A tool-change scheduling model for machining centres

Abstract

Robert P. Davis, Richard A. Wysk and Delbert L. Kimbler Department of lndustrial Enghzeering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061, USA (Received October 19 78; revised January 19 79) Introduction Because of the increased cost of direct labour, as well as the shortage of competent machinists, the metal cutting industry is looking toward automation as a means to improve its stagnating productivity. Since 1950, the metal machining industry has seen the advent of Numerical Control (NC), Direct Numerical Control (DNC), Computer Numerical Control (CNC), and Computer Integrated Manu- facturing Systems (CIMS). NC essentially eliminated the machinist from metal cutting. DNC and CNC facilitated part programming and increased control over NC machines. And finally, CIMS integrated material handling and machin- ing under the control of a common central computer. Today, CIMS exist where all of the machining and material handling is done under the control of a single computer (or under the control of a network of computers), and the system is virtually devoid of expensive direct labour. 1,2 The use of automation, however, has brought about some difficult analytical problems. Many problems formerly resolved by a machinist's experience and intuition, coupled with his adaptive interpretation of the system, must now be resolved by means of a static control strategy. A par- ticular example of this situation is that of the toot-changing cycle. In a Conventional machining system, the machine operator decided when a particular tool should be changed based on the accuracy of the last part produced, the sound produced by the metal cutting operation, and the number of parts which were left to be machined. The accuracy of the last part and the sound produced in the metal cutting operation are indicators of the extent of tool wear. The queue of parts waiting for a particular tool is viewed to determine the maximum wear rate which will allow tool replacement after the batch is completed. In today's more modern m~chining systems, an operator is seldom solely responsible for the monitoring of a single machine tool. This would be especially true for DNC, CNC and CIMS and may also be true of stand-alone NC. Because an operator is not present to monitor and 'adaptively control' the machine, a mathematical formulation of the problem is required in order to develop algorithms for the efficient operation of automated machining systems. Several models have been developed for the selection of the optimum machining parameters: feed, speed and depth of cut. 3-s All of these models employ a functional relationship between the machining parameters and 'expected tool life'. The most commonly used expression for tool life is one developed by F. Taylor 6 in 1907. Taylor's tool life equation has been expanded to include several variables, such as workpiece hardness, tool approach angle, slenderness ratio, etc. However, for a given tool and workpiece, tool life can most simply be expressed as: C T L = Vaf#d ~ where: