Development of mathematical model of oscillatory processes at turning of materials with reverse hardness distribution

Abstract

For technological guarantee of the required quality indicators of the surface layer of metallic rotation body parts at finishing machining needs the correct assignment of technological modes. During finishing turning, vibrational processes have a significant (and often decisive) effect on the formation of surface roughness. It is necessary to choose such values of technological modes, which provide an acceptable level of vibration (previously it is advisable to solve this problem by modelling). Mathematical model was carried out based on the determination of the turning tool deformations under the influence of cutting forces. To determine the  amplitudes of the cutter oscillations, the Mohr integral was used, and the amplitude-frequency characteristics were determined using the Duhamel integral. Cutting forces were determined taking into account the shape and nature of chip formation, the value of technological modes and processing conditions. As the material to be machined, the authors considered the cast iron with a layer hardened by diffusion alloying. Determination of input data for model was carried out directly during machining on the lathe and with the help of measurements of chip parameters. As cutting tools, we used standard cutters with mechanically fastened plates. The evaluation of the modelling results showed high convergence with the experimental results: the error in amplitude was 8.5 percent, in oscillation frequency - 12.3 percent; in general, the error did not exceed 15 percent. Thus, the developed model can be used for preliminary vibration assessment at the design stage of turning operations.