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.

Quality control is an important factor for manufacturing companies looking to prosper in an era of globalization, market pressures, and technological advance. The functionality and product quality cannot be guaranteed without this important aspect. Manufactured parts have deviations from their nominal (CAD) shape caused by the manufacturing process. Thus, geometric inspection is a very important element in the quality control of mechanical parts. We have focused here on the profile inspection of non-rigid parts which are widely used in the aeronautic and automotive industries. Non-rigid parts can have different forms in a freestate condition compared with their nominal models due to residual stress and gravity loads. To solve this problem, dedicated inspection fixtures are generally used in industry to compensate for the displacement of such parts for simulating the use state in order to perform geometric inspections. These fixtures and the inspection process are expensive and time-consuming. Our aim is therefore to develop an inspection method which eliminates the need for specialized fixtures by acquiring a point cloud from the displaced part using a contactless measuring system such as optical scanning and comparing it with the CAD model for the identification of deviations. Using a non-rigid registration method and finite element analysis, we will numerically inspect the profile of a non-rigid part. To do so, a simulated displacement is performed using an improved definition of boundary conditions for simulating unfixed parts. In this paper, we will apply an improved method on two industrial non-rigid parts with free-form surfaces simulated with different types of displacement, defect, and measurement noise.

Dimensional inspection is an important element in the quality control of mechanical parts that have deviations from their nominal (CAD) model resulting from the manufacturing process. The focus of this research is on the profile inspection of non-rigid parts which are broadly used in the aeronautic and automotive industries. In a free-state condition, due to residual stress and gravity loads, a non-rigid part can have a different shape compared with its assembled condition. To overcome this issue, specific inspection fixtures are usually allocated in industry to compensate for the displacement of such parts in order to simulate the use state and accomplish dimensional inspections. These dedicated fixtures, their installation, and the inspection process consume a large amount of time and cost. Therefore, our principal objective has been to develop an inspection plan for eliminating the need for specialized fixtures by digitizing the displaced part's surface using a contactless (optical) measuring device and comparing the acquired point cloud with the CAD model to identify deviations. In our previous work, we developed an approach to numerically inspect the profile of a non-rigid part using a non-rigid registration method and finite element analysis. To do so, a simulated displacement was performed using an improved definition of boundary conditions for simulating unfixed parts. In this paper, we will improve on the method and save time by increasing the accuracy of displacement boundary conditions and using automatic node insertion and finite element analysis. The repeatability and robustness of the approach will be also studied and its metrological performance will be analyzed. We will apply the improved method on two industrial non-rigid parts with free-form surfaces simulated with different types of displacement, defect, and measurement noise (for evaluation of robustness).