The optimization of the control logic of a redundant six axis milling machine
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The optimization of the control logic of a redundant six axis milling machine Antonio Caputi1
· Davide Russo1
Received: 29 June 2020 / Accepted: 24 October 2020 © The Author(s) 2020
Abstract The primary task of machine tools is simultaneously positioning and orienting the cutting tool with respect to the work piece. The mechanism must avoid positioning errors, and limit forces and torques required to the motors. A novel approach for combined design and control of manufacturing means is proposed in this work. The focus is on the optimization of the control logic of a redundant 6 axis milling machine, derived from the 5 axis milling machine by adding redundant degree of freedom to the work piece table. The new mechanism is able to fulfill a secondary task due to the introduction of redundancy. The proposed methodology sets as secondary task the minimization of the rotary motors torque, or the minimization of the norm of the positioning error. The control is based on the solution of a constrained optimization problem, where the constraints equations are the kinematic closure equations, and the objective function is the table motor torque or the positioning error of the tool tip. The implementation of this framework in the virtual machine model of the mechanism shows an improvement of the performances: actually, the introduction of a redundant axis allows the minimization of the torques and position errors. Keywords Machine tool · Additive manufacturing · Mechanism redundancy · Optimization
Introduction One of the main tasks of machine tools, such as 5 axis milling machines, is realizing the simultaneously positioning and orienting the cutting tool respect to the work piece. This task must be fulfilled with the higher possible precision, and this means that the machine must avoid positioning errors. An error is defined as the norm of the vector representing the distance between the ideal configuration of the machine, and the actual position of the tool respect to the finished part reference frame. Errors of the machine tool directly affects the deviation of the dimensions of the work piece from the nominal specifics. Many authors (Kiridena and Ferreira 1993) refer to this quantity as volumetric error, which represents an index for the errors of a machine tool (Cheng et al. 2018). Volumetric errors are the result of the propagation of geometric unconformity of machine’s components, in the way they are assembled, and in their mechanical behaviour. In
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Antonio Caputi [email protected] DIGIP-Department of Management, Information and Production, Universita’ Degli Studi Di Bergamo, Viale Marconi 5, 24044 Dalmine, Italy
order to study this phenomena, different models have been used to describe the kinematic behaviour of the machine, such as the one based on the Denavit and Hartenberg convention (Lamikiz et al. 2008; Ziegert and Kalle 1994), or the one proposed by Suh et al. (1998). More recently, a model for the evaluation of the machining accuracy has been proposed by Cheng et al. (2016). The first efforts in
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