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DEVELOPMENT OF SPECIAL MATHEMATICAL MODELS FOR RESEARCH OF ACCURACY OF REAL SURFACES OF TEETH WHEELS OF CYCLOIDAL TRANSMISSIONS

Promising areas for improving robotic systems based on cycloidal gears aimedto increase their accuracy and other performance characteristics. The accuracy of the rotary unit and the mechanism as a whole is determined by errors in the manufacture of the transmission. Integral quantities are not enough to assess the accuracy of the transmission wheels. To determine the errors of the geometry of parts requires a technique that includes modeling of its real surface. The cyclic nature of the curve that defines the generating surface of the wheel allows the use of optimized mathematical models based on Fourier series. The technique allows for accurate processing of experimentaldata and compare them with the theoretical profile. Approbation of the concept requires modeling of the theoretical profile and research of the manufactured parts. The method allows to determine the parameters of the wheels by analyzing the differences between the simulated surface of the part and the theoretical profile. A hole in the part can be used as a base surface in the manufacture. Determination of the surface profile of the transmission wheel is carried out on a coordinate measuring machine, which allows to get a set of points. Surface modeling by discrete values is performed by spline interpolation. In the future, the description of the surface is performed using harmonic functions. The proposed mathematical apparatus allows the use of spectral analysis tools and statistical methods. The harmonic series is obtained by means of the Fourier transform. Monte Carlo methods allow to compare the mathematical model of the real profile of the mechanical transmission wheel and the theoretical surface. This makes it possible to take into account the presence of eccentricity, phase shift and other features of the part when determining the accuracy parameters. The mathematical model allows to effectively use experimental data in determining the characteristics of the surface of the part. The use of stochastic parameters in modeling makes it possible to take into account the accuracy of the wheel and increase the accuracy of determining the parameters of mechanical transmission.