T-Maps based Tolerance Analysis of Composites Assembly Involving Compensation Strategies

Clamping force and shimming are two important compensation processes in the composites assembly. Their effects on variation propagation should be investigated in tolerance analysis. The paper presents a tolerance analysis method for composites assembly based on the T-Maps method, mainly concerning the anisotropic variations accumulation and propagation where there is the clamping force modification and the shimming. Variations of the composite parts in different directions are represented by the T-Maps. Since the different axial deviations are represented in the same Euclidean point-space, the T-Maps based tolerance analysis of the composite parts assembly provides more accurate and reliable results. Compensation processes, the clamping force, and the shimming, on assembly tolerance synthesis of the composite parts, are analyzed clearly in the T-Map. This procedure is found to be effective for the anisotropy oriented assembly tolerance analysis, especially concerning about effect of the clamping force and the shimming on variations accumulation and propagation. The assembly of an aircraft composite elevator is considered to demonstrate the effectiveness of the T-Maps based method. The procedures outlined in the paper are quite general and can be used for assembly tolerance analysis of anisotropic parts.

Assembly variation analysis of the non-rigid assembly with a deformation gradient model

Purpose This paper aims to develop a mathematical method to analyze the assembly variation of the non-rigid assembly, considering the manufacturing variations and the deformation variations of the non-rigid parts during the assembly process. Design/methodology/approach First, this paper proposes a deformation gradient model, which represents the deformation variations during the assembly process by considering the forces and the self-weight of the non-rigid parts. Second, the developed deformation gradient models from the assembly process are integrated into the homogenous transformation matrix to model the deformation variations and manufacturing variations of the deformed non-rigid part. Finally, a mathematical model to analyze the assembly variation propagation is developed to predict the dimensional and geometrical variations due to the manufacturing variations and the deformation variations during the assembly process. Findings Through the case study with a crosshead non-rigid assembly, the results indicate that during the assembly process, the individual deformation values of the non-rigid parts are small. However, the cumulative deformation variations of all the non-rigid parts and the manufacturing variations present a target value (w) of −0.2837 mm as compared to a target value of −0.3995 mm when the assembly is assumed to be rigid. The difference in the target values indicates that the influence of the non-rigid part deformation variations during the assembly process on the mechanical assembly accuracy cannot be ignored. Originality/value In this paper, a deformation gradient model is proposed to obtain the deformation variations of non-rigid parts during the assembly process. The small deformation variation, which is often modeled using a finite-element method in the existing works, is modeled using the proposed deformation gradient model and integrated into the nominal dimensions. Using the deformation gradient models, the non-rigid part deformation variations can be computed and the accumulated deformation variation can be easily obtained. The assembly variation propagation model is developed to predict the accuracy of the non-rigid assembly by integrating the deformation gradient models into the homogeneous transformation matrix.

Variation propagation modeling in multistage machining processes considering form errors and N-2-1 fixture layouts

Variation propagation modeling of multistage machining processes enables variation reduction by making an accurate prediction on the quality of a part. Part quality prediction through variation propagation models, such as stream of variation and Jacobian-Torsor models, often focus on a 3-2-1 fixture layout and do not consider form errors. This paper derives a mathematical model based on dual quaternion for part quality prediction given parts with form errors and fixtures with N-2-1 (N>3) layout. The method uses techniques of Skin Model Shapes and dual quaternions for a virtual assembling of a part on a fixture, as well as conducting machining and measurement. To validate the method, a part with form errors produced in a two-stationed machining process with a 12-2-1 fixture layout was considered. The prediction made following the proposed method was within 0.4% of the prediction made using a CAD/CAM simulation when form errors were not considered. These results validate the method when form errors are neglected and partially validated when considered.

A Probabilistic Approach for Three-Dimensional Variation Analysis in Aero-engine Rotors Assembly

Rotor assembly is a core tache in the whole process of aero-engine manufacturing. Preventing out-of-tolerance of concentricity is one of the primary tasks. Conventional assembly approaches are based on a manual test with the dial indicator, depending on experience appraises, which lack systematic and quantitative precision design theory. As a result, two issues need to be solved: the modeling problem of complicated geometric variations in three-dimensions, as well as the abnormal distribution of ubiquitous actual deviations. This work attempts to propose a novel probabilistic approach for three-dimensional variation analysis in rotor assembly. Based on rotor’s revolving characteristics and multistage stacking process, Jacobian–Torsor model is adopted to establish the variation propagation, and Pearson distribution family is used to derive the probability density function, which can quickly determine the variation distribution pattern and efficiently perform statistical variation analysis. A real case of mechanical assemblies consisting of revolving axisymmetric components is concerned. The results show that the suggested method has a similar accuracy, but much higher efficiency than conventional methods. Calculations agree with the experimentations, and the probability distribution type of the part’s variation has an appreciable impact on the final assembly precision.

A novel error compensation method for multistage machining processes based on differential motion vector sets of multiple contour points

Modeling the variation propagation based on the stream of variation (SoV) methodology for multistage machining processes (MMPs) has been investigated intensively in the past two decades, however little research is conducted on the variation reduction and the existing work fails to be applied to irregular features caused by the machining-induced variation varying with the positions of the contour points on the machined surface. This paper proposes a novel error compensation method for MMPs through modifying the tool path to reduce variation for general features. The method based on differential motion vector (DMV) sets of multiple contour points is presented to represent the deviation of the irregular feature. Then the conventional SoV model is further extended to more accurately describe variation propagation for irregular features considering the actual datum-induced variations and the varying machining-induced variations, especially the deformation errors for the low stiffness workpiece. Based on the extended SoV model and error equivalence mechanism, the datum error and fixture error are transformed to the equivalent tool path error. Then the original tool path is modified through shifting the machine zero point of machine tools with no need for changing the original G code and workpiece setup. A real cutting experiment validates the effectiveness of the proposed error compensation method for MMPs with an average precision improvement of over 60%. The application of the extended SoV model significantly contributes to compensating more complex error sources for MMPs, such as the clamp force, the internal residual stress, etc.

Variation propagation modelling in multistage machining processes using dual quaternions

Variation propagation models play an important role in part quality prediction, variation source identification, and variation compensation in multistage manufacturing processes. These models often use homogenous transformation matrix, differential motion vector, and/or Jacobian matrix to represent and transform the part, tool and fixture coordinate systems and associated variations. However, the models end up with large matrices as the number features and functional element pairs increase. This work proposes a novel strategy for modelling of variation propagation in multistage machining processes using dual quaternions. The strategy includes representation of the fixture, part, and toolpath by dual quaternions, followed by projection locator points onto the features, which leads to a simplified model of a part-fixture assembly and machining. The proposed approach was validated against stream of variation models and experimental results reported in the literature. This paper aims to provide a new direction of research on variation propagation modelling of multistage manufacturing processes.

An improved Jacobian-Torsor model for statistical variation solution in aero-engine rotors assembly

Rotor assembly is one of the core components of aero-engine, which basically consists of multistage revolving components. With the influence of parts’ manufacturing errors and practical assembly technology, assembly variations are unavoidable which will cause insecurity and unreliable of the whole engine. Statistical variation solution is a feasible means to analyze assembly precision. When using the three-dimensional variation analysis in rotor assembly, two key issues cannot be well solved, which involve the variation expression (the over-positioning problem of multiple datums) and the variation propagation (revolving characteristic of the rotors). To overcome the deficiency, extended Jacobian matrix and updated torsor equation were derived and unified, which eventually resulted in the improved Jacobian-Torsor model. This model can both provide rotation regulating mechanism by introducing the revolution joint, and characterize the interaction between essential mating features. Multistage rotational optimization of four-stage aero-engine rotors assembly has been performed to demonstrate this solution in statistical way. Results showed that the proposed model was applicable and conducive to precision prediction and analysis in design preliminary stage.

A multilayer shallow learning approach to variation prediction and variation source identification in multistage machining processes

Variation propagation modelling in multistage machining processes through use of analytical approaches has been widely investigated for the purposes of dimension prediction and variation source identification. Yet the variation prediction of complex features is non-trivial task to model mathematically. Moreover, the application of the variation propagation approaches and associated variation source identification techniques using Skin Model Shapes is unclear. This paper proposes a multilayer shallow neural network regression approach to predict geometrical deviations of parts given manufacturing errors. The neural network is trained on a simulated data, generated from machining simulation of a point cloud of a part. Further, given a point cloud data of a machined feature, the source of variation can be identified by optimally matching the deviation patterns of the actual surface with that of shallow neural network generated surface. To demonstrate the method, a two-stage machining process and a virtual part that has planar, cylindrical and torus features was considered. The geometric characteristics of machined features and the sources variation could be predicted at an error of 1% and 4.25%, respectively. This work extends the application of Skin Model Shapes in variation propagation analysis in multistage manufacturing.

Research on global coupling analysis and approximate decoupling of quality characteristics in the early design stage

Due to the existence of coupling relationships, quality characteristics form a variation propagation process, which increases the risk possibility of product quality. In order to improve the robustness of quality characteristics, this paper proposes a fuzzy clustering-based key quality characteristics decoupling planning considering risk criticality. Firstly, based on the design structure matrix, a modular correlation matrix of key quality characteristics was established to quantify the coupling relationships among them. Secondly, according to the variation characteristics of quality characteristics, the variation propagation model is constructed to identify the potential quality risk. Thirdly, the fuzzy clustering algorithm is used to obtain the optimal control sequence of key quality characteristics. Finally, the computerized numerical control machine tool is taken as an actual case, the effectiveness and superiority of this method are verified by the comparison of the numerical result and method. This method provides a new indicator system solution for the coupling analysis of product design.