M2000-174

Model-Aided Adaptive Control Constraint on Machine Tools

Michael F. Zäh, Germany

Abstract

On machine tools, chatter often prevents installed drive power being exploited to the full. The compliance of the machine frame and of the drive systems are usually responsible for this kind of dynamic instability. A dynamic process model with a closed loop structure can be used to simulate the operating behavior of the machine, which is characterized by the chatter-free workable depth of cut. The results of this simulation can be employed for stability-constrained adaptive control with a personal computer connected to a machine tool.

Introduction

A low-disturbance production cycle is a prerequisite for the cost-effective operation of complex production systems. For machine tools being the building blocks of such systems there is a particular need to exploit the full installed drive power in order to obtain high material removal rates. This entails a goal conflict for the user, since any machine tool approaches its dynamic loading limits when its cutting power is progressively increased. If the stability threshold is crossed, chatter vibrations will disturb the production cycle.

Chatter as a Disturbing Variable on Machine Tools

A variety of disturbances affect the production system "machine tool". The most important are self-excited chatter vibrations resulting from dynamic instability of the overall machine-tool/machining-process system. There is a variety of effects of chatter on machine tools. Apart from much increased tool wear extending to breakouts of entire cutting edges, chatter generates greatly enhanced and usually intolerable noise emissions. In extreme cases, it may damage the machine. It invariably results in unsatisfactory workpiece-surface quality. For this reason alone, it is essential that chatter should be prevented. Often, however, this entails operating the system at well below its performance limit. Cost-effective operation may no longer be possible. The objective of the machine tool user must be to minimize the influence of this disturbing variable, in order to utilize the installed drive power to the fullest possible extent.

Structure of a Dynamic Process Model

For this purpose the author created a dynamic process model. The model has a feedback structure and is based on closed-loop control methods. In the model, the machine constitutes a multidimensional compliant system influenced by dynamic and static components of the cutting force. These force components cause displacements of the tool in relation to the workpiece in the spatial axes x, y and z, which are superimposed on the selected feed and cutting speed values. Owing to the dependence of the components of the cutting force on these two variables, the forces in cutting, feed and passive direction exhibit a dynamic component superimposed on the static force values. When these two paths interact unfavorably, a feedback system of this kind tends towards instability, which results in chatter.

Dynamic Behavior of Machine Tools

A dynamic process model of this kind provides sufficiently accurate information only if the process-dependent specific dynamic properties of the particular combination of cutting process and machine type are adequately reflected in the model. Therefore special characteristics of the cutting process have to be taken into consideration, such as rotating workpiece (turning) versus rotating tool (milling, drilling, grinding, circular sawing) or one cutting edge versus multiple cutting edges among several others. The special dynamic behavior of the machine tool has to find is representation in the model as well. For circular sawing machines, which are used as an example, this is the high compliance of the saw blade and the torsional weakness of the main drive as a result of the application of a complex gearbox between main motor and saw shaft.

Instability Mechanisms

Various mechanisms inherent in the machining process may push the innately stable machine tool system to its stability limits. Of these mechanisms, the regenerative effect (repeated contact of the tool with a vibration-induced waviness of the workpiece), the F-v-characteristic (cutting force components decreasing with rising cutting speed) and mode coupling (mutual excitation of mode shapes via the machining process) are represented in the model.

Simulation and Results

For the purpose of process simulation, the model described above can be implemented in a computer program. Of particular interest is the susceptibility of the system to self-excited chatter, characterized by the stability of the closed loop system described above. This can be determined with the aid of the Nyquist stability criterion. The conventional representation of stability behavior is the form of stability charts, in which the stability limit is plotted versus different cutting parameters. The maximum chatter-free depth of cut is suitable for standardizing the stability limit of the machine. Taking one cutting parameter, e.g. cutting speed or feed, as the input variable for a simulation run leads to a two-dimensional stability chart while using two parameters provides a three-dimensional graph.

Adaptive Control

The author has developed a PC-based control system connected to a machine tool, which extends support for machine tool users beyond the simulation itself. Simulation results are integrated in a system, which identifies chatter as it occurs and automatically alters the cutting speed and feed rate in such a way that the chatter decays. A circular sawing machine was used to demonstrate the functionality of this system. Systems of this kind, automatically adjusting, correcting or even optimizing the cutting speed and feed rate within given constraints, are known as Adaptive Control (AC) systems. A system intended to operate the machine as closely as possible to its stability limit and to counteract any occurring instability by modifying the setting values is an ACC (Adaptive Control Constraint) system, in which the stability limit represents the constraining parameter.

In the system to be presented, a personal computer is used as the control unit. This is linked with the machine via a digital/analogue interface (A/D-D/A) and a number of sensors. It relieves the machine operator of the task of specifying the cutting speed and feed rate, as these are selected automatically from a database. The sensor signals are processed during the cutting operation. If the chatter related signal crosses a previously determined voltage threshold, the PC interprets the event as chatter and modifies the cutting speed and feed rate to stabilize the process. Stability analysis indicates the way in which these variables should be altered to achieve rapid stabilization at the highest possible material removal rate.

In the procedure described above the use of a chatter sensor closes the loop, providing a feedback adaptive control. There may be other cutting situations that are not suitable for the application of a closed loop system. In this case, an off-line simulation of the cutting process is used to determine a favorable setting of cutting speed and feed rate, which provide stable cutting conditions throughout the process.