Calculation methodology for composite material gear meshing

Modern mechanical engineering industries, including aerospace, automotive, and robotics, are characterized by dynamic development, which places increasingly high demands on mechanical transmissions. Key aspects in the design of such transmissions now encompass not only traditional parameters of strength and reliability but also the minimization of mass and dimensions, reduction of noise and vibration levels, and an increase in service life under extreme loading conditions. In this context, traditional metal-based materials often reach their operational limits. This paper presents an advanced engineering methodology for calculating the contact strength of gear transmissions in which one gear is made of composite materials and the other is steel. Existing approaches, based on classical Hertzian theory, do not fully account for the anisotropic properties of composites and functionally graded materials. The study proposes a mechanical-mathematical model that considers the contact of a tooth from a rigid (steel) gear with a tooth from a composite gear as a problem of indentation of a rigid cylinder into an orthotropic or functionally graded half-plane. The aim of the work is to develop analytical relationships for determining the stress-strain state, including the distribution of normal and maximum shear stresses along the tooth depth. The methodology was validated using the example of gear teeth made from orthotropic (glass fiber-reinforced) and functionally graded materialы with a variable elastic modulus.
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