A New Failure Mode and Effects Analysis Model of CNC Machine Tool using Fuzzy Theory

A New Failure Mode and Effects Analysis Model of CNC Machine Tool using Fuzzy Theory

Zhaojun Yang

, Binbin Xu

, Fei Chen

, Qingbo Hao

, Xiaocui Zhu

, Yazhou Jia

1

College of Mechanical Science and Engineering, Jilin University Changchun 130022, China

2

Department of Mechanics, Aviation University of Air Force Changchun 130000, China

*

[email protected]

Abstract - Failure mode analysis is important in CNC

machine tool. In order to assess the failure mode of CNC machine tool, this paper described a new fuzzy FMEA model integrating with fuzzy linguistic scale method. The model proposed a risk- space diagram to explicit the relationship of S,O and D. On the basis of the risk-space diagram, risk priority number is calculated by weighted Euclidean Distance formula and centroid defuzzification based on Alpha-level. This study is used to analysis a type of CNC lathe. Compared with the criticality ranking about another similar type of CNC lathe, the risk ranking of FMEA model revealed that the method is basically same with the actual situation. The results indicated that the fuzzy FMEA used in CNC lathe is a reasonable method corresponding to the manufacturing, and it is a validity foundation for constructing reliability design model or supporting control plan of manufacturing.

Index Terms –FMEA, CNC machine tool, fuzzy theory, risk- space diagram, weighted Euclidean Distance

I. I

Failure mode analysis is a critical but challenging issue in CNC machine tool industry. In recent years, with the development of high-efficiency and accurate industrial products, it demands more features on CNC machine tool. As a result, it may cause more failure modes for complicated structure and multifunction. Consequently, the importance of CNC machine tool reliability had drawn attentions of the companies and institutions to investigate CNC machine tool reliability technologies

.

Failure modes and effects analysis (FMEA) is a significant procedure in the whole process of reliability engineering, and widely applied extensively in most of manufacture industries

6,13-16]

. Nevertheless, the drawbacks of the traditional FMEA method were shown in the process of the physical applications.

The scholars and engineers did some research in improving FMEA technology. In order to overcome the subjectivity while scaling the risk factors, FMEA integrated with fuzzy inference or approximate reasoning has been proposed which improved the model more objective

. However, substantial quantity of the inference rules made the computational process complicated. Besides, the risk factors Severity (S), Occurrence

(O) and Detectivity (D) are diversity with different implications whose weights should be considered

. The multiple risk factors has a fatal weakness-the dilution phenomenon

. In addition, the research on FMEA of CNC machine tool, failure mode criticality combined with FTA is designed to analysis the field test on the basis of certain amount of failure data on CNC machine tool

. But it is difficult to collect the data because the corporate users are distributed throughout the country and the filed tests expend substantial time and cost.

To solve these shortcomings, a new FMEA model applied to CNC machine tool is devised composed with fuzzy scale method, risk-space diagram and weighted Euclidean Distance.

II. M

2.1 Fuzzy linguistic rule of FMEA

Fuzzy theory is adept in dealing with uncertain events and widely applied in many aspects of industries. In this paper, the FMEA model is applied to CNC machine tool. The fuzzy linguistic rule is defined by the characteristic of the failure modes on CNC machine tool. A five-points linguistic scale V=

{remote, low, moderate, high, very high} is the evaluation value of the FMEA risk factors in Table I.

2.2 Fuzzy membership function of S, O and D

Based on the fuzzy linguistic rule and relative research on FMEA

, the membership of risk factors are defined by a trapezoid fuzzy number to measure the linguistic scale values in aggregate V(Fig.1).

TABLE I

FUZZY LINGUISTIC RULE OF S, O AND D Rating S

Remote A failure has little or no impact on the system, and the operator probably will not notice.

Low A failure causes slight annoyance to operator, and no deterioration on system.

Moderate A failure causes slight deterioration in system performance and a high level of operator dissatisfaction.

High A failure causes significant deterioration or inoperation on the system.

Very high A failure causes extremely impact on system, production loss and/or serious injury to operators.

Proceedings of the 2010 IEEE

International Conference on Information and Automation June 20 - 23, Harbin, China

Rating O

Remote A failure probability is essentially zero.

Low A failure is likely occurred once, but unlikely to occur more frequently.

Moderate A failure occurs in a moderate probability.

High A failure occurs in a high probability.

Very high A failure occurs in a extremely high probability.

Rating D

Remote A failure will be detected almost certainly by the inspection automatically of the whole process.

Low A failure will be detected until the review inspected or test but not automatically.

Moderate A failure will be detected until manual inspection or test carried out.

High A failure will be detected only with thorough inspection or test, and it is not feasible to be done.

Very high A failure will be detected hardly because of no known measure to solve.

Fig.1 Membership function plot of S, O and D.

To avoid the influence of the experts experience and knowledge in traditional FMEA, a FMEA team composed with several cross-functional experts was constituted that would reduce the subjectivity of the scores rating by experts. By means of scoring for each failure mode, trapezoidal fuzzy number of S O D   

,

,

are given by

1 2 1 2

1

( , , , ) ( , , , ) /

m

i iL iM iM iR ijL ijM ijM ijR

j

S S S S S ­ S S S S ½ m

® ¾

¯ ¦ ¿

 (1)

1 2 1 2

1

( , , , ) ( , , , ) /

m

i iL iM iM iR ijL ijM ijM ijR

j

O O O O O ­ O O O O ½ m

® ¾

¯ ¦ ¿

 (2)

1 2 1 2

1

( , , , ) ( , , , ) /

m

i iL iM iM iR ijL ijM ijM ijR

j

D D D D D ­ D D D D ½ m

® ¾

¯ ¦ ¿

 (3)

1,..., ; 1,...,

i n j m

where S

represents the fuzzy S scores of the ith failure mode;

S

, S

S

and S

represent the membership function parameters of S

respectively. Eq.(2) and (3) indicate O

and

D measurement scores in the same way; j represents the jth

expert, the totally of experts is m.

2.3 Algorithm of Risk Priority Number

Risk priority number (RPN) is the measurement of the failure modes with multiple S, O and D in traditional FMEA.

To avoid dilution phenomenon, a risk-space diagram is applied according to the risk assessment on aviation safety management

.

Firstly, -level algorithm is introduced to the model according to Zadehl’s extension principle. The left-hand and right-hand of S

, O

and D

are calculated by -level which is expressed by:

(

)

iL iL iM iL

S

S  D S  S (4)

(

)

iR iR iR iM

S

S  D S  S (5)

(

)

iL iL iM iL

O

O  D O  O (6)

(

)

iR iR iR iM

O

O  D O  O (7)

(

)

iL iL iM iL

D

D  D D  D (8)

(

)

iR iR iR iM

D

D  D D  D (9) where 0.0<İ1.0, [ S

, S

] represents S interval of the ith failure mode by -level; [ O

, O

] and [ D

, D

] represent O and D interval respectively with the same algorithm.

Secondly, the risk space-diagram (RSD) is built based on S, O and D by -level. Fig.2 shows the configuration and inter- relations of the risk factors and RPN in one coordinate system.

Each failure mode owns its RSD. The axis in the coordinate represents the risk factor S

, O

and D

of the ith failure mode.

In RSD, RPN

denotes left-hand of RPN

by -level which is the combination of S

, O

and D

. Similarly, RPN

denotes right-hand of RPN

in the coordinate. The initial point O denotes the minimum index, and the vertex point G denotes the maximum index respectively. As seen from RSD, the bigger RPN is, closer it is to the point G, and the sequencing of RPN is further forward.

(0,0,10) (0,10,10)

(10,0,10)

G(10,10,10)

(10,0,0) (10,10,0)

(0,10,0) O(0,0,0)

Fig.2 Risk Space Diagram of ith failure mode.

Subsequently, the weighted Euclidean distance formula is employed to induce RPN

and RPN

according to the relationship in RSD. Considering the discrepancy of the risk factors, importance weights are indicated to calculate of RPN.

According to the research of weighting Euclidean distance,

RPN

is expressed in multiplicative weighted format, given by:

2 2 2 2

min max min

1 1

( ) ( )

n n

iL k iL i k i i

i i

RPN

¦ w x

 x

¦ w x

 x

(10)

2 2 2 2

min max min

1 1

( ) ( )

n n

iR k iR i k i i

i i

RPN

¦ w x

 x

¦ w x

 x

(11)

1 2

( , , , )

i iL iM iM iR

RPN RPN RPN RPN RPN (12) where w

denotes the weights of the risk factor (k=S, O, D), weights normalized eigenvector [0.5396, 0.2970, 0.1634] is employed

. Generally, x

indicates the minimum index of x

value which equals 0 according to the Fig.1. On the contrary, x

indicates the maximum index which equals 10 identical with Fig.1. RPN

is the membership function of the fuzzy RPNi.

Finally, it is a critical procedure which is ranking fuzzy RPN

by defuzzification number. Centroid method is applied to calculate the fuzzy RPN

according to the membership function, which is given by:

0 1 2

( ) 1 [

i

3

x RPN  RPN  RPN  RPN  RPN

2 1

2 1

· ·

( ) ( ) ]

iR iM iL iM

iR iM iL iM

RPN RPN RPN RPN

RPN RPN RPN RPN

 

   (13)

where x A 

( ) reveals the centroid number of fuzzy RPN

III. F

3.1 Composition of CNC lathe

CNC lathe is a typical CNC machine tool composed by several subsystems which contains mechanics, electronic

system, CNC control system, supplementary and so on. The following descript the main composition of the CNC lathe:

1) Mechanical system: the main component of the machine, which could transform the action orders issued by control system to actual and accuracy mechanical operations in order to accomplish the function. It includes spindle, slide axes, turret or ATC, machine body, auxiliary device, detecting sets and so on. Machine body is composed by bed, pedestal, working bench, column, slide etc. Spindle is driven by main transmission system which could implement continuous or stepped continuous speed change composed by AC or DC motor. The slide axes are driven by feed drive system through associated movements by the ball guide screws and guide rails. All of these are controlled by CNC system.

2) CNC system: the heart of CNC lathe. The CNC system could read the manufacture programming from the internal storage, and then compiling by the logic circuit or software. Finally, send out the control order to the machine to complete the function. It contains. It contains I/O equipment, CNC control system, servo drive and PLC.

3) Supplementary subsystems: It is composed by hydraulic, lubrication, coolant, chip removal and so on. As the package subsystems, it is used to guarantee the stable operation of CNC lathe.

3.2 A FMEA model of CNC lathe

In this paper, a certain type of CNC lathe is the study object in the FMEA model. According to discussion of the FMEA team experts, the main failure mode of CNC lathe is summarized in Table II.

TABLE II

MAIN FAILURE MODE OF A CERTAIN CNC LATHE

No. Subsystem Failure mode Principal Failure effects

F1 Spindle Cylindricity on the workpiece overproof Spindle encoder failed, radial or axial clearances

F2 Abnormal noise Bearings failed or nicked, screws loosen

F3 No rotation action Protection switch failed, no clamping chuck,

F4 Spindle vibration Small pretightening force on bearing, too large clearance F5 Turrent No translocation stop Reset switch failed, power supply string of turrent breakage

F6 No action No input order, solenoid disconnected, mechanical connected with turrent scarified F7 Turrent delocalization Turrent encoder failed, lock-switch position changed

F8 CNC system Work but not follow the command Cable break, control panel failure F9 No display after power Power panel failure, system failure

F10 CRT failure CRT failed, 24V power failure

F11 Feed system Dimension in radial/axial overproof Coupling loosen, gear ration error setting

F12 Feed system out of control Servo unit failure

F13 Abnormal noise Servo motor failed, brake sticking

F14 Electrical system Transformer thermal-overload or burn down Thermal sensor failure

F15 No power Power poor contacted, transformer breakdown

F16 Hydraulic system Pressure out of control Trim of throttle valve failed or oil spill

F17 No action Seal ring failure, oil spill, solenoid valve failed

F18 Chip removal No tramping chip Drag on conveyor seizure, clutch failed F19 Lubricate system Insufficient lubrication Lubrication motor failed, oil-way jammed

Seen from Table II, it is a challenge work to do a accurate analysis on risk factors because of the shortage of the failure data and numerous principal failure causes. Hence, the new fuzzy FMEA is employed to solve these problems. The FMEA team is composed with four cross-functional experts in the whole FMEA process. The scores ranked by experts is given by:

TABLE III

SCORES ON MAIN CNC LATHE FAILURE MODE BY FMEA EXPERTS

TM1 TM2 TM3 TM4 No. S O D S O D S O D S O D

F1 VH, H, H M, VH, M H, VH, M M, L, R

F2 H, M, H L, L, M H, M, M M, M, L

F3 M, M, VH L, M, L M, L, VH M, L, L

F4 H, M, M H, L, R L, M, M M, L, R

F5 VH, M, L M, M, L M, M, L M, L, R

F6 M, M, H H, M, R H, M, M L, R, R

F7 H, M, H VH, L, R H, L, H M, R, R

F8 H, M, VH L, R, M M, L, L H, L, L

F9 L, L, L R, R, R L, L, L L, M, R

F10 L, L, L R, L, L L, H, L R, L, L

F11 VH, H, H L, M, H L, H, M M, M, L

F12 H, M, M H, L, H M, M, M H, M, M

F13 H, M, M L, M, L L, L, H M, M, L

F14 H, L, L H, L, L M, L, M M, L, L

F15 L, L, L R, L, R M, L, M L, M, L

F16 M, H, L H, R, H M, L, M L, L, R

F17 H, H, M M, H, VH M, VH, L M, M, L

F18 M, M, L R, L, R L, M, R R, R, R

F19 H, L, L H, R, H M, L, M M, M, L

The membership function of the risk factors are deduced by (1) to (3) that shown in Table IV.

TABLE IV

MEMBERSHIP FUNCTION OF S,O AND D OF MAIN FAILURE MODE

No. S O D

F1 (5.00, 6.00, 7.50, 8.25) (5.75, 6.75, 7.75, 8.25) (3.25, 4.00,5.25, 6.25) F2 (4.00, 5.00, 6.25, 7.25) (2.50, 3.50, 5.25, 6.25) (3.25, 4.25, 5.75, 6.75) F3 (2.50, 3.50, 5.25, 6.25) (2.00, 3.00, 4.50, 5.50) (4.50, 5.50, 6.50, 7.00) F4 (4.00, 5.00, 6.25, 7.25) (2.00, 3.00, 4.50, 5.50) (2.00, 2.50, 3.50, 4.50) F5 (4.25, 5.25, 7.00, 7.75) (2.50, 3.50, 5.25, 6.25) (1.00, 1.75, 2.50, 3.50) F6 (4.00, 5.00, 6.25, 7.25) (2.50, 3.25, 4.75, 5.75) (2.75, 3.25, 4.00, 5.00) F7 (5.75, 6.75, 8.00, 8.75) (1.50, 2.25, 3.25, 4.25) (3.50, 4.00, 4.50, 5.50) F8 (4.00, 5.00, 6.25, 7.25) (1.50, 2.25, 3.25, 4.25) (3.25, 4.25, 5.50, 6.25) F9 (1.00, 1.75, 2.50, 3.50) (1.50, 2.25, 3.25, 4.25) (1.00, 1.50, 2.00, 3.00) F10 (1.00, 1.50, 2.00, 3.00) (2.25, 3.25, 4.25, 5.25) (1.00, 2.00, 3.00, 4.00) F11 (3.25, 4.25, 5.50, 6.25) (4.50, 5.50, 7.00, 8.00) (4.00, 5.00, 6.25, 7.25) F12 (5.25, 6.25, 7.50, 8.50) (2.50, 3.50, 5.25, 6.25) (3.75, 4.75, 6.50, 7.50) F13 (2.75, 3.75, 5.00, 6.00) (2.50, 3.50, 5.25, 6.25) (2.75, 3.75, 5.00, 6.00) F14 (4.50, 5.50, 7.00, 8.00) (1.00, 2.00, 3.00, 4.00) (1.50, 2.50, 3.75, 4.75) F15 (1.50, 2.25, 3.25, 4.25) (1.50, 2.50, 3.75, 4.75) (2.25, 3.00, 3.75, 4.75) F16 (3.25, 4.25, 5.75, 6.75) (2.25, 2.75, 3.25, 4.25) (2.75, 3.50, 4.50, 5.50) F17 (3.75, 4.75, 6.50, 7.50) (5.75, 6.75, 8.00, 8.75) (3.25, 4.25, 5.50, 6.25) F18 (1.50, 2.00, 2.75, 3.75) (2.00, 2.75, 4.00, 5.00) (1.00, 1.25, 1.50, 2.50) F19 (4.50, 5.50, 7.00, 8.00) (1.50, 2.25, 3.25, 4.25) (2.75, 3.75, 5.00, 6.00)

By means of the weighted Euclidean Distance formula and centroid defuzzified method, in (10), (11), (13) and (14), the centroid RPN and ranking consequence are calculated and expressed in Table V.

F1 and F11 is the most significant failure mode to improve with RPN 6.67 and 6.52. F1 and F11 are the overproof of cylindricity and radial/axial dimension on the work piece. The rest of the risk priority result that followed by F3 (Turrent delocalization) > F12 (Feed system out of control)

> F17 (No action on Hydraulic system) > F5 (No translocation stop) etc.

TABLE V

FUZZY RPN AND RANKING OF MAIN FAILURE MODE No. 

0 0.5 1 Centriod Ranking

F1 [5.08, 8.13] [5.57, 7.78] [6.06, 7.43] 6.67 1 F2 [3.68, 7.01] [4.17, 6.51] [4.67, 6.01] 5.34 9 F3 [3.57, 7.21] [4.07, 6.73] [4.56, 6.25] 5.40 8 F4 [3.55, 6.75] [4.03, 6.26] [4.50, 5.76] 5.14 11 F5 [3.79, 7.24] [4.27, 6.84] [4.76, 6.44] 5.55 6 F6 [3.65, 6.82] [4.11, 6.32] [4.57, 5.83] 5.22 10 F7 [5.00, 7.80] [5.45, 7.42] [5.90, 7.04] 6.43 3 F8 [3.56, 6.65] [4.03, 6.16] [4.50, 5.68] 5.10 12 F9 [1.13, 3.65] [1.49, 3.15] [1.86, 2.65] 2.33 19 F10 [2.19, 5.18] [2.69, 4.67] [3.18, 4.18] 3.68 16 F11 [4.84, 8.13] [5.33, 7.73] [5.83, 7.32] 6.52 2 F12 [4.70, 8.00] [5.18, 7.50] [5.67, 7.01] 6.34 4 F13 [2.70, 6.06] [3.20, 5.56] [3.70, 5.06] 4.83 14 F14 [3.86, 7.13] [4.32, 6.65] [4.79, 6.17] 5.49 7 F15 [1.56, 4.40] [1.96, 3.90] [2.36, 3.40] 2.94 17 F16 [3.03, 6.21] [3.48, 5.72] [3.92, 5.23] 4.60 15 F17 [4.24, 7.72] [4.73, 7.26] [5.22, 6.80] 5.99 5 F18 [1.60, 3.99] [1.87, 3.50] [2.15, 3.01] 2.70 18 F19 [3.25, 6.71] [3.71, 6.24] [4.18, 5.74] 4.97 13

The main purpose of the experts is quality first which is corresponding to the idea of the manufacturing enterprises. The overproof of cylindricity and radial/axial dimension is mainly caused by poor assembling. Turrent and feed system maybe badly damaged because of turrent delocalization and feed system out of control. On the whale, the key function systems such as spindle, turrent, CNC system play a huge role in the overall machine. However, the supplementary system made up by hydraulic system, lubricate system and chip removal is absolutely necessary for the steady operation of CNC lathe.

Both key function systems and supplementary system must be paid more attention to.

3.3 Comparison with similar CNC lathe

For the sake of validating the FMEA model in CNC lathe,

a number of failure data about the similar type products is

collected from the user enterprises at the same time. The

quantitative index-Criticality is calculated with the failure

data

. The comparison of the RPN ranking with Criticality

ranking of the similar type lathe is shown in Table VI.

TABLE VI

COMPARISON OF RPN AND CRITICALITY OF SIMILAR CNC LATHE No. RPN

Ranking Cr Cr

Ranking No. RPN

Ranking Cr Cr Ranking

F1 1 0.107 1 F11 2 0.071 2

F2 9 0.027 8 F12 4 0.043 5

F3 8 0.025 10 F13 14 0.018 13

F4 11 0.021 11 F14 7 0.029 7

F5 6 0.043 4 F15 17 0.007 17

F6 10 0.027 9 F16 15 0.011 15

F7 3 0.054 3 F17 5 0.036 6

F8 12 0.018 12 F18 18 0.005 18

F9 19 0.004 19 F19 13 0.018 14

F10 16 0.007 16

The filed data is summarized from the maintenance record of 23 similar CNC lathes which was observed for 4000 hours per machine. Seen from Table VI, the ranking consequence of RPN and Criticality is basically identical. However, it is a hard puzzle to tackle with the collections of field data or maintenance records. This new FMEA model combined with experts’ knowledge and experience may give the ranking consequence of CNC machine tool. Therefore, it saves a lot of time, cost and labour to collect the field data while using fuzzy FMEA. Moreover, the rational result of FMEA is an important support to analysis the other aspects of reliability models in accordance with the ranking of the failure modes.

IV. C

A new FMEA model integrating with fuzzy linguistic scale method, experts system and Euclidean distance considering the weights of the relative factors of RPN is proposed in the paper. Compared with the traditional FMEA, the new FMEA approach can overcome the drawbacks of different importance of FMEA factors, the uncertain evaluation because of the variety degrees of experts’ knowledge and experience. This method is applied to a new type CNC lathe, and the results show that the risk ranking in this way is consistent with the quantitative criticality sort results of similar products. Effectiveness, accuracy and practicality of the method have been proved through practice. The method laid a foundation for failure analysis, reliability modeling and reliability design, and saved a lot of time and cost.

A

This research is supported by the Important National Science and Technology Specific Projects of China (No.

2009ZX04014-011), and National Natural Science Foundation of China (No. 50875110). Critical comments and suggestions from referees have been very helpful in revision of this manuscript.

R

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