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 Fig . 2. The trajectory of the M point of the laser sensor With small values of the radial pitch S p and large values of the scanning radii i r it is possible to condi- tionally represent the Archimedes spiral as a set of circles with a pitch S . Then the radius i of the circle i r can be determined by the formula: -1 , i i r r S = + (6) where i r – the radius of i circle at i revolution that is equal to the maximum value, i r ; -1 i r – the radius of ( i– 1) circle at ( i– 1) revolution that is equal to the maximum value -1 i r , At the same time, the circumference of the circle will change: î -1 2 2 ( ). i i i L r r S   = = + (7) The laser sensor has a fi xed frequency of measurement, therefore the circular pitch î i S of i circle at i revolution at constant motor speed can be determined by the formula: 2 13 2 , 2 2 30 circ i i i i circ i L r r r n S i          = = = = (8) where  – updating frequency of the laser sensor, Hz;  – constant angular rate of carrier 6, rad/s; 2 13 i – gear ratio of the cylindrical transmission from satellite 1 to carrier 3, with supporting wheel 2; L circ i – length of the i circle, mm. The formula (8) shows that the circular pitch S circ i will increase when the motor rotates uniformly and the laser sensor moves away from the center of the pro fi lograph. Therefore, in order to maintain the stability of the circular pitch on any circle, the movement must be slowed down when motor rotates and the laser sensor moving away from the center. Then the formula (8) can be rewritten in the following form: ñð , i i circ i r S   = (9)