Formation of conjugate curved surfaces that exclude interference

Abstract

The object of the study is the method of geometric design of conjugate curved surfaces. The subject of the study is the possibility of achieving the absence of interference of the designed surfaces of kinematic pairs of technical structures, for example, products in mechanical engineering (cutting tools, gearing), based on an invariant method. This problem is of significant importance for a wide class of products, but especially for gears from the point of view of the precision of manufacturing the tooth surface, load-bearing capacity, and, consequently, the reliability and durability of the transmission. When calculating the strength, each tooth of the gear can be considered as a cantilever beam, loaded at the free end by the force of interaction with the second gear wheel. In the presence of interference (for trimming gears), not only the shape of the tooth surface is disrupted, but also the cross-sectional area of the tooth base is significantly reduced. Therefore, solving such a problem is important when designing and manufacturing gears. That is why, when forming the initial curved tool surface of a cutting tool, the conjugacy condition between the points of the product and the tool is taken into account. As a result, when designing a cutting tool using the proposed invariant method using a unified methodology, a wide class of complex curved surfaces can be formed. In particular, this applies to technological operations on numerically controlled machines. The generated conjugate curvilinear transformations of the cutting tool using an invariant method make it possible to avoid interference of mating surfaces at the design stage. At the same time, the curvilinear characteristics of surfaces are analyzed, defining a family of normals as common to two conjugate surfaces with linear contact, which is essential for the design process