Проведено тривимірне геометричне моделювання процесу формоутворення циліндричних деталей при шліфуванні зі схрещеними осями її та круга. Шліфування валів, які широко використовуються у автомобілебудуванні, верстатобудуванні, та валків стрічкопрокатних станів здійснюється за один установ орієнтованим широким абразивним кругом. На базі отриманої просторової моделі формоутворення та зняття припуску досліджено розподіл припуску вздовж різальної ділянки інструмента при шліфуванні орієнтованим інструментом. Показано, що на периферійній різальній ділянці шліфувального круга суміщаються чорнова, чистова обробки та калібрування. Розроблена модульна тривимірна модель правки периферійної ділянки шліфувального круга однокристальним алмазним інструментом при шліфуванні зі схрещеними осями інструмента та деталі з використанням уніфікованих модулів правлячого інструмента, орієнтації та формоутворення. На базі поданої моделі проведені дослідження геометричної точності формоутворення периферійної ділянки інструмента після його правки. З метою отримання необхідної мікрогеометрії та різальних властивостей абразивних кругів відповідно до особливостей процесу обробки валків стрічкопрокатних станів орієнтованим інструментом пропонується правка із зменшеною подачею правлячого інструмента до калібрувальної ділянки. При цьому величина подачі правлячого однокристального інструмента залежить від величини припуску. Різна подача правлячого інструмента забезпечує різну розвиненість різальної периферійної ділянки інструмента. Це, в свою чергу, збільшує інтервали між правками шліфувального круга, який працює у режимі затуплення. А отже, підвищується стійкість та зменшується собівартість обробки. Впровадження запропонованого способу правки кругів при однопрохідному шліфуванні зі схрещеними осями інструмента та циліндричної деталізабезпечить високіточність, якість оброблених поверхонь, а також значно підвищить ефективність та продуктивність процесу обробки. Розроблений спосіб правки може бути застосований для процесів круглого шліфування зі схрещеними осями оброблюваної деталі та абразивних кругів Ключові слова: двостороннє торцеве шліфування, схрещені осі, правка кругів, розвиненість поверхні круга, циліндричні деталі

Three-dimensional geometrical modeling of the processes of allowance removal and shaping of support necks and cams of camshafts when milling with crossed axes of the tool and part is proposed. Singlesetup milling of camshafts, which are widely used in automotive, tractor, shipbuilding and other industries, is carried out by a cutter with crossed axes of it and the part. The rotation angle of the cutter is selected from the condition of providing the required roughness of the treated surface and is regulated by the feed. At the same time, high processing productivity is provided by an increase in camshaft speed. A method of milling support necks and cams is developed, where the processing is carried out by a cutter, the height of which is less than the lengths of the processed surfaces. When processing the passage, the main allowance is removed by the end face of the quadrangular roughing carbide plate, and the finishing is carried out by the unloaded periphery of the cermet finishing plate. This allowance distribution increases the productivity and accuracy of processing, and the ability to rotate the roughing plate saves material and reduces the cost of processing. In the process of milling the curved surface of the camshaft cam, the depth of cut along the machined profile is always greater than the value of the removed allowance. This causes a decrease in the accuracy and productivity of processing. In order to eliminate this problem, it is proposed to stabilize the depth of cut and feed along the contour with uneven rotation of the part. The uniformity of the depth of cut and feed along the curved contour of the cam is achieved by simultaneous vertical and transverse movements of the cutter and uneven rotation of the camshaft. When milling the curved surface of the cam, the center of which does not coincide with the camshaft center, there is an uneven rotation of the latter and synchronous vertical and transverse movement of the cutter. When machining the cam section, the center of which coincides with the camshaft center, the cutter is given only rotation

This paper reports the spatial modeling of the dressing process of grinding wheels with a conical calibration area to enable two-sided end grinding of cylindrical parts. Components with cylindrical end surfaces are common in the industry, for example, bearing rollers, crosses, piston fingers, and others. High requirements are put forward for the accuracy and quality of the end surfaces. The most efficient is to machine them simultaneously on a double-sided face grinding machine. To improve the quality, grinding is carried out by oriented wheels. The wheel’s angle of rotation in the vertical plane is chosen subject to the uniform distribution of the allowance along a working surface; this makes it possible to reduce the temperature in the cutting zone and improve machining conditions. To improve the accuracy, grinding wheels are provided with a conical calibration area whose rectilinear generatrix is in the plane passing through the axis of wheel rotation and is perpendicular to the end of the part. The minimum permissible length of the calibration area depends on the diameter of the parts being machined; that makes it possible to utilize the work surface more efficiently. Two wheels are dressed simultaneously using diamond pencils that are symmetrically installed in a part feed drum. The angular velocity when dressing the rough area of the wheel is constant, which ensures its different development, and it gradually decreases when dressing the calibration area to provide for its constant roughness. In general, this prolongs the resource of grinding wheels and the quality of machining. The wheels are given axial movement to ensure the straightness of the cone calibration area. The dressing technique reported here can be used on machines equipped with a numerical software control system and without it. It could also be applied in the machining of parts with non-round ends

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.

Purpose. Improvement of schemes for processing the cylindrical surfaces of the shafts of gearboxes and transmissions of large-sized equipment. Development of modular spatial models of the processes of milling and grinding of the cylindrical surfaces of the shafts of gearboxes and transmissions of military and civil vehicles. Development of a model for dressing a grinding wheel with a diamond tool. Methodology. Creation of general and particular modular mathematical models of the processes of removal of allowance and shaping during rough and finish milling and finishing grinding of non-rigid cylindrical surfaces was carried out using a matrix apparatus for transforming coordinate systems. This made it possible to describe the treatment process using standard matrices. The calculations were carried out in the mathematical package Mathcad. To obtain a graphic display of the mathematical model of the instrumental and machined surfaces, the standard functions of the software package and the developed logical blocks were used. Findings. A technique for processing cylindrical surfaces of revolution with an oriented tool is proposed. Roughing, finishing and polishing are carried out in one setup. Roughing and finishing are carried out with an oriented cutter with replaceable multifaceted carbide inserts. The angle of orientation of the cutter is selected from the condition of maximum loading of the end section. Thus, the roughing stock is removed by the end face and by the finishing periphery, while the maximum component of the cutting force is directed along the axis of the part and does not cause deformations in the radial direction. Final finishing is carried out with a wide grinding wheel. The angle of orientation of the grinding wheel is selected from the condition of uniform distribution of the allowance along the periphery. A scheme for dressing the working surface of a grinding wheel with a diamond pencil with a constant feed is proposed. Originality. Modular spatial models of the processes of milling and grinding of the cylindrical surfaces of the shafts of gearboxes and transmissions of military and civil vehicles were developed. A model for dressing a grinding wheel is proposed. The use of the proposed models makes it possible to conduct a more detailed analysis of the processes of stock removal and shaping. Practical value. Dependencies are proposed for choosing the optimal angles of orientation of the cutter for roughing and finishing milling and the grinding wheel for finishing. The accuracy of parts is increased due to the elimination of the resetting error. The cost of manufacturing is reduced due to the maximum full use of cutting carbide inserts, by turning them and operating the worn finishing edge in the rough milling mode, as well as by increasing the resource of the grinding wheel.