The concept of Skin Model Shape has been introduced as a method for a close representation of manufactured parts using a discrete geometry representation scheme. However, discretized surfaces make irregular polyhedra, which are computationally demanding to model and process using the traditional implicit surface and boundary representation techniques. Moreover, there are still some research challenges related to the geometrical variation modelling of manufactured products; specifically, methods for geometrical data processing, the mapping of manufacturing variation sources to a geometric model, and the improvement of variation visualization techniques. To provide steps towards addressing these challenges this work uses Octree, a 3D space partitioning technique, as an aid for geometrical data processing, variation visualization, variation modelling and propagation, and tolerance analysis. Further, Skin Model Shapes are generated either by manufacturing a simulation using a non-ideal toolpath on solid models of Skin Model Shapes that are assembled to non-ideal fixtures or from measurement data. Octrees are then used in a variation envelope extraction from the simulated or measurement data, which becomes a basis for further simulation and tolerance analysis. To illustrate the method, an industrial two-stage truck component manufacturing line was studied. Simulation results show that the predicted Skin Model Shapes closely match to the measurement data from the manufacturing line, which could also be used to map to manufacturing error sources. This approach contributes towards the application of Octrees in many Skin Model Shape related operations and processes.

The concept of Skin Model Shapes has been proposed as a method to generate digital twins of manufactured parts and is a new paradigm in the design and manufacturing industry. Skin Model Shapes use discrete surface representation schemes, such as meshes and point clouds, to represent surfaces, which makes them enablers to perform an accurate tolerance analysis and surface inspection. However, online inspection of manufactured parts through use of Skin Model Shapes has not been extensively studied. Moreover, the existing geometric variation inspection techniques do not detect unfamiliar changes within tolerance, which could be the precursors to the onset of the manufacturing of out of tolerance part. To detect the unfamiliar changes, as anomalies, and categorize them as systematic and random variations, some unique surface characteristics can be extracted and studied. Random surface deviations exhibit narrow normal distributions, and systematic deviations, on the other hand, exhibit wide, skewed, and multimodal distributions. Using those surface characteristics as key traits, machine learning classifiers can be used to classify deviations into systematic and random variations. To illustrate the method, multiple samples from a truck component manufacturing line were scanned and the collected 3D point cloud data was used to extract features. A prediction score of 97-100% can be achieved by decision tree, k-nearest neighbor, support vector machines, and ensemble classifiers. The purposed approach is expected to extend the existing online inspection approaches and applications of Skin Model Shapes in quality control.

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 tomodel mathematically.Moreover, the application ofthevariation propagation approaches and associated variation source identification techniques using SkinModel Shapes is unclear. This paper proposes amultilayer 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.

Variation propagation modelling 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 gave 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. 

The mathematical modelling of variation propagation in multistage machining processes helps to perform a quick analysis and diagnosis of the processes. The models for part quality prediction, such as Stream of Variation, include homogeneous transformations of the vectorial representations of parts and fixtures. However, these prediction models are complex when considering fixtures with locating surfaces and the associated matrix size is large. Towards mitigating the mathematical complexity, dual quaternions are proposed in representing and transforming a virtual part and fixture. To achieve this, the primary feature datum is assembled to the primary locating surface, followed by sliding the part to secondary and tertiary locating surfaces by reducing the distance between the vertices of the part and the locating surface. The prediction following the proposed approach gave a result within 0.36 % of the prediction made using CAD/CAM models and maintained the largest matrix size of 9 by 8 for a part with 9 features.

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 ofvariation 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 ofvariation models and experimental results reported in the literature. This paper aims to provide a new direction of research on variation propagation modelling ofmultistage manufacturing processes.

The classical variation compensation methods that apply variation modeling are often based on homogenous transformation matrices and coordinate systems. However, the mathematical models are complicated, require large matrices and do not consider form errors. This paper presents a reformulation of the variation compensation techniques using dual quaternions. The compensation values are obtained from the difference between locators’ initial positions and their projected points on the part’s datum features, whose nominal machining feature is aligned with the toolpath plane. The proposed approach, besides its capability to include form errors, provides the same result with the prediction made using a classical method, while maintaining the mathematical conciseness.