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


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


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

List of Symbols


Measuring coordinate system


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


Planning coordinates index


Precise measuring coordinates index




Zero spot of sensor PS


Zero spot of sensor MS

x1, y1, z1

Coordinates of O1

x2, y2, z2

Coordinates of O2


Deviation of O1 and O2 in Z-axis direction


Radius of lens


Angle between incident light and the principal optical axis of lens


Reference distance of the sensor


Distance between CCD and lens


Structural coefficient of sensor


Inclination error


Inclination angle


Measured depth of field

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

Coordinates for the fine adjustment of fixture attitude


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


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


Chord length


Leading edge radius


Trailing edge radius


Maximum deflection


Maximum thickness


Leading edge angle


Trailing edge angle


Profile camber angle


Chord line angle

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

Origin coordinate of the parameter coordinate system


Normal line angle of the center point of fitted circular arc


Center angle of the fitted circular arc

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

Planning coordinates for piecewise circle fitting


Center coordinates of piecewise circle


Radius of piecewise circle


Fitting error of each point of piecewise circle

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

Maximum of fitting error for piecewise circle


Limit value of fitting error for piecewise circle


Limit value of inclination angle


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


Model of mean camber line


Model of thickness distribution


Standard deviation of form-free measurement


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


Measurement errors of coordinates for the form-free metrology system



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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