Method for calculating the accuracy parameters of manufacturing wheels with multi-period tracks of planetary ball gears

The precision of manufacturing wheels with multi - period tracks significantly affects the smoothness of operation and the load capacity of the planetary ball gear. An urgent task is to determine the manufacturing errors of the transmission wheel. The article discusses a calculation method that allows to determine the position errors of the processed profile relative to the base surface of the part for linear dimensions. It can be used for processing workpieces on metal - cutting machines in normal production conditions. On the basis of known mathematical dependencies, a method for calculating manufacturing errors of a wheel with a multi - period track has been developed. The method consists in determining random and systematic errors associated with various technological factors, calculating and summing these errors using the laws of distribution of random variables of probability theory and developed computer programs. Based on the developed method, formulas for calculating the total error of processing a wheel with a multi - period track are derived, characterizing the displacement of the workpiece along the coordinate axes of the machine. To determine the errors from displacements and rotations of parts with multiperiod tracks, a calculation method based on the use of the matrix method has been developed. Graphs are presented that characterize the influence of the shape error of the base surface of the wheel blank on the total processing error of the multi - period track. Optimization of processing modes, reducing and stabilizing the cutting force, is proposed. A diagram of the largest values of the total error of processing a wheel with a multi - period track is presented.