A numerical approach for 3D manufacturing tolerances synthesis

Making a product conform to the functional requirements indicated by the customer suppose to be able to manage the manufacturing process chosen to realise the parts. A simulation step is generally performed to verify that the expected generated deviations fit with these requirements. It is then necessary to assess the actual deviations of the process in progress. This is usually done by the verification of the conformity of the workpiece to manufacturing tolerances at the end of each set-up. It is thus necessary to determine these manufacturing tolerances. This step is called "manufacturing tolerance synthesis". In this paper, a numerical method is proposed to perform 3D manufacturing tolerances synthesis. This method uses the result of the numerical analysis of tolerances to determine influent mall displacement of surfaces. These displacements are described by small displacements torsors. An algorithm is then proposed to determine suitable ISO manufacturing tolerances

3D manufacturing tolerancing with probing of a local work coordinate system

International audienceThe safety and performance requirements for mechanisms are such that the necessary accuracy of part geometry is difficult to reach using classical manufacturing processes. This paper proposes a manufacturing tolerance stack-up method based on the analysis line method. This technique enables both the analysis and the synthesis of ISO manufacturing specifications through a new approach which relies on production specifications, adjustment specifications and their analysis to stack up the 3D resultant. The originality of the method resides in the 3D calculation for location requirements, which takes into account angular effects and probing operations on numerical-control machine-tools in order to define a local Work Coordinate System (WCS). For achieving tolerance analysis, deviations are modelled using Small-Displacement Torsor. This tolerance analysis method enables one to determine explicit three-dimensional linear relations between manufacturing tolerances and functional requirements. These relations can be used as constraints for tolerance optimization

Allocation of geometric tolerances in one-dimensional stackup problems

Many tolerancing problems on mechanical assemblies involve a functional requirement depending on a chain of parallel dimensions on individual parts. In these one-dimensional cases, simple methods are available for the analysis and the allocation of dimensional tolerances. However, they are difficult to extend to geometric tolerances, which must be translated into equivalent dimensional tolerances; this allows the analysis but makes the allocation generally impossible without Monte Carlo simulation and complex search strategies. To overcome this difficulty, the paper proposes a way of dealing directly with geometric tolerances in the allocation problem. This consists in expressing the functional requirement as a linear model of geometric tolerances rather than equivalent dimensional tolerances; the coefficients of the model (sensitivities) are calculated considering both the dimension chain and the standard definition of the geometric tolerances. The approach can be combined with any constrained optimization method based on sensitivities. The optimal scaling method, previously proposed for dimensional tolerances, is extended to geometric tolerances and used in two examples to demonstrate the simplicity of the overall workflow and the quality of the optimal solution

Tolerancing and Sheet Bending in Small Batch Part Manufacturing

Tolerances indicate geometrical limits between which a component is expected to perform its function adequately. They are used for instance for set-up selection in process planning and for inspection. Tolerances must be accounted for in sequencing and positioning procedures for bending of sheet metal parts. In bending, the shape of a part changes not only locally, but globally as well. Therefore, sheet metal part manufacturing presents some specific problems as regards reasoning about tolerances. The paper focuses on the interpretation and conversion of tolerances as part of a sequencing procedure for bending to be used in an integrated CAPP system

A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation

Tolerancing decisions can profoundly impact the quality and cost of the mechanism. To evaluate the impact of tolerance on mechanism quality, designers need to simulate the influences of tolerances with respect to the functional requirements. This paper proposes a mathematical formulation of tolerance analysis which integrates the notion of quantifier: ‘‘For all acceptable deviations (deviations which are inside tolerances), there exists a gap configuration such as the assembly requirements and the behavior constraints are verified’’ & ‘‘For all acceptable deviations (deviations which are inside tolerances), and for all admissible gap configurations, the assembly and functional requirements and the behavior constraints are verified’’. The quantifiers provide a univocal expression of the condition corresponding to a geometrical product requirement. This opens a wide area for research in tolerance analysis. To solve the mechanical problem, an approach based on optimization is proposed. Monte Carlo simulation is implemented for the statistical analysis. The proposed approach is tested on an over-constrained mechanism

Manufacturing variation models in multi-station machining systems

In product design and quality improvement fields, the development of reliable 3D machining variation models for multi-station machining processes is a key issue to estimate the resulting geometrical and dimensional quality of manufactured parts, generate robust process plans, eliminate downstream manufacturing problems, and reduce ramp-up times. In the literature, two main 3D machining variation models have been studied: the stream of variation model, oriented to product quality improvement (fault diagnosis, process planning evaluation and selection, etc.), and the model of the manufactured part, oriented to product and manufacturing design activities (manufacturing and product tolerance analysis and synthesis). This paper reviews the fundamentals of each model and describes step by step how to derive them using a simple case study. The paper analyzes both models and compares their main characteristics and applications. A discussion about the drawbacks and limitations of each model and some potential research lines in this field are also presented

Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces

The tolerancing process links the virtual and the real worlds. From the former, tolerances define a variational geometrical language (geometric parameters). From the latter, there are values limiting those parameters. The beginning of a tolerancing process is in this duality. As high precision assemblies cannot be analyzed with the assumption that form errors are negligible, we propose to apply this process to assemblies with form errors through a new way of allowing to parameterize forms and solve their assemblies. The assembly process is calculated through a method of allowing to solve the 3D assemblies of pairs of surfaces having form errors using a static equilibrium. We have built a geometrical model based on the modal shapes of the ideal surface. We compute for the completely deterministic contact points between this pair of shapes according to a given assembly process. The solution gives an accurate evaluation of the assembly performance. Then we compare the results with or without taking into account the form errors. When we analyze a batch of assemblies, the problem is to compute for the nonconformity rate of a pilot production according to the functional requirements. We input probable errors of surfaces (position, orientation, and form) in our calculus and we evaluate the quality of the results compared with the functional requirements. The pilot production then can or cannot be validated

Experiments in fixturing mechanics

This paper describes an experimental fixturing system wherein fixel reaction forces, workpiece loading, and workpiece displacements are measured during simulated fixturing operations. The system's configuration, its measurement principles, and tests to characterize its performance are summarized. This system is used to experimentally determine the relationship between workpiece displacement and variations in fixed preload force or workpiece loading. We compare the results against standard theories, and conclude that commonly used linear spring models do not accurately predict workpiece displacements, while a non-linear compliance model provides better predictive behavior