FUZZY INFERENCE SYSTEM (FIS) BASED DECISION-MAKING ALGORITHMS FOR CMM MEASUREMENT IN QUALITY CONTROL

Fuzzy Inference System (FIS) Based Decision-Making Algorithms for CMM Measurement in Quality Control

E. Orady

Professor

University of Michigan-Dearborn (UMD)

4901 Evergreen Rd., Dearborn 48128, U.S.A

 

Amir El-Baghdady

Graduate Student Research Assistant

University of Michigan-Dearborn (UMD)

4901 Evergreen Rd., Dearborn 48128, U.S.A

 

Y. Chen

Associate professor

University of Michigan-Dearborn (UMD)

4901 Evergreen Rd., Dearborn 48128, U.S.A

 

S. Li

Research Associate

University of Michigan-Dearborn (UMD)

4901 Evergreen Rd., Dearborn 48128, U.S.A

 

A. Shaout

Associate professor

University of Michigan-Dearborn (UMD)

4901 Evergreen Rd., Dearborn 48128, U.S.A

 

 

Abstract

The sampling strategy for CMM inspection processes is a property of the operator while the accuracy level is a property of the machine itself. The advancements in hardware technology over the last few years allowed for the production of a new generation of CMM machines that are capable of high-precision measurements, yet, the  inspection quality of these machines are impaired by improper sampling strategy. This paper discusses the research work done on the development of a fuzzy logic based decision-making system as a means for soft computing for CMM sampling strategies. It also presents the use of fuzzy logic to relate the machine tool accuracy to the part measurement accuracy, and to make a knowledge data base which contains machine tool accuracy and part measurement data to be used for prediction of the sampling strategy for subsequent parts.  Finally, at the end of the paper, system implementation, theoretical analysis, and experimental work are presented and discussed.

 

Keywords: CMM measurement, Fuzzy logic, Fuzzy Knowledge Based Control (FKBC), Sampling strategies

 

1  Introduction

                Ever since the introduction of Coordinate Measuring Machines (CMMs), there has always been debate on the determination of proper sampling strategies (sampling size and distribution) and the accuracy level or uncertainty level.  The sampling strategy is a property of the operator i.e. different operators might use different strategies to measure the same part while the accuracy level is a property of the machine itself.  The advancements in hardware technology over the last few years allowed for the production of a new generation of CMM machines that are capable of high-precision measurements which have earned them popularity over traditional hard gauging equipment.  However, the  inspection quality can be impaired by an inappropriate data analysis technique or an improper sampling strategy.  Therefore, there is a need for automatic determination of the sampling strategy based on proper data analysis. 

                The advancement of computer technology has led to establishment of highly sophisticated data acquisition and analysis systems.  An outcome  of this technology is the decision making systems.  These systems are software systems that can be developed to carry out intelligent decision based on data collected during an experiment.  The decision making system architecture is indeed a multi-dimensional problem that has to be tackled carefully.  In order to apply this technology to CMMs, the quantitative estimation of CMM measurement error, evaluated with uncertainty as suggested by NIST, which could be critical to make the exact  accept/reject decision of a machined part.  In general, we are faced with attempting to measure a  part feature or true position using CMM.  A sampling strategy and fitting algorithm have to be adopted prior to completing this task.  Eventually, uncertainty theory and estimation technique are expected to be used to give an estimation of the accuracy of the results.  In production coordinate measurement using CMMs, however, due to the limitations in speed of most machines, much more limited sampling, i.e., under-sampling, is desirable.  Therefore difficulties are introduced to the decision-making methodology of CMM sampling strategy, algorithms and uncertainty estimation because of the following factors:

·         The measurement  system (CMM) contains systematic and random errors.

·         The feature deviates from ideal over a range of wavelengths and amplitudes that are representative of manufacturing processes.  These deviations are usually unknown prior to accomplishing an error-free measurement which is believed impossible from metrology point of view.

·         Algorithms are used to fit these measurement data that can never be completely tested and, in some cases, are quite sensitive to "outliers" [Orady, 1996].

·         In production lines, efficiency is a major consideration.  It would be required to  measure a part feature as quickly as possible, i.e., with the minimum number of points.  At the same time,  the measurement accuracy has to be controlled within an acceptable level.

                Unfortunately, it is the CMM operator who faces these difficulties.  As a matter of fact, one can not expect him to deal with all these difficulties because of his limited knowledge of coordinate metrology and inability to relate the measurement to the accuracy of the manufacturing process. This human-originated decision-making procedure is recognized as one of the major uncertainty factors to the practical CMM measurement in quality control.

 

2  Background and Literature Survey

2.1 Sampling Strategy

                The accuracy of the CMM is in itself an important factor in determining the accuracy of the part.  When measuring a part using a CMM, the results that are acquired depend to a great extent on the sampling strategy.  With the ever increasing demand for higher accuracy and lower tolerances,  the CMM measuring techniques have to be developed to satisfy the industry’s needs.  The measuring strategy and data sampling technique can no longer be controlled by the CMM operator.  Several articles have been published that address the issue of the sampling strategy [Odayappen, 1993; Caskey 1991; Hocken, 1993].  In their research project, rules were developed for measuring circles.  They developed computer programs to simulate parts with different types of errors that resemble the errors that are usually obtained.  The data was then processed with least-squares, minimum zone, minimum circumscribed and maximum inscribed circle algorithms.

                In the field of efficient sampling strategies, Woo et. al. [Woo, 1993; 1995] investigated two deterministic sequences of numbers as sample coordinates by presenting their computations and their applications to metrology.  Three variables control the efficient sampling for surface measurements.  These are the sample size, accuracy and  the sample point distribution.  They introduced the application of the Hammersley sequence for surface measurement to bring some convergence to the sampling methods.  Comparing with uniform sampling, the Hammersley sequence results in a quadratic reduction in the number of samples and consequently in the time of the sampling process while maintaining the accuracy of the results. 

                The more the data points collected, the higher the accuracy of the measurement, yet, this contradicts with the concept of efficiency of the data acquisition system.  Studies on the sampling length and sampling rates have been done by Liu et. al. [Liu, 1995] to find out their effects on CMM data processing.  The previous studies were based on theoretically corrected data.  Therefore, Orady et. al., [Orady, 1994 and 1996, and Ma 1994] studied the effect of sample size on the uncertainty of measurement.  Their research concluded that there is significant difference among the measurement results from different sampling strategies, even on the same part, CMM, conditions, features and characteristics.  This difference could be represented by uncertainty index by using uncertainty analysis.  In their study, the uncertainties decreased dramatically with the increase in the sampling size in CMM measurement, specially for size (diameter) and position (center of circular or cylindrical) features.

 

2.2 Fitting Algorithms

                Most current CMM software packages employ algorithms using Least Squares Method (LSM), for the evaluation of the geometric dimension and form errors for basic geometric elements.  LSM has been recognized to be efficient and reliable in practice since it is based on sound mathematical principles.  However, it does not closely follow  the intent of the minimum zone evaluation (MZE) criterion as defined in the ANSI standard and always over evaluates the form errors of the investigated geometric features [Fukuda, 1984].  Such over-evaluation often results in serious discrepancies and misguides accept/reject decisions in practical applications.

                Some recently developed algorithms are based on computational geometric approaches (CGA) for the estimation of form errors for geometric elements.  Some of them have been  proven successful in the evaluation of the minimum zone form errors of geometric features.  Mark et. al. [Mark, 1989] utilized the concept of convex hull approach to the problem of evaluating coordinate data for straightness and flatness errors.  They proved that the new algorithm guarantees the minimum form zone and is computationally efficient.  Etesami and Qiao [Etesami, 1990] used CGA -- convex hull and Voronoi diagrams -- for the definitions and analysis of the form errors for both planar and circular features.  Minimax approximation was introduced by Fukuda et. al. [Fukuda, 1984] for straightness, flatness, roundness and cylindricity evaluation.  Huang et. al. [Huang, 1993] concentrated on a simple and rapid algorithm, called the control line (plane) rotation scheme, for the evaluations of minimum zone straightness/flatness.  Lai et. al. [Lai, 1988]  investigated new calculation methods to realize a computational geometry approach for the evaluation of straightness and roundness.  They concluded that the study of CGA will benefit the development of geometric tolerancing both in theory and in practice.

                Besides the computational geometric approach (CGA), many researchers interpreted the MZE criterion mathematically and have shown that MZE yields a nonlinear discontinuous optimization problem.  To tackle the problem, various computational techniques and methods have been tested.  Shunmugam [Shunmugam, 1986] presented a general algorithm which establishes the reference figures as outlined in the standards.  The optimized minimum zone figure is established on the basis of the theory of discrete and linear Chebyshev approximation.  Kanada et. al. [Kanada, 1993] introduced a nonlinear optimization technique by applying both the downhill simplex method and the repetitive bracketing method for the evaluation of minimum zone flatness.  Elmaraghy et. al. [Elmaraghy, 1990] developed an algorithm, using an unconstrained nonlinear optimization approach and Hooke-Jeeve direct search method, to adjust the position and orientation of  the center of a circle or axis of a cylinder in order to achieve the minimum deviation zone for a given set of measurement data.  Carr et. al. [Carr, 1995] and Wang [Wang, 1992] also developed algorithms, based on the nonlinear optimization theory, for the evaluation of form tolerances such as straightness, flatness, cylindricity,  etc.

                Orady et. al. [Orady, 1996] developed an algorithm called NOM (Nonlinear Optimization Method), using simplex search techniques, for the evaluation of straightness, flatness and circularity.  Improved NOM is also accomplished, by implementing multiple loci strategy to direct searching optimization technique, for the minimum zone evaluation of cylindricity.  Verification and comparison of NOM with LSM and CGA led to the conclusions that NOM guarantees the minimum zone criterion and possesses good robustness and reliability.  The convergence characteristics of the NOM algorithm were also discussed, and the influence of random errors attached to CMM measured data sets was experimentally indicated and investigated.

 

3  The Fuzzy Decision-Making Algorithms

                Figure 1 is a diagram for the decision-making system.  Based on fuzzy inference methodology, the decision-making engine accepts input data and information from related data bases.  Consequently, the data and information are interpreted and processed in accordance with the knowledge data base and fuzzy rules.  Thus, proper CMM measurement strategies will be made and exported to the controller of CMM to implement during the measuring activities.  Further, the CMM measuring process controlled by these strategies will be monitored and fed back to the knowledge bases as well as the decision making engine in order to update the corresponding knowledge, rules, and inference methodologies.  In this way, the system will possess self-learning capability which is believed to be effective in improving the accuracy and practicality of the designed decision-making system.  The system consists of the following four major modules:

·         Knowledge data bases

·         Fuzzy inference based decision-making engine

·         On-line Feed-Back and Adaptation (FBA) module

Feature Fitting Software (FFS)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


3.1 Knowledge Data Bases

                The knowledge data bases are collections of the information and data related to design, manufacturing, metrology methods and previous experience.  Accordingly, the information and data are to be imported to the decision making module.  It is the premise of the prediction of the CMM sampling strategy.

 

3..2 Decision-Making Module (DMM)

                The DMM implements a nonlinear mapping from its input space to the output space with CMM measurement strategies for particular geometric features on a machined part.  This mapping is accomplished by a number of fuzzy 'IF-THEN' rules, each of which describes the local behavior of the mapping technique.

                The input information and data are managed and expressed in either crispy data sets or  linguistic words/sentences.  Hence, a fuzzification interface is indispensable to convert the data into fuzzy sets being comprehensible for the fuzzy decision-making engine.  On the contrary, a defuzzification interface is utilized to extract  a crisp value that best represents the exported fuzzy set and is compatible with CMM data managing system.

                As the core of the decision-making module,  three conceptual components: a fuzzy decision making engine (DME) incorporating with a rule base and a local database.  The rule base contains a selection of fuzzy if-then rules;  the database defines the membership functions for each of the fuzzy linguistic values used in the fuzzy rules;  and the  fuzzy decision making  engine performs the inference procedure based upon the rules and given facts to derive reasonable outputs.

 

3.3 On-line Feedback and Adaptation (FBA)

                Supervised by the exported strategies from DMM, the CMM will probe a surface feature on the part to collect a number of data points at specific locations.  Meanwhile the coordinates of the inspected points and the fitting results of these points are sent to the FBA module.  The module will process these on-line data in comparison with the related data in the knowledge base in order to determine the reasonableness of the decisions made by DMM.  If the conformity is obvious and satisfactory, FBA will command the DMM to continue the decision-making process until the accomplishment of CMM measuring task.  Otherwise the FBA will adapt the system by updating the related fuzzy rules and the related data in the knowledge base according to the on-line feedback data and other information in the knowledge base.

 

3.4 Feature Fitting Software (FFS)

                The decision making system interfaces with a feature fitting software that was developed by Orady et. al. [Orady, 1995, 1996, 1997].  The FFS has been developed to fit the measured points to a geometric feature and to determine the feature parameters and form errors.  The feature fitting software package has been developed by the authors through the course of a previous project for CMM fitting algorithms for several geometric features including lines, circles, planes, and cylinders.  The software package with a user friendly Windows 3.1 application interface has been developed to realize a new data set fitting algorithm by incorporating new optimization searching strategies with developed mathematical models.  The software is programmed in C and MATLAB computer languages in the Windows 3.1 operating system.

 

4  Research Tasks

4.1 Implementation of  Knowledge Base

                The knowledge base consists of a group of information, experience and data related to design, manufacturing, and measurement.  It is the basis of the prediction process and the decision-making function.  Based on the knowledge base framework, the following research activities were carried out in order to accomplish and maintain the knowledge base for the decision-making system:

·         Enrich the knowledge base by collecting data, experiences, and information relating to design (CAD), manufacturing (CAM and CNC), metrology (CMM) and other knowledge and experience.

·         Utilize data processing techniques and database management tools to enable importing the collected data to the knowledge base.

·         Test new methodologies and algorithms to abstract experience, information and data in the knowledge base into a ready-to-export data format that is comprehensible to the decision-making system.

·         Improve the fuzzification interface by enhancing its capability of dealing with a variety of data exported from the knowledge data base.

 

4.2  Development of New Methodologies and Algorithms for the Decision-Making Module

                The decision-making module (DMM) maps the data in the knowledge base into the output decisions that relate to the CMM measurement strategies.  The mapping procedure will be conducted by a fuzzy inference based algorithm.  To determine this algorithm, the following research activities were carried out:

·         Define and test various fuzzy sets to interpret the knowledge base.  The linguistic property of a fuzzy set was utilized to establish a sound information channel between the knowledge base and the decision-making module.

·         Test different fuzzy inference models in order to determine the one that is applicable to the proposed decision-making  system.

·         A set of fuzzy 'IF-THEN' rules for the selected fuzzy inference model were defined based on researchers' experiences, simulation, and experiment.

·         Software was programmed to integrate the output decisions (sampling strategy) and the CMM control software (MM4 for Brown & Sharpe CMM) as well as the developed data fitting software.

 

4.3  Implementation of the On-line Feedback and Adaptation Loop

                The on-line Feed-Back and Adaptation loop (FBA), as illustrated in  Figure 1, is an intelligent information channel feeding the on-line measurement data of CMM to the knowledge base and the decision-making module by updating related data in order to improve the reasonability of the  system output decisions.  To realize this loop, new methodologies and algorithms are required.  Therefore, the  research activities were carried out in the following aspects:

·         Utilize the discrete data points with an interpolating technique to fit the on-line data points to a geometrical feature segment;

·         Utilize statistic methods to estimate and evaluate the deviation of this feature segment from the DMM predicted feature segment;

·         Develop an algorithm to update the knowledge base and DMM in accordance with the above mentioned deviation.

        These steps allow the decision-making system to possess the ability of self-learning.

 

4.4 Tests and Experiments

                Several tests and experiments were carried out using the CNC machine, Hewlett Packard 5528A Laser measurement system, Brown and Sharpe Micro Val PFx CMM and other metrology gauges at the MSEL laboratories at UM-D.  The test procedure involves:

·       Design and carry out experiments to obtain enough information for the knowledge base.

·       Design and perform experiments in order to define the rule base and test its practicality.

·       Design and perform experiments to verify the performance of the whole decision- making system under various simulated manufacturing conditions.

 

4.5 Software Development

                The needed programs and software were developed to support the aforementioned tasks.  To accomplish all this, the following operating systems, computer languages and software systems and tools were used for the programming activities during the research progress, namely; DOS, Windows, UNIX, Matlab + toolboxes, MM4 for CMM (Brown & Sharpe Micro Val PFx), Algorithm Testing System (ATS)(NIST), Algorithms for CMM (LSM, NOM), Utility Software Package.

 

Fuzzy Decision-Making Algorithms

5.1  Data Processing Methods and Techniques

                When probing on the surface of a part feature with a relatively small intervals between points, CMM is scanning the feature to obtain detailed feature information.  In Figure 2a, one hundred points are scanned along a line on a machined surface.  In this research, the data points set is regarded as a discrete signal.  The Fast Fourier Transform (FFT) results indicate the characteristics of this signal in frequency domain as plotted in Figure 2c.  Obviously, the signal has been contaminated with noise due to the following factors:

·         The roughness of the finished surface of the feature;

·         The dirt particles on the surface; and

·         The CMM measuring inaccuracy and  possible outliers.

                This randomly distributed noise has no information value to the decision-making process.  They might, frequently, misguide the decision-making process to faulty reports.  Hence, digital filters have been  designed to filter the discrete signal.

                In general, a digital filter's transfer function is

                                                                         (1)

here, n is the number of data points, b(i) and a(i) are the filter coefficients.  The order of the filter is the maximum of na and nb. 

                Importing such a discrete digital signal, X(z), the z-transform of the digital filter's output is:

                                                                                                                         (2)

                Considering the filter coefficients  b=1,  a= -0.75,  zero-phase forward and reverse digital filtering has been utilized in this research.  The filter can be described by the difference equation:

 

                      (3)

 

                After filtering in the forward direction, the filtered sequence is then reversed and run back through the filter.  The resulting sequence has precisely zero-phase distortion and double the filter order.  The output data set (the filtered input signal) is plotted in Figure 2b.  Corresponding FFT analysis is shown in  Figure 2d.  It is clear that the filter has smoothed the curve by eliminating the noise out of the data set.

Figure 2   Processing the data set measured along a surface line

 

5.2  Fuzzification and Defuzzification

                The data obtained in  practice, such as CMM measured data points,  CAD feature definition and NC codes etc., are crisp sets which are a special case of fuzzy sets.  The fuzzy inference engine shown in Figure 1  is unable to accept such  data sets in a raw state.  Therefore, there should be an interface between the data base and the fuzzy inference system (FIS) to transform the crisp inputs from the information data base into fuzzy sets.

                The transition  from "belong  to a set" to "not belong to a set" in a fuzzy set is gradual, and this smooth transition is characterized by membership functions that express the degrees of match with linguistic values.  To realize this transformation, the machined surface represented with  e(u,v) model is  divided into n1*n2  elements  expressed  with a matrix:

 

                                                                                     (4)

 

Every individual segment (patch) of the surface feature is represented with the corresponding element in the matrix.  For each one of them, three fuzzy inputs are introduced, namely, input 1 which is the relative errors, input 2 which is the feature variation and input 3 which is the CNC error.  Figure 3 show the transition from raw data into fuzzy linguistic values.  The transition from normalized data to fuzzy linguistic values is done through knowledge, experience and trials.  The advantage of having linear membership functions for the fuzzy linguistic values is that they use less memory and are considerably faster to process by the computer. 

 

 

 

 

 

 

 

 

 

 


                Fuzzy set 1 (Relative Error): It is  the level of the relative errors of  the two extreme points (maximum and minimum) in comparison with the global extremes.  Relative errors has three linguistic values low, average and high.  These linguistic values are shown in Figure 4.  For example, the membership values for Low is defined as:

Low = {(x,mLow(x)) | " x Î X}                                                          (5)

where

X is referred to as the universe of discourse and defined by  a  continuous space of .   is called  the membership function (MF) for  the fuzzy set Input 1.

Figure 4  Linguistic values for the input fuzzy variable (relative errors)

 

                This fuzzy input is used to indicate the superlative level of the segment within the feature definition domain.

 

                Fuzzy set 2 (Feature Variation): It is the level of feature variation evaluated by the number of peak and valley points within each and  every segment.  This input fuzzy variable will have three linguistic values; low, average and high.  For example, the membership values for Low is defined as:

                Low = {(x,mLow(x)) | " x Î X}                                                              (6)

where  is for the number of peak and valley (p-v)  points within segment S(i,j);   represents the overall p-v points associating with the error model of the investigated feature S.  Index b is determined as:

                                                                          (7)

This is to assure that the fuzzy set  possesses linear performance by locating x = 0.5 at  the center of "average" curve on the MF plot.  The corresponding membership function, is illustrated in Figure 5.

Figure 5  Fuzzy linguistic values for feature variation

 

                Fuzzy set 3 (CNC Error): It is the fuzzy set concerned with the CNC error measurement result.  This variable assigns importance to each segment according to the ratio of slope variation that happened in that segment.  The crisp input is the vertical straightness of the X-axis of the CNC machine.  The crisp input is fuzzified by first normalizing the data and dividing the data set into segments.  After that, the slopes between the midpoints of all segments are calculated and the ratio of change between every two consecutive segments is also calculated.  Fuzzy values for the fuzzy set are assigned according to the magnitude of the ratio of change of the slope.

                To end up with five slope ratios corresponding to the five segments and the five input values for the third fuzzy set, six slopes are needed.  The first and last slopes are those of the first half and the last half of the first and last segment respectively.  The middle four slopes are calculated between the midpoints of the five segments.

first slope (segment #1)

                                                                           (8)

 

slopes (2-5) (segment(j); j = 1-5)

                                                   (9)

 

slope (6) (segment # 6)

                                           (10)

ratio(j); j = 1-5

                                      (11)

 

The fuzzy values are then assigned according to values of ratio(j).

Figure 6  Fuzzy linguistic values for CNC error

 

                Output (Importance Number): The output fuzzy variable is computed by applying the input values to the FIS rules.  The output has three fuzzy linguistic values; low, average, high and dense.

                By employing Mamdani fuzzy model [Mamdani 1975], the output will be a fuzzy set that describes the significance of a specific segment (patch) of the error model.  To transform the fuzzy output into a crisp set being accessible for the CMM strategy-making module, one needs a defuzzification method.  Among five known general methods, centroid method is the most widely adopted defuzzification strategy and has been employed in this project.  The method  produces a crisp value, wCOA, by determining the centroid of the area of the aggregated  output MF as:

                                                                                                (12)

where W is the universe of the output fuzzy set w;  is the aggregated output membership function.

 

 

 

5.3 Programming the Fuzzy Sets

                Since the MATLAB Fuzzy toolbox was used for the fuzzy inference system, most of the programming done to generate the fuzzy sets was done in MATLAB. The program starts by loading an  ASCII file containing the CMM measurement of the part.  The program then extracts the point coordinates out of the raw data file and splits them into matrices as a preparation step to be ready for mathematical manipulation.  The control is then transformed into DOS environment where the data is processed by a C program to determine the parameters of the LS fitting equation.  The main control subroutine then reads the LS fitting output file and calculates the angle between the best fit line and the x-axis.  As part of the data standardizing procedure before generating the fuzzy sets, the data is aligned with the x-axis based on the LS fitting line.

                The last step in the data formatting process is filtering the noise out of the data set and then normalizing the data such that [] and [].  After plotting the data, the program then starts to fuzzify the data set to create the fuzzy sets.  A data set is divided into five segments of twenty points each and for every segment three fuzzy values will be generated based on the mathematical model described previously.

 

5.4  Fuzzy Inference System (FIS)

                The FIS  developed in this project is the actual process of mapping from fuzzified inputs to the output fuzzy set.  This output fuzzy set indicates the improved CMM measurement strategy.  The Fuzzy Logic Toolbox of MATLAB was used in this project.  The MATLAB’s Toolbox is based on Mamdani fuzzy inference model.  Figure 8 illustrates the interface of the system and configurations from where one can configure the fuzzy operators and algorithms such as:

·         Fuzzy operators;

·         Implication/Aggregation methods;

·         Defuzzification algorithm; and

·         The input/output variables

 

 

Figure 8  Diagram of  FIS interface

 

5.5 FIS Rules

                With the previously defined input variables and membership functions, a set of linguistic controlled fuzzy rules has been extracted  based on our experience in metrology and CMM operation.  Eighteen rules for CMM are illustrated in Figure 9.. There are three levels (Low (1), Average (2) and High (3) for every input and four levels for the output (Low (1), Average (2), High (3) and Dense (4).  Since there are 3 inputs with 3 levels each, then there exists a total of 33 i.e. 27 possible combinations for our rules.  However, 18 rules were sufficient to cover all the situations needed for the model.  This helps in cutting down the computation time.  Figure 9 shows the above rules as displayed by MATLAB’s Fuzzy Logic Toolbox rule viewer.

 

Figure 9   Roadmap of the fuzzy inference rules

 

5.6 FIS Surface

 

                The overall performance of the FIS system is represented with a FIS surface as illustrated in Figure 10.   Figure 10 shows the output (importance number) plot for input 1 versus input 2, input 1 versus input 3 and input 2 versus input 3.  This plot helps in visualizing the behaviour or the system.

 

Figure 10   FIS interface

 

6  Experiments

6.1 Design and Machining of a Sample Part

                A set of experiments were designed to examine the straightness.  The straightness of the CNC machine was first measured using the Hewlett Packard 5528A Laser measurement system.  The test part is a steel block of dimensions shown in Figure 11.

 

 

 

 

 

 

 

 

 

 

 

 


Figure 11 Test Part

 

                The part was machined at constant speed and feed rate is to simulate the production of a batch of 14 parts.  The steel block was machined with a 7/16 in. Cutter at 2000 r.p.m., 24 in./min. feed rate and 2 mm depth of cut.  The results of measurement of the first line will be used to establish a sampling strategy for the second line.  Then the results for the second line will be used for the third line, and so on.  This would make the system self-learning and able to improve the sampling strategy with time.  After collecting the data and running the analysis of that block, the same block was remachined but  along the Y-axis.  Ten  lines were also cut on the block with a cutting speed of 1500 r.p.m. and feed rateof 3 in./min.

 

6.2 CMM Programming and Data Acquisition

                The next step in our experiment is to perform a high density scan of the part.  This was done by performing high density sampling of the part using the Brown and Sharpe Micro Val PFx CMM in the Metrology Lab at UMD.  Since the CMM measurements is an integral part of our analysis, it had to be done carefully to ensure the accuracy of the results.  To reduce the CMM measurement uncertainty, all measurements were performed under the following conditions of a) controlled temperature, b) same machine set-up parameters and c) same machine set-up.

 

6.3 Data Processing

                After acquiring the data in ASCII format, the next step becomes importing the data to Matlab environment for further data processing.  Several steps have been carried out in that area, first of which is the statistical analysis of the data.  The next step deals with removing the outliers from the data matrix.  The third step was applying curve fitting algorithms to obtain the fitting equation for the straight line.  We used least square method to fit our data points into a straight line equation.  The fourth step is that of applying a data filter to obtain a smooth curve so that we can get the true shape of the curve without getting affected by noise factors.  The fifth step is to use the fitting equation to rotate the axes as part of the data standardization process.  To do this for our 100 points data set, we needed a subroutine to generate a (100x100) rotation matrix to be multiplied by the original data set in order to obtain rotated set of points.  After that, the data is normalized between (0 & 100) for the X and between (-1 & 1) for the Z.  The following step is to divide every line into five segments of 20 points each and then identifying the number of peaks and valleys in each segment.  By doing this, the importance of each segment is determined and based on that the number of points needed in each segment can be established.

 

6.4 CNC Machine Calibration Results:  Vertical Straightness, CMM Inspection of the Machined Blocks

                The following plot (Figure 12a, b) is that of the raw results obtained from the CMM inspection of the X-axis part and the Y-axis part respectively.  A relatively high density scanning was used for the data acquisition of that part.  From the examination of the graphical representation of the data points, it is clear that the same pattern persists in the 14 cuts for the part machined along the X-axis and another pattern persisted for the 10 cuts machined along the Y-axis.  These patterns are characteristics or attributes of the CNC that machined that part.

Figure 12 Raw data points obtained from the CMM machine for the X axis and Y-axis blocks

 

                The data is analyzed one line at a time rather than the data for the whole blocks.  Every set of 100 data points for each line (Figure 13) is separated and then formatted individually as explained earlier.  After the data formatting, the data set would look like Figure 13b, which shows one of the lines of the X-axis block after being filtered and normalized.  This figure shows the normalized data set [] and [].  These normalized data sets are very important because they will serve as the inputs for the fuzzy logic inference system.  The significance of these plots is that they show the trend of the cutting line by smoothing the data points to eliminate cluttering and noise.  Figure 13c shows the data acquired from the straightness tests done on the CNC using the laser interferometer for the X-axis.  It is clear from examining Figures 13a and 13b that the pattern acquired from the CNC vertical straightness test of the X-axis is similar to the result obtained from examining the straightness of a machined line from the X-axis block using the CMM.

                Similarly, Figures 14a and 14b show one line from the Y-axis block as examined by the CMM which have the same pattern as Figure 14c which shows the CNC vertical straightness test of the Y-axis. Hence, the strategy of using the results of measuring the first part to predict the sampling strategy of subsequent parts should be feasible and promising.  Figures 13 and 14 show the plots obtained from the data processing of one line cut along the X-axis  and one line cut along the Y-axis respectively.

Figure 13 Typical line from the X-axis block

 

Figure 14 Typical line from the X-axis block

 

7  Results

7.1 FIS Output

 

                The first output generated by the system contains the importance numbers for every segment in the part along with a plot of the surface profile of the cut to help in visualizing why these numbers were assigned by the system.  The importance numbers will be used to determine the significance of the segment in relation to the evaluation of the part straightness.  A summary of the output (importance numbers) of that stage is shown in and Figure 15 for the X-axis block.  The importance number ranges from zero to one, zero being a segment of least importance and one being a segment of utmost importance.  From examining the and the accompanying Figure 15, segments 2, 3 and 4 seem to have a higher importance value than segments 1 and 5.  Recalling Figure 13a, b, the middle portions of the lines (where the line resembles a bell shape) coincide with segments 2, 3 and 4 while portions 1 and 5 coincide with the straight end parts of the line.  This explains the output of the fuzzy decision making system which assigned more importance and, therefore, more points to the middle portion of the line than to the ends. Examining Figure 16 (Y-axis block), segments 3 also had the highest importance for all the lines.  However in some lines other segments had high importance numbers as well.  This can be understood from examining the plots of the raw data for the Y-axis part, Figure 7.5a and b, as there was more fluctuations in the data points at these areas of the lines. Thess results were obtained through the application of the rules in the fuzzy decision making system to the inputs obtained for the X-axis and Y-axis experimental parts.

 

Figure 15 Plot of FIS output (importance number) for X-axis block

Figure 16 Plot of FIS output (importance number) for X-axis block

 

 

7.2 Feedback Loop Output

                The function of the feedback loop is to use the importance numbers for every segment to assign the number of points to be taken on subsequent measurement.  The feedback loop is a self learning mechanism where it can use the data of the current line and the CNC error measurement to determine the number of points and their locations to be measured on the subsequent lines.  Implementing this loop leads to the reduction of the sampling rate on subsequent lines.

                The summary of the results obtained from the first trial of the feedback loop are as shown in Table 1.  To test the system, the error from the fuzzy distributed points was calculated and compared with the error obtained from the same number of points but taken equidistantly across the part.  From examining the difference between the fuzzy distributed points error and the equidistant points error in Table 1, it is clear that the fuzzy decision-making system did not just decrease the number of points substantially but has greater accuracy.

 

Line

Number

Number

 of points based on fuzzy distribution

Straightness (100 points)

Straightness (fuzzy distributed points)

Fuzzy points

error (%)

Equidistant

points

error (%)

Percent Reduction in measurement points

2

30

0.0157

0.0148

5.9

25.8

333

3

26

0.0124

0.0124

0

1.9

385

4

27

0.0097

0.0097

0

14.5

370

5

29

0.0097

0.0097

0

3.1

344

6

29

0.0088

0.0088

0

2.7

344

7

29

0.0112

0.0102

8.7

10.16

344

8

30

0.0119

0.0107

10

0

333

9

25

0.0103

0.008

22.9

23.89

400

10

27

0.0096

0.009

6.6

2.5

370

11

27

0.0134

0.0117

12.2

12.2

370

12

29

0.0124

0.0108

13

1

344

13

29

0.012

0.011

8.1

8.1

344

Table 1 Summary of feedback loop output for X-axis part (first trial)

 

                After running the system and obtaining the first trial results, the quality of the system outputs  is now asserted and the system can be run continuously.  The results of the continuous runs are shown in  Table 2 for the X-axis part.  The number of points decreased from 30 points for line 2 to 5 points for lines 12 and 13.  This indicates that the system is self learning and capable of using previous knowledge to determine proper sampling rate.

 

Line

Number

Number

 of points based on fuzzy distribution

Distribution in every segment

Error (%)

2

30

5-7-8-8-2

5.9

3

16

2-4-4-3-3

0

4

13

2-3-3-3-2

1

5

10

2-2-2-2-2

1.8

6

9

1-2-2-2-2

3.8

7

9

2-2-2-2-1

8.7

8

8

1-1-2-2-1

10.1

9

7

2-1-1-1-2

23.8

10

6

1-1-1-1-2

8.1

11

7

2-1-1-1-2

22.3

12

5

1-1-1-1-1

23.6

13

5

1-1-1-1-1

31.8

14

6

1-1-1-1-2

45

Table 2 Summary of feedback loop output for X-axis part

 

                From examining Table 2 that shows the results of the X-axis block after running the system continuously, it is clear that the system is performing adequately.  It is also clear that the error percentage increases with the reduction in the number of points taken which is expected.  At the beginning of every run, the system was able to achieve remarkably low error percentages even with a considerable reduction in the number of points taken.

 

Line

Number

Number

 of points based on fuzzy distribution

Distribution in every segment

Error (%)

2

36

5-6-9-7-9

8.4

3

20

5-4-5-3-3

17.3

4

12

2-2-3-2-3

49.6

5

12

2-3-3-2-2

49.5

6

10

2-2-2-2-2

34.7

7

7

1-1-2-2-1

59.3

8

7

2-1-2-1-1

67.1

9

8

2-2-2-1-1

46

10

5

1-1-1-1-1

30.8

Table 3 Summary of feedback loop output for Y-axis part

 

                The same deductions can be reached from examining Table 3 for the Y-axis block.  The higher error percentages obtained for this block can be attributed to the high levels of fluctuations found on the surface of that block.  The fluctuations found on the Y-axis block’s surface are higher than those found on the X-axis block.

 

                These results would help the CMM operator to have an idea about the important segments on the part.  Furthermore, the system makes recommendations about the adequate sampling size and measurement location in each segment which can be directly fed  to the CMM.  Therefore, integration of the system to the CMM software would substantially improve the inspection technique.  Thus, the part can be inspected with minimum number of points at a minimum uncertainty of measurements.  This is a step ahead for improving coordinate metrology techniques.  Implementation of the system would benefit both the CMM users and manufacturers.

 

Conclusions

                By introducing the fuzzy logic based decision-making system, the machine tool accuracy has been successfully linked to the finished part accuracy and thus the project objectives were met.               Using the system, the human-originated decision-making procedure is reduced and thus one of the major sources of uncertainty in CMM measurements is reduced.  With the help of the system, the operator knows the important areas where measurements should be taken on the part and is advised as to the proper sampling size at every area.  The decision making system presented  here greatly reduced the number of points needed for part inspection.  This is an advancement for practical CMM measurements.  Using the knowledge data base containing the machine tool error measurements and measurement of previous parts, the system can predict the importance of every segment in the subsequent parts and assign a measurement strategy accordingly.

 

Acknowledgements

                This work was supported by the University of Michigan-Dearborn and the Research Excellence and Economic Development Fund (REEDF) of the state of Michigan.

 

References

1.        Buckingham, E., Principles of Interchangeable Manufacturing, The Industrial Press, 1941.

2.        Carr, K., and Ferrira, P.,  “Verification of Form Tolerances, Part  [SoE1] I:  Basic Issues, Flatness, and Straightness,"  Precision Engineering, Vol. 17, No. 2,  April 1995, 131-143.

3.        Carr, K., and Ferrira, P., “Verification of Form Tolerances, Part II[SoE2] :  Cylindricity and Straightness of a Median Line,"  Precision Engineering, Vol. 17, No. 2,  April 1995, 144-156.

4.        Caskey, G., et. al., "Sampling Techniques for Coordinate Measuring Machines," Proc. of the NSF Conference, 1991, 779-786.

5.        Elmaraghy, W. H.,  Elmaraghy, H. A., and Wu, Z.,  “Determination of Actual Geometric Deviations Using Coordinate Measuring Machine Data,"  Manufacturing Review, Vol. 3, No. 1, March 1990, 32-39.

6.        Etesami, F., Qiao, H.,  “Analysis of Two-dimensional Measurement Data for Automated Inspection,"  Journal of Manufacturing Systems, Vol. 9, No. 1,  1990, 21-34.

7.        Fukuda, M., and Shimokohbe, A,  “Algorithms for Form Evaluation, Methods of  Minimum Zone and Least Squares," Proc. Int. Sym. Metrol Quality Prod, Tokyo, 1984, 197-202.   

8.        Hocken, R. J., Raja, J. and Babu, U.,  "Sampling Issues in Coordinate Metrology," Proceedings of the 1993 International Forum on Dimensional Tolerancing and Metrology,  June 1993, 97-111.

9.        Huang S.T., and John, H.W., “A Minimum Zone Method for Evaluating Flatness Error of Gage Blocks Measured by Phase-shifting Interferometry,"  Journal of the Chinese Institute of Engineers, Vol. 16, No. 5, 1993, 641-650.

10.     Huang S.T., Fan, K.C., and John, H.W., “A New Minimum Zone Method for Evaluating Straightness Errors,"  Precision Engineering, Vol. 15, No. 3, July. 1993, 158-165.

11.     Huang, S.T., Fan, K.C., and John, H.W., “A New Minimum Zone Method for Evaluating Flatness Errors," Precision Engineering, Vol. 15, No. 1, Jan. 1993,  25-32.

12.     Kanada, T., and Suzukit, S.,  “Evaluation of Minimum Zone Flatness by Means of Nonlinear Optimization Techniques and its Verification," Precision Engineering, Vol. 15, No. 2, Apr. 1993,   93-99.

13.     Lai, K. W., and Wang, J.,  “A Computational Geometry Approach to Geometric Tolerancing,"   Northwestern University 16th NAMRI, May 1988, 376-379.

14.     Liu, Q., Zhang, C. C. and Wang, H. B., "On the Sampling Length and Sampling Rate for CMM Data Processing,"  Engineering Design and Automation, Vol. 1, No. 1,  1995, 59-68.

15.     Ma, C., “Uncertainty Analysis for Application of CMM in Manufacturing Process,” Masters Thesis, The University of Michigan, 1994.

16.     Mamdani, E. And S. Assilian, “An Experiment in Linguistic Synthesis with a fuzzy Logic Controller,” International Journal of Machine Studies, Vol. 7, No. 1, pp. 1-13, 1975.

17.     Mark, T. T., Sanjay J., Richard A. W., and Tom M. C., “Evaluation of Straightness and Flatness Tolerances Using the Minimum Zone," Manufacturing Review, Vol. 2, No. 3, Sept. 1989,  189-195.

18.     Odayappan, O., Raja, R., Hocken, J. and Chen, K , “Sampling Strategies for Circles in Coordinate Measuring Machine," Precision Engineering Group, UNC Charlotte, NC, 1993.

19.     Orady, E.A., Chen, Y., and Ma, C., “Uncertainty Analysis for Application of CMM in Manufacturing Process," The 1994 Quality and Metrology Symposia, Bowling Green State University, August 10-11, 1994.

20.     Orady, E. A., Chen, Y. and Ma, C., “Uncertainty Analysis for the Cylindrical Feature with Application of CMM," Proceedings of SME GAGETECH ‘94 Conference, Troy, MI, October 24-27, 1994.

21.     Orady, E., Chen, Y., Ma, C., "Sampling Strategies for Measurement of Circular Features Using Coordinate Measuring Machines (CMM),"  Proceedings of the 1996 Canadian Society of Mechanical Engineering (CSME) Forum, 13th Symposium on Engineering Applications of Mechanics , Manufacturing Science and Engineering, May 7-9, 1996, pp. 488-494.

22.     Orady, E., Li, S. , and Chen, Y., " A Fitting Algorithm for Determination of Minimum Zone Form Tolerances,"  SAE Transactions,  Journal of Passenger Cars, 1996, Section 6, pp. 1502-1508.

23.     Orady, E., Li., S. and Chen, Y., " Evaluation of Minimum Zone Circularity Using Non-Linear Optimization Techniques," Proceedings of the 1996 Canadian Society of Mechanical Engineering (CSME) Forum, 13th Symposium on Engineering Applications of Mechanics, "Manufacturing Science and Engineering,"  May 7-9, 1996, pp. 495-501.

24.     Orady, E., Li, S. and Chen, Y., "Evaluation of Minimum Zone Straightness by Nonlinear Optimization Method," Proceedings of the 1996 ASME International Mechanical Engineering Congress, Manufacturing Science and Engineering, MED-Vol. 4, Nov. 1996, pp. 413-23.

25.     Orady, E. A., Li, S. and Chen, Y., "Minimum Zone Evaluation of Cylindricity Using Non-Linear Optimization Method," Proceedings of 5th CIRP International Seminar on Computer-Aided Tolerancing, Toronto, Ontario, Canada, April 27-29, 1997, pp. 317-328.

26.     Orady, E. A., Li, S. and Chen, Y., "Minimum Zone Cylindricity Evaluation Using Improved Non-Linear Optimization Method(NOM)," Transactions of The North American Manufacturing Institution of SME, 1997, pp. 287-292.

27.     Orady, E., et al., “Development of Decision-Making System and Fitting Algorithm Software for CMM Measurement in Quality Control” , Progress Report to REEDF, Product Quality Center UM-D, 1997.

28.     Shunmugam, M.S.,  “On Assessment of Geometric Errors," Int. J. Prod. Res., Vol. 24, No. 2, 1986.

29.     Vadiee, N., “Fuzzy Rule-Based Expert Systems” Fuzzy Logic and Control, Prentice Hall, 1993.

30.     Wang, Y., “Minimum Zone Evaluation of Form Tolerances,"  Manufacturing Review, Vol. 5, No. 3, Sept. 1992,  213-220.

31.     Woo, T.C., Liang, R., Hsieh, C.C. and Lee, N.K.,  "Efficient Sampling for Surface Measurements," Journal of Manufacturing Systems, Vol. 14, No. 5, 1995, 345-354.

32.     Woo, T.C. and Liang, R., "Dimensional Measurement of Surfaces and Their Sampling," Computer-aided Design, Vol. 25, No. 4, 1993, 233-239.

 

 [SoE1]

 [SoE2]