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A High-Precision Form-Free Metrological Method of Aeroengine Blades

  • Zhao-Yao ShiEmail author
  • Xue-Zhe LiEmail author
  • Yu-Kun Li
  • Jia-Chun Lin
Regular Paper
  • 43 Downloads

Abstract

In order to solve the problems in existing methods for blade profile metrology, such as low accuracy and efficiency, poor flexibility, various constraints, a high-precision form-free method for blade profile metrology is proposed. In the paper, the operational principle, key technologies and evaluation methodology are analyzed in detail. A high-precision method for blade profile metrology based on the concept of “Synchronization of Planning and Measurement” is proposed to solve three key problems for blade metrology synchronously: theoretical data acquisition, path planning and sampling strategy analysis, and profile measurement. A form-free evaluation methodology for blade profile based on parametric modeling is also discussed. The results show that the metrology and evaluation for blade profile are executed automatically without theoretical model data, thus improving the efficiency and flexibility greatly. In addition, all the measurements are completed in the positions near the reference distance of the sensor, thus the depth of measurement approaches 0 mm and the measurement error is no more than 10 μm. The method proposed in the paper is a form-free method with a high precision and has a good application prospect in the field of free-form surface measurement.

Graphic Abstract

Keywords

Blade metrology Form-free measurement Synchronization of planning and measurement Parametric modeling 

List of Symbols

O-XYZ

Measuring coordinate system

O′-X′Y′Z′

Parameter coordinate system

\(P_{1pi} (x_{1pi} ,y_{1pi} ,z_{1pi} )\)

Planning coordinates for section 1

\(P_{1mi} (x_{1mi} ,y_{1mi} ,z_{1mi} )\)

Precise measuring coordinates for section 1

\(P_{2pi} (x_{2pi} ,y_{2pi} ,z_{2pi} )\)

Planning coordinates for section 2

pi

Planning coordinates index

mi

Precise measuring coordinates index

i

Index

O1

Zero spot of sensor PS

O2

Zero spot of sensor MS

x1, y1, z1

Coordinates of O1

x2, y2, z2

Coordinates of O2

Δz

Deviation of O1 and O2 in Z-axis direction

RL

Radius of lens

β

Angle between incident light and the principal optical axis of lens

l

Reference distance of the sensor

l

Distance between CCD and lens

KS

Structural coefficient of sensor

Eα

Inclination error

α

Inclination angle

d

Measured depth of field

\(Q_{i} (x_{i} ,y_{i} )\)

Coordinates for the fine adjustment of fixture attitude

γ

Adjustment angle, angle between the normal line on the side of base platform and Y axis

\((x_{c} ,y_{c} )\)

Center coordinates for the fitting circular of the selected profile of the mounting column

\(R_{c}\)

Radius for the fitting circular of the selected profile of the mounting column

b

Chord length

Rq

Leading edge radius

Rh

Trailing edge radius

fmax

Maximum deflection

cmax

Maximum thickness

χ1

Leading edge angle

χ2

Trailing edge angle

θ

Profile camber angle

\(\varphi\)

Chord line angle

\(O'(x_{0} ,y_{0} )\)

Origin coordinate of the parameter coordinate system

\(\delta_{i}\)

Normal line angle of the center point of fitted circular arc

\(\omega_{i}\)

Center angle of the fitted circular arc

\(P_{i} (x_{i} ,y_{i} )\)

Planning coordinates for piecewise circle fitting

\((m,n)\)

Center coordinates of piecewise circle

\(R\)

Radius of piecewise circle

\(\Delta_{i}\)

Fitting error of each point of piecewise circle

\(\left| {\Delta_{i} } \right|_{{\rm max} }\)

Maximum of fitting error for piecewise circle

\(e_{0}\)

Limit value of fitting error for piecewise circle

\(\omega_{0}\)

Limit value of inclination angle

\(\omega_{center}\)

Center angle of piecewise circle

j, h

Cycle variables

\(A(x_{A} ,y_{A} )\), \(B(x_{B} ,y_{B} )\)

Coordinates of the endpoints of arc AB

\(O_{1} (x_{O} ,y_{O} )\)

Center coordinates of arc AB

\(y(x)\)

Model of mean camber line

\(r(x)\)

Model of thickness distribution

σ

Standard deviation of form-free measurement

\(r_{s}\)

Radius of the standard mandrel

\(P_{di} (x_{di} ,y_{di} )\)

Measurement coordinates of the standard mandrel

\(P_{si} (x_{si} ,y_{si} )\)

Datum coordinates of the standard mandrel

\(E_{i}\)

Measurement errors of coordinates for the form-free metrology system

Notes

Acknowledgements

This study was co-supported by the Key Project of National Natural Science Foundation of China (No. 51635001) and the Innovation Ability Promotion Plan Project of Education Commission of Beijing (No. TSJHG201310005004).

Author’s Contributions

Z-YS and X-ZL have proposed a high-precision and form-free method for blade profile metrology based on “Synchronization of Planning and Measurement” and “Parametric Modeling”, the operational principle, key technologies and evaluation methodology are analyzed, the software and hardware of the system are designed, the validation of technical scheme is verified, and the manuscript is written. Y-KL has offered help for the experiment, data processing and simulations. J-CL has proposed the revising suggestions of manuscript.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.Beijing Engineering Research Center of Precision Measurement Technology and Instruments, College of Mechanical Engineering and Applied Electronics TechnologyBeijing University of TechnologyBeijingChina
  2. 2.College of Mechanical and Electrical EngineeringNorth China Institute of Science and TechnologyHebeiChina

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