François Thiébaut

CNC tool path in terms of B-spline curves

Abstract We present an accurate and efficient method to generate a CNC tool path for a smooth free-form surface in terms of planar cubic B-spline curves which will be fed into a free-form curve interpolator. We assume the use of a three-axis CNC machine tool with a ball end-mill cutter. We first interpolate break points, which are generated by computing the offset surface – driving plane intersection curve reflecting the curvature, by a planar cubic B-spline curve. We then evaluate the maximum scallop height along a scallop curve by computing the stationary points of the distance function between the scallop curve and the design surface. Furthermore, we compute the maximum pick feed such that the maximum scallop height along a scallop curve coincides with the prescribed tolerance. Illustrative examples show the substantial improvements this method achieves over conventional methods where the tool path consists of linear or circular paths.

Assembly Sequence Influence on Geometric Deviations of Compliant Parts

This paper presents a non-rigid part variation simulation method for fulfilling functionnal requirements on compliant assemblies. This method is based on the propagation of different geometrical deviations (manufacturing and assembly process defects) using the method of influence coefficient. Tolerance analysis of compliant assemblies is also achieved very early in the design stage. As a consequence, designers and manufacturing engineers can efficiently analyse the assembly design principles both in terms of installed stresses and geometric variation clearance. They can also set optimised sequences that enable ridding of geometric variations.

Determination of relative situations of parts for tolerance computation

This work is to contribute to three goals: a mathematical model of part geometric deviations, computation principles for three dimensional tolerance chains and a tolerance scheme in a mathematical form. We use an example to show present conclusions of this work according to the second goal. Then, we focus on a new problem faced in achieving the whole process of tolerancing. If the small displacement torsor is a useful tool to describe the relative situation of two simple surfaces, it’s more difficult to describe the relative situation of two parts involving several different couples of surfaces, what is wanted in mechanism study. We first explain the combinatory nature of this problem and ways to reduce it.

DIMENSIONAL METROLOGY OF FLEXIBLE PARTS: IDENTIFICATION OF GEOMETRICAL DEVIATIONS FROM OPTICAL MEASUREMENTS

This paper deals with an approach to identify geometrical deviations of flexible parts from optical measurements. Each step of the approach defines a specific issue to which we try to give an answer. The problem of measurement uncertainties is solved using an original filtering method, leading to only consider a few number of points. These points are registered on a mesh of the CAD model of the constrained geometry. From finite element simulation of the measuring setup and of external forces, the shape resulting from deflection can be identified. Finally, geometrical deviations are obtained by subtracting geometrical deflections to measured geometrical deviations.

Towards an Approach for Rapid Copying of Free-Form Surfaces in 5-Axis Machining

The paper deals with the various steps of free-form copying from surface acquisition to machining using five “positioned” axes. The originality of the proposed approach is to be free from surface reconstruction.

Functional and Manufacturing Specifications

During all steps of product life cycle, especially at the design level and manufacturing level, a coherent model for functional geometry of the product is required. The inherent imperfections of manufacturing processes involve a geometrical deterioration of functional geometry of the product, and therefore of its quality.

Assisted Decision-Making for Assembly Technique Selection and Geometrical Tolerance Allocation

Assembly process planning involves many aspects from geometrical matters to operational research. Though, the literature shows very few works about assembly technique selection.

Contribution of a mathematical model of specifications of a part to their coherence analysis

This paper presents a method to check the validity of the geometric specifications of a given part. We use a substitute part constituted with exact surfaces and we assemble this part on another which represents both the specified datum frame and the location of the tolerance zone. This model permits to know if some part features are over constrained or if the specification is not sufficient to define the location of the tolerance zone.

A certification method for the milling process of free-form surfaces using a test part

It is generally admitted that the manufacturing of free-form surfaces requires the use of a CAD-CAM system. The toolpath accuracy and the dimensional quality of the final shape have to be in accordance with the geometrical specifications. But most of the time, the final parts present deviations from the expected shape. These deviations may be due to either the toolpath calculation (CAM system) or the cutting process itself. In the paper, we propose an analysis of the whole milling process to point out the possible sources of errors. These errors generally lead to geometrical deviations and the final part does not meet the required specifications. As the errors can be linked to geometrical particularities of the shape, we propose a test part associated with check means to bring out problems. The milling of this part using two different techniques of toolpath generation shows that obviously both toolpaths are not error-free and that errors result from different geometrical particularities of the part surfaces.

Toward a Computer Aided Tolerancing System for Parts and Mechanisms

The works carried out in the fields of tolerancing or mechanism specifications are performed using two complementary approaches: the mathematization of tolerances and the definition of efficient tools for Computer Aided Tolerancing. After explaining our model of geometric deviations, we present the different possibilities to aid the designer. A tolerancing strategy is then presented and exemplified with a gear. This study permits to bring out the contribution of the behavior laws of a mechanism to the part specification. Indeed, the sensible choice is made with the help of the mathematical description of the functional requirements. This mathematical description gives all the necessary deviations to be constrained for each part.