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.

Multidomain Simulation Model for Analysis of Geometric Variation and Productivity in Multi-Stage Assembly Systems

Nowadays, the new era of industry 4.0 is forcing manufacturers to develop models and methods for managing the geometric variation of a final product in complex manufacturing environments, such as multistage manufacturing systems. The stream of variation model has been successfully applied to manage product geometric variation in these systems, but there is a lack of research studying its application together with the material and order flow in the system. In this work, which is focused on the production quality paradigm in a model-based system engineering context, a digital prototype is proposed to integrate productivity and part quality based on the stream of variation analysis in multistage assembly systems. The prototype was modelled and simulated with OpenModelica tool exploiting the Modelica language capabilities for multidomain simulations and its synergy with SysML. A case study is presented to validate the potential applicability of the approach. The proposed model and the results show a promising potential for future developments aligned with the production quality paradigm.

Research on Fault Diagnosis of Flexible Material R2R Manufacturing System Based on Quality Control Chart and SoV

The Stream of Variation (SoV) model and control chart are combined to study the fault diagnosis method of flexible materials R2R manufacturing system. Based on the analysis of the correlation between the fault source and product quality in the manufacturing process and also the statistical distribution rule of the processing quality characteristic vector Li and the fault source fi, SoV model under controlled or uncontrolled states and the mathematical model of the probability distribution of the statistic Ti,m2 of the quality characteristic variable Li are deduced. And the calculation equation of the centerline, the upper limit, and the lower limit of the control chart are deduced. The experimental results show that, under controlled or uncontrolled condition, when the program runs to 500 steps, the Average Run Length (ARL) of the performance parameters tends to be stable; and when program reaches 1000 steps, the actual ARL value is almost the same as the theoretical value. The fault diagnosis experiment shows that, under the condition when the fault source is strongly correlated or the fault source correlation coefficient is the same, using the control chart established in this paper can simply and quickly determine the fault location in the system.

Stream of Variation Modeling and Analysis for Compliant Composite Part Assembly— Part II: Multistation Processes

Part I of this paper (Zhang and Shi, 2015, “Stream of Variation Modeling and Analysis for Compliant Composite Part Assembly—Part I: Single-Station Processes,” ASME J. Manuf. Sci. Eng.,) has studied the variation modeling and analysis of compliant composite part assembly in a single-station process. In practice, multiple assembly stations are involved in assembling the final product. This paper aims to develop a variation propagation model for stream of variation analysis in a multistation assembly process for composite parts. This model takes into account major variation factors, including part manufacturing error (PME), fixture position error (FPE), and relocation-induced error (RIE). With the help of a finite element method (FEM), a state space model (SSM) is established to represent the relationships between the sources of variation and the final assembly variation. The developed methodology is illustrated by using a case study of three composite laminated plates assembled in a two-station assembly system. The validity of the developed SSM is verified by Monte Carlo simulation (MCS), which is implemented on the basis of FEM. The SSM provides a potential application for diagnosis of variation sources and variation reduction.

Roll-to-Roll Manufacturing System Modeling and Analysis by Stream of Variation Theory

A multistage system that consists of multiple stages for sequential operations to finish products is widely employed in modern manufacturing systems. Due to the characteristics of multistage systems, the product quality not only depends on operations in current stage but is also affected by operations in upstream stages. Most existing studies use Stream of Variation models to analyze error propagation and interactions among multiple stages in discrete manufacturing systems such as machining shops and assembly systems. In this paper, a multistage model based on the “Stream of Variation” concept is developed to investigate the tension propagation in a flexible material roll-to-roll manufacturing system. This modeling method uses a physical model coupled with a data-driven model to correlate the roller operation performance and product quality characteristics. Torque equilibrium analysis and Hooke’s law are employed for physical model and the censored regression model is used to explore unknown structures/parameters. A web unwinding process demonstrates the feasibility and prediction performance of the proposed model. The result shows that the proposed multistage model can serve as a virtual metrology method to increase system visibility, enhance health management capability and eventually improve product quality.