Prediction of Life Time of Rail Rubber Pad using Reliability Analysis Method

Transcription

1 IJR International Journal of Railway Vol. 6, No. 1 / March 2013, pp Prediction of Life Time of Rail Rubber Pad using Reliability Analysis Method Dae-Geun Park Abstract Railpad prevents damage of the tie and ballast by reducing the impact and high frequency vibration, which occurs when a vehicle load transfers to a tie. But elasticity of the railpad can decrease under vehicle load and over usable period. If that happens, railpad will become stiffer. Increase in stiffness of the railpad also translates into a rise in track maintenance cost because it accelerates the damage of the track. In this study, accelerated heat ageing was performed to predict an expectable lifetime of the railpad. As a result, it was predicted to be about sixteen years at 25 o C that life time of railpad using NR rubber from Arrhenius relationship. Also, it was predicted to be about thirty-two days at 100 o C. At this time, a standard rate of thickness change is approximately within 12%. Keywords : Rail pad, Lifetime, Prediction, Arrhenius 1. Introduction As rail fasteners are required in a lot of quantity and relatively easy to replace, they are designed to be replaceable components rather than permanent structures. Since a rail fastener consists of several components that differ in nature such as steel, synthetic resin and rubber, it develops imbalance, as each component deteriorates. Rail pad, which is made of rubber, has the shor life time, requiring replacement in a specified period of time. The life time of rail pad is basically dictated by a combination of oxidation of rubber molecules (under the synergy effects of heat, temperature, light, ozone and moist, etc.) and mechanical stress (under vehicle load, vibration, twisting moment, etc.) and impacted significantly by composition and configuration of rubber compound. To analyze rail failure (deterioration) mode and impact analysis, this paper analyzed the results of accelerated thermal ageing (thermal ageing at 70 o C, 85 o C, 100 o C for 1, 2, 4, 7, 11, 15, 20, 25, 30, 35, 40, 45, 50 and 55 days) to calculate time to failure at each temperature and used Weibull distribution per acceleration level as well as Arrhenius life time-stress relationship model to estimate Corresponding author: Korea Rail Network Authority, Overseas rail Projects Division, Engineering Support Dept. ktx2136@kr.or.kr Fig. 1 Impacts on rail track Vol. 6, No. 1 / March

2 Dae-Geun Park / IJR, 6(1), 13-25, 2013 Fig. 2 Factors leading to rubber deterioration(temperature and repeat load) life time distribution and to predict life time depending on operational conditions, respectively. 2. Failure Analysis & Test Method 2.1 Analysis of cause of rubber part failure (ageing) As Fig. 2 illustrates, factors leading to deterioration of rubber includes circumstantial ones such as oxygen in the air, heavy metal, ozone, UV ray, radioactivity or temperature as well as mechanical ones encompassing deformation under load, vibration, wear and tear and fatigue. Such deterioration factors determine the life time of product. 2.2 Failure mode & effect analysis It is necessary to identify the effects to which each failure mode has on system and eliminate the most critical failure mode from design phase. The aim of FMEA is to ensure high reliability and safety from initial design phase and Table 1 illustrates several failure modes of rail pad 14

3 Prediction of Life Time of Rail Rubber Pad using Reliability Analysis Method Functions Reduce noise & vibration Dampen shock Potential failure Wear & tear, Deterioration Design rubber mix in consideration of thermal & ozoneresistance Fatigueinduced crack Change in properties Peeling Table 1 Vibration-proof Rubber Component Failure Types & Effects Analysis (Design FMEA) Potential effect of failure Potential cause / development process of failure Faultprevention measures Reduction of Strength & Vehicle load strength tude durability to cyclic load Thermal & ozone-induced rubber ageing Fatigueinduced crack develops Reduction of passenger comfort & vibrationdamping capability due to performance deterioration Crack & damage by peeling Lack of heat and ozoneresistance of rubber Fatigue due to cyclic load and ageing Change in properties due to extended use & ageing Peeling due to defective molding & vulcanization process Rubber ageing & ozoneresistance Fatigue Environmenta l stressresistance Property (Static load, dynamic load, vibration s) Peeling & environmenta l stress Solution for improvement Enhance durability Change properties in reference to operational environment Enhance durability & environmenta l stressresistance Modify rubber property & configuration Review bonding strength between rubber and metal Result of Action Action Severity Frequency Detection Improve fatigueendurance design & rubber mix Improve durability design & environmenta l stressresistance Design structure in consideration of rubber hardness & configuration Improve mixing, kneading, molding & vulcanization processes Risk priority that have the most significant effects on the system. Fault Tree Analysis is a method of interpretation that describes system reliability or safety in a tree-like diagram. It places undesirable events such as failure, malfunctioning or damage on the top and expands the other events that are the causes of such undesirable events in a tree-like causal relationship configuration using a diagram to investigate possible causes of system failures from top-down. In other words, as Fig. 3 shows, it is a method failure analysis and reliability assessment that drills down into system failure probability from probability of each cause of failure and addresses such causes to improve system reliability Step program Quality features of vibration-damping rubber component is examined to identify failure modes, mechanical Fig. 3 Rubber fault tree analysis(fta) performance requirements and a ing method that can develop failure mode. 15

4 Dae-Geun Park / IJR, 6(1), 13-25, 2013 C) 3-Step : Investigate usage & operating conditions of item and identify dominant failure mechanism A) 1-Step : Identify failure mode by examining structure & material Table 2 Failure Mode Classification Component Function failure Inspection Shoulder type Spring clip Insulator Rail pad Shoulder Elastic fastening Insulation, Lateral load resistance Elasticity, Insulation fastening, Lateral load resistance Damage, Corrosion, Yield Damage, Wear & Tear Hardening, Wear & Tear Damage, Corrosion Visual inspection Elasticity Visual inspection Visual inspection B) 2-Step : Identify potential failure mechanism resulting in failure mode No Table 3 Failure Mechanism Resulting in Failure Mode Failure location Material & potential stress 1 Clip Steel/vibration, shock 2 Rail pad Fig 4 Procedure of program Fig. 5 Rail-fastening system components Rubber/vibration, heat, moist 3 Bolt Steel/vibration, shock Potential failure mechanism Damage under vibration, shock Wear & tear, deterioration by heat, vibration, ozone Damage under vibration, shock Table 4 Investigate Usage & Failure Mechanism Failure Modes Damage Fatigue Abrasion Hardening Requirements Crack Wear (Softening) Vibration (Stresses/Performance) Vehicle load Thermal ageing Vibration Ozone Oxygen * Mark as per criticality relative to reliability : :(Most critical) :(Critical) :(Average) D) 4-Step : Define conditions in which dominant failure mechanism shows up Table 5 Define Methods in which Dominant Failure Mechanism Failure Modes/ Mechanisms Test Methods Tensile Ageing Ozone Wear 3. Thermal Acceleration Test & Arrhenius Equation Vibration Damage Fatigue crack Reduction of strength Abrasion wear Hardening Vibration * Mark as per criticality relative to reliability : :(Most critical) :(Critical) :(Average) * Failure Mode/Mechanism represents all types of failure that may possibly occur to material * Test Methods indicate methods that can develop applicable failure 3.1 Test sample & rig To predict ageing properties & life time of rail pad, sample of finished product and thermal-ageing property rig shown in Fig. 6 and 7 were used and, given that temperature was the most important property deterioration factor for rail pad, the sample was thermalaged for 1, 2, 4, 7, 11, 15, 20, 25, 30, 35, 40, 45, 50 and 55 days at 70 o C, 85 o C, 100 o C and change in rail pad thickness was measured to understand ageing properties of rail pad. 16

5 Prediction of Life Time of Rail Rubber Pad using Reliability Analysis Method Fig. 6 Rail pad sample Fig. 8 Activation energy Fig. 7 Thermal ageing property rig 3.2 Arrhenius equation Arrhenius Equation to estimate life time, if the rubber property is P in the 1st ageing response, can be expressed as following Equation (1). dp P = kp namely, ln = kt dt P0 Fig. 9 Property change relative to temperature change (1) Where, P : rubber properties(extension rate, tension strength, etc.), P0 : initial value, t : time, k : reaction rate (1/time) Reaction rate k in Equation (1) is a constant representing the ageing response of property P and S. Arrhenius developed the following empirical formula in k = A e Ea RT Ea ln k ( T) = C RT (2) (3) Where, A, C : constant Ea : activation energy (J/mol) R : gas constant (8.314 J/molK), T : absolute temperature (K) If the time of aged property P in Equation (1) is the life time, life time t at the location can be calculated from Equation (4), where, P P0 = C. t = ln ( C ) k Fig. 10 Arrhenius curve words, with property P, life time t1 at temperature T1 is equal to life time t2 at temperature T2, as expressed in the following equation. t E 1 1 ln ---1 = R T1 T2 t2 (4) In Equation (4), life time t is expresses in relationship with temperature from reaction rate in Equation (2) to enable conversion of life time from temperature. In other (5) Activation energy resulting from rubber ageing is the minimum age required for a transition from initial state A to post-ageing state B as shown in Fig. 8, which var 17

6 Dae-Geun Park / IJR, 6(1), 13-25, 2013 Failure statistics analysis employes a graph such as probability paper or analytical method like maximum likelihood method. Analysis method is as shown in Fig Data collection & Application model Mathematical model fit for data collected via accelerated deterioration needs to be developed and goodness of fit of application mode determined. As power model is most fit for the data dispersion graph and R 2, as a scale of goodness of fit of application model, is 0.99, applied model can be said to be fit. - Power model y = ax b - Coefficient of determination R 2 = 0.99 (6) Fig. 11 Accelerated deterioration data analysis flow ies, subject to rubber material & ageing mode. To calculate activation energy (E a ), it must be understood how rubber property change across different temperature range. If longitudinal axis is the algebraic value of life time ( ln( t m )) and lateral axis is converted to reciprocal number of absolute temperature ( 1 T ), a diagram such as Fig. 8 can be drawn. 4. Test Results Analysis 4.1 Statistical data analysis 4.3 Service distribution Weibull Distribution, probability distribution used as an integral life time model in reliability sector and fit for predicting strength of metal and composite material and life time of electronic and mechanical component, is adopted and goodness of fit ed, parent shape and scale parameters estimated. t -- f() t -- t ηη -- η = 1e e t 0, η, > 0 A) Fit distribution & Goodness of fit A simulation of fit distribution based on deterioration data identified 3-parameter Weibull distribution, G- Gamma distribution and Lognormal distribution in the (7) Fig. 12 Data dispersion graph & regression curve 18

7 Prediction of Life Time of Rail Rubber Pad using Reliability Analysis Method Table 6 Test Results Data Time (hr) 70 o C 85 o C 100 o C Fig. 13 Fit distribution & distribution order of fitness. 2-parameter Weibull distribution ranked the 3rd and applied to life time distribution genetically was selected and K-S(Kolmogorov-Smirnov) procedure was used for goodness of fit. K-S calculates absolute difference between cumulative failure probability F0(ti) of observation values from failure history data and cumulative distribution function Fe(ti) of theoretical distribution and the biggest value is defined as statistics D CRIT and compared with allowable goodness of fit D and, if D < D CRIT, theoretical distribution assumed within significant level is adopted. As K-S value is close to 0, observed values and theoretical distribution are deemed to be fit. In addition, as Kolmogorov-Smirnov result against 2-parameter Weilbull distribution that is selected is close to 0% and cumulative distribution function drawn in probability paper indicates straight line, assumed distribution is deemed to be fit. B) Parameter estimation & Distribution features 2-parameter Weibull distribution was found to be fit and maximum likelihood method was used for analysis. If life time follows Weibull distribution, log-likelihood function divides into fault portion and censoring portion as follows. Fe ln( L) Λ N i -- T i = = ln ηη T --- i η e 19

8 Dae-Geun Park / IJR, 6(1), 13-25, 2013 S FI T N i i N η i ln[ R Li R Ri ] R Ri T Ri η = e, = e R Li T Li η (8) (9) Where, Fe : no. of actual failure data groups, Ni : no. of failure data in the ith group : shape parameter, η : scale parameter, Ti : time of the ith failure data group S : no. of censored data groups, N i : no. of data in the ith censored group T i : Censoring time of data in the ith censored group FI : no. of interval data group, N i : interval in the ith data intervals T Li : start of the ith interval, T Li : end of the ith interval Maximum likelihood values, η can be obtained from likelihood equation by partial differentiation of and η. Λ Fe Fe 1 T = -- N i N i + ln i --- η i Fig. 14 Probability density function Table 7 Parameter a,b Temperature Parameter a Parameter b 70 o C o C o C Fe T N i i --- η --- T i T N η t ' i ' ---- η ln ln T ---- ' i η S T Ri T Li T Li RLi T Ri FI ln + ln RRi η η η η + N i (10) R Li R Ri Λ η Fe Fe T = N η i -- N i + η i --- η -- N (11) η i T i T Li N η i T R η -- η Li Ri s FI R η Ri R Li R Ri Mathcad Program was used to calculate shape parameter and scale parameter. As for parameter estimation and distribution characteristics analysis, scale parameter (η) was estimated to be and shape parameter () to be As scale parameter (η) always points to cumulative distribution function F(x) - value X where failure probability is (63.2%), it means lifetime of characteristic. If it is big, overall life time is deemed to be long and, if it is small, overall life time is deemed to be short. Estimated shape parameter () is , indicating a rise in failure rate. Fig. 15 Deterioration graph at 12% degradation C) Calculation of time to failure per temperature If using linear curve regression curve, y = ax b (12) If applying log to the function in Equation (10), ln( y) = ln( a) + b ln( x) (13) As this equation has linear relationship between ln(y) and ln(x), it becomes a linear regression problem. Intercept and slope can be calculated by Mathcad's intercept 20

9 Prediction of Life Time of Rail Rubber Pad using Reliability Analysis Method Ageing Temperature Table 8 Time to Failure at Each Temperature 12% Degradation time ln (time, hrs) 1/T (Absolute temperature, K) 70 o C o C o C Time to failure 12% ( ) ( ) ( ) ln ln ln a1 a3 a b1 b3 b2 t1 := e t3 := e t2 := e t1 = t2 = t3 = (15) and slope functions. Ln(a) = intercept (ln(x), In(y)), a = exp(intercept(ln(x), In(y)), b = slope((ln(x), In(y)) a = 1.005, b = a,b obtained from data at 85 o C, 100 o C as in the above equation follows. Following equations are obtained. D) Reliability scale Distribution function, reliability function, failure rate function, mean time to failure (MTTF), dispersion, percentile and B p life time of Weibull distribution are calculated. 4.4 Life time prediction by arrhenius-weibull distribution model A) Arrhenius-weibull distribution If life time follows Weibull distribution at each stress level, life time distribution is as shown in Equation (16). y a = x y b = x y c = x (14) t -- f() t -- t ηη -- 1 η = e t 0, η, > 0 (16) Where, η : Weibull distribution's scale parameter. If η is serivce life L (V) of Arrhenius equation in Arrhenius-Weibull distribution model, Table 9 Weibull Distribution Estimated parameters F(t) Cumulative distribution function Shape parameter()= Scale parameter= Calculation formula R(t) Reliability function f(t) Probability density function λ(t) Failure rate function MTTF Calculation formula Calculation formula Calculation formula Calculation formula B p life time Calculation formula 21

10 Dae-Geun Park / IJR, 6(1), 13-25, 2013 Estimated parameters Shape parameter()= Scale parameter= F(t) Cumulative distribution function R(t) Reliability function f(t) Probability density function λ(t) Failure rate function Fig. 16 Evaluation scale graph η = LV ( )( = Ce BV ) life time is as shown in Equation (18). f( tv, ) t = Ce BV Ce BV t Ce e BV (17) (18) B) Arrhenius plot Fig. 17 Arrhenius plot ln() t = T (19) t: thermal-ageing time(hrs), T:ageing temperature(absolute temperature, K) 22

11 Prediction of Life Time of Rail Rubber Pad using Reliability Analysis Method C) MTTF per temperature condition Table 10 Life Time Service Temperature( o C) ln(t) Time(hrs) Time(Year) , temperature ( o C) log (t) D) B p life time per usage temperature condition Analysis of 10%, 5%, 63.2%, 50% percentiles at arbitrary temperature indicates that the confidence interval of B10 life time is between years and years at 25 o C and confidence level of 95%. E) Test time estimation hrs day year , , , , , , , , Percent Temp.( o C) B10(10%) 25 B5(5%) 25 B63.2(63%) 25 Mean(50%) 25 Table 11 B p Life Time Percentile (year) 142,470 (16.26) 138,130 (15.77) (17.91) 153,311 (17.52) 95%CL Lower(hrs) Upper(hrs) 109, , , , , , , ,260 Table 12 Estimation of Acceleration Factor Test Time Per Acceleration Condition Temperature( ) Acceleration Factor Upper Median Lower Temperature ( o C) Accelerated ageing time (h) 70 2, , Acceleration factor = Characteristiclife time usage condition Characteristiclife time at condition F) Life time prediction criteria To guarantee life time of rail pad for 16 years, thickness of NR rubber component made of natural rubber must vary 12% or less when subject to accelerated thermal ageing for 772 hours at 100 o C. G) Evaluation scale 6. Conclusion Accelerated thermal ageing was performed at 70, 85, 100 o C to predict expected life time of rail pad made of rubber and used for rail-fastening system. The end of life time for the rubber component was defined as when its thickness was reduced by 12% under compression and life time distribution was analyzed. Failure rate increased over time and Arrhenius-Weibull distribution was used for life time prediction. Service life at constant vehicle load (2 ton) and usage temperature(25 o C) was predicted to be about 16 years and a new acceleration that could save time and efforts was designed from the identified Arrhenius equation. It was found that using the rail pad for 16 years at 25 o C was equal to thermal ageing for about 772 hours (32 days) at 100 o C. It was concluded that, to guarantee life time of rail pad for 16 years, thickness of NR rubber component made of natural rubber must vary 12% or less when subject to accelerated thermal ageing for 772 hours at 100 o C. 1) For evaluation reliability, rail pad durability prediction and reliability criteria were developed from deterioration data by Arrhenius-Weibull model. 2) factors leading to deterioration of rubber includes circumstantial ones such as oxygen in the air, heavy metal, ozone, UV ray, radioactivity or temperature as well as mechanical ones encompassing deformation under load, vibration, wear and tear and fatigue. Deterioration mechanism explaining how such deterioration factors determine the life time of product was analyzed. 3) By predicting the life time of rail pad which is the 23

12 Dae-Geun Park / IJR, 6(1), 13-25, 2013 Estimated parameters =23.28 B= C= V=298(25 o C) F(t) Cumulative distribution function FtV (, ) : = 1 R( t, V) R(t) Reliability function RtV4 (, ) : = e t B V4 C e f(t) Probability density function ftv4 (, ) : t = B B V4 V4 Ce Ce t B V4 C e e λ(t) Failure rate function λ( tv4, ) : = ftv4 (, ) RtV (, ) B(x) Life function tp ( ) : = C e B V4 ( ln( 1 P) ) 1 -- Fig. 18 Arrhenius-Weibull distribution evaluation scale least durable component of rail-fastening system, such deterioration mechanism can provide basic inputs for RAMS and LCC analysis of rail track structure. 4) Future rail pad life time prediction criteria that will find application in rail-fastening system manufacturing specification were developed. 24

13 Prediction of Life Time of Rail Rubber Pad using Reliability Analysis Method 1. R.P.Brown, T.Burtler and S.W.Hawley, Ageing of rubberaccelerated heat ageing results, Rapra Technology, R.P.Brown, Physical ing of rubber, Chapman &Hall, 3rd, KS M6518, Vulcanized rubber physical method-(7) compressed permanent reduction rate,