Investigation of complex surfaces of propellers of vehicles by a mechatronic profilograph

OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 The controlled blade is positioned is in the operating range of the sensor. Besides, there should be no foreign objects in the area of incident radiation on the blade and re fl ected radiation from it. When controlling the blade of a complex shape and texture, the penetration of the mirror component of the re fl ected radiation into the input window of the sensor should be minimized. The blade to be measured is placed on a fl at surface whether a calibration plate or a table so that the length of blade should not exceed the length of the surface. The blade on a fl at surface should not be subjected to any external forces, such as pressure, tension, torsion. Due to the fact that the information from the sensor is transmitted from each turn of the spiral, there may be an overlap of curves in polar coordinates. The obtained information is presented with the well-known polar equation of the spiral put in the measurement information system, for example, for the Fermat spiral: 2 , r a  = (15) where r – the radius vector, м ; а – the coef fi cient of the spiral; φ – the angle of the position of the radius vector from the zero mark in degrees. To translate to the Cartesian coordinate system, use the equations: cos , sin , , x r y r z z   ì =ïïïïï =íïïï =ïî (16) where х – the longitudinal coordinate, m; у – the transverse coordinate, m; z – the vertical coordinate of the surface of the part at a given point, m. Results and discussion The proposed approach signi fi cantly simpli fi es the research even in the case of complex surface shape, the description of which involves the use of special functions (for example, Riccati , Bessel or Jacobi ), as well as their combinations. Scanning allows to get a large array of fairly accurate digital data, analyze and select the most adequate digital surface models [19–21]. When scanning objects, the sensor moves over the studied surface along the Archimedean spiral r =  φ (or Fermat r 2 =  2 φ ), there is a relatively high speed of surface area processing, since the process is continuous and there is no need to reduce the speed due to stops, associated with shuttle scanning. In the developed device the pitch of the spiral is selected according to each speci fi c problem situation and can be quite small. Therefore, even a linear model allows achieving high accuracy of description for adja- cent points of the studied surface not to mention nonlinear variants. Experience shows that models with R 2 > 0.99 are selected relatively quickly and easily, i.e. less than 1 % of statistical data is not described by the selected formulas. And these fi gures should be considered taking into account the fact that defects of the objects, such as various chipping, bends, etc., lead to at least 5…10 % discrepancies in the data. With the help of data extrapolations it is possible to obtain the functions describing the surface taking into account the necessary conditions. This can be data in a Cartesian coordinate system, as well as data with a constant polar angle, a constant radius, or any other conditions. If it is necessary to make some changes, the values calculated from the functions can be compared with those directly scanned, since the developed device can scan along any given trajectory. One of the options for practical use can be an express analysis of the state of the surface of objects with rotary symmetry. The use of cylindrical coordinates is appropriate in this case and has the following advantages: – tracking the dynamics of changes in the distance Н along the polar radius r at a constant polar angle φ , in the form of functions   ( r ). They are obtained by selecting values corresponding to certain polar angles