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A model for optimal armature maintenance in electric haul truck wheel motors: a case study

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Industrial Case Study
A model for optimal armature maintenance in electric haultruck wheel motors: a case study
Benjamin Lhorente
a
, Diederik Lugtigheid
b,
*, Peter F. Knights
c
, Alejandro Santana
d
a
Komatsu Chile, Av. Americo Vespucio 0631, Quilicura, Santiago, Chile
b
Condition-Based Maintenance Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto,5 King’s College Road, Toronto, Ont., Canada M5S3G8
c
Canadian Chair of Mining and Associate Professor, Pontiﬁcia Universidad Catolica de Chile, Centro de Mineria, Av. Vicuna MacKenna 4860, Santiago, Chile
d
Reliability and Development of Komatsu Chile, Av. Americo Vespucio 0631, Quilicura, Santiago, Chile
Received 25 September 2003; accepted 24 October 2003
Abstract
The objective of the work presented in this paper is the determination of an optimal age-based maintenance strategy for wheel motorarmatures of a ﬂeet of Komatsu haul trucks in a mining application in Chile. For such purpose, four years of maintenance data of thesecomponents were analyzed to estimate their failure distribution and a model was created to simulate the maintenance process and itsrestrictions. The model incorporates the impact of successive corrective (on-failure) and preventive maintenance on necessary newcomponent investments. The analysis of the failure data showed a signiﬁcant difference in failure distribution of new armatures versusarmatures that had already undergone one or several preventive maintenance actions. Finally, the model was applied to calculate estimatedcosts per unit time for different preventive maintenance intervals. From the resulting relationship an optimal preventive maintenance intervalwas determined and the operational and economical consequences and effects with respect to the actual strategy were quantiﬁed. Theapplication of the model resulted in the optimal preventive maintenance interval of 14,500 operational hours. Considering the failuredistribution of the armatures, this optimal strategy is very close to a run-to-failure scenario.
q
2004 Elsevier Ltd. All rights reserved.
Keywords:
Weibull analysis; Armatures; Electric motors; Repairable system; Maintenance optimization
1. Background
In 1996, Komatsu Chile (KC) put into operation a ﬂeet of haul trucks in a mining application in Chile. KC deliveredthese machines under a repair and maintenance contract,taking full responsibility of all repair and maintenance work at guaranteed availability and maintenance costs.The haul truck is an electric drive DC truck. This meansthat propulsion is delivered to the rear wheels by means of two parallel electric DC wheel motors. The wheel motorsreceive rectiﬁed electric power from the main alternatorworking in conjunction with a diesel engine. The wheelmotors are mounted on the truck’s axle box and providethe function of axle, transmission and wheel motor at thesame time. The wheel motor’s main components are thewheel hub, ring gear structure, planetary gears, sun gear andarmature, see Fig. 1.The armature is the rotor of the electric motor andcan be removed from it independently. It primarilyconsists of bearings, commutator, brushes, spools andpoles. The armature commutator consists of copper barsand mica plates. The mica plates physically separate andisolate the copper bars and provide a radial pressure toensure the commutator’s stability. The mica bars haveless altitude than the copper bars and are located belowthe commutator’s superﬁcial area to prevent interactionwith the sliding brushes on the area. The copper barshave a wedge shape form and together form a cylinder.Each bar has a riser for connection to the armature’sspools.
0951-8320/$ - see front matter
q
2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.ress.2003.10.016Reliability Engineering and System Safety 84 (2004) 209–218www.elsevier.com/locate/ress* Corresponding author. Tel.:
þ
1-416-946-5528; fax:
þ
1-416-946-5462.
E-mail addresses:
lugtigh@mie.utoronto.ca (D. Lugtigheid),blhorente@komatsu.cl (B. Lhorente), knights@ing.puc.cl (P.F. Knights),asantana@komatsu.cl (A. Santana).
According to a recent study on the trucks at the samemining operation, the wheel motors together with itsarmatures are the most critical system of the machine. Itcan be classiﬁed ‘acute and cronic’ (Knights [1] andTurina [2]), meaning a high failure frequency and a highmean time to repair. At the same time the armature isconsidered to be critical because of its high maintenancecosts.Due to the high criticality of the armatures in terms of reliability, availability and costs, a study was performed todeﬁne how the component’s operational parameters as wellas its costs could be improved. This was done through thedevelopment and application of an optimal preventivemaintenance (PM) model to determine the PM strategy thatminimizes costs per unit time. As well, the impact of thisstrategy on the haul trucks’ operational parameters wasevaluated. The ﬁndings of this study are presented in thispaper.
2. Problem formulation
The current PM strategy is to carry out PMs at intervalsof 9,000 operational hours. If an armature failure occursbeforehand, a corrective maintenance (CM) is carried out.Although PMs and CMs are different types of events, thearmature reconditioning activities to be undertaken are thesame. The occurrence of armature failures is directly relatedto the PM interval. Longer PM intervals will cause morefailures to occur, and vice versa. The objective of this studyis to determine the optimal trade-off between CM and PMthat minimizes the operating costs per unit time of thearmature.A key activity of the reconditioning process is commu-tator resurfacing. This activity consists of equalizing thecommutator’s surface by removing a thin layer of materialfrom the external surface of the copper bars and mica plates.A new commutator has a diameter of 16.5
00
and the limit forproper operation is 15.5
00
. In case of a CM, on average 0.25
00
of material is removed and, in case of a PM, only 0.15
00
. Thismeans that the total useful life is limited by the amount of material that is removed
1
and whenever an armature reachesthe diameter limit of 15.5
00
, the PM or CM activity cannotrestore the proper functioning of the component and a newarmature must be purchased. The repair costs for recondi-tioning are the same for both a PM or a CM. Besides thediameter restriction, the armature has a maximum totaluseful life of 40,000 h. This means that after 40,000accumulated operating hours, independently of its diameter,the armature must be replaced by a new one. The costs of anew armature are approximately 13 times the cost of reconditioning and we shall refer to the purchase of a newarmature as a result of any of these two restrictions as‘renewal’.The optimization horizon is 40,000 hours. This meansthat if a new armature is needed within this period, KC mustincur full cost.On the contrary, no costs for KC are incurred.The objective is to deﬁne an optimal age-based PMstrategy over a period of 40,000 h. In practical terms, thismeans deﬁning a PM interval resulting in the least cost perunit time.
3. The general PM model
For every component under an age-based PM policythere exist two types of maintenance actions: preventive(PM) and corrective (CM). The mean time to failure (atwhich a CM must be carried out) and the PM intervaltogether with their probabilities of occurrence areinterrelated. Longer PM intervals result in greater meantimes to failure. But at the same time the probability of occurrence of a failure at higher PM intervals is higher.These relationships can be used to deﬁne the optimalPM interval that minimizes the costs per unit time.Deﬁning:
C
p
PM Costs (US$)
C
f
CM Costs (US$)
T
p
PM interval (operating hours)
F
ð
T
p
Þ
Probability of a failure occurring before reachingthe PM interval
T
p
R
ð
T
p
Þ
Survival probability equal to 1
2
F
ð
T
p
Þ
Thus, within the age-based PM policy two differentcycles can be distinguished: the component survives
T
p
anda PM is carried out incurring a cost
C
p
or the componentfails beforehand and a CM must be carried out incurringa cost
C
f
:
For this model the expected costs per unit time in
Fig. 1. Wheel motor components.
1
It is important to mention that the amount of material removed from thecommutator’ssurfaceperPMor CMis less thanthegivenvalues.However,while in operation, the commutator looses material as well and the givenvalues are average values of the differences in diameter between twoconsecutive maintenance actions.
B. Lhorente et al. / Reliability Engineering and System Safety 84 (2004) 209–218
210
function of
T
p
can be written as (Jardine [3]),
C
ð
T
p
Þ ¼
C
p
R
ð
T
p
Þ þ
C
f
F
ð
T
p
Þ
T
p
R
ð
T
p
Þ þ
M
ð
T
p
Þ
F
ð
T
p
Þ
;
ð
1
Þ
where
M
ð
T
p
Þ
represents the mean time to failure of anarmature subject to corrective maintenance with a PMinterval of
T
p
and,
F
ð
T
p
Þ ¼
ð
T
p
0
f
ð
t
Þ
d
t
ð
2
Þ
M
ð
T
p
Þ ¼
ð
T
p
0
tf
ð
t
Þ
d
t F
ð
T
p
Þ
;
ð
3
Þ
where
f
ð
t
Þ
is the probability density function (p.d.f.) of thetimes to failure.Whenever the p.d.f. of the times to failure of thecomponent is known, the costs per unit time can beminimized over
T
p
;
resulting in the optimal PM interval
T
p
p
:
4. Data treatment and analysis
From the model presented above it can be seen that thedeﬁnition of the p.d.f. is critical to the process of determining
T
p
p
:
The p.d.f. describes the component’sfailure characteristics. Before using the component’smaintenance history to estimate its p.d.f., the data shouldbe thoroughly analyzed.The nature of the reconditioning process is to restore theproper functioning of the component and reduce its risk of failure. Although the probability of failure should bereduced by a CM or PM, it is unlikely that its behaviorwill be identical to that of a new component (so called good-as-new or GAN). It is more likely that its failure rate ishigher than that of a new component, but less than justbefore the maintenance action was carried out (so calledbetter-than-old-but-worse-than-new or BOWN). The samereasoning holds for armatures undergoing a second, third,etc. maintenance.It has been shown that an armature’s physical statechanges with each maintenance through a reconditioningprocess. This might affect the armature’s p.d.f. For thisreason, the failure data was separated into three groups:new armatures (before the ﬁrst PM or CM, group 1), afterthe ﬁrst but before the second PM or CM (group 2), andafter the second PM or CM (group 3). At the same time aseparation was made between right-hand and left-handside armatures. This was done to verify whether or not thefailure characteristics of armatures are different in thesecases. The amount of data in each data set is shown inTable 1.The data in each set consisted of failures and suspen-sions. The latter correspond to PMs (reconditioning beforefailure has occurred). These data were gathered fromAugust 1996 until March 2001.
4.1. Data distribution and independence
The ﬁrst check undertaken was to examine whether ornot the data in each data set were independent andidentically distributed. If this were not the case, an
Table 1Amount of data in data setsGroup Left-hand armature Right-hand armature1 64 632 40 373 41 35Total 145 135Fig. 2. Trend plots for left-hand side (left) and right-hand side (right).
B. Lhorente et al. / Reliability Engineering and System Safety 84 (2004) 209–218
211
erroneous estimation of the p.d.f.’s would result. A serialcorrelation test was applied to test for independency of thedata. This test consists of ranking the failure times (notsuspensions) according to their date of occurrence, makingpairs
ð
X
i
;
X
i
2
1
Þ
of each two subsequent failure times for
i
¼
2
…n
where
n
is the amount of observed failures andplotting them. If the position of the data points is randomlydistributed among the graph, the data can be consideredindependent (Vagenas et. al. [4]). All subsets showed thisbehavior, so it was assumed that the data in each of the sixdatasets were independent.To verify whether the data in the different data sets wereidentically distributed, trend plots were used. These areobtained by plotting the accumulated times to failure againstaccumulated failure number (ordered according to date of occurrence). In the case that the graph shows a unique lineartrend, the failure data of the subset can be consideredidenticallydistributed.Inthecasethatthegraphshowstwoormore linear segments, it can be concluded that at a certainmomentintimethefailuredistributionofthesubsetchanged.This can occur due to changes in maintenance procedures orin operational parameters such as, haul routes, climaticconditions or other external factors. In this study, wheneverthis was detected, only data belonging to the most recentdistribution was considered. This was done because theobjective of this study is to determine the best strategy underactual circumstances. In Fig. 2 the trend plots for leftand right-hand armatures before the ﬁrst maintenance areshown.
4.2. Histograms
The next step in the data analysis process was toanalyze how failure frequencies relate to accumulatedoperating hours and month of occurrence for each of thedifferent data sets. This was done to get a clearerunderstanding of the variation of failure frequencies withrespect to the position of the armature, accumulatedoperating hours and calendar time. The followingobservations were made.
Fig. 3. Failure frequencies versus time (all groups).
B. Lhorente et al. / Reliability Engineering and System Safety 84 (2004) 209–218
212
†
The failure frequencies versus time and operatinghours are very similar for left and right hand armatures.This was conﬁrmed by a statistical hypothesis test.See Fig. 3.
†
The failure data of group 1 showed higher failurefrequencies at higher operating hours. However, groups2 and 3 showed more failures concentrated at loweroperating hours.
†
Failure frequencies are highest during ﬁrst quarters.First quarters contain 39% of the total failures and thesecond, third and fourth 23, 18 and 20%, respectively.The ﬁrst quarter of each year coincides with theoccurrence of adverse climatic conditions in the regionwhere the mine is located. This particular climaticevent is associated with heavy rain and electric storms,which affects the operating parameters of the armatureand causes additional failures (see Fig. 4).
4.3. Causes of failure
The 280 data of the six data sets consisted of 156 failures(CMs) and 124 suspensions (PMs). Table 2 shows thecauses of failure of the 156 failures.The dominant failure mode is ﬂashovers and for aconsiderable amountoffailures (32) no cause was identiﬁed.
4.4. Distribution ﬁtting
For the determination of the p d.f. in this study, theWeibull distribution was chosen, due to its ﬂexibility inrepresenting components with constant, increasing anddecreasing failure rates. This property is particularly usefulwhen dealing with different failure distributions among thedata sets of groups 1, 2 and 3, as was the case in this study.The p.d.f. of the three parameter Weibull distribution is,
f
ð
t
Þ ¼
b h
t
2
t
0
h
b
2
1
e
2
t
2
t
0
h
;
for
t
.
t
0
:
ð
4
Þ
Where
b
is the shape parameter,
h
is the scale factor orcharacteristic life and
t
o
is the failure-free time. The datain this study consisted of times to failure (CMs) as well asPMs (suspended or censored data). For this reason thedata were adjusted according to mean and median ranksbefore the actual ﬁtting process (O’Connor [5]). Theﬁtting process was carried out in Excel, using linearregression. The results of the ﬁtting process are shown inTables 3–5.From these tables it may be concluded that:
†
For new armatures (group 1), the shape parameter variesbetween 0.8 and 0.9 and is less than 1 which indicatesinfant mortality.
†
For armatures that have undergone one or moremaintenance (groups 2 and 3), the shape parameter variesbetween 1.0 (constant failure rate) and 1.3, indicatingnear-randomnessofthefailuredata.Somewearisevidentand the characteristic life is much smaller than group 1.
†
In all data sets the shape parameter increases with everymaintenance. This validates the conclusions drawn fromthe histograms, that with every maintenance actionthe mean life of the component diminishes and failurerates increase.
Fig. 4. Failure frequency versus time (all groups).Table 2Causes of failureCause AmountFlashover 118Ground fault/short circuit 7Unknown 32Table 3Left-hand armature Weibull parametersParameter Group 1 Group 2 Group 3 Total
b
0.809 1.247 1.235 1.043
h
36,286 6,382 5,264 12,304
t
0
0 0 0 0Table 4Right-hand armature Weibull parametersParameter Group 1 Group 2 Group 3 Total
b
0.897 1.012 1.215 1.119
h
11,014 7,538 5,149 6,914
t
0
0 0 0 0
B. Lhorente et al. / Reliability Engineering and System Safety 84 (2004) 209–218
213

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