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This paper presents an application of type-2 fuzzy logic on acoustic emission (AE) signal modeling in precision manufacturing. Type-2 fuzzy modeling is used to identify the AE signal in precision machining. It provides a simple way to arrive at a definite conclusion without understanding the exact physics of the machining process. Moreover, the interval set of the output from the type-2 fuzzy approach assesses the information about the uncertainty in the AE signal, which can be of great value for investigation of tool wear conditions. Experiments show that the development of the AE signal uncertainty trend corresponds to that of the tool wear. Information from the AE uncertainty scheme can be used to make decisions or investigate the tool condition so as to enhance the reliability of tool wear.

Related to advances in machine tools, manufacturing systems and material technology, machining practice is changing from conventional machining to precision machining, even high-precision machining. The scale of precision machining becomes finer and closer to the dimensional scale of material properties. As a result, the acoustic emission (AE) from microscopic sources becomes significant [

AE is the class of phenomena whereby transient elastic waves are generated by the rapid release of energy by a localized source or sources within a material, or transient elastic wave(s) so generated (ANSI/ASTM E 610-89). Emissions from process changes, like tool wear, chip formation, can be directly related to the mechanics of the process. AE-based sensing methodologies for tool condition and cutting process monitoring have been studied since 1977 [

It is believed that a relatively uncontaminated AE signal can be obtained because AE frequency range is much higher than that of machine vibrations and environmental noises and does not interfere with the cutting operation. AE can be effectively used for TCM applications at the precision scale. In fact, it is impossible to get an accurate AE signal. It is because that machining process varies considerably depending on the part material, temperature, cutting fluids, chip formation, the tool material, temperature, chatter and vibration, and so forth. Additionally, AE sensors are very sensitive to environmental changes such as changes in temperature, humidity, circuit noise, and even the locating error of the sensors. Moreover, changes of cutting conditions also affect the behaviour of acoustic emission signals. None of previous studies considered the uncertainty in AE signal.

The aim of this paper is to present an innovative type-2 Takagi-Sugeno-Kang (TSK) fuzzy modeling to capture the uncertainties in the AE signal in machining process in order to overcome the challenges in TCM. Type-2 TSK fuzzy modeling method is not only a powerful tool to model high complex nonlinear physical processes, but also a great estimator for the ambiguities and uncertainties associated with the system. It is capable to arrive at a definite conclusion without understanding the exact physics of the machining process. In this paper, type-2 TSK fuzzy modeling is implemented to filter the raw AE signal directly from the AE sensor during turning process. Furthermore, its output interval set assesses the uncertainty information in AE, which is of great value to a decision maker and can be used to investigate the complicated tool wear condition during machining process.

This paper is divided into four sections. Section

Fuzzy logic has been originally proposed by Zadeh in his famous paper “Fuzzy Sets” in 1965 [

A generalized type-1 TSK model can be described by fuzzy IF-THEN rules which represent input-output relations of the system. For a MISO first-order type-1 TSK model, its

A Gaussian MF can be expressed by the following formula for the

Based on Zadeh’s concept of type-2 fuzzy sets and extension principle [

An example of a type-2 MF, whose vertices have been assumed to vary over some interval of value, is depicted in Figure

Type-2 Gaussian MF.

A generalized

One way to obtain a type-2 model directly form a type-1 model is by extending the cluster center,

Spread of cluster center.

Consequent parameter

Hence, the premise MF is changed from type-1 fuzzy set into type-2 fuzzy set, that is,

Type-2 FLSs are very useful in circumstances in which it is difficult to determine an exact membership function for a fuzzy set. They can be used to handle rule uncertainties and even measurement uncertainties. Type-2 FLSs moves the world of FLSs into a fundamentally new and important direction. To date, type-2 FL moves in progressive ways where type-1 FL is eventually replaced or supplemented by type-2 FL [

The diagram of type-2 TSK fuzzy modelling algorithm is shown in Figure

Diagram of subtractive clustering-based type-2 TSK fuzzy approach.

Compared with traditional methods and its type-1 counterpart, type-2 fuzzy modeling can not only obtain a modeling result directly from the input-output data sets, but it can also capture the uncertainty interval of the result [

The experiment described in this paper was taken on the BOEHRINGER CNC lathe. The workpiece material was Titanium Metal matrix Composite (Ti MMC) 10% wt. TiC/Ti-6Al-4V where the microstructural response of cast Ti-6Al-4V-based composite contains 10 vol.-% TiC reinforcement. This kind of material is widely used in aerospace and military applications for its high hardness, light weight, high bending strength, fracture toughness, higher modulus, and elevated temperature resistance and high wear resistance. Consequently, its machining is very difficult.

The cutting tool insert was carbide from SECO tools (CNMG 120408 MF1 CP200). Turning test was done on a cylinder of Ti MMC

The aim of this study was to find out the relation between AE and tool wear. During the test, every time when cutting length reached 10 mm, the machine was stopped to manually measure the tool wear parameter (

AE signal from cutting process.

First, type-1 TSK fuzzy filtering (top part of Figure

Number of rules and parameters of type-1 TSK modeling.

Cutting section (mm) | 0~10 | 10~20 | 20~30 | 30~40 | 40~50 |
---|---|---|---|---|---|

Number of data sets | 5500 | 8200 | 5700 | 4500 | 4000 |

Number of rules | 24 | 23 | 29 | 34 | 22 |

Standard deviation | 1.1209 | 0.9016 | 1.034 | 1.1932 | 1.0606 |

Traditionally, the AE signal is characterized using AE root-mean-square (RMS) measurement in well-controlled tensile tests. To compare AE signal obtained by fuzzy filtering with the one by traditional filter, AE RMS values (illustrated in Figure

AE RMS value for different cutting section.

From 0 mm to 10 mm

From 10 mm to 20 mm

From 20 mm to 30 mm

From 30 mm to 40 mm

From 40 mm to 50 mm

AE mean value for different cutting section.

From 0 mm to 10 mm

From 10 mm to 20 mm

From 20 mm to 30 mm

From 30 mm to 40 mm

From 40 mm to 50 mm

The second step consists of expanding the type-1 fuzzy system to a type-2 system. Because the AE signals used are relatively uncontaminated, uncertainty in the AE signal is much smaller than the raw AE signal value. The spreading percentage for clusters is confined to the range [0.0%; 0.01%] with a step size of 0.0001%. The spreading percentage for the consequent parameters is considered as 2%. Spreading percentage for clusters and consequent parameters can be found in [

Uncertainties in AE signal in different cutting sections.

From 0 mm to 10 mm

From 10 mm to 20 mm

From 20 mm to 30 mm

From 30 mm to 40 mm

From 40 mm to 50 mm

Enlarged view for uncertainty interval on (e)

As indicated on Figure

The variations in modeling results from the five AE signal sets.

Cutting section (mm) | Variation (mv) | ||||||||

MAX | MIN | MAX | MIN | MAX | MIN | MAX | MIN | ||

0~10 | 1.1092 | 0.0262 | 1.0257 | 0.0003 | 2.1350 | 0.0108 | 13.6804 | 0.0670 | 0.050 |

10~20 | 4.7649 | 0.0214 | 4.5361 | 0.0006 | 9.3011 | 0.0018 | 28.7809 | 0.1597 | 0.100 |

20~30 | 5.9340 | 0.0604 | 5.660 | 0.0155 | 11.5940 | 0.0759 | 92.8960 | 0.1784 | 0.146 |

30~40 | 4.2204 | 0.0270 | 3.9954 | 0.0007 | 19.3474 | 0.0296 | 117.362 | 0.1980 | 0.196 |

40~50 | 12.630 | 0.0210 | 12.097 | 0.0001 | 24.7279 | 0.0040 | 128.294 | 0.0464 | 0.373 |

The greatest variation of each cutting instant is

As shown in Figures

Maximum and minimum variations in different cutting sections.

maximum

minimum

Tool wears in different cutting sections.

This paper presented a type-2 fuzzy modelling method to determine AE in precision machining. The interval output of type-2 fuzzy modelling provides the information of uncertainty in AE estimations. The sufficient information from AE uncertainty scheme can be used to make decision or investigate tool condition so as to enhance the reliability of tool wear estimation. By applying type-2 fuzzy logic to AE-based tool conditions monitoring, it is possible to automate online diagnosis of cutting tool condition.

Type-2 FLS can model and analyse the uncertainties in machining from the vague information obtained during machining process. The estimation of uncertainties can be used for proving the conformance with specifications for products or autocontrolling of machine system. The application of type-2 fuzzy logic on uncertainty estimation in high precision machining can enable the unmanned use of flexible manufacturing systems and machine tools. It has great meaning for continuous improvement in product quality, reliability, and manufacturing efficiency in machining industry.

Subtractive clustering identification algorithm [

Consider a collection of

After the potential of every data point has been computed, the data point with the highest potential is selected as the first cluster center. Assume

When the potential of all data points have been reduce, by (

The process of acquiring new cluster center and revising potential repeats by using the Algorithm

if

else if

else let

if

else reject

as the new

end if

end if

end if

For the most general structure of T2 TSK FLS—Model I, antecedents are T2 fuzzy sets and consequents are T1 fuzzy sets. Membership grades are interval sets, that is,

The explicit dependence of the total firing interval for

The interval value of the consequent of the

Here

So, the extended output of the IT2 TSK FLS can be calculated by using following equation:

Hence

This interval set of the output has the information about the uncertainties that are associated with the crisp output, and this information can only be obtained by working with T2 TSK FLS. To compute

Without loss of generality, assume that the precomputed

Compute

Find

Compute

If

Set

The procedure for computing

In an interval type-2 TSK FLS, output