Stream Of Variation Model Research Articles

A methodology for data-driven adjustment of variation propagation models in multistage manufacturing processes

In the current paradigm of Zero Defect Manufacturing, it is essential to obtain mathematical models that express the propagation of manufacturing deviations along Multistage Manufacturing Processes (MMPs). Linear physical-based models such as the Stream of Variation (SoV) model are commonly used, but its accuracy may be limited when applied to MMPs with a large amount of stages, mainly because of the modeling errors at each stage that are accumulated downstream.In this paper we propose a methodology to calibrate the SoV model using data from the inspection stations and prior engineering-based knowledge. The data used for calibration does not contain information about the sources of variation, and they must be estimated as part of the model adjustment procedure. The proposed methodology consists of a recursive algorithm that minimizes the difference between the sample covariance of the measured Key Product Characteristic (KPC) deviations and its estimation, which is a function of a variation propagation matrix and the covariance of the deviation of the variation sources. To solve the problem with standard convex optimization tools, Schur complements and Taylor series linearizations are applied. The output of the algorithm is an adjusted model, which consists of a variation propagation matrix and an estimation of the aforementioned variation source covariance.In order to validate the performance of the algorithm, a simulated case study is analyzed. The results, based on Monte Carlo simulations, show that the estimation errors of the KPC deviation covariances are proportional to the measurement noise variance and inversely proportional to the number of processed parts that have been used to train the algorithm, similarly to other process estimators in the literature.

Extension of the Stream-of-Variation Model for General-Purpose Workholding Devices: Vices and Three-Jaw Chucks

Nowadays, advanced manufacturing models, such as the stream-of-variation (SoV) model, have been successfully applied to derive the complex relationships between fixturing, manufacturing, and datum errors throughout a multistage machining process. However, the current development of the SoV model is still based on 3-2-1 fixturing schemes, and although some improvements have been done, e.g., N-2-1 fixtures, the effect of general workholding systems, such as bench vices or three-jaw chucks, has not yet been included into the model. This article presents the extension of the SoV model to include fixture and datum errors considering both bench vices and three-jaw chucks as fixturing devices in multistage machining processes. The model includes different workholding configurations, and it is shown how to include the workholding accuracy to estimate part quality. The extended SoV model is validated in a three-stage machining process by both machining experimentation and CAD simulations. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Part quality estimation in multistage machining systems is a challenging issue. The stream-of-variation (SoV) model is a straightforward model that can be used for this purpose. However, the current model is limited to fixture based on punctual locators, and common shop-floor devices are not considered yet. To overcome this limitation, this article extends the current SoV model to include vices and three-jaw chucks as workholding devices. The proposed methodology lets practitioners estimate the manufacturing capability of a process considering the technical specifications of these devices (e.g., parallelism and perpendicularity of vice surfaces and total indicator runout of chucks), or it can be used for diagnosing workholding issues. The model assumes that the workpiece acts as a rigid part and errors as deformations during clamping are assumed to be negligible in comparison with fixture- and datum-induced errors.

Control strategies comparison for a multi-stage assembly system using simulation

The goal of Zero Defect Manufacturing (ZDM) is to reduce part scrap by compensating manufacturing deviations and avoiding their propagation on multi-stage production systems. In particular, the joint use of in-process measuring and flexible locating systems enables the application of different control strategies to proactively improve the geometrical quality of the product and to achieve the productivity targets. In this work, focused on the production quality paradigm, two compensation strategies based on the adjustment of part locators are simulated to compare how different control loops can reduce the out-of-control parts in multi-stage assembly systems. For this purpose, a simulation tool developed on OpenModelica is used taking into account the logistic flow and the quality characteristics flow based on the Stream of Variation model.

A Novel Error Compensation Method for Multistage Machining Processes Based on Differential Motion Vector Sets of Multiple Contour Points

Abstract 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 by 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 stream of variation (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 points 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.

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.

State space modelling of variation propagation in multistage machining processes for variable stiffness structure workpieces

Satisfying the quality requirement of products in multistage machining processes (MMPs) is significant and challenging nowadays. In spite of the success of the stream of variation (SoV) theory in variation propagation modelling for MMPs, the absence of elastic deformation variations could be an important factor that limits its application in variable stiffness structure (VSS) workpieces. To this end, a generic variation propagation framework in MMPs for VSS workpieces is established, incorporating the induction and propagation of elastic deformation variations. Region division strategy is adopted according to the characteristics of VSS workpieces, and the analytic solutions of elastic deformation in different regions are solved by contact theory and elastic theory. The effectiveness and accuracy of the proposed model are verified by a six-stage machining process on a four-cylinder engine block, and the proposed model is compared with the conventional SoV model resulting in a significant improvement on quality prediction.

Three-Dimensional Tolerance Analysis Modelling of Variation Propagation in Multi-stage Machining Processes for General Shape Workpieces

The quality control of general shape workpieces has become one of research hotspots because of the increasing diversity of products. The theory of stream of variation (SoV) for machining processes is a successful method in researching variation propagation rule. However, with the consideration of all key elements in manufacturing system, there is no unified and integrated model for workpieces in different kinds of shapes. In this paper, a new variation propagation model in multi-stage machining processes for general shape workpieces is established. It visually demonstrates the variation propagation chain and expands the universality of current SoV models. The connection of all key elements in manufacturing system is defined as an assembly chain, in which the variations are defined and propagated by modified three-dimensional tolerance analysis method. The equivalent conversion of the connection between workpiece and fixture realizes the modelling of general shape workpiece regardless of its machining method and locating scheme. Real experiments validate the effectiveness and accuracy of the new SoV model for different shape workpieces. This model has great potential to be applied toward multi-scale variation modelling, process control, and fault diagnosis for general shape workpieces.

Variation propagation of bench vises in multi-stage machining processes

Variation propagation has been successfully modeled by the Stream of Variation (SoV) approach in multistage machining processes. However, the SoV model basically supports 3-2-1 fixtures based on punctual locators and other workholding systems such as conventional vises are not considered yet. In this paper, the SoV model is expanded to include the fixture- and datum-induced variations on workholding devices such as bench vises. The model derivation is validated through assembly and machining simulations on Computer Aided Design software. The case study analyzed shows an average error of part quality prediction between the SoV model and the CAD simulations of 0.26%.

A method for the concurrent design and analysis of networked manufacturing systems

ABSTRACTMultistage manufacturing processes (MMPs) require multiple stations and operations. Traditionally, analysis of MMPs focused on material planning and control strategies. For a given MMP, the effect of the strategy on the volume and rate of production, ability to handle product type variability, and the effects of process variability on production rate, on-process inventory, etc., have been studied individually. Such approaches, while necessary, do not address the combined effects of MMP design choices on the final product quality. In this article, a method based on the compromise decision support problem and stream of variation model is proposed to provide a way to evaluate suitable designs for the implementation of MMPs. Using the dimensional quality of the product as a measure of quality, the proposed method is illustrated using a three-stage MMP in an automobile panel stamping process while considering the conflicting requirements of diagnosability and controllability.

Derivation and application of the stream of variation model to the manufacture of ceramic floor tiles

ABSTRACTOne of the main problems in the manufacture of floor tiles is the dimensional variability of the ceramic product, which leads to the product having to be classified into different dimensional qualities with an increase in cost. In this article we propose a novel way of modelling the dimensional variability of ceramic floor tiles by the adaptation of the Stream of Variation model. The proposed methodology and its potential applicability contribute to the integration of process knowledge in the ceramic tile industry and allow tile manufacturers have a new methodology for process improvement, variation reduction and dimensional control.

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.

Variation Analysis of Automated Wing Box Assembly

Manufacturing process variability is a major issue of concern in high value industries. Manufacturing small batches and in some cases batches of one is a very expensive process with specific requirements for manufacturing operations, tooling and fixturing and their level of automation and informatics provision. The automation targets cost reduction and a counterbalancing of the ever lower numbers of skilled shop floor workers. However, these small series typically are products that contain complex and compliant parts, and often also a high number of parts and components. The automation of this type of low-volume high-value production can be a daunting task.Each process has its own key parameters that are required to be within a certain tolerance band in order to ensure product quality, such as e.g. the dimensions and location of assembly mating features. Dimensional quality assurance is typically done with in-process measurement, or the measurement of certain key characteristics (KCs) in the current setup, but a special setup may have to be used in a measurement-only step in the manufacturing process. Each manufacturing stage introduces errors stemming from uncertainties in the fixturing, used processes etc. These errors will propagate in downstream stages and can even worsen errors introduced in the latter stages.The paper presents a new generic methodology for the use of stream of variation (SoV) analysis within a Smart Factory environment such as the Evolvable Assembly Systems (EAS) framework. The research is demonstrated using a simplified case study of one of EAS demonstrators for an aircraft wing box assembly. The wing box assembly and its KCs are described using formal representation. The SoV model is applied to model and simulate the assembly process. The simulation results are then analysed to predict, control and minimise the error propagation coming from uncertainties in process and equipment.

A comprehensive study of linear variation propagation modeling methods for multistage machining processes

Stream of variation (SoV) model is an effective tool, which can describe the dimensional variation and propagation for multistage machining processes. Compared with traditional single-stage error models considering errors from a single machining stage only, SoV model can depict the complicated interactions between different errors at different stages. This paper reviews three major linearized SoV modeling methods for multistage machining processes based on the literature published over the last two decades. These three linearized SoV modeling methods are based on differential motion vectors, equivalent fixture error, and kinematic analysis, respectively. Each method has its corresponding advantages and disadvantages. The model using differential motion vector (DMV) concept from robotics incorporates fixture-, datum-, and machining-induced variations in the multistage variation propagation for orthogonal 3-2-1 fixturing layout while the primary datum deviation is currently overlooked. The kinematic analysis method can address general fixture layouts rather than being limited to orthogonal 3-2-1 fixture layouts. The variation propagation model using the equivalent fixture error concept can directly model the process physics regarding how fixture, datum, and machine tool errors generate the same pattern on the features of the workpiece. The results of these three models with respect to an example are also given to make a comparison. Finally, a perspective overview of the future research about SoV methods is presented.

Variation propagation modelling for multi-station machining processes with fixtures based on locating surfaces

Modelling the dimensional variation propagation in multi-station machining processes (MMPs) has been studied intensively in the past decade to understand and reduce the variation of product quality characteristics. Among others, the Stream-of-Variation (SoV) model has been successfully applied in a variety of applications, such as fault diagnosis, process planning and process-oriented tolerancing. However, the current SoV model is limited to the MMPs where only fixtures with punctual locators are applied. Other types of fixtures, such as those based on locating surfaces, have not been investigated. In this paper, the derivation of the SoV model is extended to model the effect of fixture- and datum-induced variations when fixtures with locating surfaces are applied. Due to the hyperstatic nature of these fixtures, different workholding configurations can be adopted. This will increase the dimension of the SoV model exponentially and thus may make the model-based part quality prediction extremely complex. This paper presents a method of reducing the complexity of the SoV model when fixtures based on locating surfaces are applied and evaluates the worst-case approach of the resulting part quality.

Process-oriented tolerancing using the extended stream of variation model

Current works on process-oriented tolerancing for multi-station manufacturing processes (MMPs) have been mainly focused on allocating fixture tolerances to ensure part quality specifications at a minimum manufacturing cost. Some works have also included fixture maintenance policies into the tolerance allocation problem since they are related to both manufacturing cost and final part quality. However, there is a lack of incorporation of other factors that lead to increase of manufacturing cost and degrade of product quality, such as cutting-tool wear and machine-tool thermal state. The allocation of the admissible values of these process variables may be critical due to their impact on cutting-tool replacement and quality loss costs. In this paper, the process-oriented tolerancing is expanded based on the recently developed extended stream of variation (SoV) model which explicitly represents the influence of machining process variables in the variation propagation along MMPs. In addition, the probability distribution functions (pdf) for some machining process variables are analyzed, and a procedure to derive part quality constraints according to GD&T specifications is also shown. With this modeling capability extension, a complete process-oriented tolerancing can be conducted, reaching a real minimum manufacturing cost. In order to demonstrate the advantage of the proposed methodology over a conventional method, a case study is analyzed in detail.

State Space Modeling of Variation Propagation in Multistation Machining Processes Considering Machining-Induced Variations

In spite of the success of the stream of variation (SoV) approach to modeling variation propagation in multistation machining processes (MMPs), the absence of machining-induced variations could be an important factor that limits its application in accurate variation prediction. Such machining-induced variations are caused by geometric-thermal effects, cutting-tool wear, etc. In this paper, a generic framework for machining-induced variation representation based on differential motion vectors is presented. Based on this representation framework, machining-induced variations can be explicitly incorporated in the SoV model. An experimentation is designed and implemented to estimate the model coefficients related to spindle thermal-induced variations and cutting-tool wear-induced variations. The proposed model is compared with the conventional SoV model resulting in an average improvement on quality prediction of 67%. This result verifies the advantage of the proposed extended SoV model. The application of the new model can significantly extend the capability of SoV-model-based methodologies in solving more complex quality improvement problems for MMPs, such as process diagnosis and process tolerance allocation, etc.

Manufacturing variation models in multi-station machining systems

In product design and quality improvement fields, the development of reliable 3D machining variation models for multi-station machining processes is a key issue to estimate the resulting geometrical and dimensional quality of manufactured parts, generate robust process plans, eliminate downstream manufacturing problems, and reduce ramp-up times. In the literature, two main 3D machining variation models have been studied: the stream of variation model, oriented to product quality improvement (fault diagnosis, process planning evaluation and selection, etc.), and the model of the manufactured part, oriented to product and manufacturing design activities (manufacturing and product tolerance analysis and synthesis). This paper reviews the fundamentals of each model and describes step by step how to derive them using a simple case study. The paper analyzes both models and compares their main characteristics and applications. A discussion about the drawbacks and limitations of each model and some potential research lines in this field are also presented.

Dimensional errors of rollers in the stream of variation modeling in cold roll forming process of quadrate steel tube

In the cold roll forming process, the sheet metal strip is gradually bent into a desired profile by successive roller stations. During this process the roller locating errors of each roller station are introduced, transformed and accumulated until the sheet metal is bent into the final desired profile, which does influence the product’s dimension quality, affect the end-welding of quadrate steel tube, and elongate the costly error-and-trial phase in ramp-up. This paper introduces procedures for expressing the influence of roller locating errors in the forming process of quadrate steel tube, which is based on the formulation of the stream of variation (SOV) model of roller dimensional errors using the CAD/CAPP parameters of the cold roll forming process. The SOV model is utilized to reveal the variation propagation in the manufacturing process. The modeling process is experimentally validated in a two-station forming process.

Diagnosibility and sensitivity analysis for multi-station machining processes

Dimensional variation is a major problem affecting product quality in discrete-part manufacturing. The stream of variation (SoV) methodology has been proposed as one of the systematic approaches to identify the root causes of process variation based on part measurements. This paper presents the results of the diagnosibility and sensitivity analysis study of the SoV methodology in a multi-station V8 cylinder head machining process used by a major domestic automotive manufacturer. The SoV model of dimensional machining errors has been derived based on the CAD description of the part and CAPP description of the process. Variation patterns of the final product were assessed based on the measurements of 20 automotive cylinder heads machined under normal process conditions, and the relative contributions of each machining station were assessed. In addition, one faulty product was observed and SoV model was used to identify the machining station that caused this quality problem. A station-level error decomposition method has been introduced and the SoV model correctly identified the culprit station. Furthermore, the sensitivities of dimensional features of the cylinder head to departures in fixture parameters away from their nominal values are evaluated based on the SoV model. Finally, four major issues arising from this implementation study of SoV in industry have been identified. Those are: non-diagnosibility of available measurements, vectorial representation of features, random sampling of parts at inspection and inadequate level of details in modeling of the process faults.

Modeling Machining Errors on a Transfer Line to Predict Quality

This paper introduces a methodology for predicting part quality based on the expected and measured process variations (geometric, static, and dynamic errors). Part quality in terms of dimensional (location), orientation, form, and profile tolerances can be predicted using a “stream of variation model” in a multistation machining system (serial, parallel, or hybrid) and validated on an engine cylinder head. The understanding gained from an application of this methodology to a machined component can help achieve substantial part-quality and process improvements.