Singularity Issue in Dimensional Variation Diagnosis of Multi-Station Assembly Processes

Manufacturing ◽  
2003 ◽  
Author(s):  
Yu Ding ◽  
Abhishek Gupta ◽  
Daniel W. Apley
Keyword(s):  
Least Squares ◽  
Singular Systems ◽  
Dimensional Accuracy ◽  
Complete Information ◽  
Propagation Model ◽  
Error Sources ◽  
Process Error ◽  
Dimensional Variation ◽  
Discrete Part ◽  
Traditional Approaches

This paper presents a new method of diagnosing variation components of process error sources in a manufacturing system. Quite often in a complex multi-station assembly system only limited numbers of sensors are present due to which complete information of fixture errors is unavailable. This makes the system of variance components singular and not solvable by using regular least-squares estimation. The method suggests reformulation of the original error propagation model into a variation relation by using a matrix transformation. With the development of a new variation estimator and its diagnosability condition, some singular systems that are not diagnosable using traditional least squares methods become diagnosable. Difference between the new approach and the traditional approaches has been elaborated. Modified procedures of the new estimator are also presented to enhance its estimation performance. The idea is presented in the specific context of panel assembly processes, but the application of the idea should not be limited therein. Conclusions can be extended to general discrete-part manufacturing processes where fixtures are extensively used to ensure dimensional accuracy of the final product.

Singularity Issues in Fixture Fault Diagnosis for Multi-Station Assembly Processes

2004 ◽  
Vol 126 (1) ◽  
pp. 200-210 ◽  
Author(s):  
Yu Ding ◽  
Abhishek Gupta ◽  
Daniel W. Apley
Keyword(s):  
Variance Components ◽  
Manufacturing Systems ◽  
Singular Systems ◽  
Dimensional Accuracy ◽  
Propagation Model ◽  
Estimation Methods ◽  
Singularity Problem ◽  
Sample Covariance ◽  
Ls Estimator ◽  
Discrete Part

This paper presents a method of diagnosing variance components of process error sources in singular manufacturing systems. The singularity problem is studied and the cause examined in the context of fixture error diagnosis in multi-station assembly processes. The singularity problem results in nondiagnosable fixture errors when standard least-squares (LS) estimation methods are used. This paper suggests a reformulation of the original error propagation model into a covariance relation. The LS criterion is then applied directly to the sample covariance matrix to estimate the variance components. Diagnosability conditions for this variance LS estimator are derived, and it is demonstrated that certain singular systems that are not diagnosable using traditional LS methods become diagnosable with the variance LS estimator. Modified versions that improve the accuracy of the variance LS estimator are also presented. The various procedures are thoroughly contrasted, in terms of accuracy and diagnosability. The results are illustrated with examples from panel assembly, although the application of the approach and the conclusions extend to more general discrete-part manufacturing processes where fixtures are used to ensure dimensional accuracy of the final product.

A Quality Prediction Framework for Multistage Machining Processes Driven by an Engineering Model and Variation Propagation Model

2007 ◽  
Vol 129 (6) ◽  
pp. 1088-1100 ◽  
Author(s):  
Jianming Li ◽  
Theodor Freiheit ◽  
S. Jack Hu ◽  
Yoram Koren
Keyword(s):  
Dimensional Accuracy ◽  
Software Tool ◽  
Propagation Model ◽  
System Level ◽  
Quality Prediction ◽  
Machining Processes ◽  
Propagation Modeling ◽  
Variation Propagation ◽  
Quality Modeling ◽  
Dimensional Variation

This paper proposes a comprehensive quality prediction framework for multistage machining processes, connecting engineering design with the activities of quality modeling, variation propagation modeling and calculation, dimensional variation evaluation, dimensional variation analysis, and quality feedback. Presented is an integrated information model utilizing a hybrid (feature/point-based) dimensional accuracy and variation quality modeling approach that incorporates Monte Carlo simulation, variation propagation, and regression modeling algorithms. Two important variations (kinematic and static) for the workpiece, machine tool, fixture, and machining processes are considered. The objective of the framework is to support the development of a quality prediction and analysis software tool that is efficient in predicting part dimensional quality in a multistage machining system (serial, parallel, or hybrid) from station level to system level.

A Bounded Variation Approach to Inverse Interferometry

1995 ◽  
Author(s):  
B. G. Fitzpatrick ◽  
S. L. Keeling ◽  
S. G. Rock
Keyword(s):  
Least Squares ◽  
Flow Measurement ◽  
Optical Methods ◽  
Optical Data ◽  
Reconstruction Technique ◽  
Direct Inversion ◽  
Variation Approach ◽  
Mathematical Techniques ◽  
Traditional Approaches ◽  
Least Squares Techniques

Abstract A least squares reconstruction technique is examined for determining flow-field densities from optical data. Nonintrusive optical methods have long been used for flow visualization; however, the goal of this work is to devise mathematical techniques with which optical data can be used for quantitative flow measurement. The ill-posedness of density computation from interferogram measurements is recognized as a serious limitation in direct inversion methods. Here, least squares techniques employing compactness constraints are developed to avoid the difficulties encountered in traditional approaches.

scholarly journals A Progress Report on Numerical Solutions of Least Squares Adjustment in GNU Project Gama

10.14311/662 ◽  
2005 ◽  
Vol 45 (1) ◽  
Author(s):  
A. Čepek ◽  
J. Pytel
Keyword(s):  
Singular Value Decomposition ◽  
Numerical Solution ◽  
Least Squares ◽  
Numerical Solutions ◽  
Singular Systems ◽  
Progress Report ◽  
Singular Value ◽  
Geodetic Networks ◽  
Least Squares Adjustment ◽  
Value Decomposition

GNU project Gama for adjustment of geodetic networks is presented. Numerical solution of Least Squares Adjustment in the project is based on Singular Value Decomposition (SVD) and General Orthogonalization Algorithm (GSO). Both algorithms enable solution of singular systems resulting from adjustment of free geodetic networks. 

Multi-Operational Machining Processes Modeling for Sequential Root Cause Identification and Measurement Reduction

2004 ◽  
Author(s):  
Hui Wang ◽  
Qiang Huang ◽  
Reuven Katz
Keyword(s):  
Machine Tool ◽  
Propagation Model ◽  
Machining Processes ◽  
Error Sources ◽  
Variation Reduction ◽  
Measurement Reduction ◽  
Propagation Modeling ◽  
Root Cause ◽  
Variation Propagation ◽  
Root Cause Identification

Variation propagation modeling has been proved to be an effective way for variation reduction and design synthesis in multi-operational manufacturing processes (MMP). However, previously developed approaches for machining processes did not directly model the process physics regarding how fixture, and datum, and machine tool errors generate the same pattern on part features. Consequently, it is difficult to distinguish error sources at each operation. This paper formulates the variation propagation model using the proposed equivalent fixture error (EFE) concept. With this concept, datum error and machine tool error are transformed to equivalent fixture locator errors at each operation. As a result, error sources can be grouped and root cause identification can be conducted in a sequential manner. The case studies demonstrate the model validity through a real cutting experiment and model advantage in measurement reduction for root cause identification.

A RSS Method for Estimating Hole Dimension Error in a Batch Micro-EDM Process

2007 ◽  
Author(s):  
J. J. Wang ◽  
J. L. Hou ◽  
F. C. Hsu ◽  
Y. Y. Liao ◽  
Steven Liang
Keyword(s):  
Geometric Dimension ◽  
Statistical Error ◽  
Dimensional Accuracy ◽  
Statistical Characteristics ◽  
Micro Edm ◽  
Production Environment ◽  
Fixed Dimension ◽  
Process Error ◽  
Hole Dimension ◽  
Edm Process

In an attempt to estimate the spread of errors in an EDM hole making process, a new Root-Sum-Square (RSS) method is proposed to combine the dimensional spread of a batch of electrodes with the over-cut variation in the micro-EDM process. Two sources of errors are commonly associated with an EDM process and contribute to the dimensional accuracy of the EDMed hole: the dimensional variation of the electrodes and the process over-cut error and its variation. Especially in a micro-EDM process, it is often difficult and time-consuming to measure the geometric dimension and tolerance of either a batch of electrodes or holes of small dimensions. By quantitatively establishing the relationship among the spreads in geometric errors of the electrodes and holes and the process capability, this new method provides an analytical tool in predicting hole error and allows allocating the tolerance budget when selecting the appropriate electrode making process, the EDM machine and process parameters. A series of experiments are carried out to establish and verify the RSS method. Given a set of EDM parameters and a batch of electrodes, the process error in the average over-cut and its spread is first obtained by the RSS method. The process error is then verified by separate experiments with electrodes of fixed dimension under the same EDM conditions. The validity of RSS method is further confirmed by experiments under different electrode dimensions. The RSS method is shown to well represent the contribution of both electrode and process errors to the statistical characteristics of the hole dimension. The establishment of this statistical error model should facilitate the design and control of hole quality by balancing the requirements for the dimensional accuracy of the electrodes and the process accuracy in a batch production environment.

Comparison of Dimensional Accuracy for Different Investment Casting Shells and Binders Based on Selective Laser Sintering

2011 ◽  
Vol 120 ◽  
pp. 243-247 ◽  
Author(s):  
Qing Song Yan ◽  
Xu Xiong ◽  
Gang Lu ◽  
Hong Wan ◽  
Can Cheng Liu ◽  
...  
Keyword(s):  
Investment Casting ◽  
Colloidal Silica ◽  
Selective Laser Sintering ◽  
Dimensional Accuracy ◽  
Laser Sintering ◽  
Ethyl Silicate ◽  
Comprehensive Properties ◽  
Variation Rate ◽  
Dimensional Variation ◽  
Production Cost Control

The dimensional accuracy of shells and binders of investment casting which incorporation with selective laser sintering is investigated. The results show that the dimensional accuracy of colloidal silica is higher than that of ethyl silicate, and the dimensional variation rate of investment casting shells produced with colloidal silica is much lower than ethyl silicate shells. Moreover, colloidal silica possesses better performance on environmental protection and production cost control. These indicate that the comprehensive properties of colloidal silica are better than that of ethyl silicate. Meanwhile, the average dimensional variation rate of the single colloidal silica shell and the ethyl silicate-colloidal silica alteration shell was almost identical and it was much lower than that of the other shells which were produced in this study. This means two kinds of shells are optimized in all five types of shells studied in the aspect of dimensional accuracy. The unique properties of two shells show clearly direction to choose the type of shell.

scholarly journals Chatter Detection in Milling Process Based on the Combination of Wavelet Packet Transform and PSO-SVM

2021 ◽  
Author(s):  
Qingzhen Zheng ◽  
Guangsheng Chen ◽  
Anling Jiao
Keyword(s):  
Wavelet Packet ◽  
Dimensional Accuracy ◽  
Vibration Signal ◽  
Pso Algorithm ◽  
Milling Process ◽  
Wavelet Packet Transform ◽  
Wavelet Packets ◽  
Limiting Factor ◽  
Novel Method ◽  
Traditional Approaches

Abstract Chatter has become the mainly limiting factor in the development of rapid and stable machining of machine tools, which seriously impacts on surface quality and dimensional accuracy of the finished workpiece. In this paper, a novel method of chatter recognition was proposed based on the combination of wavelet packet transform (WPT) and PSO-SVM in milling. The collected vibration signal was pre-processed by wavelet packet transform (WPT), and the wavelet packets with rich chatter information were selected and reconstructed. The selected wavelet packets can reduce the redundant noise and useless information. a combination of 10 time-domain and 4 frequency-domain feature parameters were obtained through calculating the reconstructed vibration signals. Compared to three methods of k-fold cross validation (k-CV), genetic algorithm (GA) and particle swarm optimization (PSO) to optimize the input parameters of SVM, the experiment results were shown that the PSO algorithm has is characterized by high accuracy. The proposed approach can recognize the stable, chatter and transition states more accurately than the other traditional approaches.

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