Синтез профілю зубчатих коліс малошумного шестеренного насоса з низькою пульсацією

Abstract

Low-noise gear pumps with non-involute gear profiles, which have undeniable advantages over pumps with involute gear profiles (low noise characteristics, low pressure and volumetric pulsation, inseparability of gear contact), have not gained wide popularity due to difficulties in designing and manufacturing the working profiles of the gears. Companies manufacturing low-noise pumps provide only promotional information, while information about the meshing geometry, profile, and manufacturing technology is practically absent. The aim of the research is to obtain universal formulas for calculating the complex sinusoidal profile of gears for low-noise pumps. This will allow designing sinusoidal meshings with different input parameters (number of teeth, center distance, etc.). Additionally, for the helical sinusoidal meshing, it is necessary to derive a formula for determining the minimum tooth helix angle that ensures inseparability of contact in the meshing. Several stages are involved in obtaining the universal formulas. In the first stage, the construction of a base sinusoidal curve is performed. The obtained profile is not mutually enveloping, meaning that when positioning the gears at the center distance and forming the meshing, there is interference of curves. Hence the need for forming a unified profile where both gears have identical profiles and can be processed by the same tool. In the second stage, the generation of the conjugate gear profile is performed as an enveloping family of circular sine waves, by rolling a dividing circle of the sine wave around the generating circle of the formed gear. Segments of this profile will be further involved in forming the final gear profile. In the third stage, the circular sine wave and its enveloping positions are overlaid to a common center of coordinates. As a result, the conjugate profile points lying on the dividing circle are formed. The unification of the gear profile is achieved by removing certain sections of the curve within the dedendum and addendum, while the remaining sections that have a common tangent at the end points of the conjugation form the final gear profile. As a result of the conducted research, a mathematical apparatus has been developed that allows building gear tooth profiles for low-noise gear pumps with arbitrary geometric parameters and number of teeth. The minimum value of the tooth helix angle required to ensure contact inseparability and absence of clearances has been determined.