MATHEMATICAL MODELING OF ANGULAR DIFFERENCE BETWEEN TEETH DIRECTION IN ZONE OF ENGAGEMENT AND COMPLETENESS OF CONTACT IN GEARS

The paper presents a mathematical model of the difference in the angles of the teeth direction in the engagement zone of cylindrical and bevel gears, which are widely used in drives of various machines and units, as well as in measuring devices. A particular solution is considered based on the performed analysis. It is a mathematical model of the difference in the angles of the teeth direction in the engagement zone, covering the factors generated only by structural elements of keyed joints. A numerical experiment revealed a quantitative effect of the angular deviations of the keyed elements on the difference in the angles of the teeth direction in the engagement zone. The difference in the angles of the gear teeth direction turns out to be the main source that affects the teeth contact completeness, which is one of the indicators of the reliability and performance of gears. The elements of keyed joints in the shaft-wheel conjugation are also considered. The analysis is carried out and the effect of design parameter deviations of the keyed joint elements on the nature and position of the locked teeth contact is revealed. Design and technological directions are proposed that minimize the effect. of keyed joint errors on the formation of the difference in the angles of the gear teeth direction. Recommendations are given on the use of multi-stage gearboxes of the AN type. They use the keyed joints in conjugations of shaft-wheel only in the drive and driven shafts. We also give recommendations on applying the new design of the keyed joints, providing self-adjustment of one of the teeth (gear) during their engagement. An effective method is proposed for setting up a technological system when cutting a keyway on a shaft.