ANALYTICAL CALCULATION OF THE SMOOTHNESS OF CONNECTING SURFACES AND TRAJECTORIES OF FORMING FOR THEIR TREATMENT ON CNC MACHINES

Abstract

The purpose of this work is to improve the cam mechanisms qualities under operating conditions. For present purpose, the task of determining the condition of smooth conjugation of the screw and radius surfaces of the cam running was set and solved as the simulating model for the CNC program of machine tools. This paper considers the processing of non-folding surfaces, the geometric properties of which have not been studied sufficiently. Therefore, the smoothness of graphic packages does not always satisfy the design and technological conditions of the part from the point of view of tangency along the entire perimeter of the conjugating surfaces. In addition, it is not clear where the surfaces can be joined with the best smoothness of the surfaces and how this will affect the law of motion of the output link of the mechanism and its dynamic characteristics that depend on the monotony of the first and second derivatives. In this paper, the conjugation of surfaces is obtained on the basis of the laws of the mathematical concept of smoothness with an indication of the coordinates of their common generating line, according to which this property will be achieved. The obtained conditions for smooth conjugation of helical and radial surfaces, as well as the proposed scheme for their calculation, can be used as the basis for engineering design of complex technical surfaces, parts of which are joined according to smoothness conditions, i.e., have tangential transition between surfaces of different types. The method of kinematic obtaining of screw and radial surfaces by means of the functional ratio of the axial feeds of the machine with the CNC, calculated with parametrized modules has been considered. The tool for the development of this method and its prospects are new functionals for the regulation of axial feeds of modern CNC systems. The above scheme for calculating smoothness can be applied to a wide range of surfaces of the second order and, based on the results of calculations, build a program for machining parts on CNC machines. The cost-effectiveness of design solutions for smooth interfacing has been confirmed in the manufacture of copying mechanisms, increasing their reliability and durability.