Abstract:In the work the analysis of existent methods of determination of local and general forces of cutting at polishing of surfaces with a type as the arc of circumference is given. The dependence for determination of speed polishing and method for determination of thickness of the cut away layer on condition of equality of the tricked into and taken off volumes of material are offered. The method of determination of cutting forces, which takes into account cutting and deforming grain, is suggested. The method of determining the thickness of a cutting layer of one of the cutting edge, from the condition that the volume of material that is brought and is cut in each local point of contact spots has been proposed. The proposed method takes into account the compliance of the processing system and the discontinuity of the abrasive surface of the tool. By experimental way upper limits of thickness cutting layer when using different abrasive materials for a wide range of cutting speeds have been obtained.

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In the article the method of grinding with crossed axes of the tool and the workpiece got further developed. The work discloses a method of processing details having an external surface with a profile in the form of an arc of a circle of variable radius (for example, rolls of pipe rolling mills). The particular three-dimensional geometric models of the processing, shaping and profiling of abrasive wheels have been developed. A method for controlling the grinding process, which ensures the removal of allowances along equidistant curves has been offered. The developed method of grinding provides a constant depth of cutting according to the coordinate of profile processing. This is achieved at the expense of the synchronous inclination of the wheel and its insertion by the size of the allowance. The diameter of grinding wheel affects on the maximum angle of orientation of the wheel has been proven. It has been shown that increasing the diameter of the abrasive wheel has led to a slight decrease in value orientation angle.

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This paper reports the spatial mathematical modeling of the process of dressing the working surface of grinding wheels for implementing the double-sided grinding of the ends of cylindrical components. Parts with high-precision end surfaces that are commonly used include bearing rollers, piston fingers, crosspieces of cardan shafts, and others. The geometric accuracy of surfaces is ensured by simultaneously grinding the ends at two-sided end-grinding machines with crossed axes of the part and wheels that operate under a self-blunting mode. Before starting the machining, the wheels are dressed in a working position. Moreover, the total orientation angle of the tools is selected subject to the condition of uniform distribution of allowance along the rough sections of wheels. Dressing involves a single-crystal diamond tool with a variable feed. That ensures different development of the surface of abrasive tools, which prolongs their operating time between dressings and improves overall stability. The constant size of micro irregularities at the calibration site enhances the quality of machining. The calibration site is made in the form of a straight line belonging to the plane that passes through the axis of rotation of the wheel and is perpendicular to the plane of the machined part. Based on the spatial mathematical models of the processes of removal of allowance and shape formation when dressing the wheel, the surface of the grinding wheel was investigated. Mathematical models for shaping the ends of parts when grinding with wheels with conical calibration sites have been proposed; it is shown that when applying the proposed machining scheme, there is no geometric error in the size of the part. In addition, due to the uniform distribution of the allowance along the rough area of the wheel, the quality of the surface layer of the ends of parts increases. The devised method for dressing the working surface of wheels could be used to grind the ends of non-circular components.