This paper deals with a topical method for avoiding the tool to traverse singular positions in 5-axis machining. It is well known that the inverse kinematics transformation generates singular positions for which incoherent movements of rotary axes appear. However, in the paper, we show that due to uncertainties on the positioning, the singular position is actually characterized by a cone. We thus adopt the concept of singular cone. Following, we propose a method to deform the tool path so that the tool does not traverse the singular cone during machining. This method takes advantage of the description of the tool trajectory as B-spline curves. Therefore, the deformation corresponds to the displacements of certain control points wisely chosen. As the corrected tool path must still verify the machining tolerance, the displacement is limited by the admissible displacement which can be calculated in function of the geometrical characteristics of the tool and of the specified machining tolerance. The deformation method we propose can be extended so that the contact point is preserved. Our purpose is illustrated through the example of the machining of a surface in 5-axis high-speed machining (HSM). This illustration shows the efficiency of our method: incoherent movements are eliminated after tool path deformation and the dynamic performance of the machine tool is improved.

Avoiding 5-axis singularities using tool path deformation

The aim behind applying functional tolerancing to a mechanism is to widen the tolerances used in parts manufacturing according to the effective functional properties of the product. This step may be performed using CAD systems and geometrical specifications defined by ISO standards. The present paper will describe the complete process involved in functional tolerancing. The CLIC tolerancing method has been implemented within an Excel software environment. CAD models for parts have been imported via a STEP interface. According to this approach, the designer describes the assembly process; the CLIC system then determines the functional requirements corresponding to the joints between parts and generates all datum reference frames and tolerancing of set-up surfaces in compliance with ISO standards. CLIC also determines both the geometrical conditions of minimum distances in order to avoid interference between parts and the conditions for assembling small standard components. The designer next adds other functional requirements. For each such requirement, a tolerancing process creates location and orientation specifications for influential parts using datum reference frames derived during the previous stage. Excel formulae focusing on the sum of tolerances are generated using a three-dimensional statistical approach. Moreover, the tolerance database allows optimizing the tolerances and nominal dimensions of parts.

Generation of functional tolerancing based on positioning features

This paper deals with optimization of 5-axis trajectories in the context of high-speed machining. The objective is to generate tool paths suited to high speed follow-up during machining in order to respect cutting conditions, while ensuring the geometrical conformity of the machined part. For this purpose, the optimization of the tool axis orientations is performed using a surface model for the tool path, which allows integrating kinematical limits of the machine tool as well as classical geometrical constraints. The illustration of the optimization through an example highlights the gain in machining time, thereby demonstrating the feasibility of such an approach.

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Optimization of 5-axis high-speed machining using a surface based approach

Chatter is one of the main causes affecting the surface quality of machined parts. Since it occurs when a machining process is unstable, it is important to select process parameters that promote stability. However, this condition alone is not sufficient to ensure good surface shape because the dynamics of the machining system as a whole also affects the resulting surface. Thus, even in the absence of chatter, significant movement of the tool or the part may occur causing surface defects. This effect is significant in high speed milling. In order to select optimal machining parameters, a computationally efficient simulator has been developed based on a novel machined surface generation model capable of accurate and reliable prediction of the surface shape. The programme written in MATLAB® predicts the surface shape from which surface finish, waviness, form and position parameters can be determined. A test bench consisting of a relatively low frequency second order dynamic mode is used to hold a test sample. The results obtained on a machining centre show that the predictions favourably compare with experimental results.

Gerard Cognet

Papers

Integrated Design and Manufacturing in Mechanical Engineering

Contribution to a Multi-Views, Multi-Representations Design Framework Applied to a Preliminary Design Phase