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

OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 where ñð i  – the average angular rate of the carrier 6 at the i revolution, rad/s. To determine the angular rate, we equate the circular pitches at different revolutions: ( -1) . circ i circ i S S = (10) Considering equation (8), equation (10) will take the form: -1 1 const, i i i i r r     - = = (11) . circ i i S r   = (12) The equation (12) shows that the numerator has a constant value that depends on the selected param- eters: the frequency of updating the laser sensor data set during programming, as well as selected circular pitch set by the user which depends on various measured surface parameters. The denominator is a variable value in the range: min max ( , ), i r r r Î (13) where r min – minimum scanning radius that is equal to the outer radius of the pro fi lograph base, m; r max – maximum scanning radius that is equal to the maximum radius of the pro fi lograph arm, m The graph of the dependence of the angular rate i  on the scanning radius r i is a hyperbola and is shown in Figure 3, a . The formula (12) for determining the angular rate  i depending on the scanning radius r i with the se- lected circular pitch S circ , for example, equal to 2 mm and the speci fi ed data updating frequency of the laser sensor  – 100 Hz, will take the form: 0.002 100 0.2 . circ i i i i S r r r   ⋅ = = = (14) After processing the obtained data in Excel , a graph of the dependence of the angular rate i  on the scanning radius i r or on the number of revolutions N for the experimental installation of the pro fi lograph was obtained (Figure 3, b ). According to the graph obtained with the given technological parameters of the mechatronic pro fi lograph (Figure 3, b ) it can be concluded that for a constant spiral pitch of 2 mm, the value of the angular rate should gradually decrease from a maximum value of 2 rad/s to a minimum value of 0.574 rad/s. Thus, the technological rate of the measurement operation has decreased by 3.484 times. The choice of electric motors was made according to the torque and did not depend on the angular velocity graph. The obtained dependence of the angular velocity on the scanning radius allowed establishing more ef fi cient motor control as part of the drive when scanning the surface along the Archimedes spiral. When scanning along the Fermat spiral, the fi rst pitch is made along a circle, and the second pitch is made along a spiral, which is a fl at curve-the trajectory of a point moving uniformly along the radius vector starting at O (Figure 4). The trajectory of the sensor movement along the Fermat parabolic spiral covers optimal area of the plots by a given number of measurement points, which are evenly distributed over the entire area under study. For example, the area of the plot between the fi rst and second turns will be equal to the area of the plot between the second and third turns as well as to the area of the plot between the third and fourth turns, etc. Next, the pro fi le of the complex surface of the part, in our case it is the blade of the vehicle propeller, is determined along this spiral or curve, moving the laser position sensor from the zero mark and further along a given trajectory. Figure 1 shows one of the stages of reverse engineering, obtaining and verifying a 3D model of a duralumin blade.