In the context of product quality, the methods that can be used to estimate machining defects and predict causes of these defects are one of the important factors of a manufacturing process. The two approaches that are presented in this article are u
sed to determine the machining defects. The first approach uses the Small Displacement Torsor (SDT) concept [BM] to determine displacement dispersions (translations and rotations) of machined surfaces. The second one, which takes into account form errors of machined surface (i.e. twist, comber, undulation), uses a geometrical model based on the modal shapes properties, namely the form parameterization method [FS1]. A case study is then carried out to analyze the machining defects of a batch of machined parts.
Traditional tolerancing considers the conformity of a batch when the batch satisfies the specifications. The characteristic is considered for itself and not according to its incidence in the assembly. Inertial tolerancing proposes another alternative
of tolerancing in order to guarantee the final assembly characteristic. The inertia I2 = sqrt{delta^2 + sigma^2} is not toleranced by a tolerance interval but by a scalar representing the maximum inertia that the characteristic should not exceed. We detail how to calculate the inertial tolerances according to two cases, one aims to guarantee an inertia of the assembly characteristic the other a tolerance interval on the assembly characteristic by a Cpk capability index, in the particular but common case of uniform tolerances or more general with non uniform tolerances. An example will be detailed to show the results of the different tolerancing methods.
This work is a development from the Inetforsmep European project. We proposed to realize a global optimization of a deep drawing industrial progression (made of several stages) for a cup manufacture. The objectives of the process were the thickness d
ecrease and the geometrical parameters (especially the height). This paper improves on this previous work in the aim of mastering the contour error. From the optimal configuration, we expect to cut down the amount of the needed material and the number of forming operations. Our action is focused on the appearance of unexpected undulations (ears) located on the rim of the cups during forming due to a nonuniform crystallographic texture. Those undulations can cause a significant amount of scraps, productivity loss, and cost during manufacture. In this paper, this phenomenon causes the use of four forming operations for the cup manufacture. The aim is to cut down from four to two forming stages by defining an optimal blank (size and shape). The advantage is to reduce the cost of the tool manufacturing and to minimize the needed material (by suppressing the part flange). The chosen approach consists in defining a particular description of the ears part by modal decomposition and then simulating several blank shapes and sizes generated by discrete cosine transformation (DCT). The use of a numerical simulation for the forming operation and the design of an experiment technique allow mathematical links between the ears formation and the DCT coefficients. An optimization is then possible by using mathematical links. This original approach leads the ears amplitude to be reduced by a factor of 10, with only 15 numerical experiments. Moreover, we have limited the number of forming stages from 4 to 2 with a minimal material use.
The [ISO 1101] standard specifies the form errors with geometrical tolerances using the zone concept.To complete this concept, we present a generic method which adapts to any geometry and allows to describe any kind of errors. Thus,we can dissociate
the part errors according to reference categories: position, orientation,form, waviness and roughnesses. Starting from a cloud of poinds representing the error measurement, the modal method decompose, like Fourier series,this error in a sum of sorted errors according to the ircomplexity degree (a number of wavinesses). In addition, we propose to show, on a simple example, that according to error complexity to be characterized, an interpolation by the modal method allows to optimize the measuring strategy.
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 p
rocess 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.
