Trajectory Tracking and Contouring Control of Three Dimensional CNC



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electronics and communication engineering



Abstract­-­­In this study we analyzed a three- axes computer
numeric control (CNC) machine. Here improve the trajectory tracking of both
linear and circular trajectories using different controllers. Also introduce an
autonomous method for better trajectory tracking by different sensors are
placed on three-axes of CNC machines. There are different controller approaches
for improving trajectory tracking and contour performance are
proportional-integral –derivative (PID), observer based PID and feedforward
computed torque (FFCT). But in this paper introduce a new method is autonomous
method control with help of position sensors. This method is best solution for
improve the trajectory tracking ability of a CNC machine for both linear and
circular trajectories.


Index Terms­­­ computer numerical control (CNC), feedforwar
computed torque (FFCT),PID controller, autonomous



Computer numerical
control (CNC) machines tools are now widely used in manufacturing industry.
With an increasing demand on the accuracy of the CNC machines, now we are
research for various method to improve the accuracy of CNC machines. Contouring
accuracy in terms of contour error is a big concern for designers and
contouring type of CNC machines. Contouring error is defined as the  deviation of actual contour from that desired

   In CNC machines, a part is manufactured by a
part program which is tool type and feederate. The programme can be written by
computer-aided manufacturing (CAM)  or
manually written.

    This paper order to improve the trajectory
tracking ability of a CNC machines for both circular and linear trajectories by
using position sensors. There are different sensors are used according to their
applications. There are different controller approaches are also used for
better trajectory tracking, that is proportional-integral –derivative (PID),
observer based PID and feedforward computed torque (FFCT). Although computing
time increases, the autonomous method is found as the best solution for the
considered case to improve the trajectory tracking ability of the manipulator
for both liner and circular trajectories.

   In manufacturing system, the precision
motion control is a very importance, especially in CNC machines. For precision
motion control at CNC machines all axes must be controlled simultaneously. Axial
tracking errors may cause  simultaneously
coordination of axes. This coordination problem between axes can cause for
contour errors, that is it is the shortest distance between actual path and
desired contour. The best way to reduce tracking error is to improve tracking
accuracy of each axis individually. This is done by taking into account their
dynamic interaction tracking control 
approaches  to improve not only
tracking accuracy but also contouring accuracy. 

   Necessity of high precision CNC machine tool
system has been motivating advanced model-based control approaches to machining
process with high tolerance, better surface finishing and high speed. The
surface finishing is directly related to the deviation of the cutting tool from
the tool path trajectory. This deviation is contouring error, it measure the
cutting process quality. In the tracking control, the objective is to minimize
the tracking error in each axis separately, which cause for small contouring
errors. Small contouring errors can be achieved even when it  is impossible to attain small tracking errors
due to saturation of servo motor. Contouring control techniques have been
developed to take advantage of this fact, by placing higher priority in
minimizing contouring error than tracking errors.


Contouring accuracy

The contour
accuracy is the deviation of the actual path from the desired path. At any
point on the path, it is defined it is the orthogonal distance between actual
path and desired path. The relationship between the contour error and axial
tracking is shown in Fig. 1 in contouring system,










Actual point





Actual path




1 Contour error in CNC machines


 contour error are our primary concern than
axial tracking errors. In this figure, the desired path is shown as solid line
while the actual path taken is shown by dashed line. The figure also illustrate
an instance of time t when the desired position of the tool, as provided by the
outputs of the interpolator is at R. While, because of axial tracking errors, the
actual position of the tool is at P. From the figure it can be easily seen that
depending upon the relative magnitude of the axial tracking errors ,it is well
possible to have zero contour errors even for non- zero axial tracking errors.



Controlling a
machine tool by means of a prepared programme which contain numerical data
specifying the desired motion of the machine’s axis is called as numerical
control (NC). NC is founded by US Air Force in the early 1950s, after that
computer numeric control was developed.

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