## 2 Characterization and Measurement of Blade Twist
### Measurement Method of Blade Twist  
In this study, a high-precision special machine for blade measurement shown in Figure 3 is applied to the measurement research of the blade twist. The measuring machine is essentially a four-coordinate laser measurement system, and consists of a four-axis motion platform, a fixture system and a high-precision laser probe. The four-axis motion platform is made up of three linear shaftings of X, Y, and Z with a resolution of 0.1 \(\upmu\)m, a rotary shafting of C with a resolution of 0.0002\({}^{\circ}\) and a precision CNC (Computer Numerical Control) system [17; 18]. The fixture system solves the problems of clamping, positioning and measurement calibration. The high-precision laser probe is designed with a conoscopic holography sensor CP-3 from Optimet (Israel), with a measurement range of -1 mm to +1 mm and a resolution of 0.1 \(\upmu\)m. The measuring machine provides a precise hardware platform for the research of the measurement method, and the subsequent experimental verification is also implemented on the high-precision special machine. Coordinate measurements and chord angle extraction with high precision are two key issues to be solved in blade twist measurement. Figure 2: Model of characterization and evaluation for blade twist. In order to improve the accuracy and adaptability of the coordinate measurement, an a priori planning measurement method is proposed in this study. Firstly, the test profiles of the blade are measured without theoretical model data by the laser probe, and the theoretical model of the blade is self-constructed based on feature recognition. Then, the measuring path is planned and the sampling strategy is optimized based on the theoretical model solved of blade, and the high-precision acquisition of the blade coordinates is achieved. All coordinates are collected in the positions near the reference distance of the laser probe based on a priori planning technology, thus the depth of measurement approaches 0 mm and the measurement error is no more than 10 \(\upmu\)m. In addition, this method is a form-free measurement method and does not need the theoretical model of the blade, which improves the adaptability of the measurement. By optimizing the measurement method, the accuracy level can meet the measuring requirements of aero-turbine blades with a first precision grade. The a priori planning measurement method is an innovation of this study. In order to improve the measurement accuracy of the chord angle, an algorithm for edge extraction based on sampling optimization and least squares fitting is proposed, which can provide the authentic measurement data for the extraction of the profile chord. The statistical uncertainty of the method is less than 3 \(\upmu\)m.  
The principle and the process of the blade twist measurement are summarized as follows:  
Step 1. Establishment of workpiece coordinate system and registration of engine axis. The workpiece coordinate system is established by scanning the selected section of the mounting column of the fixture, and the axial line of the engine is matched and aligned with the \(X\) axis by measuring the side of the base  
Figure 3: High-precision special machine for blade measurement. platform of the fixture. In this study, the least squares fitting algorithm is used to process the measured data, which greatly improves the datum accuracy of the twist measurement. Step 2. Acquisition of coordinates of the test profiles. The high-precision coordinate data is obtained by scanning and measuring test profiles I and II with measurement technology of a priori planning. Step 3. Feature recognition and profile fitting. By feature recognition and piecewise fitting for the collected coordinate data, the test profiles I and II are extracted, which provides authentic and accurate measurement data for subsequent parameter calculation and evaluation. Step 4. Basic parameters calculation of test profiles.