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

OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. No. 4 2021 from the data array. Pitch  between the polar angles is chosen on the basis of the speci fi c goals of the study; – tracking the dynamics of the change in the shape of the distance H along the polar angle φ at a constant polar radius r , in the form of functions  r (  ). They are obtained from the data array by selecting values cor- responding to certain values of the radius with a necessary pitch  r . In general, the simultaneous use of   ( r ) and  r (  ) for surface analysis makes it possible to study the “evolution” of the surface shape with radial or angular displacement along each propeller blade. Thus, the defects of the pressure and suction surfaces of each blade, leading and trailing edges, can be evaluated quite quickly and easily: the number, area, maximum depth and the average volume of chipping. Further, defects in the shape of the blades are evaluated and the shapes of different blades are compared with each other, studying deviations, bends or deformations in the radial and perpendicular directions as well as the differ- ences in the areas of the blades. As mentioned above, high values of determination coef fi cients of the models describing the surface make it possible to extrapolate effectively data and move from one coordinate system ( r i ,  i , H i ) to another ( x k , y k , z k ). In addition to formula (16) , when recalculating areas and volumes, it should be remembered that the Jacobian transition J ( r,  ,H ) = r H r H r H x x x y y y z z z    ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ = r , (17) that is dS xyz = rdS r  H , and dV xyz = rdV r  H . After the experimental data are obtained, they are divided into arrays. For each blade, the “smooth- ness/roughness” is estimated by analyzing the ∆ H i – deviations of the experimental values from the values calculated by regression dependencies. According to the values that statistically signi fi cantly exceed the average deviation on the surface, the boundaries of chipping and other defects are determined, and then its parameters are calculated: area, maximum depth, average volume based on the approximation, the cavity of a ball bearing or elliptical segment. The next stage is to study the differences in the shapes of the blades surfaces. To implement it, the data corresponding to the same values of the radius r when the angle  changes along each blade are compared, and vice versa the data corresponding to the same values of the angle φ when the polar radius r changes along each blade are compared, that is, the functions   ( r ) and   (  ) are used. Denoting the deviations in the values between j and k blade by ∆ z jk , both the deviation values along the radius  , and  – the angle of deviation in the direction perpendicular to the radius can be determined. For propellers with axially variable pitch (the pitch of the helical lines varies both along the axis and along the radius), the angle between the curves of the adjacent blade surfaces corresponding to the same values of radii changes, the distances between the curves increase as well. Taking into account the results of experimental studies and considering the array of deviation values ∆ Н i for the corresponding points of different propeller blades, the dependence of the increase in deviations from the polar radius and angle is obtained (Figure 5). A two-factor power model, describing the deviation with the coef fi cient of determination R 2 = 0.967, has the form H = 1.071  10 -4 r 5.487  9.017 , with an average angle of deviation perpendicular to the radius direction δ increases from 0 to 0.3  , and the angle of de fl ection along the radius  increases from 0 to 5.4  . Thus, studying complex surfaces of propellers of vehicles by reverse engineering using the developed mechatronic pro fi lograph, we speci fi ed its design and technological parameters, made an express analysis of the surfaces of propellers with rotary symmetry and found out differences in the shapes of the surfaces of the propeller blades by the deviation values in the longitudinal and transverse directions for different radii.