Control of Machining of Axisymmetric Low-Rigidity Parts

The specific character of the process of machining of axisymmetric low-rigidity parts makes it difficult to obtain finished products with a required accuracy of shape and dimensions and surface quality. The methods traditionally used to achieve accuracy in the machining of low-rigidity shafts considerably reduce the efficiency of the process, fail to meet modern automation requirements, and are uneconomical and not very productive, which means new methods for controlling the machining of low-rigidity shafts need to be looked for. This article presents a structural and a calculation scheme of a machining system for the turning of low-rigidity parts and a control model based on the second-order Lagrange equation. The first section of this paper presents qualitative relationships among variables in the proposed technological system for machining axisymmetric low-rigidity parts. Moreover, schematic of the machining system for the processing of such parts as well as equations describing the energy state of the machining system is presented. Next, mathematical model of optimal system control during the machining process, which permits to control a system under specific conditions and obtains a higher shape accuracy were introduced. The key stage of the verification process concerns the numerical validation of proposed solutions. Experimental studies confirm that the utilization of the proposed mathematical models describe the properties of the original object with sufficient accuracy and allow to obtain a higher machined shaft shape accuracy.