Study of surface quality using quasi-optimal correlation algorithms

. The article proposes a new approach for evaluating roughness of the profile surface of gas turbine engine blade airfoils after vibratory polishing. An optical electronic unit was used to study microgeometry of blade suction and pressure sides: video imagery of the surface was processed using computer methods to obtain the average amplitude of the autocorrelation function variable component. The applied optical electronic method of evaluating microgeometry of compressor/turbine blades allows obtaining fields of surface roughness and tension concentration coefficients as well as analyzing the finish machining technology to a greater depth.


Introduction
Nowadays, the machine building technology takes on a new level which requires creation of a scientific basis for systematic development of new technological processing and control methods. Such methods include mechanical, physical, and chemical methods to ensure required operation qualities of gas turbine engine (GTE) parts as well as to develop a module-based principle of technological process organization.
A particular attention is given to development of new research areas such as computer-based smart process environments or diagnostic & control systems for figurine-shaped parts. Progress in this area can substantially advance the methodology of GTE surface control.
Development of modern methods and means of surface quality technical control using roughness data (surface microgeometric deviations) obtained with computer-based technologies is one of the greatest challenges of the modern machine building industry.

Research objective
One of the most important characteristics of the GTE blade surface quality is a microrelief of its working surface: reliability and durability parameters of many blades depend on a pattern of microgeometric deviations of their working surfaces [1]. It is known that the smoother is the surface, the higher is fatigue resistance of the part; many studies show that fatigue fracture nuclei first appear on the part surface. Surface roughness areas are hotspots of tensions and are one of the reasons for fatigue resistance degradation: tension at the bottom of a groove mark is 2-2.5 times higher than average on the surface layer.
Experimental results reveal that roughness decrease from Ra=0,74 µm to Ra=0,74 µm increases fatigue strength limit of a specimen by 14% on average and prolongs its service life more than three times.

Solution method
Creating modern systems of technical quality control and a methodological basis for researching microgeometric deviations of figurine machine part surfaces in production environment via development of an optical electronic information measurement system (IMS) is a challenging issue.
This problem includes a number of requirements than modern portable surface microrelief measurement devices [2] must meet. Such devices must be compact, produce real-time measurement data without physical contact in a production environment, allow digital processing of the produced data and evaluating microreliefs of figurine surfaces, such as inner cavities of small orifices or working surfaces of molds and dies [3,4]. Moreover, metrological characteristic of such measurement devices must also be constant regardless of changes in the production environment; finally, the devices must be provided with an energy saving mode.
Existing methods and measurement means of microrelief parameters Xµi, (i=1,…,r) do not allow reducing measurement error below the order of a few tens percent; therefore the objective of this study is development of quality control systems and a methodological basis for research of microrelief of figurine surfaces in a production environment using an optical electronic information measurement system (IMS).

Theoretical basis
The IMS evaluates the microrelief of a studied surface by means of comparing the surface with images of reference surfaces with roughness parameters defined using standard methods [5] and known. As a result, the studied surface is matched with a certain reference surface with a preset recognition probability. This method allows optimally solving the task using a signal-matched 2D spatial filter which response can be defined as following: (1) is a 2D convolution of signal 1 2 ( , ) u k k and the filter impulse characteristic 1 1 The impulse characteristic is produced from the expected 2D signal by means of reflecting it relative to the reference axes 1 n and 2 n and shifting the reflected signal toward the input by 01 02 , n n counts. The output 1 2 ( , ) y n n will be proportional to the correlation function of the 2D input signal, and the maximum signal/noise ratio will be achieved at the filter output.
In the original half-toned frame sized 1 2 K K × pixels, a strip 2 N pixels wide is highlighted, beginning with the first line. The reference image sized 1 2 N N × pixels is inserted in the center of this strip. Then the reference image is moved along the strip with 1 pixel steps, beginning from the leftmost position. Whenever the reference image is superimposed onto the current fragment of the half-tone image 1 2 ( , ) x n n , a correlation coefficient is calculated using the following formula: As the above expression shows, its structure corresponds with the structure of expression (1), and the influence function is reduced.
Known quasi-optimal correlation algorithms and criterial functions were analyzed in order to quicken the calculation procedure. The analysis has shown the most promising to use are twin criteral functions and binary images where N is a number of compared elements in the reference and the current image fragments, was used to achieve the fastest calculation rate.

Experimental results
Profile roughness of turbine 1st stage blade airfoils made without allowance (ЖС6ФУ material) after vibratory polishing using a ЛВП-4 machine was studied. The movement path of a blade during polishing is a result of geometric addition of mutually perpendicular oscillations generated by two crank mechanisms and is shaped as a mesh with controlled parameters, geometrically complex and practically nonreproductible. Such movement path allows creating a uniform microgeometry over the surface of the pressure and suction sides of the blade. Vertical and horizontal oscillation modes directly influence the processing capacity and dynamic loads appearing in the oscillating system. Usually, the oscillation frequency is taken as 20-25 s -1 and the amplitude as 5-10 mm which results in the machining rate of 30-120 m/min. The machining process simulation has shown the maximum machining capacity is provided by a discrepancy in the proportion of frequencies of figures ωо= ωh/ωv, where ωh is frequency of horizontal oscillations, ωv is frequency of vertical oscillations. The 1/2 ≤ ωо≤ 1 frequency range was studied. By setting equal rotation speed of two adjacent figures within ranges: В1=1/2, В2=3/5, В3=2/3, В4=3/4, В4=4/5, В5=5/6, В6=1, the following dependency is obtained: The first part of the equation is a hyperbola, the second one is a tangensoid. By solving this equation for ωо, , we obtain the following series of frequency proportions: 0.543, 0.617, 0.704, 0.763, 0.833, 0.917.
An optical electronic unit was used to study microgeometry of blade suction and pressure sides. The unit [6] ( fig. 1) includes the following components: 1-studied surface, 2-television camera with a CCD sensor, 3-analog to digital converter, 4-memory storage, 5-device for setting window coordinates and sizes for transformation of the input halftone surface image to a binary image as well as for setting reference image size in the binary image, 6-digital computer, 7-device for setting coordinates of the current binary image fragment, 8-correlator and software for processing of video imagery of studied surfaces. Blade surface spots after vibratory polishing were analyzed. Fig. 2. shows half-tone and binary images of the selected surface area, a correlation surface and the correlation coefficient change diagram for this area [7].
The surface area format stored in the computer memory was 320×240 pixels in this case. Processing of the experimental results has shown that the average of the variable component of the correlation function calculated for 30 images is Ucp = 23.1 rel. units.

Conclusion
The study proves that the optical electronic method for evaluation of turbine blade surface quality allows developing surface roughness fields and use them to better analyze the vibratory polishing technology. The research proves that using optimal proportions of vertical and horizontal oscillation frequencies allows creating a uniform surface structure of the blade airfoil profile. The first ever study of surface areas of a turbine 1st stage adjacent to orifices along the entry edge has shown the roughness increases by 1.5-1.7 times around the orifice.