Alex Ballu

Tolerance synthesis: quantifier notion and virtual boundary

Abstract The purpose of functional tolerancing process is to define the geometrical specifications of parts ensuring functional requirements. For automotive and aircraft industries, the tolerance synthesis has become an important issue in product design process. Indeed, designers need methods and rules to determine the tolerances. To define rules, a mathematical formulation of tolerance synthesis is detailed. This mathematical formulation of tolerance synthesis simulates the influences of geometrical deviations on the geometrical behavior of the mechanism, and integrates the quantifier notion (existential quantifier ‘there exists’ and universal quantifier ‘for all’). It takes into account not only the influence of geometrical deviations but also the influence of the types of contacts on the geometrical behavior of the mechanism; these physical phenomena are modeled by convex hulls (compatibility hull, interface hull and functional hull) which are defined in parametric space. With this description by convex hulls, a mathematical expression of the admissible deviations of parts integrates the quantifier notion. This notion translates the concept that a functional requirement must be respected in at least one acceptable configuration of gaps (existential quantifier there exists), or that a functional requirement must be respected in all acceptable configurations of gaps (universal quantifier for all). With this approach, some rules are formalized to determine the modifier (maximum material condition or minimum material condition) function from the type of quantifier. These rules have been performed with success in French automotive industries.

Choice of functional specifications using graphs within the framework of education

The teaching of three-dimensional tolerancing is relatively new and has to be improved. This paper develops the teaching of the choice of specifications. Two fundamental concepts are pointed out: the independence of the functional requirements and the influence of the parts, surfaces and deviations on a requirement

Biomechanical Analysis Comparing Natural and Alloplastic Temporomandibular Joint Replacement Using a Finite Element Model

PURPOSE Prosthetic materials and bone present quite different mechanical properties. Consequently, mandible reconstruction with metallic materials (or a mandible condyle implant) modifies the physiologic behavior of the mandible (stress, strain patterns, and condyle displacements). The changing of bone strain distribution results in an adaptation of the temporomandibular joint, including articular contacts. MATERIALS AND METHODS Using a validated finite element model, the natural mandible strains and condyle displacements were evaluated. Modifications of strains and displacements were then assessed for 2 different temporomandibular joint implants. Because materials and geometry play important key roles, mechanical properties of cortical bone were taken into account in models used in finite element analysis. RESULTS The finite element model allowed verification of the worst loading configuration of the mandibular condyle. Replacing the natural condyle by 1 of the 2 tested implants, the results also show the importance of the implant geometry concerning biomechanical mandibular behavior. The implant geometry and stiffness influenced mainly strain distribution. CONCLUSION The different forces applied to the mandible by the elevator muscles, teeth, and joint loads indicate that the finite element model is a relevant tool to optimize implant geometry or, in a subsequent study, to choose a more suitable distribution of the screws. Bone screws (number and position) have a significant influence on mandibular behavior and on implant stress pattern. Stress concentration and implant fracture must be avoided.

Assembly specification by Gauge with Internal Mobilities (GIM)—A specification semantics deduced from tolerance synthesis

Abstract Currently, standards such as ISO 1101 are used for the geometrical specification of mechanical parts. However, these standards are not sufficient to express exact functional requirements, even for assembly. The objective of this paper is to determine what to express exactly for assembly, that is, create the necessary specification semantics. A tolerance synthesis model is developed based on variational geometry. The model takes into account not only manufacturing deviations and gaps, but also the assembly process and nature of contacts between parts. The specification semantics is deduced from this tolerance synthesis. This semantics is based on virtual gauges, which are composed of an interface with the part and of a structure. The main contribution on the virtual gauge is the concept of internal mobilities allowing displacements between different entities of the gauge. This gauge takes also in account the nature of the contact between parts.

Global view of geometrical specifications

This paper deals with geometrical specifications, more particularly, with the geometrical concepts used.

Discrimination of objective kinematic characters in temporomandibular joint displacements.

Designing a temporomandibular joint (TMJ) total prosthesis requires the assessment of joint displacements for open/close movements. Current knowledge presents disc-condyle motions as involving both translation and rotation but there may be substantial variations from human to human. The aim of this study is to discriminate objective kinematic characters amongst thirty-two volunteers. The displacements are determined using 3D video analysis. The ratio between rotation and translation can be defined by introducing a coefficient. This coefficient varies relatively to the opening amplitude and presents the same dispersion rate whatever the variations. Then it allows to discriminate amongst volunteers, regardless of any jaw opening values. Three groups can be isolated relatively to three kinematic models: a translatory preponderant group, a common group and a rotatory preponderant group. All subjects in the first group present concomitant rotatory/translatory displacements up to maximal opening. The other two groups present variations due to different quasi-pure rotation phases at the end of the opening movement. These investigations will make it possible to establish a correlation between the kinematic characters and the disc-condyle trajectories. The disc-condyle glides along the temporal facet and the condyle centre describes the tubercular morphology. The temporal facet geometry, useful for the TMJ prosthesis design, will be studied in a next paper.

Formal Language for GeoSpelling

In order to tackle the ambiguities of Geometrical Product Specification (GPS), GeoSpelling language has been developed to express the semantics of specifications. A detailed syntax of GeoSpelling is proposed in this paper. A specification is defined as a sequence of operations on the skin model. The syntax is based on instructions used in computer programming language: call to functions and flow control by condition and loop. In GeoSpelling, the call to functions corresponds to the declaration of operations; loops make it possible to manage a set of features with rigor and conditions to select features from a set.

The processing of measured points in coordinates metrology in agreement with the definition of standardized specifications

Increasingly, coordinate measurement techniques are used to ensure that mechanical parts conform to their geometric specifications. The analysis of the possibilities of the software in use brought to light an important number of tools, which however are not always adapted to the problem which is to be solved. Generally these tools only give one approximate answer to the problem ser out by the verification of the dimensional and geometrical specifications . An indept study of the standards lead to be presentation, in this paper, of the problem typology. The two aspects of the verification of the specifications (measurement and control) will be presented and also the implication which these have on the solution algorithms. Finally, an attempt to define new processes giving the true value of the size to be verified is proposed. These proposals will be illustrated by an example, and the numerical results will be analysed and compared .

Tolerancing Analysis by Operations on Polytopes

Geometric tolerancing analysis consists of simulating the behavior of a mechanical system according to geometric defects in the constituent parts. The aim is to verify system compliance in terms of the functional requirements for its expected operation. When carrying out the simulation the geometric specifications of the constituent parts and specifications of parts potentially in contact must be taken into account. One approach using polytopes consists of characterizing the specifications of the parts, the specifications of the contacts and the functional requirements of the mechanical system using sets of geometric constraints. This article describes modeling different sets of constraints manipulated by polytopes. We introduce the operations that are applied (Minkowski sum and intersection) to determine the relative position of any two surfaces of a mechanical system. Finally, tolerancing analysis of a simple mechanical system is described.

The influence of condylar geometry and positions of bone fixation screws on a TMJ implant

There are several diseases that can affect the human temporomandibular joint (TMJ), among which we highlight cancer, trauma or fracture, congenital malformation and osteochondritis (Mercuri et al. 2007). TMJ reconstruction was developed to improve mandibular function and reduce disability (Mercuri 2009). Although implants have widely documented records of short-term successes, the recent arrival of failures and complications related to the placement of such implants again feed the discussions (Wolford et al. 2003). In the UK, the three currently available systems were implanted in 60–65 patients annually (Speculand et al. 2000). Total replacement of the TMJ involves the removal of the ‘non-functional’ joint and placing an artificial one. Owing to the nature of the bone structures involved in the joint, design of prostheses is complex. Materials and geometry play an important key role in enhancing the long-term life of the artificial joint (Britton et al. 2002). The most applied TMJ implants are rigid plates. Surgeons spend a very long time bending the plate to fit it to the contours of the bones (Speculand et al. 2000). This study aims to describe the influence on the strain distribution of different geometries and screw fixations.