Parametric interpolation algorithms for motion control

Chow, Y.K., 2003. Parametric interpolation algorithms for motion control. PhD, Nottingham Trent University.

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Computer numerical controlled machine tools have been used in a wide range of applications. Machine drives have used both stepper motors and servomotors to control the motion. Stepper motors are a less costly alternative and are suitable for low-cost machining. Leadscrews convert the stepper motor's rotary motion to linear motion. This project has concentrated on stepper motors but it is expected that the algorithms could be extended for use with servomotors. Most stepper motor driven machine tools are used in an open-loop system. Since there is no feedback from the actual motion of the machine, extreme care has to be taken when designing the controller.

Investigations into multi-axis stepper motor continuous path machining systems have revealed problems affecting machining performance, such as vibrations. Earlier work within the research group has demonstrated how these vibrations arise from the excitation of machine dynamics, which are sometimes due to sudden variations in pulse rates. For high speed machining, the machine must be accelerated and the problem with vibrations becomes more severe. Such rough motion can then result in unsatisfactory path following, if it increases any positional error (deviation of the machined path from the desired path). Besides vibrations, another cause of positional errors may be the approximations made by the interpolation algorithms used. Many motion control systems also suffer from the disadvantage that they are not able to maintain a constant speed round a curve.

Previous researchers in the group have addressed the above problems with some success. Their work includes smoothing of unevenly spaced pulse timings after they have been generated. However, such smoothing may increase the positional errors. The work described in this thesis addresses the problems from a more fundamental viewpoint, by generating pulse timings that are smooth initially.

New line and arc interpolation algorithms have been developed for stepper motors, which calculate the timing for every individual pulse. These algorithms exploit recent advances in microprocessor technology which allow the use of a high-speed digital signal processor. A new, more general approach to interpolation has been applied, which avoids the need for the path to pass through particular intermediate points. A novel approach is to use the distance along the path as a parameter, which ensures synchronisation of the axes. With these algorithms sudden changes in speed can be avoided. Four partial simulation techniques have been developed in order to evaluate the algorithms. Simulation results show that we can expect not only significant reduction in positional errors but also greatly diminished fluctuations in speed. Therefore vibrations are also likely to be reduced.

New acceleration algorithms have been developed, so that the new interpolation algorithms can be used for high-speed machining. The algorithms are based on linear and parabolic acceleration algorithms described by previous authors. Simulation results show that the new acceleration algorithms are expected to allow the machine to follow the required curve closely while changing speed as required. Thus vibrations are again expected to be reduced.

An initial evaluation of the practical implementation of the new algorithms has been undertaken on a CNC machine. The results are promising and broadly in agreement with the simulation results.

Item Type: Thesis
Creators: Chow, Y.K.
Date: 2003
ISBN: 9781369324945
Rights: This thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with the author and that no information derived from it may be published without the author’s prior written consent.
Divisions: Schools > School of Science and Technology
Record created by: Laura Ward
Date Added: 24 Jun 2021 10:20
Last Modified: 26 Oct 2023 08:51

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