J.M. Freeman

Modal parameter identification for CNC machine tools using Wavelet Transform

Abstract The paper presents a new use of the Continuous Wavelet Transform for modal parameter identification applied to CNC machine tools. Firstly, the resonant frequencies and damping ratios of the CNC machine tool axis drive are estimated in the frequency domain using the transmissibility relation at resonance. The experimental Bode diagrams are determined using a novel measurement practice for the decoding of signals generated by a position encoder. This paper focuses on a novel application of the Continuous Wavelet Transform to identify the resonance frequencies and corresponding damping ratios of the CNC machine tool axis drive. The proposed method has the ability to detect variations in the amplitude levels of weak components embedded in strong noise and non-stationary processes. The superior ability of the Wavelet Transform to identify accurately modal parameters is demonstrated by comparing the results of the two different methods.

Modelling and simulation of a feed drive using the transmission line modelling technique

The paper focuses on the modelling and simulation of a test rig and a digital drive is based on the transmission line modelling technique. The rig is a positioning system equivalent to a CNC machine tool feed drive. Accurate representations of dynamic systems included in electromagnetic, power electronic and some mechanical applications have been obtained until now by applying the transmission line modelling technique. The paper proposes a novel application of th~s method for simulation of closed loop control of the position of a test rig. The model includes the distributed parameter dynamics of the feed drive and the effect of mass distribution. This is based on the flexibility of transmission line modelling to develop lumped and distributed parameter systems. Also a transmission line model for the controller integrated into the digital drive is developed. Encouraging simulation results are obtained by using MATLAB. In this way, the CNC machine tools feed drives could be modelled with increasing accuracy as hybrid, distributed-lumped representations using numerical methods.

A New Approach To The Modelling AndSimulation Of A CNC Machine Tool Axis Drive

The paper presents a new approach to the modelling and simulation of a CNC machine tool axis drive. Modules have been created for different parts of the CNC machine tool. This allows greater flexibility in the construction of the model and an investigation of the interaction between model components. In this way all the shortcomings of the traditional methods are overcome. MATLAB / SIMULINK package has been used to simulate this new model for a CNC machine tool. Simulation results are very good, in accordance with CNC machine tool theory. The described approach allows the easy construction of detailed machine tool drive models. It represents the basis for future incorporation of geometric, non-rigid and thermal models of machine tool behaviour.

Ball-screw thermal errors - a finite element simulation for on-line estimation

Ball-screws are often used in machine tools with only a rotary encoder feedback on the end of the screw. Since this provides position feedback to the controller, any errors in the screw affect the accuracy of the machine. Also, these errors may change significantly when heating of the screw occurs during machining. This is often overcome by using a linear scale to provide the feedback. Unfortunately, fitting such scales to many machines may be mechanically difficult and costly. This paper describes the development of a system that utilises a minimum of temperature measurements as inputs to a thermal simulation model of the ballscrew. Thus it is possible to estimate on-line the thermal errors of the ball-screw, assuming that position measurements of the nut are available from the rotary encoder. From these positions and the temperatures of the nut and bearings it is possible to estimate the speed of the screw and hence, assuming a knowledge of the frictional and heat transfer characteristics, the heat generated in the nut, bearings and screw. The thermal model constitutes a one-dimensional finite analysis of the whole length of the screw. The output of the model is a temperature distribution along the screw and an estimate of the thermal errors along the screw. Also described is an experimental test rig, which provides facilities to test the model on-line. A laser position measurement is used to compare with the estimated position derived from the model. The results are graphically displayed and saved for future use in optimisation software to determine the parameters of the thermal model which best fit the experimental data. Improvements of better than 90% in the thermal error have been obtained.

Automated error analysis of serial manipulators and servo heads

Abstract This paper presents a general mathematical treatment of serial manipulators, an important example of which is the servo head. The paper includes validation by application to the angle head via comparison with the previously known transformations and a new application to the error analysis of the angle head. The usual approach to the error analysis of a servo head is to develop a geometrical model by elementary geometrical considerations using trigonometric relationships and various simplifying assumptions. This approach is very error prone, difficult to verify and extremely time consuming. The techniques described here constitute matrix methods that have been programmed in a general way to derive automatically the analytical equations relating the angles of rotation of the head and alignment errors in the head to the position of the tool and errors in that position. The approach is to use rotation and transformation matrices to evaluate the influence of the various errors such as offsets and angular errors. A general approach to the sign convention and notation for angular errors is presented in an attempt to reduce the possibility of errors of definition.

The digital injection of signals into machine feedback loops via incremental encoder interfaces

Abstract The paper outlines the methods available for the application of test inputs and the measurement of the response of computer numerical control (CNC) machines to changes in position set point. A new approach is described where a signal is injected digitally into the feedback loop of a CNC machine, and how this can be done using the compensation register of an incremental encoder interface board is considered. In principle, any signal can be added in this way, error correction, a test signal, etc. Indeed, several signals can be added ‘simultaneously’ into the various axes of the machine. However, the controller has built-in limits to the unpro-grammed moves that it will tolerate and will shut down the machine if these are violated. Hence, there is a limit in practice to the size of signal that can be injected, but the limit depends on the rate of change in the signal rather than its magnitude. Results are presented for a typical milling machine both for a step input and for system identification using pseudo-white-noise input. The method is very simple to apply on a machine having the necessary incremental encoder cards in the feedback loop, since no extra hardware is required.

Identification Of Modal Parameters AffectingThe Dynamic Performance Of CNC MachineTools

To compute, predict and eliminate the instantaneous errors in CNC machine tools requires computationally fast and efficient algorithms. One important aspect of proficient condition monitoring is the use of a mathematical model, which adequately replicates the dynamic behaviour of the machne tool. Recent studies established that the models of the machne tool feed drives have to incorporate explicit damping factors in order to achieve a realistic dynamic performance. The necessity of determining fast and accurately the modal parameters of the model became very important. In answer to ths, a novel application of wavelet transform for the determination of damping coefficients and resonance states for the feed drives was developed. It is based on wavelet analysis, which permits the simultaneous identification of signal characteristics in time and frequency domains. The wavelet transform is proved again to be an excellent analysis method for non-stationary signals allowing the individual identification of modes that are close to each other in frequency or damping ratios that are high.

A general data logger for the measurement of the dynamics and the parameter estimation of machine tools

The measurement of the static and dynamic response of machine tools requires sophisticated data acquisition systems. It is often required in the same experiment to access measurements from lasers, linear scales, rotary encoders, non-contact probes, temperature sensors etc. These usually need to be accessed in real time and at high sampling rates. It is sometimes necessary to output data to the machine tool for identification and control purposes. The resulting data needs to be processed by powerful but flexible signal processing software in order to extract the frequency responses and machine parameters such as damping ratios. Finally, the results need to be presented graphically and made available for transfer to other systems such as Matlab. As outlined in this paper, many commercial systems are available to accomplish these tasks, but a custom-built system has overcome problems and limitations associated with their use. A simple application of the resulting bespoke data logger system is presented involving the measurement of static and dynamic errors of a machine tool.

The reconstruction of cyclically perturbed signals from aliased data

There are many applications where data could satisfactorily be sampled at low rates if it were not for the influence of some high frequency cyclic perturbation caused by an external influence. For example, the static sampling of error data for a ball-screw, where the perturbations are approximately sinusoidal and are caused by cyclic errors in the screw. Another example is the cyclic effect that errors in gear teeth have on the transmission error in gear systems. Signals from ball-screws often contain a component of known frequency above the Nyquist frequency. This is here assumed to be sinusoidal and caused by errors in the screw, but it could be any periodic signal of known shape from any source. The magnitude of the effect of the perturbations at any point along the signal is unknown, except that it shows up as an envelope of the aliased data. Also, the phase angle of the perturbations in relation to the start of the signal must be found. In favourable circumstances it has been possible to estimate the phase and magnitude of the perturbations and to reconstruct the original signal at a sampling frequency above the Nyquist frequency by adding the estimated sinusoidal effect to the smoothed data. It is common practice to obtain aliased or non-aliased data using static measurements of ballscrew errors. Also, it is possible to obtain non-aliased data at a very high sample rate using a dynamic measurement technique. Thus the validity of the methods presented above have been tested. The methods and results arc described and confirm that the reconstruction of periodically perturbed data from aliased samples is possible under favourable conditions.

Practical calibration of tracking laser systems

Tracking lasers have potential for the fast, automatic gathering of static calibration data for measuring the position of the end effector for robotic systems. There are two fundamental designs for tracking laser measurement systems. The first uses a tracking laser interferometer, which provides displacement and angular measurement data, giving a polar coordinate measurement. The second provides only angular data, which requires multiple laser units to allow measurement of the position of a target by triangulation. This paper describes the calibration of iMe LaserTrace system, which has the latter configuration.