Compensation of machining errors of Bspline and Cspline
El Bechir Msaddek
Received: 5 February 2018 /Accepted: 8 May 2018 /Published online: 6 June 2018
Springer-Verlag London Ltd., part of Springer Nature 2018
The evolution of the interpolation methods towards a very high technicality requires a good choice of used type in the operation
of high-speed milling (HSM). The “Bspline” and “Cspline” interpolations present good solutions to guarantee the tool’scontin-
uous movement during machining. However, in a previous article, we have shown by a simulation tool that they generate
significant dimensional errors that decrease the precision of the machined part. In this article, a method of compensating for
these errors based on the insertion of the nodes, while respecting the predefined tolerance, has been developed. To do this, we
have modeled and simulated machining errors before and after compensation for each type of interpolation. To validate our
results, we have machined a test piece with the compensated and uncompensated Bspline and Cspline interpolations on the Huron
KX10 machine and we have measured the corresponding machining errors. The results have shown that the method of com-
pensation by the insertion of the nodes causes a significant reduction of the machining errors.
Nowadays, a lot of studies are focused on the types of inter-
polation that increase the smoothing of the toolpath when
machining the free-form parts. Among these interpolations
object of the study, we find the polynomial or spline functions
(NURBS, Bspline). Our previous research [1, 2] has shown
the influence of the interpolation type, such as the functions:
Bspline and Cspline, on the machining errors in HSM of a free
form (Fig. 1).
As results, we have noticed that the Bspline interpolation
generates fewer errors on the convex and concave shapes of
the warped shape, but it generates large errors when crossing
the discontinuities in tangency. In contrast for the interpolation
Cspline, the passage of the trajectory by the reference points
increases the precision in changes of direction, but it causes
the deceleration of the machine. Indeed, it is necessary to
develop a compensation method for these errors to ensure
trajectory smoothing while respecting the predefined (CAM)
tolerance. The goal is to obtain a relevant precision result
about high-speed machining of complex-shaped forms by
polynomial interpolations: Bspline and Cspline.
Recent studies have been interested in the compensation of
complex shape machining errors. Zuo et al. andZhuetal.
 have developed methods of compensation of geometrical
errors of machining system NC by the correction of the NC
codes. Poniatowska  has proposed a method for compen-
sating for systematic errors of free-form surfaces. The method
is based on MPM modeling by NURBS interpolation. Zhong
et al.  have developed a model of identification and com-
pensation of geometric errors of position (5-axis machine)
based on servo loops and recursive correction. Raksiri et al.
 have modeled and compensated machining errors in time
masked by “neural network” taking into account cutting
forces and geometrical defects. Lei et al. andHsuetal.
 have corrected geometric errors in real time or not by
compensation algorithms for 5-axis CNC machine tools.
Very little research has addressed the problem of errors
* El Bechir Msaddek
ENIS, Unit of Applied Fluids Mechanics of Process Engineering and
Environment, University of Sfax, Sfax, Tunisia
ENIT-INPT, Laboratoire Génie de Production, University of
Toulouse, Tarbes, France
The International Journal of Advanced Manufacturing Technology (2018) 97:4055–4064