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1、ANNALS of the ORADEA UNIVERSITY.Fascicle of Management and Technological Engineering, Volume VII (XVII), 2008MATHEMATIC MODEL TO DETERMINE THE PREVENTIVE MAINTENANCE OF BALL MILLSTeodor VASIU, Adina BUDIUL BERGHIANEngineering Faculty of Hunedoara, Department of Engineering and ManagementRevolutiei s
2、tr., no.4, 331128 Hunedoarae-mail teodor.vasiufih.upt.ro, adina.budiulfih.upt.roKeywords: mathematical model, ball mills, maintenanceAbstract : In this study is presented a mathematical model of preventive maintenance which takes into account several stochastic factors that influence the failure rat
3、e and working life of an entity. It is assumed that preventive maintenance is done through imperfections: it is not reduced only the proper operation but the failure probability as well as much as the number of maintenance works is increased. The objective of this study is to determine the optimal d
4、iagram for planned maintenance works so that the failure rate to not exceed a certain prescribed value.1. INTRODUCTIONA condition for preventive maintenance success is to determine the moment of its execution. One of the most used concepts is periodical preventive maintenance, which specifies interv
5、entions done at equal times of continuous operation (for example in the case of ball mills this is of 670 hours 8). Another concept is the so-called sequential preventive maintenance, which means that planned interventions to be done at unequal times of continuous operation. The first concept is mor
6、e comfortable, but the sequential preventive maintenance is more realistic because it takes into account that an entity should be often recovered as much as its working life increases. The bond between these two concepts is done by corrective maintenance, which is applied when the entity fails. Corr
7、ective maintenance solves the cause of that failure only and not all the status problems of the entity. By other words, corrective maintenance doesnt change the failure rate and doesnt increase the working life either.The most used two methods to determine the periods of performing the preventive ma
8、intenance are based on minimization of maintenance costs and keeping the failure rate under a prescribed value, but this study approaches the second method only, the first method being approached in 9.In 5 are adopted some correction factors for failure rates h(t) and for the proper operation time e
9、lements t within the preventive maintenance i.e.:1. Failure rate during the next operational time element is ah(t), where h(t) refers to the previous time element, a 1 is a correction factor and t 0 represents the time refluxed from the previous intervention.2. Time element t for proper operation of
10、 the entity before preventive maintenance is reduced to bt after intervention, where b 1 is a proper operation reduction factor. According to the proposal of survey 5, for a failure rate h(t), t(0, t1), the preventivemaintenance started at the moment t1 determines a new failure rate g(t), t(t1, t2),
11、 which depends on the previous failure rate and maintenance work. In the survey 5 is proposed a675form for g(t), using both the concept of increasing the failure rate and reducing the proper operation according to the entity exploitation:g(t1 + x ) = ah(bt1 + x )(1)where a 1, 0 b 1 and x(0, t2-t1).
12、For a = 1, the proposed model is resized to the one of working life reduction, and b = 0 is the equivalent of increasing the failure rate.Using the proposed model is developed an optimal policy of preventive maintenance, with a major implication i.e. renunciation to the classic, uneconomical approac
13、h of constant periods for preventive maintenance execution.2. DESCRIPTION OF THE MODEL AND OPTIMAL SOLUTIONSAt this moment is necessary to specify the notations that follow to be used:h(t) failure rate;H(t) cumulated failure rate; - maximum value accepted for the failure rate;xk moments of preventiv
14、e maintenance execution, k = 1, 2,., N;tk = x1 + x2 + . + xk, k = 1, 2,., N;yk continuous operation time immediately after the number k” of preventive maintenance, k= 1, 2,., N;N number of proper operation time elements;ak failure rate correction factor after the number k” of preventive maintenance;
15、1 = a0 a1 a2 . aN 1;k 1Ak = ai , k = 1, 2,., N;i =0bk correction factor of proper operation time;0 = b0 b1 b2 . bN 1 1;cm corrective maintenance cost;cp preventive maintenance cost;cr overhaul cost (entity replacement);C average cost of entity;It is considered the situation in which an entity is subjected to the preventive maintenance at the moments t1, t2, ., tN-1 and overhauled or replaced at the moment tN. Corrective maintenance is executed as a consequence of failures appeared between the works of preventive maintenance. The overhaul from the mom
