails to comprehensively analyze issues involving each blade’s machined distortion area according to the measurement data,particularly with blades of complex curvatures and small datum.

Non-uniformly distributed errors can still be observed even when bending and torsion deviations are tolerable.The imbalance of rotors,which is caused by non-uniformly distributed errors and scallop heights after machining is one of the main causes of vibration and noise in aero-engines,12directly decreasing work performance and fatigue life.13Adaptive machining or adaptive repairing of curved blades through geometric reconstruction has been widely adopted.14,15Given a small datum or the lack of an assistant datum to help locate a blade,it is difficult to inspect a manufactured surface that best fits a design model.Therefore,a rapid and accurate measurement method should be developed to locate distortions.Existing tools such as the touch trigger probe have several disadvantages,such as slow sampling speed and the radius compensation error of its stylus ball.16,17The present study proposes a method for analyzing and evaluating distortions based on non-contact measurements and the shape of a blade.Li et al.18,19systematically presented an introduction of simplification,smoothing and parameter extraction with respect to point-sampled blades,and achieved section curve reconstruction and mean-camber curve extraction with the representation of a point cloud.This work promotes the development of optical measuring as applied to blade inspections.

Fig.1 Deviation of a contact CMM.

The remaining parts of this paper are organized as follows:Section 2 analyzes several problems in existing contact measurement blade inspection techniques by investigating a sharply curved blade with small datum,then presents how highprecision and high-speed data measurements of the blade can be obtained.Section 3 discusses the measurement process of a blade’s curved sections and how distortion is accurately inspected in three steps.Finally,a sample blade is validated in Section 4 to demonstrate the overall procedure and to illustrate the necessity and feasibility of the proposed method.

2.Measurement principles of blade distortion

2.1.Problems in blade distortion inspections

2.1.1.Mismatched contact points

The profile and positional error of a cross-section curve are generally used to evaluate blade surface measurements.A blade surface is typically composed offour areas:pressure surface,suction surface,leading edge,and trailing edge.The leading and trailing edges are extremely small and sharp and,with a curvature radius of approximately 0.1 mm,are difficult to measure.Whencontactcoordinatemeasuringmachines(CMMs)are used for blade inspection,the distortion of the workpiece,particularly near the leading/trailing edges,may result in a substantial deviation between the workpiece and the computer-aided design(CAD)measurement model.As shown in Fig.1,r is radius of ruby ball stylus,point p is the planned position of the measurement path.However,the real contact point is point q,which corresponds to the model profile.This phenomenon leads to the data of point q re flecting the position of point p′.In addition,the contact probe records the center of its ball end.The data used for workpiece localization are the coordinates of the points where the probe is in contact with the workpiece.Compensating for the probe radius also introduces errors during a sharp change in the curvature of a surface.Moreover,a high-precision measurement using a CMM requires scanning in small steps,thus measuring the sheer volume of data points is a time-consuming process.

With the advancement of laser technologies and the improvement of measurement accuracy,non-contact 3D scanners have been successfully applied to surface data acquisition in the industry.15Fast and large CCD arrays have been commercially developed for spectroscopic applications.The introduction of CCD arrays is an important breakthrough in range sensors based on 3D active triangulation.Coupled with enhanced processing,these devices have improved range accuracy to 0.01%,which enables the acquisition of huge amounts of data to provide high-quality results.16The optical CMM based inspection system has advantages in performing rapid data acquisition,measuring complex(narrow)geometry,and performing global inspections for a component with freeform surfaces.11,20,21

2.1.2.Inaccurate location of small datum

Many turbine blades have small,single-ended datum located away from the blade body as shown in Fig.2.The datum and the extra parts will be cut off as indicated by the cutting lines in the figure.When inspecting such blades,the construction of the measurement coordinate system generates errors caused by the small datum as it moves away from the body surface.

2.1.3.Non-uniform distribution errors

Machining distortion can be controlled within the tolerance limits by using novel distortion control methods and processes.These include a machining distortion control method that uses an adaptive dual-arm fixture22or a cantilever grinding process,23an adaptive sliding mode control based on extended state observer24and a non-uniform offset surface rigidity compensation strategy.9However,the machining error exhibits a non-uniform distribution feature on the blade surface as shown in Fig.3.The non-uniform distribution negatively affects the work performance of an aero-engine.Nevertheless,the machining distortion problem has been largely overlooked in numerical control machining,especially in the blade manufacturing process.

2.1.4.Measuring method by meshing structure

As shown in Fig.4(a),the measurement path of a blade usually uses the constant height curves method,which is conducive to computational profile tolerance.Measurement curves commonly adopt the constant height curves of the design plan.However,traditional methods cannot satisfy the perfect distortion evaluation of non-uniform blade errors.The number of section curves for inspection is increased with lengthways sections.These curves are defined in the original isoparametric curves in Fig.4(b).The ends of blade are the most distortional parts;therefore,additional offset curves are made based on the constant height.The constant height curves and the isoparametric curves together make up a meshing structure measurement.The distortions in different areas are evident because of errors in the measurement of the meshing structure.

Fig.2 Blades with small datum.

Fig.3 Distortion distribution of a blade.

Fig.4 General measurement and meshing structure method.

There are thousands of blades on each engine,all of which need to be inspected.But,at present,the CMM method is too time-consuming to restrict the spread and application of the meshing structure measurement.

To solve the aforementioned problems,a rapid and accurate inspection based on 3D optical measurements is used to measure non-uniform errors.This method requires multiple measurements,and the number of cross-section curves may be more than that in traditional error evaluation.

2.2.Evaluation of machining distortion

2.2.1.Precision of blade machining

The profile tolerance of the blade surface is illustrated in Fig.5,where θ is the directional angle of blade and is an angle between the chord width direction and the X axis,which lies in the radial plane of the engine axis.The integrated profile is controlled by the profile tolerance of a series of section curves that lie between sections 0 and XX.In addition to profile tolerance,bend and torsion are generally used to determine the degree to which distortion is close to its allowance.

Bend distortion is controlled by the positional tolerance of the section stacking point.The positional tolerance of the stacking point is ØE,(Fig.5).After the bend distortion,each stacking point error falls into the circle with a diameter of E,as show in Fig.6.If the bending distortion value does not exceed ØE,then it satisfies the requirements of the design plan.UV is the manufacturing coordinate system,and XY is assembling coordinate system.

Torsion is controlled by the torsion angle for measuring the section curve relative to the section curve of the model.This requirement is given in technical conditions of the design drawing.In the technical conditions offig.5,an allowance is required for the torsion angle in the specifications of the design plan(torsion distortion is±H).

2.2.2.Localization between the manufactured surface and the design model

Given the inaccurate location of the small datum,the manufactured surface and the design model are located in two different coordinate systems.The inaccuracy of the coordinate system based on the datum is one of main reasons why inspection results are untrustworthy.Determining the corresponding relationship between two coordinate systems is essential.Only after localization is processed will the next step be appropriately measured.The root mean square error(eRMS)is defined as an objective function of localization.25,26According to the corresponding points piand qi,the localization relationship is assumed to be

Fig.5 Dimensions and tolerances of design plan.

where piis the measured point coordinate in the measuring coordinate system;qiis corresponding point coordinate on the design model coordinate system;eiis the deviation of this point,and ei=T-1pi-qi;T is the transfer matrix that contains rotation transformation R,translation transformation M,and six variables,i.e.,mx,my,mz,α,β,γ,which are the translation and rotation quantities along the X,Y,Z coordinate axes,respectively.

Therefore,the objective function F is defined as

where n is the total number of measurement points.

The minimum objective function can be expressed as

The localization process is shown in Fig.7.Given that the coordinate system is not uniform and the spatial surface equation is complex,the detection of the transfer matrix Tktransforms into a nonlinear equation.The limited memory quasi-Newton code for bond-constrained optimization(L-BFGS-B)algorithm is an effective method for solving large-scale nonlinear optimization equation at the cost of a significantly more complex code.25,27The main advantages of L-BFGS-B are its low computational cost per iteration,its modest storage requirements,and its ability to solve problems in which the Hessian matrices are large,unstructured,dense,and unavailable.It is less likely to be competitive,in terms offunction evaluations,when an exact Hessian is available,or when significant advantage can be taken of structure.Therefore,the L-BFGS-B algorithm can be used to solve the objective function.In Fig.7,ε is the allowable calculation error value.

Fig.6 Tolerance zone of section stacking point.

Fig.7 Localization process of the manufactured surface and the design model.

2.2.3.Calculation and analysis of distortion

The error expressions are formulated from the calculation of blade distortion,which will use the parameters in the localization process.

According to the positional tolerance of the stacking point for the design plan,bend distortion is defined as

Considering the torsion angle requirement for the speci fication of the drawing,torsion distortion is de fined as

where γ is the torsion angle along the Z coordinate axis in fine measurement localization,as shown in Fig.11.

3.Inspection of machining distortion

A procedure of distortion inspection that uses the meshing measurement method contains a three step workflow:rough measurement,registration of coordinate systems and fine measurement.

Given that a small datum plane is far from the machining surface,acquiring accurate measurement data is difficult.Inspection will be performed for a rough measurement and a registration process.

3.1.Rough measurement

In this study,the workpiece coordinates are established using a 3–2–1 mode.Fig.8 shows the 3–2–1 mode for the rough workpiece coordinate system(CSr),which forms a datum plane with three points(1,2,3)and a straight line with two points(4,5).The origin of the coordinates is determined by one point(6)located on the underside.The blade is measured with the three typical section curves,i.e.,tip,middle,and base section curve,which can form a rough measurement model.

3.2.Registration of coordinate systems

After performing rough measurements,all measurement point data are imported into the 3D CAD software.The registration of the design model with the positional relationship is obtained by the software.This relationship refers to the relative position between the rough measurement model and the design model of the blade.

The registration procedure includes rotating and translating the coordinate system as shown in Fig.9.In coordinate rotation,CSrrotates α from XYZ to X1Y1Z1,β from X1Y1Z1to X2Y2Z2,and γ from X2Y2Z2to X3Y3Z3as shown in Fig.9(a).Then,the transformation algorithm is used to convert the modified coordinates X3Y3Z3into the fine coordinate system(CSf),as shown in Fig.9(b).

3.3.Fine measurement

After the registration of the coordinate system is completed,the geometric accuracy of the blade surface is measured via scanning cross-section curves.This process uses a measurement path shown in Fig.9(b).

4.Application example

Fig.8 Blade coordinate system.

Fig.9 Schematic diagram of coordinate system registration.

The compressor rotor blade is selected as an object in Fig.2(b),and its parameters are shown in Table 1.The test blade is a near-net-shape blank15with a machining allowance of 1 mm.The requirements of the design plan are as follows:positional tolerance of the section stacking point is Ø0.08 mm,tolerance of the surface profile(G)is±0.06 mm,and tolerance of the torsional angle(H)is ±10′.

The measurement system of the blade is MAXOS optical CMM(WENZEL®,Germany),which is comprised of an optimal sensor placement with a sampling speed of 70 points per second.This optical system satisfies the high standards of the aerospace industry as MAXOS is ideal for the measurement of large turbine blades and complex components.It can have up to six axes,with three being rotary axes,and can measure shiny and highly reflective surfaces.Even areas that are diff icult to access can be measured rapidly and accurately using this system.

The registration parameters are then analyzed in reverse engineering software.Table 2 provides the registration parameters between CSrand the fine workpiece coordinate system(CSf).Finally,the measurement path is revised based on the modified coordinate system(CSf),and the final result is used as the fine measurement path.

Fig.10 shows that for some surface points,the maximum deviation value before registration of the coordinate system is 0.116 mm,which does exceed tolerance levels.This devia-tion in section TIP is far from the datum of the blade.However,a uniform distribution of the deviation is realized after registration.This finding demonstrates that the measured datum cannot accurately determine the actual position of the workpiece.

Table 2 Registration parameters.

Fig.10 Results of proposed registration method.

In fine measurement,as shown in Fig.11,the cross-section curves(S1–S13)will be measured in accordance with the blade design blueprint.To evaluate distortions of non-uniform distribution,the number of section curves for inspection is increased with lengthways sections.These curves are definedas isoparametric curves(S14–S21).The blade is inspected by the meshing structure method with the fine measurement as shown in Fig.11.

Table 1 Blade parameters.

Fig.11 Schematic diagram of the meshing measurement.

5.Results and discussion

The distortions of different areas are evident because of errors in the measurement of the meshing structure.A total of 21 cross-section curves should have fine measurements,whereas only 3 basic curves have rough measurements.The measurement of all section curves with approximately 3400 points only takes 7 min to complete because an automated optical measuring machine with a light-weight point sensor is used for the entire procedure.

Bend and torsion distortions are calculated as Eqs.(6)and(7),respectively,using the measured data from the crosssection curves(S1–S13).The bending distortion is 0.057 mm,whereas the torsion distortion is-3′.The machining errors of the 13 cross-section curves fluctuate within the range of-0.06 mm to 0.054 mm.This result shows that machining distortions satisfy the profile tolerance demand of the design blueprint.However,as shown in Fig.11,machining errors exhibit a non-uniform distribution on the blade surface.

To validate the preceding measurement results,the same procedure is performed on a contact CMM(Century 977).Fig.12(b)shows the deviation of six cross-section curves(S1,S3,S5,S7,S10,and S13)using contact CMM.The overall range of error is within±0.06 mm,and maximum error occurs in the leading/trailing edge areas.Fig.12(a)shows two crosssection curves(S3 and S13)which appear at maximum deviation.The two measurement curves are inspected with the optical CMM.The contact measurement results agree with the optical measurement data,which demonstrates sufficient optical measuring accuracy to meet requirements.

Fig.12 Deviation of cross-section curves between optical CMM and contact CMM.

The same blade was measured by a coordinate measuring machine(CENTURY 977).We compared the deviation data on the representative cross-section curves(S3 and S13)in Table 3.The results indicate that the distortion trend and the deviation range are consistent with optical measurement values.The error between optical CMM and contact CMM can be controlled in a range of 3 μm.

Fig.13(a)shows the deviation of the isoparametric curves(S18).S18-S on the graph indicates the distortion trend of the suction surface after machining,whereas S18-P shows the pressure surface.The results indicate that errors vary from the upper to lower deviations of the zero line,which shows that the distortion of the blade should look like View-P.The distortion is thinner in the TIP and thicker in the BASE.Errors onthe blade surface are characteristic of non-uniform distributions as shown in Fig.13(b).

Table 3 Comparison between optical and contact CMM.

Fig.13 Final evaluation of blade distortion.

Conclusively,the new approach(measurement of a meshing structure based on an optical inspection system)has most of the efficiency of intuitive observation for non-uniform distribution errors.The errors are within the tolerance of design plans.Since the traditional constant height curves method compares structures singly,it cannot clearly present accurate positions of non-uniform distribution errors.

The pre-research aero engine has high requirements for precision and consistency of blades.The blades examined in this paper are among hardest machining blades that can belong to this engine.Non-uniform distribution errors will lead to stress concentrations in weak areas when the engine rotates at high speed,affecting the fatigue life of the blade.In addition,non-uniform distribution errors will also influence the dynamic balance of the engine and further affect the engine performance.Therefore,non-uniform distribution errors should be fully considered as a future evaluation target of blade distortion.The pre-research work done here will provide powerful support for application.

6.Conclusions

A complete measurement procedure and an evaluation method for blades with small datum are presented in this paper.The results can be summarized as follows:

(1)Deviation within tolerance levels is attributed to nonuniform distributions even when bend and torsion satisfy design blueprints.Thisfinding indicatesthat machining distortions with bend and torsion cannot be evaluated exactly for such blades.

(2)Accurate registration parameters of a coordinate system are easily obtained by selecting the section curves tip,middle,and base.Registration effectively corrects the positioning error of small datum during measurement.

(3)Clear distribution of a blade’s local distortion can be obtained through intuitive observation and positioning via the measurement of a meshing structure.This measurement technology can be applied to the distortion of various small blade parts.

Acknowledgments

This study was supported by a grant from the National Science and Technology Major Projects of China (No.2013ZX04001051).

Appendix A.Supplementary material

Supplementary data associated with this article can be found,in the online version,at http://dx.doi.org/10.1016/j.cja.2016.05.004.

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Yu Jianhua is a Ph.D.candidate at School of Mechanical Engineering and Automation,Beihang University.He received his B.S.and M.S.degrees from Beijing Information Science and Technology University in 2007 and 2011.His areas of research include machining distortion control technology of thin-walled parts,free surface CAD/CAM,and multi-axis machining technology.

Chen Zhitong is a professor and Ph.D.supervisor at the School of Mechanical Engineering and Automation,Beihang University,China.He received his Ph.D.degree from the same university in 2001.His current research interests are multi-axis NC machining technology and equipment,free surface CAD/CAM,and machining surface integrity.

28 December 2015;revised 9 January 2016;accepted 8 April 2016

Available online 21 October 2016

Free surface;

Machining distortion;

Optical testing;

Thin-walled workpiece;

Turbine blades

Ⓒ2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is anopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.Tel.:+86 10 82339151.

E-mail addresses:numerical@126.com(J.Yu),ztchen@sina.com(Z.Chen).

Peer review under responsibility of Editorial Committee of CJA.

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http://dx.doi.org/10.1016/j.cja.2016.05.004

1000-9361Ⓒ2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).