Electronic Circuit Simulation and Digital PC-Based Implementation of Dynamic MRR Optimization

Dynamic MRR (material removal rate) modeling is constructed and optimum solution through Calculus of Variations in maximize the machining profit of an individual cutting tool under fixed tool life is introduced. The mathematical model is formulated by reverse experiments on an ECOCA PC-3807 CNC lathe, and the electronic circuit is developed using linear regression technique for virtual machining. The inaccuracy between actual and simulated voltage is assured to be within 2%. By introducing a real-world CNC (computerized numerical control) machining case from AirTAC into the virtual system, the simulated cutting forces are shown to promise the feasible applicability of the optimum MRR control. Additionally, the implementation of dynamic solution is experimentally performed on a proposed digital PC-based lathe system. The surface roughness of all machined work-pieces is found to not only stabilize as the tool consumed, but also accomplish the recognized standard for finish turning. Nomenclature a = average volume of material machined per unit part. B = upper MRR limit. ) (t M b ′ = marginal operation cost at ) (t M ′ ; where b is a constant. ) ( 2 t M b ′ = operational cost at time t. v C = transforming factor from voltage to cutting force. c = overall holding cost of unit chip per unit time. l c = labor cost per unit time. d = depth of cut. c F = cutting force. v F = voltage of cutting force. f = feed rate. s K = constant in the steady cutting force model. ) (t M = cumulated volume of material machined at time t. ) (t M ′ = MRR at time t. b O = machining cost per tool for the dynamic machining model. b O = machining cost per tool for the traditional machining model. P = revenue per unit part machined. p = constant in the steady cutting force model. T = tool life for the dynamic machining model. T = tool life for the traditional machining model. t ~ = time for the optimum MRR to reach B . Introduction Virtual reality (VR) is an emerging technology that aims at generating a perception of reality in a human subject, using devices that not only simulate more than one sense organ and a dynamic model of a real or fictitious environment [1] but also present complex plans to both experts and non-specialist [2,3]. In a CNC system, the cutting tool is driven to a desired position with guaranteed accuracy and speed according to a programmed command. In other words, they are inclined to be chosen at excessively low values with a view to prevent any physical damage or mechanical chattering of the CNC system, thus resulting in a lowering of machining efficiency. The MRR is an important control factors of machining operation [4,5,6]. As the MRR optimization under fixed tool life for is presented in the previous research [4], the attention to analyse cutting force economically has become necessary to the field. Since the virtual manufacturing (VM) is a kind of knowledge and computer-based system technology that integrates diverse manufacturing activities under a common umbrella, using VR technology [7], the interest to analyse the cutting forces prior to realization of the optimum MRR control through electronic circuit is arising. Additionally, many developments of PC-based machining systems have been in progress for the purpose of dynamic MRR control by manipulating feed-rate in accordance with constant depth of cut, a few of which are presented in this paper. Fuh et al. [8] have designed a variable structure system (VSS) controller on CNC turning machines. Rober and Shin [9] have also overridden the programmed feed-rate on the CNC milling machines as well as Kim and Kim [10] on the machining centers. Many case studies can also be found where adaptive control has been applied for the selection of optimal feed-rate [11,12,13,14]. Although the basic objective of adaptive control is to maintain consistent performance of a system in the presence of uncertainty or unknown variation in plant parameters, none of these existing on-line control schemes guarantee to achieve the maximum machining profit. As a way of command feed-rate transmission, most researches employed the method of driving servo-motor directly to rotate the ball-screw shaft. Such method guaranteed continuous adjustment of feed-rate; nevertheless, it had been pronounced by some practical limitations. In this paper, the virtual machining to analyse the cutting force by the electronic circuit is well proposed and studied. The accuracy between the actual and simulated voltages is guaranteed to be more than 98%. By introducing a real-world CNC machining case, the simulated cutting forces are found to agree the achievability of the theoretical study. To realize the dynamic solution, the control scheme on a commercialized lathe system with DSP (Digital Processor Controller) and a man-machine interface are then developed. Moreover, the real-word industrial machining case is experimentally performed on our proposed digital PC-based lathe system. Theoretical background The mathematical modeling and solution of single-tool turning operation under fixed tool life from the previous work are introduced and shown as below [5]. There are two feasible cases to be discussed.