The subject of research is the process of formation of surface layer when cutting non-rigid polymer composite prod-ucts. The objective of research is to improve the quality of machined surface and productivity of cutting of non-rigid cylindrical products, made of polymer composites, due to the integration of kinematic schemes of cutting. Methods: the analytical study, based on the fundamentals of machining process, theory of cutting and elasticity of anisotropic materials. The mathematical model of cutting process was built on the basis of the theory of vibration of elastic system. The surface roughness was measured by both contact and non-contact methods. The depth of defective layer was determined by means of the oblique cutting method with the use of scanning electron microscopy or scanning optical microscopy. The defect of geometric form was determined by the direct method of evaluation. The calculation of mathematical model of machining was performed, using the Computer Algebra System, referred to the class of computer-aided design systems Mathcad. The theoretical and practical results help to enhance the quality of machined surfaces and productivity of cutting of non-rigid cylindrical products, made of polymer composites, due to the integration of kinematic schemes of cutting, aimed at the mutual compensation of cutting forces and torque, acting on the product. Scientific novelty: the efficiency of multi-instrumental machining of non-rigid polymer composite products, based on the integration of kinematic schemes of cutting according to individual instruments to provide the compensation of forces and moments, acting on the product, was first theoretically based and experimentally confirmed, which allowed to obtain required roughness, crispness, depth of defective layer and defect of geometric form of surfaces together with the increase in the productivity of cutting process; the conditions, required for the mutual compensation of cutting forces and torque, acting on the product, were first specified on the basis of a developed general mathematical model of cutting process according to the integrated kinematics, and a rational cutting schedule and the boundary condition for vibration swing in the zone of cutting were first set; the condition for ensuring the desired quality of surface layer of non-rigid polymer composite products was first specified not to allow the vibration swing in the zone of cutting to exceed the size of roving, reinforcing the product in the direction normal to the machined surface. Degree of implementation: the practical value was confirmed by the acts of implementation of the results of thesis work at the State-Owned Enterprise "V.O. Malyshev" (city of Kharkiv) and in the learning process at the Ukrainian Engineering and Pedagogical Academy to train specialists in the field of machine-building industry. Sphere of implementation: machine-building industry, namely, material cutting.
