Pierre Bourdet

A new format for 5-axis tool path computation, using Bspline curves

Abstract This article presents a new format of tool path polynomial interpolation in 5-axis machining. The linear interpolation usually used produces tangency discontinuities along the tool path, sources of decelerations of the machine tool whereas polynomial interpolation reduces the appearance of such discontinuities. The new format involves a faster tool path and a better surface quality. However, it imposes a modification of the process so as to take the interpolation format and the inverse kinematics transformation (necessary to 5-axis machining) into account. This article deals with the geometrical problem of tool path calculation. Validation tests are detailed. They show that profits concern the reduction of machining time as well as the quality of the machined surfaces. Indeed, the trajectory continuity avoids the appearance of marks and facets.

A Study of Optimal-Criteria Identification Based on the Small-Displacement Screw Model

Summary The geometric identification of a N-point measured surface may be obtained by means of 4 different optimalization criteria: least-squares on the error form, minimum form error, greatest interior tangential surface, smallest exterior tangential surface. In this paper a general and unique identification model based on the small-displacement screw is shown to be usefull for any surface and any criterion. On the basis of experimental results, dealing with planes, circles and cylinders, we have established a comparaison between the different optimalizing criteria.

A Computation Method for the Consequences of Geometric Errors in Mechanisms

The work presented here goes along the research for the principles that, starting from functional requirements, allow to compute the nature and value of tolerances on each part of a mechanism. In comparison with A.Clement’s or J.Turner’s works, our contribution is included in the formal description of the elements of tridimensional tolerance chains. This approach is built upon two elements, a modelization of geometric errors and a method of computation for their propagation inside of a mechanism. The modelization of geometric variations proposed here is founded upon the association of small displacement torsors to the different types of deviations that can be met in a mechanism. From then on, determining the parts’ small displacements under the effect of deviations and of gaps of the parts in a mechanism, becomes a computation of the composition of the modelized geometric errors. This computation of each part’s position yields two results. First, the formal determination of the part’s position in the mechanism in relation with the chains of influent geometric variations influenced by the parts’ surfaces. Then, the description of a combina- tory of a mechanism’s configurations. The application of this method shows the results obtained as well as the possibilities of extension towards a tolerancing aiding tool.

Geometrical Behavior Laws for Computer-aided Tolerancing

The analysis of the difficulties encountered with traditional dimension chains in the description of the behaviour of a set of parts, with variation, has led us to develop a tridimensional model of variations. It is therefore designed to treat the problem of transfer of dimensions.

Digitised point quality in relation with point exploitation

This paper deals with the quality of digitised points obtained with noncontact probes. The digitising system is analysed so that each source of inaccuracy can be isolated. In particular, for systems such as triangulation laser sensors, the use of the CCD camera is not influence free, and generates nonhomogeneous errors. All sources of inaccuracy of the digitising system lead to a point cloud, the quality of which is described through indicators. These indicators correspond to the digitising noise and the density of the data. In addition to those usual indicators, we suggest qualifying the point cloud through completeness and accuracy. The completeness identifies the dimension of the digitising gaps, while the accuracy is associated with the measurement uncertainty of a 3D point. For each indicator, an evaluation method is presented and then applied. However, the use of those quality indicators only makes sense if they are related to the point exploitation.

Aide in decision-making: contribution to uncertainties in three-dimensional measurement

Abstract The authorities of the standards organization International Organization of Standardization (ISO) advocate mastering any uncertainties in all parts of the industrialization process. In the three-dimensional (3D) measurement process, uncertainty is usually obtained at the end of a battery of tests. It is defined as a whole because it includes several types of errors, known systematic components, unknown systematic components and random components. Automated calculations of uncertainty can be made based on statistics. This method is based on statistical concepts, which are in accordance with “The Guide to the expression of the uncertainty in measurement” (GUM). It also enables us to generate uncertainties on the verification of ISO specifications (or specs in the ISO directives). In the course of this article, a usage will be presented that takes the knowledge of uncertainties into account: this usage will help the operator to take a decision on the conformance of a mechanical part in reference to its conformance to geometric tolerance.

A New Concept for the Design and the Manufacturing of Free-Form Surfaces: The Machining Surface

Abstract This paper deals with a modeling method of free-form surfaces based on the new concept of the machining surface. The machining surface is built so that design intents and manufacturing requirements are ensured and so that it completely defines the tool movement necessary to produce a part. Therefore, approximations appearing during the elaboration process (CAD modeling, tool path calculation and free-form machining) are minimized. The concept of the machining surface described here relies on an analysis of the process quality.

Uncertainties in CMM Measurements, Control of ISO Specifications

Abstract In the scope of quality control, accurate evaluation of measurement uncertainties is a real challenge to improve the use of Coordinate Measuring Machines (CMM). In our work, a new method, based on a statistical approach of the problem, was therefore developed, to deduce instantaneous measurement uncertainties directly from the set of acquired coordinates. The covariance matrix of the intrinsic parameters which characterize each analyzed surface is also evaluated, thus allowing an accurate propagation of the measurement uncertainties to the ISO specifications to be controlled. The experiments carried out in our study illustrate this new statistical approach and demonstrate its relevance.

Geometrical Tolerancing in Process Planning: A Tridimensional approach

Abstract A method to perform tridimensional analysis and tridimensional synthesis of machining tolerances is presented. The model relies on the small displacement torsor concept and on the computer aided tolerancing approach. The link between process planning and functional tolerances with torsor chains according to workpiece set-ups is exposed. An example shows how the model is used to determine automatically geometrical variations of the workpiece knowing geometrical variations of each part (part-holder, positioning devices, machined surfaces, etc.).

Quality of 3D digitised points obtained with non-contact optical sensors

Abstract Today digitising systems deliver large sets of data points which are representative of an object surface, in a relatively short time. These digitised data are generally exploited by applications such as reverse engineering, inspection or free form copying. However, the quality of the point exploitation is widely linked to the point quality, i.e. to the quality of the digitising process. To answer a part of this problem, we propose a method to locally evaluate the uncertainty of location of a 3D point in the whole measuring space. This uncertainty integrates errors due to digitising noise and optical phenomena. In particular, the use of noisy data in the calibration method implies a dispersion on the resulting 3D point as obtained from its 2D CCD location.