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The general structure of geometrically‐based automatic finite element modelling systems is discussed. The development of a specific system employing the modified‐quadtree and modified‐octree mesh generators is presented. The application of this approach to metal forming analysis is then given.

Preparing digital mock-ups (DMUs) for finite element analyses (FEAs) is currently a long and tedious task requiring many interactive CAD model transformations. Functional information about components appears to be very useful to speed this preparation process. The purpose of this paper is to shows how DMU components can be automatically enriched with some functional information.

DMUs are widespread and stand as reference model for product description. However, DMUs produced by industrial CAD systems essentially contain geometric models, which lead to tedious preparation of finite element Models (FEMs). Analysis and reasoning approaches are developed to automatically enrich DMUs with functional and kinematic properties. Indeed, geometric interfaces between components form a key starting point to analyze their behaviors under reference states. This is a first stage in a reasoning process to progressively identify mechanical, kinematic as well as functional properties of components.

Inferred semantics adds up to the pure geometric representation provided by a DMU and produce also geometrically structured components. Functional information connected to a structured geometric model of a component significantly improves FEM preparation and increases its robustness because idealizations can take place using components’ functions and components’ structure helps defining sub-domains of FEMs.

Future research will carry on improving algorithms for geometric interfaces identification, processing a wider range of component functions, which will contribute to a formalization of the concept of functional consistency of a DMU.

Simulation engineers benefit from this automated enrichment of DMUs with functional information to speed up the preparation of FEAs of large assemblies.

The purpose of this paper is to carry out a tolerance analysis with geometric tolerances by means of the Jacobian model. Tolerance analysis is an important task to design and to manufacture high-precision mechanical assemblies; it has received considerable attention by the literature. The Jacobian model is one of the methods proposed by the literature for tolerance analysis. The Jacobian model cannot deal with geometric tolerances for mechanical assemblies. The geometric tolerances may not be neglected for assemblies, as they significantly influence their functional requirements.

This paper presents how it is possible to deal with geometric tolerances when a tolerance analysis is carried out by means of a Jacobian model for a 2D and 3D assemblies for which the geometric tolerances applied to the components involve only translational deviations. The three proposed approaches modify the expression of the stack-up function to overcome the shortage of Jacobian model that the geometric error cannot be processed.

The proposed approach has been applied to a case study. The results of the case study show how, when a statistical approach is implemented, the Jacobian model with the three developed methods gives results very similar to those due to other models of the literature, such as vector loop and variational.

In particular, the proposed approach may be applied only when the applied geometrical tolerances involve translational variations in 3D assemblies.

Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease of the manufacturing costs.

The original contribution of the paper is due to three methods to make a Jacobian model able to consider form and geometric deviations.

One major problem preventing further application and benefits from additive manufacturing (AM) nowadays is that AM build parts always end up with poor geometrical quality. To help improving geometrical quality for AM, this study aims to propose geometrical deviation identification and prediction method for AM, which could be used for identifying the factors, forms and values of geometrical deviation of AM parts.

This paper applied the skin model-based modal decomposition approach to describe the geometrical deviations of AM and decompose them into different defect modes. On that basis, the approach to propose and extend defect modes was developed. Identification and prediction of the geometrical deviations were then carried out with this method. Finally, a case study with cylinders manufactured by fused deposition modeling was introduced. Two coordinate measuring machine (CMM) machines with different measure methods were used to verify the effectiveness of the methods and modes proposed.

The case study results with two different CMM machines are very close, which shows that the method and modes proposed by this paper are very effective. Also, the results indicate that the main geometrical defects are caused by the shrinkage and machine inaccuracy-induced errors which have not been studied enough.

This work could be used for identifying and predicting the forms and values of AM geometrical deviation, which could help realize the improvement of AM part geometrical quality in design phase more purposefully.

Both geometric and non-geometric parameters have noticeable influence on the absolute positional accuracy of 6-dof articulated industrial robot. This paper aims to enhance it and improve the applicability in the field of flexible assembling processing and parts fabrication by developing a more practical parameter identification model.

The model is developed by considering both geometric parameters and joint stiffness; geometric parameters contain 27 parameters and the parallelism problem between axes 2 and 3 is involved by introducing a new parameter. The joint stiffness, as the non-geometric parameter considered in this paper, is considered by regarding the industrial robot as a rigid linkage and flexible joint model and adds six parameters. The model is formulated as the form of error via linearization.

The performance of the proposed model is validated by an experiment which is developed on KUKA KR500-3 robot. An experiment is implemented by measuring 20 positions in the work space of this robot, obtaining least-square solution of measured positions by the software MATLAB and comparing the result with the solution without considering joint stiffness. It illustrates that the identification model considering both joint stiffness and geometric parameters can modify the theoretical position of robots more accurately, where the error is within 0.5 mm in this case, and the volatility is also reduced.

A new parameter identification model is proposed and verified. According to the experimental result, the absolute positional accuracy can be remarkably enhanced and the stability of the results can be improved, which provide more accurate parameter identification for calibration and further application.

The traditional precision design only takes the influence of geometric tolerance of the parts and does not involve the load deformation in the assembly process. This paper aims to analyze the influence mechanism of flexible parts deformation on the geometric precision, and then to ensure the reliability and stability of the mechanical system.

Firstly, this paper adopts the N-GPS to analyze the influence mechanism of flexible parts deformation on the geometric precision and constructs a coupling 3D tolerance mathematical model of the geometric tolerance and the load deformation deviation based on the SDT theory, homogeneous coordinate transformation theory and surface authentication idea. Secondly, the least square method is used to fit the deformation surface of the mating surface under load so as to complete the conversion from the non-ideal element to the ideal element.

This paper takes the horizontal machining center as a case to obtain the deformation information of the mating surface under the self-weight load. The results show that the deformation deviation of the parts has the trend of transmission and accumulation under the load. The terminal deformation cumulative amount of the system is up to –0.0249 mm, which indicated that the influence of parts deformation on the mechanical system precision cannot be ignored.

This paper establishes a comprehensive 3D tolerance mathematical model, which comprehensively considers the effect of the dimensional tolerance, geometric tolerance and load deformation deviation. By this way, the assembly precision of mechanical system can be accurately predicted.

This paper aims to present a new numerical model for the stability and load‐bearing capacity computation of space reinforced‐concrete (R/C) frame structures. Both material and geometric nonlinearities are taken into account. The R/C cross‐sections are assumed to undergo limited distortion under torsional action.

A simple, global discretization using beam‐column finite elements is preferred to a full, global discretization using 3D elements. This is more acceptable from a practical point of view. The composite cross‐section is discretized using 2D elements to apply the fiber decomposition procedure to solve the material and geometrical nonlinear behavior of the cross‐section under biaxial moments and axial forces. A local discretization of each beam element based on the comparative body model (i.e. a prismatic body discretized using brick elements, element by element, during the incremental‐iterative procedure) allows determining the torsional constant of the cross‐section under limited warping. The classical global iterative‐incremental procedure is then used to solve the resulting material and geometric nonlinear problem.

It has been noticed that, in case of a limited distortion of the cross‐section, the torsional constant of homogeneous (linear elastic) materials is greater than the one obtained from the Saint‐Venant theory. However, due to low‐tensile strength of concrete materials, the torsional constant decreases significantly after an early loading phase, primarily due to the lack of reinforcing flanges.

The current study does not cover the torsion analysis of R/C cross‐section with stirrups. Besides, the bond‐slip effect between concrete and steel reinforcement is not taken into account, nor is the local buckling of the beam flanges and rebar.

This new numerical model has been implemented in a computer program for effectively computing the nonlinear stability and load bearing capacity of space R/C frames.

The authors believe that the comparative body model should bring a new approach to the solution of torsion problems with limited distortion of cross‐sections in material and geometric nonlinear analysis of space R/C frames.

Remanufacturing of worn blades with various defects normally requires processes such as scanning, regenerating a geometrical reference model, additive manufacturing (AM) through laser cladding, adaptive machining and polishing and quality inspection. Unlike the manufacturing process of a new part, the most difficult problem for remanufacturing such a complex surface part is that the reference model adaptive to the worn part is no longer available or useful. The worn parts may suffer from geometrical deformation, distortion and other defects because of the effects of harsh operating conditions, thereby making their original computer aided design (CAD) models inadequate for the repair process. This paper aims to regenerate the geometric models for the worn parts, which is a key issue for implementing AM to build up the parts and adaptive machining to reform the parts. Unlike straight blades with similar cross sections, the tip geometry of the worn tip of a twist blade needs to be regenerated by a different method.

This paper proposes a surface extension algorithm for the reconstruction of a twist blade tip through the extremum parameterization of a B-spline basis function. Based on the cross sections of the scanned worn blade model, the given control points and knot vectors are firstly reconstructed into a B-spline curve D. After the extremum of each control point is calculated by extremum parameterization of a B-spline basis function, the unknown control points are calculated by substituting the extremum into the curve D. Once all control points are determined, the B-spline surface of the worn blade tip can be regenerated. Finally, the extension algorithm is implemented and validated with several examples.

The proposed algorithm was implemented and verified through the exampled blades. Through the extension algorithm, the tip geometry of the worn tip of a twist blade can be regenerated. This method solved a key problem for the repair of a twist blade tip. It provides an appropriate reference model for repairing worn blade tips through AM to build up the blade tip and adaptive machining/polishing processes to reform the blade geometry.

The extension errors for different repair models are compared and analyzed. The authors found that there are several factors affecting the accuracy of the regenerated model. When the cross-section interval and the extension length are set properly, the restoration accuracy for the blade tip can be improved, which is acceptable for the repairing.

The lack of a reference geometric model for worn blades is a significant problem when implementing blade repair through AM and adaptive machining processes. Because the geometric reference model is unavailable for the repair process, reconstruction of the geometry of a worn blade tip is the first crucial step. The authors proposed a surface extension algorithm for the reconstruction of a twist blade tip. Through the implementation of the proposed algorithm, the blade tip model can be regenerated.

Remanufacturing of worn blades with various defects is highly demeaned for the aerospace enterprises considering sustainable development. Unlike straight blades, repair of twist blades encountered a very difficult problem because the geometric reference model is unavailable for the repair processes. This paper proposed a different method to generate the reference model for the repair of a twist blade tip. With this model, repair of twist blades can be implemented through AM to build up the blade tip and adaptive machining to subtract the extra material.

The authors proposed a surface extension algorithm to reconstruct the geometric model for repair of twist blades.

Assembly accuracy is the guarantee of mechanical product performance, and the characterization of the part with geometrical deviations is the basis of assembly accuracy analysis.

The existed small displacement torsors (SDT) model cannot fully describe the part with multiple mating surfaces, which increases the difficulty of accuracy analysis. This paper proposed an integrated characterization method for accuracy analysis. By analyzing the internal coupling relationship of the different geometrical deviations in a single part, the Monomer Model was established.

The effectiveness of the Monomer Model is verified through an analysis of a simulated rotor assembly analysis, and the corresponding accuracy analysis method based on the model reasonably predicts the assembly deviation of the rotor.

The Monomer Model realizes the reverse calculation of assembly deformation for the first time, which can be used to identify the weak links that affect the assembly accuracy, thus support the accuracy improvement in the re-assembly stage.

The purpose of this paper is to present coordinate measuring system possibilities in the meaning of the geometric accuracy assessment of hot zone elements in aircraft engines. The aim of the paper is to prove that this method, which uses blue light and is most sufficient and cost-saving method, can to be used in the production line for serial manufacturing of elements, for which a high level of accuracy is required.

The analysis of the geometric accuracy of the blades was performed using non-contact optical coordinate scanner ATOS Triple Scan II Blue Light, manufactured by GOM Company, at the Department of Mechanical Engineering, Rzeszów University of Technology. Geometric analysis was conducted for blades manufactured from different waxes (A7Fr/60 and RealWax VisiJet CPX200), thus comparing injection technique and rapid prototyping (RP) method, and for casting made of Inconel 713C nickel-based superalloy.

The analysis of the criteria for the method of blades’ measuring selection showed that the chosen system successfully met all criteria for the verification of blades’ geometry at the selected stages of the process. ATOS II optical scanner with blue light technology allows measurement almost regardless of daylight or artificial (white) light. This allows the application of the measurement system in the production cycle, thus eliminating the need to create special conditions for measurements.

Requirements related to the accuracy of measured values, diversity and allowable measurement time are linked with the methods of production. Modern manufacturing methods based on computer-aided design systems/manufacturing/engineering systems require a non-contact optical measurement method based on the computer-aided-based coordinate measuring technique. In case of the non-contact optical scanning method based on the ATOS GOM measuring system, time and measurement costs depend on the methodology of measurement and the possibility of its automation. This is why the presented paper has a practical impact on possibilities for the automation of geometric accuracy measurements of obtained elements in the series production line.

The use of ATOS Triple Scan II Blue Light by GOM Company allows the reduction of cost and time of production because of the possibility of the introduction of this system in an automated production line. Additionally, the measurement of hot section blades of aircraft engines by using the blue light method is much more accurate and has implication as it impacts safety of further used manufactured elements.

This paper presents the possibility of using the ATOS Triple Scan II Blue Light measuring system for geometric accuracy measurements in case of hot section blades of aircraft engines. This research is original because it describes three model geometric accuracy measurements, wax model obtained using the injection technique, wax model obtained using the I RP process and casting made of Inconel 713C nickel-based superalloy.