ANALYSIS OF THE INFLUENCE OF THE DISPLACEMENT OF THE INITIAL RACK ON THE TEETH PROFILES CURVATURES OF GEARS WITH EVOLUTE MESH

Abstract

The article is devoted to the modification of the evolute gearing with a convex-concave contact and the assessment of its influence on the curvature of the conjugate profiles of the gear and wheel teeth. This mesh is promising, as it is a family of profiles with a wide range of geometric and quality indicators. Based on the Bobilier construction, a second-order differential equation is obtained, which describes an evolute mesh. The solution to the differential equation is obtained in the form of a polynomial. The instrument rack profile can be obtained by substituting the polynomial in the parametric curve equation. To construct the profile of the gear tooth, a system of equations for the transition from the profile of the tool rack was used. A displacement coefficient has been added to the equation of the side profile of the tool rack tooth, which has the same value for the gear and wheel teeth, but the opposite sign. When adding the displacement coefficient to the tool rack equation, two separate calculations were performed to obtain positive and negative offset on the gear and wheel teeth, respectively. A pair of gears with parameters z1 = 20, z2 = 80, m = 10 was investigated. Several values of the displacement coefficient with a positive and negative sign for the gear teeth are considered. The research results make it possible to assess the influence of the rack displacement on the curvature of the tooth profiles and on the height of the biconvex contact zone in the near-pole zones. It is shown that a negative displacement for a gear at values of more than 0.4 leads to a significant violation of the curvature of the tooth profile. With a negative displacement, the DCC zone (the area where the curvatures of the gear and wheel teeth have the same sign) slightly decreases. However, an area with a sharp change in curvature appears on the profile of the gear tooth, which in the future will lead to a higher contact pressure compared to the unmodified profile. Positive displacement reduces the tooth curvature, but the area of the DCC is noticeably increased. In both cases, the rack displacement does not have a significant effect on the curvature of the tooth and on the height of the DCC zone on the contact part of the profile.

Keywords: evolute gearing, gearing, tooth, rack displacement, profile curvature, convex-concave contact