OBRABOTKAMETALLOV TECHNOLOGY Vol. 24 No. 2 2022 of the shape of these surfaces by machining during the technological rotation of the unit [6, 7]. Hence, it is critical to develop a technology ensuring the shape accuracy of the rolling surface of riding rings, for which it is possible to calculate the modes and predict the result of processing. It is important for this technology to apply active methods to control the processing based on the measurement of surface accuracy parameters directly during processing. At the same time, the most relevant issues include modeling and calculation of processing modes based on data obtained after measurement [8]. The introduction of the mechanical processing technology with regard to rollers and riding rings of cement kilns and elements of any large structures requires the development and manufacture of special equipment, namely a measuring device and a processing module [9]. The most complete information on a complex technical system obtained on the basis of mathematical modeling and measurement serves the basis for the design of automated and regulated technological processes [10–12]. Solutions in the fi eld of measuring cylindrical parts and calculating the shape error [13-16] in conditions of basing uncertainty, complex operating conditions are based on statistical and deterministic mathematical models describing cylindrical bodies in statics and dynamics. There are mathematical models describing the behavior of cement kiln elements (riding rings, support rollers) and similar units and mechanisms based on various approaches and assumptions [17–19]. There are non-contact measurement systems [20–22] that improve the accuracy of measurements under conditions of vibration and dustiness of cement production, using laser research methods. Besides, there is a need to develop the appropriate software for these devices. It is obvious that this requires a lot of time and considerable fi nancial costs. Therefore, for the initial analysis of the effectiveness and applicability of the proposed technology, it should be tested using virtual modeling or a digital twin of the riding ring machining process. The purpose of this work is to improve mobile processing technologies using special measuring devices and processing modules. This will signifi cantly increase the interrepair cycle and reduce the time of mechanical processing of large parts – rotary bodies. The objectives of the study are to develop and analyze the mathematical models describing the basing and machining of a riding ring as a cylindrical object with a non-stationary rotation axis, to study the proposed methodology, to develop the control schemes and to implement the equipment for mobile machining. Materials and methods A full cycle of works was implemented during the study, which utilized the original control method: from determining the shape accuracy parameters to processing simulation along the calculated scheme. A riding ring is a large cylindrical body with a non-stationary rotation axis. During operation it is based on support rollers, while the unit itself does not have the rotation axis. Typically, the rollers are mounted at an angle of 60° relative to the kiln axis. Depending on the length and weight of such a technological drum, the number of supports may vary from 2 to 8–10 pieces. The location scheme does not change during repair machining or shape control (without the unit removal), while the processing module with the tool is based on the processed surface, and a centerless processing scheme is implemented. According to one of the existing technologies, the machining of support elements of rotating cement kilns is assigned after detecting the error in the shape of these parts exceeding the specifi ed value. The shape parameters of the rolling surface of operating kilns riding rings were taken for the virtual model. This allowed a comparative analysis of the machining techniques used. The rolling surface directly adopted for the model (Fig. 1) has a nominal diameter of 6.1 m, a width of 1 m, with a total radial runout value of about 12 mm, and a barrel-shaped profi le of the longitudinal section. The virtual model of the riding ring and devices was performed in the Siemens NX computer-aided design system. The calculation of the machining allowance requires data on the accuracy parameters of the shape of the entire machined surface. The following measurement technique with three-dimensional digital
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